Find the value of x to the nearest tenth.

Answer and Step-by-step explanation:

Angle B' is congruent to Angle B.

The measure of an angle stays the same when dilating, translating, and other transformations.

#teamtrees #PAW (Plant And Water)

Answer:

[tex](a)\ \sec^2(\theta) = 82[/tex]

[tex](b)\ \cot(\theta) = \frac{1}{9}[/tex]

[tex](c)\ \cot(\frac{\pi}{2} - \theta) = 9[/tex]

[tex](d)\ \csc^2(\theta) = \frac{82}{81}[/tex]

Step-by-step explanation:

Given

[tex]\tan(\theta) = 9[/tex]

Required

Solve (a) to (d)

Using tan formula, we have:

[tex]\tan(\theta) = \frac{Opposite}{Adjacent}[/tex]

This gives:

[tex]\frac{Opposite}{Adjacent} = 9[/tex]

Rewrite as:

[tex]\frac{Opposite}{Adjacent} = \frac{9}{1}[/tex]

Using a unit ratio;

[tex]Opposite = 9; Adjacent = 1[/tex]

Using Pythagoras theorem, we have:

[tex]Hypotenuse^2 = Opposite^2 + Adjacent^2[/tex]

[tex]Hypotenuse^2 = 9^2 + 1^2[/tex]

[tex]Hypotenuse^2 = 81 + 1[/tex]

[tex]Hypotenuse^2 = 82[/tex]

Take square roots of both sides

[tex]Hypotenuse =\sqrt{82}[/tex]

So, we have:

[tex]Opposite = 9; Adjacent = 1[/tex]

[tex]Hypotenuse =\sqrt{82}[/tex]

Solving (a):

[tex]\sec^2(\theta)[/tex]

This is calculated as:

[tex]\sec^2(\theta) = (\sec(\theta))^2[/tex]

[tex]\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2[/tex]

Where:

[tex]\cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]

[tex]\cos(\theta) = \frac{1}{\sqrt{82}}[/tex]

So:

[tex]\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2[/tex]

[tex]\sec^2(\theta) = (\frac{1}{\frac{1}{\sqrt{82}}})^2[/tex]

[tex]\sec^2(\theta) = (\sqrt{82})^2[/tex]

[tex]\sec^2(\theta) = 82[/tex]

Solving (b):

[tex]\cot(\theta)[/tex]

This is calculated as:

[tex]\cot(\theta) = \frac{1}{\tan(\theta)}[/tex]

Where:

[tex]\tan(\theta) = 9[/tex] ---- given

So:

[tex]\cot(\theta) = \frac{1}{\tan(\theta)}[/tex]

[tex]\cot(\theta) = \frac{1}{9}[/tex]

Solving (c):

[tex]\cot(\frac{\pi}{2} - \theta)[/tex]

In trigonometry:

[tex]\cot(\frac{\pi}{2} - \theta) = \tan(\theta)[/tex]

Hence:

[tex]\cot(\frac{\pi}{2} - \theta) = 9[/tex]

Solving (d):

[tex]\csc^2(\theta)[/tex]

This is calculated as:

[tex]\csc^2(\theta) = (\csc(\theta))^2[/tex]

[tex]\csc^2(\theta) = (\frac{1}{\sin(\theta)})^2[/tex]

Where:

[tex]\sin(\theta) = \frac{Opposite}{Hypotenuse}[/tex]

[tex]\sin(\theta) = \frac{9}{\sqrt{82}}[/tex]

So:

[tex]\csc^2(\theta) = (\frac{1}{\frac{9}{\sqrt{82}}})^2[/tex]

[tex]\csc^2(\theta) = (\frac{\sqrt{82}}{9})^2[/tex]

[tex]\csc^2(\theta) = \frac{82}{81}[/tex]

Answer:

72 crayons

Step-by-step explanation:

8/3 × 27 = 72 crayons

Answer:

let the number of adult tickets = x

Then the number of student tickets = 3x

Total tickets x+3x = 416

4x = 416

x = 416/4

x = 104

Therefore the number of adult tickets sold is 104

Step-by-step explanation:

Answer:

Step-by-step explanation:

If the radius of the circle is equal to

[tex]\sqrt{\frac{A}{3} }[/tex] and the area is given as 45, then

[tex]r=\sqrt{\frac{45}{3} }[/tex] which simplifies to

[tex]r=\sqrt{15}[/tex] and to the nearest tenth,

r = 3.9

Answer:

The margin of error is of 20, option B.

Step-by-step explanation:

Confidence interval concepts:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The margin of error is the subtraction between the bounds, divided by 2.

In this question:

Lower bound: 200

Upper bound: 240

Margin of error:

(240 - 200)/2 = 40/2 = 20

The margin of error is of 20, option B.

Answer:

Step-by-step explanation:

In order to write the equation of the line perpendicular to the given line, we first have to know what the slope of the given line is, and there's no way to tell by looking at it in its current form, which is standard. We need to solve that equation for y to determine the slope of that line. Solving for y:

[tex]-3y=-4x+5[/tex] and

3y = 4x - 5 (just change all the signs so our y term isn't negative anymore...yes, you're "allowed" to do that!) and

[tex]y=\frac{4}{3}x-\frac{5}{3}[/tex] So we can see now that the slope of this line is 4/3. That means that the perpendicular slope is -3/4. Passing through the given point (3, 5):

[tex]y-5=-\frac{3}{4}(x-3)[/tex]* and

[tex]y-5=-\frac{3}{4}x+\frac{9}{4}[/tex] and

[tex]y=-\frac{3}{4}x+\frac{9}{4}+\frac{20}{4}[/tex] so

[tex]y=-\frac{3}{4}x+\frac{29}{4}[/tex]** and, in standard form:

4y = -3x + 29 and

3x + 4y = 29***

* : point-slope form

** : slope-intercept form

*** : standard form

Answer:

The 90% confidence interval for the mean is (170.87 , 189.13)

Step-by-step explanation:

Using the calculator we can easily calculate   the 90% confidence interval for the mean, the given values are:

mean=180

sx : 38.5

n : 50

c - Level : 0.90

Then the output will be [170.87 , 189.13]

Answer:1 inch = 0.0833333 feet so 74 x 0.0833333 = 6.16667

Step-by-step explanation:

Answer:

Average rate of change = 5

Step-by-step explanation:

Average rate of change of a function is defined by the expression over the interval a ≤ x ≤ b,

Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]

Using this rule for the average rate of change of the function (defined by the table) over the interval 4 ≤ x ≤ 5,

Average rate of change = [tex]\frac{f(5)-f(4)}{5-4}[/tex]

From the table,

f(5) = 10

f(4) = 5

Therefore, average rate of change of the function = [tex]\frac{10-5}{5-4}[/tex]

                                                                                    = 5

Answer:

=5

Step-by-step explanation:

Answer:

Step-by-step explanation:

x²+7x+10=0

ur answer is there in image

Answer:

Question 4 is B and Question 5 is C

Step-by-step explanation:

Question 4 is B because the DIFFERENCE between the two terms is 15 therefore when you subtract the terms it must equal 15 so B could no be an answer. Also since they both equal 24 they both add up to 24

Answer:

18 L

Step-by-step explanation:

a = 36,864 * (1/2)^(11)

a = 18

36 L of water will be left after 11 days

GP is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number .

Constituting an GP according to the question

36,864 , 18432 , 9216 , ...........

In order to find nth term  of an GP, formula used will be :

a(n) = a (r^(n-1))

considering above GP ,

a(n) = ? water left after 11 days

a = 36864

r= 18432 /36864 = 1/2

n = 11

a(n) = 36864 ((1/2)^(11-1))

  a(n) =   36

Hence 36 L of water will be left after 11 days

Learn more about GP:

https://brainly.com/question/4853032?referrer=searchResults

#SPJ2

Answer:

225cc

Step-by-step explanation:

the solution is attached to the picture.

The amount of the 10% solution should he use if the nurse mixes 90 cc of a 45% saline solution with a 10% saline solution is 225cc

Let the amount of 10% solution she should use be x.

If a nurse mixes 90 cc of a 45% saline solution with a 10% saline solution to produce a 20% saline solution, the equivalent equation will be:

90(0.45) + 0.1x = 0.2(90+x)

Simplify the resulting equation for "x"

40.5 + 0.1x = 18 + 0.2x
0.1x = 40.5 - 18
0.1x = 22.5
x = 225cc

Hence the amount of the 10% solution should he use if the nurse mixes 90 cc of a 45% saline solution with a 10% saline solution is 225cc

Learn more on proportion here: https://brainly.com/question/19994681

Answer:

376 inches squared.

Step-by-step explanation:

Answer:

ur dog water kid *take the L dance

Step-by-step explanation:

cheese

Answer:

1/6x1/2=1/12

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

180 - 90 - 63 = 27

all angles in a triangle add up to 180 degrees

Answer:

Step-by-step explanation:

430

x4%

_________

$17.20+ $430= $447.20

Answer:

tan C is 90

tan B is 60

tan A is 60

Answer:

B

Step-by-step explanation:

Hi there!

We are given the points (-1,2) and (3,3) and we need to find the slope.

The formula for slope calculated from two points is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex], where ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex]) are points

since we have two points, we can substitute them into the formula, but let's label their values to avoid any confusion

[tex]x_{1}[/tex]=-1

[tex]y_{1}[/tex]=2

[tex]x_{2}[/tex]=3

[tex]y_{2}[/tex]=3

now substitute into the formula (m is the slope); remember: we have a negative number in this, so we'll be subtracting a negative.

m=[tex]\frac{3-2}{3--1}[/tex]

simplify

m=[tex]\frac{3-2}{3+1}[/tex]

m=[tex]\frac{1}{4}[/tex]

so B is your answer

Hope this helps! :)

Answer:

Step-by-step explanation:

Which rational function models the time, y, in hours, that it takes the train to travel between the two cities at an average speed of x miles per hour?  

✔ y = 160/x

What does the number 160 represent in the rational function that models the situation?

✔distance, in miles, between the cities

amount of fuel, in gallons, used by the train

time, in minutes, needed to travel between the cities  

Answer: NOTE Pictures Are not in order! Make sure you check page number.

Step-by-step explanation:

On page 6 the answers are ”C” and ”5lbs”

On page 7 the answers are “C”, “$ 418”, “ The cat”, and then “ $960”.

On page 8 the answers are : < Just copy paste this below.>

“Based on the calculation, they should purchase the second television as the cost is cheaper.

Based on the information given in the question, the cost of the first television will be:

= $330 + ($14 × 8)

= $330 + $102

= $442

The cost of the second television will be:

= $369 + ($9 × 8)

= $369 + $72

= $441

Therefore, the second television is cheaper.”

                   ^    

<Just copy paste this. >           [Then check. “A,B,C,”.]

On page 9 the answer is “ D “.

Answer:

55%

Step-by-step explanation:

Just do 33/60 and multiply by 100

Answer:

A

Step-by-step explanation:

Answer:

The two minimum numbers = 5, 5

Step-by-step explanation:

Let the first number = x

let the second number = y

Their sum: x + y = 10

Sum of their squares:  = x² + y²

y = 10 - x

f(x) = x² + (10 - x)²

f(x) = x² + 100 - 20x  + x²

f(x) = 2x² - 20x  +  100

Find the derivative of f(x), to obtain the critical points;

f'(x) = 4x - 20

4x - 20 = 0

4x = 20

x = 5

The value of y is calculated as;

y = 10 - x

y = 10 - 5

y = 5

The two minimum numbers = 5, 5

Answer:

lx-3l

Step-by-step explanation:

negative in the abs means moving to the right

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

Explanation:

We start with the parent function y = |x|

Shifting it 3 units to the right will make the equation y = |x-3| and that's the equation of the green curve shown.

The x-3 is because each input is 3 units smaller than it used to be. Imagine the xy axis moved 3 units to the left while the V shaped graph stayed fixed in place. It would give the illusion the V shape moved while the xy axis stay fixed.

The graph doesn't shift up or down, so k = 0

The value of 'a' stays the same at a = 1.