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2 years ago

6

Jill has a small treasure box that is 6 in Long. it can hold a volume of 72 inches cubed and the width of the box is 5 in less t

han twice the height of the box. What are the dimensions of the box?

2 answers:

Fofino [41]2 years ago

7 0

V=l*w*h
72=6*4*3
72=72

dusya [7]2 years ago

3 0

Answer:

Step-by-step explanation:

60

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Ben and Landon took turns driving on their recent 820 mile road trip. Ben averaged 60 miles per hour while landon averaged 56 mi

Furkat [3]

Landon drove for 5 hours.

<u>Step-by-step explanation</u>:

Given that,

Total distance of the road trip = 820 miles

Speed of Ben = 60 miles per hour

Speed of Landon = 56 miles per hour

<u><em>Step 1 </em></u><em>:</em>

Let 'x' be the number of miles Ben drove

Let 'y' be the number of miles Landon drove

<u><em>Step 2</em></u><em> :</em>

The trip took them 14 hours to complete 820 miles together.

x + y = 14

60x + 56y = 820

<u><em>Step 3 </em></u><em>:</em>

Solve the linear system x+ y= 14 and 60x+ 56y= 820

x + y = 14

x = 14 - y

<u><em>Step 4 </em></u><em>:</em>

Substitute x= 14-y in the second equation,

60(14-y) + 56y = 820

840 - 60y + 56y = 820

<u><em>Step 5</em></u><em> :</em>

Keeping y terms on one side and constants on other side,

60y - 56y = 840 - 820

4y = 20

y = 20/4

y = 5

Since 'y' is the number of miles Landon drove, the time Landon drove is 5 hours.

3 0

2 years ago

What is the greatest common factor of 16x4y3 and 12x2y7?

Marta_Voda [28]

The greatest common factor, or GCF, is the greatest factor that divides two numbers. To find the GCF of two expression

<span>1. </span>List the prime factors of each number.

<span>2. </span>Multiply those factors both numbers have in common. If there are no common prime factors, the GCF is 1.

16x^4y^3 = ( 4*4)(x*x*x*x)(y*y*y)

12x^2y^7 = (4*3)(x*x)(y*y*y*y*y*y*y)

<span>So common to them is 4x^2y^3 </span>

4 0

2 years ago

Carol ate 2/5 of the cake, Dima ate 3/8 of the REMAINING cake, mom ate the rest.

Anarel [89]

She would've eaten half of the cake, or 8 oz.

4 0

2 years ago

A pendulum is set swinging. its first oscillation is through 30 and each succeeding oscillation is through 95% of the angle of t

Marat540 [252]

<u>Answer-</u>

<em>After 76 swings</em><em> the angle through which it swings less than 1°</em>

<u>Solution-</u>

From the question,

Angle of the first of swing = 30° and then each succeeding oscillation is through 95% of the angle of the one before it.

So the angle of the second swing = $(30\times \frac{95}{100})^{\circ}$

Then the angle of third swing = $(30\times (\frac{95}{100})^2)^{\circ}$

So, this follows a Geometric Progression.

$(30,\ 30\cdot \frac{95}{100},\ 30\cdot (\frac{95}{100})^2............,0)$

a = The initial term = 30

r = Common ratio = $\frac{95}{100}$

As we have to find the number swings when the angle swept by the pendulum is less than 1°.

So we have the nth number is the series as 1, applying the formula

$T_n=ar^{n-1}$

Putting the values,

$\Rightarrow 1=30(\frac{95}{100})^{n-1}$

$\Rightarrow \frac{1}{30} =(\frac{95}{100})^{n-1}$

Taking logarithm of both sides,

$\Rightarrow \log \frac{1}{30} =\log (\frac{95}{100})^{n-1}$

$\Rightarrow \log \frac{1}{30} =(n-1)\log (\frac{95}{100})$

$\Rightarrow -1.5=(n-1)(-0.02)$

$\Rightarrow 1.5=(n-1)(0.02)$

$\Rightarrow n-1=\dfrac{1.5}{0.02}$

$\Rightarrow n-1=75$

$\Rightarrow n=76$

Therefore, after 76 swings the angle through which it swings less than 1°

8 0

2 years ago

Lisa the numbers least to greatest -2/5 -2.47 -2 1/2 5 21/4

Paraphin [41]

Answer:

least to greatest are:

-2.5, -2.47, -2/5, 5, 21/4

3 0

2 years ago