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Mila [183]
1 year ago
12

The perimeter of a rectangle is 80x. The base is two times the height. In terms of x, what are the dimensions of the rectangle?

Mathematics
2 answers:
kirza4 [7]1 year ago
5 0
By definition we have that the perimeter of a rectangle is given by:
 P = 2b + 2h
 Where,
 b: base
 h: height
 Also, as a data of the problem we have:
 base is two times the height:
 b = 2h
 Substituting we have:
 P = 2 (2h) + 2h
 Clearing h:
 6h = P
 h = P / 6
 h = (80x) / 6
 h = (40/3) x
 The base will be
 b = 2h
 b = (80/3) x
 Answer:
 the dimensions of the rectangle are
 b = (80/3) x
 h = (40/3) x
 b. h = 13.3x; b = 26.6x
arlik [135]1 year ago
5 0
Answer:
<span>h = 13.3x; b = 26.6x
</span>
Explanation:
Perimeter of the rectangle = 2(base+height)
80x = 2(base+height)
base + height = 40x ........> I

Now, we are given that the base is 2 times the height, this means that:
base = 2*height ..........> II

Substitute with II in I:
base + height = 40x
2*height + height = 40x
3*height = 40x
height = 13.3x 

Substitute with the height in equation II to get the base as follows:
base = 2*height 
base = 2 * 13.3x = 26.6x

Hope this helps :)

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The student to faculty ratio at a small college is 17:3 the total number of students and faculty is 740. How many faculty member
larisa86 [58]

Answer:

111

Step-by-step explanation:

It is given that the student to faculty ratio at a small college is 17:3.

Let number of students and faculty members are 17x and 3x respectively.

It is given that total number of students and faculty is 740.

17x+3x=740

20x=740

Divide both sides by 20.

x=37

Number of student =17\times 37=629

Number of faculty members =3\times 37=111

Therefore, there are 111 faculty members at the college.

3 0
2 years ago
Charmaine pays $848 for landscaping rocks for a project. The cost per pound is 32 cents. How many pounds did she purchase?
otez555 [7]
Okay so since it is 32 cents, it will be 0.32
You need to find the number of pounds
So, do 848/0.32
You get 2650
Charmaine purchased 2,650 pounds of rocks
hope this helps:)
6 0
1 year ago
Read 2 more answers
A motorboat takes 3 hours to travel 144 km going upstream. The trip takes 2 hours going downstream. What is the rate of the boat
allsm [11]
Let x be rate of boat in still water
let y be rate of current

we use this equation to relate quantities:
distance = speed · time

we have two unknowns so we might need to create a system of equationss

upstream:

speed (in km/h) = x - y
(we get speed of boat then subtract the current's speed from it since current is going against boat direction)

time = 3 hours

distance = 144 km

downstream:

speed (in hm/h) = x + y
(we get speed of boat then add the current's spd from it since current is going against boat direction)

time = 2 hours

distance = 144 km (same distance upstream and downstream)

using distance = speed times time

for upstream
144 =  3(x-y)
144 = 3x - 3y

for downstream
144 = 2(x+y)
72 = x + y

system of eqns:
144 = 3x - 3y
72 = x + y

solve by substitution: move 72 = x + y into x = 72 - y and subst into other equation for x

144 = 3(72 - y) - 3y
144 = 216 - 3y - 3y
144 = 216 - 6y
144 - 216 = -6y
-72 = -6y
y = 12 km/h

Use x = 72 - y to find x with y = 12: x = 72 - 12 = 60 km/h

rate of boat in still water is 60 km/h
rate of the current is 12 km/h
6 0
2 years ago
I need to increase the number of customers by 20% daily, I talk to an average of 8 customers per hour during an 8 hour shift so
MA_775_DIABLO [31]

Before we figure out how many customers you will need to talk per day to reach your goal, let's calculate what is 20% of how many customers you normally talk to a day.


current no. = 8

goal = 8 + 20%

20% = 8 x 0.20

(a percent is really just a fraction with the percent number over 100)

20% = 1.60

goal = 8 + 1.60

goal = 9.60


However, there is no such thing as .60 of a person so we will have to round up. You will need to talk to 10 customers per day.

6 0
2 years ago
Read 2 more answers
Given g(x) = x2 + 3x - 19, find g(-2)
BlackZzzverrR [31]

Answer:

-4 + -6 -19

-10 -19

-29

5 0
2 years ago
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