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3 years ago

In an orchestra, there are 42 woodwind players to 56 brass is ratio of woodwinds to brass written as a fraction in simplest form

1 answer:

8 0

$\frac{42}{56} = \frac{6}{8} = \frac{3}{4}$

I could do that because both numbers are divisible by 7, and then they are divisible by 2. You could also have divided them by 14, but I think it's easier to do and explain this way.

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For what values of a and b are x+1 and x+2 factors of x3 – ax2 – bx –8? Write down the other factor.

emmainna [20.7K]

<h2>For a = 1 and b = 10 x+1 and x+2 factors of x³-ax²-bx-8 = 0</h2><h2>Other factor is (x-4)</h2>

Step-by-step explanation:

We have

x³-ax²-bx-8 = 0

Its factors are x+1 and x+2

That is x = -1 and x = -2 are its roots

Substituting x = -1

(-1)³-a(-1)²-b(-1)-8 = 0

-1 - a + b - 8 = 0

b - a = 9 ---------------------eqn 1

Substituting x = -2

(-2)³-a(-2)²-b(-2)-8 = 0

-8 - 4a + 2b - 8 = 0

2b - 4a = 16 ---------------------eqn 2

eqn 1 x -2

-2b + 2a = -18 ---------------------eqn 3

eqn 2 + eqn 3

-2a = -2

a = 1

Substituting in eqn 1

b - 1 = 9

b = 10

For a = 1 and b = 10, x+1 and x+2 factors of x³-ax²-bx-8 = 0

The equation is x³-x²-10x-8 = 0

Dividing with x + 1 we will get

x³-x²-10x-8 = (x+1)(x²-2x-8)

Dividing (x²-2x-8) with x + 2 we will get

x²-2x-8 = (x+2)(x-4)

So we have

x³-x²-10x-8 = (x+1)(x+2)(x-4)

Other factor is (x-4)

8 0

3 years ago

18. Find the measure of each numbered angle.

DiKsa [7]

Answer:

m∠1 = 50°, m∠2 = 90°, m∠3 = 40°, and m∠4 = 50°

Step-by-step explanation:

Angles on straight line are equal;

$m \angle1 + 130 = 180$

$m \angle1= 180 - 130 \\ m \angle1= 50$

Vertical angles are equal,

$m \angle4= m \angle \: 1= 50 \degree$

Complementary angles add up to 90°.

$m \angle3 + m \angle4 = 90 \degree \\ 40 + m \angle3 = 90 \degree. \\ m \angle3 = 90 \degree - 50 \degree \\ m \angle3 = 40 \degree$

Angles on straight line adds up to 180°

$m \angle1 + m \angle2 + m \angle3 = 180 \degree$

$40 + m \angle2 + 50 = 180 \\ m \angle2 = 180 - 50 - 40 = 90$

7 0

3 years ago

Alicia ran 5 miles over the weekend. Approximately how many kilometers did she run? [Use the conversion 1 mile ≈ 1.6 kilometers.

Svet_ta [14]

Answer:

Total distance Alicia run in kilometer = 8 Kilometer

Step-by-step explanation:

Given:

Total distance Alicia run = 5 miles

1 mile ≈ 1.6 kilometer

Find:

Total distance Alicia run in kilometer

Computation:

Total distance Alicia run in kilometer = 1.6 × 5

Total distance Alicia run in kilometer = 8 Kilometer

3 0

2 years ago

Read 2 more answers

Which number best represents the slope of the graphed line?

ryzh [129]

Answer:

$\frac{1}{2}$

Step-by-step explanation:

refer to solution in the picture

3 0

2 years ago

Find cot θ if csc θ = negative square root of thirty seven divided by six and tan θ > 0.

Ket [755]

You can use the trigonometric identity $1+\cot^2{x}=\csc^2{x}$ .

$1+\cot^2{\theta}=(\frac{-\sqrt{37}}{6} )^2 \\ 1+\cot^2{\theta}=\frac{37}{36} \\ \cot^2{\theta}=\frac{1}{36} \\
\cot{\theta}=\frac{1}{6}$

The requirement that $\tan{\theta}\ \textgreater \ 0$ eliminates -1/6 from being another solution.

6 0

2 years ago