Answer:
slope = -6
Step-by-step explanation:
slope = Δy/Δx
slope = (4+2)/(2-3)
= 6/-1
slope = -6
For positive acute angles AA and B,B, it is known that \tan A=\frac{28}{45}tanA= 45 28 and \cos B=\frac{3}{5}.CosB= 5 3 . Find the value of \cos(A+B)cos(A+B) in simplest form.
Answer:
[tex]\cos(A + B) = \frac{23}{265}[/tex]
Step-by-step explanation:
Given
[tex]\tan A=\frac{28}{45}[/tex]
[tex]\cos B=\frac{3}{5}[/tex]
Required
[tex]\cos(A+B)[/tex]
In trigonometry:
[tex]\cos(A+B) = \cos\ A\ cosB - sinA\ sinB[/tex]
We need to solve for cosA, sinA and sinB
Given that:
[tex]\tan A=\frac{28}{45}[/tex] and the tangent of an angle is a ratio of the opposite side (x) to the adjacent side (y),
So, we have:
[tex]x =28[/tex] and [tex]y = 45[/tex]
For this angle A, we need t calculate its hypotenuse (z).
Using Pythagoras,
[tex]z^2 = x^2 + y^2[/tex]
[tex]z = \sqrt{x^2 + y^2[/tex]
[tex]z = \sqrt{28^2 + 45^2[/tex]
[tex]z = \sqrt{2809[/tex]
[tex]z = 53[/tex]
From here, we can calculate sin and cos A
[tex]\sin A= \frac{opposite}{hypotenuse}[/tex] and [tex]\cos A= \frac{adjacent}{hypotenuse}[/tex]
[tex]\sin A= \frac{x}{z}[/tex]
[tex]\sin A= \frac{28}{53}[/tex]
[tex]\cos A= \frac{y}{z}[/tex]
[tex]\cos A= \frac{45}{53}[/tex]
To angle B.
Give that
[tex]\cos B=\frac{3}{5}[/tex] and the cosine of an angle is a ratio of the adjacent side (a) to the hypotenuse side (c),
So, we have:
[tex]a = 3[/tex] and [tex]b = 5[/tex]
For this angle B, we need to calculate its opposite (b).
Using Pythagoras,
[tex]c^2 = a^2 + b^2[/tex]
[tex]5^2 = 3^2 + b^2[/tex]
[tex]25 = 9 + b^2[/tex]
Collect like terms
[tex]b^2 = 25 - 9[/tex]
[tex]b^2 = 16[/tex]
[tex]b = \sqrt{16[/tex]
[tex]b = 4[/tex]
From here, we can calculate sin B
[tex]\sin B= \frac{opposite}{hypotenuse}[/tex]
[tex]\sin B = \frac{b}{c}[/tex]
[tex]\sin B = \frac{4}{5}[/tex]
Recall that:
[tex]\cos(A+B) = \cos\ A\ cosB - sinA\ sinB[/tex]
and
[tex]\cos B=\frac{3}{5}[/tex] [tex]\sin B = \frac{4}{5}[/tex] [tex]\sin A= \frac{28}{53}[/tex] [tex]\cos A= \frac{45}{53}[/tex]
[tex]\cos(A + B) = \frac{45}{53} * \frac{3}{5} - \frac{28}{53} * \frac{4}{5}[/tex]
[tex]\cos(A + B) = \frac{135}{265} - \frac{112}{265}[/tex]
[tex]\cos(A + B) = \frac{135-112}{265}[/tex]
[tex]\cos(A + B) = \frac{23}{265}[/tex]
The value of [tex]\cos (A+B)[/tex] is [tex]-\frac{96}{265}[/tex].
Trigonometrically speaking, the sine, cosine and tangent of an angle are described by the following formulas:
[tex]\sin \theta = \frac{y}{\sqrt{x^{2}+y^{2}}}[/tex] (1)
[tex]\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}[/tex] (2)
[tex]\tan \theta = \frac{y}{x}[/tex] (3)
Where:
[tex]\theta[/tex] - Angle, in sexagesimal degrees.[tex]x[/tex] - Adjacent leg.[tex]y[/tex] - Opposite leg.And we have the following trigonometric identity for the cosine of the sum of angles:
[tex]\cos (A+B) = \cos A\cdot \cos B - \sin A \cdot \sin B[/tex] (4)
By (1) and (2), we rewrite (4):
[tex]\cos (A+B) = \frac{x_{A}\cdot x_{B}}{\sqrt{x_{A}^{2}+y_{A}^{2}}\cdot \sqrt{x_{B}^{2}+y_{B}^{2}}} - \frac{y_{A}\cdot y_{B}}{\sqrt{x_{A}^{2}+y_{A}^{2}}\cdot \sqrt{x_{B}^{2}+y_{B}^{2}}}[/tex]
If we know that [tex]x_{A} = 28[/tex], [tex]y_{A} = 45[/tex], [tex]x_{B} = 3[/tex] and [tex]y_{B} = 4[/tex], then the cosine for the sum of angles is:
[tex]\cos (A+B) = \frac{28\cdot 3}{\sqrt{28^{2}+45^{2}}\cdot \sqrt{3^{2}+4^{2}}}-\frac{45\cdot 4}{\sqrt{28^{2}+45^{2}}\cdot \sqrt{3^{2}+4^{2}}}[/tex]
[tex]\cos (A+B) = -\frac{96}{265}[/tex]
The value of [tex]\cos (A+B)[/tex] is [tex]-\frac{96}{265}[/tex].
We kindly invite to check this question on trigonometric identities: https://brainly.com/question/24836845
1) Choose the correct answer.
Which of the following statements is NOT a reasonable statement about geometry?
A.You need to take geometry so you will learn how to drive farther and faster.
B.You need to take geometry so you will learn concepts about shapes and relationships that you
can apply to many jobs or careers in the future.
C.You need to take geometry so you will earn the credit toward graduation.
D.You need to take geometry so you will learn to apply logical reasoning skills that you can use
in almost every aspect of life.
Answer:
A
Step-by-step explanation:
Geometry has nothing to do with driving.
anyone question 8 pleaseeeeeeeeeee
Answer:
$200 and $450
Step-by-step explanation:
We can start by assigning variables to our unknowns.
Our unknowns are the price for a DVD player and the price for a television.
x= price of a television
y= price of a DVD player
Next, let's translate the given information into a system of equations.
two televisions and three DVD players for $1750
2x+3y=1750
four televisions and one DVD player for $1250
4x+y=1250
Since the instructions did not specify, I will use substitution to solve, however you can also use elimination.
First, from the second equation, we subtract 4x from both sides.
4x+y-4x=1250-4x
y=1250-4x
Now we plug 1250-4x for y in the first equation.
2x+3y=1750
2x+3(1250-4x)=1750
Distribute.
2x+3*1250-3*4x=1750
Simplify.
2x+3750-12x=1750
Combine like terms.
-10x+3750=1750
Subtract 3750 from both sides
-10x+3750-3750=1750-3750
-10x=-2000
Divide both sides by -10
x=200
A television costs $200.
Now using that, we can plug that into one of the original equations. I'll use the second one.
4x+y=1250
4(200)+y=1250
800+y=1250
Subtract 800 from both sides.
y=450
A DVD player costs $450
You can plug those values back into the other equation (the first one) to double-check if you'd like as well.
Find all solutions of
- 2r +4-8=0
Answer: -2
Step-by-step explanation: 4-8= -4 then it ends up being -2r-4=0
Then you add 4 to 0 so -2r=4 then divide
I WILL MARK YOU BRAINLIST!!!!If the team's average time is less than one minute per leg, then the eighth graders earn 50 points. If not, the seventh graders earn 50 points. Which grade should be awarded 50 points?
Answer:
The 7th graders earn the 50 points.
Step-by-step explanation:
3.89 is in minutes I assume?
3.89 > 1
7th graders earn the 50 points.
A pair of designer sneakers was purchased for $100. Since they were purchased, their price has increased by 15%. What is the new price?
Answer:
115
Step-by-step explanation:
6. The variable n represents the figure number
in the following algebraic pattern rules:
A. 4n B. 2n + 2 C. 3n + 1 D. 4n - 1
Which of these pattern rules describes the
toothpick pattern shown below? Explain
how you know.
A
Figure 1
Figure 2
Figure 3
Figure 4
Write the expression for the phase 7 inches shorter than Sue
Answer:I'm pretty sure its -7
Step-by-step explanation:
HELP THIS IS TIMED
2/11z-5/11z+4-1/11z-8
simplify plssss i can give reward
Answer:
-145/88z+4
Step-by-step explanation:
Answer: -4/11z - 4
Step-by-step explanation: We can combine like terms to simplify the expression 2/11z - 5/11z + 4 - 1/11z - 8. The terms 2/11z, -5/11z, and -1/11z are like terms because they all have the same variable part z. When we add them together, we get (2 - 5 - 1)/11z = -4/11z. The constants 4 and -8 are also like terms. When we add them together, we get 4 + (-8) = -4. So the simplified expression is -4/11z - 4.
need the answer asap
Answer:
10,15
Step-by-step explanation:
Answer:
AC=39
Step-by-step explanation:
-x+25=3(2x-8)
-x+25=6x-24
49=7x
x=9
AC = 2(-9+25)=-11+50=39
consider these functions f(x)=1/3x^2+4 g(x)=9x-12 what is the value of g(f(x))
Given:
Functions are
[tex]f(x)=\dfrac{1}{3}x^2+4[/tex]
[tex]g(x)=9x-12[/tex]
To find:
The value of [tex]g(f(x)).[/tex].
Solution:
We have,
[tex]g(f(x))=g(\dfrac{1}{3}x^2+4)[/tex] [tex][\because f(x)=\dfrac{1}{3}x^2+4][/tex]
[tex]g(f(x))=9(\dfrac{1}{3}x^2+4)-12[/tex] [tex][\because g(x)=9x-12][/tex]
[tex]g(f(x))=9(\dfrac{1}{3}x^2)+9(4)-12[/tex]
[tex]g(f(x))=3x^2+36-12[/tex]
[tex]g(f(x))=3x^2+24[/tex]
Therefore, the required function is [tex]g(f(x))=3x^2+24[/tex].
Following are the calculation to the given function:
Given:
[tex]f(x)=\frac{1}{3}x^2+4 \\\\g(x)=9x-12[/tex]
To find:
[tex]g(f(x))=?[/tex]
Solution:
[tex]f(x)=\frac{1}{3}x^2+4 \\\\g(x)=9x-12[/tex]
[tex]\to g(f(x))=g( \frac{1}{3} x^2+4) \\\\[/tex]
[tex]=9( \frac{1}{3} x^2+4)-12 \\\\=\frac{9}{3}x^2+36-12 \\\\=3x^2+24 \\[/tex]
Therefore, the answer is "[tex]24+3x^2[/tex]" .
Learn more about the g(f(x)):
brainly.com/question/17022176
Which wheelchair would be more difficult to stop? (check one)
more massive wheelchair
_ less massive wheelchair
Answer: less massive wheelchair?
Step-by-step explanation:
I need help with this problem please
Answer:
j = 2/3
Step-by-step explanation:
-1/3 = -1/2 j
Multiply each side by -2
-1/3 * -2 = -1/2 j * -2
2/3 =j
Answer:
j = 2/3
Step-by-step explanation:
-2/3 = -j
j = 2/3
HELP ME PLEZ
Im timed lol
Answer:
1.) $1
2.)$4
3.)$12
4.)3/4
Step-by-step explanation:
32(.5)=16
she had 16 left after lunch. 16(.25)=4
16-4=12
1/2=2/4
2/4+1/4=3/4
Answer:
1) lunch 16
2) coffee 4
3) 12
4) 3/4ths or .75 or 75%
Please help. Its due in 30 mins.
Answer:
Step-by-step explanation:
Hey! I also asked this question before lol! Someone solved it so this is not my work:
"N+ 1 = 3+2/2
The answer is 3
This is a odd number"
Hope this helps ∞<3
3 times a number less than 7 times the same number is 32. Find the number.
Answer:
x = 8
Step-by-step explanation:
7x-3x= 32
4x=32
/4 /4
x= 8
When surveyed 5 out of 32 students said they ride their bikes to school. Predict how many students in a school of 800 ride their bikes to school.
And please show your work!
Answer:125 students
Step-by-step explanation:if 5 out of every 32 students bikes
5=32
X=800
800(5)=4000
4000/32=125
What keeps us from flying into the sky? Why?
Answer:
Gravity.
Step-by-step explanation:
Gravity is what holds the planets in orbit around the sun and what keeps the moon in orbit around Earth. The gravitational pull of the moon pulls the seas towards it, causing the ocean tides. Gravity creates stars and planets by pulling together the material from which they are made.
This is actually a physics problem, but the force of Gravity keeps us from flying into the sky. Gravity is the force by which a planet or other body draws objects toward its center. This force gives us a tendency to remain on the ground and not to float off into the atmosphere.
Which of the following sentences could not be used to represent the equation x - 5 = -10? the real answer, please
Answer:
you didn't add options for the sentences, but
x-5 =-10 (add 5 to both sides to get x alone)
x= -5
so anything that has to do with x equaling - 5 would be correct
after reading through the sentences, the correct answer is:
a number subtracted from five is equal to negative ten
because that sentence is saying " 5 - n = - 10 " and that's not what's happening
Step-by-step explanation:
The principal of East High School wants to buy a new cover for the sand pit used in the long-jump competition. He measured the sand pit and found the length is 29.2 feet and the width is 9.8 feet. What will the area of the new cover be?
Answer:
286.16
Step-by-step explanation:
To find the area, you simply multiple length by width. And the product of 29.2 and 9.8 is 286.16
What was the primary religlon of India?
O Buddhism
O Christianity
O Islam
O Hinduism
Like terms must have the same
variables and
Answer:
Like terms have to have the same variables and powers
Answer:
and powers
Step-by-step explanation:
HELP ME PLEASE ILL GOVE YOU BRAINLESY ANSWER
Answer:
300ft²
Step-by-step explanation:
Step 1)
Multiply The Walkway
(3 × 30)2 = 180ft²
(3 × 20)2 = 120ft²
Step 2)
Add The Walkway
180ft² + 120ft² = 300ft²
Step 3)
Multiply The Whole Area Including The Walkway and The Garden
30 × 20 = 600ft²
Step 4)
Subtract The Whole Area By The Walkway
600ft² - 300ft² = 300ft²
Step 5)
The Area Of The Garden is 300ft²
x + 2y = 24
2x + y = 9 -)
A) y = -2
B) y = 13
C) y = -13
D) y = 2
Answer:
y=2
Step-by-step explanation:
Solve the system of linear equations using the
substitution method.
y=-2x + 3
6x + 3y = -3
Answer:
no solution
Step-by-step explanation:
y = -2x + 3
6x + 3y = -3
the substitution method means you plug one equation into the next, because the first equation gives us a solution for y we can go ahead and plug that into y of the second equation
6x + 3(-2x + 3) = -3
6x - 6x + 9 = -3
9 = -3
which is false meaning that there are no solutions and the lines don't touch at any point
guys help me yall for 20 point
Answer:
7
Step-by-step explanation:
9/m+4
9/3+4 (m=3)
3+4
7
Answer:
-9
Step-by-step explanation:
9 divided by -9 is -1
-1 +4 = 3
Jeremy is paid $90 for 3 hours of work. How many minutes does it take him to earn $1?
Answer:
He makes $1 every 2 minutes
Step-by-step explanation:
If you break it down 60 minutes is in an hour and he works for 3 hours total so you multiply 60×3 which is 180 that's how many minutes he works for. Then you take the money he made and take the minutes and divide it by the money 180÷90=2 so he make $1 every 2 minutes
Does Y= -2/3x + 3 & Y=2/3x + 2 have unlimited solutions?
Answer:
x = 3/4
y = 2.5
Step-by-step explanation:
No there is just one.
Equate the ys
-2/3 x + 3 = 2/3 x + 2 Add 2/3 x to both sides
3 = 2/3 x + 2/3x + 2 Combine
3 = 4/3 x + 2 Subtract 2
3-2 = 4/3 x Multiply by 3
1 * 3 = 4x Divide by 4
3/4 = x
====================
y = 2/3 x + 2
y = 2/3 * 3/4 + 2
y = 6/12 + 2
y = 1/2 + 2
y = 2 1/2
y = 2.5
Determine which set of numbers represent the lengths of the sides of a triangle.
A.
15, 12,9
B.
20, 10,9
C.
47, 21, 70
D.
12, 2.2, 14.3
will give brainliest!!
Answer:
I think its A
Step-by-step explanation:
Please mark brainliest
Solve for x.
3x-5=7x+5
Answer:
x = -2.5 or -5/2
Step-by-step explanation: