Please help with 3 questions thank you.

The area of the rectangle is 72 square ft and this can be determined by using the formula of the area of the rectangle.

Given :

Length is 6 ft more than its width.

The following steps can be used in order to determine the area of the rectangle when its width is 12 ​ft:

Step 1 - Let the length of the rectangle be 'L' and the width of the rectangle be 'W'.

Step 2 - According to the given data, length is 6 ft more than its width that is:

L = 6 + W

Step 3 - The formula of the area of the rectangle is given below:

A = LW

Step 4 - Substitute the value of 'L' in the above expression.

A = (6 + W)W

Step 5 - Now, at W = 6ft the area of the rectangle becomes:

A = (6 + 6)6

A = 72 square ft.

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Answer:

75 105 75 in that order

Step-by-step explanation:

Without a specific figure provided, it is not possible to determine the measures of angles x, y, and z.

In order to find the measures of angles x, y, and z in the given figure, we need more information about the figure. Without any specific figure mentioned in the question, it is not possible to determine the values of those angles. Please provide more context or a specific figure for further assistance.

[tex]\( y \) is the value obtained by substituting \( x = 60 \)[/tex] into the given function.

To determine [tex]\( y \) when \( x = 60 \)[/tex], we need to refer to the specific function or equation provided. This function could be linear, quadratic, exponential, or any other mathematical expression involving [tex]\( x \) and \( y \)[/tex]. Let's consider a hypothetical linear equation [tex]\( y = mx + b \)[/tex] for illustration purposes.

In the case of a linear equation, [tex]\( m \) represents the slope, and \( b \)[/tex] is the y-intercept. When [tex]\( x = 60 \),[/tex] we substitute this value into the equation to find [tex]\( y \). For example, if \( y = 2x + 5 \), then \( y = 2 \times 60 + 5 = 125 \).[/tex] Therefore, the final answer is [tex]\( y = 125 \) when \( x = 60 \)[/tex] in this particular linear equation.

It's crucial to emphasize that the specific nature of the function or equation will dictate the process of finding [tex]\( y \) for a given \( x \).[/tex] This explanation serves as a general guide, and the procedure may vary based on the mathematical form provided. Whether it's a polynomial, trigonometric, or logarithmic function, the fundamental principle remains consistent: substitute the given [tex]\( x \) value to obtain the corresponding \( y \) value.[/tex]

The value of y when x = 60 + 24y is y = 2.

Explanation:

In the given equation, x = 60 + 24y, we are asked to find the value of y when x is expressed in terms of y. To solve for y, we'll isolate the variable on one side of the equation.

Isolating y:

Subtract 24y from both sides of the equation to collect all y terms on one side:

x - 24y = 60

Solving for y:

Now, isolate y by dividing both sides by -24:

y = 60 / -24

y = -5/2

However, the value of y obtained from the calculation above is not the final answer. We made a mistake in the process of isolating y. Let's correct that:

Correction:

Subtract 24y from both sides correctly:

x - 24y = 60 - 24y

Now, add 24y to both sides:

x = 60

Subtract x from both sides:

-24y = 60 - x

Divide by -24 to isolate y:

y = (60 - x) / -24

Final Answer:

Simplifying the expression further:

y = (x - 60) / 24

Now, we can substitute the given value of x (x = 60 + 24y) back into the equation:

y = (60 + 24y - 60) / 24

y = 24y / 24

y = 1

However, there's one more adjustment needed. We forgot to account for the initial 24y in the expression:

y = 1 + 1

y = 2

Therefore, the correct and final answer is y = 2 when x = 60 + 24y.

Complete Question:

What is y when x = 60+ 24y?

The value of the digit '7' in the number 43782 is 7000, because it's at the thousands place.

In the number 43782, the value of the digit 7 is determined by its place in the number. In our decimal number system, each digit's value depends on its position starting from the right. If we start counting from right to left, the 1st place is units or ones place, 2nd place is tens place, 3rd place is hundreds place, 4th place is thousands place and so on. Here, the number '7' is located in the thousandth place. Therefore, the value of the digit 7 in 43782 is 7000.

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Answer:

21.

Step-by-step explanation:

We have been given that Reaner Recycling shreds 7/8 ton of aluminum each day.The machines can shred 1/24 ton aluminum per cycle.

To find the number of cycles needed to shred the aluminum, we will divide amount of aluminium by 1/24 as:

[tex]\text{Number of cycles}=\frac{7}{8}\div \frac{1}{24}[/tex]

Convert into multiplication problem by flipping the 2nd fraction:

[tex]\text{Number of cycles}=\frac{7}{8}\times \frac{24}{1}[/tex]

[tex]\text{Number of cycles}=\frac{7}{1}\times \frac{3}{1}[/tex]

[tex]\text{Number of cycles}=7\times 3[/tex]

[tex]\text{Number of cycles}=21[/tex]

Therefore, 21 cycles will be needed to shred the aluminum.

Answer:

y = 4x - 14 is equivalent from of y = 4x - 14.

Step-by-step explanation:

Given : 4x-y= 14

To find : Which is an equivalent form of the equation.

Solution : We have given 4x - y = 14.

We can write it in slope intercept form y = mx  + b

Where, m = slope , b = y intercept.

4x - y = 14.

On subtracting both sides by 4x

- y= -4x + 14.

On dividing both sides by -1.

y = 4x - 14.

Therefore, y = 4x - 14 is equivalent from of y = 4x - 14.

we know that

If △JKL≅△QRS

then

the corresponding angles are congruent

so

m∠Q=m∠J

m∠R=m∠K

m∠S=m∠L

we have

m∠J=[tex]37\°[/tex]

therefore

the answer is

m∠Q=[tex]37\°[/tex]

Answer:

m∠Q = 37°

Step-by-step explanation:

It has been given that ΔJKL ≅ ΔQRS

∠J = 37° and ∠K = 105°

Since these triangles are congruent so we will apply the condition of ASA (theorem of congruence)

In ΔJKL and ΔQRS sides JK and QR along with their corresponding angles will be equal.

Side JK = side QR

and ∠K = ∠R = 105°

∠J = ∠Q = 37°

Therefore m∠Q = 37° will be the answer.

Final answer:

To solve the equation 5x^2-40=0 using square roots, start by isolating x^2, divide by 5 and then apply the square root. The solutions are x = 2√2 and x = -2√2.

Explanation:

To solve the equation 5x^2-40=0 using square roots, we can start by isolating x^2 by adding 40 to both sides of the equation, resulting in 5x^2 = 40. Next, divide both sides of the equation by 5 to get x^2 = 8. Now, we can take the square root of both sides to solve for x. Since the solution involves a square root, we need to include both the positive and negative square root:

x = ±√8

Simplifying the square root of 8, we have:

x = ±√(4*2)

x = ±√4 * √2

x = ±2 * √2

So, the solutions to the equation 5x^2-40=0 are x = 2√2 and x = -2√2.

The length of the shorter base of the trapezoid is found by solving the equation generated by using the formula for the area of a trapezoid. After finding this length, it is substituted into the equation representing the length of the longer base to find its value, which is 76 feet.

To solve this problem, let's denote the length of the shorter base of the trapezoid as 'a'. According to the problem, the length of the longer base is then 5a - 19. We also know that the area of a trapezoid is given by the formula: (1/2) * (sum of lengths of bases) * height. So, by substituting the given trapezoid area (477 ft squared) and height (18 ft) into the this formula, we get: 477 = 1/2 * (a + (5a - 19)) * 18. Solving this equation will give us the value of 'a'. As calculating 'a' we find it to be 19. After that, we insert 'a' into the longer base equation: 5a - 19, we find the length of the longer base to be 76 ft.

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The area of the segment of circle 'C' is 353.66 sq. units.

Therefore, option (A) is the correct answer.

"It is a region bounded by the chord and the corresponding arc lying between the endpoints of the chord."

[tex]A = (\frac{1}{2} ) \times r^2\times [(\frac{\pi}{180}) \theta - sin \theta][/tex]

where, angle is measured in degree

For given example,

radius r = 24,

angle [tex]\theta[/tex] = 120°

In given diagram, the area of the segment of circle is given by the shaded part.

Using the formula of the area of the segment of the circle,

⇒ [tex]A = (\frac{1}{2} ) \times r^2\times [(\frac{\pi}{180}) \theta - sin \theta][/tex]

⇒ [tex]A = (\frac{1}{2} ) \times (24)^2\times [(\frac{\pi}{180} \times 120) - sin(120)][/tex]

⇒ [tex]A = 288\times [\frac{2\pi}{3} - 0.87][/tex]

⇒ [tex]A=353.66[/tex] sq. units.

Therefore, the area of the segment of circle 'C' is 353.66 sq. units.

Therefore, option (A) is the correct answer.

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Mary gets paid $2,365.83 on a semimonthly period basis.

Mary gets around $56,780 per year.

To answer this question, you need to divide the annual salary by the number of semimonthly periods we have in a year.

There are 12 monthly periods. Semi means half so a month has 2 semi periods.

The number of semimonths in a year are:

= 12 months x 2

= 24 semimonths

Mary's semimonthly pay is therefore:

= Annual salary / Number of semimonthly periods

= 56,780 / 24

= $2,365.83

In conclusion, Mary's semimonthly pay is $2,365.83.

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