Unit 8 test study guide right triangles and trigonometry

Answer:

Step-by-step explanation:

cc

Answer:

x = 0

Step-by-step explanation:

[tex]{2}^{x} - {3}^{x} = \sqrt{ {6}^{x} } - \sqrt{ {9}^{x } } \\ \\ {2}^{x} - {3}^{x} = \sqrt{ {6}^{x} } - \sqrt{ {( {3}^{2}) }^{x } } \\ \\ {2}^{x} - {3}^{x} = \sqrt{ {6}^{x} } - \sqrt{ {({3)}^{2x}}}\\ \\ {2}^{x} - \cancel{{3}^{x}} = \sqrt{ {6}^{x} } - \cancel{ {3}^{x} } \\ \\ {2}^{x} = \sqrt{ {6}^{x} } \\ squaring \: both \: sides \\ \\ {( {2}^{x} )}^{2} = {(\sqrt{ {6}^{x} })}^{2} \\ \\ {2}^{2x} = {6}^{x} \\ \\ {2}^{2x} = {(2 \times 3)}^{x} \\ \\ {2}^{2x} = {2 ^{x} \times 3}^{x} \\ \\ \frac{ {2}^{2x} }{ {2}^{x} } = 3^{x} \\ \\ {2}^{2x - x} = {3}^{x} \\ \\ {2}^{x} = {3}^{x} \\ \\ \frac{ {2}^{x} }{ {3}^{x} } = 1 \\ \\ \bigg( \frac{2}{3} \bigg)^{x} = 1 \\ \\ \implies \: x = 0 \\ \\ \because \: for \: x = 0 \\ \\ \bigg( \frac{2}{3} \bigg)^{0} = 1[/tex]

Answer:

The value of x is 3

Step-by-step explanation:

Here, we want to find the value of x

to do this, we apply the principle of similar triangles

That would work as follows;

4/x + 5 = 7/(2x + x + 5)

4/x + 5 = 7/3x + 5

4(3x + 5) = 7(x + 5)

12x + 20 = 7x + 35

12x - 7x = 35-20

5x = 15

x = 15/5

x = 3

Answer:

[tex]( - inf, - 3.5) \\ ( - 1, 2.5)[/tex]

These are interval for increasing (doesnt include relative max-min)

Step-by-step explanation:

Increasing means when we input the value of x and we get the increase of y-value.

A bit hard to imagine? You can look at the graph instead. The name already says it all, Increasing Graph. The graph keeps rising and rising till the max and that is increasing.

The decreasing is when the graph decreases to minimum. The graph would face down for decreasing.

Since we only want the increasing. We look at the graph and tell which region does the graph face up and that is the increasing.

Answer:

=0

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

if f(x)=1/5(6-x)^2 when f(16)you will replace x by 16 then solve it like this

f(16)=1/5(6-16)^2

= 1/5(-10)^2

=1/5(100)

=20

Answer:

on product side there will also 6 carbon atom

Answer:

y = 28

Step-by-step explanation:

Answer: The answer is s = 14 * 5 = (70) So each swaeter is $3.50

Answer:

s>7

Step-by-step explanation:

she spent more than $42 total so

x>42

we factor in the 14 dollar shirt and 4 sweaters

14+4s>42

isolate x on one side

4s>28

s>7

here's the graph from desmos

Answer:

-5

Step-by-step explanation:

The axis of symmetry is the x- axis of the vetex.

Answer:

541.1 square feet

Step-by-step explanation:

A = πr²

1) convert in. to ft because answer is in sq. ft

78 in => 6.5 ft

2) Find radius of entire area

6.5 ft + radius of inner circle

6.5 + 10 = 16.5

3) Calculate area of combined circles

A = π(16.5)²

A = 855.3 sq. ft

4) Find area of inner circle

A = π(10)²

A = 314.2 sq. ft

5) Subtract area of inner circle from combined area

855.3 sq ft - 314.2 sq. ft = 541.1 sq. ft

Answer:

The range of #1 is 13

The range of #2 is 9

The range of #3 is 20

The range of #4 is 59

Step-by-step explanation:

I had a math teacher in 6th grade who taught me a corny, but helpful rhyme.

It is

Hey diddle-diddle

The median's the middle (organize the numbers from least to greatest, then find the number in the middle)

You add (all the numbers), then divide (by how many numbers there are) for the mean

The mode is the one that appears the most (which number do you see more than once?)

The range is the difference between (find the smallest number and the largest number, then subtract the small one from the large one)

See? Corny huh? I hope this helps bro!

The range of data: [tex]52,48,57,47,49,60,59,51[/tex] is [tex]13[/tex]

The range of data:[tex]5,9,13,6,4,5,8,12,12,6[/tex] is [tex]9[/tex]

The range of data:[tex]97,106,99,97,115,95,108,100[/tex] is [tex]20[/tex]

The range of data : [tex]27,13,35,19,71,12,66,47,39[/tex] is [tex]59[/tex]

What is range?

In statistics, the range of a set of data is the difference between the largest and smallest values. Difference here is specific, the range of a set of data is the result of subtracting the sample maximum and minimum.

According to question, we have to find different range.

The range of data: [tex]52,48,57,47,49,60,59,51[/tex]

[tex]=60-47=13[/tex]

The range of data:[tex]5,9,13,6,4,5,8,12,12,6[/tex]

[tex]=13-4=9[/tex]

The range of data: [tex]97,106,99,97,115,95,108,100[/tex]

[tex]=115-95=20[/tex]

The range of data : [tex]27,13,35,19,71,12,66,47,39[/tex]

[tex]=71-12=59[/tex]

Hence, we can conclude that

The range of data: [tex]52,48,57,47,49,60,59,51[/tex] is [tex]13[/tex]

The range of data:[tex]5,9,13,6,4,5,8,12,12,6[/tex] is [tex]9[/tex]

The range of data:[tex]97,106,99,97,115,95,108,100[/tex] is [tex]20[/tex]

The range of data : [tex]27,13,35,19,71,12,66,47,39[/tex] is [tex]59[/tex]

Learn more about  range here:

https://brainly.com/question/12777994?referrer=searchResults

#SPJ2

Answer:

Step-by-step explanation:

1) elimination

2) elimination

3)add

4)subtract

5) Variable

6) add

7) eliminate

8) subtract

9) eliminate

10) adding

11) adding

12) 2

13)2

14) 0

15) (2 , 0)

16) (2 , 0)

17) solution

Answer:

225%

Step-by-step explanation:

Find the difference between the two prices, then divide it by the original price:

78 - 24 = 54

54/24

= 2.25

So, the markup rate is 225%

Answer: D.  T <-9, -2> (ΔABC) = ΔDEF

Step-by-step explanation:

D = A

A (3, 0) --> D (-6, -2)

To get the x-coordinate of D, you add -9 to 3

To get the y-coordinate of D, you add -2 to 0

T <-9, -2> (ΔABC) = ΔDEF

Hope this helped!

Step-by-step explanation:

23.1+x=-6.2

x=-6.2-23.1

x= -29.3

hope it helped

Answer:

х= -29.3

Step-by-step explanation:

Subtract 23.1 from both sides then simplify

Answer:

77

Step-by-step explanation:

I am right for sure

Answer:

h=−5/49

Step-by-step explanation:

Answer:

x= -8, y= -9

Step-by-step explanation:

(try and use m a t h w a y. It gives answers to everything) :)

Answer:

-2x+8

32x+8-34x

32x-34x=-2x

-2x+8

Answer:

Step-by-step explanation:

Choose 0 to substitute in for x to find the ordered pair. Remove parentheses. Simplify 3(0)−10 3 ( 0 ) - 10 .

Answer:

x +10 =0 (1)

-8x -9y=1 (2)

x=-10 => (2) 80-9y=1 =>y=9

=> x=-10, y=9

Step-by-step explanation:

Answer:

I don't know if I understood correctly but here is the answer I think could be right.

-5-(-8)=3

2+1=3

Answer:

2000

Step-by-step explanation:5%= 100 nickels

1%= 20 nickels

20 x 100 = 2000

Answer:

2,000

Step-by-step explanation:

If 5%=100 nickels , then 20x100=the number of nickels Chi has.  

20x100=2,000

3a² - 24ab + 48b² = 3 ( a - 4b )²

We will start by rewriting the given quadratic polynomial,

3a² - 24ab + 48b²

Taking out the common "3",

=> 3 ( a² - 8ab + 16b² )

Splitting the middle term i.e. " - 8ab " appropriately,

=> 3 ( a² - 4ab - 4ab + 16b² )

=> 3 [ a ( a - 4b ) - 4b ( a + 4b ) ]

=> 3 ( a - 4b ) ( a - 4b )

Hence, option C is correct.

Answer:

[tex]\huge\boxed{\tt{ 3 (a-4b)(a-4b)}}[/tex]

Step-by-step explanation:

[tex]\sf 3a^2-24ab+48b^2\\\\Taking \ 3 \ as \ common\\\\= 3 (a^2-8ab+16b^2)\\\\= 3 [(a)^2 - 2 (a)(4) + (4b)^2]\\\\Using \ Formula \ a^2 - 2ab + b^2 = (a-b)^2\\\\= 3 (a-4b)^2\\\\= 3 (a-4b)(a-4b)\\\\\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

38

Step-by-step explanation:

If you’re adding it’s 38

If you’re multiplying its 325

but I think you’re adding so it’s 38

Answer:

356

Step-by-step explanation:

13 x 12= 156

25 x 12= 300

300+156= 356

So the answer is 356