Which expression is equivalent to

The length f the diagonal of the square is

The marked points represents the diagonal hence we find the distance between the points

The distance between them is calculated using the following formula:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Using the points (3, 5) and (12, 14), we can substitute the values into the formula and calculate the length of the line segment:

d = √((12 - 3)² + (14 - 5)²)

= √(9² + 9²)

= √(81 + 81)

= √162

≈ 12.73

Therefore, the length of the line segment between (3, 5) and (12, 14) is approximately 12.73 units.

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The surface area of the box increases by 27.4 cm² when the height is increased by 0.2 cm.

To find the increase in surface area, we first need to calculate the initial surface area of the box and then calculate the surface area after increasing the height.

The formula for the surface area of a rectangular prism is given by:

Surface Area = 2*(length width + length height + width*height)

Initial Surface Area:

Length (L) = 13 cm

Width (W) = 8.7 cm

Height (H) = 28 cm

Initial Surface Area = 2*(138.7 + 1328 + 8.7*28)

Next, we calculate the new surface area after increasing the height by 0.2 cm. The new height is:

New Height = Initial Height + Increase in Height = 28 cm + 0.2 cm

New Surface Area = 2*(138.7 + 13(28+0.2) + 8.7*(28+0.2))

To find the increase in surface area, we subtract the initial surface area from the new surface area:

Increase in Surface Area = New Surface Area - Initial Surface Area

Let's calculate the values:

Initial Surface Area = 2*(138.7 + 1328 + 8.728) = 2(113.1 + 364 + 243.6) = 2*(720.7) = 1441.4 cm²

New Surface Area = 2*(138.7 + 13(28+0.2) + 8.7*(28+0.2)) = 2*(113.1 + 377.2 + 244.1) = 2*(734.4) = 1468.8 cm²

Increase in Surface Area = New Surface Area - Initial Surface Area = 1468.8 cm² - 1441.4 cm² = 27.4 cm²

Therefore, the surface area of the box increases by 27.4 cm² when the height is increased by 0.2 cm.

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Answer:

To find the sum of (-2.1x + 3.7) and (5 + 4.9x), we need to add the like terms (terms with the same variable and exponent). In this case, the x term is the like term. Therefore:

(-2.1x + 3.7) + (5 + 4.9x) = -2.1x + 4.9x + 3.7 + 5

Combining like terms, we get:

(-2.1x + 4.9x) + (3.7 + 5) = 2.8x + 8.7

Therefore, the sum of (-2.1x + 3.7) and (5 + 4.9x) is 2.8x + 8.7.

So, the answer is: 2.8x+8.7.

Step-by-step explanation:

Solution 2:

The correct answer is 2.8x+8.7.

Here's the solution:

(-2.1x +3.7) + (5 + 4.9x) =

-2.1x + 3.7 + 5 + 4.9x =

-2.1x + 4.9x + 3.7 + 5 =

2.8x + 8.7: answer

Answer: 10

Step-by-step explanation:

The value of slope of line is,

⇒ m = - 1

We have to given that,

Two points on the line are (- 4, 5) and (- 7, 8).

Now, We know that,

Slope of the line passing through the points (x₁ , y₁) and (x₂, y₂) is,

m = (y₂ - y₁) / (x₂ - x₁)

Here, Two points on the line are (- 4, 5) and (- 7, 8).

Hence, Slope is,

m = (8 - 5) / (- 7 + 4)

m = 3 / - 3

m = - 1

Therefore, The value of slope of line is,

⇒ m = - 1

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Answer: (x+3)(x-4)

Step-by-step explanation:

Answer:

sec B = [tex]\frac{15}{8}[/tex]

Step-by-step explanation:

using the identity

sec B = [tex]\frac{1}{cosB}[/tex]

cos B = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{CD}[/tex] = [tex]\frac{8}{15}[/tex]

then

sec B = [tex]\frac{1}{\frac{8}{15} }[/tex] = [tex]\frac{15}{8}[/tex]

The solution has been explained below.

We will use the following equation, x² + y² = 81, where x and y are the pool's dimensions in feet, to determine the necessary estimations for the pool project.

1. Calculate the pool's diameter and radius:

We can infer that the radius of the pool is equal to the square root of 81 because the equation depicts a circle. As a result, r = 81 = 9 ft.

The pool's diameter is simply equal to twice its radius, or d = 2r = 18 feet.

2. Calculate the amount of water in the pool:

Since the pool is 4 feet high, we can determine its volume by multiplying the area of its circle-shaped base by the height.

The formula A = πr² can be used to calculate the area of the pool's base,

Therefore, V = Ah = πr²h = 1017.87 cubic feet represents the volume of water in the pool.

3. Determine the pool's total material cost:

There are 7.48 gallons in a cubic foot and a gallon of water costs $0.22.

As a result, Cw = V × 7.48 × 0.22 = 1017.87 × 7.48 × 0.22 = $1,619.72 is the entire cost of water for the pool.

If the radius of the pool is $185 per foot, then the cost of the materials is Cm = r × 185 = 9 × 185 = $1,665.

4. Calculate the pool's total labour hours:

A pool's construction is estimated to take 2.5 hours for every foot of its radius.

So, L = r × 2.5 = 9 × 2.5 = 22.5 hours of labour would be needed to complete this pool.

5. Calculate the total cost of labour for the project:

If you pay someone $19 per hour, Cl = L × 19 = 22.5 × 19 = $427.5.

6. Find the project's overall cost:

The project's overall cost is the product of its labour and material costs:

Cost as a whole equals Cm + Cw + Cl, which is 1,665 + 1,619.72 + 427.5, or $3,712.22.

In conclusion, the pool has an 18-foot diameter and a 9-foot radius according to the supplied equation. There are roughly 1017.87 cubic feet of water in the pool. Water and building supplies are included in the pool's projected material cost of $3,284.72. 22.5 hours of labour in total are needed, with a labour cost estimate of $427.5. Consequently, $3,712.22 is the expected final cost of the pool renovation.

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The value of the expression 28 - {15 (3+2)} is -47.

To evaluate the expression 28 - {15 (3+2)}, we need to follow the order of operations (also known as PEMDAS/BODMAS) which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Let's break down the expression step by step:

First, we solve the expression inside the parentheses:

3 + 2 = 5

Now, we substitute the result back into the original expression:

28 - {15 * 5}

Next, we perform the multiplication:

15 * 5 = 75

Now, we substitute the result back into the expression:

28 - 75

Finally, we perform the subtraction:

28 - 75 = -47

Therefore, the value of the expression 28 - {15 (3+2)} is -47.

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The average value of f(x) over the interval [ - 16, 16] is found to be  0.

The average value of f(x) = 16x over the interval [ - 16, 16] is:

F_average  = (1/(b-a)) * ∫(a to b) f(x) dx,

where the value of

a = -16 and b = 16

F_average = (1/(16-(-16))) x ∫(-16 to 16) 16x dx

F_average = (1/32) x [8x²] from -16 to 16

F_average = (1/32) x [8(16² - (-16)²)]

F_average = (1/32) x [8(256 - 256)]

F_average = 0

In concluaion,  the average value of f(x) over the interval [ - 16, 16] is determined as 0.

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The length of the arcs are;

1. s = 6. 4π

2. s = 11. 0π

The formula for calculating the length of an arc is expressed as;

s = rθ

Such that;

From the information given, we have that;

s = 4.25 × 3π/2

Multiply the values, we get

s = 12.75π/2

Divide by the coefficient , we get;

s = 6. 4π

2. The length of the arc would be;

s = 6.62 × 5π/3

Multiply the values, we have;

s = 33. 1π/3

Divide by the value, we get;

s = 11. 0π

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The only one that can possibly cause lower your credit score is "You apply for a student loan and the lender requests a copy of your credit report."

The lender normally does a hard inquiry on your credit record when you apply for a new loan or line of credit.

Your credit score may be slightly lowered as a result of this hard inquiry, typically by a few points.

However, the effect is often short-lived, and your credit score should gradually improve.

Hence the correct option is You apply for a student loan and the lender requests a copy of your credit report.

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Answer:

Step-by-step explanation:

The value of x is 1/3 and y is -5/3. using substitution method.

We have,

A linear equation has one or two variables.

No variable in a linear equation is raised to a power greater than 1.

No variable is used as the denominator of a fraction.

A linear equation is defined as an equation that is written in the form of ax+by=c.

When solving the system of linear equations, we will get the values of the variable, which is called the solution of a linear equation.

solving this we will get the valve of Y if x is given.

CALCULATION:-

Y=x-2 -----(1)

y=-2x+7 ---------(2)

putting the value of y in the equation (2)

x-2= -2x+7

x+2x=7+2

3x=9

x=9/3

x=1/9

putting the value of X in equation(1)

Y=x-2 -----(1)

y=1/3-2

y=-5/6  

Hence, The value of x is 1/3 and y is -5/3. using substitution method.

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complete question:

Use the substitution method to solve the system of equations write your answer as an ordered pair Y=x-2 and y=-2x+7

Step-by-step explanation:

To find the perimeter, we add all side lengths.

Two of the side lengths are given, to find the third side length, we use the following equation based on similarity ratio:

[tex] \frac{kj}{nm} = \frac{kl}{no} [/tex]

[tex] \frac{8}{18.4} = \frac{9}{no} [/tex]

8NO = 165.6

NO = 20.7

20.7 + 23 + 18.4 = 62.1 square units.

Answer:

40

Step-by-step explanation:

For finding the surface area of this rectancular prism, or any, we find the area of each shape. Then, we add up all of the areas together to get the surface area. There are 2 squares with 2 as a side length for each side. To find the area of a square, we can multiply any 2 sides. That is because the sides of the square is equal to eachother, so 2•2=4. Being 2 squares, they are both have area of 4. Looking at the 4 rectangles, they have a length of 4 and a width of 2. We multiply the height and width of a rectangle to get the area. 4•2=8, the area of each rectangle is 8. Now, we add up all of our areas. Two squares, each are 4 for their area. Add them up, you get 8 for the 2 squares. Then, we have 4 rectangles each are 8 for their area. 4•8=32 since they all have the same area. 32+8=40! 40 is the surface area of this net. I hope this helps, and have good day

The sum of money is approximately Rs. 6250.

Given that the difference is Rs. 40, we must calculate the difference between compound interest and simple interest over a period of two years at an annual rate of 8%.

Assume that P represents the principal amount of money.

The formula for simple interest is: SI = (P * R * T) / 100

The formula for compound interest is: [tex]CI = P * (1 + R/100)^T^ - ^P[/tex]

Where

The difference between compound interest and simple interest is Rs. 40. Therefore:

CI - SI = Rs. 40

Substituting the formulas and values into the equation:

[tex](P * (1 + 8/100)^2 - P) - (P * 8 * 2 / 100) = 40[/tex]

Simplifying further:

[tex](P * (1.08^2) - P) - (0.16P) = 40[/tex]

[tex](P * 1.1664 - P) - 0.16P = 40[/tex]

[tex]1.1664P - P - 0.16P = 40[/tex]

[tex]0.0064P = 40[/tex]

[tex]P = 40 / 0.0064[/tex]

[tex]P[/tex] ≈ [tex]6250[/tex]

Therefore, the sum of money is approximately Rs. 6250.

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As per the given data, Focus: (0, 16.44), Directrix: y = -16.44, Focal Diameter: 32.88, Vertex: (0, 0), and Axis of Symmetry: x = 0 (y-axis).

To determine the focus, directrix, focal diameter, vertex, and axis of symmetry for the given parabola equation, we can rewrite it in standard form, which is of the form [tex](x - h)^2[/tex] = 4p(y - k), where (h, k) represents the vertex.

16.44y = x²

Divide both sides of the equation by 16.44 to isolate y:

y = (1/16.44)x²

Comparing this equation to the standard form, we can see that h = 0 and k = 0.

Therefore, the vertex is (h, k) = (0, 0).

The general equation for a parabola in standard form is given by (x - h)^2 = 4p(y - k), where p is the distance between the vertex and the focus (or the vertex and the directrix). In this case, p can be found using the coefficient of y in the equation (1/4p = 1/16.44).

Thus, p = 16.44.

The focus is located at a distance of p units above the vertex, so the focus is (0, p) = (0, 16.44).

The directrix is located at a distance of p units below the vertex, so the directrix is the horizontal line y = -p, which gives us y = -16.44.

The focal diameter is twice the value of p, so the focal diameter is 2p = 2 * 16.44 = 32.88.

Therefore:

- The focus is (0, 16.44).

- The directrix is y = -16.44.

- The focal diameter is 32.88.

- The vertex is (0, 0).

- The axis of symmetry is the vertical line passing through the vertex, which is the y-axis (x = 0).

Thus, Focus: (0, 16.44), Directrix: y = -16.44, Focal Diameter: 32.88, Vertex: (0, 0), and Axis of Symmetry: x = 0 (y-axis).

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The answer to the equation 9s + 13 = 10s + 12

We must place the variable s on one side of the equation in order to solve the equation 9s + 13 = 10s + 12. Here's how to accomplish it:

9s + 13 = 10s + 12

First, by taking 9s away from both sides of the equation, let's move all the terms containing s to one side:

9s - 9s + 13 = 10s - 9s + 12

That amounts to:

13 = s + 12

Next, take 12 off of both sides to isolate the variable s:

13 - 12 = s + 12 - 12

1 = s

As a result, s = 1 is the answer to the equation 9s + 13 = 10s + 12

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The solutions to the circle equations in the attached figure are: (5) (x + 2)² + (y - 1)² = 20, (6) x² + y² = 9, (7) (x + 3)² + (y - 1)² = -9 and (8) (x - 4)² + (y - 3)² = -16

Equation of a Circle in the Cartesian coordinate system (x, y) is given by:

(x - h)² + (y - k)² = r²

where

(h, k) = coordinates of the center of the circle

r = radius.

The expression (x - h)² + (y - k)² represents the squared distance between any point (x, y) on the circle and the center point (h, k). By setting this expression equal to the square of the radius, r², we ensure that all points on the circle are equidistant from the center.

You can also expand the equation to get the standard form:

x² - 2hx + h² + y² - 2ky + k² = r².

Using the information above, let us solve the circle equations:

5) y² + 4x - 20 - 2y = -x²

First we need to find the coordinates (h, k) of the circle

x² + 4x + y² - 2y = 20

-2h = 4 => h = -2

-2k = -2 => k = 1

(h,k) = (-2, 1)

Rewrite the equation in a standard circle format

Recall: (x - h)² + (y - k)² = r²

(x - (-2))² + (y - (1))² = 20

(x + 2)² + (y - 1)² = 20

Therefore the solution to the circle equation is: (x + 2)² + (y - 1)² = 20 and the curve is attached.

6) -9 = -y² - x²

First we need to find the coordinates (h, k) of the circle

x² + y² = 9

-2h = 0 => h = 0

-2k = 0 => k = 0

(h, k) = (0, 0)

Rewrite the equation in a standard circle format

Recall: (x - h)² + (y - k)² = r²

(x - (0))² + (y - (0))² = 9

x² + y² = 9

Therefore the solution to the circle equation is: x² + y² = 9 and the curve is attached.

7) 9 = 2y - y² - 6x - x²

First we need to find the coordinates (h, k) of the circle

x² + 6x + y² - 2y = -9

-2h = 6 => h = -3

-2k = -2 => k = 1

(h, k) = (-3, 1)

Rewrite the equation in a standard circle format

Recall: (x - h)² + (y - k)² = r²

(x - (-3))² + (y - (1))² = -9

(x + 3)² + (y - 1)² = -9

Therefore the solution to the circle equation is: (x + 3)² + (y - 1)² = -9 and the curve is attached

8) 16 + x² + y² - 8x - 6y = 0

First we need to find the coordinates (h, k) of the circle

x² - 8x + y² - 6y = -16

-2h = -8 => h = 4

-2k = -6 => k = 3

(h,k) = (4, 3)

Rewrite the equation in a standard circle format

Recall: (x - h)² + (y - k)² = r²

(x - (4))² + (y - (3))² = -16

(x - 4)² + (y - 3)² = -16

Therefore the solution to the circle equation is: (x - 4)² + (y - 3)² = -16 and the curve is attached.

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The option that represents shapes of the sampling distribution of p hat  is:

c. Because n (1 minus p) = 20 (1 minus 0.87) = 2.6 less-than 10 , the sampling distribution of p hat is not approximately Normal. Because p = 0.87 is closer to 1 than 0, the sampling distribution of p hat is skewed to the left.

Normal distribution is defined as the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

Because the requirement for normal is greater than 10, n×p is greater than 10 and nx(1-p) is also greater than 10.

This situation is abnormal because it is not valid. If p is close to 1 in a normal graph, then p is left skewed.

Thus, the option third is correct because nx(1-p)=2.6 less than equal to 10 then the sampling distribution  is not approximate normal because p=0.87 is closer to 1 than zero. Sampling distribution  is skewed to the left.

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Answer:

Solution in attached photo.

Step-by-step explanation:

This question tests on the properties of angles, such as corresponding angles and sum of angles in a straight line.

The algebraic expression representing 6 added to x is given as follows:

x + 6.

The sentence in the context of this problem is given as follows:

"If x is a number, the number added do 6 is given by".

The number is given as follows:

x.

The addition by 6 means that the number 6 is added to the variable x, as follows:

x + 6.

Which is the algebraic expression.

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Applying Pythagoras theorem and trigonometry In the figure the length of x is

Using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let y be the required distance

y² = 10² + 15²

y² = 325

y = √18.03

y = 5√13

y = 18.03

To solve for x we use trigonometry tan

tan 45 = 5√3 / x

x = 5√13 / tan 45

x = 5√13

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Nina's average cost per day for these four services is $5.

Since, Nina's monthly cost for the cable TV services is $99, and her monthly cost for cell phone calls and text messages is $59.70.

So her total monthly cost is:

$99 + $59.70 = $158.70

Now we need to find the number of days in a month.

Since, There are different ways to do this, but if we assume a month has 30 days,

= $158.70 / 30

= $5.29 (rounded to the nearest cent)

Therefore, Nina's average cost per day for these four services is $5.29. Rounded to the nearest dollar, her average cost per day is $5.

So, Nina's average cost per day for these four services is $5.

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The net decrease in calories after walking for 5 hours will be 50 calories.

we have given that the 25-year old woman burns 300-60tcal/hr and Her caloric intake from drinking Gatorade is 110t calories during the t hour.

And we have to find the net decrease in calories after walking for 5 hours.

So, For this purpose,

We know that the

calories burns in one hour = 300-60tt

calories burns in 5 hours = 5(300-60t)

calories burns in 5 hours = 1500- 300t

Now,

Calorie intake in t hours = 110t

And net decrease in calories after walking for 5 hours =  1500- 300t + 140t

the net decrease is 50 cal.

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Answer:

Step-by-step explanation:

[tex]1c-0.25c=0.75c[/tex]

Answer: B

Step-by-step explanation:

Amplitude will be half the distance from 28 to 50

one cycle is given to be 8 hrs, so thats all you need for the right answer choice.

The experimental probability that the next train to pull into Lakeside Station will be full is 7/10.

The experimental probability of the next train to pull into Lakeside Station being full can be calculated by dividing the number of times a full train occurred by the total number of trains observed.

Given that out of the last 20 trains, 14 were full, we can express the experimental probability as a fraction:

P(full) = Number of full trains / Total number of trains observed

P(full) = 14 / 20

Simplifying the fraction, we get:

P(full) = 7 / 10

Therefore, the experimental probability that the next train to pull into Lakeside Station will be full is 7/10.

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The length of PN in the circle is 4√2 units.

The length of GN in the circle is 8 units and length of KP in the circle is 4.

Therefore, let's find the length PN in the circle as follows:

PM is perpendicular to the chord GH. Therefore, the length KH is equals to the length GK.

Hence,

GH = 8 units

GK = 4 units

KH = 4 units

Therefore,

MP is the radius of the circle just like PN.

PN = MP

Hence, using Pythagoras's theorem,

4² + 4² = PN²

PN = √16 + 16

PN = √32

PN = 4√2 units

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