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3 years ago

Hanks pickup can travel 85 miles on 5 gallons of gas. How many gallons will his pickup need to travel 34 miles?

1 answer:

7 0

Hank will need 2 gallons of gas. 85/5 is 17, so Hank can go 17 miles on 1 gallon of gas. 17•2= 34, to go 34 miles you will need 2 gallons of gas.

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What happens to the Law of Cosines if the known angle is 90 degrees?

poizon [28]

Answer:

See below.

Step-by-step explanation:

It transforms to the Pythagoras theorem.

c^2 = a^2 + b^2 - 2ab cos C

If C = 90, cos C = zero so the last term disappears.

c^2 = a^2 + b^2 - 2ab * 0

c^2 = a^2 + b^2.

8 0

3 years ago

16% of a number is 60. What is that number? A375 B 432 C 456 D753

Vlad1618 [11]

Answer:

Its A: 375

Because, if you take 26.6 you have to round it. So, the 6 behind the decimal is over 5 so make the other 6 in front of the decimal a 7. So, the 7 will add 1 to the 2 to make it 3. And i forgot how to get the 5, but trust me dis is right. :3

4 0

3 years ago

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

How do I do this my hwk id due tomoorw

nexus9112 [7]

The perimeter of the given circle is 25.1 square cm.

Step-by-step explanation:

From the given diagram, the radius of the given circle is 4 cm.

The perimeter of any given circle is calculated by multiplying 2π with the radius. The radius of this circle is 4 cm and it says π = 3.142

The Perimeter for the given circle = 2π × r = 2 × 3.142 × 4 cm = 6.284 × 4 cm = 25.136 cm. Rounding this off to one decimal 25.136 square cm, the perimeter equals 25.1 square cm.

6 0

3 years ago

I will look stupid in front of my teacher if this doesn't get answered. ☠️ please answer..

bulgar [2K]

Answers: a = 35, b = 13

Explanation:

The numbers to the left of the line represent whole numbers. The numbers to the right of the line represent decimals. Each decimal represents a person.

a) How many numbers are on the right side of the line? 35

b) How many numbers are greater than 14.0? 13

7 0

3 years ago