classify the triangle.

- isosceles acute
- isosceles obtuse
- scalene acute
- scalene obtuse

Given:

[tex]\cos^4 \alpha+\sin^4\alpha=\dfrac{1}{4}(3+\cos 4 \alpha)[/tex]

To prove:

The given statement.

Proof:

We have,

[tex]\cos^4 \alpha+\sin^4\alpha=\dfrac{1}{4}(3+\cos 4 \alpha)[/tex]

[tex]LHS=\cos^4 \alpha+\sin^4\alpha[/tex]

[tex]LHS=(\cos^2 \alpha)^2+(\sin^2 \alpha)^2[/tex]

[tex]LHS=(\cos^2 \alpha+\sin^2\alpha)^2-2\sin ^2\alpha\cos^2 \alpha[/tex]     [tex][\because a^2+b^2=(a+b)^2-2ab][/tex]

[tex]LHS=(1)^2-2(1-\cos^2 \alpha)\cos^2 \alpha [/tex]      [tex][\because \cos^2 \alpha+\sin^2\alpha=1][/tex]

[tex]LHS=1-2\cos^2 \alpha+2\cos^4 \alpha [/tex]

Now,

[tex]RHS=\dfrac{1}{4}(3+\cos 4 \alpha)[/tex]

[tex]RHS=\dfrac{1}{4}[3+(2\cos^2 2\alpha-1)][/tex]        [tex][\because \cos 2\theta=2\cos^2\theta -1][/tex]

[tex]RHS=\dfrac{1}{4}[2+2\cos^2 2\alpha][/tex]

[tex]RHS=\dfrac{1}{4}[2+2(2\cos^2 \alpha-1)^2][/tex]        [tex][\because \cos 2\theta=2\cos^2\theta -1][/tex]

[tex]RHS=\dfrac{1}{4}[2+2(4\cos^4 \alpha-4\cos \alpha+1)][/tex]        [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]

[tex]RHS=\dfrac{1}{4}[2+8\cos^4 \alpha-8\cos \alpha+2][/tex]

[tex]RHS=\dfrac{1}{4}[4+8\cos^4 \alpha-8\cos \alpha][/tex]

[tex]RHS=1+2\cos^4 \alpha-2\cos \alpha[/tex]

[tex]RHS=1-2\cos^2 \alpha+2\cos^4 \alpha [/tex]

[tex]LHS=RHS[/tex]

Hence proved.

Answer:

-2x-3x=4

-5x=4

x= -4/5

Step-by-step explanation:

Answer:

its eight on the y axis

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Becuase 4 divided that number is 2

6 divided by 3 is 2

and so on

Answer:

x≥25

Step-by-step explanation:

Step one:

given data

Jaxon must sell at least 49 rolls of wrapping paper to support the robotics club fundraiser

We are told that he has already sold 24 rolls of wrapping paper.

Step two:

let x be the number of rolls remaining to be sold,

hence,

x≥49-24

x≥25

Therefore the inequality for the situation is  x≥25

which reads that x must be greater than or equal to 25

Step-by-step explanation:

yes dear. .............

Answer:

flaimgo/albert

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

it does not have any (0,0) value

I'm not too sure but I think it's option

1. No, because only one angle of the triangle is congruent.

Answer:

C

Step-by-step explanation:

First of all, we can see for both of the slopes, the Y intercept is both -4, and +4. Now that we know that information, we can go on to "mx" or the slope. now since we've narrowed down the answers, we have C and D left. Now in C, the x for "x+4" doesn't specifically say the value. Now for the equation below x+4 (for C) shows -2x-4, which does show the value of X, which is correct, because it shows in the graph that there's -2x. Now on D, they put the negative symbol on X, which doesn't say the value, but there's no negative in "2x-4" for 2x. and there's no slope that goes through positive 2. Therefore it would be C.

Answer:

-6x - 8

Step-by-step explanation:

-2(3x+4) = -6x - 8

this means the -6x - 8 is equivalent

Answer: 141 i think

Step-by-step explanation:

Answer:

The answer would be C, hope i helped

Step-by-step explanation:

First you have to get x by itself. So you do 90-90= 0 and 30-90= -60 which gets:

90 - 3/2x < 30       to     -3/2x < -60

Then, you do -3/2 - (-3/2)= 0 and do the same to -60. -60 - (-3/2) = -58.5

which makes it look like      

X = -58.5

-58.5 is a smaller number than -40 which means, when you fill it in for x it works      

-58.5 ≤ -40

P.S. to put a line under the < and > you    (≤ and ≥)   hold option then click on which ever one you need

Answer:

All answers apply

Step-by-step explanation:

Although it may seem like it doesnt, the absolute value of -12 is just 12, which ends up still being less than 14.

Absolute value takes away the negative and leaves positive number as a result.

Answer:

all of them since it's absolute value all numbers are below 14

Answer:

I believe the answer is D

Step-by-step explanation:

after 3 hours it traveled 120 miles so divide that by the 3 hours and it gives you 40 miles per hour giving you the slope and the y int would be negative 300 because he started 300 miles aways from Denver

Answer:

The answer seems to be D

Step-by-step explanation:

I cannot really confirm but I am most certain it is D.

Answer:

80%

Step-by-step explanation:

Hope this helps :)

Answer:

M = 9

Step-by-step explanation:

94 = 31 + 7m

63 = 7m

9 = m

Hope this helps. Pls give brainliest.

Answer:

560

Step-by-step explanation:

2 x (40+30) x 4

2 x 70 x 4

560

hope this helps, pls mark brainliest :D

560

Step-by-step explanation:

2 x (40+30) x 4

2 x 70 x 4

560

Answer:

Sheet metal costs $20 per square foot.

Step-by-step explanation:

7.6x - 2.3x = 106

We are finding the value of x.

5.3x = 106

Divide both sides by 5.3.

x = 106 ÷ 5.3

x = 20

                                       Answer and Explanation

__________________________________________________________

__________________________________________________________

Sheet metal costs 20 dollars per square foot, and we can figure this out by multiplying the 20 by the numbers and subtracting them.

__________________________________________________________

[tex]7.6x-2.3x=106[/tex] but what does x equal? ( 20 )

[tex]7.6\cdot20[/tex] = [tex]152[/tex]

[tex]2.3\cdot20[/tex] = [tex]46[/tex]

__________________________________________________________

[tex]152-46[/tex] = [tex]106[/tex]

Which is the same in the question, so x = 20.

__________________________________________________________

Hope this helps! <3

__________________________________________________________

Answer:  c) 2x² - 2x + 4

Step-by-step explanation:

Answer:

t+b_< 155

Step-by-step explanation:

Answer:

i got you fam

Step-by-step explanation:

its b fam because the top x value goes by 1 then 2 and the y value goes from 2 to 4  

Answer:

decrease

Step-by-step explanation:

Answer:

decrease

Step-by-step explanation:

Answer:

X intercepts (-30,0)

Y intercepts (0,-3)

Answer:

The correct Option is Option A

Account B because the principal of Account B is $300 and the principal for Account A is $150

Step-by-step explanation:

Interest earned from Account A = $ 4.50

Interest earned from Account B = $22.50

Time t = 18 months

Interest rate for Account A = 2%

Interest rate for Account B = 5%

We need to find which account has greater principal

The formula used to calculate principal is: [tex]Interest=Principal\times r \times t[/tex]

where r is rate and t is time

Finding Principal for Account A:

Interest earned from Account A = $ 4.50

Time t = 18 months = 1.5 years

Interest rate for Account A = 2% = 0.02

Putting values and finding Principal

[tex]Interest=Principal\times r \times t\\4.50=Principal\times0.02\times1.5\\Principal=\frac{4.50}{0.02\times1.5} \\Principal=\frac{4.50}{0.03} \\Principal=150[/tex]

So, The Principal Amount for Account A = $150

Finding Principal for Account B:

Interest earned from Account B = $ 22.50

Time t = 18 months = 1.5 years

Interest rate for Account A = 5% = 0.05

Putting values and finding Principal

[tex]Interest=Principal\times r \times t\\22.50=Principal\times0.05\times1.5\\Principal=\frac{22.50}{0.05\times1.5} \\Principal=\frac{22.50}{0.075} \\Principal=300[/tex]

So, The Principal Amount for Account B = $300

So, the correct Option is Option A

Account B because the principal of Account B is $300 and the principal for Account A is $150

Answer:

F&H are vertical angles, D&H are corresponding angles, E&H are adjacent angles, and B&H are alternate interior angles.

Step-by-step explanation:

Hope this helps. Tell me if you need and explanation.

Answer: F&H are vertical angles, D&H are corresponding angles, E&H are adjacent angles, and B&H are alternate interior angles.

Step-by-step explanation:

Hope this helps. Tell me if you need and explanation.