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Answer:

[tex]\displaystyle cos\theta = \frac{2\sqrt{13}}{13}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

[Right Triangles Only] SOHCAHTOA

[Right Triangles Only] cosθ = adjacent over hypotenuse

Step-by-step explanation:

Step 1: Define

Identify variables

a = 8

b = 12

c

Step 2: Solve for c

Step 3: Define Pt. 2

Identify variables

Angle θ

Adjacent leg = 8

Hypotenuse = 4√13

Step 4: Find

Answer:

Solution given;

In right angled triangle with respect to θ

perpendicular: opposite side: [P]=12

base:adjacent:[b]=8

hypotenuse [h]=?

cosθ=?

According to the Pythagoras law

h²=p²+b²

h²=12²+8²

h=[tex] \sqrt{208}[/tex]

h=[tex] 4\sqrt{13}[/tex]

Now

we have

Cos θ=[tex]\frac{adjacent}{hypotenuse}[/tex]

Cos θ=[tex]\frac{8}{4\sqrt{13}}[/tex]

by rationalising it

Cos θ= [tex] \frac{2\sqrt{13}}{\sqrt{13}×\sqrt{13}}[/tex]

Cos θ= [tex] \frac{2\sqrt{13}}{13}[/tex]

is a required answer.

Answer:

1.6 ft.

Step-by-step explanation:

Given that the conical pylons had a radius (r) of 1 foot and a height (h) of 2 foot. The volume of the conical pylons is:

Volume = πr²h/3

Therefore substituting gives:

Volume = π(1)²(2)/3 = 2π/3 ft³

Since the same amount of concrete is used to construct a spherical barrier, hence the volume of the sphere would be the same as the volume of the conical pylon.

Volume of sphere = 4πr³/3

4πr³/3 = 2π/3

2r³ = 1

r³ = 1/2 = 0.5

r = ∛0.5 = 0.8 ft.

Therefore the radius of the spherical barrier would be 0.8 ft. and the height would be 2r = 2(0.8) = 1.6 ft.

Answer:

[tex]C = 45 * 2\pi[/tex]

[tex]C = 90\pi[/tex]

Step-by-step explanation:

Given

[tex]h = 90[/tex] -- height of the wheel

Required

The expression for the distance traveled in 1 revolution

The height of the wheel implies that:

[tex]d =90[/tex] --- diameter equals height

The distance in 1 revolution is calculated by calculating the circumference of the wheel using:

[tex]C = 2\pi r[/tex] or [tex]C = \pi d[/tex]

Where

[tex]r = \frac{1}{2} * d[/tex]

[tex]r = \frac{1}{2} * 90[/tex]

[tex]r = 45[/tex]

So, we have:

[tex]C = 2\pi r[/tex]

[tex]C = 2\pi * 45[/tex]

[tex]C = 45 * 2\pi[/tex]

[tex]C = \pi d[/tex]

[tex]C = \pi * 90[/tex]

[tex]C = 90\pi[/tex]

15.56 in.

Step-by-step explanation:

i'm pretty sure i did it right, but im not sure. i haven't done geometry in like over 2 years.

find the hypotenuse of the triangle with 7 in. and 12 in. as your legs with the Pythgorean theorem (a^2 + b^2 = c^2, c equals the hypotenuse)

use that number you just got (I got ) and use it as one leg, and 7 in. as the other leg, with d as your hypotenuse

use the Phythagorean theorem again to find d, andddd... you've got your answer!

Answer: Ok well when you do the math you get 14.76 then round to the nearest tenth of an inch you get 17.8. So, d ≈ 14.8

Step-by-step explanation:

I did the math...

Answer:

C. (-5, -2)

Step-by-step explanation:

I used

x1 + / (x2 - x1), y1 + / (y2 - y1)

so

-7 + 1/5(3 - (-7)

-7 + 1/5 (10)

-7 + 10/5

-7 + 2 = -5 (X)

then

-4 + 1/5(6 - (-4)

-4 + 1/5(10)

-4 + 10/5

-4 + 2 = -2 (Y)

(-5, -2)

Answer:

The answer would be 71 because x = 9 so y = 71

Answer: Mean

Step-by-step explanation:

Mean is best used when the numbers in the data set are close together and the number of outliers are limited because outliers will either increase or decrease the mean such that it would not be a true representation of the data set.

In cases like the above however where the numbers are generally in the same range, the mean would provide a center measure that is the most representative because it would simply be a simple average of the numbers.

Answer:

v = 2c

Step-by-step explanation:

Answer:

C) The fossil is between 10 million and 50 million years old.

Step-by-step explanation:

Since Layer B is located between Layer A and C, option C is the only reasonable answer because Layer A is 50 million years old and Layer C is 10 million years old.

Answer:

I don't know how to explain it well but i got part of my notes and i solved it and i got D. 144 and i got it checked and it was correct

Step-by-step explanation:

Sorry for not helping sooner

Answer:

[tex]n = -3[/tex]

Step-by-step explanation:

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

Answer:

-5-2n=8n+25

-5-25=8n+2n

-30=10n

-30/10=n

-3=n

Step-by-step explanation:

therefore n=-3

Hope this helps u!!

Given:

The equation is:

[tex]y=-x+4[/tex]

To find:

The graph of the line that contains ordered pairs that are solutions of the given equation.

Solution:

We need to find the graph of the given equation.

We have,

[tex]y=-x+4[/tex]

At [tex]x=0[/tex], we get

[tex]y=-0+4[/tex]

[tex]y=4[/tex]

So, the x-intercept of the given equation is at point (0,4).

At [tex]y=0[/tex], we get

[tex]0=-x+4[/tex]

[tex]x=4[/tex]

So, the y-intercept of the given equation is at point (4,0).

From the given graphs it is clear that the line in option C has x-intercept at point (0,4) and y-intercept at point (4,0).

Therefore, the correct option is C.

Answer:

Step-by-step explanation:

6 no answer 0,9

7 no answer -3,-10

8 no answer -10,2

9 no answer 2,0

hope this helps u!!

Answer:

The rate of change would be $3.50 per gallon.

Step-by-step explanation:

In the graph depicted in the picture, when the number of gallons increases by 2, the price increases by $7. Since the graph maintains a constant rate of change, that means the rate of change would be [tex]\frac{7}{2}[/tex] or $3.50 per gallon.

Answer:

4/3π(0.973r³)

Step-by-step explanation:

Volume of a sphere = 4/3πr³

Given the radius of dodge ball rd = r

radius of tennis ball rt = 0.3r

Taking their difference

Volume difference  = 4/3πrd³ - 4/3πrt³

Volume difference  = 4/3π(r)³ - 4/3π(0.3r)³

Volume difference  = 4/3π(r³ - 0.027r³)

Volume difference = 4/3π(0.973r³)

Hence the differmce in volume is  4/3π(0.973r³)

Square root of 9340 = 96.64

nearby number = 96

square of 96 = 9216

9340- 9216= 124

the smallest number 124 should be subtracted from 9340 so as to get a perfect square.

Answer:

9.24

Step-by-step explanation:

Formula Cylinder = πr² * h

Let's work backwards

Use 3.14 for π

3.14 * (6)² * h = 1044

3.14 * 36 * h = 1044

113.04 * h = 1044

h = 1044 ÷ 113.04

h ≈ 9.24

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

[tex]21(2-x)+12x=44[/tex]

[tex]42-21x+12x=44[/tex]

[tex]42-9x=44[/tex]

[tex]42-9x-42=44-42[/tex]

[tex]-9x=2[/tex]

[tex]-9x=2\\-9 ~~-9[/tex]

[tex]x=-2/9[/tex]

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

hope it helps..

have a great day!!

Answer: [tex]518.4\ cm^3[/tex]

Step-by-step explanation:

Given

The volume of the small block is [tex]300\ cm^3[/tex]

The ratio of the surface area of small to large block is [tex]25:36[/tex]

Suppose the length of the small and large box is a and b

[tex]\therefore \left(\dfrac{6a^2}{6b^2}\right)=\dfrac{25}{36}\\\\\Rightarrow \left(\dfrac{a}{b}\right)^2=\dfrac{25}{36}\\\\\Rightarrow \left(\dfrac{a}{b}\right)=\dfrac{5}{6}\\\\\therefore \text{Ratio of the volumes of two is }\\\\\Rightarrow \dfrac{a^3}{b^3}=\dfrac{5^3}{6^3}\\\\\Rightarrow \dfrac{V_s}{V_l}=\dfrac{125}{216}\\\\\Rightarrow V_l=300\times \dfrac{216}{125}\\\\\Rightarrow V_l=518.4\ cm^3[/tex]

Answer:

Step-by-step explanation:

Formula for total surface area of of the triangular prism is:

Total Surface area (S) = Ph+ 2B

P = Perimeter of the triangular base

P = 6 + 8 + 10

P = 24 cm

h = height of the prism = 10 cm

B = area of the base

B = ½*bh = ½*8*6

B = 24 cm

S = 24*10 + 2(24)

S = 240 + 48

S = 288 cm²

Total surface area = 288 cm²

Answer:

triangular prism

Step-by-step explanation:

Answer:

Step-by-step explanation:

Below is the pic of how this would be set up in order to determine what it is you are looking for. The angle is set in QI, and since csc A is the reciprocal of sin, the ratio is hypotenuse over side opposite. Solve for the missing side using Pythagorean's Theorem:

[tex]37^2=12^2+b^2[/tex] and

1369 = 144 + b² and

1225 = b² so

b = 35

The sec ratio is the reciprocal of cos, so if cos is adjacent over hypotenuse, the sec is hypotenuse over adjacent, which is 37/35

The number line inequality will be true for the following condition given in this problem:

When a = 0 and c = -8.

On a number line, real numbers increase from left to right, meaning that:

Large negative numbers come before small negative numbers, which come before small positive numbers, and finally, come the large positive numbers.

For this problem, the inequality is:

c > b > a.

Which means that:

We have that b < -1, hence:

Then the conditions that make the statement b < -1 true are given as follows:

When a = 0 and c = -8.

More can be learned about number line inequalities at https://brainly.com/question/24372553

#SPJ1

Answer:

C) this is the false statement

Step-by-step explanation:

data set in list form:

35, 42, 45, 55, 65, 65, 68, 76, 85

Range: 85-35 = 50

Median: 65

Mean: 536/9 = 59.5

Mode:  65

The statement that is not true about this data set is C. The mean is 65 people.

This Stem-and-Leaf Plot shows the number of people who attended a local nine-day carnival.

The data set in list form:

35, 42, 45, 55, 65, 65, 68, 76, 85

Mean is the ratio of sum of the observations to the total number of observations.

Mean: 536/9 = 59.5

Median is such a number for the arranged data set(ascending or descending order) such that to its left and to its right belong same number of observations.

Median: 65

Range = Maximum value of the data set - Minimum value of the dataset

Range: 85-35 = 50

Mode is the number in given data that occurs frequently.

Mode:  65

Learn more about skewed distribution here:

https://brainly.com/question/13111221

#SPJ2

Answer:

should be the third (81,90)

Step-by-step explanation:

Answer:

3/8 tablespoons

Step-by-step explanation:

When we add fractions, we have to make each fraction a common denominator.

So we get 1/4 into 2/8 and we have 1/8

So we add and get 3/8

Answer:

Length=3/4 mi  and width=1/2 mile so

L:W=(3/4):(1/2)  by convention we will express this ratio with integers...multiplying both fractions by 4 we get:

Area =3:2