URGENT SOS

so apparently this is too short so more words yeah sorry pls help

URGENT SOSso Apparently This Is Too Short So More Words Yeah Sorry Pls Help

Answers

Answer 1

Answer:

x-2 and y(-1) -1

Step-by-step explanation:

Explained
it made a reflection of the y-axis (-1) and lowered it by 1 unit (-1)

It moved to the left by two units so x-2

X-2 and y(-1) -1


Related Questions

Question If f(x)=2x−3 and g(x)=4x+5, what is (f⋅g)(x)?

Answers

Answer:

f * g)(x) = 8x^2 - 2x - 15

Step-by-step explanation:

Since we want to find (f * g)(x), we want to multiply the entire functions and leave the answer in terms of x (in terms of x simply means we do the multiplication and the simplified answer will be in terms of x):

Thus, we have (2x - 3)(4x + 5).  This is a binomial expression and we can multiply binomials using the FOIL method, where

"F" refers to the first terms (2x and 4x in this case),"O" refers to the outer terms (2x and 5),"I" refers to the inner terms (-3 and 4x),and "L" refers to the last terms (-3 and 5)

We add all the terms and combine like terms to find (f * g)(x):

(2x * 4x) + (2x * 5) + (-3 * 4x) + (-3 * 5)

8x^2 + 10x - 12x - 15

8x^2 - 2x - 15

Thus, (f * g)(x) is 8x^2 - 2x - 15

Which is more, 6 yards or 218 inches?

Answers

In terms of length, 218 inches is greater than 6 yards.

To determine which is more, 6 yards or 218 inches, we need to convert one or both of the measurements to a common unit of measurement. In this case, we can convert yards to inches or inches to yards for comparison.

Since there are 36 inches in a yard, we can convert 6 yards to inches by multiplying it by 36:

6 yards * 36 inches/yard = 216 inches.

Now, we can compare the converted measurements: 216 inches and 218 inches.

Since 218 inches is greater than 216 inches, we can conclude that 218 inches is more than 6 yards.

This comparison can also be verified by considering the conversion factors. 6 yards is equivalent to 216 inches, which is smaller than 218 inches.

It is important to note that when comparing measurements, it is crucial to ensure that both measurements are in the same unit for an accurate comparison. Converting them to a common unit helps provide a clear understanding of which value is greater or smaller.

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Solve me the question

Answers

The mean, mean deviation mode, median standard deviation, and coefficients of variation, CV, are as follows;

1. The mean deviation about the mean, median mode are;

2.653, 3.709, and 3.709, respectively

The coefficients of variation are;

0.364, 0.337, 0.337, respectively

The variance is about 9.462

The standard deviation is about 3.076

2. Section A has a higher relative dispersion than section B

3. City 2

4. a. Mean ≈ 43.85

b. Mode 40 - 54 inches

c. Median ≈ 45.16

The variance ≈ 125.8056

Standard deviation ≈ 11.216

Coefficient of variation ≈ 0.268

What is a coefficient of variation?

The coefficient of variation of a data quantifies or is a measure of the variability of the values in the set of data.

The mean for the data can be calculated as follows;

Mean  = (3×10 + 6×15 + 11×25 + 2×6 + 4×4 + 10×3 + 5×2 + 7×8 + 8×9 + 9×4)/(10+15+25+6+4+3+2+8+9+4) ≈ 7.29

The median is the 86/2 value = 43rd value

10 + 15 + 25 = 50

Therefore, the median is in the class with a frequency of 25, which is 11

The mode of the data, which is the value with the highest frequency in the data set is 11

The mean deviation from the mean is therefore;

(|3 - 7.29|×10 + |6 - 7.29|×15 + |11 - 7.29| ×25 + |2 - 7.29| ×6 + |4 - 7.29| ×4 + |10 - 7.29| ×3 + |5 - 7.29| ×2 + |7 - 7.29|×8 + |8 - 7.29| ×9 + |9 - 7.29| ×4)/(10+15+25+6+4+3+2+8+9+4) ≈ 2.653

The coefficient for the mean deviation about the mean is therefore; 2.653/7.29 ≈ 0.364

The mean deviation about the median is therefore;

(|3 - 11|×10 + |6 - 11|×15 + |11 - 11| ×25 + |2 - 11| ×6 + |4 - 11| ×4 + |10 - 11| ×3 + |5 - 11| ×2 + |7 - 11|×8 + |8 - 11| ×9 + |9 - 11| ×4)/(10+15+25+6+4+3+2+8+9+4)

The mean deviation about the median = 319/86 ≈ 3.709

The coefficient ≈ 3.709/11 ≈ 0.337

The median = The mean deviation about the mode ≈ 3.709

The coefficient is about 0.337

The variance = (10×(3 - 7.29)² + 15×(6 - 7.29)² + 25×(11 - 7.29)² + 6×(2 - 7.29)² + 4×(4 - 7.29)² + 3×(10 - 7.29)² + 2×(5 - 7.29)² + 8×(7 - 7.29)² + 9×(8 - 7.29)² + 4×(9 - 7.29)²)/(10+15+25+6+4+3+2+8+9+4) ≈ 9.462

The standard deviation, s ≈ √(9.462) ≈ 3.076

2. The coefficient of variation, CV, can be used to compare the variability of the datasets comprising of different scales as follows;

CV = Standard deviation/( The mean of the data)

Therefore; CV for section A = 23/79 ≈ 0.2911

CV for section B = 11/64 ≈ 0.172

The higher CV value for section A indicates that the scores of section A have a higher relative dispersion than the scores for the section B

3. The consistency values can be obtained by finding the standard deviation for the values in the data for each city, using a web based tool as follows;

City 1; Mean = 23

Variance = 50/4

Standard deviation, City 1 = (√(50))/2 = 5·√2/2

City 2; Mean = 21.8

Sample variance = 2.2

Standard deviation, City 2 = √(2.2) ≈ 1.483

City 3; Mean = 29.2

Sample variance = 18.7

Standard deviation, City 3 = √(18.7) ≈ 4.324

The standard deviation of city 2, which is the smallest compared tom the other cities, indicates that the City 2, has the most consistent temperature

4. The mean of the data obtained from the data using the midpoint of the data, is; Mean = ∑fx/∑f

Therefore; The mean obtained using an online tool is; 43.85

The mode is the data that occurs most frequently, which is the data with the value; 40 - 54 inches

The median is the value at the middle of the data set, which is the value with a frequency of 53, and in the interval 40 - 54 inches

The median is; 39.5 + (54.5 - 39.5) × (50 - 30)/53 ≈ 45.16

The standard deviation found for the grouped data, using an online tool is as follows;

Variance, σ² ≈125.8056

The standard deviation, σ ≈ √(125.8056) ≈ 11.216

The coefficient of variation is; 11.216/41.83 ≈ 0.268

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Thabo wants to buy wireless Bluetooth earphones which costs R700. He is impatient and does not want to wait and save the money to buy himself the earphones. He applies for a bank loan. The bank approves the loan and gives Thabo four (4) years to amortise the loan. The bank charges an interest rate of 6% compounded yearly for the loan. Find the yearly instalment that Thabo has to pay to the bank. A. R212, 01 B. R202, 79 c. R202, 01 D. R205, 73​

Answers

The yearly installment that Thabo has to pay to the bank is c. R202.

How to compute the yearly installment to pay?

We shall use the formula for calculating the amortized loan payment to estimate the yearly installment that Thabo has to pay to the bank:

Installment = (Loan amount (L) * Interest rate (I)) / (1 - (1 + Interest rate)^(-Number of years (N))):

In short: Installment = (L * I) / (1 - (1 + I)⁽⁻ⁿ⁾)

Given:

L = R700

I = 6% = 0.06

N = 4

Plugging the values into the formula, we have the yearly installment:

Installment = (700 * 0.06) / (1 - (1 + 0.06)⁽⁻⁴⁾)

= 42/(1 - (1 + 0.06)⁽⁻⁴⁾ )

= 42/ (1 - (1.06)⁽⁻⁴⁾ )

= 42/(1 - 0.792)

= 42 / 0.2079 ≈ 202.01

Installment ≈ 202.01

Therefore, the yearly installment that Thabo has to pay to the bank is  R202.

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17.
If the height of the cone below were increased
to 16 inches and the diameter stayed the same,
by approximately how much would its
volume increase?

Answers

If the height of the cone were increased to 16 inches and the diameter stayed the same, the volume of the cone would increase by approximately 12π or around 37.7 cubic inches.

How to solve

The formula for the volume V of a cone is given by:

V = 1/3 * π * r² * h

The height of an object is denoted as "h" and its base radius as "r", while the constant π is approximately equal to 3. 1416

Initially, it is crucial to determine the initial capacity of the triangular object.

The radius r is half the diameter, so r = 6/2 = 3 inches. Substituting the given height h = 12 inches and r = 3 inches into the formula, we get:

V1 = 1/3 * π * (3²) * 12 = 36π cubic inches

Then, calculate the new volume of the cone, using the same radius but the new height of 16 inches:

V2 = 1/3 * π * (3²) * 16 = 48π cubic inches

The increase in volume is the difference between the new volume and the original volume:

ΔV = V2 - V1 = 48π - 36π = 12π cubic inches

Therefore, if the height of the cone were increased to 16 inches and the diameter stayed the same, the volume of the cone would increase by approximately 12π or around 37.7 cubic inches.

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The Complete Question

Suppose you have a cone with a height of 12 inches and a base diameter of 6 inches. If the height of the cone were increased to 16 inches and the diameter stayed the same, by approximately how much would its volume increase?

If there are penguins in the aquarium is full of fish, then this is an octopus write
this in Symbolic form

Answers

The compound statement "If there are penguins and the aquarium is full of fish, then this is an octopus" can be written in symbolic form as: r ∧ q → o

How to explain the information

Let's assign variables to represent the statements:

q: The aquarium is full of fish.

r: There are penguins.

The compound statement "If there are penguins and the aquarium is full of fish, then this is an octopus" can be written in symbolic form as: r ∧ q → o

∧ represents the logical operator "and" which connects the statements r and q.

→ represents the logical operator "implies" or "if...then".

o represents the statement "this is an octopus".

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the sum of three consecutive even integers is 216. find the intergents

Answers

Answer:

12, 14, 16

Step-by-step explanation:

Let's say x is the lowest number:

x+x+2+x+4=42

Simplify the equation:

3x+6=42

Subtract 6 on each side to isolate 3x:

3x=36

x=12

So the lowest number is 12, which means the next number(x+2) would be 14, and the following number(12+4) would be 16.

Happy learning!

Step-by-step explanation:

Solve for x find the side

Answers

The length of x is 3.42cm

How to determine the value

To determine the value, we have to know the different trigonometric identities.

These identities are listed thus;

sinetangentcotangentsecantcosecantcosine

From the information shown in the diagram, we have that;

Opposite side = x

The hypotenuse side = 10

The angle = 20 degrees

Now, using the sine identity, we get;

sin 20 = x/10

cross multiply the values, we get;

x = 10(0.3420

Multiply the values, we have;

x = 3.42cm

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If you know the answer please put the answer and the explanation thank you.

Answers

In the class, Lucy's score is 6.

How to work out Lucy's score?

In statistics, the median is the middle value in a sorted, ascending or descending list of numbers. Thus, it represents the midpoint of the data.

The median is often compared with other descriptive statistics such as the mean (average), mode, and standard deviation.

Since Lucy is one of the 29 students in the class and her score was the same as the median score for her class.

Thus, the median score will be 15th score (i.e. the midpoint of 29). Using the frequency in of each score from the figure, let's keep adding the frequency until we reach 15 and we will then check the corresponding score at the 15th position:

2 + 2 + 4 + 7 = 15

Thus, the the corresponding score at the 15th position is 6.

Therefore, the median score is 6 and consequently Lucy's score is 6.

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Please help ASAP
If two similar solids have volumes of 1715 cm^3 and 320 cm^3.

a. Calculate the ratio of the surface areas

b. If the larger solid has a surface area of 196 cm^2, what is the surface area of the smaller solid.

Answers

a. The ratio of the surface areas of two similar solids is equal to the square of the ratio of their corresponding side lengths. Since volume is proportional to the cube of the side length, we can find the ratio of the side lengths by taking the cube root of the ratio of the volumes:

1715/320 = (x/y)^3

where x and y are the side lengths of the larger and smaller solids, respectively. Solving for x/y, we get:

x/y = (1715/320)^(1/3) = 2.5

So the ratio of the surface areas is:

(2.5)^2 = 6.25

b. We can use the same ratio of surface areas to find the surface area of the smaller solid:

196/6.25 = 31.36

So the surface area of the smaller solid is approximately 31.36 cm^2.

an amount of 27000 is invested in a fund that pays 11,15% simple interest per year. the total amount in this fund after 129months will equal​

Answers

The total amount in the fund after 129 months will be approximately $59,392.90.

To calculate the total amount in the fund after 129 months, we need to use the formula for simple interest:

A = P(1 + rt)

Where:

A = Total amount (including interest)

P = Principal amount (initial investment)

r = Interest rate per period

t = Number of periods

Given:

P = $27,000

r = 11.15% per year (or 0.1115 as a decimal)

t = 129 months

First, we need to convert the interest rate from a yearly rate to a monthly rate since the time period is given in months. We divide the yearly rate by 12 to get the monthly rate:

monthly interest rate = 0.1115 / 12 = 0.0093 (rounded to four decimal places)

Now, we can plug in the values into the formula and calculate the total amount (A):

A = $27,000(1 + 0.0093 * 129)

A = $27,000(1 + 1.1997)

A = $27,000 * 2.1997

A ≈ $59,392.90

Therefore, the total amount in the fund after 129 months will be approximately $59,392.90.

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-2log (6x + 1) = -6.

Answers

the exact form is x = 333/2 the decimal form is x = 166.5

El primer término de una sucesion es 1/2 y aumenta constantemente 1/3. ¿Cuales son los primeros 10 términos de la sucesión?

Answers

Por lo tanto, los primeros 10 términos de la sucesión son:

1/2, 5/6, 7/6, 3/2, 11/6, 13/6, 17/6, 19/6, 23/6, 25/6.

La sucesión que se describe tiene un primer término de 1/2 y aumenta constantemente en 1/3 en cada término subsiguiente. Podemos encontrar los primeros 10 términos de la sucesión calculando cada término de manera sucesiva.

El primer término es 1/2.

Para encontrar el segundo término, sumamos 1/3 al primer término:

1/2 + 1/3 = 3/6 + 2/6 = 5/6

El segundo término es 5/6.

Para encontrar el tercer término, sumamos 1/3 al segundo término:

5/6 + 1/3 = 10/12 + 4/12 = 14/12 = 7/6

El tercer término es 7/6.

Podemos continuar este proceso para encontrar los siguientes términos:

4to término: 7/6 + 1/3 = 14/12 + 4/12 = 18/12 = 3/2

5to término: 3/2 + 1/3 = 9/6 + 2/6 = 11/6

6to término: 11/6 + 1/3 = 22/12 + 4/12 = 26/12 = 13/6

7mo término: 13/6 + 1/3 = 26/12 + 8/12 = 34/12 = 17/6

8vo término: 17/6 + 1/3 = 34/12 + 4/12 = 38/12 = 19/6

9no término: 19/6 + 1/3 = 38/12 + 8/12 = 46/12 = 23/6

10mo término: 23/6 + 1/3 = 46/12 + 4/12 = 50/12 = 25/6

Por lo tanto, los primeros 10 términos de la sucesión son:

1/2, 5/6, 7/6, 3/2, 11/6, 13/6, 17/6, 19/6, 23/6, 25/6.

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A cylindrical steel pipe with a liquid is 21 cm long with radius 0, 4 cm and its hollow part is of radius 0, 1 cm. What is the volume of liquid, in litres, in the pipe? A. 9000 litres B. 9400 litres C. 9900 litres D. 10100 litres​

Answers

Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters. Therefore, none of the options A, B, C, or D provided is the correct answer.

To calculate the volume of the liquid in the cylindrical steel pipe, we need to find the difference in volume between the solid cylinder (hollow part) and the hollow cylinder.

Given:

Length of the cylindrical steel pipe (hollow part) = 21 cm

Radius of the solid cylinder = 0.4 cm

Radius of the hollow cylinder = 0.1 cm

First, let's calculate the volume of the solid cylinder (hollow part):

V1 = π × [tex]r1^2[/tex] × h

V1 = π × [tex](0.4 cm)^2[/tex] × 21 cm

Next, let's calculate the volume of the hollow cylinder:

V2 = π × [tex]r2^2[/tex] × h

V2 = π × [tex](0.1 cm)^2[/tex] × 21 cm

Now, we can find the volume of the liquid in the pipe by subtracting V2 from V1:

Volume of liquid = V1 - V2

Let's calculate these values:

V1 = π ×[tex](0.4 cm)^2[/tex] × 21 cm ≈ 10.572 cm³

V2 = π × [tex](0.1 cm)^2[/tex] × 21 cm ≈ 0.693 cm³

Volume of liquid = V1 - V2 ≈ 10.572 cm³ - 0.693 cm³ ≈ 9.879 cm³

To convert the volume from cubic centimeters (cm³) to liters (L), we divide by 1000:

Volume of liquid in liters ≈ 9.879 cm³ / 1000 ≈ 0.009879 L

Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters.

Therefore, none of the options A, B, C, or D provided is the correct answer.

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The length of segment Ac.

Answers

Answer:

AC = 3 + 2√15

Step-by-step explanation:

Call the center of the circle O.

(OB)² = 2² + 3²

(OB)² = 13

OD = OB

(OD)² + (DC)² = (CO)²

13 + 51 = (CO)²

(CO)² = 64

(CX)² + 2² = (CO)²

(CX)² = 64 - 4

(CX)² = 60

CX = √60 = 2√15

AX = BX = 3

AC = AX + CX

AC = 3 + 2√15

Find the sum of the first 27 terms
of the arithmetic sequence.
First, fill in the equation.
a₁
= 5 and a27
Sn = 2/(a₁ + an)
Sn
=
[?]
2
+
=
83

Answers

Answer:

S₂₇ = 1188

Step-by-step explanation:

using the given formula for [tex]S_{n}[/tex] , that is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] (a₁ + [tex]a_{n}[/tex] )

with a₁ = 5 and [tex]a_{n}[/tex] = a₂₇ = 83 , then

S₂₇ = [tex]\frac{27}{2}[/tex] (5 + 83) = 13.5 × 88 = 1188

find the angle ACB of the given triangle with sides AB= 9cm and BC= 5cm. (give your answer to the nearest degree)​

Answers

Step-by-step explanation:

This is a law of sines problem.

Law of sines states that

A / sin (a) = B(sin b) = C (sin c)

5 / sin (60) = 9 / sin (x)

Simplifying this equation gives us sin (x) = (9 * sin (60)) / 5. Now we take the arc sin of both sides, to get that x = arc sin ((9 * sin (60)) / 5). Plugging this into a calculator gives us..... no solutions

I think thats the right solution as I plugged it into a law of sines calculator as well.

Write the equation in standard form for the circle passing through (5/2, - 6) centered at the origin.

Answers

The equation in standard form for the circle passing through (5/2, -6) and centered at the origin is [tex]4x^2 + 4y^2 = 169.[/tex]

To write the equation in standard form for the circle passing through (5/2, -6) and centered at the origin, we'll use the general equation of a circle:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

where (h, k) represents the center of the circle and r represents the radius.

Given that the circle is centered at the origin (0, 0), we can substitute these values into the equation:

[tex](x - 0)^2 + (y - 0)^2 = r^2\\x^2 + y^2 = r^2[/tex]

Now, we need to determine the radius of the circle. Since the circle passes through the point (5/2, -6), we can find the distance between the origin (0, 0) and this point, which represents the radius.

Using the distance formula:

d = √([tex](x2 - x1)^2 + (y2 - y1)^2)[/tex]

Substituting the values of the point (5/2, -6) and the origin (0, 0):

r = √([tex](5/2 - 0)^2 + (-6 - 0)^2)[/tex]

r = √(([tex]5/2)^2 + (-6)^2)[/tex]

r = √(25/4 + 36)

r = √(25/4 + 144/4)

r = √(169/4)

r = 13/2

Now, we can substitute the value of the radius (r = 13/2) into the equation:

[tex]x^2 + y^2 = (13/2)^2\\x^2 + y^2 = 169/4[/tex]

Multiplying both sides of the equation by 4 to eliminate the fraction:

[tex]4(x^2 + y^2) = 4(169/4)\\4x^2 + 4y^2 = 169[/tex]

Therefore, the equation in standard form for the circle passing through (5/2, -6) and centered at the origin is:

[tex]4x^2 + 4y^2 = 169.[/tex]

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Create similar right triangles by changing the scale factor of the right triangle.

When the scale factor is 1, what is the ratio of the side length of the side opposite ∠A and the length of the hypotenuse?

Change the scale factor to 3. What is the ratio of the side length of the side opposite ∠A to the length of the hypotenuse?
✔ 1/2

What is the ratio of the side length of the side opposite any 30° angle and the length of the
hypotenuse?

Answers

The ratio of the side length of the side opposite any 30° angle to the length of the hypotenuse is 1/2.

A right triangle has one angle measuring 90°. This angle is also known as the right angle. The side opposite to the right angle is known as the hypotenuse. The other two sides of a right triangle are known as the adjacent side and the opposite side.

The adjacent side is the side adjacent to the angle that is not the right angle, while the opposite side is the side opposite the angle that is not the right angle. A ratio is a comparison of two quantities. In a right triangle, some ratios are of great importance. These ratios are known as trigonometric ratios. The three important trigonometric ratios are sine, cosine, and tangent.

The sine of an angle is the ratio of the opposite side to the hypotenuse. The cosine of an angle is the ratio of the adjacent side to the hypotenuse. The tangent of an angle is the ratio of the opposite side to the adjacent side.  Changing the scale factor of a right triangle results in the creation of similar right triangles. Two triangles are similar if they have the same shape but different sizes.  

When the scale factor is 1, the ratio of the side length of the side opposite angle A to the length of the hypotenuse is 1/2. Change the scale factor to 3. The ratio of the side length of the side opposite angle A to the length of the hypotenuse is still 1/2.What is the ratio of the side length of the side opposite any 30° angle and the length of the hypotenuse?

Therefore, the ratio of the side length of the side opposite any 30° angle to the length of the hypotenuse is 1/2.

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19.
A triangle ABC is right angled at point A. The vertices of the triangle are A(1, -2), B(5, 4) and
C(m. N).
The equation of line BC is 5y-x = 15.
(a)
Determine:
12
(i)
the equation of line AC in the form ax+ by + c = 0, where a, b and are
integers.
(

Answers

The equation of line AC in the form ax + by + c = 0, where a, b, and c are integers, is:

5x + y - 3 = 0.

To determine the equation of line AC in the form ax + by + c = 0, where a, b, and c are integers, we need to find the coordinates of point C.

Since triangle ABC is right-angled at point A, we know that the slope of line BC[tex](m_{BC})[/tex] multiplied by the slope of line AC [tex](m_{AC})[/tex]  is equal to -1 (because the two lines are perpendicular to each other).

The equation of line BC is given as 5y - x = 15.

By rearranging it in the form y = mx + b, we can determine its slope.

The slope of BC[tex](m_{BC})[/tex] is 5.

Using the perpendicularity condition, we have:

[tex]m_{BC} \times m_{AC} = -1[/tex]

[tex]5\times m_{AC} = -1[/tex]

[tex]m_{AC} = -1/5[/tex]

Now, let's find the coordinates of point C.

We have the coordinates of points A and B, so we can find the slope between points A and C using the formula:

[tex]m_{AC} = (N - (-2)) / (m - 1)[/tex]

-1/5 = (N + 2) / (m - 1)

Cross-multiplying, we get:

-5(m - 1) = N + 2

-5m + 5 = N + 2

-5m - N = -3

Rearranging this equation, we obtain:

5m + N = 3

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Solve the following equation for f.

Answers

Answer:

[tex]f=\frac{N^2-H}{6}[/tex]

Step-by-step explanation:

[tex]N^2=6f+H\\\mathrm{or,\ }6f=N^2-H\\\mathrm{or,\ }f=\frac{N^2-H}{6}[/tex]

Given: The coordinates of rhombus WXYZ are W(0, 4b), X(2a, 0), Y(0, -4b), and Z(-2a, 0).
Prove: The segments joining the midpoints of a rhombus form a rectangle.
As part of the proof, find the midpoint of YZ.

Answers

The midpoint of segment YZ is (-a, -2b).

Given the coordinates of the rhombus WXYZ:

W(0, 4b)

X(2a, 0)

Y(0, -4b)

Z(-2a, 0)

Find the midpoint of YZ:

The midpoint formula is given by:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Substituting the coordinates of Y and Z:

Midpoint of YZ = ((0 + (-2a)) / 2, (-4b + 0) / 2)

= (-a, -2b)

Therefore, the midpoint of segment YZ is (-a, -2b).

Show that the segments joining the midpoints are perpendicular:

To demonstrate that the segments joining the midpoints of the rhombus are perpendicular, we need to prove that the slopes of these segments are negative reciprocals of each other.

Let's consider the segments joining the midpoints:

Segment joining the midpoints of WX and YZ:

Midpoint of WX: ((0 + 2a) / 2, (4b + 0) / 2) = (a, 2b)

Midpoint of YZ: (-a, -2b)

Slope of WX = (2b - 4b) / (a - 0) = -2b / a

Slope of YZ = (-2b - (-4b)) / (-a - 0) = 2b / a

The slopes of WX and YZ are negative reciprocals of each other, indicating that these segments are perpendicular.

Conclusion:

We have shown that the segments joining the midpoints of a rhombus are perpendicular to each other and have equal lengths. Therefore, these segments form a rectangle.

Additionally, the midpoint of segment YZ is (-a, -2b).

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1. The perimeter of a square is 16.
What is the length of the diagonal?
2. The perimeter of an equilateral triangle is 36. What is the length of the altitude?
3. Find the missing side lengths on the figure.

Answers

1.)The length of the diagonal of the square would be = 5.7

2.) The perimeter of the equilateral triangle = 12.

How to calculate the length of the diagonal of a given square?

To calculate the length of the diagonal of a given square, the Pythagorean formula should be used and it's given below as follows:

1.) C² = a² + b²

But the perimeter = 16

The length = 16/4 = 4

C² = 4²+4²

= 16+16

= 32

C = √32= 5.7

2.) The perimeter of the equilateral triangle = length×3 = 36.

The length = 36/3 = 12

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A school plans to build a wheelchair ramp from the sidewalk to the front entrance of the school. the slope must be 5/32. the entrance to the school is 81cm above the ground. what is the horizontal distance needed for the ramp?​

Answers

The horizontal distance needed for the ramp is 518.4 cm to ensure a slope of 5/32 and reach the entrance of the school, which is 81 cm above the ground.

To find the horizontal distance needed for the ramp, we can use the formula:

Horizontal distance = Vertical distance / Slope

Given that the slope must be 5/32 and the entrance to the school is 81 cm above the ground, we can substitute these values into the formula:

Horizontal distance = 81 cm / (5/32)

To divide by a fraction, we can multiply by its reciprocal:

Horizontal distance = 81 cm * (32/5)

Simplifying:

Horizontal distance = (81 cm * 32) / 5

Horizontal distance = 2592 cm / 5

Horizontal distance = 518.4 cm

Therefore, the horizontal distance needed for the ramp is 518.4 cm to ensure a slope of 5/32 and reach the entrance of the school, which is 81 cm above the ground.

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Passing through (7,4) and (6,3) what is the point-slope form of the equation?​

Answers

Answer:

y - 3 = 1(x - 6)  or y - 4 = 1(x - 7)

Step-by-step explanation:

to find the slope: m = (3-4) / (6-7) = -1 / -1 = 1

next, substitute the values into the equation: y2 - y1 = m(x2 - x1)

you can use any x or y value from the given.

y - 3 = 1(x - 6)

or

y - 4 = 1(x - 7)

When the scale factor is 1, what is the ratio of the side length of the side opposite ∠A and the length of the hypotenuse?

Answers

when the scale factor is 1, we have:

(side length of side opposite ∠A) / (length of hypotenuse) = sin A

When the scale factor is 1, the ratio of the side length of the side opposite ∠A to the length of the hypotenuse remains the same as in the original triangle. In a right triangle, the side opposite ∠A is referred to as the "opposite" side, and the hypotenuse is the longest side.

The ratio of the side length of the side opposite ∠A to the length of the hypotenuse is commonly known as the sine of angle A (sin A). So, when the scale factor is 1, the ratio of the side length of the side opposite ∠A to the length of the hypotenuse is equal to sin A.

In mathematical terms, when the scale factor is 1, we have:

(side length of side opposite ∠A) / (length of hypotenuse) = sin A

It's important to note that this ratio holds true for any right triangle, regardless of its size or dimensions, as long as the angle A remains the same.

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divide 16 into the ratio 3:5

Answers

5.3 : 26.5

Hope that makes sense and it helps!!

Answer:

[tex]6,10[/tex]

Step-by-step explanation:

Method 1:

[tex]\mathrm{Let\ two\ numbers\ be\ x\ and\ y\ such\ that:}\\\mathrm{x:y=3:5\ \ \ \ and\ \ \ \ x+y=16}\\\mathrm{or,\ \frac{x}{y}=\frac{3}{5}}\\\\\mathrm{or,\ 5x=3y..........(1)}\\\mathrm{Also\ we\ have}\\\mathrm{x+y=16}\\\mathrm{or,\ 5(x+y)=5(16)}\\\mathrm{or,\ 5x+5y=80}\\\mathrm{or,\ 3y+5y=80\ [From\ equation\ 1]}\\\mathrm{or,\ 8y=80}\\\mathrm{or,\ y=10}\\\mathrm{From\ equation\ 1,}\\\mathrm{5x=3y}\\\mathrm{or,\ 5x=3(10)=30}\\\mathrm{\therefore x=6}[/tex]

[tex]\mathrm{So,\ the\ two\ numbers\ are\ 6\ and\ 10.}[/tex]

Alternative method 1:

[tex]\mathrm{Let\ the\ two\ numbers\ be\ x\ and\ 16-x.}\\\mathrm{Then,\ we\ have}\\\mathrm{x:(16-x)=3:5}\\\\\mathrm{or,\ \frac{x}{16-x}=\frac{3}{5}}\\\\\mathrm{or,\ 5x=3(16-x)=48-3x}\\\mathrm{or,\ 5x+3x=48}\\\mathrm{or,\ 8x=48}\\\mathrm{\therefore x=6}\\\mathrm{So,\ the\ other\ number=16-x=16-6=10}[/tex]

[tex]\mathrm{So,\ the\ two\ numbers\ are\ 6\ and\ 10.}[/tex]

Alternative method 2:

[tex]\mathrm{Let\ the\ two\ numbers\ be\ 3x\ and\ 5x.}\\\mathrm{Then,}\\\mathrm{3x+5x=16}\\\mathrm{or,\ 8x=16}\\\mathrm{or,\ x=2}\\\mathrm{So,\ first\ number=3x=3(2)=6}\\\mathrm{Second\ number=5x=5(2)=10}[/tex]

[tex]\mathrm{So,\ the\ two\ numbers\ are\ 6\ and\ 10.}[/tex]

Construct a box-and-whisker
16, 12, 13, 14, 16, 18, 15, 17, 20, 12, 14, 15, 15
graph using the following data.

Answers

Given statement solution is :-  Box-and-whisker plot, the box represents the interquartile range (IQR), which is the range between Q1 and Q3 (13 to 18). The line inside the box represents the median (15). The whiskers (lines extending from the box) represent the minimum and maximum values (12 and 20).

To construct a box-and-whisker plot using the given data, you first need to find the minimum, maximum, median, and quartiles. Here are the steps to create the box-and-whisker plot for the given data set:

Sort the data in ascending order:

12, 12, 13, 14, 14, 15, 15, 15, 16, 16, 17, 18, 20

Find the median (middle value) of the data set. Since the data set has an odd number of values, the median will be the middle value:

Median = 15

Find the lower quartile (Q1), which is the median of the lower half of the data set.

Counting from the start, the lower half of the data set is:

12, 12, 13, 14, 14

Q1 = 13

Find the upper quartile (Q3), which is the median of the upper half of the data set.

Counting from the end, the upper half of the data set is:

17, 18, 20

Q3 = 18

Find the minimum and maximum values in the data set:

Minimum = 12

Maximum = 20

Now that we have the necessary values, we can construct the box-and-whisker plot:

lua

Copy code

       |                 |

 12  |      -------------|    

 13  |                 |

 14  |              ----  

 15  |           -------

 16  |      -------------|    

 17  |                 |

 18  |              ----  

 20  |                 |

       |_________________|

In this box-and-whisker plot, the box represents the interquartile range (IQR), which is the range between Q1 and Q3 (13 to 18). The line inside the box represents the median (15). The whiskers (lines extending from the box) represent the minimum and maximum values (12 and 20).

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How do I find the value

Answers

A = 139°

B = 139°

You can see A and B are coefficients of each other, which means they have the same angle because they are opposite each other on the straight line. just like the two 41° angles are.

The angle around a point always add up to 360°, so add the 41° angles.

41 + 41 = 82°

Then minus this by 360°.

360 - 82 = 278°

And to work out one angle, which gives you the angle for both, divide 278 by two.

278 ÷ 2 = 139°

Both A and B have an angle of 139°

Example:

To find the value of two intersecting lines, you need to know the equations of both lines. Then, you can set the equations equal to each other and solve for the variable x. This will give you the x-coordinate of the point where the lines intersect. To find the y-coordinate, you can plug the value of x into either equation and solve for y. For example, if one line is y = 3x - 5 and another line is y = -2x + 7, then you can set 3x - 5 = -2x + 7 and solve for x:

3x - 5 = -2x + 7

5x = 12

x = 12/5

Then, plug x = 12/5 into either equation and solve for y:

y = 3(12/5) - 5

y = 36/5 - 25/5

y = 11/5

Therefore, the point of intersection is (12/5, 11/5).

If one of the lines has a given angle, such as 41 degrees, then you can use trigonometry to find its equation. For example, if one line passes through the origin and has an angle of 41 degrees with the positive x-axis, then you can use the slope formula to find its equation:

slope = tan(41 degrees) ≈ 0.87

y = mx + b

y = 0.87x + 0

Then, you can use the same method as before to find the point of intersection with another line.

_______________________________________________________

The answer is 139 degrees, using the method I gave.

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Determine the equation of the midline of the following graph.

Answers

The equation of the midline of the graph is y = -2

How to determine the equation of the midline of the graph.

From the question, we have the following parameters that can be used in our computation:

The graph

Where we have

Max = 1

Min = -5

Using the above as a guide, we have the following:

Midline, y = (Max + MIn)/2

substitute the known values in the above equation, so, we have the following representation

y = (1 - 5)/2

Evaluate

y = -2

Hence, the equation of the midline of the graph is y = -2

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