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Negative exponents

3

: Rational Numbers These five rational numbers are plotted on a horizontal number line.

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-\frac{5}{3}

\frac{5}{5}

-\frac{1}{2}

\frac{7}{10}

-\frac{4}{3}

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Which statement about the locations on the number line of the rational numbers is true?

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\frac{2}{3}

is farthest to the left, and

\frac{7}{8}

is farthest to the right.

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-\frac{1}{3}

is farthest to the left, and

\frac{7}{8}

is farthest to the right.

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-\frac{2}{3}

is farthest to the left, and

\frac{7}{10}

is farthest to the right.

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-\frac{4}{3}

is farthest to the left, and

\frac{7}{10}

is farthest to the right.

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These five rational numbers are plotted on a horizontal number line.

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-\frac{3}{3}, \frac{5}{5},-\frac{1}{5}, \frac{7}{10},-\frac{1}{3}

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Which statement about the locations on the number line of the rational numbers is true?

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\frac{2}{3}

is faithest to the left, and

\frac{7}{8}

is farthest to the right.

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-\frac{4}{3}

is farthest to the left, and

\frac{7}{8}

is farthest to the right.

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-\frac{2}{3}

is farthest to the left, and

\frac{7}{10}

is farthest to the right.

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\frac{4}{3}

is farthest to the left, and

\frac{7}{10}

is farthest to the right.

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Consider this matrix:

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\left[\begin{array}{cc} -10 & -10 \\ 6 & 9 \end{array}\right]

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Find the inverse of the matrix.

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Give exact values. Non-integers can be given as decimals or as simplified fractions.

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4

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AA khanacademy.org

Select all the expressions that are equivalent to

3^4 \times 7^4

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Multi-select Choices:

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\frac{1}{21^{-4}}

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21^8

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21^{16}

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21^4

f^{\prime}(x)=1 / f(x)

f(0)=2

f(4)

can be written in fully simplified form as

m \sqrt{n}

for some integers

m

n

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m

n

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\begin{array}{l} m= \square \\ n= \square \end{array}

0

8

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\qquad

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\qquad

10

, ind the range of

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Nothe length for

\overline{A B}

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\mathrm{m} \overline{A B}

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\begin{array}{l} \mathrm{m} \overline{A B}<5+9 \rightarrow \mathrm{m} \overline{A B} \\ \mathrm{~m} \overline{A B}>9-5 \rightarrow \mathrm{m} \overline{A B} \end{array}

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50

\overline{A B}

4 \mathrm{~cm}

14 \mathrm{~cm}

4 \mathrm{~cm}<\mathrm{m} \overline{A B}<14 \mathrm{~cm}

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Qlsoify each triangle by angles and sides.

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01

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3

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4

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\begin{array}{l} \text { obtuse triangle } \\ \text { scalene triangle } \end{array}

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\qquad

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\qquad

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\qquad

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The measure of two of the three angles of a triangle are given. Find the neasure of the remaining angle. Then classify the triangle by its angles.

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2

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6

\qquad

3

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7

\qquad

4

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8

\qquad

5

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\qquad

6

\qquad

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\qquad

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\qquad

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9

\qquad

0

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10

\qquad

1

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11

\qquad

2

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12

\qquad

3

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\qquad

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\qquad

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\qquad

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\qquad

peview Score Image

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5

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Simplify the expression, if possible. If the

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\frac{x^{2}-3 x-18}{x^{2}-7 x+6}=\square, x \neq 6

in the figure below,

m \angle 2=63^{\circ}

m \angle 1, m \angle 3

m \angle 4

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\begin{array}{l} m \angle 1= \\ m \angle 3= \\ m \angle 4= \end{array}

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\square^{\circ}

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\square

5

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x^{3}+2 x^{2}+p x-3

has the same remainder when it is divided by

x+1

x

-2

. Find the value of

p

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3

\{(\overline{12-3} \times 2)-11\} \div 7+17

2

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Menyelesaikan SPLDV Menggunakan Metode Substitusi

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Kerjakan soal secara individu.

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1 \mathrm{~kg}

kentang dan harga

1 \mathrm{~kg}

wortel dengan menyelesaikan SPLDV berikut menggunakan metode substitusi.

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\begin{array}{l} 2 x+3 y=66.000 \\ 3 x+y=57.000 \end{array}

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Ikuti langkah-langkah berikut.

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1

. Nyatakan variabel

y

x

pada persamaan (

2

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2

. Substitusikan persamaan

y

x

ke dalam persamaan (

1

) sehingga diperoleh nilai

x

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3

. Substitusikan nilai

x

ke dalam persamaan

y

x

sehingga diperoleh nilai

y

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4

. Buatlah kesimpulan harga

1 \mathrm{~kg}

kentang dan harga

1 \mathrm{~kg}

2

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Menyelesaikan SPLDV Menggunakan Metode Substitusi

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Kerjakan soal secara individu.

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1 \mathrm{~kg}

kentang dan harga

1 \mathrm{~kg}

wortel dengan menyelesaikan SPLDV beriku menggunakan metode substitusi.

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\begin{array}{l} 2 x+3 y=66.000 \\ 3 x+y=57.000 \end{array}

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Ikuti langkah-langkah berikut.

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1

. Nyatakan variabel

y

x

pada persamaan (

2

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2

. Substitusikan persamaan

y

x

ke dalam persamaan (

1

) sehingga diperoleh nilai

x

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3

. Substitusikan nilai

x

ke dalam persamaan

y

x

sehingga diperoleh nilai

y

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4

. Buatlah kesimpulan harga

1 \mathrm{~kg}

kentang dan harga

1 \mathrm{~kg}

Identify each as rational or irrational by typing the word in the blank. These must all be correct to earn

2

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\sqrt{144}

\qquad

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\sqrt{\frac{4}{36}}

\qquad

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\sqrt{8}

\qquad

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\pi

\qquad

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\sqrt{0.64}

a / a n

\qquad

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\qquad

1

\qquad

4

2

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10

a Use a calculator to find

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1

1

Irrational numbers

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(\sqrt{2}+1)\times(\sqrt{2}-1)

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(\sqrt{3}+1)\times(\sqrt{3}-1)

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b Continue the pattern of the multiplications in part a.

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(\sqrt{4}+1)\times(\sqrt{4}-1)

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c Generalise the results to find

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(\sqrt{N}+1)\times(\sqrt{N}-1)

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N

is a positive integer.

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d Check your generalisation with further examples.

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11

Here is a decimal:

5.020020002000020000

k

whose domain is the set of positive integers is defined as

k(1)=4

k(n)=k(n-1)-2

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k

was evaluated for several numbers. Which of the following are true?

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Select each correct answer.

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k(-1)=-4

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k(0)=-2

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k(2)=2

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k(3)=0

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k(6)=3

Complete each number sentence with + or -. Use the number line tool to check your answer.

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\begin{array}{l} 7+(-7)=0 \\ -4-(-4)=0 \end{array}

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\begin{array}{l} 2+(-2)=0 \\ 5+(-5)=0 \end{array}

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-6-(-6)=0

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A number and its opposite are called additive inverses. Additive inverses have a sum of

0

Write the expression as a whole number with a negative exponent. Do not evaluate the expression.

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\frac{1}{8^6}

Write the expression as a whole number with a negative exponent. Do not evaluate the expression.

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\frac{1}{4^3}

Which is equal to

\frac{1}{31^{79}}

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\frac{1}{(-31)^{79}}

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(-31)^{-79}

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31^{-79}

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31^{79}

Write the expression as a fraction with a positive exponent. Do not evaluate the expression.

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\frac{1}{53^{15}}

Write the expression as a fraction with a positive exponent. Do not evaluate the expression.

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\frac{1}{21^9}

Write the expression as a whole number with a negative exponent. Do not evaluate the expression.

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\frac{1}{7^{17}}

Write the expression as a fraction with a positive exponent. Do not evaluate the expression.

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\frac{1}{47^{79}}

Write the expression as a whole number with a negative exponent. Do not evaluate the expression.

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\frac{1}{49^6}

Write the expression as a fraction with a positive exponent. Do not evaluate the expression.

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\frac{1}{80^{-4}}

Write the expression as a whole number with a negative exponent. Do not evaluate the expression.

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\frac{1}{5^3}

Write the expression as a fraction with a positive exponent. Do not evaluate the expression.

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\frac{1}{3^{68}}

Which is equal to

\frac{1}{28^9}

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-\frac{1}{28^{-9}}

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\frac{1}{28^{-9}}

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28^{-9}

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(-28)^{-9}

Write the expression as a fraction with a positive exponent. Do not evaluate the expression.

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\frac{1}{3^7}

Which is equal to

\frac{1}{83^{81}}

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(-83)^{81}

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83^{-81}

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-83^{81}

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-\frac{1}{83^{-81}}

Write the expression as a whole number with a negative exponent. Do not evaluate the expression.

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\frac{1}{4^{23}}

Which is equal to

\frac{1}{23^8}

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23^{-8}

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-23^8

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(-23)^8

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-\frac{1}{23^{-8}}

Write the expression as a whole number with a negative exponent. Do not evaluate the expression.

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\frac{1}{82^5}

Which is equal to

\frac{1}{19^9}

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19^{-9}

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-\frac{1}{19^{-9}}

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-19^9

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19^9

Write the expression as a fraction with a positive exponent. Do not evaluate the expression.

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\frac{1}{94^{-42}}

Write the expression as a whole number with a negative exponent. Do not evaluate the expression.

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\frac{1}{76^{38}}

Write the expression as a fraction with a positive exponent. Do not evaluate the expression.

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\frac{1}{8^9}

Write the expression as a whole number with a negative exponent. Do not evaluate the expression.

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\frac{1}{72^{92}}

Write the expression as a whole number with a negative exponent. Do not evaluate the expression.

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\frac{1}{66^7}

Write the expression as a fraction with a positive exponent. Do not evaluate the expression.

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\frac{1}{5^{42}}

Write the expression as a whole number with a negative exponent. Do not evaluate the expression.

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\frac{1}{3^9}

Write the expression as a whole number with a negative exponent. Do not evaluate the expression.

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\frac{1}{8^{54}}

Which is equal to

\frac{1}{4^{34}}

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-\frac{1}{(-4)^{-34}}

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-\frac{1}{4^{-34}}

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-4^{34}

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4^{-34}

Write the expression as a fraction with a positive exponent. Do not evaluate the expression.

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\frac{1}{75^{-6}}

Which is equal to

\frac{1}{94^{10}}

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(-94)^{10}

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94^{-10}

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-\frac{1}{94^{-10}}

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\frac{1}{(-94)^{-10}}

Write the expression as a whole number with a negative exponent. Do not evaluate the expression.

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\frac{1}{84^4}

Write the expression as a fraction with a positive exponent. Do not evaluate the expression.

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\frac{1}{7^6}

Which is equal to

3^{-49}

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(-3)^{-49}

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\frac{1}{3^{49}}

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-(-3)^{49}

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\frac{1}{(-3)^{-49}}

Write the expression as a whole number with a negative exponent. Do not evaluate the expression.

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\frac{1}{89^{78}}