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3 years ago

Without multiplying, determine the sign of the product (356,864)(−194,758)

Mathematics

1 answer:

Anon25 [30]3 years ago

7 0

Answer:

-6.95 x 10^10

Step-by-step explanation:

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Which point is not on the graph of the equation y=10+x

SCORPION-xisa [38]

Answer:

Step-by-step explanation:

Check all points:

A: x=0, y=10, then from the equality $10=10+0$ follows that A lies on the line.

B: x=3, y=13, then from the equality $13=10+3$ follows that B lies on the line.

C: x=8, y=2, then from the inequality $2=10+8$ follows that C doesn't lie on the line.

D: x=5, y=15, then from the equality $15=10+5$ follows that D lies on the line.

8 0

3 years ago

S=4\pi r^{2} Solve for r[/tex]

Veronika [31]

S = 4pi r^2

S/4pi = r^2

taking square root on both sides,
r = sqrt (S/4pi)

8 0

3 years ago

The lcm of 20,30 and 60

beks73 [17]

The LCM of 20,40,60 is gonna be 60

8 0

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

The sum of the measures of three angles in a triangle is 180 degrees. The measure of one angle of a triangle is one degree more

sineoko [7]

Answer:

19, 58 and 103

Step-by-step explanation:

Okay. Here we need to convert whatever statements we have into a mathematical expression.

Firstly, let’s give the smallest angle a value of x. Where do we now go from here? The measure of one angle is 1 degree greater than 3 times the size of the smallest angle. This means the value of the second angle is 3x + 1

Now for the third angle, the question stated that the third angle is thirteen degrees less than twice the measure of the second angle. The value for this is: 2( 3x + 1) - 13

Now when we add all these angles, surely, we get a result equal to 180.

x + 3x + 1 + 2(3x + 1) - 13 = 180

4x + 1 + 6x + 2 - 13 = 180

10x - 10 = 180

10x = 190 and x = 19.

Now the measure of the other angles are as follows:

3x + 1 = 3(19) + 1 = 57 + 1 = 58

2(3x + 1) - 13 = 2(58) - 13 = 103

6 0

3 years ago