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2 years ago

How do I slove 96-2r=6r-112

2 answers:

8 0

96-2r=6r-112
Add 2r to both sides
96=8r-112
Add 112 to both sides
208=8r
Divide 8 on both sides
Final Answer: 26=r

lyudmila [28]2 years ago

5 0

96-2r=6r-112

Divide everything by 2
48-r=3r-56

add r to each side
48=4r-56

add 56 to each side
104=4r

divide each side by 4
26=r

Hope this helps :)

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Marysya12 [62]

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2 years ago

A rectangle has width that is 6 meters less than the length. The area of the rectangle is 280 square meters. Find the dimensions

salantis [7]

Dimensions are length 20 meter and width 14 meter

Solution:

Let "a" be the length of rectangle

Let "b" be the width of rectangle

Given that,

A rectangle has width that is 6 meters less than the length

Width = length - 6

b = a - 6

The area of the rectangle is 280 square meters

The area of the rectangle is given by formula:

$Area = length \times width$

Substituting the values we get,

$Area = a \times (a-6)\\\\280 = a^2-6a\\\\a^2-6a -280=0$

Solve the above equation by quadratic formula

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\\quad x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\mathrm{For\:}\quad a=1,\:b=-6,\:c=-280:\quad a_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:1\left(-280\right)}}{2\cdot \:1}$

$a =\frac{6 \pm \sqrt{36+1120}}{2}\\\\a = \frac{6 \pm \sqrt{1156}}{2}\\\\a = \frac{6 \pm 34}{2}\\\\Thus\ we\ have\ two\ solutions\\\\a = \frac{6+34}{2} \text{ or } a = \frac{6-34}{2}\\\\a = 20 \text{ or } a = -14$

Since, length cannot be negative, ignore a = -14

Thus solution of length is a = 20

Therefore,

width = length - 6

width = 20 - 6 = 14

Thus dimensions are length 20 meter and width 14 meter

6 0

2 years ago

Simplify 2.4 : 0.88 : 4.8 as ratios

vovangra [49]

Answer:

61:22:120

Step-by-step explanation:

Multiply each by 100

244:88:480

Now simply

122:44:240

61:22:120

(Just check to see or compare with others to see if answer is right)

5 0

1 year ago

Solve the quadratic equations by factorisation method.

finlep [7]

The answer is 2x^2+5/2=0

4 0

2 years ago

Tomorrow Noelle wants to travel a total of 4 miles by walking and running she plans to run for 20 minutes at a rate of 6 miles p

elixir [45]

Answer:

Noelle will need to walk at a rate of 3 miles per hour for 2/3 of an hour to finish traveling the 4 miles.

Step-by-step explanation:

This will be a two part problem.

Noelle wants to travel 4 miles in total.

If she wants to run for 20 minutes at a rate of 6 miles/hour, we need to convert 20 minutes into terms of hours

20 minutes * 1 hour/60 minutes = 1/3 of an hour

let's find the distance she has traveled by running then using

d = r*t

where d is our distance in miles,

r is our speed in miles/hour, and

t is the time taken in hours

if r = 6 miles/hour and

t = 1/3 hours

we have

d = (6 miles/hour) * (1/3 hours)

hours will cancel out, leaving us with

d = 2 miles

If Noelle has covered 2 miles by running, how many minutes then will she need to walk at a rate of 3 miles per hour to cover the remaining two miles?

d = 2 miles

r = 3 miles/hour

2 miles = (3 miles/hour) *t divide both sides by 3 miles/hour

miles will cancel out, leaving us with

2/3 hours = t

Therefore, Noelle will need to walk at a rate of 3 miles per hour for 2/3 of an hour to finish traveling the 4 miles.

3 0

2 years ago