HELPPPP ???
Select the correct statement about the system of equations.

Answer:

131.25 feet.

Step-by-step explanation:

We can use the concept of similar triangles to find the length of the monument's shadow.

Since the pole and the monument are casting the shadows, we can assume that the ratio of the height of the pole to the length of its shadow is equal to the ratio of the height of the monument to the length of its shadow.

12/5 = 315/x

Where x is the length of the monument's shadow.

We can cross-multiply and solve for x:

12x = 5315

x = 5*315/12

x = 131.25

So, the length of the monument's shadow is approximately 131.25 feet.

The plumber bought 5 pieces of copper wire and 5 pieces of plastic wire.

What is an equation?

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign.

Length of each piece of copper wire = 6 m

Length of each piece of plastic wire = 1 m

Total number of pipes bought = 10

Total length of pipes = 35 m

Let the number of copper pipes be x.

Let the number of plastic pipes be y.

The equation for number of pipes will be -

x + y = 10...(1)

The equation for length of pipes will be -

6x + y = 35...(2)

Subtracting equation (1) from (2) -

5x = 25

x = 5

Substituting the value of x in equation (1) -

5 + y = 10

y = 10 - 5

y = 5

Therefore, the number of copper and plastic wires is 5 each.

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Step-by-step explanation:

Possible values of the correlation coefficient range from -1 to +1, with -1 indicating a perfectly linear negative, i.e., inverse, correlation (sloping downward) and +1 indicating a perfectly linear positive correlation (sloping upward). A correlation coefficient close to 0 suggests little, if any, correlation

We can simplify the expression to get:

2³ + 3*(2) + 14/2 = 21

The correct option is E.

Here we want to simplify the expression below:

2³ + 3*(2) + 14/2

The additions are the last thing we need to do, we can replace:

2³ = 8

3*(2) = 6

14/2 = 7

Replacing that in the expression we will get:

2³ + 3*(2) + 14/2 = 8 + 6 + 7

8 + 6 + 7 = 21

So the correct option is E.

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The given system of equations has infinitely many solutions. Option A is correct.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
Given equation,
- 6x - 2y = 10 - - - -1

y = - 3x - 5  - - - -2

From equation 1
-6x - 2y = 10
Reform the equation,
-2y = 6x + 10

Divide the above equation by -2,
y = -3x - 5

Since the above equation is equivalent to equation 2, therefore the system of equations has infinitely many solutions.

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Answer:255

Step-by-step explanation:

The value of x on the diagram is given by the following option:

D) 50º.

When two parallel lines are cut by a transversal line, the corresponding angles are the angles that are in the equivalent position for each parallel line.

The parallel lines for this problem are given as follows:

L1 and L2.

Hence the corresponding angles are given as follows:

The bases of the rectangle are also parallel, hence two extra pairs of corresponding angles are given as follows:

As all these angles are corresponding, they have the same measure, hence:

4a = 100º

a = 100º/4

a = 25º.

The angle x is twice the measure of these angles, hence:

x = 2 x 25º

x = 50º.

Meaning that option D is correct.

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Answer:

A = 12.5663706 yd2

Step-by-step explanation:

the plot is attached below and the slope is 4.

What is the slope of line?

Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.

We know that formula two find the slope of the line joining two points which is

The equation y = 4x + 3 models the data below.

x 1   2  3  4   5    6   7   8

y 8 13 16 21 26 29 33 37

The plot will be using this data.

Hence the plot is attached below and the slope is 4.

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If the brain volumes (cm³) of 20 brains have a mean of 1085.2 cm³ and a standard deviation of 125.6 cm³. For such data: it is significantly low for a brain because 1386.4 cm³ is less than the upper limit.

Mean = 1085.2 cm³

Standard deviation = 125.6 cm³

Hence,

Lower limit = Mean - 2 x Standard deviation

Lower limit  =1085.2 - 2 x 125.6

Lower limit =1161.2 - 251.2

Lower limit  =910

Upper Limit = Mean + 2 x Standard deviation

Upper Limit = 1161.2 +  2 x 125.6

Upper Limit =1161.2 +251.2

Upper Limit =1412.4

The limit of values is from 910 to 1412.4.

A value below 910 will be is considered low and a value above 1412.4  will be considered high

Therefore 1386.4 cm³ is less than the upper limit. Thus it is significantly low for a brain.

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Answer:

A) 4 batches

B) 1 1/2 batches

C) 10 batches

D) 1 2/3 batches

Step-by-step explanation:

A) A 1/4 goes into 1, 4 times so it would make 4 batches.

B) 1/4 = 2/8 so 3/8 = 1.5/4 and that would make 1.5 batches.

C) since 1 cup of sugar can make 4 batches, 2 cups can make 8 batches and 1/2 cup makes 2, so 8+2= 10 batches

D) 1/4=3/12 that means 5/12 = 1/4+1/6 and 1/6 divided by 1/4 = 2/3 so that means that it can make 1 2/3 batches.

Answer:

Step-by-step explanation:

The balance of an account after a year, when the interest rate is 3% per year and there are no additional withdrawals or deposits, can be represented by the formula:

Balance = Principal + Interest

where Principal is the initial amount of money invested (m) and Interest is the interest earned on that amount for the year.

Interest is calculated as the product of the principal, the interest rate, and the time period. In this case, the interest rate is 3% (or 0.03), and the time period is one year. Therefore the Interest can be represented by the following expression:

Interest = Principal * Interest Rate * Time

Substituting the given values:

Interest = m * 0.03 * 1

So the expression that represents Arianys balance after a year is:

Balance = m + (m*0.03)

= m + 0.03m

= 1.03m

This expression represents her balance after a year, assuming she makes no additional withdrawals or deposits.

Step-by-step explanation:

(4-2)*180=360

80+7t+7t+14t=360

28t=280

t=10

The choice that shows 13 · (7 · 4) correctly rewritten using the associative property and then correctly simplified is presented as follows;

The associative property of multiplication stated that the multiplication of three numbers produces the same result in any way the numbers are grouped.

Mathematically, the associative property of multiplication can be presented as follows;

(a × b) × c = a × (b × c)

The specified operation involving the multiplication of three numbers are presented as follows;

13 · (7 · 4)

The associative property of multiplication indicates that we get;

13 · (7 · 4) = (13 · 7) · 4

13 × 7 = 91

Therefore, (13 · 7) · 4 = (13 × 7) × 4

(13 × 7) × 4 = 91 × 4 = 364

The option that shows the associative property correctly written and then correctly simplified is therefore;

The possible options in the question, obtained from a similar online question are;

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The solution of the equation (x - 5)² + 3(x - 5) + 9 = 0 is x = -7 ± √35/2. Option B

From the information given, we have the equation as;

(x - 5)² + 3(x - 5) + 9 = 0

To solve the equation, take the following steps;

(x -5)(x-5) + 3x - 15 + 9 = 0

x² - 5x - 5x + 25 + 3x - 15 + 9 = 0

Now, collect like terms

x² - 5x - 5x + 3x + 25 - 15 + 9 = 0

add or subtract the like terms

x² - 7x + 21 = 0

The quadratic formula is is given as;

x =[tex]-b[/tex] ± [tex]\frac{\sqrt{b^2 - 4ac} }{2a}[/tex]

substitute the values

x = -(7) ± [tex]\frac{(-7)^2 - 4(1)(21)}{2(1)}[/tex]

expand the bracket

x = -7 ± [tex]\sqrt{\frac{49 - 84}2} }[/tex]

x = -7 ± √35/2

Hence, the value is x = -7 ± √35/2

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Hope it helps.

If you have any query, feel free to ask.

The equation that models the scenario and number of years for the population to reach 656,000 will be option A.

i.e. y=100(3)^t and 8 years.

What are equations?

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”. For example, 2x – 5 = 13.

Here,

2x – 5 and 13 are expressions

The sign that connects these two expressions is “=”.

Algebra considers two prominent families of equations, namely polynomial equations and linear equations. Polynomial equations with one variable can be written in P(x) = 0, where P is a polynomial, and ax + b = 0 is the general form of linear equations. Here, a and b are parameters. We can practice geometric or algorithmic methods from linear algebra or mathematical analysis to solve these equations. Also, there are different types of equations, such as:

Linear equations

Quadratic equations

Cubic equations

Quartic equations

Differential equations

Parametric equations

Now,

The equation as the population is compounding annually for the scenario

will be y=P*(1+R)^t

Here p=Initial population

R=rate of increment/ decrement of population

t=time

Hence,

y=100*(1+2)^t                    (R=2 )

y=100*3^t

Time for which the population will be 656,000 will be

656000=100*3^t

6560=3^t

therefore,

t=8 years.

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Circle the equation that models the scenario and the number of years it takes for the population to reach 656,000 is y = 100(3)^x, 8 years.

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10 Km²  is the area of the triangular section that the forest managers plant with trees.

A sector is the area between any two circle radii and any arcs that connect them. Segment: A line segment in geometry is a section of a line that has two clearly defined end points and includes every point on the line in between them.

Firstly count how many cells are there

First line = 6

Second line = 1

Last line = 3

So the area of the section that the forest managers plant with tree is

6 + 1 + 3 = 10 Km²

( count more than half a grid or not count )

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The boat and the whale are about 218.5 miles apart.

Using the Pythagorean theorem to calculate the distance between the boat and the whale.

Let's call the distance between the boat and the whale "d" and the time they moved apart "t".

1st movement:

d = 45t

2nd movement:

d = (45t + 25(t+35))²

To calculate the final distance, we need to square d from the second movement and add the result from the first movement.

d² = (45t)² + (25(t+35))²

We know that the boat and the whale were moving apart for 35 minutes and 25 minutes, so we can substitute t = 35 and t = 25 in the equation.

d² = (4535)² + (2560)²

Taking the square root of the result and get the final distance between the boat and the whale.

d =  ([tex]\sqrt{4535 ^{2} +2560^{2} }[/tex])

d ≈ 218.5 miles

Hence, the boat and the whale are about 218.5 miles apart.

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Answer:

d. x-700=35

Step-by-step explanation:

The statement says that the variations will stay within a range of +5%, so the resistance can be increased by 5% of 700 ohms. To find the highest resistance that can be achieved, you can use the formula:

x = 700 + (700 * 5%) = 700 + 35 = 735 ohms

To find the lowest resistance that can be achieved, you can subtract the same percentage (5%) of 700 ohms:

x = 700 - (700 * 5%) = 700 - 35 = 665 ohms

So the lowest and highest resistance that can be achieved are 665 ohms and 735 ohms respectively.

The equation of the line passing through the point (0, 2) and (2, 12) is y = 5x + 2

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The slope intercept form of a linear equation is:

y = mx + b

Where m is the slope (rate of change) and b is the y intercept.

Let us assume the line passes through the point (0, 2) and (2, 12), hence:

y - 2 = [(12 - 2)/(2 - 0)](x - 0)

y = 5x + 2

The equation of the line is y = 5x + 2

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Answer:

Newton's 3rd law of motion

Step-by-step explanation:

Newton's 3rd law of motion states that for every force in nature there is an equal and opposite reaction.

So, assuming the people are both pushing with the same force, their forces are basically canceling each other out, and a net force of 0 is acting uponm the box, which explains why it is not moving.

The smiley face is solved to get a value of 72

The solution to the value of the smiley face is solved by forming some equations

Using the third row that have only squares

8 square - 6 square + 3 square = 60

2 square + 3 square = 60

5 square = 60

dividing through by 5

square = 60 / 5 = 12

hence a square is 12

Using the second row

12 square + 5 star = 234

substituting a square = 12

12 * 12 + 5 star = 234

144 + 5 star = 234

5 star = 234 - 144

5 star = 90

dividing through by 5

star = 90 / 5 = 18

hence a star is 18

using the first row

square + 3 triangle + star = 57

substituting square = 12 and star = 18

12 + 3 triangle + 18 = 57

3 triangle + 30 = 57

3 triangle = 57 - 30

3 triangle = 27

dividing through by 3

triangle = 27 / 3 = 9

hence triangle = 9

solving for the smiley face

substituting the values of the figures

18 (9 + 18 - 12) + 12 (18 + 9 + 9) = smiley face

solving the parenthesis

smiley face = 18 (15) + 12 (36)

smiley face = 18 * 15 + 12 * 36

smiley face = 702

hence the smiley face is 702

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Answer:

Kathy is 48 years old and Samantha is 12.

Step-by-step explanation:

This is a challenging question that requires some interpretation.  Let K and S stand for the current ages of Kathy and Samatha.

We are told that:  K+S = 60

And, in 8 years:  K+8 and S+8

"Kathy will be 5 years older than 3 times as old as Samantha was 3 years ago"  ["3 years ago:"  from now or in 8 years.  I'll interpret it as from now, or (S-3)]

(K+8) = 3(S+8-3)+5   ["5 years older than 3 times as old as Samantha was 3 years ago"]

(K+8) = 3(S+5)+5

K+8 = 3S+20

 K = 3S+12

---

Rearrange the firts equation to isolate K

K = 60-S

Now use this definition of K in the previous equation:

K = 3S+12

60-S = 3S+12

4S = 48

S = 12

K+S = 60

K+12 = 60

K = 48

=====

CHECK

Does K + S = 60?   48+12 = 60 YES

In 8 years, will Kathy will be 5 years older than 3 times as old as Samantha was 3 years ago?

   K = 48+8 = 56

   S = 12+8 = 20

Three years ago S was 9.

(K+8) = 3(S+8-3)+5

(K+8) = 3(12+8-3)+5

K + 8 = 3(17)+5

K = 48

===

Kathy is 48 years old and Samantha is 12.

Answer:

600 ml

Step-by-step explanation:

One of the rules of ratio includes sorting ratio in order according to the question. In this case, squash is mentioned first, then water. Hence, the ratio is:

squash:water = 1:6

Use cross multiplication:

1       :       6

100  :        ?

Multiply 100 by 6 then divide it by 1: which basically means 100 * 6 = 600 ml.

If you are unfamiliar with cross multiplication, then simply find out how many times did you have to multiply the 1 in the squash ratio to result to 100, which is 100, then multiply 6 by that answer = 6 * 100.

Hope you understood :)

The domain of the function 5h + 2d = 15 is [0, 3].

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The function 5h + 2d = 15

Where h is the number of hours and d is the distance remaining after h hours.

Now,

5h + 2d = 15

2d = 15 - 5h

d = (15 - 5h)/2

For h = 0, d = 15/2 = 7.5

For h = 1, d = (15 - 5)/2 = 10/2 = 5 miles.

For h = 2, d = (15 - 10)/2 = 5/2 = 2.5 miles.

For h = 3, d = (15 - 15)/2 = 0 miles

The domain of the function is [0, 3].

Thus,

The domain is [0, 3].

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A function to calculate the average attendance for all of the locations for the year 2018 would be: =average(F5:F11).

To enter a function to calculate the average attendance for the year 2022 we have to follow the following steps.

Note: This question is incomplete because the information is incorrect, and some information is missing. Here is the complete information and the correct information:

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Answer:

( - inf, 5) (9, inf )

Step-by-step explanation:

The arrow(s) at the end of the line indicate that the highlighted green line does not stop at a specific number, hence the use of infinity signs (inf). If the arrow is going to the left on a line, then the value would be negative infinity. If it is going to the right, then it would be positive.

As for the space in between the green arrows pointing separate ways, there are two points, one which is positioned at the number 5 and the other at the number 9. Because there are two separate points which are both solid green, the use of parentheses is needed. The final answer is, as mentioned, ( - inf, 5) (9, inf ).

Answer:

a) Common ratio r = [tex]\boxed{2}[/tex]

b) Formula for common ratio:
[tex]\dfrac{a_{n+1}}{a_n} , n = 1, 2, 3, 4....\\[/tex]

Formula for nth term:
[tex]a_n = a_1r^{n-1}[/tex]

(see explanation below for part b)

c) [tex]a_{10} = \boxed{1024}[/tex]

d) Recursive formula: [tex]\boxed{a_{n+1} = 2a_n}[/tex]

Step-by-step explanation:

a) The common ratio r for a geometric sequence is the ratio of any term(except the first) to the previous term. And this is a constant for that sequence

If we have a sequence [tex]a_1, a_2, a_3, a_4, a_5,....\\[/tex]

[tex]r = \dfrac{a_2}{a_1} = \dfrac{a_3}{a_2} = \dfrac{a_4}{a_3} = \dfrac{a_5}{a_4}[/tex]

Here [tex]a_1[/tex] is the first term in the sequence

The sequence we have here is
2, 4, 8, 16

So
[tex]r = \dfrac{4}{2} = \dfrac{8}{4} = \dfrac{16}{8} = 2\\[/tex]
Answer to a)

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b) This part is confusing. Are they asking for a formula for the common ratio or a formula for the nth term? You can write both or check with your teacher

The explicit formula for the common ratio is

[tex]\dfrac{a_{n+1}}{a_n} , n = 1, 2, 3, 4....\\[/tex]

The explicit formula for the nth term, [tex]a_n[/tex] of a geometric sequence is
[tex]a_n = a_1r^{n-1}[/tex]

where [tex]a_1[/tex] is the first term of the sequence and r is the common ratio
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c)
The formula for finding the nth term of a geometric sequence is
[tex]a_n = a_1r^{n-1}\\\\[/tex]

Therefore

[tex]a_{10} = a_1 r^{(10-1)} = a_1 \times r^9\\\\[/tex]

[tex]a_1 = 2, r = 2\\\\[/tex]

So
[tex]a_{10} = 2 \cdot 2^9 \\\\= 2 \cdot 512\\\\= 1024\\[/tex]ANSWER c)

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d)

A recursive formula is just an expression that denotes the relationship between one term and the next

We know that
[tex]r= \dfrac{a_{n+1}}{a_n} \\\\[/tex]

Multiplying both sides by [tex]a_n[/tex],

[tex]ra_n = a_{n+1}[/tex]

Or

[tex]a_{n+1} = ra_n\\\\[/tex]

For the specific case of r = 2 we get the recursive formula as

[tex]a_{n+1} = 2a_n[/tex]

ANSWER d)