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valentina_108 [34]
2 years ago
5

To complete bookshelves, a customer at your store needs to purchase vertical brackets to attach to the wall. The customer wants

the shelving to be 9 feet high and 10 feet long. The wall brackets come in 48-inch and 60-inch sections. The 48-inch sections cost $12.95; the 60-inch sections cost $16.95. The brackets should be 1 foot from each end and no more than 24 inches apart. What will be the total cost of the brackets, before tax?
Mathematics
1 answer:
stiks02 [169]2 years ago
8 0
We are given with
height = 9 feet
length = 10 feet
wall brackets:
48-in costing $12.95
60-in costing $16.95
distance of brackets from ends = 1 foot
maximum distance between brackets= 24 inches

The brackets are
48/12 = 4 feet
and
60/12 = 5 feet

One of each must be used to cover the height of the shelf

The length of the shelf is
60 inch
subtracting 1 in from each side for the allowance
60 - 2 = 58 in
Dividing by 24 inches
58/24 = 2.41 ~ 3 

The total cost is
($12.95 + <span>$16.95) * 3 = $89.7
The total cost of the brackets is </span>$89.7
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ikadub [295]

Answer:

508.8 seconds

Step-by-step explanation:

The most accurate determination mathematically is to assume that Lola will maintain an average of 5.3 seconds per signature as she signs all 96 invitations.

Therefore, multiply the time it takes her to sign each invitation (5.3 seconds) by the total number of invitations there are (96 invitations) to get the projected total amount of time that it will take Lola to sign all 96 invitations:96\cdot 5.3=\boxed{508.8\text{ seconds}}

8 0
2 years ago
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One cube has an edge length 5 cm shorter than the edge length of the second cube. The volume of the smaller cube is 216 cm?. Wha
VLD [36.1K]

Answer:

The volume of the  larger cube is V=1,331\ cm^3

Step-by-step explanation:

Let

x ---> the length of the smaller cube

y ---> the length of the larger cube

we know that

the volume of a cube is equal to

V=b^3

where

b is the length side of the cube

we have

x=y-5 ----> equation A

The volume of the smaller cube is 216 cm^3

so

substitute in the formula of volume

216=x^3

solve for x

x=\sqrt[3]{216}\ cm

x=6\ cm

<em>Find the value of y</em>

x=y-5

6=y-5

y=6+5=11\ cm

<em>Find the volume of the larger cube</em>

V=y^3

substitute the value of y

V=11^3

V=1,331\ cm^3

4 0
2 years ago
Pietro made 18 baskets during a basketball game.The number of 3 pointers are 3 more than half of the 2 point shots.how many type
blagie [28]

Total points is 23

<u>Explanation:</u>

Given:

Total number of baskets = 18

Let the number of 2 pointer shots be x

Let the number of 3 pointer shots be y

According to the question:

y = \frac{x}{2} + 3                  -1

The equation can be formed as:

\frac{x}{2} + 3 + x = 18

On solving this equation further we get:

\frac{x+6+2x}{2} = 18\\\\9x = 36\\\\x = 4

Putting the value of x = 4 in equation 1

y = \frac{x}{2}+3\\ \\y = \frac{4}{2} + 3\\\\y = 5

Points for 2 pointer shots = 4 X 2

                                        = 8

Points for 3 pointer shots = 5 X 3

                                        = 15

Total points = 8 + 15

                  = 23

Therefore, total points is 23

5 0
2 years ago
Mary was told that a line goes through the points (1, 3) and (6, -2) and has a slope of 3.
ki77a [65]

Answer:

a. The slope is incorrect

b. y = 3x, ( 0 , 0 )

c) y = 4 - x

Step-by-step explanation:

Given:-

The slope between two points (1, 3) and (6, -2) is 3.

a. Explain why the information Mary was given cannot be correct.

- The slope between two arbitrary points, ( x1 , y1 ) and  (x2 , y2) is given by the following relationship:

                         slope = ( y2 - y1 ) / ( x2 - x1)

- Use the given points (1, 3) and (6, -2) and determine the slope:

                        slope = ( -2 - 3 ) / ( 6 - 1 )

                        slope = ( -5 ) / ( 5 )

                        slope = -1

- Yes, the given slope is incorrect it should be = -1

b.If the given point (1, 3) and the given slope are correct, what is the equation for the line? Give the  coordinates of another point on the line

- We will assume the point (1,3) lies on line with a slope = 3.

- We will use the slope-intercept equation of line:

                              y = slope*x + c

Where,      m : Slope

                 c : y-intercept

                             y = 3x + c

Using the given correct point to evaluate the y-intercept (c):

                             3 = 3*1 + c

                             c = 0

- The equation of line is,

                            y = 3x

- The origin (0,0) lies on the line y = 3x.

c. If the given points are correct for the line, what is the slope? Write an equation for the line

- We will assume the points (1, 3) and (6, -2) lies on line with a slope calculated in part (a) to be = -1.

- We will use the slope-intercept equation of line:

                              y = slope*x + c

Where,      m : Slope

                 c : y-intercept

                             y = -x + c

Using the given points to evaluate the y-intercept (c):

                             3 = -1 + c

                             c = 4

- The equation of line is,

                            y = -x + 4

4 0
2 years ago
Factories 24x^2-41x+12
andriy [413]

Answer:

(3x - 4)(8x - 3)

Step-by-step explanation:

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 24 × 12 and sum = - 41

The required factors are - 32 and - 9

Use these factors to split the x- term

24x² - 32x - 9x + 12 ( factor the first/second and third/fourth terms )

= 8x(3x - 4) - 3(3x - 4) ← factor out (3x - 4) from each term

= (3x - 4)(8x - 3) ← in factored form

5 0
2 years ago
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