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4 years ago

I’m stuck between 2 answers C and D plz help

Mathematics

1 answer:

Temka [501]4 years ago

7 0

Answer:

Option: C. (6,7)

Step-by-step explanation:

Acute Triangle

An acute triangle is a type of triangle with three angles that measure less than 90°. If one of the angles is 90°, then it's a right triangle.

In the given figure, we must find what point makes an acute triangle with the red colored segment. Let's analyze the options

The point (7,7) has the same x-coordinate as the right vertex, thus it will form a reight triangle, not an acute triangle

The point (8,5) would form an angle of more than 90°. It's not the correct option. The same situation applies to the point (2,4)

The only valid option is the point (6,7) because the x-coordinate is inside of the x-coordinates of the given segment.

Option: C. (6,7)

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The birth rate of a population is b(t) = 2300e0.021t people per year and the death rate is d(t)= 1450e0.018t people per year, fi

Cerrena [4.2K]

Answer:

38,674.This area represents the increase in population over a 10-year period.

Step-by-step explanation:

When graphed over the interval 0 ≤ t ≤ 10, the birth rate is more than the death rate. This means the area between the two curves is the amount of births subtract the amount of deaths. This results in an area which means the increase of the population.

The birth rate is graphed in green and the death rate is graphed in blue.

To find the area, take the integral of the difference of the functions:

$\int\limits^{10}_0 {2300e^{0.021t} - 1450e^{0.018t} } \, dt \\\\\frac{2300e^{0.021t}}{0.021} - \frac{1450e^{0.018t}}{0.018} \\\\(\frac{2300e^{0.21}}{0.021} -\frac{1450e^{0.18}}{0.018} ) - (\frac{2300}{0.021}- \frac{1450}{0.018} ) \\\\135117.12 - 96442.51 \\\\38,674$

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3 years ago

Four friends go to an amusement arcade.

galben [10]

Answer:

The rule is:

T(x) = 8x + 20

Explanation:

We are given that:

The rule for the amount that one friend pays is:

C(x) = 2x + 5

Now, we know that:

Each of the four friends will pay the entry fee which is $5 per person

The 4 friends will play the same number of games represented by x

This means that:

We can simply get the rule for the total amount to be paid by the four friends (T(x)) by multiplying the amount paid by each friend by 4

This means that:

T(x) = 4 * C(x)

T(x) = 4(2x + 5)

T(x) = 8x + 20

Hope this helps :)

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4 years ago

Solve the equation -5.1 + 8 = -7

photoshop1234 [79]

Answer: 2.9 ≠ −7 (False)

Step-by-step explanation:

5 0

3 years ago

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What is the equation of a line perpendicular to y=-2/5X-1 that passes through (2,-8)

AysviL [449]

Answer:

$y=\frac{5}{2}x-13$

Step-by-step explanation:

Given the equation

$y=-\frac{2}{5}x-1$

comparing the equation with the slope-intercept form $y=mx+b$

Here,

m is the slope

b is the intercept

so the slope of the line is m = -2/5

As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line,

so the slope of the perpendicular line will be: 5/2

Therefore, the point-slope form of the equation of the perpendicular line that goes through (2,-8) is:

$y-y_1=m\left(x-x_1\right)$

$y-\left(-8\right)=\frac{5}{2}\left(x-2\right)$

$y+8=\frac{5}{2}\left(x-2\right)$

subtract 8 from both sides

$y+8-8=\frac{5}{2}\left(x-2\right)-8$

$y=\frac{5}{2}x-13$

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3 years ago

A manufacturer finds that the revenue generated by selling x units of a certain commodity is given by the function R(x) = 60x −

bonufazy [111]

R(x) = 60x - 0.2x^2

The revenue is maximum when the derivative of R(x) = 0.
dR(x)/dx = 60 - 0.4x = 0
0.4x = 60
x = 60/0.4 = 150

Therefore, maximum revenue is 60(150) - 0.2(150)^2 = 9000 - 4500 = $4,500
Maximum revenue is $4,500 and the number of units is 150 units

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3 years ago

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