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3 years ago

Draw a factor tree the prime factorization of 45 and 90 in the space provided below

Mathematics

1 answer:

Ann [662]3 years ago

3 0

45 90
/ \ / \
5 9 45 2
/ \ / \
3 3 5 9
5x3x3 / \
3 3
2x5x3x3

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PLEASE HELP!!!

AlekseyPX

Answer:

Step-by-step explanation:

Find the average rate of change of each given function over the interval [-2, 2]]:

✔️ Average rate of change of m(x) over [-2, 2]:

Average rate of change = $\frac{m(b) - m(a)}{b - a}$

Where,

a = -2, m(a) = -12

b = 2, m(b) = 4

Plug in the values into the equation

Average rate of change = $\frac{4 - (-12)}{2 - (-2)}$

= $\frac{16}{4}$

Average rate of change = 4

✔️ Average rate of change of n(x) over [-2, 2]:

Average rate of change = $\frac{n(b) - n(a)}{b - a}$

Where,

a = -2, n(a) = -6

b = 2, n(b) = 6

Plug in the values into the equation

Average rate of change = $\frac{6 - (-6)}{2 - (-2)}$

= $\frac{12}{4}$

Average rate of change = 3

✔️ Average rate of change of q(x) over [-2, 2]:

Average rate of change = $\frac{q(b) - q(a)}{b - a}$

Where,

a = -2, q(a) = -4

b = 2, q(b) = -12

Plug in the values into the equation

Average rate of change = $\frac{-12 - (-4)}{2 - (-2)}$

= $\frac{-8}{4}$

Average rate of change = -2

✔️ Average rate of change of p(x) over [-2, 2]:

Average rate of change = $\frac{p(b) - p(a)}{b - a}$

Where,

a = -2, p(a) = 12

b = 2, p(b) = -4

Plug in the values into the equation

Average rate of change = $\frac{-4 - 12}{2 - (-2)}$

= $\frac{-16}{4}$

Average rate of change = -4

The answer is D. Only p(x) has an average rate of change of -4 over [-2, 2]

3 0

3 years ago

A sailor is 30m above the water in the crow's nest on a sailboat. The sailor encounters an orca surface at an angle of depressio

Natali [406]

Given :

A sailor is 30 m above the water in the crow's nest on a sailboat.

The sailor encounters an orca surface at an angle of depression of 15 degrees.

The crows nest is 20 m horizontally from the bow (front) of the boat.

To Find :

How far in front of the boat is the orca.

Solution :

Let, distance of boat front from the crow's nest is x.

So,

$\dfrac{30}{20+x}=tan \ 15^{\circ}\\\\x=\dfrac{30}{tan \ 15^{\circ}}-20\\\\x=111.94-20\\\\x=91.94\ m$

Hence, this is the required solution.

4 0

3 years ago

10 Pts Multiplying fractions: 5 1 — x — = 6 2

Flauer [41]

Multiply the numerators together. Multiply the denominators together. Then reduce if necessary.

$\dfrac{first~numerator}{first~denominator} \times \dfrac{second~numerator}{second~denominator} = \dfrac{(first~numerator)\times(second~numerator)}{(first~denominator)\times(second~denominator)}$

$\dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{a \times c}{b \times d}$

$\dfrac{5}{6} \times \dfrac{1}{2} = \dfrac{5 \times 1}{6 \times 2} = \dfrac{5}{12}$

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4 years ago

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2x-ay=3 8x-12y=b I'm supposed to find what a-b equals.

PolarNik [594]

Answer:

Step-by-step explanation:

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3 years ago

The amount Denise charges to repair computers is $50 an hour plus a $25 service fee. Write an expression to show how much she wi

k0ka [10]

The expression is

50h+25

50 times the number of hours, "h"
25 representing the one time service fee

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4 years ago

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