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The best way to describe the solution of the given system of equation is option (c) Line y = −2x + 9 intersects the line y = −x + 8 at point ( 1, 7).

System of equation are equal to,

y = −2x + 9

y = −x + 8

To find the solution to this system of equations,

Find the values of x and y that satisfy both equations.

We can do this by setting the two equations equal to each other and solving for x.

−2x + 9 = −x + 8

Adding x to both sides,

⇒ x − 2x + 9 = 8

Simplifying it,

⇒ −x + 9 = 8

Subtracting 9 from both sides we get,

⇒ −x = −1

Dividing both sides by −1

⇒ x = 1

Now that the value of x =1

Substitute it back into either equation of the line to find the value of y.

y = −x + 8

⇒ y = −(1) + 8

⇒ y = 7

Therefore,  the solution to the system of equations is (1, 7) option c. the line y = −2x + 9 intersects the line y = −x + 8 .

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The piston P is found to be 7.97 inches away from the center O of the crankshaft.

The reciprocating engine has crankshaft and the piston and we will be using the trigonometry to find the distance. Now, the angle in the crankshaft and the rod is to be used to find the distance in the center and the piston. Now assume that the crankshaft O and piston P are connected with each other and then the rod is horizontal so the angle is 15 degrees.

When OPQ is 15 degrees, we can use the law of cosines to find the distance OP, as follows:

OP² = 3² + 9² - 2(3)(9)cos(15)

OP² = 81 - 54cos(15)

OP ≈ 7.97 inches (rounded to two decimal places to get the accurate results)

Therefore, when OPQ is 15 degrees, the piston is approximately 7.97 inches from the center of the crankshaft.

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The scale factor used in the dilation is 1/3

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

The scale factor is calculated as

Scale factor  = A'/A

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

Scale factor  = (-1, -1)'/(-3, -3)

Evaluate

Scale factor  = 1/3

Hence, the scale factor  = 1/3

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Answer:

d

Step-by-step explanation:

d) 3[tex]x^{2}[/tex] + 5x - 8 has the same value as the given expression.

To simplify the given expression, we can combine like terms by subtracting the second expression from the first one.

8[tex]x^{2}[/tex] + 2x - 6 - (5[tex]x^{2}[/tex] - 3x + 2) = (8[tex]x^{2}[/tex] - 5[tex]x^{2}[/tex]) + (2x + 3x) + (-6 - 2)

Simplifying further, we get:

= 3[tex]x^{2}[/tex] + 5x - 8

Therefore, the expression that has the same value as the given expression is option d) 3[tex]x^{2}[/tex] + 5x - 8.

To check our answer, we can substitute a value of x in the original expression and the simplified expression and compare the results. For example, if we substitute x = 2, we get:

8 [tex](2)^{2}[/tex] + 2(2) - 6 - (5 [tex](2)^{2}[/tex] - 3(2) + 2) = 8(4) + 4 - 6 - (5(4) - 6 + 2) = 32 - 5(4) = 12

And,

3 [tex](2)^{2}[/tex] + 5(2) - 8 = 3(4) + 10 - 8 = 12

As both results are the same, we can confirm that our answer is correct.

Correct Question :

Which expression has the same value as the expression 8[tex]x^{2}[/tex] + 2x - 6) - (5[tex]x^{2}[/tex] - 3x + 2)?

a) 13[tex]x^{2}[/tex] - 5x - 4

b) 13[tex]x^{2}[/tex] - x - 8

c) 3[tex]x^{2}[/tex] - x - 4

d) 3[tex]x^{2}[/tex] + 5x - 8

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The area of a triangle ABC is 496.25 square feet. Therefore, option B is the correct answer.

Given that, in the triangle ABC, m∠B = 83°, a = 25 feet, and c = 40 feet.

The area of a triangle can be expressed using the lengths of two sides and the sine of the included angle. Area of a triangle = ½ ab sin C.

Here, area of a triangle = 1/2 ×25×40 sin83°

= 25×20×0.9925

= 496.25 square feet

Therefore, option B is the correct answer.

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In the case of Alicia, The single net increase is 5.821% of the original price.

Alicia is buying shoes at a department store that offers a 15% discount on all shoes. Additionally, she has a store card that gives her another 5% discount. However, at checkout, the cashier tells her that there will be two increases, one of 2% for commissions and another of 18% for general sales tax. To determine if there is a net discount or increase, we need to calculate the total discount and total increase separately and compare them.

First, let's calculate the total discount:

Next, let's calculate the total increase:

If the total discount is greater than the total increase, then there is a net discount. If the total increase is greater than the total discount, then there is a net increase.

Therefore, we need to compare:

Simplifying both expressions, we get:

Since 1.0506 x Original Price is greater than 0.20 x Original Price, we can conclude that there is a net increase.

To calculate the amount of the single net increase, we can subtract the discounted price from the increased price:

Simplifying the expression, we get:

Therefore, the single net increase is 5.821% of the original price.

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Complete Question:

Alicia will buy shoes in a department store that advertises a 15% discount on all shoes, plus she has the store card and therefore they will give her another 5% discount. When paying: the cashier tells you that they will make 2 increases, one of 2% for commissions and the other of 18% for general sales tax. Determine if it is the case, how much is the discount or single increase?

Answer:

The formula for the area of a circle is A=pir^2. A stands for the area, r is the radius. Ignore the pi, you don't need that. Just take the radius^2 and multiply it. For example, if I had A=pi5^2, my answer would be A=25pi, because 5^2=25. :)

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

The area of a circle is:

[tex]A=\pi r^{2}[/tex] in terms of pi

with [tex]\pi[/tex] being 3.14..., r being radius, and ²-ing the radius.

Hope this helps! :)

Yes, Both triangles ABC and DEF are congruent.

Given that;

To show that, all steps for triangles ABC and DEF are congruent.

Now, By given figure of the triangle;

⇒ ∠ C = 90°

⇒ ∠ F = 90°

And, Distance between B and C and E and F are equal to each other.

And, Also, Distance DF = AC

Hence, By SAS congruency;

Both triangles ABC and DEF are congruent.

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The value of the function (f - g)(x) is given as -

(f - g)(x) =  4x³ + 7x² - 6x + 1.

The given functions are -

f(x) = 4x³ +7x² - 2x - 1

g(x) = 4x - 2

We can write the function (f - g)(x) as -

(f - g)(x) = f(x) - g(x)

(f - g)(x) = 4x³ + 7x² - 2x - 1 - (4x - 2)

(f - g)(x) = 4x³ + 7x² - 2x - 1 - 4x + 2

(f - g)(x) =  4x³ + 7x² - 6x + 1

Therefore, the value of the function (f - g)(x) is given as -

(f - g)(x) =  4x³ + 7x² - 6x + 1.

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The probability of getting a diamond or a king from a standard 52-card deck is 4/13.

In mathematics, probability is a measure of the likelihood that an event will occur. It is a way to quantify the chances of different outcomes or events in a random experiment or process. Probability is typically expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event

In a standard deck of 52 cards, there are 13 diamonds and 4 kings. However, the king of diamonds is also a diamond, so we must subtract one from the total count to avoid double-counting.

So there are 13 + 4 - 1 = 16 cards that are either diamonds or kings.

The probability of picking a diamond or a king is therefore 16/52.

Simplifying the fraction, we get:

16/52 = 4/13

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Answer:

Step-by-step explanation:

a=70

b=45

c=65

e=70

c=65

f=110

d=45

c=130

d=50

b=50

a=65

x=36   I can't see the number in the triangle so i can't finish this one

a=50

b=60

Mark has read 37.5 more pages than Sara, therefore the answer is (b) 55 pages.

To determine how many more pages Mark has read than Sara, we first need to find out how many pages each of them has read so far.

Lin has read 38% of the book, which is

38 percentage of 250 pages = 0.38 x 250 = 95 pages

Mark has read 3/5 of the book, which is

3/5 of 250 pages = (3/5) x 250 = 150 pages

Sara has read 0.45 of the book, which is

0.45 of 250 pages = 112.5 pages (rounded to the nearest half-page)

Mark has read 150 - 112.5 = 37.5 more pages than Sara.

Therefore, the correct option is (b) 55 pages

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The given question is incomplete, the complete question is:

Lin, mark, and Sara were assigned to read a book for language class. the book has a total of 250 pages. the current progress of each student is shown in the table below. how many more pages has mark read than Sara? a 150 pages b 55 pages c 105 pages d 45 pages

The Answer is D

When you divide a negative by a positive the answer will be negative

When you divide negative by negative the answer will be positive

By performing a chi-squared test of independence on the sample of 2100 GMU students, we can determine whether their demographics match those of the US population, and either reject or fail to reject the null hypothesis.

Based on the information provided, the expected proportions of different races in the US population are: 76% white, 14% black, 1% American Indian or Alaskan Native, 6% Asian, 1% Native Hawaiian, and 2% two or more races.

To determine whether the demographics of GMU students match those of the US population, we can use a hypothesis test. We will use a chi-squared test of independence to compare the observed frequencies of each race in the sample to the expected frequencies based on the US population demographics.

Assuming a significance level of 0.05, if our calculated chi-squared value is greater than the critical value from the chi-squared distribution with (6-1=5) degrees of freedom, we will reject the null hypothesis that the demographics of GMU students match those of the US population.

If we obtain a p-value less than 0.05, we reject the null hypothesis and conclude that the demographics of GMU students are significantly different from those of the US population. If the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant difference between the demographics of GMU students and those of the US population.

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There are 56 different sequences of coin toss results that Kathy could have gotten, given that she got 3 heads and 5 tails in 8 tosses.

To find the total number of different sequences of coin toss results that Kathy could have gotten, we can use the formula for permutations:

nPr = n! / (n - r)!

where n is the total number of objects (in this case, the total number of coin tosses) and r is the number of objects selected (in this case, the number of heads or tails that Kathy got).

Since Kathy got 3 heads and 5 tails, there are 8 choose 3 (or 8 choose 5) ways to arrange the sequence of heads and tails. This is equivalent to the number of ways to select 3 objects out of 8, or 5 objects out of 8:

8C3 = 8! / (3! x (8 - 3)!) = 56

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Answer:

2.83 seconds

Step-by-step explanation:

In the given equation, h represents the height (in feet) of the rock above the river at time t seconds after it is dropped, and the equation is h = -16t^2 + 128.

When the rock reaches the river, its height above the river will be zero. So, we can set h = 0 in the equation and solve for t:

0 = -16t^2 + 128

Dividing both sides by -16, we get:

t^2 = 128/16

t^2 = 8

Taking the square root of both sides, we get:

t = ±√8

Since time cannot be negative, we take the positive square root:

t = √8 ≈ 2.83 seconds

Therefore, it will take the rock approximately 2.83 seconds to reach the river.

Answer: the last one, (-1, 1), (7, 1), (3, 5)

Step-by-step explanation: If you take point A and move it 7 units to the right, A' would be (-1, 1) because the y-value does not change, and the x-value was previously at -8.

None of the other answers have (-1, 1) as A' except the last one, so by the process of elimination, the last one, or answer D, is correct.

The ordered pair that is a solution to the inequality y>x+5 is:

None of the above

We are given the inequality as:

y > x + 5

Let us look at each of the given options to get:

a) At (12, 8):

8 > 12 + 5

8 > 17

This is false

b) At (11, 7):

7 > 11 + 5

7 > 16

This is false

c) At (8, 6):

6 > 8+ 5

6 > 14

This is false

d) At (4, 7):

7 > 4+ 5

7 > 9

This is false

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If Ms. Egeregor removes 3 notebooks from each-box, then the number of notebooks at the start was 27 notebooks.

Let number of notebooks in each-box at the beginning be denoted by "x";

After Ms. Egeregor removes 3 notebooks from each box, there will be x - 3 notebooks in each box. since she has 4 boxes, the total number of notebooks remaining is: 4(x - 3) ⇒ 4x - 12;

We know that the remaining number of notebooks is 96, so, the equation is written as:

⇒ 4x - 12 = 96,

4x = 96 + 12

4x = 108

x = 27

Therefore, each box started with 27 notebooks.

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Answer:

3√(-2a)^4

Step-by-step explanation:

or If u want to further simplify distribute the power 4 onto the -2 and a and it will become 3rd root of -8a^4

The discounted price of the hat at store A is $4.50 less than the discounted price of the hat at store B.

Given information:

Two stores each advertise a discount on the same type of hat at both stores.

The original price of the hat was $45 store A discounted the price of the hat by 25% store B discounted the price of the hat by 15%.

The discount at store A is 25% off $45, which is $11.25. So the discounted price at store A is $33.75 ($45 - $11.25).

The discount at store B is 15% of $45, which is $6.75. So the discounted price at store B is $38.25 ($45 - $6.75).

The difference between the discounted price at store A and store B is $38.25 - $33.75 = $4.50.

Therefore, the discounted price of the hat at store A is $4.50 less than the discounted price of the hat at store B.

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The maximum possible height for the fish tank is 23.772 inches.

The total cost to ship the fish tank when it is empty is $66.44.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

Since 100 gallons represent the desired capacity of the fish tank and 7.48 gallons of water are equivalent to one (1) cubic foot, the desired volume of the fish tank is given by;

Desired volume of fish tank = (100/7.48) = 13.369 cubic feet.

Next, we would convert the given dimensions in inches to feet as follows;

Length, L = 54 inches × 1/12 = 4.5 feet.

Width, W = 18 inches × 1/12 = 1.5 feet.

For the maximum possible height, we have;

13.369 = 4.5 × 1.5 × h

13.369 = 6.75h

Height, h = 13.369/6.75

Height, h = 1.981 feet × 12 = 23.772 inches.

Next, we would calculate the total cost to ship the fish tank when it is empty;

Volume of completed fish tank, V = 4.5 × 1.5 × 1.981

Volume of completed fish tank, V = 13.369 cubic feet.

Weight of water = (13.369 × 62.4) pounds per cubic foot

Weight of water = 834.226 pounds

Weight of fish tank alone = 1,100 pounds - 834.226 pounds

Weight of fish tank alone = 265.774 pounds.

Total cost of shipping = 265.774 × $0.25

Total cost of shipping = $66.44.

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The paired t-test this test is appropriate for comparing the means of two interval variables drawn from related populations, where related means that the same subjects or matched subjects were used in each group.

The paired t-test compares the means of the two variables by calculating the difference between the pairs of scores and then calculating the mean difference.

It then determines whether the mean difference is significantly different from zero using a t-test.

Hence, the appropriate test for comparing the scores of two interval variables drawn from related populations is the paired t-test. It compares the means of the two variables by calculating the difference between the pairs of scores and then determining whether the mean difference is significantly different from zero using a t-test.

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So the missing length in the given triangle is approximately 6.4.

In geometry, a triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry and has many properties and applications in mathematics and other fields. The sum of the interior angles of a triangle is always 180 degrees, and the area of a triangle can be calculated using various formulas depending on the given information, such as the base and height, the lengths of the sides, or the angles. Triangles can also be classified based on the length of their sides and the measure of their angles, such as equilateral, isosceles, scalene, acute, right, and obtuse triangles. Triangles are used in many fields, including engineering, architecture, physics, and computer graphics, among others.

Here,

If we draw a right triangle with hypotenuse length 21, perpendicular length 20, and base length x, we can use the Pythagorean theorem to solve for x:

c² = a² + b², where c is the hypotenuse and a and b are the other two sides.

So we have:

21² = 20² + x²

441 = 400 + x²

x² = 41

x = √(41)

In such a triangle, the sides are in the ratio 1:1:√(2). Since we know the length of the perpendicular side (20), which is opposite the 45-degree angle, we can find the length of the hypotenuse of this triangle:

h = 20 * √(2)

We also know that the hypotenuse of the original right triangle is 21, and it is divided into two parts by the altitude, so the other part must be:

21 - h = 21 - 20*√(2)

Therefore, the missing length (base) is:

x = √(41)

≈ 6.4

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The new amount for Jim's hourly rate is A = $ 15.40

Given data ,

To find Jim's new hourly rate after a 10% raise, we need to add 10% of his current hourly rate to his current hourly rate.

Let's call Jim's current hourly rate "x".

10% of x is 0.10x, so the new hourly rate would be:

x + 0.10x = 1.10x

Therefore, Jim's new hourly rate would be:

On simplifying the equation , we get

$14 x 1.10 = $15.40

Hence , Jim's new hourly rate would be $15.40

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Comparing the z-scores, a score of 94 on a test with a mean of 72 and a standard deviation of 11 is relatively better than a score of 687 on a test with a mean of 447 and a standard deviation of 150, as the z-score of the first test (2) is higher than the z-score of the second test (1.6).

To determine which score is relatively better, we will calculate the z-scores for both test results using the given mean and standard deviation values. A z-score represents how many standard deviations a data point is away from the mean. The higher the z-score, the better the performance relative to the mean.

For the first test:
1. Subtract the mean (72) from the score (94): 94 - 72 = 22
2. Divide the difference (22) by the standard deviation (11): 22 / 11 = 2

The z-score for the first test is 2.

For the second test:
1. Subtract the mean (447) from the score (687): 687 - 447 = 240
2. Divide the difference (240) by the standard deviation (150): 240 / 150 = 1.6

The z-score for the second test is 1.6.

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Answer:

Step-by-step explanation:

Given 3 points, you want the fourth point that defines a rectangle. Then you want the length, width, and area of the rectangle. {(3, 2), (3, -3), (-5, -3)}

A rectangle is a quadrilateral (4-sided polygon) with opposite sides the same length and parallel, and all corners 90°.

We can name the given points A(3, 2), B(3, -3), and C(-5, -3).

When you plot the given points, you can imagine they form a right triangle with the right angle at B. The missing sides of the rectangle are ...

A line parallel to BC through A, and a line parallel to AB through C.

The equation of the first line is y = 2, and the equation of the second line is x = -5. These two lines meet at the point (x, y) = (-5, 2)

The missing point is (-5, 2).

We generally think of "length" as being the longer dimension of the figure. Here, the points B and C are farther apart than the points A and B. The distance between those points is the difference of their x-coordinates:

  length = 3 -(-5) = 8

The length of the rectangle is 8 units.

As with length, we can determine the distance between points A and B as the difference of their y-coordinates:

  width = 2 -(-3) = 5

The width of the rectangle is 5 units.

The area of a rectangle is the product of its length and width:

  A = LW

  A = (8)(5) = 40 . . . . square units

The area of the rectangle is 40 square units.

__

Additional comment

When the sides of the rectangle are on grid lines, as here, finding the missing point and the various lengths is pretty easy.

You will notice that there are two different x-coordinates and two different y-coordinates among the four points. The four points are those coordinates in every combination. One way to find the missing point is to find the missing combination. The side lengths are the difference between x-coordinates and the difference between y-coordinates. (This works for rectangles aligned to the grid.)

When the sides are skew with respect to the grid lines, a different strategy for locating the missing point and for finding side lengths is required. That strategy can make use of the fact that the diagonals cross at their midpoints, and the length is given by the distance formula.

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It seems that you are referring to the exponential growth formula which is:

N(t) = N₀ * (1 + r)^t

Where:
N(t) is the number of individuals at time t
N₀ is the initial number of individuals (in this case, 25 alive in 1955)
r is the growth rate
t is the time period (in years)

In this problem, we have:
N₀ = 25 individuals (alive in 1955)
N(t) = 500 individuals (existed in 2013)
t = 2013 - 1955 = 58 years

We need to solve for r. To do that, rearrange the formula:

r = [(N(t) / N₀)^(1/t)] - 1

Plug in the given values:

r = [(500 / 25)^(1/58)] - 1

r ≈ 0.029

So, the answer is (d) 0.029.

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