Through: (-4,4), perp. To y=4/5x-1

The length of AM is:

                                21 units.

Point M is the midpoint of AB.

AM= 3x+3, and AB=8x−6

Since, the midpoint divides the line segment into two equal parts i.e. it bisects the line segment.

Hence, we have:

                         AM+MB=AB

Also, AM=MB

Hence, we have:

     [tex]3x+3+3x+3=8x-6[/tex]

on combining the like terms in the left hand side of the equation we have:

[tex]3x+3x+3+3=8x-6\\\\6x+6=8x-6[/tex]

Now, on subtracting both side of the equation by 6x we have:

[tex]6=8x-6-6x\\\\6=8x-6x-6\\\\6=2x-6[/tex]

on adding 6 on both side of the equation we have:

[tex]6+6=2x\\\\12=2x\\\\2x=12\\\\x=\dfrac{12}{2}\\\\x=6[/tex]

Hence, we have:

[tex]AM=3\times 6+3\\\\AM=21\ \text{units}[/tex]

The amount of water flowing each second is:

rate = 5.2 x 10^5 gallons / second

Since we know that:

1 hour = 3600 seconds

Therefore:

rate = (5.2 x 10^5 gallons / second) * (3600 seconds / hour)

rate = 1.872 x 10^9 gallons / hour

Final answer:

The average volume of water that flows over the falls in an hour is 1.89 x 10^9 gallons/hour.

Explanation:

To calculate the amount of water that flows over the falls in an hour, we need to convert the given flow rate from gallons per second to gallons per hour.

There are 3600 seconds in an hour, so we can multiply the flow rate (5.25 x 105 gallons per second) by 3600 to find the flow rate in gallons per hour.

The calculation would be: 5.25 x 105 gallons/s * 3600s/hour = 1.89 x 109 gallons/hour.

The result, in scientific notation, is 1.89 x 109 gallons/hour.

The option that represents cos M is MN / MO

Using trigonometric ratios, we can find the ratio of sides of a right angle triangle.

Therefore,

cos M = adjacent / hypotenuse

cos M = MN / 0M

Therefore, cos M = MN / MO

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Answer:

x=3

Step-by-step explanation:

The equation that represents the cost y (in dollars) of renting a jet ski for x hours is y = -87.50x + 525.

The equation that represents the cost y (in dollars) of renting a jet ski for x hours can be found by analyzing the given information. Let's break it down step by step:

Therefore, the equation that represents the cost y (in dollars) of renting a jet ski for x hours is y = -87.50x + 525.

we will proceed to resolve each case to determine the solution

we have

[tex]2x+y>-4[/tex]

[tex]y>-2x-4[/tex]

we know that

If an ordered pair is the solution of the inequality, then it must satisfy the inequality.

case a) [tex](5,-12)[/tex]

Substitute the value of x and y in the inequality

[tex]-12>-2*5-4[/tex]

[tex]-12>-14[/tex] ------> is True

therefore

the ordered pair [tex](5,-12)[/tex] is a solution of the inequality

case b) [tex](-3,0)[/tex]

Substitute the value of x and y in the inequality

[tex]0>-2*-3-4[/tex]

[tex]0>2[/tex] ------> is False

therefore

the ordered pair [tex](-3,0)[/tex] is not a solution of the inequality

case c) [tex](-1,-1)[/tex]

Substitute the value of x and y in the inequality

[tex]-1>-2*-1-4[/tex]

[tex]-1>-2[/tex] ------> is True

therefore

the ordered pair[tex](-1,-1)[/tex] is a solution of the inequality

case d) [tex](0,1)[/tex]

Substitute the value of x and y in the inequality

[tex]1>-2*0-4[/tex]

[tex]1>-4[/tex] ------> is True

therefore

the ordered pair [tex](0,1)[/tex] is a solution of the inequality

case e) [tex](4,-12)[/tex]

Substitute the value of x and y in the inequality

[tex]-12>-2*4-4[/tex]

[tex]-12>-12[/tex] ------> is False

therefore

the ordered pair [tex](4,-12)[/tex] is not a solution of the inequality

Verify

using a graphing tool

see the attached figure

the solution is the shaded  area above the line

The points A,C, and D lies on the shaded area, therefore the ordered pairs A,C, and D are solution of the inequality

Answer: D (Neither option A nor option B will allow them to meet their goal.

Hope this helps!

Answer:

Factor of [tex]64-x^{15}[/tex] is [tex](4-x^{5})(16+4x^{5}+x^{10})[/tex]

Step-by-step explanation:

We need to factor the expression [tex]64-x^{15}[/tex]

Re-write the given expression  [tex]64-x^{15}[/tex] as;

[tex]4^{3}-(x^{5})^{3}[/tex]

Since, [tex]a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})[/tex]

so, here [tex]a = 4[/tex] and [tex]b = x^{5}[/tex]

[tex](4-x^{5})(4^{2}+4x^{5}+(x^{5})^{2})[/tex]

[tex](4-x^{5})(16+4x^{5}+x^{10})[/tex]

Hence, factor of  [tex]64-x^{15}[/tex] is

[tex](4-x^{5})(16+4x^{5}+x^{10})[/tex]

The value of factor of expression 64 - x¹⁵ is,

⇒ (4 - x⁵) (16 + 4x⁵ + x¹⁰)

We have to given that;

To factor the expression,

⇒ 64 - x¹⁵

Now, We can simplify as;

⇒ 64 - x¹⁵

⇒ 4³ - (x⁵)³

⇒ (4 - x⁵) (4² + 4x⁵ + (x⁵)²)

⇒ (4 - x⁵) (16 + 4x⁵ + x¹⁰)

Therefore, The value of factor of expression 64 - x¹⁵ is,

⇒ (4 - x⁵) (16 + 4x⁵ + x¹⁰)

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The number of tickets sold to students by Sam will be 14.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Sam and Chad are ticket-sellers at their class play. Sam is selling student tickets for $2.00 each, and Chad selling adult tickets for $5.50 each. if their total income for 24 tickets was $83.00.

Let x be the number of tickets sold to students and y be the number of tickets sold to adults. Then the equation is given as,

x + y = 24               ...1

2x + 5.5y = 83       ...2

From equations 1 and 2, then we have

2(24 - y) + 5.5y = 83

48 - 2y + 5.5y = 83

3.5y = 35

y = 10

Then the value of x will be given as,

x + 10 = 24

x = 24 - 10

x = 14

The number of tickets sold to students by Sam will be 14.

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As per the slope of a line, the value of 'b' is 4.

The slope of a line(m) passing through two points (x₁, y₁) and (x₂, y₂)can be represented as:

m = (y₂ - y₁)/(x₂ - x₁)

Given, the slope of the line is (m) = 0.

Here the given points are  (–2, 4) and (3, b).

Therefore, substituting the values, we get:

0 = (b - 4)/[(3 - (- 2)]

⇒  (b - 4)/5 = 0

⇒ b - 4 = 0

⇒ b = 4

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To find the answer the question first write it out. 3*x-5=40. move the five over next to the 40 and cancel out -5. so the new equation looks like this. Then add 40+5 which is 45.Lastly you have the number 3 and the variable x. now you have to divide 3 by 45 to get your final answer 15. so x=15.

                                                                            3*x=40+5

                                                                            3*x=45

Hope this helps!!

The approximate attendance at the movie theater in nine years, with a continuous growth rate of 4.2%, is around 79,918.

The question provided can be solved using the formula for continuous growth, A = P ert, where A is the final amount, P is the initial principal amount (56,000 in this case), r is the rate of growth (4.2% or 0.042 when expressed as a decimal), and t is time in years (9 years here).

To find the approximate attendance at the movie theater in nine years, we substitute our values into the formula: A = 56000 x e(0.042 x 9). After calculating this, we find that the approximate attendance at the movie theater after nine years is about 79,918.

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To calculate the sum of 12x² + 9x², add the coefficients (12 and 9) to get 21 and then multiply by x², resulting in a sum of 21x².

To find the sum of the expression 12x² + 9x², you simply add the like terms. Both terms have an x² component, so they can be combined.

Here's how you do it:

First, identify the coefficients of the x² terms, which are 12 and 9.

Next, add these two coefficients together: 12 + 9 = 21.

Finally, multiply the sum of the coefficients by x2 to get the final answer: 21x².

Therefore, the sum of 12x² + 9x² is 21x².

a. Probability density function (pdf) of X: 0.247 for 0.20 < x < 4.25.

b. Probability that diameter exceeds 2 mm: 0.556.

c. Probability that diameter is within 2 mm of the mean diameter: 0.988.

(a) Probability density function (pdf) of X:

For a uniform distribution with A = 0.20 and B = 4.25, the pdf is constant within the range A to B and 0 elsewhere. Therefore:

f(x) = 1 / (B - A) = 1 / (4.25 - 0.20) = 1 / 4.05 ≈ 0.247 for 0.20 < x < 4.25

(b) Probability that diameter exceeds 2 mm:

P(X > 2) = (4.25 - 2) * f(x) = 2.25 * 0.247 ≈ 0.556

(c) Probability that diameter is within 2 mm of the mean diameter:

The mean of a uniform distribution is (A + B)/2 = (0.20 + 4.25)/2 = 2.225.

So, we need to find P(2.225 - 2 < X < 2.225 + 2), which is P(0.225 < X < 4.225).

P(0.225 < X < 4.225) = (4.225 - 0.225) * f(x) = 4 * 0.247 ≈ 0.988

Complete question:

An article considered the use of a uniform distribution with

A = 0.20 and B = 4.25

for the diameter X of a certain type of weld (mm).

(a) Determine the pdf of X. (Round your answers to three decimal places.)

0.2<x<4.25

(b) What is the probability that diameter exceeds 2 mm? (Round your answer to three decimal places.)

(c) What is the probability that diameter is within 2 mm of the mean diameter? (Round your answer to three decimal places.)

Charli,

First find what 1/4 of 2/3 is.

1/4 of 2/3 = 1/6

(That is 1/4 times 2/3 = 1/6)

So, the bottle was 2/3 full, it is now ...

2/3 - 1/6

=4/6 - 1/6

= 3/6 or 1/2 full.

We know that the bottle of soft drink has a remaining volume which is 2 / 3 of the original.

Since Jack drank 1 / 4 of the remaining volume, hence only 3 / 4 now finally remains, the total is:

(2 / 3) * (3 / 4) = 6 / 12 = 1 / 2

Hence the bottle is now one half full

multiply 300.5 feet by -0.2 mph

300.5 * -0.2 = -60.1 change

Answer:

A. The ball is at the same height as the building between 8 and 10 seconds after it is thrown.

C. The ball reaches its maximum height about 4 seconds after it is thrown

Step-by-step explanation:    • The ball is at the same height as the building between 8 and 10 seconds after it is thrown. TRUE - the height is zero somewhere in that interval, hence the ball is the same height from which it was thrown, the height of the roof of the building.

• The height of the ball decreases and then increases. FALSE - at t=2, the height is greater than at t=0.

• The ball reaches its maximum height about 4 seconds after it is thrown. TRUE - the largest number in the table corresponds to t=4.

• The ball hits the ground between 8 and 10 seconds after it is thrown. FALSE - see statement 1.

• The height of the building is 81.6 meters. FALSE - the maximum height above the building is 81.6 meters. Since the ball continues its travel to a distance 225.6 meters below the roof of the building, the building is at least that high.

Answer:

Option A is correct

The value of (h ∘ g)(−5) is, 104

Step-by-step explanation:

Given the functions:

g(x) = 2x

[tex]h(x) = x^2 + 4[/tex]

We have to find (h ∘ g)(−5).

[tex](h o g)(-5) = h(g(-5))[/tex]          ....[1]

At x = -5

g(-5) = 2(-5) = -10

then

Substitute the g(-5) in [1] we have;

[tex](h o g)(-5) = h(-10)[/tex]

⇒[tex](h o g)(-5) = (-10)^2+4 = 100+4 = 104[/tex]

⇒[tex](h o g)(-5) = 104[/tex]

therefore, the value of (h ∘ g)(−5) is, 104