What is the equation
in slope-intercept
form of the line that
passes through the
points (-4, 20) and
(2,-34)?

Answer:

The dimensions of the square, that will result in a box of maximum volume is a square with side length of approximately 1.585 inches

Step-by-step explanation:

The  given dimension of the steel sheet are;

The width = 8.5 inches

The length = 11 inches

Let 'x' represent the side length of the squares cut out, we have;

The length of the box formed, l = 11 - 2·x

The width of the box formed, w = 8.5 - 2·x

The height of the box, h = x

The volume of the box, V = (11 - 2·x) × (8.5 - 2·x) × (x) = 4·x³ - 39·x² + 93.5·x

The maximum or minimum volume is found from dV/dx = 0 at max. or min.

dV/dx = d(4·x³ - 39·x² + 93.5·x)/dx = 12·x² - 78·x + 93.5 = 0

Which gives;

x = (78 ± √((-78)² - 4×12×93.5))/(2 ×12)

x = 4.915 or 1.585

When x = 4.915, V = 4 × 4.915³ - 39 × 4.915² + 93.5 × 4.915 = -7.65

When x = 1.585, V = 4 × 1.585³ - 39 × 1.585² + 93.5 × 1.585 = 66.15

Therefore, the local maximum occurs at x ≈ 1.585

Therefore, the dimensions of the square, 'x' that will result in a box of maximum volume is x ≈ 1.585 inches.

Answer:

The answer is A.

Y=64x²

X=64y²

X/64=y2

Then y = + or - root of x /8

Answer:

55 inches

Step-by-step explanation:

4 feet x 12 inches per foot = 48 inches + 7 inches = 55 inches

Answers:   49,   1,   49

Those values go in the blanks from left to right

=====================================================

Explanation:

The rule we use is x^(-k) = 1/(x^k)

That means if we're evaluating something like 7^(-1), then it's the same as 1/(7^1) = 1/7 which explains how x = -1 leads to y = 1/7.

Similarly, 7^(-2) = 1/(7^2) = 1/49 is the y value when x = -2. So you'll type 49 into the first box to fill in that missing denominator.

Raising any nonzero value to the zeroth power leads to 1. That rule is x^0 = 1 where x can be anything you want but it can't be zero. Therefore 7^0 = 1 goes in the second box.

Lastly, 7^2 = 7*7 = 49 will go in the third box.

The required value of the given expression is 6x3 - 13x2 - 13x + 20. Option B is correct.

A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the monomial, binomial and trinomial, etc. ax+b is a polynomial.

here,
= (3x² + x - 4)(2x - 5)
= [6x³-13x² - 13z + 20]

Thus, the required value of the given expression is 6x3 - 13x2 - 13x + 20. Option B is correct.

Learn more about polynomial functions here:

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Answer:

$10,400

Step-by-step explanation:

Step-by-step explanation:

a)

[tex]\sin^{2}x + \cos^{2}x = 1[/tex]

Dividing both sides by sin^2x, we get

[tex]1 + \frac{\cos^{2}x }{ \sin^{2}x} = \frac{1}{\sin^{2}x } [/tex]

The 2nd term on the LHS is simply cot^2x and the RHS is simply csc^2x

[tex]1 + \cot^{2}x = \csc^{2}x[/tex]

b)

[tex]2 \sin x = 1[/tex]

[tex] \sin x = \frac{1}{2} [/tex]

[tex]x = \sin^{ - 1} (\frac{1}{2}) = \frac{\pi}{6} [/tex]

You can also graph it to arrive at the solution.

Did u get help

On you question?

Answer: x^2 (the ^ represents that the next number is an exponent)

Step-by-step explanation:

Any number squared (to the power of 2) is just itself multiplied by itself. Remember, multiplication is repeated addition and exponents are repeated multiplication.

Answer:

A) 24

Step-by-step explanation:

Answer:

m = 24

Step-by-step explanation:

Answer:

$33750

Step-by-step explanation:

Replace t with 2.  The correct formula is

[tex]60000(.75)^t[/tex]   (t is an exponent)

With t = 2, the value of the truck is

[tex]60000(.75)^2=33750[/tex]

Answer:

its basically the relationship between sets of numbers. the anwser is D if the line on the graph is curved it is a function and if the number repeat on the x value it is a function.

-by-step explanation:

Add 1.50 to each time the price goes up

Step-by-step explanation: Multiply by two each time and you will have your answer 1 hot dog is 1.50 two are 3.00 use that method and you will have the correct answer

Answer:

1/3 chance she will chose a Mystery Book.

Step-by-step explanation:

I hope This helps?

Total= 18

mystery=6

6/18= 1/3

Answer:

the answer is 1/3 or 6 out of 18

Answer:

1

Step-by-step explanation:

depends if you have a table , to pick the right one always choose a one that pass more through and between the points and the one that is straight

Answer:  The Real answers are 1) ✔ skewed left and 2) ✔ 1-3

Step-by-step explanation:

Please mark me brainliest

I need 3 more to move to a higher level but

i'm just glad to help.

Answer:

The answer is "A mean of 0 and a standard deviation of 1".

Step-by-step explanation:

The standard answer of its following formula is calculated by:

[tex]\to z=\frac{X-\mu}{\sigma}[/tex]

Its standard score relates to the sampling distribution with the normal distribution average standard variation of 0 and 1, correspondingly. The mean for a standard scoring is 0, and the normal deviation is 1. that's why the mean=0, standard deviation=1.

Figure 1

Since the diameter is 8, this cuts in half to the radius of r = 4. Plug the given values into the cone volume formula below

V = (1/3)*pi*r^2*h

V = (1/3)*pi*(4)^2*4

V = (64/3)pi  ..... exact volume in terms of pi

V = (64/3)*3.14

V = 66.98667 .... approximate volume when using pi = 3.14

========================================================

Figure 2

V = volume of cylinder

V = pi*r^2*h

V = pi*4^2*4

V = 64pi ..... exact volume

V = 64*3.14

V = 200.96 .... approximate volume when using pi = 3.14

========================================================

Figure 3

b and h* are dimensions along the bottom face, aka floor

h is the height or vertical dimension of the 3D room

V = volume of rectangular prism = volume of 3D room

V = length*width*height

V = (b)(h*)(h)

V = (32)(12)(4)

V = 1536 is the exact volume

There is no approximate volume for this figure because the result above is an integer.

========================================================

Combining the figures

Adding up the volumes for figures 1 through 3 gets us

(64/3)pi + 64pi + 1536 = (256/3)pi + 1536

The exact total volume in terms of pi is (256/3)pi + 1536

If we used pi = 3.14, then it leads to

(256/3)pi + 1536 = (256/3)*3.14 + 1536 = 1803.94667

The approximate total volume of all three figures combined is roughly 1803.94667 cubic units

Answer:

Time taken to elapse the remaining $861  = 10.25 days

Step-by-step explanation:

Assuming that I am spending at a rate of -x dollars per day

Let initial amount be A

The rate of expenditure = 1281-861/5 = 84 dollars per day

Time taken to elapse the remaining $861 = $861/$84 per day

= 10.25 days

Answer:

8 quarts, in 2 gallons

Step-by-step explanation:

The inequality equation is x ≥ ( by - c - d ) / a

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

by - d ≤ ax + c    be equation (1)

On simplifying the equation , we get

Subtracting c on both sides of the equation , we get

by - d - c ≤ ax

And , ax ≥ by - d - c

Divide by a on both sides of the equation , we get

x ≥ ( by - c - d ) / 2

Hence , the inequality is x ≥ ( by - c - d ) / a

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Answer:

5 + 2√6 or 9.898979

Step-by-step explanation:

(√3 + √2) (√3 + √2)

= 5 + 2√6

decimal = 9.898979

Answer:

I’ll put a picture because I can’t like write down the answer…. So yeah.

Step-by-step explanation:

1) expand expression: (sqrt3 + sqrt2)^2

Then calculate: 3 + 2sqrt6 + 2

Andddd: 5 + 2sqrt6

* sqrt: square root

I hope this helps! Good luck :)

Answer: 5.5 inches, 3.5 inches

Step-by-step explanation:

Given

Barry wants to make a drawing i.e. half the size of original

The length and width of the original drawing are  11 inches and 7 inches respectively.

So, the intended drawing is obtained by multiplying the original dimensions by [tex]\frac{1}{2}[/tex]

The length of barry's drawing is

[tex]\Rightarrow 11\times \frac{1}{2}\\\\\Rightarrow 5.5\ \text{inches}[/tex]

The breadth of barry's drawing

[tex]\Rightarrow 7\times \frac{1}{2}\\\\\Rightarrow 3.5\ \text{inches}[/tex]

Answer:

Look at the image.

Step-by-step explanation:

(36 ÷ 4) - (36 ÷ 9)

9 - 4

5

(8 × 3) - 12 = 12

24 - 12

12

Answer:

4/5

Step-by-step explanation:

5cosA=4

divide both sides by 5

cosA=4/5

Answer:

yes

Step-by-step explanation:

yes