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1 year ago

Will give brainlest

Mathematics

1 answer:

stealth61 [152]1 year ago

7 0

Answer:

Option C (15 + n)

Step-by-step explanation:

The phrase "the sum of" indicates addition.

This means we would write the sum of 15 and a number as 15 + n, where 'n' is the unknown value.

Option C should be the correct answer.

Hope this helps.

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Factor each completely. <br><br>10a² - 9a + 2 <br><br>

Sophie [7]

Answer:

a= $\frac{2}{5}$ or $\frac{1}{2}$

Step-by-step explanation:

Equate the equation to zero

$10a^{2}$ -9a+2=0

$10a^{2}$ -5a-4a+2=0

5a(2a-1)-2(2a-1)=0

Write out the factors

(5a-2)(2a-1)=0

Then equate each factor to zero

5a-2=0 OR 2a-1=0

5a=2 OR 2a=1

a= $\frac{2}{5}$ OR a= $\frac{1}{2}$

a= $\frac{2}{5}$ or $\frac{1}{2}$

3 0

2 years ago

Ryan has 4 cups of grape juice and Kelsey has 7 cups of lemonade they want to combine what they have to make punch how many 1/2

svp [43]

Answer:

5.5 servings

Step-by-step explanation:

4+7=11

11/2=5.5 sevings

5 0

3 years ago

Rewrite with only sin x and cos x. cos 3x

Gekata [30.6K]

$\cos (3x)=4\cos^3 x-3\cos x$

6 0

2 years ago

Find constants a and b such that the function y = a sin(x) + b cos(x) satisfies the differential equation y'' + y' − 5y = sin(x)

vichka [17]

Answers:

a = -6/37

b = -1/37

============================================================

Explanation:

Let's start things off by computing the derivatives we'll need

$y = a\sin(x) + b\cos(x)\\\\y' = a\cos(x) - b\sin(x)\\\\y'' = -a\sin(x) - b\cos(x)\\\\$

Apply substitution to get

$y'' + y' - 5y = \sin(x)\\\\\left(-a\sin(x) - b\cos(x)\right) + \left(a\cos(x) - b\sin(x)\right) - 5\left(a\sin(x) + b\cos(x)\right) = \sin(x)\\\\-a\sin(x) - b\cos(x) + a\cos(x) - b\sin(x) - 5a\sin(x) - 5b\cos(x) = \sin(x)\\\\\left(-a\sin(x) - b\sin(x) - 5a\sin(x)\right) + \left(- b\cos(x) + a\cos(x) - 5b\cos(x)\right) = \sin(x)\\\\\left(-a - b - 5a\right)\sin(x) + \left(- b + a - 5b\right)\cos(x) = \sin(x)\\\\\left(-6a - b\right)\sin(x) + \left(a - 6b\right)\cos(x) = \sin(x)\\\\$

I've factored things in such a way that we have something in the form Msin(x) + Ncos(x), where M and N are coefficients based on the constants a,b.

The right hand side is simply sin(x). So we want that cos(x) term to go away. To do so, we need the coefficient (a-6b) in front of that cosine to be zero

a-6b = 0

a = 6b

At the same time, we want the (-6a-b)sin(x) term to have its coefficient be 1. That way we simplify the left hand side to sin(x)

-6a -b = 1

-6(6b) - b = 1 .... plug in a = 6b

-36b - b = 1

-37b = 1

b = -1/37

Use this to find 'a'

a = 6b

a = 6(-1/37)

a = -6/37

8 0

2 years ago

Choose the ratio that you would use to convert 1.5 feet to miles. Remember

AleksandrR [38]

Answer: B, 1 mile / 5280 ft.

Step-by-step explanation: If you need to convert feet to miles the unit multiplier (ratio) that you use should have miles on top and feet on the bottom so that the feet cancel when you multiply, leaving miles as the unit. B is the only answer that has miles on top and feet on the bottom as well as the correct amounts (1 mile and 5280 ft).

7 0

2 years ago

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