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3 years ago

Ava solved the compound inequality+7<-1 or 2x-129 for all possible values of x. Which graph represents

Mathematics

1 answer:

andre [41]3 years ago

4 0

Answer:

Step-by-step explanation:

To get the graph, we will need to solve each inequality differently

For the first one, we have that

x/4 < -1-7

x/4 < -8

x < -8 * 4

x < -32

For the second side;

2x-1 ≥ 9

2x ≥ 10

x ≥ 5

So we have two arrows facing different directions

On the left should be unshaded while the right hand side should be shaded

So, the correct answer here is the 4th option

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What is the value of (2/3)^-4 A. -81/16 B. -16/81 C. 16/81 D. 81/16

Alisiya [41]

For this case, we must find the value of the following expression:

$(\frac {2} {3}) ^ {- 4}$

By properties of powers we have that:

$a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}$

Thus, we can rewrite the expression as:

$\frac {1} {(\frac {2} {3}) ^ 4} =\\\frac {3 ^ 4} {2 ^ 4} =\\\frac {81} {16}$

So, we have to:

$(\frac {2} {3}) ^ {- 4} = \frac {81} {16}$

Answer:

$\frac {81} {16}$

Option D

5 0

3 years ago

Find cos y and tan y if csc y = -√6/2 and cot y >0.

fomenos

Answer:

$\cos y = -\dfrac{\sqrt{3} }{3}$

$\tan y = \sqrt{2}$

Step-by-step explanation:

Recall that

$\boxed{\csc y := \dfrac{1}{\sin y}}$

$\boxed{\cot y := \dfrac{\cos y}{\sin y}}$

We know that

$\csc y = \dfrac{-\sqrt{6} }{2}$

Note that according to the definition of $\csc y$ it is true that both sine and cosine are negative, once $\csc y = \dfrac{-\sqrt{6} }{2}$ . Because $\cot y > 0$ , this conclusion is true. We basically have

$\boxed{(-a)(1/-b)=a/b \text{ such that } a,b\in\mathbb{R}_{\geq 0}}$

Sure it is true $\forall y\in\mathbb{R}$ but perhaps this way is better to understand.

In order to find sine, we can use the definition and manipulate the rational expression.

$\csc y = \dfrac{-\sqrt{6} }{2} = \dfrac{-\sqrt{6} / -\sqrt{6} }{2/-\sqrt{6} } = \dfrac{1 }{-\dfrac{2}{\sqrt{6} } }$

Therefore,

$\sin y =-\dfrac{2}{\sqrt{6} }$

Here I just divided numerator and denominator by $-\sqrt{6}$ .

Now, to find cosine we can use the identity

$\boxed{\sin^2y +\cos ^2y =1}$

Thus,

$\left(-\dfrac{2}{\sqrt{6} }\right)^2 + \cos ^2y =1 \implies \dfrac{4}{6 } +\cos ^2y =1$

$\implies \cos ^2y =1 - \dfrac{4}{6 } \implies \cos ^2y =\dfrac{1}{3 } \implies \cos y = \pm \dfrac{\sqrt{1} }{\sqrt{3} } = \pm \dfrac{\sqrt{1} \sqrt{3} }{3} = \pm \dfrac{\sqrt{3} }{3}$

$\cos y = \pm\dfrac{\sqrt{3} }{3}$

Once we have $\cot y > 0$ , we just consider

$\cos y = -\dfrac{\sqrt{3} }{3}$

FInally, for tangent, just consider

$\boxed{\tan y := \dfrac{\sin y}{\cos y}}$

thus,

$\tan y = \dfrac{\sin y}{\cos y} = \dfrac{-\frac{2}{\sqrt{6} }}{-\frac{\sqrt{3} }{3}} = \dfrac{6}{\sqrt{18} } =\dfrac{6}{3\sqrt{2} } =\dfrac{2}{\sqrt{2} } = \sqrt{2}$

5 0

3 years ago

PLEASE HELP! Solve for x. A.108 degrees B.72 C.18 D.17

sleet_krkn [62]

Answer:

Step-by-step explanation:

90 - 72 = 18

4 0

3 years ago

What are solutions to the following equation? a^2 =6.4

Stels [109]

Answer:2.5

Step-by-step explanation:

if u multiply 2.5 x 2.5 u will get 6.25 and that will be the closes to 6.4 because if u multiply 2.6 x 2.6 that would be over 6.4 i hope this is right and it helps!

3 0

4 years ago

I want to know what 64 take away 3 is

Kaylis [27]

The
answer is 61 one because 64-3

8 0

3 years ago

Read 2 more answers