Find an equation for the line that passes through the points (-1, 4) and (-5, 6).

Answer:

This system of equations can be solved using substitution or elimination methods.

Using substitution, we can solve for one of the variables in one of the equations and substitute that expression into the other equation.

Solving for x in the second equation:

x + 3y = 1

x = 1 - 3y

Substituting this expression for x into the first equation:

-4(1 - 3y) - 15y = -10

Expanding and solving for y:

-4 + 12y - 15y = -10

12y - 4 = -10

12y = -6

y = -1/2

Now that we know y = -1/2, we can substitute this value back into the expression for x:

x = 1 - 3(-1/2) = 1 + 3/2 = 7/2

So the solution to the system of equations is (7/2, -1/2).

Checking the solution in both equations:

-4(7/2) - 15(-1/2) = -4(7/2) + 15/

Step-by-step explanation:

The length of gasket material needed to obtain 19 sq ft of the material is approximately 25.33 ft.

What is length?

The length of something measured from end to end or along its longest side, or the length of a specific section of something.

Convert the width from inches to feet:

Since there are 12 inches in a foot, the width in feet is:

9 / 12 = 0.75 ft

Calculate the length needed:

We know that the area of the gasket material is 19 sq ft, and the width is 0.75 ft. Let L be the length needed in feet. Then we have:

Area = Width x Length

19 sq ft = 0.75 ft x L

Solving for L, we get:

L = 19 sq ft / 0.75 ft

L = 25.33 ft (rounded to two decimal places)

Therefore, the length of gasket material needed to obtain 19 sq ft of the material is approximately 25.33 ft.

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Using a system of equations, the number of each type of coffee that Julia and her husband should buy is as follows:

A system of equations is two or more equations solved concurrently or at the same time.

A system of equations can also be described as simultaneous equations.

The cost per pound of City Roast Columbian coffee = $6.50

The cost per pound of French Roast Columbian coffee = $8.20

The total quantity of the blend = 34 pounds

The cost per pound of the blend = $6.90

The total cost of the 34 pounds = $234.60 ($6.90 x 34)

Let the number of pounds of City Roast coffee = x

Let the number of pounds of French Roast coffee = y

x + y = 34 ... Equation 1

6.5x + 8.2y = 234.6 ... Equation 2

Multiply Equation 1 by 6.5:

6.5x + 6.5y = 221 ... Equation 3

Subtraction Equation 3 from Equation 2:

6.5x + 8.2y = 234.6

-

6.5x + 6.5y = 221

1.7y = 13.6

y = 8

Substitute, y = 8 in Equation 1:

x + y = 34

x = 34 - 8

x = 26

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Answer:

I have graphed it and attached an image in the explanation part.

Step-by-step explanation:

The measure of other sides of a triangle are 15.11 units and 10.76 units.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

In the given triangle, ∠B=45°, ∠C=52° and AB=12 units.

By using angle sum property of a triangle,

∠A+∠B+∠C=180°

∠A+45°+52°=180°

∠A+97°=180°

∠A=83°

Now, by using sine rule, we get

sin83°/a=sin45°/b=sin52°/12

0.9925/a=0.7071/b=0.788/12

0.9925/a=0.788/12 and 0.7071/b=0.788/12

0.788a=11.91 and 0.788b=8.4852

a=11.91/0.788 and b=8.4852/0.788

a=15.11 units and b=10.76 units

Therefore, the measure of other sides of a triangle are 15.11 units and 10.76 units.

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On solving the provided question we can say that here trigonometry  y = Asin(Bx + C)+D

Trigonometry is a branch of mathematics that studies the relationship between triangle side lengths and angles. From the use of geometry in astronomical study, the area first appeared in the Hellenistic era, around the third century BC. Exact methods is a branch of mathematics that deals with specific trigonometric functions and how they can be used in calculations. In trigonometry, there are six popular trigonometric functions. Their names and acronyms are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of the properties of triangles, particularly right triangles. However, the study of geometry is the characteristics of all geometric figures.

(x)=sin(x) consider y = Asin(Bx + C)+D adjusts the amplitude of the function (how high or low it is).

if you want to

B determines how many full wavelengths will occur during a certain time period, and C determines the phase shift (left/right on the axis) (positive values will shift left)

The vertical shift, or D, is up or down. For example, a +3 would move the entire function up 3 units.

In your situation, the amplitude is 4 since you wish to stretch vertically.

Additionally, you want to move it right three units. C = -3 (always the opposite of the direction you wish to go) (always the opposite of the direction you want to go)

g(x) = 4sin(x - 3)

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The balance in the account after 16 years, given interest rate and the compounding period, is $ 10, 421. 83.

To find the balance after 16 years, the formula to be used is the compound interest formula which is:

= Amount invested x ( 1 + rate ) ^ number of periods

Rate :

= 6 % / 12 months per year

= 0. 5 %

The number of periods :

= 16 years x 12 months a year

= 192 periods

The value would be :

= 4, 000 x ( 1 + 0. 5% ) ¹⁹²

= $ 10, 421. 83

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The limits lim x→ −4 f(x) is 5

The method is substitution method

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

−5x − 15 ≤ f(x) ≤ x² + 3x + 1

The limits is given as

lim x→ −4 f(x)

By direct substitution, we have

−5(-4) − 15 ≤ f(x) ≤ (-4)² + 3(-4) + 1

Evaluate the exponents and the products

20 − 15 ≤ f(x) ≤ 16 - 12 + 1

Evaluate the difference

5 ≤ f(x) ≤ 5

This means that

f(x) = 5

So, we have

lim x→ −4 f(x) = 5

The method used is the direct substitution method

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Answer:

C. 5x²-7x-8

Step-by-step explanation:

(-3x²-5x +1 ) + (8x²-2x-9)

Grouping like terms:
(- 3x² + 8x²)  + (- 5x - 2x) + (1 - 9)

=> (5x²) + (-7x) + (-8)

=> 5x² - 7x - 8

Answer: x=35

Step-by-step explanation:

The value the function given by (A ∪ B) = {1, 2, 4, 5, 7, 9, 11, 12, 15, 16, 18} and (A ∩ B) = {7}.

We carry out specific operations in mathematics, such as addition, subtraction, multiplication, etc. Generally speaking, these operators accept two or more operands and output a result dependent on the operation carried out. Similar to this, in set theory, several operations are typically done on two or more sets to obtain a new set of elements depending on the operation. The number of elements supplied by the operation and processing the result of a collective set is represented by the union and overlap of sets. All of the components are taken into account in the outcome when there is a union, but only the ones that are shared when there is an intersection.

The union of the two sets depict all the terms present in both the sets.

Thus, the value of (A ∪ B) is:

(A ∪ B) = {1, 2, 4, 5, 7, 9, 11, 12, 15, 16, 18}

The intersection of the sets depict all the common terms present in the two sets thus the value of (A ∩ B) is:

(A ∩ B) = {7}

Hence, the value the function given by (A ∪ B) = {1, 2, 4, 5, 7, 9, 11, 12, 15, 16, 18} and (A ∩ B) = {7}.

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The numbers on a number line is

    |-------|-------|-------|-------|

    0      1       2       3       4

                  *       *

               1 1/2   2 2/5

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

Plot 1 1/2 and 2 2/5

To plot 1 1/2 and 2 2/5 on a number line, we can follow these steps:

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Answer:

Common ratio, r = 3

Step-by-step explanation:

Common ratio is given by the ratio of one of the terms to the previous term and is a constant for the entire sequence

Here the first term is 17

Second term is 51

Second Term ÷  First Term
= 51 ÷ 17 =3

Third Term ÷ Second Term
= 153 ÷ 51 = 3

So common ratio is 3

In general, if aₙ is the nth term and aₙ₊₁ then the common ratio is given by:
aₙ₊₁ / aₙ

Step-by-step explanation:

we all know that development is positive change in society and fidelity is a process of fertilization of human in society that explain us development and fertilization are the process of positive changes in our environment and province

The units of water the friends used in one month is 820 units.

The total units of water used as read by the meter = 789 units + 820 units

= 1609 units

Therefore, the friends used a total of 820 units of water.

Complete question:

A water meter shows how many units of water Riya and her friends use.

Riya reads the meter when they move in. It shows 789 units.

She reads the meter again after one month. It reads 820 units.

How many units of water did the friends use in one month?

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Answer:

hi

Step-by-step explanation:

[tex]x {}^{3} - 27 = {x}^{3} - {3}^{3} \\ = (x - 3)( {x}^{2} + 3x + 9) \\ {x}^{3} + 27 = {x}^{3} + {3}^{3} \\ = (x + 3)( {x}^{2} - 3x + 9)[/tex]

The next number in this sequence is 63, which is the result of multiplying the previous number (39) by 2 and then adding 6.

The equation is f(x) = -0.4x + 60. The solution has been obtained by using slope - intercept form.

What is slope-intercept form?

The graph of the equation y = mx + b is a line with a slope of m and a y-intercept of b. The form of the linear equation is called the slope-intercept form, and the values of m and b are real integers.

We are given that f(-10) = 64 and f(15) = 54.

So, we get the points as (-10 , 64) and (15 , 54)

Using the slope intercept form, we get

Slope(m) = (54 - 64)/(15 + 10)

Slope(m) = -0.4

We know that y = mx + b

For calculating b. we will put in the values

⇒64 = -0.4(-10) + b

⇒64 = 4 + b

⇒b = 60

From this we get the equation as

f(x) = -0.4x + 60

Hence, the equation is f(x) = -0.4x + 60.

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Answer:

              The area of the quadrilateral is C: 12 square feet.

Step-by-step explanation:

               In the photo, the quadrilateral is divided into two triangles, both having a base length of 4 feet and a height of 3 feet. Therefore, we can find the area of the entire quadrilateral by adding the areas of the two triangles together. Since the triangles have a base length of 4 feet and a height of 3 feet, their individual areas will be [tex]4*3*\frac{1}{2} =12*\frac{1}{2} = 6[/tex] square feet. As there are two triangles, we need to multiply the area of one triangle by 2 to get the total area of the quadrilateral, which would be [tex]6 * 2=12[/tex] square feet. Hence, we can conclude that the correct answer will be C.

Have a great day! Feel free to let me know if you have any more questions :)

Answer:

b

Step-by-step explanation:

make sure the y axis doesnt repeat

The two provided payments of $17,000 and $3,300 due in 1 year and 2 years, respectively, would be replaced by two equal payments of $2,287.87 made in 6 months and 5 years.

To solve this problem, we need to find two equal payments that would replace the two given payments, given the time and interest rate. We can use the present value formula to calculate these payments:

PV = C / (1 + r)^n

Where

PV is the present value,  

C is the future value of the payment,

r is the interest rate per compounding period, and

n is the number of compounding periods.

For the first payment of $17,000 due in 1 year, its present value in 6 months can be calculated as:

PV1 = 17,000 / (1 + 0.08/4)^(2*2) = $14,785.28

For the second payment of $3,300 due in 2 years, its present value in 5 years can be calculated as:

PV2 = 3,300 / (1 + 0.08/4)^(4*2) = $2,424.67

To find the equal payments that would replace these two payments, we can use the annuity formula:

PMT = PV / [(1 - (1 + r)^(-n)) / r]

Where

PMT is the equal payment,

PV is the present value,

r is the interest rate per compounding period, and

n is the number of compounding periods.

For the two payments to be made in 6 months and 5 years, respectively, the total number of compounding periods is

4*2.5 = 10.

The equal payment can be calculated as follows:

PMT = (PV1 + PV2) / [(1 - (1 + 0.08/4)^(-10)) / (0.08/4)] = $2,287.87

Therefore, two equal payments of $2,287.87 made in 6 months and 5 years would replace the two given payments of $17,000 and $3,300 due in 1 year and 2 years, respectively.

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Answer:

Step-by-step explanation:

(a) (i) The mean of the original data set is denoted as μ and the constant value being added to each data point is denoted as c.

The formula for the new mean is simply μ + c, so the new mean is μ + 6 = 10 + 6 = 16.

(a) (ii) The standard deviation of the original data set is denoted as σ. Adding a constant value to each data point does not change the spread of the data set, so the new standard deviation is still σ = 3.

(b) (i) The mean of the original data set is denoted as μ and the constant value being multiplied to each data point is denoted as k.

The formula for the new mean is μ * k, so the new mean is μ * 6 = 10 * 6 = 60.

(b) (ii) The variance of the original data set is denoted as V. To find the new variance after multiplying each data point by k, we can use the formula: k^2 * V.

So, the new variance is 6^2 * V = 36 * V.

--------

Here is a definition of each variable:

μ: The mean of a set of data is the sum of all the values divided by the number of values. It represents the average value of the data set.

σ: The standard deviation of a set of data is a measure of the spread of the data set about the mean. It is the square root of the variance.

V: The variance of a set of data is the sum of the squares of the deviations of each value from the mean, divided by the number of values. It is a measure of the spread of the data set about the mean, but it is measured in squared units.

c: A constant value added to each data point.

k: A constant value multiplied to each data point.

Answer:
5.6%

Step-by-step explanation:

2/100 x 100 = 2
100-2 = 98 Boys on new Honor Roll
1/10 x 80 = 8
80-8 = 72 Girls on  new Honor roll
180 Original Roll
170 On new Roll
x/100 x 180 = 170
x/100 = 17/18
x = 1700/18
x = 94.4444444
Round 94.4
5.6 percent decrease.

Size of the house should be 2900 ft².

Correct option is B.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Given,

Equation for the line that expresses price of house

y = 0.06x + 60.5

where y is the price in thousand dollars, x is area in square feet.

Price of the house = $235000

⇒ y = 235

Then,

235 = 0.06x + 60.5

0.06x = $235 - 60.5

0.06x = 174.5

x = 174.5/0.06

x = 2908.33 ≈ 2900

Hence, 2900 ft² should be the size of the house.

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Answer:

22/22X22-22+22= 22÷5 =4.5

33/33X33-33+33=33÷5=6.6

Answer:

10 miles

Step-by-step explanation:

Let's call the number of miles driven in a day "x". The total cost for Triangle Truck Rental can be expressed as:

Cost (Triangle) = $35 + 0.5x

The total cost for Circle Rent-A-Truck can be expressed as:

Cost (Circle) = $55 + 0.3x

We want to find the value of x such that Cost (Triangle) = Cost (Circle). So we can set the two expressions equal to each other and solve for x:

$35 + 0.5x = $55 + 0.3x

0.2x = $20

x = 100 miles

So the man would need to drive 100 miles in one day for both companies to have the same total cost.

The base-nine system of 76 base 10 is 84

We will divide 76 by 9 and write down the remainder

9 | 76 R

9 | 8 | 4

9 |8 | 8

The remainder is then written from the bottom value giving us 84

Consequently, base 10 numbers can be converted to base 9 by dividing by 9 and writing the remainder in the reverse order of bottom to top.

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The local maximum for the graph below is given at point b.

A function has a local maximum when it changes from increasing to decreasing.

For the graphed function, we have that the function is increasing until point b, and then it starts to decrease, hence the local maximum is given at point b.

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The capacity of the trophy that us 30 cm high is 0.4286 liter

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

7 cm height cup holds 100 ml. Therefore:

7 cm = 100 ml

For a 30 cm height trophy:

30 cm = 30 cm * 100 ml per 7 cm = 428.57 ml

1000 ml = 1 l

428.57 ml = 428.57 ml * 1 liter per 1000 ml = 0.4286 liter

The capacity of the trophy is 0.4286 liter

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Answer: 70˚

Step-by-step explanation:

Goal: find the other angles in the triangle and subtract them from 180 to find x:

180 - 105 = 75˚

the other angle is 35˚, (alternate interior angles).

.: x = 180 - 75 - 35 = 70˚