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2 years ago

The base of an open rectangular box is of length (2x + 5) cm and width x cm.

Mathematics

1 answer:

Westkost [7]2 years ago

3 0

Answer:

a) x = 8.29 cm

D) V = 1125.27 cm³

Step-by-step explanation:

a) We can solve the equation as follows:

$2x + 5x - 58 = 0$

$2x + 5x = 58$

$x = \frac{58}{7} = 8.29$

D) The volume of the box is given by:

$V = l*w*h$

Where:

l: is the length

w: is the width

h: is the height

The length of the rectangular box is:

$l = (2x + 5) cm = (2*8.29 + 5) cm = 21.58 cm$

The width is x = 8.29 cm.

And the height is:

$h = (x - 2) cm = (8.29 - 2) cm = 6.29 cm$

Hence, the volume is:

$V = l*w*h = (21.58*8.29*6.29) cm^{3} = 1125.27 cm^{3}$

I hope it helps you!

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Jillian is selling boxes of cookies to raise money for her basketball team. The 10 oz. box costs $3.50, while the 16 oz. box cos

RideAnS [48]

Answer:

Jillian sold 15 ten-oz bags and 9 sixteen-oz bags.

Step-by-step explanation:

Let x represent number of 10-oz bags and y represent number of 16-oz bags.

We have been given that Jillian sold 24 boxes of cookies in total. We can represent this information in an equation as:

$x+y=24...(1)$

We are also told that 10 oz. box costs $3.50, while the 16 oz. box costs $5.00, so the cost of x 10-oz bags would be $3.50x$ and cost of y 16-oz bags would be $5y$ .

At the end of one week, she collected $97.50. We can represent this information in an equation as:

$3.5x+5y=97.50...(2)$

Now, we will use substitution method to solve our system of equations. From equation (1), we will get:

$y=24-x$

Substitute this value in equation (2):

$3.5x+5(24-x)=97.50$

$3.5x+120-5x=97.50$

$-1.5x+120=97.50$

$-1.5x+120-120=97.50-120$

$-1.5x=-22.5$

$\frac{-1.5x}{-1.5}=\frac{-22.5}{-1.5}$

$x=15$

Therefore, the number of 10-oz boxes sold be Jillian is 15.

Now, we will substitute $x=15$ in equation (1) to solve for y.

$15+y=24$

$15-15+y=24-15$

$y=9$

Therefore, the number of 16-oz boxes sold be Jillian is 9.

8 0

2 years ago

One student solved the inequality −4 > x −7 and got 28 < x. Another student solved the inequality and got x > 28. Are t

faltersainse [42]

-4 > x -7

Move the "-7" to the left hand side which will also change the sign
-4 + 7 > x ( "-4 + 7" is the same as "7 - 4")

3 > x OR x < 3 (3 is greater/bigger than x which also means x is smaller/lesser than 3)

They are both incorrect.

4 0

2 years ago

Read 2 more answers

Writing two column proofs Given: BC bisects. ABD M ABD =52° prove: mABC=26°

Artemon [7]

Given

BC bisects ABD

∠ ABD =52°

prove: m ∠ABC=26°

To proof

As given in the question

BC bisects ∠ABD

This means BC divided ∠ABD into the two equal parts.

Therefore

$\angle ABC = \frac{1}{2}\angle ABD$

As given

∠ABD = 52°

put this in the above value

we get

$\angle ABC =\frac{1}{2}52^{\circ}$

∠ABC = 26°

Hence proved

8 0

2 years ago

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What other points are on the line of direct variation through (5, 12)? Check all that apply. (0, 0) (2.5, 6) (3, 10) (7.5, 18) (

aalyn [17]

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form $y/x=k$ or $y=kx$

in this problem we have

the point $(5,12)$ is on the line of direct variation

Find the constant of proportionality k

$y/x=k$ -------> substitute ------> $k=12/5$

the equation is

$y=\frac{12}{5}x$

Remember that

If a point is on the line of direct variation

then

the point must satisfy the equation of direct variation

we're proceeding to verify each point

case A) point $(0,0)$

$x=0\ y=0$

Substitute the value of x and y in the direct variation equation

$0=\frac{12}{5}*0$

$0=0$ -------> is true

therefore

the point $(0,0)$ is on the line of direct variation

case B) point $(2.5,6)$

$x=2.5\ y=6$

Substitute the value of x and y in the direct variation equation

$6=\frac{12}{5}*2.5$

$6=6$ -------> is true

therefore

the point $(2.5,6)$ is on the line of direct variation

case C) point $(3,10)$

$x=3\ y=10$

Substitute the value of x and y in the direct variation equation

$10=\frac{12}{5}*3$

$10=7.2$ -------> is not true

therefore

the point $(3,10)$ is not on the line of direct variation

case D) point $(7.5,18)$

$x=7.5\ y=18$

Substitute the value of x and y in the direct variation equation

$18=\frac{12}{5}*7.5$

$18=18$ -------> is true

therefore

the point $(7.5,18)$ is on the line of direct variation

case E) point $(12.5,24)$

$x=12.5\ y=24$

Substitute the value of x and y in the direct variation equation

$24=\frac{12}{5}*12.5$

$18=30$ -------> is not true

therefore

the point $(12.5,24)$ is not on the line of direct variation

case F) point $(15,36)$

$x=15\ y=36$

Substitute the value of x and y in the direct variation equation

$36=\frac{12}{5}*15$

$36=36$ -------> is true

therefore

the point $(15,36)$ is on the line of direct variation

therefore

the answer is

$(0,0)$

$(2.5,6)$

$(7.5,18)$

$(15,36)$

5 0

2 years ago

Read 2 more answers

Two movie tickets and 3 snacks are $24. Three movies tickets and 4 snacks are $35. How much is a movie ticket and how much is a

Vsevolod [243]

Answer: A movie ticket is $9 while a snack is $2

Step-by-step explanation: We shall let a movie ticket be m while a snack is s. So, from the clues given, if two movie tickets and three snacks cost $24, we can write it as the following expression;

2m + 3s = 24

Also if three movie tickets and four snacks cost $35, we can as well write another expression as follows;

3m + 4s = 35.

Now we have a pair of simultaneous equations which are

2m + 3s = 24 ----------(1)

3m + 4s = 35 ----------(2)

We shall solve this by using the elimination method, since none of the variables has a coefficient of 1. We'll start by multiplying equation (1) by 3 and multiplying equation (2) by 2 (so as to eliminate the m variable)

2m + 3s = 24 -------- x3

3m + 4s = 35 ---------x2

We now arrive at the following

6m + 9s = 72--------(3)

6m + 8s = 70--------(4)

Subtract equation (4) from equation (3) and we arrive at

s = 2

Having determined that s equals 2 we can now substitute for the value of a into equation (1)

2m + 3s = 24

2m + 3(2) = 24

2m + 6 = 24

Subtract 6 from both sides of the equation

2m + 6 - 6 = 24 - 6

2m = 18

Divide both sides of the equation by 2

m= 9

Therefore one movie ticket costs $9 while one snack costs $2

6 0

2 years ago