The lengths of the sides of a triangle are consecutive integers. If the perimeter of the triangle is 111, find the lengths of the sides.

Answer:

Step-by-step explanation:

Volume of the shipping container = Lengt * Breadth * Height

Given

Length = 4x² + 3x

Breadth = x² – 8

Height = 6x +15

Volume of the container = ( 4x² + 3x)( x² - 8)(6x+15)

( 4x² + 3x)( x² - 8)  = 4x⁴-32x²+3x³-24x

( 4x² + 3x)( x² - 8) = 4x⁴+3x³-32x²-24x

(4x⁴+3x³-32x²-24x)(6x+15) = 24x⁵+60x⁴+18x⁴+45x³-192x³-480x²-144x²-360x

Collect like terms

( 4x² + 3x)( x² - 8)(6x+15) = 24x⁵+78x⁴-147x³-624x²-360x

Hence the standard form polynomial representing the volume of this shipping container is expressed as V = 24x⁵+78x⁴-147x³-624x²-360x

Answer:

V = 24x^5+78x^4-147x^3-624x^2-360x

Answer:

(Negative 6) (4) + (negative 6) (two-thirds

Answer: 13

Step-by-step explanation:

let m = Matt's age

let a = Andy's

:

Write an equation for each statement

:

Matt is four years younger than twice his cousin Andy’s age.

m = 2a - 4

The sum of their ages is greater than 35.

m + a > 35

What is the youngest age that Andy can be?

replace m with (2a-4) from the 1st statement

2a - 4 + a > 35

3a > 35 + 4

a > 39/3

a > 13

least integer has to be a = 14

:

:

Check, find m

m = 2(14) - 4

m = 24

24 + 14 = 38 greater than 35

If a = 13

m = 2(13) - 4

m = 22

22 + 13 = 35 which is not greater than 35

Answer:

well assuming that it's linear the

Step-by-step explanation would be: something but you don't want that you want the answer assuming that 7 people came in every 4 trailers the slope or rate of change would be 7/4 and the initial value would be 5.

Answer:

[tex]s = -\frac{3}{2}[/tex]

Step-by-step explanation:

Solve for the value of [tex]s[/tex] :

[tex]0.5s + 1 = 7 + 4.5s[/tex]

-Combine both [tex]0.5s[/tex] and [tex]4.5s[/tex] by subtracting [tex]0.5s[/tex] by [tex]4.5s[/tex] :

[tex]0.5s + 1 - 4.5s = 7 + 4.5s - 4.5s[/tex]

[tex]-4s + 1 = 7[/tex]

-Subtract [tex]1[/tex] to both sides:

[tex]-4s + 1 - 1 = 7 - 1[/tex]

[tex]-4s = 6[/tex]

-Divide both sides by [tex]-4[/tex] :

[tex]\frac{-4s}{-4} = \frac{6}{-4}[/tex]

[tex]s = -\frac{3}{2}[/tex]

So, the value of [tex]s[/tex] is [tex]-\frac{3}{2}[/tex].

Answer:

B is the answer

Step-by-step explanation:

Given :

Peter velocity , P = 30 mph .

Mitchell velocity , M = 40 mph .

Mitchell leaves 15 min later .

To Find :

If they drive along the same route how long will it take Mitchell to catch Peter.

Solution :

Distance covered by Peter in 15 min .

[tex]D = 30\times \dfrac{15}{60}=7.5\ miles[/tex]

Let , time taken is x .

So , distance covered b them is equal :

[tex]7.5+30\times x=40\times x\\\\x=\dfrac{7.5}{10}=0.75\ hours\\\\x=0.75\times 60\ min\\\\x=45\ min[/tex]

Therefore , time taken by them is 45 minutes .

Hence , this is the required solution .

Answer:

length= 84

width= 36

the answer is $4750.

Answer:

23

Step-by-step explanation:

19346 ÷ 841 = 23.003567.. ( that is 23 with a remainder ), then

23 × 841 = 19343, thus

19346 ÷ 841 = 23 remainder 3

The divisor is 23

Answer:

Step-by-step explanation:

let length=l

breadth=b

l×b=660

2(l+b)=104

l+b=104/2=52

b=52-l

l×(52-l)=660

52l-l²=660

l²-52l+660=0

l²-22l-30l+660=0

l(l-22)-30(l-22)=0

(l-22)(l-30)=0

l=22,30

when l=22,b=52-22=30

when l=30,b=52-30=22

l>b

so l=30m

b=22m

Answer:

W = 22 m

L = 30 m

Step-by-step explanation:

given:

area is 660square metre and perimeter is 104metre​

find:

the length and breadth of a rectangular plot

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

1. area of rectangle (A) = L x W

2. Perimeter of a rectangle (P) = 2L + 2W

where:

A = 660 m²

P = 104 m

solve for L using formula 1.

A = L x W

660 = L x W

L =  660 / W

solve W using formula 2 and use L = 660 / W

P = 2L + 2W

104 = 2 (660)  +  2W

               W

104W = 1320 + 2 W²

-2W² + 104W = 1320

solve W using quadratic equation:

W = 22 m; ( 30 m = L)

plugin W=22 into L =  660 / W to solve L:

L = 660 / 22

L = 30 m

its B sorry if Im wrong have a nice day

Answer:

15:20:8

Step-by-step explanation:

You have to find a common factor between 4 and 5 because there are 3 men to 4 women and 5 women for 2 children, those numbers don't directly correlate. The easiest waay would be to multiply 4 and 5.

4 x 5 = 20

So we can correct the first ratio.

3 X 5 = 15

So the ratio of men to women is 15:20.

Now we find the ratio of women to children.

4 x 5 = 20

4 x 2 = 8

The ratio of women to children is 20:8.

Now that we have the same number in each ratio for women, we can combine them.

The ratio of men to women to children is:

15:20:8

Answer:

[tex]y=4-3x[/tex]

Step-by-step explanation:

[tex]3x+y=4[/tex]

Subtract 3x from both sides:

[tex]3x+y-3x=4-3x[/tex]

[tex]y=4-3x[/tex]

Answer:

its answer is

y=4-3x ok

Answer:

n > -2

Step-by-step explanation:

7(1 - 2n) < 33 - n

7 - 14n < 33 - n

Subtract 7

-14n < 26 - n

Add n

-13n < 26

Divide by -13

n > -2

Answer:

n > -2

Step-by-step explanation:

Distribution property:

7 - 14n < 33 - n

Bring n over:

7 - 13n < 33

Bring 7 over:

-13n < 26

n > -2

Answer:

If it was 9:38 it would be 10:08

Step-by-step explanation:

Adding 30 to 38 would be 68. And since an hour is only 60 minuets long you would change the hour to 10 and add the 8 minuets.

Hope this helped! :))

Answer:

[tex]MP= (5,4)[/tex]

Step-by-step explanation:

[tex]MP= (\frac{x_1+x_2}{2} )(\frac{y_1+y_2}{2} )[/tex]

[tex]MP= (\frac{2+8}{2} )(\frac{8+0}{2} )[/tex] 2+8=10 8+0=8

[tex]MP= (\frac{10}{2} )(\frac{8}{2})[/tex] 10/2=5 8/2=4

[tex]MP= (5,4)[/tex]

Answer:

an hour would make it 10, then another 30 minutes added to the 30 would make it 11, so 11:06 pm

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step-by-step explanation:

Think of 4.29 and 4.3 as 429 and 430.

Now which is greater, 429 or 430?

430, right? Then we convert them back to decimals.

4.29<4.3

Hope it helps!

Answer:

C -2 < x ≤ 1

Step-by-step explanation:

-5< 4x +3 ≤ 7

Subtract 3 from all sides

-5-3< 4x +3-3 ≤ 7-3

-8< 4x  ≤ 4

Divide all sides by 4

-8/4< 4x/4  ≤ 4/4

-2 < x ≤ 1

Answer:

1

Step-by-step explanation:

The total number of classes that were taken by you was 28.

The linear equations in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution.

According to the given question.

Registration fee for the dance class = $15

Amount of money charges for each dance class = $24

Amount of money paid for c number of classes = $687

⇒ [tex]687 = 24c + 15[/tex]

Solve the above linear equation in one variable for c.

[tex]687 = 24c + 15[/tex]

⇒ [tex]687 - 15 = 24c[/tex]

⇒ [tex]672 = 24c[/tex]

⇒ [tex]c = \frac{672}{24}[/tex]

⇒ [tex]c = 28[/tex]

Hence, the number of classes is 28.

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Answer:

Step-by-step explanation:

If you have the area just divide it by 4 and that will give you the answer .

A square has all equal sides

Answer:

I believe it is C

Step-by-step explanation:

First, I decided to use the proportion method. (Before I use this method, let's change [tex]\frac{3}{8}[/tex] into a decimal. So, that will be 0.375.

We know that we can cross multiply in a proportion

[tex]\frac{0.375 cups}{12 cupcakes} = \frac{2cups}{x}[/tex]

0.375x = 24

x = 64

round to tens

60

The number of cupcakes that he could make if he has 2 cups of cocoa is C) 60.

A proportion is an equation in which two ratios are set equal to each other.

Now, it is given that,

12 such cupcakes requires ⅜ of a cup of cocoa

So ratio, cup of cocoa : cupcakes = ⅜ : 12

⇒  cup of cocoa / cupcakes = ⅜ / 12

Now, let x be  the number of cupcakes that he could make if he has 2 cups of cocoa

So ratio,cups of cocoa : number of cupcakes = 2 : x

Hence,By proportionality we get,

cup of cocoa : cupcakes = cup of cocoa : cupcakes

⅜ : 12 = 2 : x

⅜ / 12 = 2 / x

⇒ 0.375/12 = 2 / x

⇒ x = (2x12)/0.375

⇒ x = 24/0.375

⇒ x = 64

hence it is closest  to the number 60.

So,The number of cupcakes that he could make if he has 2 cups of cocoa is C) 60.

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Answer:

[tex]\frac{31}{50}[/tex]

Step-by-step explanation:

First, find how many have an Atlantic or Pacific coastline:

14 + 5

= 19

Then, subtract this from 50:

50 - 19

= 31

This means 31 out of the 50 states have neither coastlines:

This is [tex]\frac{31}{50}[/tex] as a fraction

An object is moving at 9 centimeters every 5.5 minutes have a speed of 0.01 mile per day.

Speed is the ratio of distance travelled to time taken. Speed is given by:

Speed = distance/time

Given that the 9 cm is covered every 5.5 minutes, hence:

1 mile = 160934 cm;

9 cm = 9 * 1/160934 = 9/160934 mile

1 day = 1440 minutes

5.5 minute = 5.5 *  1/1440 = 5.5/1440 day

Hence:

Speed = distance/time

Speed = (9/160934 mile)/(5.5/1440 day)

Speed = 0.01 mile per day

An object is moving at 9 centimeters every 5.5 minutes have a speed of 0.01 mile per day.

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Answer:

8

Step-by-step explanation:

the anwser is you use the formal