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3 years ago

:

Mathematics

1 answer:

gizmo_the_mogwai [7]3 years ago

5 0

Answer:

He will save $15.00

Step-by-step explanation:

You multiply $2.25 by 20 days and that is equal to 45

So $45.00 - $30.00 that would be $15.00

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If 4SINB=3SIN(2A+B) :<br> Prove that:7COT(A+B)=COTA

pickupchik [31]

Answer:

Step-by-step explanation:

Given the expression 4sinB = 3sin(2A+B), we are to show that the expression 7cot(A+B) = cotA

Starting with the expression

4sinB= 3sin(2A+B)

Let us re write angle B = (A + B) - A

and 2A + B = (A + B) + A

Substituting the derived expression back into the original expression ww will have;

4Sin{(A + B) - A } = 3Sin{(A + B)+ A}

From trigonometry identity;

Sin(D+E) = SinDcosE + CosDSinE

Sin(D-E) = SinDcosE - CosDSinE

Applying this in the expression above;

4{Sin(A+B)CosA - Cos(A+B)SinA} = 3{Sin(A+B)CosA + Cos(A+B)sinA}

Open the bracket

4Sin(A+B)CosA - 4Cos(A+B)SinA = 3Sin(A+B)CosA + 3Cos(A+B)sinA

Collecting like terms

4Sin(A+B)CosA - 3Sin(A+B)cosA = 3Cos(A+B)sinA + 4Cos(A+B)sinA

Sin(A+B)CosA = 7Cos(A+B)sinA

Divide both sides by sinA

Sin(A+B)CosA/sinA= 7Cos(A+B)sinA/sinA

Since cosA/sinA = cotA, the expression becomes;

Sin(A+B)cotA = 7Cos(A+B)

Finally, divide both sides of the resulting equation by sin(A+B)

Sin(A+B)cotA/sin(A+B) = 7Cos(A+B)/sin(A+B)

CotA = 7cot(A+B) Proved!

4 0

3 years ago

Calculate the area of triangle ABC with altitude CD, given A(−7, −1), B(−1, 5), C(0, 0), and D(−3, 3). 9 square units 18 square

Kruka [31]

9514 1404 393

Answer:

18 square units

Step-by-step explanation:

Referring to the figure, we see that the base AB has a slope of 1, and the altitude CD has a slope of -1. The number of unit squares crossed by these segments are, respectively 6 and 3, so the length of each is ...

AB = 6√2

CD =3√2

The area is half the product of the base (AB) and height (CD) so is ...

A = 1/2bh = (1/2)(6√2)(3√2) = 18

The area of ΔABC is 18 square units.

_____

<em>Additional comment</em>

It is useful to remember that the diagonal of a unit square is √2. We used that fact here. If you need to figure it using the Pythagorean theorem, you find ...

c² = a² +b²

c = 1² +1² = 2

c = √2

5 0

3 years ago

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Testing the equality of three or more population proportions Select one: a. is not possible, since proportions deal with only tw

VladimirAG [237]

Answer:

Option D

Step-by-step explanation:

To test the equality of three or more population proportions, it is appropriate to use the chi square test to allowing for equation multiple proportions.

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3 years ago

What are the terms and like terms?<br> 1. 3n + 7 - n - 3

NikAS [45]

The like terms are 3n and -n and the terms are 7 and 3

8 0

3 years ago

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If grandma lives in Palm Springs which is 100 miles away. How long does it take to get there if you drive a constant speed of 50

alexira [117]

Answer:

Step-by-step explanation:

i dont know unit rate 50 miles every hour

50/1

it take 2 hours to get to palmm springs

8 0

3 years ago