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3 years ago

12

HELP ASAP solve the equation using the properties of equality.89= -5d+9

1 answer:

sergey [27]3 years ago

8 0

Answer:

d = -16

Step-by-step explanation:

Step 1: Write equation

89 = -5d + 9

Step 2: Solve for <em>d</em>

<u>Subtract 9 on both sides:</u> 80 = -5d

<u>Divide both sides by -5:</u> -16 = d

Step 3: Check

<em>Plug in x to verify if it's a solution.</em>

89 = -5(-16) + 9

89 = 80 + 9

89 = 89

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The terminal side of θ passes through the point (10, 6). What is the exact value of cos θ in simplified form?

seraphim [82]

Answer:

$\frac{5\sqrt{34}}{34}$

Step-by-step explanation:

The formula for cos θ is a/r. A is the first number (10) and b is the second number (6). R is the hypoteneuse which can be found through r = $\sqrt{a^{2} + b^{2} }$ .

In the equation you'd write that as r = $\sqrt{10^{2} + 6^{2}$ which can be simplified to $\sqrt{136$ .

You end up with $\frac{10}{\sqrt{136} }$ and you simplify this by doing $\frac{10 }{\sqrt{136} } * \frac{\sqrt{136} }{\sqrt{136} }$ , ending with the result of $\frac{5\sqrt{34}}{\sqrt{34} }$ .

(I also got this answer right on the test.)

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3 years ago

Using principle of mathematical induction prove that 6^-1 divisble by 5 .

salantis [7]

I suppose the claim is $5 \mid 6^n - 1$ for $n\in\Bbb N$ .

When $n=1$ , we have $6^1 - 1 = 6 - 1 = 5$ , and of course 5 divides 5.

Assume the claim holds for $n=k$ , that $5 \mid 6^k - 1$ . We want to use this to show it holds for $n=k+1$ , that $5 \mid 6^{k+1} - 1$ .

We have

$6^{k+1} - 1 = \left(6^{k+1} - 6\right) + \left(6 - 1) = 6\left(6^k - 1\right) + 5$

Since $5 \mid 6^k - 1$ , we can write $6^k - 1 = 5\ell$ for some integer $\ell$ . Then

$6^{k+1} - 1 = 6\cdot5\ell + 5 = 5(6\ell + 1)$

which is clearly divisible by 5. QED

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1 year ago

Which of the following expressions are factors of p(x)=60x4+24x3−45x2−18x?

Whitepunk [10]

The factors are 3x, 4x^2-3 and 5x+2

So, Option B, C and F are correct.

Step-by-step explanation:

We need to find factors of the expression $p(x)=60x^4+24x^3-45x^2-18x$

Solving the expression: $p(x)=60x^4+24x^3-45x^2-18x$

Taking 3x common:

$p(x)=3x(20x^3+8x^2-15x-6)$

Now, factor by grouping, the terms inside the bracket.

$p(x)=3x((20x^3+8x^2)+(-15x-6))$

$p(x)=3x(4x^2(5x+2)-3(5x+2))$

$p(x)=3x(4x^2-3)(5x+2)$

So, the factors are 3x, 4x^2-3 and 5x+2

So, Option B, C and F are correct.

Keywords: Finding Factors

Learn more about finding factors at:

#learnwithBrainly

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