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photoshop1234 [79]
3 years ago
9

1.Graph the functions on the same coordinate plane.

Mathematics
1 answer:
mel-nik [20]3 years ago
4 0
1. solutions are intersection points
they intersect at x=4 and x=1 or the points (4,0) and (1,0)
select 4 and 1



2.
sub -x for x
if you get the same function, it is even
if you get the exact negative of the function, it is odd
if neither, then neither
basically
f(-x)=f(x) is even
f(-x)=-f(x) is odd
and neither is neighter

so
f(-x)=-2(-x)²+3(-x)
f(-x)=-2(x)²-3x
f(-x)=-2x²-3x
that is not the same function nor is it the exact oposite
neither even nor odd




3.
domain is the time you can use
obvioulsy start at time=0
and stop when it hits the ground because it shouldn't go underground
so domain is all real numbers from 0 to 5 including 0 and 5
that is [0,5]



4. (the (f+g)(x) one)
(f+g)(x)=f(x)+g(x)
so that is just
x²-36+x³+2x²-10=
x³+3x²-46


5. just mulitply them
x⁷+9x⁴-9x³-81

6. minus them
(3x⁵+6x²-5)-(2x⁴+7x²-x+16)
3x⁵+6x²-5-2x⁴-7x²+x-16
3x⁵-2x⁴-x²+x-21
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The data in the table represents the volume of helium, in cubic feet, inside a balloon relative to the elapsed time in minutes.
Mila [183]

The volume of helium inside the balloon decreased at a rate of 0.1 cubic feet per minute. The linear equation that represents the given data is y = -0.1x + 6 and its slope m = -0.1.

<h3>What is the equation of a line passing through two points?</h3>

The equation of the line passing through the points (x1, y1) and (x2, y2) is

(y - y1) = m(x - x1).

Where m is the slope of the line and is calculated by

m = (y2 - y1)/(x2 - x1)

<h3>Calculation:</h3>

The given data in the table represents the volume of helium (cu ft), inside a balloon relative to the elapsed time in minutes.

x: 5, 10, 15, 20, 25, 30, 35, 40

y: 5.5, 5, 4.5, 4, 3.5, 3, 2.5, 2

From this table, consider two points (5, 5.5) and (10, 5)

So, the equation of the line is

y- y1 = m(x - x1)

Where slope m = (y2 - y1)/(x2 - x1)

⇒ m = (5 - 5.5)/(10 - 5)

⇒ m = -0.5/5

∴ m = -0.1

Thus, the equation is

y - 5.5 = -0.1(x - 5)

⇒ y - 5.5 = -0.1x + 0.5

⇒ y = -0.1x + 0.5 + 5.5

⇒ y = -0.1x + 6.0

∴ y = -0.1x + 6

Since the slope of the line is negative, the volume of the helium inside the balloon decreased at a rate of 0.1 cubic ft per minute.

So, option 2 is correct.

Learn more about the slope of a line here:

brainly.com/question/3493733

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3 0
1 year ago
X<br> 451<br> 412<br> 451<br> Find the value of x.<br> A. 42<br> 2<br> B. 4<br> C. 43<br> D. 43
marysya [2.9K]

Answer:

B. 4

Step-by-step explanation:

cos(45°) = x/4√2

√2/2 = x/4√2

x = 4√2•√2/2

x = 4

8 0
3 years ago
Heights of Women. Heights of adult women are distributed normally with a mean of 162 centimeters and a standard deviation of 8 c
Bogdan [553]

Answer:

a) 6.68% of heights less than 150 centimeters

b) 58.65% of heights between 160 centimeters and 180 centimeters

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\mu = 162, \sigma = 8

a) The percentage of heights less than 150 centimeters

We have to find the pvalue of Z when X = 150. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{150 - 162}{8}

Z = -1.5

Z = -1.5 has a pvalue of 0.0668

6.68% of heights less than 150 centimeters

b) The percentage of heights between 160 centimeters and 180 centimeters

We have to find the pvalue of Z when X = 180 subtracted by the pvalue of Z when X = 160.

X = 180

Z = \frac{X - \mu}{\sigma}

Z = \frac{180 - 162}{8}

Z = 2.25

Z = 2.25 has a pvalue of 0.9878

X = 160

Z = \frac{X - \mu}{\sigma}

Z = \frac{160 - 162}{8}

Z = -0.25

Z = -0.25 has a pvalue of 0.4013

0.9878 - 0.4013 = 0.5865

58.65% of heights between 160 centimeters and 180 centimeters

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3 years ago
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elixir [45]

The equation in the form of the given expression is (0)² + (1)² = 1

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sin^2 0+cos^2 0=1

This can also be expressed as:

(sin0)² + (cos0)² = 1

Substitute

(0)² + (1)² = 1

Hence the equation in the form of the given expression is (0)² + (1)² = 1

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8 0
2 years ago
A men's department store sells 3 different suit jackets, 6 different shirts, 8 different ties, and 4 different pairs of pants. h
Ksenya-84 [330]
Jackets = 3
Shirt = 6
Ties = 8
Pants = 4

Number of combination = 3 x 6 x 8 x 4 = 576

Answer: There are 576 possible combinations.
3 0
3 years ago
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