Write an equation
that goes through
(8.1) and is
perpendicular to 2y
+4x =12

The final answer of inverse function for f(x)=2/5 (x-5)^2 is y = √(5/2 * x) + 5

The inverse function for f(x)=2/5 (x-5)^2 would become x= 2/5 (y-5)^2, and

We need to solve for y. Here is a step-by-step explanation of how to solve for y:

Now, multiply both sides of the equation by 5/2 to get rid of the fraction on the right side of the equation:

5/2 * x = (y-5)^2

Then, Take the square root of both sides of the equation to get rid of the exponent on the right side of the equation:

√(5/2 * x) = y-5

Add 5 to both sides of the equation to isolate y on one side of the equation:

√(5/2 * x) + 5 = y

Simplify the equation to get the final answer:

y = √(5/2 * x) + 5

Therefore, the inverse function for f(x)=2/5 (x-5)^2 is y = √(5/2 * x) + 5.

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As our calculated t-value of 3.032 is greater than the critical value of ±1.645, we can reject the null hypothesis at the 0.1 significance level and conclude that the coefficient for the variable is statistically significant and different from zero.

The hypotheses that we want to test are:

H0: The coefficient for the variable is equal to zero.

H1: The coefficient for the variable is not equal to zero.

Using the given output, we can see that the coefficient for the variable is 15.509, and the standard error of the coefficient is 5.123. The t-value for the coefficient is calculated by dividing the coefficient estimate by its standard error, so:

t = 15.509 / 5.123 = 3.032

To test the hypothesis, we can compare the calculated t-value with the critical value of the t-distribution with n-k-1 degrees of freedom (where n is the sample size and k is the number of independent variables), at a significance level of 0.1 and using a two-tailed test.

Since the sample size and number of independent variables are not provided, we cannot determine the degrees of freedom or the critical value directly. However, we can use a t-distribution calculator or look up the critical value from a t-distribution table. For example, with n=50 and k=2 (based on the given output), the critical value for a two-tailed test at a significance level of 0.1 is approximately ±1.645.

Since our calculated t-value of 3.032 is greater than the critical value of ±1.645, we can reject the null hypothesis at the 0.1 significance level and conclude that the coefficient for the variable is statistically significant and different from zero. In other words, there is evidence to suggest that the variable has a significant effect on the outcome being predicted by the regression model.

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Kendra needs to have at least $7.35 in her purse and needs to accumulate at least $2.87 more to shop for the special bead.

To discover the total amount Kendra needs to shop for the special bead, we add the amount she already has in her purse to the amount she needs to shop for the bead:

x = $7.35 + $2.87

x = $10.22

Thus, Kendra needs a total of $10.22 to shop for the special bead.

To represent the scenario as inequalities, we can use the subsequent:

Let y be the amount Kendra wishes to buy the unique bead, then:

Kendra has at least $7.35: y + $7.35 ≥ y

Kendra needs at the least $2.87 more: y + $2.87 ≤ x

Combining these inequalities, we get:

y + $7.35 ≥ y

y + $2.87 ≤ x

Therefore, Kendra needs to have at least $7.35 in her purse and needs to accumulate at least $2.87 more to shop for the special bead.

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In response to the given query, the result we have is As a result, the expressions following statement may be used to explain how long Interstate 90 is: 2m + 153.5

Multiplying, dividing, adding, and subtracting are all mathematical operations. As an example, consider the following expression: Expression, mathematics, and a numeric value Numbers, parameters, and functions are the components of an expression in mathematics. Using opposing words and phrases is possible. An expression, sometimes referred to as an algebraic expression, is any mathematical statement that includes variables, numbers, and a mathematical action between them. For instance, the expression 4m + 5 is made up of the expressions 4m and 5, as well as the variable m from the previous equation, all of which are separated by the mathematical symbol +.

Let L represent the length of I-90. We are informed that

L = 2m + 153.5

where m is Interstate 15's length.

As a result, the following statement may be used to explain how long Interstate 90 is:

2m + 153.5

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To solve the equation 1/2 + a = 1 3/4, we need to convert the mixed number 1 3/4 to an improper fraction:

1 3/4 = 4/4 + 3/4 = 7/4

Now we can rewrite the equation as:

1/2 + a = 7/4

To isolate the variable a, we need to subtract 1/2 from both sides:

a = 7/4 - 1/2

To add these two fractions, we need to find a common denominator, which is 4:

a = (7/4 - 2/4)

a = 5/4

Therefore, a = 5/4.

To solve the equation 1/2 + ? = 7, we can follow a similar approach. We need to isolate the variable on one side of the equation, so we need to subtract 1/2 from both sides:

? = 7 - 1/2

We need to find a common denominator to add these two fractions, which is 2:

? = (14/2 - 1/2)

? = 13/2

Therefore, the missing number is 13/2.

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Kai drives 470 miles in 10 hours at a constant speed of 47 miles per hour. To find out how far Kai drives in 10 hours, we can use the distance formula d=rt, where d is the distance, r is the rate (or speed), and t is the time.

First, we need to find Kai's rate (or speed). We can do this by rearranging the formula to solve for r:

r = d/t

Plug in the values we know:

r = 376 miles / 8 hours

Simplify:

r = 47 miles per hour

Now that we know Kai's rate, we can plug it back into the distance formula to find out how far he drives in 10 hours:

d = rt

d = (47 miles per hour) (10 hours)

Simplify:

d = 470 miles

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Answer:

-1

Step-by-step explanation:

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The lateral surface area of the cylinders {W} and {Y} are same.

Volume is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -

V = ∫∫∫ F(x, y, z) dx dy dz

Given are the dimensions of the cylinder as shown in the image.

The lateral surface area of the cylinder is -

L.S.A = 2πrh

{ 1 } -

L.S.A {W} = 2π x 3 x 9 = 54π

{ 2 } -

L.S.A {X} = 2π x 4 x 2 = 16π

{ 3 } -

L.S.A {Y} = 2π x 4.5 x 6 = 54π

Therefore, the lateral surface area of the cylinders {W} and {Y} are same.

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The answer is \( f(3) = 5 \) with no spaces.

Given the function \( f(x) = \left\{ \begin{array}{llr} -x^2 & \text{for} & x < 0 \\ x+2 & \text{for} & x \ge 0 \end{array} \right. \), we need to evaluate \( f(3) \).

Since \( 3 \ge 0 \), we will use the second part of the function, which is \( f(x) = x + 2 \).

So, we plug in \( x = 3 \) into the function and get:

\( f(3) = 3 + 2 = 5 \)

Therefore, the answer is \( f(3) = 5 \) with no spaces.

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Answer:

A: x

Step-by-step explanation:

So with problems like this when it saids f(g(x) it wants you to plug those values in. In some cases you have a value where the x is but you don't so you can't solve g(x) so you move on to the next step. You plug in g(x)= x-1/2 everywhere there is a x in f(x). So our equation would be 2(x-1/2) + 1. Then you solve by canceling the 2 by dividing it out so we would have x-1 +1. Then you combine like terms which -1 +1 is 0 so our final answer would be x.

Carlota's rate on a bicycle who is 74 miles away is approximately 6.1667 miles per hour.

Carlota's rate can be found by using the formula: rate = distance ÷ time. To find her rate for the first part of the trip, we can plug in the given values:

To find her rate for the second part of the trip, we need to subtract the distance and time she had already traveled from the total distance and time:

Then we can plug these values into the formula:

Since Carlota's rate is the same for both parts of the trip, we can simply use the overall distance and time to find her rate:

Therefore, Carlota's rate is approximately 6.1667 miles per hour.

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The values of w and v in the given right triangle are 1.68 and 4.7

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle.

Given is a right triangle, with hypotenuse 5, and an acute angle of 71°, we need to find the value of v and w, using trigonometric ratios,

The other acute angle will be = 90°-71° = 19°

Taking 19° as reference angle,

Sin 19° = w/5

w = 1.68

Cos 19° = v/5

v = 4.7

Hence, the values of w and v in the given right triangle are 1.68 and 4.7

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The value of the segments DB = 23.32 in, RK = 18.22 in and YK = 6.83 in.

The Pythagorean Theorem states that the square on the hypotenuse of a right triangle is equal to the sum of the squares on the triangle's legs.

The connection between the four edges of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem.

For the given figure we see the right triangle DHB.

Here, DH = 20 in and HB = 12 in.

Using the Pythagoras theorem we have:

DB² = DH² + HB²

DB² = 20² + 12²

DB² = 400 + 144

DB = 23.32

For the right triangle RHK we have:

HR = 16 and HK = 8.72

Using the Pythagoras theorem:

RK² = 16² + 8.72²

RK= 18.22

Also, KY = YK = 6.83 in.

Hence, the value of the segments DB = 23.32 in, RK = 18.22 in and YK = 6.83 in.

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The two triangles cannot be similar, because they have one pair of corresponding angles that are not equal.

What is triangle ?

A triangle is a geometric shape consisting of three straight sides and three angles. The sum of the angles in a triangle is always 180 degrees. The point where two sides of a triangle meet is called a vertex. The side opposite to a vertex is called the opposite side, and the angle opposite to a side is called the opposite angle.

To determine if two triangles are similar, we need to check if their corresponding angles are equal and their corresponding sides are proportional.

Let's start with the angles:

In triangle CBA, we can use the Law of Cosines to find the measure of angle C:

[tex]cos(C) = (a^2 + b^2 - c^2) / (2ab)[/tex]

where a, b, and c are the side lengths opposite to angles A, B, and C, respectively.

[tex]cos(C) = (72^2 + 48^2 - 84^2) / (2 x 72 x 48)[/tex]

cos(C) = -0.25

Since cos(C) is negative, we know that angle C is obtuse.

Now, let's consider triangle FGH. By the Law of Cosines, we can find the measure of angle H:

[tex]cos(H) = (f^2 + g^2 - h^2) / (2fg)[/tex]

[tex]cos(H) = (8^2 + 12^2 - 14^2) / (2 x 8 x 12)[/tex]

cos(H) = 0.25

Since cos(H) is positive, we know that angle H is acute.

Therefore, the two triangles cannot be similar, because they have one pair of corresponding angles that are not equal.

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Answer: you probly need to find the root of the number 8

Step-by-step explanation:

The Simple ratio and the ratio of the perimeters of two regular octagons are approximately 1.472

The formula for the area of the regular polygon is:

Area = (2 + 2[tex]\sqrt{2}[/tex]) × [tex]s^{2}[/tex]

Where, s = length of the side of a polygon

consider two equations for the two octagons,

48 = (2 + 2[tex]\sqrt{2}[/tex]) × [tex](s1)^{2}[/tex]

147 = (2 + 2[tex]\sqrt{2}[/tex]) × [tex](s2)^{2}[/tex]

The length of each polygon is

s1 = [tex]\sqrt{\frac{48}{(2 + 2\sqrt{2} )} }[/tex] ≈ 3.079cm

s2 = [tex]\sqrt{\frac{147}{(2 + 2\sqrt{2} )} } }[/tex] ≈ 4.532cm

The similarity ratio is,

s2 ÷ s1 ≈ 1.472

The ratio of perimeters is,

8s2 ÷ 8s1 = s2 ÷ s1 ≈ 1.472

Therefore, the similarity ratio and the ratio of the perimeters are both approximately 1.472.

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We can write the mean absolute deviation as -

1.63.

Absolute deviation or mean absolute deviation is the measure of how far a given data element is from a given mean value of the data.

Given is that Suzie's Desserts offers its customers 5 dessert options. The prices are: $5.00 $9.00 $9.00 $6.00 $6.00 $9.00 $9.00.

The formula for absolute deviation is -

[tex]$\frac {1}{n} \sum \limits_{i=1}^n |x_i-m(X)|[/tex]

We can calculate the mean as -

(5 + 9 + 9 + 6 + 6 + 9 + 9)/7 = 7.57

We can write the  absolute deviation as -

Absolute deviation =

1/7(5 - 7.57 + 9 - 7.57 + 9 - 7.57 + 6 - 7.57 + 6 - 7.57 + 9 - 7.57 + 9 - 7.57) = 1.63

Therefore, we can write the mean absolute deviation as -

1.63.

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The measure of Angle D in a parallelogram is 88 degrees.

Explain about parallelogram ?

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length and parallel to each other. The opposite angles are also equal in measure.

Properties of a parallelogram:

According to the question:
Since EFDM is a parallelogram, we know that opposite angles are equal. Therefore,

Angle E = Angle M

Angle D = Angle F

We're given:

Angle E = 16x + 12

Angle D = 18x - 2

So we have:

Angle M = 16x + 12

Angle F = 18x - 2

The sum of the angles in a parallelogram is 360 degrees. Therefore, we have:

Angle E + Angle F + Angle D + Angle M = 360

Substituting the given values, we get:

(16x + 12) + (18x - 2) + (16x + 12) + (18x - 2) = 360

72x + 20 = 360

72x = 340

x = 5

Now we can find the values of Angle E, Angle D, Angle F and Angle M:

Angle E = 16x + 12 = 16(5) + 12 = 92 degrees

Angle D = 18x - 2 = 18(5) - 2 = 88 degrees

Angle F = Angle D = 88 degrees

Angle M = Angle E = 92 degrees

Therefore, the measure of Angle D is 88 degrees.

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The value of x on the straight line is 43 degrees

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

The straight line

The sum of angles on a straight line is 180 degrees

Using the above as a guide, we have the following equation

3x + 51 = 180

Evaluate

3x = 129

Divide by 3

x = 43

Hence, the value of x is 43 degrees

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Step-by-step explanation:

Refer to pic...........

Answer:

-3 < y < -1

Step-by-step explanation:

|4y+8| < 4                                   |4y+8| > -4

4y + 8 < 4                                   4y + 8 > -4

4y < -4                                         4y > -12

y < -1                                             y > -3

So, the answer is -3 < y < -1

Answer:

Option A.) 1055.66 lbs

Step-by-step explanation:

Answer:

Step-by-step explanation:

Here's the long division of (2x³ + 3x² + 4x + 2) ÷ (x + 2):

2x^2 - x + 6

x + 2 | 2x^3 + 3x^2 + 4x + 2

- (2x^3 + 4x^2)

--------------

- x^2 + 4x

- (- x^2 - 2x)

-------------

6x + 2

- (6x + 12)

--------

-10

Therefore, the quotient is 2x^2 - x + 6, and the remainder is -10.

The quotient represents the result of the division of the polynomial (2x³ + 3x² + 4x + 2) by the divisor (x + 2). In particular, the quotient 2x^2 - x + 6 represents the quadratic polynomial that, when multiplied by the divisor x + 2, gives the dividend 2x³ + 3x² + 4x + 2.

In other words, we have:

(2x³ + 3x² + 4x + 2) = (x + 2)(2x^2 - x + 6) - 10

The remainder -10 indicates that the division is not exact, and that there is a "leftover" term of -10 when we try to divide the polynomial (2x³ + 3x² + 4x + 2) by (x + 2).

The two integers are 5 and 6.

To solve this problem, we need to set up an algebraic equation based on the information given.

Let's call the first integer x and the second integer y. According to the problem, an integer (x) is 14 less than 4 times another (y).

This can be written as: x = 4y - 14

We are also told that the product of the two integers is 30. This can be written as:

xy = 30

Now we can substitute the first equation into the second equation to solve for one of the variables.

Let's solve for y:

(4y - 14)y = 30

4y^2 - 14y = 30

4y^2 - 14y - 30 = 0

Using the quadratic formula, we can solve for y:

y = (-(-14) ± √((-14)^2 - 4(4)(-30)))/(2(4))

y = (14 ± √(196 + 480))/8

y = (14 ± √676)/8

y = (14 ± 26)/8

y = 5 or y = -1.5

Now we can plug these values of y back into the first equation to find the corresponding values of x:

x = 4(5) - 14 = 6

x = 4(-1.5) - 14 = -20

So the two integers are either 5 and 6, or -1.5 and -20. However, since the problem asks for integers, we can eliminate the second solution.

Therefore, the two integers are 5 and 6.

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Answer:

420mm^3

Step-by-step explanation:

10mm×10.5mm=105mm

105mm×8mm=840mm^3

840mm^3÷2=420mm^3

The volume of this prism is calculated by this equation:

V = (area of a triangle)(height)

So plugging in the numbers it looks something like this

V = (10 x 10.5 x 1/2)(8)

V = (105 x 1/2)(8)

V = (52.5)(8)

V = 420 mm^3

The given exponential functions are classified as exponential growth or exponential decay above.

A function is a relation between a dependent and independent variable. We can write the examples of functions as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is to check whether the given functions represent exponential growth or decay.

We can write the classified functions as -

{ 1 }.   y = 500(0.30)ˣ                     exponential decay

{ 2 }.  y = 500(1.70)ˣ                      exponential growth

{ 3 }.  y = 0.3(500)ˣ                       exponential growth

{ 4 }.  y = 500(0.30)ˣ - 6               exponential decay

{ 5 }.  y = 0.3(1.7)ˣ - 2                    exponential growth

{ 6 }.  y = 500(0.30)ˣ ⁺ ⁸               exponential growth

{ 4 }.  y = 500(0.30)ˣ ⁻ ⁶               exponential decay

Therefore, the given exponential functions are classified as exponential growth or exponential decay above.

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The solution to the inequality 5(3y+1)<15 in interval notation is (-∞, 2/3).

To solve the inequality 5(3y+1)<15, we need to isolate the variable y on one side of the inequality. Here are the steps to do so:
1. Start with the given inequality: 5(3y+1)<15
2. Distribute the 5 on the left side: 15y+5<15
3. Subtract 5 from both sides: 15y<10
4. Divide both sides by 15: y<10/15
5. Simplify the fraction: y<2/3

Now, we can write the solution in interval notation. Interval notation uses parentheses or brackets to indicate the range of values that satisfy the inequality. In this case, the solution is all values of y less than 2/3, so we use the notation (-∞, 2/3).

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The key to finding the value of x in a right triangle is to choose the appropriate trigonometric ratio based on the sides given and to use a calculator to find the value of x to the nearest tenth of a degree.

To find the value of x in a right triangle, we can use the trigonometric ratios of sine, cosine, and tangent. The ratio we choose depends on the information given in the question and the sides and angles we are trying to find.

To find x to the nearest tenth of a degree, we can use the following steps:
a. Identify the sides of the triangle that are given and the side we are trying to find.
b. Choose the appropriate trigonometric ratio based on the sides given. For example, if we are given the opposite side and the hypotenuse, we would use the sine ratio.
c. Set up the equation and solve for x. For example, if we are using the sine ratio, the equation would be sin(x) = opposite/hypotenuse.
d. Use a calculator to find the value of x to the nearest tenth of a degree.

To find x using the aulend method, we can use the following steps:
a. Identify the sides of the triangle that are given and the side we are trying to find.
b. Use the Pythagorean theorem, a^2 + b^2 = c^2, to find the missing side.
c. Use the appropriate trigonometric ratio to find the value of x.

To approximate x to the nearest tenth of a degree, we can use a calculator to find the value of x and then round to the nearest tenth.

To find x in the given right triangle, we can use the following steps:
a. Identify the sides of the triangle that are given and the side we are trying to find.
b. Choose the appropriate trigonometric ratio based on the sides given.
c. Set up the equation and solve for x.
d. Use a calculator to find the value of x.

Overall, the key to finding the value of x in a right triangle is to choose the appropriate trigonometric ratio based on the sides given and to use a calculator to find the value of x to the nearest tenth of a degree.

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The cubic inch value that most closely approximates the prism's volume is 12in³.

Any three-dimensional solid's volume is the area it takes up. The shapes of these solids include cubes, cuboids, cones, cylinders, and spheres.

Forms come in a wide range of volumes. We have looked at a variety of three-dimensional solids and shapes, including cubes, cuboids, cylinders, cones, and more. We'll learn how to calculate the volumes of each of these forms.

To find the volume of the rectangular prism in the above problem, multiply its length, width, and height. The image reveals the rectangle's measurements to be around 5.5 inches long and 4 inches broad. Volume is calculated as follows: Volume = Length x Width x Height

= 5.5 inches x 4 inches x 218 inches

= 4 x 5.5 x 218

= 4 x 1199

= 4796

4796 cubic inches is the result.

When we round this response to the nearest whole number 12 in³ is the measurement that most closely approximates the prism's volume in cubic inches.

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The complete question is:

The rectangle shown represents the base of a rectangular prism. Use the ruler provided to measure the length and width of the rectangle to the nearest 14 inch. The height of the prism is 218inches. The dimensions are 5.5 inches and 4 inches. Which measurement is closest to the volume of the prism in cubic inches?

F.33 inches3

G.23 inches3

H.11 inches 3

J.12 inches 3