Find the equation of a line containing the following points. Write the equation in slope-intercept form.
(-2, 2) and (1, 2)
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y =

The equation shows that the number of toys that must be bought for them to have equal profit will be 212 toys.

From the information, it should be noted that the equation that can be used to represent the information about Jaclyn company will be:

= 2125 + (49.99 × x)

= 2125 + 49.99x

The equation that can be used to represent the information about Richie company will be:

= (39.95 × x)

= 39.95x

Therefore, we will equate both equations:

2125 + 49.99x = 39.95x

49.99x - 39.95x =2125

10.04x = 2125

x = 212

Therefore, the number of toys that must be bought for them to have equal profit will be 212 toys.

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Answer:

C

Step-by-step explanation:

We want to simplify the expression:

\(\displaystyle 3 \sqrt{-28}\)

Rewrite:

\(\displaystyle = 3 \sqrt{ 4\cdot 7 \cdot -1}\)

Rewrite:

\(\displaystyle = 3 \cdot \sqrt{4} \cdot \sqrt{7} \cdot \sqrt{-1}\)

Simplify. Let i = √(-1). Hence:

\(\displaystyle = 3 \cdot \left(2\right) \cdot \left(i\right) \cdot \sqrt{7}\)

Multiply:

\(\displaystyle = 6i\sqrt{7}\)

In conclusion, our answer is C.

The area of the outer rectangle is 15 in²

The area of the smaller cut out rectangle is 2 in²

The area of the figure is 13 in².

Area is the region bounded by a plane shape.

To calculate the area of the shape, we use the formula below

Where:

Substitute these values into equation 2

Also,

To calculate the area of the smaller cut out rectangle, we use the formula below

Where:

Substitute these values into equation 2

Hence, the area of the figure is = 15-2 = 13 in²

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The algebraic rule for the transformation is B' = (Bx + 15, By - 12)

Given data ,

To determine the algebraic rule for the transformation from point B to point B', we need to find the equations that relate the coordinates of the preimage point B to the image point B'.

Let's denote the translation amounts in the x-direction and y-direction as (dx, dy). The coordinates of B' can be obtained by adding these translation amounts to the coordinates of B:

B' = (Bx + dx, By + dy)

Given that B is located at (5, -4) and B' is located at (20, -16), we can calculate the translation amounts:

dx = 20 - 5 = 15

dy = -16 - (-4) = -12

Hence , the algebraic rule for the transformation is B' = (Bx + 15, By - 12)

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The (A ∪ B) ∩ (A ∪ C) ∩ (B ∪ C) ∩ (B ∩ C) ∩ C is an empty set {}.To find the sets A ∪ B, A ∩ B, A ∪ C, A ∩ C, B ∪ C, and B ∩ C, we can perform the following operations:

A ∪ B: The union of sets A and B includes all unique elements from both sets, resulting in {10, 11, 12, 13, 14, 16}.

A ∩ B: The intersection of sets A and B includes only the common elements between the two sets, which are {10, 12}.

A ∪ C: The union of sets A and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 13}.

A ∩ C: The intersection of sets A and C includes only the common elements, which is {10, 11}.

B ∪ C: The union of sets B and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 14, 16}.

B ∩ C: The intersection of sets B and C includes only the common elements, which is an empty set {} since there are no common elements.

Finally, performing the remaining operations:

(A ∪ B) ∩ (A ∪ C): This is the intersection of the union of sets A and B with the union of sets A and C. The result is {10, 11, 12, 13} since these elements are common to both unions.

(B ∪ C) ∩ (B ∩ C): This is the intersection of the union of sets B and C with the intersection of sets B and C. Since the intersection of B and C is an empty set {}, the result is also an empty set {}.

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The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Answer:

-8$

Step-by-step explanation:

first, add 100 to 1,294

then multiply 350.50 by 4

and subtract them

This is the rectangular equation described by the parameter equation x = t1/3 and y = t – 4.

Elimination of the parameter means to rewrite the equations in terms of only x and y. To do this, substitute t from one equation into the other equation. Here, the two equations are:x = t1/3 and y = t – 4Substitute t from the first equation into the second equation:y = (x^3) – 4Now the equation is in terms of x and y only.

This is the rectangular equation described by the parameter equation x = t1/3 and y = t – 4.The rectangular equation, y = (x^3) – 4 can be plotted on a graph. It is a cubic equation. The graph will look like a curve that passes through the point (0, -4) and continues to move towards infinity. The graph will be symmetric to the origin because the equation involves an odd power of x.

If the equation involved an even power of x, the graph would be symmetric to the y-axis. The graph will never touch the x-axis or y-axis, it will only approach them.In conclusion, the rectangular equation y = (x^3) – 4 is derived from the two parameter equations, x = t1/3 and y = t – 4. The graph of this equation is a cubic curve that is symmetric to the origin. The curve passes through (0, -4) and approaches the x and y-axes but never touches them.

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Answer:

A

Step-by-step explanation:

may I have brainllest

Answer:

A

Step-by-step explanation:

Answer:

A would be 90

Step-by-step explanation:

Triangles always calculate to 180 degrees so with the 45+45 being 90 you would subtract that to 180 and it'd give you 90.

Answer:

1725

Step-by-step explanation:

The functions f and g are:

a. f(x) = 1/x

b. g(x) = x + 2

a) To find two functions f and g such that (fog)(x) = 1/(x + 2), we need to determine how the composition of the two functions f and g produces the given expression.

Let's start by assuming g(x) = x + a, where a is a constant. This means that g(x) adds the constant a to the input x.

Next, let's determine the function f(x) such that (fog)(x) results in the desired expression. We have:

(fog)(x) = f(g(x)) = f(x + a)

b) To simplify the expression 1/(x + 2) and make it match f(g(x)), we can consider f(x) = 1/x.

Substituting the expressions for f(x) and g(x) into (fog)(x), we have:

(fog)(x) = f(g(x)) = f(x + a) = 1/(x + a)

Comparing this with the desired expression 1/(x + 2), we see that a = 2. Therefore, the functions f and g are:

a. f(x) = 1/x

b. g(x) = x + 2

Using these functions, we can verify the composition (fog)(x):

(fog)(x) = f(g(x)) = f(x + 2) = 1/(x + 2)

Thus, (fog)(x) = 1/(x + 2), which matches the desired expression.

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Answer:

A. 12.51

Step-by-step explanation:

I had it on a test.

Answer:

Yes

Step-by-step explanation:

To find this out. If you divide the denominators by each other, they would need to be the same value as if you divide the numerators by each other

\(45 \div 9 = 5\)

^ 45 and 9 were the denominators, we divide and get 5

Now for the numerators

\(10 \div 2 = 5\)

^ 10 and 2 we're the numerators, dividing also gave 5

Answer:

yes.

Step-by-step explanation:

let us check. to be a proportion they must be equivalent

however, what do we multiply to get there? let us check..

\(\frac{2x}{9x} =\frac{10}{45}\)

cross multiply...

2x * 45 = 9x * 10

90x = 90x

yes, they will be proportional!

you can even do it without the X, i just put x in to make it clearer.

Answer:

345.575191895

Step-by-step explanation:

To solve you use the equation pie(D)

Answer:

X is equal to or greater than 7

Step-by-step explanation:

Since lx-7l is equal to x-7, this means that it can only work on places where the lines are on top of each other. In terms of x, this means that x must be at least 7. As you can see in the number line also attached.

Answer:

5

Step-by-step explanation:

5*5=25

25*5=125

The monthly payment to buy a $155,000 home at loan is  $817.32.

Given, principal amount of home carries = $155,000

Bank offering loan :

term = 30 years

rate of interest = 5.1%

The formula to calculate monthly payment is:

M = P × r(1+r)ⁿ/(1+r)ⁿ - 1

Substitute the above values:

t = 30 × 12 = 360

⇒ M = 155,000 × 0.051/12(1+0.051/12)³⁶⁰ / (1+0.051/12)³⁶⁰ - 1

⇒ M = 155000 × 17/4000(12.051/12)³⁶⁰ / (12.051/12)³⁶⁰ - 1

⇒ M = 155000 × 17/4000(1.000425)³⁶⁰ / (1.000425)³⁶⁰ -1

⇒ M = 155000 × 17/4000(4.60322) / (4.60322)-1

⇒ M = 155000 × 0.019/3.6032

⇒ M = 817.32

Hence the monthly payment is $817.32.

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Using the power reducing formulas the expression \(5cos^4(x) = 5(1 + cos(2x))^{2/4}\).

We can define higher powers of a trigonometric function in terms of lower powers of the same function using the power-reducing formulas, which are trigonometric identities. Higher powers of cosine can be expressed using this formula in terms of sine and cosine's initial powers. For the other trigonometric functions, such as sine and tangent, there are equivalent formulas. These formulas can be used to solve trigonometric equations and to simplify trigonometric expressions.

The given function is 5cos^4(x).

Now, the power reducing formulas are given by:

\(cos(2x) = cos^2(x) - sin^2(x) = 2cos^2(x) - 1\\cos^2(x) = (1 + cos(2x))/2\)

Substituting the value of second equation in 1 we have:

cos(2x) = 2(1 + cos(2x))/4 - 1

\(cos(2x) = (2cos^2(x) - 1) = cos^2(x) - sin^2(x)\)

Now we have:

\(cos^2(x) = (1 + cos(2x))/2\)

Thus,

\(cos^4(x) = (1 + cos(2x))/2)^2\)

Now multiplying by 5:

\(5cos^4(x) = 5(1 + cos(2x))^{2/4}\)

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Answer:

Option (2)

Step-by-step explanation:

Given:

∠1 ≅ ∠3

To Prove:

∠AXD ≅ ∠CXB

Solution:

Given question is incomplete; find the complete question in the attachment.

            Statements                                                              Reasons

1). m∠1 ≅ m∠3 because m∠1 ≅ m∠3          1). Given

2). m∠1 + m∠2 = m∠CXB and                    

    m∠2 + m∠3 = m∠AXD                            2). Angle addition postulate

3). m∠1 + m∠2 = m∠AXD                             3). Because you can substitute

                                                                          m∠1 for m∠3

4). m∠CXB = m∠AXD                                   4).Transitive property of equality

5). ∠AXD ≅ ∠CXB

Therefore, Option (2) will be the correct option.

The number of revolutions made by the wheel is 5.24 ≅ 5.  

One complete revolution is equal to 360 degrees, so to find the number of complete revolutions the wheel has made, we can divide the total number of degrees rotated by 360.    

Here we have

A wheel rotated by 1888°  

As we know One complete revolution is equal to 360 degrees

Hence, the angle can be rotated by the wheel in 1 rotate = 360°  

Let the wheel make 'x' revolution to make 1888°  

=> 360(x) = 1888

=> x = 1888/360

=> x = 5.24

Therefore,

The number of revolutions made by the wheel is 5.24 ≅ 5.    

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Answer: To calculate the amount of canvas needed for one tent, we need to calculate the total surface area of the tent. The tent consists of two parts: the cylindrical lower part and the conical upper part.

The surface area of the cylindrical part can be calculated as follows:

The base area of the cylinder = π × r² = π × 2.8² ≈ 24.61 m²

The lateral area of the cylinder = 2 × π × r × h = 2 × π × 2.8 × 3.5 ≈ 54.99 m²

So, the total surface area of the cylindrical part is the sum of the base area and lateral area, which is:

Total surface area of cylindrical part = 24.61 + 54.99 ≈ 79.60 m²

The surface area of the conical part can be calculated as follows:

The slant height of the cone = √(r² + h²) = √(2.8² + 2.1²) ≈ 3.44 m

The lateral area of the cone = π × r × slant height = π × 2.8 × 3.44 ≈ 24.12 m²

So, the total surface area of the conical part is the sum of the base area and lateral area, which is:

Total surface area of conical part = 24.61 + 24.12 ≈ 48.73 m²

Therefore, the total surface area of one tent is:

Total surface area of one tent = 79.60 + 48.73 ≈ 128.33 m²

To make 1500 tents, the total amount of canvas required is:

Total amount of canvas required = 1500 × 128.33 ≈ 192,495 m²

The cost of the canvas is given as Rs 120 per m². Therefore, the total cost of the canvas required to make the tents is:

Total cost of canvas = 192,495 × 120 ≈ Rs 23,099,400

As 50 schools have decided to share the expenditure equally, the amount shared by each school will be:

Amount shared by each school = Total cost of canvas / 50

Amount shared by each school = 23,099,400 / 50

Amount shared by each school ≈ Rs 461,988

Therefore, each school will have to contribute approximately Rs 461,988 to set up the tents.

Step-by-step explanation:

the daily number of absences at high school a in the state is approximately bormally distributed with mean 122 students and standard deviation of 11.5 students.

if more than 140 students are absent on the day the attendance count is taken for funding purposes ,

the school will lose some of its state funding in the subsequent year

We are to obtain the standard deviation of the given values :

{24, 18, 31,25, 34}

The standard deviation = √(Σ(x - mean)²/ n)

The mean = (ΣX) /n

Using calculator to save computation time :

The standard deviation, s = 6.27 (2 decimal places)

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Explanation:

The model is given below as

To figure out the value of the height of the we will expand the brackets

With no x-term, the vertex is at x=0

Substitute x=0,to get y

Using the graphical method, we will have

Hence,

The final answer is

Answer:

circumference of circle=2πr=2×3.14×3.5=21.98=22

The equation of the line is y = x + 6

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

The graph

On the graph, we have the following highlights

The graph intersect the y-axis at y = 6

This means that the intercept c is 6

Also, as x changes by 1, the y values changes by 1

This mean sthat the slope is 1

So, we have

y = mx + c

This gives

y = x + 6

Hence, the equation is y = x + 6

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The linear equation on the graph can be written as:

y = (3/2)*x + 6

A general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x₁, y₁), then the slope will be:

a = (y₂ - y₁)/(x₂ - x₁)

In this case we can see the points (0, 6)  (so the y-intercept is b = 6)  and (4, 10)

Then the slope will be:

a = (10 - 6)/(4 - 0) = 6/4 = 3/2

Then the linaer equation is:

y = (3/2)*x + 6

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Step-by-step explanation:

hope you can understand

Answer:

  tan(x) = -1/6

Step-by-step explanation:

We can use the relation between tan and sec:

  \(\displaystyle\tan{x}=\pm\sqrt{\sec^2{x}-1}\\\\\tan{x}=-\sqrt{\left(\dfrac{\sqrt{37}}{6}\right)^2-1}\quad\text{negative because sine is negative}\\\\=-\sqrt{\dfrac{37-36}{36}}=\boxed{-\dfrac{1}{6}}\)

The tangent of x is -1/6.

Answer:

I think b 1/3

Step-by-step explanation:

slope is rise over run

Answer:

1/2

Step-by-step explanation:

find 2 clear points A(2,0) B(8,3)

use the formula of the angular coefficient

\(c = \frac{y2 - y1}{x2 - x1} \)

Answer: C=2πr

r Radius