Find the equation of the line passing through the points (8, -16) and (1, 5).

Answer: 8.4 feet

Step-by-step explanation:

Given: Lumber required for each shelf = \(8\dfrac{3}{4}\ inches\)

For each base side = \(12\dfrac12\ inches\)

For each door stile = \(29\dfrac18\ inches\)

Total lumber required = \((2\times 8\dfrac34 + 2\times12\dfrac12+2\times29\dfrac18)\ \ in.\)

\(=(2\times\dfrac{35}{4}+2\times\dfrac{25}{2}+2\times\dfrac{233}{8})\ in\\\\= (\dfrac{35}{2}+25+\dfrac{233}{4})\ in.\\\\=\dfrac{403}{4}\ in. =\dfrac{403}{4}\times\dfrac1{12}\ feet \ \ \ \ [1 feet = 12 \ in.]\\\\\approx8.4\ feet\)

Hence, we will need 8.4 feet lumber.

Answer

its scale factor is ​4/3 and 0.75

Step-by-step explanation:

The piecewise function for this problem is defined as follows:

B.

The function is a piecewise function, as the function has different definitions based on the input of the function.

The different definitions for the graph are given as follows:

To the left of x = 0, we have a linear function with intercept of 2 and slope of 2, hence it is given as follows:

y = 2x + 2, x ≤ 0.

To the right of x = 0, we have a linear function with intercept of 4 and slope of -4/3, hence it is given as follows:

y = -4/3x + 4, x > 0.

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The value of y is 48

y= kx

let's solve for k which is the constant

y= 8 , x= 4

k= 8/4

k= 2

Next is to calculate the value of y when x is 24

y = 2 × 24

y= 48

Hence the value of y is 48

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Answer:

the percent change is 80%

Step-by-step explanation:

5 is 20% of 25 then that means that the percent change is 80%

The values of the two integers are -43 and -143.

Let the value of the smaller integer be "x".

Since, the sum of two integers is -186.

Smaller integer + Larger integer = -186

x + ( 3x - 14 ) = -186

Solve for x

x + 3x - 14 = -186

4x - 14 = -186

4x = -186 + 14

4x = -172

x = -172/4

x = -43

Hence;

The smaller integer = x = -43

The largere integer = 3x - 14 = 3(-43) - 14 = -143.

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Answer:

The answer is pretty simple it's 12+10

Step-by-step explanation:

Answer:

x = 9 and y = 15

Step-by-step explanation:

this is the answer because each side is equivalent to the parallel line so y would be whatever is across from it

Answer:

y=15

x=9

Step-by-step explanation:

they are parallel and equal to the opposite sides

Answer:

5 miles

Step-by-step explanation:

This is because to find the amount of miles in an hour, you have to multiply 1/5 by 25. This is one-fifth of 25, which is five.

Answer: y=3x-2

Step-by-step explanation:

3y-9x=-6

First you will need to add 9x to the other side so your equation will look like 3y=9x-6. Then you need to divide all the numbers by 3. So 3y divided by 3 and 9 divided by 3 and -6 divided by 3. Your final answer should be y=3x-2.

Answer:

This equation in slope intercept form would be y = 3x - 2

Step-by-step explanation:

The following is how to solve this equation:
3y - 9x = -6
+9x +9x
----------------------
3y = 9x - 6
divide each of the numbers by 3

So the answer is y = 3x - 2

The length of the diameter of the sphere is 30 cm.

The surface area of a sphere is given by the formula:

\(A = 4\pi r^2\)

where A is the surface area and r is the radius of the sphere.

We are given that the surface area of the sphere is 900π cubic cm. Therefore:

\(A = 4\pi r^2 = 900\pi\)

Dividing both sides by 4π, we get:

\(r^2 = 225\)

Taking the square root of both sides, we get:

r = 15

The diameter of the sphere is twice the radius, so:

d = 2r = 30

Therefore, the length of the diameter of the sphere is 30 cm.

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Answer:

  see attached for a sketch

  area = 5 1/3 square units

Step-by-step explanation:

You want the area under the square root curve, above y=0, from x=0 to x=4.

The area is found by integrating a differential of area over appropriate limits. A vertical slice will have hight √x and width dx, so we have ...

  dA = (√x)dx

  A = ∫(√x)dx

The power rule can be used for the integration:

  \(\displaystyle A=\int_0^4{x^{\frac{1}{2}}}\,dx=\left[\dfrac{x^{\frac{3}{2}}}{\frac{3}{2}}\right]^4_0=\dfrac{2}{3}(4^\frac{3}{2})=\dfrac{16}{3}=\boxed{5\dfrac{1}{3}}\)

The area of the region is 5 1/3 square units.

__

Additional comment

You will notice that the area is bounded by a rectangle 4 units wide and 2 units high, for an area of 4·2 = 8. The area under the parabolic curve is 2/3 of that: 2/3·8 = 16/3 = 5 1/3 square units.

This fraction will be true for any area bounded by a parabola where the vertex is one of the corners of the rectangle.

#95141404393

Answer:

Box 1. 2x

Box 2. -13 (1/3) or (-40/3)

Box 3. 2x

Box 4. (2/3)x

Box 5. 3

Box 6. 3

Box 7. -20

Box order left to right.

Step-by-step explanation:

(5/3)x + (1/3)x = 13 (1/3) + (8/3)x

add numberator ( top number ); keep the denominator the same ( bottom number )

Line 1. (6/3)x or 2x = 13 (1/3) + (8/3)

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

Line 2. -13 (1/3) = (8/3)x - 2x

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

Ex. 3 × (-13) = 39 - 1 = (-40/3)

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

Line 3. (-40/3) = (2/3)x

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

Line 4. (3) (-40/3) = (2/3)x (3)

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

               -40 = 2x

               ÷2     ÷2

Line 5.    -20 = x

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

Sorry if this is a little confusing. I hope this helped!

Step-by-step explanation:

2

-13/1/3 ; 2

2/3

3 ; 3

-40

hope it help

If \(u=x^5+2\), then \(du=5x^4\,dx\), so the integral transforms to

\(\displaystyle \int_{x=-2}^{x=4} x^4 \cos(x^5+2) \, dx = \frac15 \int_{u=-30}^{u=1026} \cos(u) \, du\)

since

\(x = -2 \implies u = (-2)^5 + 2 = -32 + 2 = -30\)

\(x=4 \implies u = 4^5 + 2 = 1024 + 2 = 1026\)

Answer:

Brooke and Tony

Step-by-step explanation:

multiply by 4 Brooke got 64 Tony got 68.

Answer:

39, 40, 41

Step-by-step explanation:

Let x= the first number

x+(x+1)+(x+2)= 120

3x+3=120

x=117/3

x=39

Thus, the three numbers are 39, 40, 41. which sums to 120

The Present value is $6,139.132.

We have,

FV=100000, pmt = 4000, I =5%, n=10

So, The present value formula is

PV=FV / (1 + \(i)^n\)

So, PV =  100, 000 / (1+ 5/100\()^{10\\\)

PV = 100,000 / (1+ 0.05\()^{10\\\)

PV = 100, 000/ (1.05\()^{10\\\)

PV = 100,000 / 1.6288946

PV= $6,139.132

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Answer:

That is not a question, Brainly is an educational app and I suggest you use it that way.

Answer:

1.35

Step-by-step explanation:

10.80 divided by 8

n = 1.35

Part A

\(-12 < 5x - 2 < 13\\\\-12+2 < 5x - 2+2 < 13+2 \ \text{ ... add 2 to all sides}\\\\-10 < 5x < 15\\\\-10/5 < 5x/5 < 15/5 \ \text{ ... divide all sides by 5 to isolate x}\\\\-2 < x < 3\\\\\)

To graph this, we plot open holes at -2 and 3 on the number line. Shade between these open holes to represent values between -2 and 3, but we don't include the endpoints.

See figure 1 below.

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

Part B

Solve the first inequality to get

\(3x < -9\\\\3x/3 < -9/3\\\\x < -3\\\\\)

Now solve the second inequality

\(2x \ge x+1\\\\2x-x \ge x+1-x\\\\x \ge 1\\\\\)

We have \(x < -3 \ \text{ or } \ x \ge 1\)

The graph will have an open hole at -3 and a closed/filled in circle at 1. We shade everywhere but the region between these marked values. The left portion in blue represents stuff smaller than -3; the right portion in red represents values equal to 1 or larger.

See figure 2 below.

The idea of consecutive of an integer n is just adding 1 to n (n+1). Then, you only have to sum 1 to -3 to get "the consecutive" of -3 (-3+1 = -2). Doing that five times, we get six consecutive integers starting from -3.

Note: This is called "defining the set by comprehension" too.

Answer:

24 times greater

Step-by-step explanation:

48,000/2000

Answer:  The correct answer is:  

___________________  

   " 5 [five] quarts of motor oil will cost:  

                →  " $ 4.72 " .

___________________

First method of solving the problem:

Set up a ratio/proportion; in the form of an equation—using fractions— as follows:

___________________

\(\frac{3qt}{2.83} = \frac{5 qt}{x}\) ;  →  in which we are to solve for "x" {value in "dollars".}.

___________________

Now, let's "cross-factor multiply" the values in the equation:

   3*(x) = (2.83) * 5 ;

___________________

Now, simplify—and rewrite the equation:

___________________

   3x = 14.15 ;

___________________

Now, divide Each side of the equation by "3" ;

   to isolation "x" on one side of the equation;

   & to solve for "x" ;

___________________

   3x / 3 = (14.15) / 3 ;

  to get:  x = 4.71666666.... (dollars);

___________________  

Let us round that number up to: "4.72" ;  

   {since: "4.71" ;  is followed by a digit higher than "4" } ;

___________________  

The correct answer is:  

           →  " 5 [five] quarts of motor oil will cost: " $ 4.72 " .

___________________  

Second method of solving this problem:

 1) First:   We treat this problem as a "unit rate" problem;

   {that is; given a numeric quantity per certain numeric value;

     →  we reduce/solve for what that Particular Quantity is,

                       per that particular [Single] Unit numeric value.

     → For this particular problem; we are given:

            $ 2.83 ["2.83 dollars"] ;  per " 3 quarts " ;

         We began by reducing/solving this cost (in dollars);

                                  →  "per quart" ; [i.e. per "one quart"] ;

                                                         [i.e. per "single, unit quart"] ;

So;  " \(\frac{2.83 dollars}{3quarts} = (\frac{2.83}{3}) \frac{dollars}{quart}\) " ;

         =  (2.83 ÷ 3)  dollars/quart  ;

         =  0.94333333333............. dollars per quart.

___________________  

2)  Second: Then: We take that value; and to find the cost of "5 (five) quarts" (as the problem asks)—we multiply that value by "5" :

   →  Using calculator:

   →  0.943333333333333333333333....  *  5 ;

         =  4.7166666666.. dollars ;  

           → which is the same answer obtained from the first method.

___________________  

Third method of solving the problem:

  This is really just an extension of the second method directed aforementioned:

___________________  

\(\frac{2.83 dollars}{3quarts} * \frac{5 quarts}{1} = ?\) ;

 →  The units of "quarts" cancel out; since: [" quarts/quarts = 1 "] ;

___________________  

and we have:

\(\frac{(2.83) *5}{3}\) dollars ;

 →  (2.83) * 5 =  14.15 ;  

 →   \(\frac{(2.83) *5}{3} = \frac{(14.15)}{3}\) ;  

=  (14.15) ÷ 3 ;  =  4.716666666666 ...

→  which is the same answer from the other 2 (two) aforementioned methods.

→ Let us round that number up to: "4.72" ;  

   {since: "4.71" ;  is followed by a digit higher than "4" } ;

___________________  

So:  The correct answer is:  

___________________  

   " 5 [five] quarts of motor oil will cost:   $ 4.72 . "

___________________  

Hope this is helpful to you!  Best of luck to you!

Answer:she can make three 5 ounce candles. she had 15 ounces left over , 15/5=3 .

Step-by-step explanation: 5 of 10% of 20 ounces is 10 ounces, and both the 5 five ounce candles and the twenty five one ounce candles are each 2.5 extra ounces left. (5 for both), making a totalm of 15 ounces left to put into new candles.

Answer:

Top left option

Step-by-step explanation:

There are a total of 10 boxes so

x + y = 10

The question states that x = 20 pound boxes and y = 30 pound boxes

20x + 30y = 280

Answer:

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

Angles at vertex V and Y are of same measure since they intercept same arc WX:

Angle measure of V and Y is:

Arc measure of WX is double the inscribed angle:

Answer:

7^-1 * 7^-1
7^-5 * 7^3
7^7 * 7^-9
so the first three are correct!

Step-by-step explanation:

The correct option is A, we have a translation of 7 units to the right.-

To find it, we need to analyze two correspondent vertices.

We can see that vertex A is at (1, 5), while the correspondent vertex A' is at (8, 5)

Taking the difference between that, we will get:

A' - A = (8, 5) - (1, 5) = (8 - 1, 5 - 5) = (7, 0)

The first value gives the horizontal translation and the second the vertical one

So,we have a translation of 7 units to the right, the correct option is A.

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