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The longest piece of wood that could fit in your trunk to build a gate for the backyard is 60.65 inches.

The length of the diagonal of the cuboid is found out using the following formula.

[tex]D=\sqrt{l^2+b^2+h^2}[/tex]

Here, (l) is the length of the cuboid, (w) is the width, and (h) is the height of the cuboid.

The wood has to buy to build a gate for backyard. The car trunk has the following dimensions (47 inches by 33 inches by 19.5 inches). Here, we have,

The longest piece of wood which fits is equal to the length of diagonal of cuboid. Put the values in the formula,

[tex]D=\sqrt{47^2+33^2+19.5^2}\\D=\sqrt{3678.25}\\D=60.65\rm\; in[/tex]

Thus, the longest piece of wood that could fit in your trunk to build a gate for the backyard is 60.65 inches.

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Using the conversion of exponent to power, the equivalent expression is given as follows:

[tex]\frac{\sqrt{x}}{\sqrt[4]{y}z^2}[/tex]

It happens according to the following rule, with the denominator as the root and the numerator as the exponent:

[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]

In this problem, we are given the following expression:

[tex]x^{\frac{1}{2}}y^{-\frac{1}{4}}z^{-2}[/tex]

Negative exponents go to the denominator, hence the equivalent expression is given by:

[tex]\frac{\sqrt{x}}{\sqrt[4]{y}z^2}[/tex]

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The function that describes the area of the rectangle in terms of one of the sides is A = 12L - L².

The perimeter of the rectangle is given as 24. Therefore, the area in terms of one of its side will be:

A = L(24 - 2L)/2

A = L(12 - L)

A = 12L - L²

The length side for the maximum area will be 6 and 6. The maximum area of the rectangle will be:

= 6 × 6

= 36

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Step-step Explanation:

Let's know how to round any number nearest to tens (Rules):-

We know tens place in any no. from left is at second place and number right to tens place need to be changed as:-

Answer:

790

Step-by-step explanation:

Answer:

7x5x2 = 70

There are no other smaller factors that include all of the given numbers

Answer:

arc = 9π units

Step-by-step explanation:

the arc is half the circumference of the circle, then

arc = [tex]\frac{1}{2}[/tex] × 2πr = πr , then

arc = π × 9 = 9π

Answer:

[tex]\boxed{\tt 9\pi }[/tex]

Step-by-step explanation:

What we want to find here is the arc length of 1/2 of a circle, we'll start by finding the of the circle.

Step 1:- find the circumference of the circle →

[tex]\boxed{\sf Circumference\; of\; the \:circle=2\pi r}[/tex]

[tex]\tt 2\pi \times 9[/tex]

[tex]\tt 9\times 2\pi[/tex]

[tex]=\tt 18\pi[/tex]

Step 2:- find the arc length of 1/2 of the circle →

The arc length is 1/2 of the circumference of the circle:-

[tex]\boxed{\sf Circumference \; of \;\cfrac{1}{2}\; of\; the \; circle=\cfrac{1}{2}\times 18\pi}[/tex]

[tex]\tt \cfrac{18}{2} \pi[/tex]

[tex]\boxed{\tt 9\pi}[/tex]

Therefore, the arc length of the semicircle is 9π.

Answer:

16 x ^ -1/5

Step-by-step explanation:

Answer:

B. 15/4 z + 12

Step-by-step explanation:

Apply the distributive property and multiply 3/4 by 5z and by 16.

3/4 (5z + 16) = 3/4 × 5z + 3/4 × 16 = 15/4 z + 12

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Question reads....}[/tex]

[tex]\large\text{Write an expression that is equivalent to }\rm{\dfrac{3}{4}(5z + 16).}[/tex]

[tex]\huge\textbf{In order to answer this question, you}\\\huge\textbf{have to distribute. If you're unsure what}\\\huge\textbf{the distributive property formula is, it is:}[/tex]

[tex]\large\textsf{a(b + c)}[/tex]

[tex]\rightarrow\large\textsf{a}\times\large\textsf{{b + a}}\times\large\textsf{c}[/tex]

[tex]\rightarrow\large\textsf{ab + ac}[/tex]

[tex]\huge\textbf{Now, that we have that much}\\\huge\textbf{information out of the way, we can}\\\huge\textbf{now begin to answer the given question.}[/tex]

[tex]\huge\textbf{Here's what your equation looks like:}[/tex]

[tex]\mathsf{\dfrac{3}{4}(5z + 16)}[/tex]

[tex]\huge\textbf{Solving it:}[/tex]

[tex]\mathsf{\dfrac{3}{4}(5z + 16)}[/tex]

[tex]\rightarrow\mathsf{\dfrac{3}{4} \times 5z + \dfrac{3}{4} \times 16}[/tex]

[tex]\rightarrow\mathsf{\dfrac{15}{4}z + 12}[/tex]

[tex]\huge\textbf{Therefore, your answer is most likely:\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] }[/tex][tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{Option\ B. \dfrac{15}{4}\mathsf{z} + 12}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer: c ???????????????????

Step-by-step explanation:

The location final image from the mirror, which is made when an object is placed 1.00 m to the left of the lens, is 0.58 right to the mirror.

The focal length of the lens is the length of the distance between the middle of the lens to the focal point.

It can be find out using the following formula as,

[tex]-\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}[/tex]

Here, (v)is the distance of the image, (u) is the distance of the object, and (f) is the focal length of the lens.

The lens and mirror in the Figure are separated by 1.00 m and have focal lengths of +79.2 cm and -50.6 cm, respectively. Change the units of focal length in meters,

[tex]f_l=79.2\text{ cm=0.792 m}\\f_m=-50.6\text{ cm=0.506 m}[/tex]

An object is placed 1.00 m to the left of the lens. Put the value in the lens formula as,

[tex]-\dfrac{1}{v_l}+\dfrac{1}{1}=\dfrac{1}{0.792}\\-\dfrac{1}{v_l}=\dfrac{1}{0.792}-1\\v_1=3.81[/tex]

The distance of the image made by lens is 3.81 meters. The distance of this image from the mirror is,

[tex]u_2=3.81-1\\u_2=2.81\rm \; m[/tex]

This distance is work as object distance for the mirror. The focal length of mirror is -0.506 m. Thus, the location of the final image is,

[tex]-\dfrac{1}{v_2}+\dfrac{1}{3.81}=\dfrac{1}{-0.506}\\\dfrac{1}{v_2}=-\dfrac{1}{3.81}-(-\dfrac{1}{0.506})\\v_2=-0.58[/tex]

Thus, the location final image from the mirror which is made when an object is placed 1.00 m to the left of the lens, is 0.58 right to the mirror.

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Answer: correct

Step-by-step explanation theoretically it is indeed correct by acknowledging by surface+height which both angles are evenly congruent now

in terms of the 990 Degree angle i know for a fact that it corresponds with it no more to say.

Answer:

(A)  " Look at the graph of the relationship.  Find the y-value of the point that corresponds to x = 1 .   That value is the unit rate. "

Step-by-step explanation:

The statement is true is: A 16,000-BTU air conditioner meets the manufacturer recommendation.

Option A

BTUs=16,000/(20 feet×20 feet×8 foot)

BTUs=16,000/3200 feet

BTUs=5 BTUs

Option B

BTUs=14,000/(10 feet×20 feet×8 foot)

BTUs=14,000/1600 feet

BTUs=8.75 BTUs

Option C

BTUs=20,000/(20 feet×40 feet×8 foot)

BTUs=20,000/6400 feet

BTUs=3.125 BTUs

Option D

BTUs=12,000/(15 feet×10 feet×10 foot)

BTUs=12,000/1500 feet

BTUs=8 BTUs

Based on the calculation above only option A with 5 BTUs fall between 4 and 6 BTUs.

Therefore the statement is true is: Option A.

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Answer:

.6 x 10^3   = 6000

Step-by-step explanation:

4.8 E5  / 8 E2   = .6 E3

Answer:

21.2 square meters

Step-by-step explanation:

The area of a parallelogram is base • height.

So:

1. Calculate the area of what you can get for $50. 5 • 212 = 1060 square meters.

2. Now you divide the first price ($50) by the desired price ($1). This one is easy because 50 / 1 = 50, but I'm putting this here for future reference in case you need to solve a problem that has a desired price that's greater than $1.

3. Divide the answer to step one by the answer to step two to get the area you can have painted for $1. 1060 / 50 = 21.2 square meters.

The result of the exponential expression is 81

Indices are written in term of exponents

According to the expoenent law of indices

a^4 = a * a * a * a

Given the expression

(-3)^4

This means the product of -3 in four places. Mathematically

(-3)^4 = -3 * -3 * -3 * -3
(-3)^4 = 9 * 9
(-3)^4 = 81

Hence the result of the exponential expression is 81

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Answer:f^-1(x) = 1/3x + 5/3

Step-by-step explanation:

Answer:

0.4 or 2/5

Step-by-step explanation:

If head is 18/30, then that means that tails must be 12/30, since they must add up to one whole.

Reduce it to simplest terms: 2/5 or 0.4

Answer:

the answer is B . 72√2 look at the picture I added

Answer:

13.69%

Step-by-step explanation:

793-54=739

739/54=13.68518519

Answer:

abc are correct

Step-by-step explanation:

i took the test

Answer:

90%

Step-by-step explanation:

We know that 9 of 10 people were less than 65. It means, that if they would ask 100 people, the number would be 90.

The percent of population less than 65 is 90%

Ninety percent of the population was less than 65.

The percentage is defined as the ratio expressed as a fraction of 100.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

The operator that perform arithmetic operation are called arithmetic operators .

According to data from the U.S. Census Bureau,

Approximately 9/10 of the U.S population was less than 65 years old.

Nine out of ten people, as far as we know, were under 65.

In other words, if they surveyed 100 persons, the answer would be 90.

Hence, Ninety percent of the population was less than 65.

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Here are the completed tables

Gallons Quart

1               4

2               8

5               20

7               28

Quart    Pint

1             2

3             6

6           12

8            16

Pint  Cup

1          2

3         6

5        10

9       18

The capacity of the objects are:

Swimming pool - 5000 gallons

Watering can - 8 quarts

Juice box - 2 pints

Soup bowl - 2 cups

The measurement from least to greatest is: 6 pints, 2 galloons, 18 cups, 6 quart.

In order to fill the tables, the unit of conversion has to be known:

1 gallon = 4 quart

1 quart = 2 pints

6 pint / 2 = 3 quarts

12 / 2 = 6 quarts

8 x 2 = 16 pints

In order to order the measurement, all the measurements have to be in the same units. All the units would be converted to cups

1 quart = 4 cups

4 x 6 = 24 cups

1 galloon = 16 cups

16 x 2 = 32 cups

1 pint = 2 cups

6 x 2 = 12 cups

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Answer:

60%

Step-by-step explanation:

There are 50 people in the class the total.

30/50 are boys. .6=60%

Answer:

Each person received 3/10 of pie

Step-by-step explanation:

3 dived by 10 equals 0.3 which is equivalent to 3/10

Answer:

[tex]x=\frac{3\pi }{4} ,\frac{7\pi }{4}[/tex]

If wrong then [tex]x=-\frac{\pi }{4}.[/tex]

Step-by-step explanation:

[tex]tan^2(x)-tan(x)=0[/tex]

Factor out the tan(x).

[tex]tan(x)*(tan(x)-1)=0[/tex]

Solve for x.

[tex]tan(x)\neq 0\\[/tex] thus only option is tan(x)-1=0

[tex]tan(x)-1=0\\tan(x)=1\\[/tex]

x=tan^-1(1)⇒

Either it is Quadrant 2 or 4.

[tex]x=\frac{3\pi }{4} ,\frac{7\pi }{4}[/tex]

If the teacher says its wrong. Then that could only mean that its range of tan(x) is between [tex]-\frac{\pi }{2} < x < \frac{\pi }{2}[/tex] thus it's only on quadrant 4. [tex]x=-\frac{\pi }{4}[/tex]

Answer:

88

Step-by-step explanation:

angles on a straight line add up to 180

180-120=60

angles in a triangle add up to 180

60+32=92

180-92=88

angle 1=88

Answer:

  (d)  x = 3  or  x = 4

Step-by-step explanation:

The zero product property can be used to find the solutions to a polynomial equation when it is written in factored form.

__

Your polynomial can be put in factored form like this:

  x² +12 = 7x . . . . . given

  x² -7x +12 = 0 . . . . . standard form

  (x -3)(x -4) = 0 . . . . . factored form*

  x = 3  or  x = 4 . . . . . . values of x that make the factors zero

_____

* The constants in the binomial factors must have a sum of -7 and a product of +12. It is often convenient to find them by listing factor pairs of 12:

  12 = (-1)(-12) = (-2)(-6) = (-3)(-4)

Negative factors are used because we know the sum must be negative. Both have the same sign so their product is positive. The sums of the pairs shown are -13, -8, -7. The last pair is what we're looking for.

Start by deciding how long is your fence going to be and how much space you want between posts. Typically, the post space is somewhere between 6 and 8 feet; or 2 and 5 meters, depending on your preference.

Answer: the answer would be 6-8 feet

Step-by-step explanation: the guy below me explains it well