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3 years ago

Write and graph an inequality that represents the numbers that are not solutions of each inequality.

Mathematics

1 answer:

o-na [289]3 years ago

8 0

A.) x + 8 < 14
-8 -8
x < 6
b.) x - 12 >/= 5.7
+12 +12
x >/= 17.7

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school teacher and needs 22 pieces of wood, 3 over 8 ft long, for a class project. If he has a 9-ft board from which to cut the

tiny-mole [99]

Answer:

Yes, he will have enough 3 over 8 ft pieces for his class.

Step-by-step explanation:

Given:

Number of wood required = 22

Length of each wood, $l=\frac{3}{8}\textrm{ ft}$

Total length of the board, $L=9\textrm{ ft}$

Therefore, the number of woods that can be made using the given board is given as:

$\textrm{Number of woods made}=\frac{\textrm{Total length of board}}{\textrm{Length of each wood}}\\\textrm{Number of woods made}=\frac{L}{l}=\frac{9}{\frac{3}{8}}=9\times \frac{8}{3}=\frac{72}{3}=24$

So, he can make 24 woods of length $\frac{3}{8}\textrm{ ft}$ using the 9 ft board. But he has to make only 22 pieces.

Therefore, he has enough of the wood to make the required number of pieces.

3 0

3 years ago

Applying Properties of Exponents In Exercise, use the properties of exponents to simplify the expression.

NemiM [27]

Answer: (a) $e^3$

(b) $e^{10}$

(c) $\dfrac{1}{e^4}$

(d) $e^{4}$

Step-by-step explanation:

Properties of exponents :

1) $a^m\times a^n=a^{m+n}$

2) $\dfrac{a^m}{a^n}=a^{m-n}$

3) $(a^m)^n=a^{mn}$

4) $a^{-n}=\dfrac{1}{a^n}$

Now , we simplify the given expression using the above properties.

a) $(e^6)(e^{-3})$

$=e^{6+(-3)}$ [By property (1)]

$=e^{6-3}=e^3$ [∵ (+)(-)=(-)]

b) $(e^{-2})^{-5}$

$=e^{-2\times-5}$ [By property (3)]

$=e^{10}$ [∵ (-)(-)=(+)]

c) $(\dfrac{e^6}{e^2})^{-1}$

$=(e^{6-2})^{-1}$ [By property (2)]

$=(e^{4})^{-1}$

$=\dfrac{1}{e^4}$ [By property (4)]

d) $(e^3)^{\frac{4}{3}}$

$=e^{3\times\frac{4}{3}}$ [By property (3)]

$=e^{4}$

7 0

3 years ago

If there are 10 Adam's on the left side of a balanced chemical equation how many will be on the right

aev [14]

Answer:4

Step-by-step explanation:

3 0

3 years ago

" 250 = x(34-x) solve x "

Andrews [41]

250=x(34-x) solve X "

the equation $x^{2} +250= 34x - x^{2} + x^{2} = 250x=34x 
$

X= 7.35

8 0

3 years ago

1 and 3/4 divided by -21

Over [174]

Let's firstly convert the mixed fractions to "improper", and then divide,

$\bf \stackrel{mixed}{1\frac{3}{4}}\implies \cfrac{1\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{7}{4}}
\\\\\\
\cfrac{7}{4}\div -21\implies \cfrac{7}{4}\div \cfrac{-21}{1}\implies \cfrac{7}{4}\cdot \cfrac{1}{-21}\implies \cfrac{7}{-84}\implies \stackrel{simplified}{-\cfrac{1}{12}}$

6 0

4 years ago

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