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3 years ago

Two angles are supplementary. They are represented by (3x)° and (12x+1)°. Find both angles.

Mathematics

1 answer:

klio [65]3 years ago

7 0

Answer:

35.8°

144.2°

Step-by-step explanation:

Definition of Supplementary Angles: They add up to 180°

Step 1: Set up equation

3x + 12x + 1 = 180

Step 2: Solve

15x + 1 = 180

15x = 179

x = 11.93

Step 3: Find angles

∠1 = 3x

m∠1 = 3(11.93) = 35.8°

∠2 = 12x + 1

m∠2 = 12(11.93) + 1 = 144.2°

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Burt's grandparents started a savings account for him when he was born. They invested

SashulF [63]

Answer:

4594.76 USD will be in the account on Burt's 18th birthday.

Step-by-step explanation:

Since interest rate is constant in time, we can use the definition of composite interest to determine how much money will be on Burt's 18th birthday, that is:

$C = C_{o}\cdot \left(1+\frac{r}{100} \right)^{t}$ (1)

Where:

$C_{o}$ - Initial amount, measured in US dollars.

$C$ - Current amount, measured in US dollars.

$r$ - Annual interest rate, measured in percentage.

$t$ - Time, measured in years.

If we know that $C_{o} = 1250\,USD$ , $r = 7.5$ and $t = 18$ , then the money in the savings account on Burt's 18th birthday is:

$C = (1250\,USD)\cdot \left(1+\frac{7.5}{100} \right)^{18}$

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4594.76 USD will be in the account on Burt's 18th birthday.

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3 years ago

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USPshnik [31]

Answer:

Slide/Transformation

Step-by-step explanation:

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4 years ago

What is the vertex of the function f (x) = x2 - 10x? (5,-25) (5.-75) (-5,75) (-5,25)

JulsSmile [24]

Option A

The vertex is (h, k) = (5, -25)

Solution:

Given function is:

$f(x) = x^2-10x$

The vertex form is given as:

$y = a(x-h)^2+k$

<h3>where (h, k) is the vertex</h3>

Rewrite the equation in vertex form

$f(x) = x^2-10x$

Complete the square for $x^2-10x$

Use the form $ax^2+bx+c$ to find the values of a, b, c

a = 1 , b = -10, c = 0

Consider the vertex form of a parabola

$a(x+d)^2+e$

Substitute the values of a and b into the following formula to find "d" :

$d = \frac{b}{2a}\\\\d = \frac{-10}{2 \times 1}\\\\d = -5$

Find the value of "e" using the formula,

$e = c - \frac{b^2}{4a}\\\\e = 0 - \frac{(-10)^2}{4 \times 1}\\\\e = -25$

Substitute the value of a, d, e into vertex form

$a(x+d)^2+e\\\\1(x-5)^2-25\\\\(x-5)^2-25$

Set y equal to above equation

$y = (x-5)^2-25$

Compare the above equation with vertex form

$y = a(x-h)^2+k$

$y = (x-5)^2-25$

We find, h = 5 and k = -25

Thus the vertex is (h, k) = (5, -25)

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