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3 years ago

Combine the like terms to create an equivalent expression: r + (−5r)

Mathematics

1 answer:

Harrizon [31]3 years ago

6 0

Answer:

-4r

Step-by-step explanation:

r+(-5r)=r-5r=-4r

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Write the ratio as a fraction in simplest form: 4ft : 2.4ft

Gekata [30.6K]

The answer would be 12:7 . You have to change feet into inches and calculate it from there . Doing that would get you 48:28 and if you put it into simplest form it'd be 12:7 dividing both by 4.

6 0

3 years ago

A 4-foot tall child walks directly away from a 12-foot tall lamppost at 2 mph. How quickly is the length of her shadow increasin

xz_007 [3.2K]

Answer:

The length of the shadow is increasing with the rate of 1.5 feet per sec

Step-by-step explanation:

Let AB and CD represents the height of the lamppost and child respectively ( shown below )

Also, let E be a point represents the position of child.

In triangles ABE and CDE,

$\angle ABE\cong \angle CDE$ ( right angles )

$\angle AEB\cong \angle CED$ ( common angles )

By AA similarity postulate,

$\triangle ABE\sim \triangle CDE$

∵ Corresponding sides of similar triangles are in same proportion,

$\implies \frac{AB}{CD}=\frac{BE}{DE}$

We have, AB = 12 ft, CD = 4 ft, BE = BD + DE = 6 + DE,

$\implies \frac{12}{4}=\frac{6+DE}{DE}$

$12DE = 24 + 4DE$

$8DE = 24$

$DE=3$

Now, the speed of walking = 2 mph = $\frac{2\times 5280}{3600}\approx 2.933\text{ ft per sec}$

Note: 1 mile = 5280 ft, 1 hour = 3600 sec

Thus, the time taken by child to reach at E

$= \frac{\text{Walked distance}}{\text{Walking speed}}$

$=\frac{6}{2.933}$

= 2.045 hours

Hence, the change rate in the length of shadow

$= \frac{\text{Length of shadow}}{\text{Time taken}}$

$=\frac{3}{2.045}$

= 1.5 ft per sec.

3 0

3 years ago

Please show work !!!!!!!!

sineoko [7]

You must first link your problems along with the question.

8 0

4 years ago

Cost of an oil change: $18.00; Markup: 3/4 answers

hjlf

I am assuming that the cost of an oil change already includes the mark-up.

So, 18 is 175%. 18 ÷ 1.75 = 10.29 is the original cost.

10.29 * 3/4 = 30.87/4 = 7.71 mark-up
10.29 + 7.71 = 18

Or if 18 is the basis of the mark-up, then,

18 * 3/4 = 54/4 = 13.50 mark-up
18 + 13.50 = 31.50 new cost of an oil change

8 0

4 years ago

Solve Quadratic Equations by Factoring:

mr_godi [17]

Answer:

x = 0 or 1
x = ±i/4
x = -5 (twice)

Step-by-step explanation:

Factoring is aided by having the equations in standard form. The first step in each case is to put the equations in that form. The zero product property tells you that a product is zero when a factor is zero. The solutions are the values of x that make the factors zero.

1. x^2 -x = 0

x(x -1) = 0 . . . . . x = 0 or 1

2. 16x^2 +1 = 0

This is the "difference of squares" ...

(4x)^2 - (i)^2 = 0

(4x -i)(4x +i) = 0 . . . . . x = -i/4 or i/4 (zeros are complex)

3. x^2 +10x +25 = 0

(x +5)(x +5) = 0 . . . . . x = -5 with multiplicity 2

5 0

3 years ago