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diamong [38]
2 years ago
13

A red balloon is 40 feet above the ground and rising at 2 feet per second. At the same time, a blue balloon is 60 feet above the

ground and falling at a rate of 3 feet per second. How long will it take for the two balloons to be the same height from the ground? Let s = the number of seconds since the balloons began moving.
WRITE AN EQUATION FOR THIS.
Mathematics
1 answer:
VikaD [51]2 years ago
4 0

Answer:

40+2s=60-3s

Step-by-step explanation:

The red balloon starts 40 feet off the ground and rises 2 feet per second. This means the height of the red ballon is 40+2s.

The blue balloon starts 60 feet off the ground at starts falling 3 feet per second. This means the height of the blue balloon is 60-3s.

Because we want to find out when the balloons will be the same height, we set them equal to each other.

40+2s=60-3s

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Doug’s family buys 7 postcards while on vacation. Each postcard costs 0.25$ including tax. How can Doug use the number line to f
larisa [96]

Answer: Total cost is $1.75

Explanation:

Since we have given that

Number of postcards bought by Doug's family= 7

Cost of each postcard including tax = $0.25

Total cost is given by

7\times 0.25=\$1.75

Now, we want to show this in number line :

On the number line put all the number with a difference of 0.25 and run the number line seven times and we get the answer.

Each step is of length 0.25 and there are 7 jumps to reach required answer.

So, after 7 jumps we reach at 1.75 which is the required answer.

Hence total cost is $1.75

3 0
3 years ago
What is the value of
MakcuM [25]

Answer:

2

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities inclu
Softa [21]

<u>Answer-</u>

<em>The polynomial function is,</em>

y=x^4-10x^3+38x^2-64x+40

<u>Solution-</u>

The zeros of the polynomial are 2 and (3+i). Root 2 has multiplicity of 2 and (3+i) has multiplicity of 1

The general form of the equation will be,

\Rightarrow y=(x-(2))^2(x-(3+i))(x-(3-i))   ( ∵ (3-i) is the conjugate of (3+i) )

\Rightarrow y=(x-2)^2(x-3-i)(x-3+i)

\Rightarrow y=(x^2-4x+4)((x-3)-i)((x-3)+i)

\Rightarrow y=(x^2-4x+4)((x-3)^2-i^2)

\Rightarrow y=(x^2-4x+4)((x^2-6x+9)+1)

\Rightarrow y=(x^2-4x+4)(x^2-6x+10)

\Rightarrow y=x^2x^2-6x^2x+10x^2-4x^2x+4\cdot \:6xx-4\cdot \:10x+4x^2-4\cdot \:6x+4\cdot \:10

\Rightarrow y=x^4-10x^3+14x^2+24x^2-40x-24x+40

\Rightarrow y=x^4-10x^3+38x^2-64x+40

Therefore, this is the required polynomial function.


4 0
3 years ago
HELP ASAP TIMED !!!! What is the exact value of cos(c + d), given Sine c = StartFraction 24 Over 25 EndFraction for c in Quadran
Keith_Richards [23]

9514 1404 393

Answer:

  D

Step-by-step explanation:

In the second quadrant, ...

  c = 180° -arcsin(24/25) ≈ 106.26°

In the third quadrant, ...

  d = 360° -arccos(-3/4) ≈ 221.41°

Then cos(c+d) = cos(327.67°) ≈ 0.84498

This is a positive irrational number, greater than 21/100, so the only reasonable choice is the last one:

  \dfrac{21+24\sqrt{7}}{100}\approx 0.84498

_____

Perhaps you want to work this out using the trig identities.

  cos(c) = -√(1 -sin(c)²) = -7/25

  sin(d) = -√(1 -cos(d)²) = -(√7)/4

Then the desired cosine is ...

  cos(c+d) = cos(c)cos(d) -sin(c)sin(d)

  cos(c+d) = (-7/25)(-3/4) -(24/25)(-√7/4)

  cos(c+d) = (21 +24√7)/100 . . . . matches choice D

8 0
3 years ago
Fifteen SmartCars were randomly selected and the highway mileage of each was noted The analysis yielded a mean of 47 miles per g
laiz [17]

Answer: a. 47 plusminus (1.753*(5 ÷ 3.8730)

Step-by-step explanation:

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

Where

s = sample standard deviation = 5

n = number of samples = 15

z represents the test statistic

From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the test statistic score

In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 15 - 1 = 14

Since confidence level = 90% = 0.90, α = 1 - CL = 1 – 0.90 = 0.1

α/2 = 0.1/2 = 0.05

the area to the right of z0.05 is 0.05 and the area to the left of z0.05 is 1 - 0.05 = 0.95

Looking at the t distribution table,

z = 1.753

Margin of error = 1.753(5 ÷ 3.8730)

Confidence interval = 47 ± 1.753(5 ÷ 3.8730)

8 0
3 years ago
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