Consider the right triangle with hypotenuse 5, horizontal leg x , vertical leg y , and angle ∅ opposite y. How can we view x as depending on y? How can we view x as depending on ∅ ? Explain by using appropriate relationships in the triangle and writing x both as a function of y and as a function of ∅ .

Answers

Answer 1

9514 1404 393

Answer:

x = √(25 -y²)x = 5cos(Ф)

Step-by-step explanation:

The Pythagorean theorem relates the sides of a right triangle.

  x² + y² = 5²

  x² = 25 -y²

  x = √(25 -y²)

__

The cosine function relates the adjacent side and the hypotenuse of an acute angle in a right triangle.

  Cos = Adjacent/Hypotenuse

  Adjacent = Hypotenuse × Cos

  x = 5·cos(Ф)


Related Questions

solve equation
6x−5y=15
x=y+3

Answers

Answer:

6x-5y=15

6x=15+5y

x=15+5y÷6

x=y+15.8

Aaron's bedroom is in the shape of a rectangular prism. The bedroom measures 10 feet by 14 feet by 8 feet. How many cubic feet of space does the room contain?

Answers

The formula for the area of a rectangular room is width x length, as shown in the figure below: This is the equation used in our square footage calculator as well.

Maria has a jewelry box and wants to increase its size. She finds one with four times the length, width, and height. How many times bigger will the volume of the box be?

Answers

Answer:

64 times bigger

Step-by-step explanation:

I will use random values for this explanation to make it more understandable.

Lets say the length of the box is 1 inch, width is 1 inch, and height is 1 inch.

The volume would be l*w*h = 1*1*1 = 1 cubic inch

If the dimensions were 4 times bigger, the length, width and height would all be 4 inches.

4*4*4 = 64 cubic inches, which is 64 times bigger than the smaller box with a volume of 1 cubic inch.

Hope this answer helped! :)

A cheery tree is 6 feet tall. A palm is 3 times as tall as the cherry tree. Which model represents this problum

Answers

Answer: Bottom left

Step-by-step explanation:

Answer:

Bottom Left

Step-by-step explanation:

Im near 100% sure if im wrong im very sorry

20. Martin sells used cars.
He earns $12.50 per hour, plus 3% commission on
any cars he sells.
On Monday, he worked 6.5 hours and sold a car for
$9,000.
How much money did Martin earn on Monday?
A. $351.25 B. $282.50 C. $243.75

Answers

Answer:

The short answer is that most car salespeople don't earn a whole hell of a lot of money. Dealership salespeople average about 10 car sales per month, and earn an average of about $40k per year. If you do the math, that's about $330 per car.

Step-by-step explanation:

Answer:

You should prob add then multiply

Step-by-step explanation:

i'm sorry if you don't understand !BRB when i get the answer(Let's hope i don't forget.


4. Your best friend's birthday is tomorrow, and you would like to give her an ice cream cone
balloon. The spherical shaped ice cream on top of the cone has a radius of 6 inches. The cone
itself has a diameter of 12 inches and height of 24 inches. How many cubic inches of helium are
nded to fill the entire ice cream cone balloon? Use 3.14 for it.

Answers

Answer:

1808.64 IN^3

Step-by-step explanation:

Helium needed = volume of spherical shaped ice cream + volume of cone

Volume of a sphere = 4/3 x pi x r^3

4/3 x 3.14 x 6^3 = 904.32 ft^3

Volume of a cone 1/3 x (nr^2h)

n = 22/7

r = radius  = 12/2 = 6

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

h = height

1/3 x 3.14 x 6^2 x 24 = 904.32

helium needed = 2 x 904.32 = 1808.64 in^3

help meeee im failing pls show your work

Answers

Answer:

63298

Step-by-step explanation:

When you divide by a fraction, you have to flip the fraction and change the sign into multiplication. This means that it will be 632.98x100. We move the dot two ways to the right and get 63298.

If this answer has helped you please mark as brainliest

Answer:

632.98 ÷ 1/100

Step-by-step explanation:

R:

Calculate the value

632.98 ÷ 1/100

31649/50 ÷ 1/100

31649/50 × 100/1

63298

I hope I've helped :)

Use the figure to answer the question. 8 8 What is the area of the shaded region of the circle in terms of a? Enter the answer in the box. The area of the shaded region is f units squared.​

Answers

Answer:

48pi

Step-by-step explanation:

pi x 8² - pi x 4²

64pi - 16pi

48pi

Please help with algebra 2 I took a pic , I have 6 questions n need proof of work

Answers

Here is what I found for this question , hope it helps

Please answer the question question correctly with factual information for brainliest.

Answers

Answer:

A

Step-by-step explanation:

Which choice represents the fraction below as a single exponential
expression?
73
79

Answers

Answer:

C.

Step-by-step explanation:

use the division rule of exponents. 7 is your base and exponents is going to be 3 - 9 which is -6

fill in the missing values in the table below. Be sure to show work on how u found each r, d or C.

Answers

The area of a circle is the region bounded by the circumference . The area of circle is equal to Pi * r ^ 2 where the circle's radius. r = The circumference of a circle is the distance around the edge of a circle, similar to perimeter . The circumference of a circle is equal to , where r = the circle's radius.

The complete table is attached below.

Use the concept of a circle defined as:

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle possesses rotational symmetry around the center.

For wagon wheel:

Diameter = 3 ft

Since radius = diameter/2

Therefore,

Radius = 3/2 ft

Radius 'r' = 1.5ft

And the circumference of the circle = 2πr

So the circumference of this wagon wheel =  2x3.14x1.5

circumference of this wagon wheel = 9.42 ft

For airplane propellors:

Radius = 24 inch

Then diameter = 2x radius

Diameter = 2x24 in

Diameter = 48 in

The circumference of this airplane propellors =  2x3.14x48

The circumference of this airplane propellor = 301.48 in

For orange slice:

Circumference = 20 cm

Therefore,

2πr = 20

r ≈ 3.18 cm

Diameter = 2x3.18 cm

Diameter = 6.36 cm

Learn more about the circle visit:

https://brainly.com/question/24810873

#SPJ6

Judith has \$70 in a savings account that earns 5% interest , compounded annually .

To the nearest cent, how much will she have in 3 years ?

Answers

Answer:

$81.03

Step-by-step explanation:

Given

[tex]n = 1[/tex] --- annually

[tex]t =3[/tex] --- time

[tex]r = 5\%[/tex] --- rate

[tex]PV = \$70[/tex] ---- Present value

Required

The future value

This is calculated as:

[tex]FV = PV * (1 + \frac{r}{n})^{nt}[/tex]

This gives:

[tex]FV = 70 * (1 + \frac{5\%}{1})^{1*3}[/tex]

[tex]FV = 70 * (1 + 5\%)^3[/tex]

[tex]FV = 70 * (1.05)^3[/tex]

[tex]FV = 70 * 1.157625[/tex]

[tex]FV = 81.03375[/tex]

The future value to the nearest cent is: $81.03

How many triangles can the polygon below be divided into? A polygon with 10 sides. 6 7 8 9

Answers

Answer:

240

I think I'm not sure but try

Answer:

C. 8

Step-by-step explanation:

Just took the test (edge)

Good luck soldiers

What is the volume of this shape in terms of π (PI)?

Answers

Answer:

Step-by-step explanation:

1/3 bh=96 pi/3=32 pi

Answer:

[tex]\displaystyle V = 32\pi \ in^3[/tex]

General Formulas and Concepts:

Symbols

π (pi) ≈ 3.14

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Geometry

Volume of a Cone Formula: [tex]\displaystyle V = \frac{1}{3} \pi r^2h[/tex]

r is radiush is height

Step-by-step explanation:

Step 1: Define

Identify

r = 4 in

h = 6 in

Step 2: Find Volume

Substitute in variables [Volume of a Cone Formula]:                                    [tex]\displaystyle V = \frac{1}{3} \pi (4 \ in)^2(6 \ in)[/tex]Evaluate exponents:                                                                                         [tex]\displaystyle V = \frac{1}{3} \pi (16 \ in^2)(6 \ in)[/tex]Multiply:                                                                                                             [tex]\displaystyle V = \frac{1}{3} \pi (96 \ in^3)[/tex]Multiply:                                                                                                             [tex]\displaystyle V = 32\pi \ in^3[/tex]

can someone please answer this asap

Answers

Answer: 90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love you.

Step-by-step explanation:

Find the slope and the y-intercept of the line. 7x-2y = -10 simplest form​

Answers

Answer:

7/2 is the slope and 5 is the y-intercept

Step-by-step explanation:

Slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.

7x-2y=-10

subtract 7x on both sides

-2y=-7x-10

divide by -2 on both sides

y=(7/2)x+5

7/2 is the slope and 5 is the y-intercept.

Slope 7/2. Y-intercept (0,5)

Enter the trigonometric equation you would use to solve for x. Do not solve the equation.

Answers

Answer:

[tex]x=12\times \text{tan}(20^0)[/tex]

Step-by-step explanation:

From the figure attached,

Measure of an angle = 20°

Measure of the opposite side = x

Measure of the adjacent side = 12

By applying tangent rule in the given right triangle,

tan(20°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

[tex]\text{tan}(20^0)=\frac{x}{12}[/tex]

[tex]x=12\times \text{tan}(20^0)[/tex]

Therefore, equation to get the value of 'x' will be,

[tex]x=12\times \text{tan}(20^0)[/tex]

What property is (4 + b) + 8= 4 + (b + 8)

Answers

Answer:

Associative Property

Step-by-step explanation:

Associative Property= Uses parethesis and it doesnt matter the order you put it in it. You are going to get the same answer.

from a random sample of 24 months from january 2006 through december 2016, the mean of number of tornadoes per month in the united states was about 100. assume the population standard deviation is 114

Answers

Wow cool nice fun yay

A journal article reports that a sample of size was used as a basis for calculating a CI for the true average natural frequency (Hz) of delaminated beams of a certain type. The resulting interval was . You decide that a confidence level of is more appropriate than the level used. What are the limits of the interval

Answers

Answer:

The limit of the (228.533, 234.735)

Step-by-step explanation:

The values are missing in the given question. Therefore, in order to attempt this question, we will make assumptions.

So, let's assume that:

sample size of the journal article that was reported = 5

which is applied for determining a 95% CI

Also, assuming that the resulting interval = (229.764, 233.504)

However, if we are to use a 99% CI which we deemed to be more appropriate;

Then, our objective is to find the limits of this particular interval in question.

To do that:

We need to first find the sample mean at 95% CI by using the formula:

[tex]\Big ( \bar {x} - t_{\alpha/2, df} \ \dfrac{s}{\sqrt{n}}}, \bar x + t_{\alpha/2, df} \ \dfrac{s}{\sqrt{n}}} \Big) = (229.764,233.504)[/tex]

Since; df = n - 1

df = 5 - 1

df = 4

Then;

[tex]\Big ( \bar {x} - t_{\alpha/2, 4} \ \dfrac{s}{\sqrt{n}}}, \bar x + t_{\alpha/2, 4} \ \dfrac{s}{\sqrt{n}}} \Big) = (233.504+229.764)[/tex]

[tex]2 \bar {x} = (463.268)[/tex]

[tex]\bar {x} =\dfrac{463.268}{2 }[/tex]

[tex]\bar {x} =231.634[/tex]

Sample mean = 231.634

Using the same formula to determine the standard deviation, we have:

[tex]\Big ( \bar {x} - t_{\alpha/2, df} \ \dfrac{s}{\sqrt{n}}}, \bar x + t_{\alpha/2, df} \ \dfrac{s}{\sqrt{n}}} \Big) = (229.764,233.504)[/tex]

[tex]\Big ( \bar {x} - t_{\alpha/2, 4} \ \dfrac{s}{\sqrt{n}}}, \bar x + t_{\alpha/2, 4} \ \dfrac{s}{\sqrt{n}}} \Big) = (233.504-229.764)[/tex]

[tex]\Big ( (\bar x + t_{\alpha/2, 4} \ \dfrac{s}{\sqrt{n}}} )- (\bar {x} - t_{\alpha/2, 4} \ \dfrac{s}{\sqrt{n}}}) \Big) = (233.504-229.764)[/tex]

[tex]\Big ( (\bar x + t_{0.05/2, 4} \ \dfrac{s}{\sqrt{4}}} )- (\bar {x} - t_{0.05/2, 4} \ \dfrac{s}{\sqrt{5}}}) \Big) = (233.504-229.764)[/tex]

At t = 0.025 and df = 4; = 2.776

[tex]2\times 2.776 \dfrac{s}{\sqrt{5}}= 3.74[/tex]

[tex]5.552 \dfrac{s}{\sqrt{5}}= 3.74[/tex]

[tex]\dfrac{s}{\sqrt{5}}= \dfrac{ 3.74}{5.552}[/tex]

[tex]\dfrac{s}{\sqrt{5}}= 0.6736[/tex]

[tex]s = 0.6736 \times \sqrt{5}[/tex]

s = 1.5063

The 99% CI is:

[tex]\implies \Big(\bar x \pm t_{\alpha/2,4} \dfrac{s}{\sqrt{n}} \Big)[/tex]

At t =0.005 and df =4; = 4.604

[tex]\implies \Big(231.634 \pm 4.604 \dfrac{1.5063}{\sqrt{5}} \Big)[/tex]

[tex]\implies \Big(231.634 \pm 4.604 (0.67364) \Big)[/tex]

[tex]\implies \Big(231.634 \pm 3.1014 \Big)[/tex]

[tex]\implies \Big((231.634 - 3.1014), (231.634 + 3.1014) \Big)[/tex]

[tex]\implies \Big( 228.533, 234.735 \Big)[/tex]

Help plz:)))I’ll mark u Brainliest

Answers

Answer:

4/5

Step-by-step explanation:

Given :

A right angled triangle with sides 24 , 3 and 40 .

And we need to find the value of sinZ .

We know that , sine is the ratio of perpendicular and Hypotenuse. So that ,

[tex]:\implies[/tex] sinZ = p/h

[tex]:\implies[/tex] sin Z = 32/40

[tex]:\implies[/tex] sin Z = 4/5

Hence the renquired answer is 4/5.

I need help pls! optional to give an explanation to help me understand :)

Answers

Answer:
I believe it should be (-4,2)

Explanation:
You can use substitution to solve this, so

1/4x+3 = 2x+10

(Because they both = y)

Then solve for x
X=-4

Then you plug x into one of the equations to solve for y. I used y=1/4(-4)+3

Hope this helps

Answer:

(-4, 2)

Step-by-step explanation:

this is a simultaneous equation;

solving by substitution method, we have;

since y= ¼x + 3 and the same y= 2x + 10

therefore we combine both equations;

¼x + 3= 2x+10

3-10=2x-¼x

to clear out fraction, multiply throughout by 4

-28= 8x-x

-28= 7x

x= -28/7

x= -4

since x is -4, therefore All we have to do is to substitute x into y, doing this, we have;

y=2x+10

y= 2(-4) + 10

y= -8 + 10

y= 2

therefore y= 2 and x= -4

so the values are (-4, 2)

if you still don't understand, check your NGM SS2 textbook or make a comment and I will explain better

The coordinate grid shows the graph of four equations:





Which set of equations has (5,0) as its solution?

A and B

C and D

B and D

A and D


*sorry for all the cracks my iPad screen broke.​

Answers

A and B is the answer good luck :)

2
Each of the following is part of your innate immune system,
except:
A
Stomach acid
B
White blood cells
С
Skin
D
Mucus

Answers

Answer:

B white blood cells

Step-by-step explanation:

20. What is the solution to the equation By -2(y + 1)-3(y-2) + 6?
A) -10
B) 6
C)-2
D) 2

Answers

The answer is C; -2 as -5y+10 is y=-2

whats 6 divided by 10?

Answers

Answer:

1 r 4

Step-by-step explanation:

 0 1

6 1 0

− 0  

 1 0

−   6

   4

When building a house, the number of days required to build varies inversely with
with the number of workers. One house was built in 21 days by 17 workers. How
many days would it take to build a similar house with 7 workers?

Answers

Answer:

51 days

Step-by-step explanation:

17/7= 2.428

2.428*21=50.988=51

Is the equation a linear function?
y = -x + 3 +

Answers

A linear function is y=mx + b so yes (assuming + sign at end is accidental)

Grandma is trying out a new recipe for raisin bread. Each batch of bread dough makes three loaves, and each loaf contains 15 slices of bread. If she puts 100 raisins into a batch of dough, what is the probability that a randomly chosen slice of bread contains no raisins

Answers

Answer:

0.108

Step-by-step explanation:

Using the poisson probability process :

Where :

P(x =x) = (e^-λ * λ^x) ÷ x!

Given that :

Each batch of bread = 3 loaves

Each loaf = 15 slices

Total slice per batch = 15 * 3 = 45 slices

Number of raising added = 100

Average number of raisin per slice, λ = 100/45 = 20/9

Hence,

Probability that a randomly chosen slice has no raising :

P(x = 0) = (e^-λ * λ^x) ÷ x!

P(x = 0) = (e^-(100/45) * (100/45)^0) ÷ 0!

P(x = 0) = (0.1083680 * 1) / 1

P(x = 0) = 0.108

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