Calculate the paychecks of the following people. They make time and a half for any hours beyond 40. Round all values to two decimal places.

Answer:

x=32

Step-by-step explanation:

i took the test

The equation of the line perpendicular to y=1/2x-1 and passing through the point (5,6) is y = -2x + 16.

To find the equation of the line perpendicular to y=1/2x-1, we need to determine its slope. We can recall that the slope of a line in slope-intercept form, y = mx + b, is given by m, the coefficient of x. So in the given equation y=1/2x-1, the slope is 1/2.

The slope of a line perpendicular to this line will be the negative reciprocal of the slope, which means it will be -2. To see why this is true, remember that the product of the slopes of two perpendicular lines is always -1. So if the slope of the original line is m, the slope of the perpendicular line will be -1/m.

Now that we know the slope of the perpendicular line is -2, we can use the point-slope form of the equation of a line to find its equation. The point-slope form is:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

We are given a point on the perpendicular line, (5, 6), so we can substitute that into the equation and also substitute in the slope, -2:

y - 6 = -2(x - 5)

y - 6 = -2x + 10

y = -2x + 16

Hence, the equation of the line perpendicular to y=1/2x-1 and passing through the point (5,6) is y = -2x + 16.

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As sets A, B, and C are subsets of the universal set U, the value of A’ ∪ B’ U C'  = {f}.

Demorgan's law can be utilised in set theory and boolean algebra to make mathematical formulations simpler. Let's say that the universal set U has two subsets, A and B. A' is A's complement, and B' is set B's complement.

Given that, (An B)' UC'.

Using the De Morgan's law we have:

(A ∩ B)’ = A’ ∪ B’.

Substituting this in (An B)' UC'. we have:

A’ ∪ B’ U C'

A' = {f, p, x, y}

B' = {f, g, h, p}

C' = {f, g, x, z}

A’ ∪ B’ U C'  = {f}

As sets A, B, and C are subsets of the universal set U, the value of A’ ∪ B’ U C'  = {f}.

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Answer:

8.60cm

Step-by-step explanation:

a/sinA=b/sinB

15/sin90⁰=x/sin35⁰

cross multiply

15sin35⁰=xsin90⁰

8.6036=x

x=8.60cm

The transformations that change the domain of a function are given as follows:

The domain of a function is defined as the set containing all the values assumed by the independent variable x of the function, which are also all the input values assumed by the function.

Hence we must look at transformations that change the values of x of the function, which are given as follows:

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Answer:

A. There are two complex roots

Step-by-step explanation:

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If the discriminant of a quadratic equation is equal to Negative 8, there are two complex roots.

The discriminant of a quadratic equation is given as;

\(b^2 - 4ac>0 \ \ ( 2 \ solutions; 1 \ positive \ and \ 1 \ negative\ solution)\\\\b^2 -4ac = 0 \ \ (1 \ real \ solution)\\\\b^2 - 4ac \ < 0 \ \ (complex \ root, \ no \ solution)\)

A discriminant of negative 8 falls with last category in the solution above.

\(b^2 - 4ac <0 \ \ (eg \ -8),\)

\(x = +/-\sqrt{-8} \\\\x = \sqrt{-8 } \ \ or \ \ -\sqrt{-8} \ \ \ \ \ (2 \ complex \ roots)\)

Thus, if the discriminant of a quadratic equation is equal to Negative 8, there are two complex roots.

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The values of x and y are 20 and 12.

The values of x and y are -3 and 2.

We have,

In a parallelogram,

- Opposite sides are congruent:

The opposite sides of a parallelogram have equal lengths.

- Opposite angles are congruent:

The opposite angles of a parallelogram have equal

Now,

a)

Opposite angles are congruent:

So,

5x + 29 = 7x - 11

29 + 11 = 7x - 5x

40 = 2x

2x = 40

x = 40/2

x = 20

And,

3y + 15 = 5y - 9

15 + 9 = 5y - 3y

24 = 2y

y = 24/2

y = 12

b)

Opposite sides are congruent:

So,

-6x = -4x + 6

-6x + 4x = 6

-2x = 6

x = -3

And,

7y + 3 = 12y - 7

12y - 7y = 3 + 7

5y = 10

y = 2

Thus,

The values of x and y are 20 and 12.

The values of x and y are -3 and 2.

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The exact value of x is √1156 and it follows the Pythagorean triple

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

Legs of the right triangle = 16 and 30

Using the pythagoras theorem, we have

Hypotenuse^2 = the sum of the squares of the other lengths

So, we have

x^2 = 16^2 + 30^2

When evaluated, we have

x^2 = 1156

This gives

x = √1156

Hence, the exact value is √1156

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Answer: 22

Step-by-step explanation:

By the corresponding angles theorem, \(5x-16=2x+50 \longrightarrow x=\boxed{22}\)

Answer: The top right

Step-by-step explanation: The top left is a line segment so incorrect,

the bottom left is a ray so also incorrect, and finally, the bottom right is just a dot so that is also incorrect.

Hope this helped!

Mark Brainliest if you want!

Answer:

Top photo on right (the one with two arrows on the sides)

Step-by-step explanation:

I hope this helps!

The complete statement is ∠PRQ ≅ ∠SRT. The correction option is A. ∠SRT

From the question, we are to complete the given statement

From the given information,

We have that ΔPQR ≅ ΔSTR

This means ΔPQR is congruent to ΔSTR

Then,

∠PQR ≅ ∠STR

∠PRQ ≅ ∠SRT

∠QPR ≅ ∠TSR  

Hence, the complete statement is ∠PRQ ≅ ∠SRT. The correction option is A. ∠SRT

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The number of square inches of cardboard that are needed to make one

the container is 18.

We have,

The volume of the triangular prism.

= Area of the triangle x height

Now,

Height = 6 in

And,

To find the area of a triangle, we can use Heron's formula.

A = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case, the side lengths of the triangle are 3.2 in, 3.2 in, and 2 in.

Let's calculate the area using Heron's formula:

s = (3.2 + 3.2 + 2) / 2 = 4.2

A = √(4.2(4.2 - 3.2)(4.2 - 3.2)(4.2 - 2))

A = √(4.2 x 1 x 1 x 2.2)

A = √(9.24)

A ≈ 3.04 square inches

Now,

The volume of the triangular prism.

= Area of the triangle x height

= 3.04 x 6

= 18.24 in²

Now,

Area of one cardboard.

= 1² in²

= 1 in²

Now,

The number of square inches of cardboard that are needed to make one

container.

= The volume of the triangular prism / Area of one cardboard

= 18.24 in² / 1 in²

= 18.24

= 18

Therefore,

The number of square inches of cardboard that are needed to make one

the container is 18.

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The expression representing the perimeter of the polygon is given as follows:

7mn³/3 + 4m² + 3mn².

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

Hence the perimeter for the polygon in this problem is given as follows:

mn³(1/3 + 2) + m²(1 + 3) + mn²(1 + 2) = 7mn³/3 + 4m² + 3mn².

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The surface element is

dS = || ∂r/∂u  x  ∂r/dv || du dv

where

r (u, v) = x (u, v) i + y (u, v) j + z (u, v) k

r (u, v) = (u + v) i + (u - v) j + (1 + 2u + v) k

is the vector parameterization for the surface S.

The normal vector to the surface is

∂r/∂u  x  ∂r/dv

… = (i + j + 2 k)  x  (i - j + k)

… = 3 i + j - 2 k

and has norm

|| ∂r/∂u  x  ∂r/dv || = √(3² + 1² + (-2)²) = √(14)

Now compute the integral:

∫∫ (x + y + z) dS = √(14) ∫₀¹ ∫₀² ((u + v) + (u - v) + (1 + 2u + v)) du dv

… = √(14) ∫₀¹ ∫₀² (3u + v + 1) du dv

… = √(14) ∫₀¹ (3/2 u² + uv + u) |₀² dv

… = √(14) ∫₀¹ (8 + 2v) dv

… = √(14) (8v + 2v²) |₀¹

… = 10 √(14)

Answer:

∠AGB or ∠EGD.

Step-by-step explanation:

∠AGB & ∠EGD make a straight line with ∠BGD which means they're supplementary.

Answer: ∠BGA

Step-by-step explanation:

Starting Angle: ∠BGD

Supplement: ∠BGA

1. The quadratic function for the Area in terms of x: A(x) = 24x.

2. The cross-sectional area is maximized when the depth of the gutter is 0.

3. The maximum cross-sectional area is square inches 0.

To determine the depth of the gutter that maximizes its cross-sectional area and allows the greatest amount of water to flow, we need to follow a step-by-step process.

1. Write a quadratic function for the area in terms of x:

The cross-sectional area of the gutter can be represented as a rectangle with a width of 24 inches and a depth of x. Therefore, the area, A(x), is given by A(x) = 24x.

2. The cross-sectional area is maximized when the depth of the gutter is:

To find the value of x that maximizes the area, we need to find the vertex of the quadratic function. The vertex of a quadratic function in form f(x) = ax² + bx + c is given by x = -b/(2a). In our case, a = 0 (since there is no x² term), b = 24, and c = 0. Thus, the depth of the gutter that maximizes the area is x = -24/(2 * 0) = 0.

3. The maximum cross-sectional area is square inches:

Substituting the value of x = 0 into the quadratic function A(x) = 24x, we get A(0) = 24 * 0 = 0. Therefore, the maximum cross-sectional area is 0 square inches.

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Answer:

Terry's initial amount = £780

Step-by-step explanation:

Given that:

Ratio of Terry's money to Faye's money = 3 : 5

Let,

x be the amount of money.

Terry's amount = 3x

Faye's amount = 5x

Now,

3x + 220 = 5x - 300

220+300 = 5x - 3x

520 = 2x

2x = 520

Dividing both sides by 2

\(\frac{2x}{2}=\frac{520}{2}\\x=260\)

Terry's initial amount = 3x = 3(260) = £780

Hence,

Terry's initial amount = £780

The graph of the proportional relationship is added as an attachment

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

Time = 3 minutes

Supply of water = 12 litres

Using the above parameters, we have the following ordered pairs

(0, 0) and (3, 12)

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) = (0, 0) and (3, 12)

The gradient of the line is then calculated using the following slope equation

gradient = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (0, 0) and (3, 12)

Substitute the known values in the above equation

So, we have the following equation

gradient  = (12 - 0)/(4 - 0)

Evaluate

gradient  = 3

The equation of the line is then calculated as

y = gradient * x

Substitute the known values in the above equation

So, we have the following equation

y = 3 * x

Evaluate the products

y= 3x

Hence, the line equation is y= 3x

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The Kristal's answer is incorrect, and the correct form for 50 x 102 in scientific notation is 5.0 x 103.

Kristal said that 50 x 102 is written in scientific notation. But, this is incorrect as the number should be written as 5.0 x 103.

The reason for this is because in scientific notation, a number is written as a coefficient (a number between 1 and 10) multiplied by 10 raised to a power.

Explanation:Scientific notation is a way of writing very large or very small numbers in a compact form. In scientific notation, a number is written as a coefficient (a number between 1 and 10) multiplied by 10 raised to a power.

For example, the number 500 can be written as 5 x 102 in scientific notation.

Here, the coefficient is 5 and the power of 10 is 2.To write 50 x 102 in scientific notation, we need to convert it into a number between 1 and 10. To do this, we can divide 50 by 10 to get 5, and multiply 102 by 10 to get 103. So, 50 x 102 = 5 x 103 in scientific notation.

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Answer:

x - 1 = 150/6.5    (because 150/6.5 = 23 spaces, it will need an end post.)

23 spaces needs 24 posts

In the proportion (5x + 1):3 = (2x + 2):7, the value of x is -1/29.

In the proportion (6x):(4x) = 7, there is no value of x that satisfies the proportion.

To find the value of x in the given proportions, let's solve them one by one:

(5x + 1) : 3 = (2x + 2) : 7

To solve this proportion, we can cross-multiply:

7(5x + 1) = 3(2x + 2)

35x + 7 = 6x + 6

Subtracting 6x from both sides and subtracting 7 from both sides:

35x - 6x = 6 - 7

29x = -1

Dividing both sides by 29:

x = -1/29

Therefore, the value of x in the first proportion is -1/29.

(6x) : (4x) = 7

To solve this proportion, we can simplify the left side:

6x / 4x = 7

Dividing both sides by 2x:

3/2 = 7

This equation is not true, as 3/2 is not equal to 7.

Therefore, there is no value of x that satisfies the second proportion.

In summary, the value of x in the proportion (5x + 1) : 3 = (2x + 2) : 7 is -1/29, and there is no value of x that satisfies the proportion (6x) : (4x) = 7.

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Step-by-step explanation:

since the whole biggest triangle is a right triangle so ,

\( {x}^{2} = {20}^{2} + {18}^{2} \\ {x}^{2} = 400 + 324 \\ {x}^{2} = 724 \\ x = \sqrt{724} = 26.907 = 26.91\)

a. The graph represents a proportional relationship.

b. The graph does not represent a proportional relationship.

c. The graph does not represent a proportional relationship.

d. The graph represents a proportional relationship.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable exists.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero presented as follows:

y = kx.

Hence graphs a and d represent proportional relationship, as they have intercepts at the origin.

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\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ \end{cases}\implies y=a(~~x-0~~)^2 + 0\hspace{4em}\textit{we also know that} \begin{cases} x=3\\ y=18 \end{cases} \\\\\\ 18=a(3-0)^2+0\implies 18=9a\implies \cfrac{18}{9}=a\implies 2=a \\\\\\ y=2(~~x-0~~)^2 + 0\implies \boxed{y=2x^2}\)

The number of standard deviations from the mean that include all

data values is two.

From the gathering of information, we will see that the minimum worth is $19.95 and also the most worth is $29.95. So , we would like to seek out the amount of normal deviations, let's decision it "a" , such that\(\overline x $\color \ - a\cdot\sigma \le 19.95}\) and   \(\overline x $\color \ +a\cdot\sigma \geq 29.95}\)

Use the given values of mean  \(\overline x\) and normal deviation (σ) to notice the worth of "a".

         \(\overline x $\color \ - a\cdot\sigma \le 19.95}\\25.07\ - 2.62a \leq 19.95\\5.12\leq 2.62a\\1.9541\leq a\)

On rounding off we get a = 2

Checking another inequality

         \(\overline x $\color \ + a\cdot\sigma \geq 29.95}\\25.07 \ + 2(2.62) \geq 29.95\\25.07 + 5.24 \geq 29.95\\30.31\geq 29.95\)

Thus , 2 standard deviation include the all values from the given set of data .

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