The expression 120 + 15m gives the volume of water in Miguel's pool (in liters) after he spends m minutes filling his pool.

Write the product (4 + i)(4 − i) in the form a + bi. A. 16 − i B. 16 − i2 C. 17 D. 8

bonufazy [111]

Answer:

A.16–i is correct.

Step-by-step explanation:

(4+i)(4–i). [(a+b)(a–b)=(a²–b²)]

(4²–i²)=16–i

I hope this answer is correct so please vote my answer

3 0

3 years ago

If tan0=-3/4 and 0 is in quadrant IV, cos20= (33/25, -17/25, 32/25, 7/25, 24/25?) and tan20= (24/7, -24/7, 7/25, -7/25, 13/7, -1

Oksana_A [137]

Answer:

cos(2θ) = 7/25
tan(2θ) = -24/7

Step-by-step explanation:

Sometimes, it is easiest to let a calculator do the work. (See below)

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The magnitude of the tangent is less than 1, so the reference angle will be less than 45°. Then double the angle will be less than 90°, so will remain in the 4th quadrant, where the cosine is positive and the tangent is negative.

You can also use the identities ...

cos(2θ) = (1 -tan(θ)²)/(1 +tan(θ)²)

cos(2θ) = (1 -(-3/4)²)/(1 +(-3/4)²) = ((16-9)/16)/((16+9)/16)

cos(2θ) = 7/25

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tan(2θ) = 2tan(θ)/(1 -tan(θ)²) = 2(-3/4)/((16-9/16) = (-6/4)(16/7)

tan(2θ) = -24/7

3 0

3 years ago

At time t, the position of a body moving along the s-axis is sequalsnegative t cubed plus 15 t squared minus 72 t m. a. Find t

larisa [96]

Answer:

Step-by-step explanation:

Given that at time t, the position of a body moving along the s-axis is sequalsnegative t cubed plus 15 t squared minus 72 t m

i.e. $s(t) = -t^3+15t^2-72 t$

Velocity is nothing but s'(t) = derivative of s

and acceleration is s"(t) = derivative of v(t)

$v(t) = -3t^2+30t-72\\=-3(t^2-10t+24)\\= -3(t-6)(t-4)$

a) v(t) =0 when t = 4 or 6

b) $a(t) = -6t+30$

a(t) =0 when t =5

c) Distance travelled by the body from 0 to 5 would be

$s(5)-s(0)\\= -5^3+15(5^2)-72(5)\\= -125+375-360\\=-110$

i.e. 110 miles (distance cannot be negative)

3 0

2 years ago

A figure has a vertex at (5,2). If the figure has line symmetry about the x axis, what are the coordinates of another vertex of

Fiesta28 [93]

X axis is the ones that goes left and right

(x,y)

symetric about the x axis means that the vertical distance from the x axis is the same for 2 points that are symetric about the x axis

y is height

(x,y)
(5,2)
2 is height
distance from x axis
therefor the other point is -2
(5,-2)

the other vertex is at (5,-2)

3 0

3 years ago

Mrs. Nguyen used 1.48 meters of netting to make 4 identical mini hockey goals. How much netting did she use per goal?

snow_tiger [21]

0.37 meters of netting

<h3>Further explanation</h3>

<u>Given:</u>

Mrs. Nguyen used 1.48 meters of netting to make 4 identical mini hockey goals.

<u>Question:</u>

How much netting did she use per goal?

<u>The Process:</u>

We will solve the problem of conversion or in other words the ratio or proportion.

Option A: the conversion

Mrs. Nguyen used 1.48 meters of netting to make 4 identical mini hockey goals.

Then for every 1 goal, she needs 0.37 meters of netting.

Because $\boxed{ \ 1 \ goal \times \frac{1.48 \ meters}{4 \ goals} = 0.37 \ meters \ of \ netting.}$

Option B: the ratio (or proportion)

In the ratio, we process as follows:

$\boxed{ \ 4 \ goals : 1.48 \ meters \ of \ netting \ }$

Both are divided by 4.

$\boxed{ \ 1 \ goals : 0.37 \ meters \ of \ netting \ }$

Thus, she uses 0.37 meters of netting per goal.

Alternative problem

How much netting did she use for 8 goals?

$\boxed{ \ 8 \ goal \times \frac{1.48 \ meters}{4 \ goals} = \ ? \ }$ meters of netting.

We cross out eight and four because they can be divided.

$\boxed{ \ 2 \times 1.48 \ meters = 2.96 \ meters \ of \ netting. \ }$

She uses 2.96 meters of netting to make 8 identical mini hockey goals.

<h3>Learn more</h3>

About the engine displacement of Kawasaki Ninja brainly.com/question/5009365
The clothing maker brainly.com/question/1594110
The unit conversion brainly.com/question/5416146

Keywords: Mrs. Nguyen, 1.48 meters of netting, to make 4 identical mini hockey goals, how much netting, she uses per goal, conversion, the ratio, proportion

8 0

3 years ago