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3 years ago

Solve the given inequality and graph the solution on a number line. -x/2 + 3/2 < 5/2 Answer?

Mathematics

1 answer:

malfutka [58]3 years ago

6 0

Answer:X>-2

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don’t contain the variable.

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I need help with this please help me

Fofino [41]

Answer:

$+ \times + = + \\ - \times - = + \\ - \times + = - \\ + \times - = -$

6 0

4 years ago

Solve the following exponential equations.<br> 2(4^x )+ 4^(x+1 )= 342

Cloud [144]

Answer:

x ≈ 2.91644500708

Step-by-step explanation:

The equation can be simplified to ...

2(4^x) +4(4^x) = 342

6(4^x) = 342

4^x = 57

Taking logarithms, we get ...

x = log₄(57) = log(57)/log(4)

x ≈ 2.91644500708

5 0

3 years ago

Cos pi/4 cos pi/6= 1/2(___pi/12+cos 5pi/12) fill in the blank

inessss [21]

Answer:

$\cos(\frac{\pi}{4})\cos(\frac{\pi}{6})=\frac{1}{2}(\cos(\frac{\pi}{12})+\cos(\frac{5\pi}{12}))$

So the blank is cos.

Step-by-step explanation:

There is an identity for this:

$\cos(a)\cos(b)=\frac{1}{2}(\cos(a+b)+\cos(a-b))$

Let's see if this is fit by your left hand and right hand side:

So $a=\frac{\pi}{4}$ while $b=\frac{pi}{6}$ .

Let's plug these in to the identity above:

$\cos(\frac{\pi}{4})\cos(\frac{\pi}{6})=\frac{1}{2}(\cos(\frac{\pi}{4}+\frac{\pi}{6})+\cos(\frac{\pi}{4}-\frac{\pi}{6}))$

Ok, we definitely have the left hand sides are the same.

Let's see if the right hand sides are the same.

Before we move on let's see if we can find the sum and difference of $\frac{\pi}{4}$ and $\frac{\pi}{6}$ .

We will need a common denominator. How about 12? 12 works because 4 and 6 go into 12. That is 4(3)=12 and 6(2)=12.

$\frac{\pi}{4}+\frac{\pi}{6}=\frac{3\pi}{12}+\frac{2\pi}{12}=\frac{5\pi}{12}$ .

$\frac{\pi}{4}-\frac{\pi}{6}=\frac{3\pi}{12}-\frac{2\pi}{12}=\frac{\pi}{12}$ .

Let's go back to our identity now:

$\cos(\frac{\pi}{4})\cos(\frac{\pi}{6})=\frac{1}{2}(\cos(\frac{\pi}{4}+\frac{\pi}{6})+\cos(\frac{\pi}{4}-\frac{\pi}{6}))$

$\cos(\frac{\pi}{4})\cos(\frac{\pi}{6})=\frac{1}{2}(\cos(\frac{5\pi}{12})+\cos(\frac{\pi}{12}))$

We can rearrange the right hand side inside the ( ) using commutative property of addition:

$\cos(\frac{\pi}{4})\cos(\frac{\pi}{6})=\frac{1}{2}(\cos(\frac{\pi}{12})+\cos(\frac{5\pi}{12}))$

So comparing my left hand side to their left hand side we see that the blank should be cos.

4 0

3 years ago

James has a piece of construction paper with an area of 65 1/4 inches. it is 9 2/3 inches long. What is the width of the pieces

sertanlavr [38]

Area = length*width
Width = area/length

width = (65 1/4 in^2)/(9 2/3 in)

width = 6 3/4 inches

Hope this helps :)

3 0

3 years ago

What is the recursive formula for this sequence . 10,14,18,22,26,...

ad-work [718]

X+4 it is add 4 digit

6 0

3 years ago