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3 years ago

The length of a rectangle is twice the width. The perimeter is 30 cm. What is the width of the rectangle?

Mathematics

1 answer:

Semmy [17]3 years ago

6 0

Answer:

B. 5 cm

Step-by-step explanation:

If the width was 5 cm, the length would be 10 cm. (5 + 10) x 2 = 30 cm.

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Match the numerical expressions to their simplest forms.

Aloiza [94]

Answer:

$(a^6b^1^2)^\frac{1}{3}$ = $a^2b^4$

$\frac{(a^5b^3)^\frac{1}{2}}{(ab)^-^\frac{1}{2}}$ = $a^3b^2$

$(\frac{a^5}{a^-^3b^-^4})^\frac{1}{4}$ = $a^2b$

$(\frac{a^3}{ab^-^6})^\frac{1}{2}$ = $ab^3$

Step-by-step explanation:

Simplify each of the expressions:

$(a^6b^1^2)^\frac{1}{3}$

Distribute the exponent. Multiply the exponent of the term outside of the parenthesis by the exponents of the variable.

$(a^6b^1^2)^\frac{1}{3}$

$a^6^*^\frac{1}{3}b^1^2^*^\frac{1}{3}$

Simplify,

$a^2b^4$

Use a similar technique to solve this problem. Remember, a fractional exponent is the same as a radical, if the denominator is (2), then the operation is taking the square root of the number.

$\frac{(a^5b^3)^\frac{1}{2}}{(ab)^-^\frac{1}{2}}$

Rewrite as square roots:

$\frac{\sqrt{a^5b^3}}{\sqrt{(ab)}^-^1}$

A negative exponent indicates one needs to take the reciprocal of the number. Apply this here:

$\frac{\sqrt{a^5b^3}}{\frac{1}{\sqrt{ab}}}$

Simplify,

$\sqrt{a^5b^3}*\sqrt{ab}$

Since both numbers are under a radical, one can rewrite them such that they are under the same radical,

$\sqrt{a^5b^3*ab}$

Simplify,

$\sqrt{a^6b^4}$

Since this operation is taking the square root, divide the exponents in half to do this operation:

$a^3b^2$

$(\frac{a^5}{a^-^3b^-^4})^\frac{1}{4}$

Simplify, to simplify the expression in the numerator and the denominator, the base must be the same. Remember, the base is the number that is being raised to the exponent. One subtracts the exponent of the number in the denominator from the exponent of the like base in the numerator. This only works if all terms in both the numerator and the denominator have the operation of multiplication between them:

$(\frac{a^8}{b^-^4})^\frac{1}{4}$

Bring the negative exponent to the numerator. Change the sign of the exponent and rewrite it in the numerator,

$(a^8b^4)^\frac{1}{4}$

This expression to the power of the one forth. This is the same as taking the quartic root of the expression. Rewrite the expression with such,

$\sqrt[4]{a^8b^4}$

SImplify, divide the exponents by (4) to simulate taking the quartic root,

$a^2b$

$(\frac{a^3}{ab^-^6})^\frac{1}{2}$

Using all of the rules mentioned above, simplify the fraction. The only operation happening between the numbers in both the numerator and the denominator is multiplication. Therefore, one can subtract the exponents of the terms with the like base. The term in the denomaintor can be rewritten in the numerator with its exponent times negative (1).

$(a^3^-^1b^(^-^6^*^(^-^1^)^))^\frac{1}{2}$

$(a^2b^6)^\frac{1}{2}$

Rewrite to the half-power as a square root,

$\sqrt{a^2b^6}$

Simplify, divide all of the exponents by (2),

$ab^3$

7 0

3 years ago

Jane’s cell phone plan is $40 each month plus $0.15 per minute for each minute over 200 minutes of call time. Janes cell phone b

san4es73 [151]

Answer:

The equation is $40+0.15m = 58.00$ whose solution is $m =120\:minutes.$

Step-by-step explanation:

Let us call $m$ the number of minutes the phone is used over 200 minutes, then we have

$\boxed{40+0.15m = 58.00}$ <em>(this says monthly bill of $40 plus the cost of phone usage over 200 minutes must equal $58 )</em>

This equation can be used to solve for $m$ u as follows:

$0.15m = 58-40$

$m = \dfrac{18}{0.15}$

$\boxed{m = 120\:minutes}$

8 0

3 years ago

A bag of chocolate mix weighed 1/4 of a kilogram could make enough brownies to feed 1/7 of the students at school how many bags

Hoochie [10]

A "whole" will be 7/7, or just 1 whole.

so we know one bag can do 1/7 of all students, how many will it be needed to do 7/7?

well, in 7/7 there are seven 7/7, so, 7 bags then, or one could say,

$\bf \begin{array}{ccll}
\stackrel{chocolate}{bag}&\stackrel{fraction}{students}\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
1&\frac{1}{7}\\\\
x&\frac{7}{7}
\end{array}\implies \cfrac{1}{x}=\cfrac{\quad \frac{1}{7}\quad }{\frac{7}{7}}\implies \cfrac{1}{x}=\cfrac{1}{7}\cdot \cfrac{7}{7}
\\\\\\
\cfrac{1}{x}=\cfrac{1}{7}\implies 7=x$

5 0

2 years ago

Please help me with this I will give brainliest please answer it right

weeeeeb [17]

Answer:

Step-by-step explanation:

RR, RY, RG, RP, YY, YG, YP, YR, GG,GP, GR, PP, PR, PY, PG.

All combinations of the four colors are provided in Option A as written out above. The other options are missing combinations.

I hope I helped, Would appreciate Brainliest! ;)

6 0

3 years ago

Solve for K<br><br> k/2+1/2=3

alexira [117]

Answer:k=5

Step-by-step explanation:

K/2+1/2=3

K/2=3-1/2

K/2=5/2

K=10/2

K=5

6 0

3 years ago