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3 years ago

I don't understand this question, picture attached.

Mathematics

1 answer:

mina [271]3 years ago

5 0

We can find this using the formula for arc length (where $r$ is the radius of the circle and $\theta$ is the central angle in radians):

$\textrm{Arc Length} = r\theta$

In our problem, we are given $12 = 8\theta$ . This means that:

$\theta = \dfrac{12}{8} = \boxed{\frac{3}{2}}$

The measure of the angle is 1.5.

You might be interested in

Ten increased by the quotient of a number and 6 is 5

jonny [76]

Let the required number be x, then 10 + x/6 = 5
x/6 = 5 - 10 = -5
x = 6 x -5 = -30
x = -30

5 0

3 years ago

Please help me ......:(

algol [13]

Answer: B) F(x) = √x and G(x) = 3x + 2

<u>Step-by-step explanation:</u>

The composite function G(F(x)) is when you replace every x-value in the G(x) function with the F(x) function.

$A)\ G(3x+2) = \sqrt{3x+2}\\\\B)\ G(\sqrt{x})=3(\sqrt{x})+2\quad =3\sqrt{x}+2\\\\C)\ G(\sqrt{x}+2) = 3\quad \text{there are no x-values in the G(x) function to replace}\\\\D) G(3\sqrt{x})=2\quad \text{there are no x-values in the G(x) function to replace}$

The only one that matches G(F(x)) = 3√x + 2 is OPTION B

5 0

3 years ago

(Due soon, please hurry!)

Ludmilka [50]

Answer:

I Dont Know

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Please show the steps

notka56 [123]

Answer:

x = -3, 0, or 7

Step-by-step explanation:

After removing common factors, the remaining quadratic can be factored by comparison to the factored form of a quadratic.

Write the equation in standard form.

4x³ -16x² -84x = 0

Factor out the common factor from all terms.

= 4x(x² -4x -21) = 0

Compare to the factored form of a quadratic:

(x +a)(x +b) = x² +(a+b)x +ab

This tells you the constants 'a' and 'b' in the factors can be found by considering ...

(a+b) = -4 . . . . the coefficient of the x term of the quadratic

ab = -21 . . . . . the constant term of the quadratic

It is often helpful to list factor pairs of the constant:

-21 = (-21)(1) = (-7)(3) . . . . integer pairs that have a negative sum

The sums of these pairs are -20 and -4. We are interested in the latter. We can choose ...

a = -7, b = 3

Put it all together.

4x³ -16x² -84 = (4x)(x -7)(x +3) = 0 . . . . . factored form of the equation

Apply the zero product rule. This rule tells you the product of factors will be zero when one or more of the factors is zero:

4x = 0 ⇒ x = 0

x -7 = 0 ⇒ x = 7

x +3 = 0 ⇒ x = -3

Solutions to the equation are x ∈ {-3, 0, 7}.

_____

<em>Additional comment</em>

What we did in Step 3 is sometimes referred to as the X-method of factoring a quadratic. The constant (ab product) is put at the top of the X, and the sum (a+b) is put at the bottom. The sides of the X are filled in with values that match the product and sum: -7 and 3. The method is modified slightly if the coefficient of x² is not 1.

A graphing calculator often provides a quick and easy method of finding the real zeros of a polynomial.

3 0

2 years ago

Calculate the a) future value of the annuity due, and b) total interest earned. (From Example 2)

vredina [299]

Answer:

value: $66,184.15
interest: $6,184.15

Step-by-step explanation:

The future value can be computed using the formula for an annuity due. It can also be found using any of a variety of calculators, apps, or spreadsheets.

<h3>formula</h3>

The formula for the value of an annuity due with payment P, interest rate r, compounded n times per year for t years is ...

FV = P(1 +r/n)((1 +r/n)^(nt) -1)/(r/n)

FV = 5000(1 +0.06/4)((1 +0.06/4)^(4·3) -1)/(0.06/4) ≈ 66,184.148

FV ≈ 66,184.15

<h3>calculator</h3>

The attached calculator screenshot shows the same result. The calculator needs to have the begin/end flag set to "begin" for the annuity due calculation.

The future value of the annuity due is $66,184.15.

The total interest earned is the difference between the total of deposits and the future value:

$66,184.15 -(12)(5000) = 6,184.15

A total of $6,184.15 in interest was earned by the annuity.

3 0

2 years ago