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3 years ago

Help me on all please

Mathematics

1 answer:

nirvana33 [79]3 years ago

4 0

Answer:

look at the rest

Step-by-step explanation:

1.)same line

2.)intersect

3.)parallel

4.)ordered pair

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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

Pilaf has a circular garden plot with an area of 125 square feet. To fence the area, how many feet of fencing does she need?

Jet001 [13]

So, to find the find the amount of fencing required, or the circumference of the gardening, pot...

Area = pi * r^2
125 square feet = pi *r^2
125/ pi = r^2
39.79 = r^2
root square of 39.79 = r
6.31 = r

To find the circumference, the formula is: pi * D (or Pi * r * 2)

therefore,

C = pi * 6.31 *2
C = 39.65 feet

therefore, 39.65 feet of fencing is needed.

hope this helps

8 0

3 years ago

Marissa bought 3 chocolate bars each week. How many chocolate bars will Marissa buy after 3 weeks?

kupik [55]

All you have to do is multiply 3 by 3, and your answer would be 9.

3 0

2 years ago

Read 2 more answers

A map is drawn using a scale of 80 mi to 1 cm. On the map , the two cities are 7.5 cm apart. What is the actual distance between

meriva

We know that
scale =measure in the map/measure in the actual
measure in the actual=measure in the map/scale
scale=1 cm/ 80 mi
for
measure in the map=7.5 cm
measure in the actual=?
measure in the actual=7.5 /(1/80)-----> 7.5*80-----> 600 mi

the answer is
<span>the actual distance between the two cities is 600 miles</span>

6 0

3 years ago

Write an equation for the linear function f with values f(6) = -4 and f(9) =-9.

leva [86]

For the first 1 is 0.6 because 2 divided by 3, and for the second 1 the answer is -1

4 0

3 years ago