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2 years ago

The circumference of a circle is 36 feet. What is the length of the radius of this circle?

Mathematics

1 answer:

omeli [17]2 years ago

3 0

The answer is D 72 ft

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What is 16% of 750?

alisha [4.7K]

Answer:

120

Step-by-step explanation:

For this, all we have to do is multiply 750 by 16%. We know, from percent to decimal conversion, that 16% is 0.16 (divide the percent by 100 to convert to a decimal). From there, if we multiply 750 by 0.16, we get our answer to be 120

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2 years ago

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Please help me <br><br><br> Grade is 6th or 7th

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Answer:

1 a)8 miles per hour 1 b) 1 hour and 90 minutes 2 a) 24 hours and 6minutes 2 b) 3hours 3 a) 260 hours and 45 minutes 3 b) 40 minutes

Step-by-step explanation:

I don't know for sure if this is all correct but at least you'll have something to write down

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3 years ago

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Practice Exercise 1:

Rudiy27

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3 years ago

What is the slope of the line 4x+y=-9

olga55 [171]

Answer:

The slope of this line is -4

Step-by-step explanation:

To find the slope, you need to solve the equation for y.

4x + y = -9

y = -4x - 9

The slope in this form is always the coefficient of x, making it -4.

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3 years ago

PLEASE ANSWER! DESPERATE, DONT KNOW HOW TO DO IT!

Annette [7]

Answer:

a) x = -7

b) x = -3/2

c) x = -3/2

d) x = 2

e) x = -1

f) x = -2

g) x = 7/3

h) z = -18/5

i) x = 6

Explanation:

The are a couple of rules you should know first.

Negative exponent rule: $a^{-x} = \frac{1}{a^{x}}$

A negative exponent means the same thing as the positive exponent as a denominator under 1.

Exponent to another exponent: $(a^{x})^{n}=a^{xn}$

When raising an exponent to another exponent, you multiply the exponents.

Fraction as a base rule: $(\frac{a}{b})^{x} = \frac{a^{x}}{b^{x}}$

Apply the exponent to the numerator and denominator.

Base 1 rule: $1^{x} = 1$

1 to the power of anything is 1.

Focus on exponents only: $a^{x} = a^{n}\\x = n$

If the bases are the same on both sides of the equation, you can solve for "x" in the exponent by focusing on it only.

Write as an exponent: Rewrite a normal number as an exponent instead. Example: $8=2^{3}$ or $125=5^{3}$

Also, you need to know how to rearrange and simplify formulas to isolate variables (by doing reverse operations in reverse BEDMAS order).

Know how to use the distributive property with brackets, when you multiply each of the terms in the brackets with the term on the outside.

Use each of these rules to solve.

a) $2^{x+4} = \frac{1}{8}$ Write 8 as exponent

$2^{x+4} = \frac{1}{2^{3}}$ Negative exponent rule

$2^{x+4} = 2^{-3}$ Focus on exponents only

$x+4 = -3$ Subtract 4 from each side to isolate

$x = -3-4$

$x = -7$

b) $9^{x}=\frac{1}{27}$ Write 27 as exponent

$9^{x}=\frac{1}{3^{3}}$ Write 9 as exponent

$(3^{2})^{x}=\frac{1}{3^{3}}$ Exponent to another exponent

$3^{2x}=\frac{1}{3^{3}}$ Negative exponent rule

$3^{2x}=3^{-3}$ Focus on exponents only

$2x=-3$ Divide both sides by 2 to isolate

$x=-\frac{3}{2}$

c) $25^{x}=\frac{1}{125}$ Rewrite 125 as exponent

$25^{x}=\frac{1}{5^{3}}$ Rewrite 25 as exponent

$(5^{2})^{x}=\frac{1}{5^{3}}$ Exponent to another exponent

$5^{2x}=\frac{1}{5^{3}}$ Negative exponent rule

$5^{2x}=5^{-3}$ Focus only exponents only

$2x=-3$ Divide both sides by 2 to isolate

$x=-\frac{3}{2}$

d) $7(3^{x})=63$ Divide both sides by 7 to isolate

$3^{x}=63/7$

$3^{x}=9$ Write 9 as exponent

$3^{x}=3^{2}$ Focus on exponents

$x=2$

e) $10^{3x}=0.001$ Write 0.001 as fraction

$10^{3x}=\frac{1}{1000}$ Write 1/1000 as exponent

$10^{3x}=\frac{1}{10^{3}}$ Neg. exponent

$10^{3x}=10^{-3}$ Focus on exponents

$3x=-3$ Divide both sides by -3

$x=-3/3$

$x=-1$

f) $6(\frac{1}{10})^{x}=600$ Divide both sides by 6

$(\frac{1}{10})^{x}=\frac{600}{6}$

$(\frac{1}{10})^{x}=100$ Write 100 as exponent

$(\frac{1}{10})^{x}=10^{2}$ Fraction as base rule

$\frac{1^{x}}{10^{x}}=10^{2}$ Base 1 rule

$\frac{1}{10^{x}}=10^{2}$ Neg. exponent

$10^{-x}=10^{2}$ Focus on exponent

$-x=2$ Divide both sides by -1

$x=-2$

g) $27^{x-3}=(\frac{1}{3})^{2}$ Write 27 as exponent

$(3^{3})^{x-3}=(\frac{1}{3})^{2}$ Exponent to another exponent

$3^{3(x-3)}=(\frac{1}{3})^{2}$ Fraction as base

$3^{3(x-3)}=\frac{1^{2}}{3^{2}}$ Base 1 rule

$3^{3(x-3)}=\frac{1}{3^{2}}$ Neg. exponent

$3^{3(x-3)}=3^{-2}$ Focus

$3(x-3)=-2$ Distribute over brackets

$3x-9=-2$ Add 9 to both sides

$3x=-2+9$

$3x=7$ Div. both sides by 3

$x=\frac{7}{3}$

h) $4^{\frac{2z}{3}} = 8^{z+2}$ Write 4 as exponent

$(2^{2})^{\frac{2z}{3}} = 8^{z+2}$ Exponent to another exponent

$2^{2\frac{2z}{3}} = 8^{z+2}$ Write 8 as exponent

$2^{2\frac{2z}{3}} = (2^{3})^{z+2}$ Exponent to another exponent

$2^{2\frac{2z}{3}} = 2^{3(z+2)}$ Focus

$2\frac{2z}{3} = 3(z+2)$ Multiply whole number with fraction

$\frac{4z}{3} = 3(z+2)$ Distribute

$\frac{4z}{3} = 3z+6$ Multiply both sides by 3

$4z = 3(3z+6)$ Distribute

$4z = 9z+18$ Subtract 9z from both sides

$4z-9z = 18$

$-5z = 18$ Div. both sides by -5

$z = -\frac{18}{5}$

i) $5(2)^{x-1}+3=163$ Subtract 3 on both sides

$5(2)^{x-1}=163-3$

$5(2)^{x-1}=160$ Div. both sides by 5

$(2)^{x-1}=160/5$

$(2)^{x-1}=32$ Write 32 as exponent

$(2)^{x-1}=2^{5}$ Focus

$x-1=5$ Add 1 to both sides

$x=5+1$

$x=6$

5 0

3 years ago