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2 years ago

40 pages read in 20 minutes. what is the unit rate?

Mathematics

1 answer:

Alenkinab [10]2 years ago

8 0

Answer:

2 pages per minute.

Step-by-step explanation:

40 pages / 20 minutes

= 40 / 20 = 4 / 2 = 2

Therefore, you read 2 pages per minute.

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Find the LCM of 8, 12, and 26

Dafna1 [17]

312 is the LCM for this set

3 0

2 years ago

The perimeter of a rectangle is 42 inches, and its area is 110 square inches. find the length and width of the rectangle.

lorasvet [3.4K]

$p = 2w + 2l$ $p = 42$
$a = l * w$ $a = 108$

You want to make either the length or width variable (I chose the width variable to be by itself. It doesn't matter) by itself by:

Divide both sides by 2.
(p) ÷ 2 = (2w + 2l) ÷ 2
$2's$ $cancel$ $out$
$\frac{p}{2} = w + l$

Subtract both sides by either length or width depending on what variable you chose to make by itself (in this case I subtracted the length variable because I wanted the width variable by itself).
$\frac{p}{2} - l = w + l - l$
$l's$ $cancel$ $out$
p/2 - l = w

$a = l * w$

You replace w with the equation above p/2 - l = w
$a = l( \frac{p}{2} - l)$

Multiply out the L.
$a = \frac{p}{2}l - l^{2}$

Plug in all your numbers a = 110 and p = 42
$110 = \frac{42}{2}l - l^{2}$
$110 = 21l - l^{2$

Move everything to the left side so $l^{2}$ would be positive (makes the equation easier when $l^{2}$ is positive).
$l^{2} - 21l + 110 = 0$

Factor.
$(l -10)(l-11) = 0$

Make each parenthesis set equal to 0.
$l-11=0$ $l-10=0$

Add.
$l = 11$ $l = 10$

By doing this you solve for both the width and length so the answer is:
w = 11 L = 10

8 0

3 years ago

Roberto is 3 years older than Carolyn. In 7 years the sum of their ages will be 81. How old is Roberto now?

Nuetrik [128]

Answer: 35

the age of Roberto is x (x > 3)(x ∈ N)

because Roberto is 3 years older than Carolyn => the age of Carolyn is x - 3

in 7 years, the age of Roberto is x + 7; the age of Carolyn is x - 3 + 7 = x + 4

because In 7 years the sum of their ages will be 81 =>

x + 7 + x + 4 = 81

⇔ 2x + 11 = 81

⇔ 2x = 70

⇔ x = 70/2 = 35

=> the age of Roberto is 35

Step-by-step explanation:

3 0

2 years ago

X + 3 4/5= 8 1/9 solve for x

Helen [10]

Answer:

Exact Form: x = 194 /45

Decimal Form: x = 4.3 1

Mixed Number Form: x = 4 14 /45

hope this helps

6 0

3 years ago

Read 2 more answers

How do I simplify rational expressions

ivolga24 [154]

Answer:

a rational expression is an expression that has a RATIO in it

look at the word "RATIO"nal

a ratio is just a fraction...

so your question is "how to simplify fractions"

lots of approaches, this is one of them...

PRIME FACTOR the numerator and denominator

$\frac{90}{135}$

90 = 2 * 3 * 3 * 5

135 = 3 * 3 * 3 * 5

= 2/3 (the two 3's cancel and the 5's cancel)

Step-by-step explanation:

6 0

2 years ago