10. SImplify. Write using rational exponents. Be sure to show any work and simplify your answer

Answer:

the missing side is 6

Step-by-step explanation:

Using the Pythagorean theorem, ([tex]a^{2} + b^{2} = c^{2}[/tex]), for right triangles, you get [tex]4^{2} + (2\sqrt{5}) ^{2} = c^{2}[/tex].  Since the square cancels the square root for side b you get [tex](2^{2})*(5)[/tex] which equals 20. This makes your equation go to 16+20 = [tex]c^{2}[/tex]. Then add the numbers to make [tex]36=c^{2}[/tex]  solve for c by taking the square root of both sides to get c = 6.

Answer:

-30a⁵b + 12a⁴b² + 16a³b² - 4a²b⁴ - 2ab³

Step-by-step explanation:

( - 6a³b + 2ab²)( 5a² - 2ab² b)

multiply the second parantheses by each term from the first parantheses.

-6a³b×(5a²- 2ab²b -b)+2ab×(5a² -2ab²b-b)

-6a³b× (5a² - 2ab² b) +2ab × (5a² - 2ab² b)

-30 a⁵b + 12a⁴b² + 6a³b²+ 10a³b² - 4a²b⁴ - 2ab

combine like terms

-30a⁵b + 12a⁴b² + 16a³b² - 4a²b⁴ - 2ab³

Answer:

(-1, 8)

the value of a is 8

Answer:

(c) 84

hope this helps!!!!

Answer:

$900.9

Step-by-step explanation:

Find the final price of a $849.99

laptop with 6% sales tax.

Given data

Price= $849.99

Tax = 6%

Let us find the amount of the tax

=6/100*849.99

=0.06*849.99

=$50.9994

Now the final price is

=50.9994+849.99

=$900.9

Answer:

B. -√13/4

Step-by-step explanation:

cos 0 = -√3/4 => x=-√3 , h=4

tan 0 > 0

y should be on quadrant III

y= √4²-3= √16-3=√13 => -√13

so, sin 0 = y/h = -√13/4

Answer:

B. -√13/4

Step-by-step explanation:

:)

The required measure of the angle m∠H is given as 94°.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,
For trapezoid, the sum of the adjacent angle is 180°
m∠H + m∠G = 180
5x + 26 + 8x - 2 = 180
x = 12

Now,
m∠H = 8x - 2
        = 8 (12) - 2
        = 94°

Thus, the required measure of the angle m∠H is given as 94°.

Learn more about Angles here:
https://brainly.com/question/13954458

#SPJ2

Answer:

C

Step-by-step explanation:

Given

2(5x + 3) + 2 = 10x + 6 ← distribute and simplify left side

10x + 6 + 2 = 10x + 6

10x + 8 = 10x + 6 ( subtract 6 from both sides )

10x + 2 = 10x ( subtract 10x from both sides )

2 = 0 ← not possible

This indicates the equation has no solution

Answer:

no solutions

Step-by-step explanation:

2(5x + 3) + 2 = 10x + 6

* solve for x *

step 1 distribute the 2 to 5x and 3

2 * 5x = 10x

2*3=6

we now have 10x + 6 + 2 = 10x + 6

step 2 combine like terms

6 + 2 = 8

we now have 10x + 8 = 10x + 6

step 3 subtract 10x from each side

10x-10x=0

10x-10x=0

we're left with 8 = 6

8 is not equal to 6 meaning that there are no solutions to the equation

Answer:

I only see 1 graph...

hksjfjf

Answer:

Step-by-step explanation:

here,

base=28 ft

height=24 ft

are of parallelogram=base*height

=28*24

=672 ft^2

Answer:

672 ft²

Step-by-step explanation:

Area of parallelogram is the same as the area of a rectangle.

28 × 24 = 672 ft²

Experimental probability of the name Alex being drawn is 4/10

This is because out of the ten times a name was drawn, Alex was drawn four times.

If the experiment was repeated 1,000 times, Ella's name could be expected to be drawn 200 times.

This is because of the ten names drawn, Ella's name was drawn twice which is 20% and 20% of 1,000 is 200.

Answer:

D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

XYZ is congruent to DEF so:

X = D

Y = E

Z = F

Answer:

Daylilies- $11, Ornamental grass- $7

Step-by-step explanation:

For this one, you want to convert this into simultaneous equations.

If we let d be cost of one daylily and o be cost of one bunch of ornamental grass, we can write the equations as 2d+3o=43 and 6d+3o=87.

From there, we can see they share a like term (3o), so we subtract one equation from the other (since they both are preceded by a +). This gives 4d=44.

Dividing both sides by 4 isolates d, leaving d=$11.

We can substitute this value into either equation to work out o (I'm using the first one as it is easier). This makes it 2×11+3o=43, or 22+3o=43.

From there, we subtract 22 from both sides, giving 3o=21, and dividing by 3 gives a final result of o=$7.

**This content involves writing and solving simultaneous equations, which you may wish to revise. I'm always happy to help!

All working out:

d- cost of one daylily o- cost of one bunch of ornamental grass

2d+3o=43 6d+3o=87

6d+3o=87

 -     -     -

2d+3o=43

=     =    =

4d      =44

÷4        ÷4

d        =11

2d+3o=43

2×11+3o=43

22+3o=43

3o=21

o=7

Answer:

i do not understand what youre asking

Step-by-step explanation:

see^^^^^

Answer:

[tex]x= 23.775.[/tex]

Step-by-step explanation:

[tex]\text{We have} \\\cos(18\textdegree) = \frac{x}{25} \\\Rightarrow x= 25\cos(18\textdegree)\\\Rightarrow x= 25 \times 0.951\\\Rightarrow x= 23.775.[/tex]

Answer:

9.9 inches

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh  where b is the length of the base and h is the length of the height

49 = 1/2 x*x

Multiply each side by 2

2*49 = x^2

98 = x^2

Take the square root of each side

sqrt(98) = sqrt(x^2)

9.899494937 =x

Rounding to the nearest tenth

9.9 =x

Answer:

No, it's not a function

Step-by-step explanation:

In a function each input has one and only one output

Here an input of -3 has two outputs 2 and 1

Answer:

[tex]\sqrt{68}[/tex]

Step-by-step explanation:

(7 , -1) = (x1 , y1)

(9 , -9) = (x2 , y2)

distance formula = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]

=[tex]\sqrt{(9 - 7)^2 + (-9 - (-1))^2}[/tex]

=[tex]\sqrt{2^2 + (-9 + 1)^2}[/tex]

=[tex]\sqrt{4 + (-8)^2}[/tex]

=[tex]\sqrt{4 + 64}[/tex]

=[tex]\sqrt{68}[/tex]

Answer:

[tex]Distance = \sqrt{ 68 } \\\\or \\\\Distance =2 \sqrt{17}[/tex]

Step-by-step explanation:

[tex]Let \ (x_1 , y_1) = ( 7 , - 1 ) \ and \ (x_2, y _ 2 ) = ( 9 , - 9 )\\\\\\Distance = \sqrt{(x_2 - x_ 1)^2 + (y_ 2 - y_ 1)^2}\\\\[/tex]

               [tex]= \sqrt{(9 - 7)^2 + ( -9 --1)^2} \\\\=\sqrt{2^2 + ( -9 + 1)^2 }\\\\=\sqrt {4 + (-8)^2 }\\\\=\sqrt{ 4 + 64 }\\\\=\sqrt{68}\\\\= \sqrt { 4 \times 17}\\\\=\sqrt{2^2 \times 17}\\\\=2 \sqrt{17}[/tex]

Answer:

whats the question

Step-by-step explanation:

Answer:

The answer is below

Step-by-step explanation:

A drink is made by adding water to juice.

Instructions

Add an amount of water that is between 3 times and 5 times the amount of juice

Tanya has 130 ml of juice.

If she follows the instructions, work out the minimum and maximum amounts

of the drink she can make.

Solution:

The minimum amount of water that can be added to the juice is 3 times the amount of the juice, hence:

Minimum amount of water = 3 * 130 ml of juice = 390 ml of water

Therefore minimum amount of drink = 390 ml of water + 130 ml of juice

minimum amount of drink = 520 ml

The maximum amount of water that can be added to the juice is 5 times the amount of the juice, hence:

Maximum amount of water = 5 * 130 ml of juice = 650 ml of water

Therefore maximum amount of drink = 650 ml of water + 130 ml of juice

Maximum amount of drink = 780 ml

Answers:

[tex]\csc(\theta) = \frac{7\sqrt{33}}{33}\\\\\sin(\theta) = \frac{\sqrt{33}}{7}\\\\\cot(\theta) = \frac{4\sqrt{33}}{33}\\\\[/tex]

=============================================

Explanation:

Before we can find the trig ratios, we need to determine the length of the missing side. Apply the pythagorean theorem

[tex]a^2+b^2 = c^2\\\\4^2+b^2 = 7^2\\\\16+b^2 = 49\\\\b^2 = 49-16\\\\b^2 = 33\\\\b = \sqrt{33}[/tex]

The vertical side is [tex]\sqrt{33}[/tex] units long.

------------------------------------

The side we just found is the opposite side to angle [tex]\theta[/tex] (greek letter theta)

The hypotenuse is 7 units long. The hypotenuse is always opposite the right angle.

Divide the hypotenuse over opposite to get the cosecant.

[tex]\csc(\theta) = \frac{\text{hypotenuse}}{\text{opposite}}\\\\\csc(\theta) = \frac{7}{\sqrt{33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33}*\sqrt{33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33*33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33^2}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{33}\\\\[/tex]

Note: In the third step, I multiplied top and bottom by sqrt(33) to rationalize the denominator.

------------------------------------

Recall that sine is the reciprocal of cosecant, and vice versa.

So we'll use the same idea as before, but flip the original fraction.

[tex]\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(\theta) = \frac{\sqrt{33}}{7}\\\\[/tex]

The denominator is already a rational number, so there's not much else to do here.

--------------------------------------

Cotangent is the ratio of adjacent over opposite

[tex]\cot(\theta) = \frac{\text{adjacent}}{\text{opposite}}\\\\\cot(\theta) = \frac{4}{\sqrt{33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33}*\sqrt{33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33*33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33^2}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{33}\\\\[/tex]

The steps are pretty much nearly identical as the section involving csc, except we're using the adjacent in place of the hypotenuse (so that means we use 4 in place of 7).

Answer:

43347

Step-by-step explanation:

just move decimal to the right 4 times.

Answer:

A. 52

Step-by-step explanation:

Find how many months are in 4 years, since there are 4 years between her 13th and 17th birthdays.

There are 12 months in a year, so multiply 12 by 4:

12(4)

= 48

So, there are 48 months in 4 years. Since she buys a new teacup every month, this means she will have bought 48 more teacups.

Add this to the 4 teacups she got on her 13th birthday:

48 + 4

= 52

So, on her 17th birthday, she will have A. 52 teacups

Answer:

x = 6 and y = 0

Step-by-step explanation:

x + 2y = 6

x = 6 - 2y                          equation(i)

substitute the value of x

x + 2y = 6

6 - 2y - 2y = 6

-4y = 6 - 6

y = 0/-4

y = 0

substitute the value of x in equation (i)

x = 6 - 2y

x = 6 - 2*0

x = 6-0

x = 6

Answer:

Step-by-step explanation:

i think it is b

Answer:

0.58823529411

Answer:0.8

Step-by-step explanation: