Which equation is set up correctly using the Pythagorean Theorem for the triangle below?

The triangle proportionality theorem, used to evaluate the figures indicates that we get;

8. [tex]\overline{ST}[/tex] ║ [tex]\overline{PR}[/tex]

9. [tex]\overline{ST}[/tex] ║ [tex]\overline{PR}[/tex]

10. [tex]\overline{ST}[/tex] ∦ [tex]\overline{PR}[/tex]

11. x = 57.6

12. x = 27.3

13. x = 11

14. x = 10

15. x = 5

16. x = 17

The triangle proportionality theorem states that, in a triangle, a line drawn parallel to one of the sides of a triangle and intersects the other two sides at two different points, then the ratio in which the other two sides are divided by the line are the same.

8. The triangle proportionality theorem indicates, if  [tex]\overline{ST}[/tex] and [tex]\overline{PR}[/tex] are parallel,   [tex]\overline{ST}[/tex] ║ [tex]\overline{PR}[/tex], we get; QS/SP = QT/TR

QS/SP = 7/11.2 = 0.625

QT/TR = 10/16 = 0.625

9. Where [tex]\overline{ST}[/tex] and [tex]\overline{PR}[/tex] are parallel,   [tex]\overline{ST}[/tex] ║ [tex]\overline{PR}[/tex], we get;

PS/SQ = RT/TQ

PS = 102 - 45 = 57

PS/SQ = 57/45 = 1.2[tex]\overline{6}[/tex]

RT/TQ = 41.8/33 = 1.2[tex]\overline{6}[/tex]

10. Where [tex]\overline{ST}[/tex] is parallel to [tex]\overline{PR}[/tex], we get;

QS/SP = QT/TR

QS/SP = 19/38 = 0.5

QT/TR =  24/52 = 6/13 ≠ 0.5

11. The triangle proportionality theorem, indicates that we get;

48/25 = x/30

x/30 = 48/25

x = (48/25) × 30 = 57.6

12. Making use of the triangle triangle proportionality theorem, we get;

(49 - 28)/28 = x/36.4

x/36.4 = (49 - 28)/28

x = ((49 - 28)/28) × 36.4 = 27.3

13. 32/60 = (2·x + 6)/52.5

(2·x + 6)/52.5 = 32/60

(2·x + 6) = (32/60) × 52.5 = 28

(2·x + 6) = 28

2·x = 28 - 6 = 22

x = 22/2 = 11

14. (x - 3)/21 = (x - 1)/27

27 × (x - 3)= 21 × (x - 1)

27·x - 27 × 3 = 21·x - 21

27·x - 21·x = -21 + 27 × 3 = 60

6·x = 60

x = 60/6 = 10

15. (7·x - 11)/(4·x - 2) = 20/(35 - 20)

(7·x - 11)/(4·x - 2) = 20/(35 - 20) = 20/15

(7·x - 11)/(4·x - 2) = 20/15

15 × (7·x - 11) = (4·x - 2) × 20

105·x - 165 = 80·x - 40

105·x - 80·x = 25·x = 165 - 40 = 125

25·x = 125

x = 125/25 = 5

16. 35/(x - 3) = (x - 7)/4

35 × 4 = (x - 3) × (x - 7)

140 = x² - 10·x + 21

x² - 10·x + 21 - 140 = 0

x² - 10·x - 119 = 0

x² - 10·x - 7 × 17 = 0

x² + 7·x - 17·x - 17 × 7 = 0

x·(x + 7) - 17·(x + 7) = 0

(x + 7)·(x - 17) = 0

x = -7, or x = 17

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4/5 + 5/6

24+25/30

49/30

hope it will help you

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The value of {z} is equivalent to 13.

Given is that SX = z, TW = 6z - 76 and UV = 3z - 24.

We can write -

{z} + {6z - 76} = {3z - 24}

7z - 76 = 3z - 24

7z - 3z = - 24 + 76

4z = 52

z = 13

Therefore, the value of {z} is equivalent to 13.

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Answer:

400 pounds equal to 0.2 tons

The length of the diagonal support lumber is given as follows:

161.5 inches.

The figure is a rectangle, hence the diagonals have equal measure, and thus the value of x can be obtained as follows:

15x + 13.25 = 17x + 4.5.

2x = 9

x = 4.5.

Hence the length of the  diagonal support lumber is obtained as follows:

2 x (15 x 4.5 + 13.25) = 161.5 inches.

We multiply by 2 as we are given half the length of the diagonal.

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This is an example of a descriptive quantitative research study.

Descriptive quantitative research involves collecting and analyzing data to describe the characteristics of a population or phenomenon. In this case, the nurse administrator is gathering and analyzing data about the employees on the units they supervise, such as work shift, number of years employed, age, gender, educational preparation, certifications, work history, and professional accomplishments. Statistical techniques such as mean, median, and mode are used to analyze the data, allowing the nurse administrator to compare the characteristics of the employees across various dimensions. This type of research is used to develop an understanding of a given population or phenomenon, allowing for informed decision-making.

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Answer:

1.  5 inches in 2 days

2.  y = (5/2)x. where y is rainfall and x is days.

3.  Yes

4.  (5/2)

5.  2.5"/day

6.  37.5 Inches

Step-by-step explanation:

See attached worksheet

.

Answer: Volume of a right prism = BH where B is the area of the base and H is its height.

So Volume = 16 × 12 = 192 cm^3

Step-by-step explanation:

Answer: x=14°

Step-by-step explanation:

All angles of a triangle added together is 180°. So we can add the angles together.

7x-11+5x-2+2x-3=180           [combine like terms]

14x-16=180                             [add both sides by 16]

14x=196                                  [divide both sides by 14]

x=14

Therefore, x=14°.

The volume is increasing at a rate of 784 * pi cubic inches per second.

The volume of a sphere is given by the formula V = (4/3) * pi * r^3, where r is the radius of the sphere.

We can find the rate of change of the volume with respect to time by taking the derivative of V with respect to time.

dV/dt = (4/3) * pi * 3r^2 * dr/dt

Given that the radius is increasing at a rate of 2 in/sec, we can substitute this value into the equation and find the rate at which the volume is increasing:

dV/dt = (4/3) * pi * 3 * 9^2 * 2 in^3/sec = 784 * pi in^3/sec

So, when the radius of the snowball is 9 inches, the volume is increasing at a rate of 784 * pi cubic inches per second.

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Answer:

5

Step-by-step explanation:

(2x4)-(3x1)

=(8)-(3)

= 5

So its  5

Answer:

128π in.² ≈ 402.1 in.²

Step-by-step explanation:

The rod can be cut into two equal sized pieces in different ways, so there are different answers to this question. I assume the question is asking when the rod's length is cut in half, so now there are two rods, each one being a cylinder with 4 inch height.

We need the area of the original rod and then add two more base areas.

C = 8π in.

r = 4 in.

total surface area = lateral area + 4 × area of base

SA = 8 in. × 8π in. + 4 × π × (4 in.)²

SA = 64π in.² + 64π in.²

SA = 128π in.² ≈ 402.1 in.²

Answer:

401.9

Step-by-step explanation:

I got this question wrong on my quiz

The circumference of the Super Pizza is 56.52 inches  and approximate area of the Super Pizza 253.34 inches2.

To calculate the circumference of the Super Pizza
Circumference = π x diameter
Circumference = 3.14 x 18
Circumference = 56.52 inches

To calculate the area of the Super Pizza
Area = π x radius2
Area = 3.14 x (18/2)2
Area = 3.14 x 81
Area = 253.34 inches2

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The ordered pair could represent the image of point C(5, 2) after the dilation is (2.5, 1)

If we have a general point (x, y) and we apply a dilation with the origin as the center of a scale factor k, then the coordinates of the image after the dilation is (k*x, k*y)

Here we want to see which point can be the image of (5, 2) after the dilation, it will must have the form (k*5, k*2)

The only point that has this form is the one on the third option, where we can write:

(2.5, 1) = (k*5, k*2)

Then we have two equations:

2.5 = k*5

1 = k*2

Solving these we should get the same value of k.

2.5/5 = k = 0.5

1/2 = k = 0.5

so that is the correct option.

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The point of intersection with x - axis is (5/3,0) and the point of intersection with y - axis is (0,5).  

Any point on AB's perpendicular bisector, P(x,y), shall be considered. Then, PA = PB.

√(x-3)²+(y-6)² = √(x+3)²+(y-4)²

(x-3)²+(y-6)² = (x+3)²+(y-4)²

x² -6x+ 9 + y²- 12y + 36 = x² +6x+ 9 + y²- 8y + 16

12x + 4y -20 = 0

3x+ y-5 =0 ---(1)  

Consequently, 3x+y-5=0 is the equation for the perpendicular bisector of AB.

We know that the coordinates of any point on x-axis are of the form (x,0). In other words, any point on the x-axis has a y-coordinate of zero. Thus, if we enter y = 0 in (1), we get

3x -5 = 0

x = 5/3

Thus, the x-axis is cut by the perpendicular bisector of AB at (5/3, 0).

(ii) Any point's y-axis coordinates have the following format: (0,y). When we enter x = 0 in (1), we obtain

y − 5 = 0

⇒ y = 5

Thus, the y-axis is where the perpendicular bisector of AB intersects (0,5).

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Answer: The coefficient of determination, r^2, is a measure of how well a linear regression model fits the data. It is calculated by squaring the linear correlation coefficient, r. In this case, r^2 = 0.845^2 = 0.7146. This tells us that 71.46% of the variation in the data is explained by the regression line, while 28.54% is unexplained.

The coefficient of determination, r^2, is a measure of how well a linear regression model fits the data. It is calculated by squaring the linear correlation coefficient, r. In this case, r^2 = 1^2 = 1. This tells us that 100% of the variation in the data is explained by the regression line, and 0% is unexplained.

The standard error of estimate (SEE) for a linear regression model is a measure of the average difference between the predicted values and the actual values. In this case, we can use the formula SEE = sqrt(SSE/n) where SSE is the sum of the squared differences between the predicted and actual values, and n is the number of observations. The given equation is y = -2.5x, so we can use this equation to find the predicted values and then calculate the SSE and SEE.

The standard error of estimate (SEE) for a linear regression model is a measure of the average difference between the predicted values and the actual values. In this case, we can use the formula SEE = sqrt(SSE/n) where SSE is the sum of the squared differences between the predicted and actual values, and n is the number of observations. The given equation is y = 1.523x + 6.343, so we can use this equation to find the predicted values and then calculate the SSE and SEE by using the given data.

Check the picture below.

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~2 - (-3)~~)^2 + (~~3 - (-2)~~)^2} \implies d=\sqrt{(2 +3)^2 + (3 +2)^2} \\\\\\ d=\sqrt{( 5 )^2 + ( 5 )^2} \implies d=\sqrt{ 25 + 25 } \implies d=\sqrt{ 50 }[/tex]

The reasonable domain for the Funtion is 0 to 14 parts. So,the correct option is B.

This function's domain is the set of all potential input values for the variable p. Because the variable p reflects the number of components generated, it must be non-negative.

Because the function is defined for p is larger than or equal to 0, the domain includes all non-negative p values. Because the function is linear, it is defined for all non-negative real numbers; however, in this case, the company manufactures custom truck parts for big rigs.

Which means the company may have a limit on the number of parts it can produce; this limit is 14 parts, so the reasonable domain for this function is 0 to 14 parts.

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Ratio of apple juice to water will make the same recipe is  42.60

Ratios are used to compare two numbers by dividing them. If you want to compare one data point (A) to another (B), your formula would be A/B. This signifies that you are dividing data A by data B. If A is five and B is ten, your ratio will be 5/10.

Add the elements of the ratio together to get the total number of shares.

Subtract the total value from the total number of shares.

Multiply by the number of necessary shares.

A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to one.

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Answer:

518.4 cm²

Step-by-step explanation:

We have two triangles so

2 × (9×10/2) = 90

We have a base so

14 × 10  = 140

We have two other rectangles so

2 × 14 × 10.3 = 288.2

Now we add it all together

288.4 + 140 + 90 = 518.4

The majority of human physical, mental, and personality factors have a mean in the middle of the distribution, where there are also the most cases. For example, in baseball, the rookie of the year often has a poor second season.

Correct answer is b) regression to the mean.

Regression to the mean is the propensity of outcomes that are extreme by chance on the first measurement to move closer to the average when tested a second time. Results that are susceptible to regression to the mean are those that are vulnerable to some degree of chance. When exceptional scores are the result of chance or a fluke, it's improbable that those extreme scores will be obtained again.

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The ratio of sedans to sports coupes on the lot is 2:3, which can also be expressed as 3:2, 3:4, or 4:3. This means that there are two sedans for every three sports coupes, or three sedans for every two sports coupes, etc.

The ratio of sedans to sports coupes on the lot can be expressed as a fraction, which is the number of sedans divided by the number of sports coupes. In this case, there are 24 sedans and 18 sports coupes, which can be written as 24/18. This fraction can be simplified to 2/3, which is equivalent to the ratio 2:3. This ratio can also be expressed as 3:2, 3:4, or 4:3, which means that there are two sedans for every three sports coupes, three sedans for every two sports coupes, three sedans for every four sports coupes, or four sedans for every three sports coupes. In summary, the ratio of sedans to sports coupes on the lot is 2:3, which can also be expressed in several other ways.

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Answer:

-3(x - 3) (x + 1)

Step-by-step explanation:

Let's check

-3(x - 3) (x + 1)

(-3x + 9) (x + 1)

-3[tex]x^{2}[/tex] -3x + 9x + 9

-3[tex]x^{2}[/tex] + 6x + 9

Answer:

-3(x-3)(x+1)

Step-by-step explanation:

A common factor that all three numbers share is that they are divisible by 3, so we can factor 3 out. Typically, I take out the negative first:

-3([tex]x^2-2x-3[/tex]) (always remember to change signs!)

Now, we are left with [tex]x^2-2x-3[/tex], and to factor that out, we need to find two numbers that add up to -2 and multiply to -3. These two numbers will be 1 and -3, so we can write our factor like this:

(x-3)(x+1)

Let's add back in the -3 from earlier to complete our factoring:

-3(x-3)(x+1)

his loan will be $37,234 in the year 2022.

ax2+bx+c=0, with a not equal to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Given, David took out a 20-year $70,000 loan from his bank in 2010.

The quadratic equation that approximates the year/loan balance relationship is y = -98*x^2 - 1,531x + 69,718,

where x is the number of years and

y is the balance

Since the Loan balance is given $37,234.

Thus to calculate the year

$37,234 = -98*x^2 - 1,531x + 69,718,

98 x² + 1534x - 32484 = 0

Comparing with the general form of the quadratic equation.

ax² + bx + c = 0

The discriminant b² - 4ac > 0 thus it has Two real roots.

using the Quadratic Formula

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

x = -27.62

and

x = 12

Thus year = 2010 + 12 = 2022

Therefore, In the year 2022, his loan will be $37,234.

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Answer:

SEE ATTACHED

Step-by-step explanation:

Answer:

53700

Step-by-step explanation:

Depreciation of every year is 8%, 2016-2017-18-19-20 - 4 years

in the beginning of 2017 it'll be 0.92*75000

so it'll be (1-8%)^4 = 0.71639

multiply by 75000 = 53729.  to the nearest 100 = 53700

a1 is a linear combination of w1, w2, and w3, and is thus a vector in w.

a. No, b is not in fa 1; a 2; a 3g. There are 3 vectors in fa 1; a 2; a 3g.

b. Yes, b is in w. There are 4 vectors in w.

c. To show that a1 is in w, we need to show that a1 is a combination of the vectors in w. We can do this by constructing a linear combination of the vectors in w that results in a1. In this case, we can take w1 = (2, 4, 1, 0), w2 = (4, 0, 3, 2), and w3 = (2, 6, 3, 3). Now we can set up a linear combination of these vectors, with coefficients c1, c2, and c3, to equal a1. Thus, we have: c1(2, 4, 1, 0) + c2(4, 0, 3, 2) + c3(2, 6, 3, 3) = (2, 0, 0, 0). Solving for c1, c2, and c3, we get c1 = 2, c2 = -2, and c3 = 0. Therefore, a1 is a linear combination of w1, w2, and w3, and is thus a vector in w.

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The area of the walkway around swimming pool is 78 square feet.

The outer sides of the walkway will have a length of 12 feet and the breadth will be 11 feet.

The area of the pool along without the walkway will be 12 X 11 = 132 square feet.

The outer sides of the walkway will have a length of 15 feet and the breadth will be 14 feet after the owner create the walkway.

The area of the pool along with the walkway will be 15 X 14 = 210 square feet.

Therefore ,

area of the walkway will be:-

= 210 - 132

= 78 square feet.

so, the area of the walkway around swimming pool is 78 square feet.

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The ordered pair that is a solution of given two expressions is (3,0) .

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants.

Given expressions,

4x + 3y < 12

-x + 3y < -3

First find where the 2 lines intersect

4x + 3y = 12

-x + 3y = -3

Subtract :

5x = 15

x = 3

and y = -3 + 3 / 3 = 0

So they intersect at the point (3,0).

Therefore , The ordered pair that is a solution of given two expressions is (3,0) .

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Answer:

Equation is   x-5 = 37

Reason:

x = starting temperature

We start with x degrees, and decrease by 5 degrees.

We go from x to x-5

The x-5 is now 37 degrees

Therefore, we arrive at the equation x-5 = 37

To solve this equation, add 5 to both sides and you'll get x = 42

Nice work on getting the correct value of 42.