Determine the intercepts of the line.
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A coordinate plane. The x- and y-axes each scale by one. A graph of a line intersects the points negative ten, zero and zero, negative forty-five.

I agree that Nicole made a mistake because the total cost of the Five year plan is $ 34, 000 and not $ 74, 000.

The total cost of the Five year plan would be:

= Payment per month for the five year plan x Number of months in year x number of years + Down payment

= 400 x 12 x 5 + 10, 000

= 4, 800 x 5 + 10, 000

= $ 34, 000

The mistake that Nicole made was to multiply the $ 14, 800 that was the cost of the five year plan in one year, by five years. This was wrong because it meant including a new down payment in every one of the five years instead of just once.

She should have multiplied $4, 800 by 5 years and then added the down payment which is paid just once.

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The total number of berry pitchers made is 15/5 or 3.

If the serving size of berry pitchers is 1/5, it means that each pitcher represents 1/5 of a full serving. To determine the total number of pitchers made, we need to calculate how many times 1/5 fits into the whole serving.

Let's assume that the total number of pitchers made is represented by "x". We can set up the following equation:

x * 1/5 = 3

To solve for "x," we multiply both sides of the equation by 5:

5 * (x * 1/5) = 5 * 3

This simplifies to:

x = 15/5

Thus, the total number of berry pitchers made is 15/5 or 3.

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The x-value on the line when y = 100 represents the estimated number of hours a student would need to study to achieve a quiz grade of 100.

We have,

Assuming that the line of best fit represents the trend between the number of hours students study and their quiz grades,

The x-value on the line when y = 100 represents the estimated number of hours a student would need to study to achieve a quiz grade of 100.

In other words,

If a student studies for this amount of time, they are predicted to achieve a quiz score of 100 based on the trend shown by the line of best fit.

Thus,

The x-value on the line when y = 100 represents the estimated number of hours a student would need to study to achieve a quiz grade of 100.

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Answer:

60°

Step-by-step explanation:

180-78-42=60

The rectangle with points (0, 0), (0, 1), (2, 0), and (2, 1) could be the result of dilating the given rectangle with a scale factor between 0 and 1.

Option B is the correct answer.

We have,

Dilation is a transformation that changes the size of an object.

When a figure is dilated with a scale factor between 0 and 1, the resulting figure is smaller than the original.

The scale factor indicates how much smaller the image is compared to the original.

For example, a scale factor of 0.5 would mean that the image is half the size of the original.

Now,

The rectangle with points (0, 0), (0, 1), (2, 0), and (2, 1) could be the result of dilating the given rectangle with a scale factor between 0 and 1.

This is because the side lengths of the second rectangle are half of the side lengths of the first rectangle, which means that the second rectangle is a dilation of the first rectangle with a scale factor of 0.5.

Thus,

The rectangle with points (0, 0), (0, 1), (2, 0), and (2, 1) could be the result of dilating the given rectangle with a scale factor between 0 and 1.

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Answer:

X=-√7 and √7

Step-by-step explanation:

To solve the equation 6x² - 42 = 0, we can begin by rearranging it to isolate the variable term:

6x² = 42

Then, we can divide both sides by 6:

x² = 7

To get the exact values of x, we need to take the square root of both sides:

x = ±√7

Therefore, the exact values of x are √7 and -√7.

The monthly payment added to your mortgage for property taxes is $270.25, rounded to the nearest cent. It is a good idea to budget for property taxes when purchasing a home, as they can be a significant expense that should not be overlooked.

To calculate the monthly payment added to your mortgage for property taxes, we can use the following steps:

1) Find the taxable value of the home by subtracting the exemption from the appraised value:

Taxable value = $315,000 - $50,000 = $265,000

2) Calculate the annual property tax by multiplying the taxable value by the tax rate:

Annual property tax = $265,000 x 0.0122 = $3,243

3) Divide the annual property tax by 12 to get the monthly payment:

Monthly property tax payment = $3,243 / 12 = $270.25

It's important to note that property tax rates can vary depending on where you live, so it's a good idea to check with your local tax authority to get an accurate estimate of your property tax bill.

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From matrix property it can be showed that A=B.

Given,

If A,B and x are matrices with x≠0 and AX=BX

Now,

X must be non-singular matrix because

A[tex]XX^{-1}[/tex]=B[tex]XX^{-1}[/tex]

AI = BI

= I( identity matrix )

⇒A = B

Hence Proved, A = B .

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Answer:  [tex]g^2-9g+14[/tex]

Step-by-step explanation:

(g-7)(g-2)

[tex]g^2 - 2g-7g+14[/tex]

[tex]g^2-9g+14[/tex]

Use FOIL method.

Answer:

Part A: The point z1 is at (4, 6) and the point z2 is at (-5, 2). The distance between them is √((4-(-5))^2 + (6-2)^2) = √(9^2 + 4^2) = √(81 + 16) = √97.

Part B: The complex conjugate of z2 is (-5, -2). Geometrically, it can be found by reflecting the point z2 across the x-axis.

Part C: To find z2 − z1 geometrically, you can draw a vector from z1 to z2. The coordinates of this vector are (-5-4, 2-6) = (-9, -4). So z2 − z1 = -9 - 4i.

The measures are given as follows:

On a parallelogram, the opposite sides are congruent, hence the value of x is obtained as follows:

2x = 4

x = 2.

Opposite angles are congruent, meaning that they have the same measure, hence the measure of angle A is given as follows:

m < A = m < C = 110º.

Consecutive angles are supplementary, meaning that the sum of their measures is of 180º, hence the measure of angle B is given as follows:

m<B = 180º - 110º = 70º.

Considering the angle addition postulate, the measure of angle ABD is given as follows:

m < ABD = 70 - 36

m < ABD = 34º.

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so first I would move -6x to the other side and -2 at the same time it would look like this

24+2=6x+7x

and simplify

26= 13x

divide both sides by 13 to find x

2= x

The area of a circle is 157 square units and the circumference of a circle is 31.4√2 units.

From the given figure, legs of triangle measure the same, that is 10 units.

Let the diameter of the circle be x.

By using Pythagoras theorem,

x²=10²+10²

x²=100+100

x²=200

x=10√2 units

Radius = 5√2 units

We know that, area of a circle = πr²

= 3.14×(5√2)²

= 3.14×50

= 157 square units

We know that, circumference of a circle = 2πr

= 2×3.14×5√2

= 31.4√2 units

Therefore, the area of a circle is 157 square units and the circumference of a circle is 31.4√2 units.

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Hello!

area

= (b x h)/2

= (18in x 7in)/2

= 126in²/2

= 63in²

Answer:

63 in²

Step-by-step explanation:

1/2 bh=area of the triangle

Seattle's sales were approximately 33.33% larger than Portland's.

Portland's sales were approximately 25% smaller than Seattle's.

Portland's sales were approximately 75% of Seattle's sales.

We have,

a)

Seattle's sales were larger than Portland's by:

= (380,000 - 285,000)

= $95,000.

To calculate the percentage difference, we can use the formula:

Percentage difference = (Difference / Original value) x 100

Percentage difference = (95,000 / 285,000) * 100 ≈ 33.33%

b)

Portland's sales were smaller than Seattle's by (380,000 - 285,000) = $95,000.

To calculate the percentage difference, we can use the formula:

Percentage difference = (Difference / Original value) x 100

Percentage difference = (95,000 / 380,000) x 100 ≈ 25%

c)

Portland's sales were a certain percentage of Seattle's sales.

To calculate this percentage, we can use the formula:

Percentage = (Portland sales / Seattle sales) * 100

Percentage = (285,000 / 380,000) * 100 ≈ 75%

Therefore,

Seattle's sales were approximately 33.33% larger than Portland's.

Portland's sales were approximately 25% smaller than Seattle's.

Portland's sales were approximately 75% of Seattle's sales.

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Step-by-step explanation:

The way you can think about volume is that we have some cross sectional area times the height of the solid.

27.

The volume of a square based pyramid is

[tex]v = {s}^{2} ( \frac{h}{3} )[/tex]

where h is the height of the pyramid

s is the side length of the square base.

S=7

h=12

[tex]v = {7}^{2} ( \frac{12}{3} ) = 49 \times 4 = 196[/tex]

28. The volume of a rectangular prism

[tex]v = l \times w \times h[/tex]

where l is length

w is width

h is height

[tex]v = 11 \times 11 \times 8 = 968[/tex]

29.

Use the same formula in 27

[tex]v = 100(3) = 300[/tex]

30.

Volume of a Cylinder is

[tex]v = \pi {r}^{2} h[/tex]

where r is the radius of the circle

where h is the height

r is half of the diameter

The diameter is 22, thus the radius is 11.

[tex]v = {11}^{2} (8)(\pi)[/tex]

[tex]v = 968\pi[/tex]

pi is approximately 3.14

[tex]v = 3041.06[/tex]

31. Volume of A Sphere

[tex] \frac{4}{3} \pi {r}^{3} = v[/tex]

The radius is half of diamter, thus r=7

[tex] \frac{4}{3} \pi( {7}^{3} ) = 1436.76[/tex]

The measures of NP and AP equals 8

First, it is important to note that;

From the information given, we have that;

The centroid of the triangle divides AN in the ratio of 1: 2

Hence, the length of AN is twice that of line NP

So;

AN = 2NP

Substitute the value

18 = 2NP

Divide by the coefficient

NP = 9

But;

AN = NP + AP

Substitute the values, we get;

AP = 18 - 9

AP = 9

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The exponential equation that models the estimated population of sage grouse in Silverton County is: [tex]y = 115,000 * (1/4)^x[/tex]

Given that the population is expected to decrease by a factor of 1/4 each decade, we know that the common ratio, b, is 1/4.

Since the most recent estimate is about 115,000 sage grouse, we can assign this value to the initial population, a.

Therefore, the exponential equation that models the estimated population of sage grouse in Silverton County is: [tex]y = 115,000 * (1/4)^x[/tex]

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Answer: 11x16x5=880

This means the answer is C

The horizontal transformations are defined as follows:

cos(ax).

They are classified as follows:

The vertical transformations are defined as follows:

acos(x).

They are classified as follows:

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Answer:

The estimated probability that exactly two of the three guests randomly picked were not there for personal reasons is 0.25.

The estimated probability that it takes at least four guests to find one who is staying for personal reasons is 0.125.

The family would need to bring home an additional $2400 annually to cover the increased cost of housing.

The family would need to bring home annually to cover the cost of increased housing need to calculate the total cost of housing for a year and subtract the current annual cost of housing.

The current monthly cost of housing is $1600 so the annual cost is:

$1600/month x 12 months = $19,200/year

Let's assume the family needs to cover an increased housing cost of $200 per month.

The new monthly cost of housing would be:

$1600/month + $200/month = $1800/month

The new annual cost of housing would be:

$1800/month x 12 months = $21,600/year

The family would need to bring home annually to cover this increased cost need to subtract the current annual cost of housing from the new annual cost of housing:

$21,600/year - $19,200/year = $2400/year

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The correct statements are:

If "positive" end behaviour:

The arrows point in the same direction.

The right arrow is up.

The graph hits the y-axis.

If "negative" end behaviour:

The arrows point in opposite directions.

The right arrow is down.

The graph hits the X-axis.

In mathematics, a graph is a visual representation of a set of data, which consists of points, called vertices or nodes, and lines connecting them, called edges or arcs.

Graphs are often used to represent mathematical functions, data sets, or relationships between objects, and they can be used to model real-world phenomena.

Graphs can be drawn on a coordinate plane or in a more abstract form, and they can be used to analyze and understand complex systems and relationships.

The correct statements are:

If "positive" end behaviour:

The arrows point in the same direction.

The right arrow is up.

The graph hits the y-axis.

If "negative" end behaviour:

The arrows point in opposite directions.

The right arrow is down.

The graph hits the X-axis.

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H contains the identity element, is closed under multiplication, and is closed under taking inverses, H is a subgroup of G, as desired.

Let [tex]\mathcal{H}[/tex]  be a non-empty directed family of subgroups of a group G. We need to show that the union [tex]H=\bigcup_{H_i\in\mathcal{H}}H_i[/tex] is a subgroup of G.

First, note that H is non-empty since[tex]\mathcal{H}[/tex] is non-empty. We also have [tex]1_G \in H_i[/tex] for all [tex]H_i\in\mathcal{H}[/tex], so [tex]1_G \in H.[/tex]

To show that H is closed under multiplication, let [tex]h_1,h_2\in H[/tex]. Then there exist [tex]H_{i_1},H_{i_2}\in\mathcal{H}[/tex] such that [tex]h_1\in H_{i_1}[/tex] and [tex]h_2\in H_{i_2}.[/tex] Since [tex]\mathcal{H}[/tex] is directed, there exists[tex]H_{i_3}\in\mathcal{H}[/tex] such that [tex]H_{i_1}\cup H_{i_2} \subseteq H_{i_3}[/tex]. Thus, [tex]h_1,h_2\in H_{i_3},[/tex]and since [tex]H_{i_3}[/tex] is a subgroup, we have [tex]h_1h_2\in H_{i_3} \subseteq H[/tex]. Therefore, H is closed under multiplication.

Finally, to show that H is closed under taking inverses, let h\in H. Then there exists [tex]H_i\in\mathcal{H}[/tex] such that [tex]h\in H_i[/tex]. Since [tex]H_i[/tex]is a subgroup, we have [tex]h^{-1}\in H_i \subseteq H[/tex]. Therefore, H is closed under taking inverses.

Since H contains the identity element, is closed under multiplication, and is closed under taking inverses, H is a subgroup of G, as desired.

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The area of the regular polygon is 311.5 in2.

We are given that;

A polygon

Now,

To find the perimeter of the regular polygon, we need to multiply the number of sides by the length of each side. The polygon has 7 sides and each side is 10 in long, so the perimeter is 7 * 10 = 70 in.

To find the apothem length, we need to use some trigonometry.

The central angle is 360/7 degrees, since there are 7 equal angles in a regular polygon. Half of the side length is 5 in, since each side is 10 in long. The apothem is the adjacent side of the right triangle. We can use the tangent function to find the apothem: tan(360/14) = 5/a, where a is the apothem. Solving for a, we get a = 5/tan(360/14) ≈ 8.9 in.

To find the area of the regular polygon, we need to plug in the values of P and a into the formula A = (1/2)P*a.

A = (1/2)708.9 ≈ 311.5 in2.

Therefore, by the area the answer will be 311.5 in2.

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The expression that represents the surface area of the cube is 25 + 25 + 25 + 25 + 25 + 25

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

The cube

The side length of the cube is

Side length = 5

The surface area of the cube is calculated as

SA = 6 * Side length²

So, we have

SA = 6 * 5²

Expand

SA = 6 * 25

Further expand

SA = 25 + 25 + 25 + 25 + 25 + 25

Hence, the expression that represents the surface area of the cube is 25 + 25 + 25 + 25 + 25 + 25

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Complete question

The following figure shows a cube. Which expression represents the surface area of the cube? Choose 1 answer

(a) 5 5 - 5 - 5

(b) 25 + 25 + 25 + 25 + 25 + 25

(c) 5 + 5 + 5 + 5 + 5 + 5

The figure is attached

Answer:

Step 4

Step-by-step explanation:

In step 3, 16 + 9 = 25, so step 4 should subtract 25 from both sides. Also, y² became -y² in step 4 which is incorrect.

Answer: Step 4

The first derivative of the parametric curve is:

dx/dt = [tex]-1/(t-1)^2[/tex] and dy/dt = [tex](2t(t-1) - t^2)/(t-1)^2.[/tex]

1. To find the first derivative of the parametric curve x = 1/(t-1) and [tex]y = t^2/(t-1)[/tex], we can use the chain rule.

2. Let's differentiate each component separately.

3. Differentiating x with respect to t, we have:

dx/dt = [tex]-1/(t-1)^2[/tex]

4. Differentiating y with respect to t, we have:

dy/dt = [tex](2t(t-1) - t^2)/(t-1)^2[/tex]

5. Therefore, the first derivative of the parametric curve is:

dx/dt = [tex]-1/(t-1)^2[/tex] and dy/dt = [tex](2t(t-1) - t^2)/(t-1)^2.[/tex]

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