(LOOK AT PHOTO) What is the quotient of the rational expression below?
x²-49 x²-14x+49
x+2
3x+6

Step-by-step explanation:

as the velocity is not constant over time, we actually have to integrate v(t) over the interval 0<=t<=5 to get the distance.

v(t) = 60×ln(t + 1)

V(t) = 60 × integral(ln(t + 1)) between 0 and 5.

integral(ln(t + 1)) = (t + 1)ln(t + 1) - t + C

V(t) = 60 × ((t + 1)ln(t + 1) - t + C)

the distance traveled between t = 0 and t = 5 is then

60 × ((5 + 1)ln(5 + 1) - 5 + C) - 60 × ((0 + 1)ln(0 + 1) - 0 + C) =

= 60×(6ln(6) - 5 + C) - 60×(1ln(1) + C) =

= 60×(5.750556815... + C) - 60×C =

= 60×5.750556815... = 345.0334089... ≈ 345 km

It is shifted 4 units right and 3 units up.

Answer:

y + 16 = 3(x + 5)

Step-by-step explanation:

When you write an equation in point-slope form, you only need two things: a point and a slope.

Given:

The standard point-slope equation is

y - y₁ = m(x - x₁)

Plug in what you know.

y - (-16) = 3(x - (-5))

Simplify.

y + 16 = 3(x + 5)

This is your equation.

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Answer:

3(4j + 7 + 2j)

12j + 21 + 6j

12j + 6j + 21

18j + 21 ----- (1)

3(6j +7)

18j + 21 --------(2)

eq 1 = eq. 2

both are equal

Step-by-step explanation:

hope you can understand

The value of the temperature in function notation is gotten as; f(x) = 91 - 11x

Let us first find the relationship between temperature and how long the turkey sits out.

The temperature after the normal 390 minutes  is equal to approximately 6.5 hours.

Let us create a ratio and solve for x, which represents the temperature change during that extra hour after the "normal time sitting out".

Thus;

(7.5/6.5) = (80/80+ x)

Solving for x gives x = -10.7.

This means that for every extra hour it sits out, the turkey cools approximately 11°. When we add that to 80°, we have 91° which is the expected temperature after 390 minutes (6.5 hours) of sitting out.

Thus, the motion as a function of time is;

f(x) = 91 - 11x

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Inequalities help us to compare two unequal expressions. The inverse of p>q is p<q.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

Given the inequality that p is greater than q, therefore, the inverse of it will be p smaller than q. Thus, The inverse of p>q is p<q.

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The remaining area of the page will be 80 square inches.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the square in a two-dimensional plane is called the area of the square.

The area of the remaining part will be calculated as;-

Area of the square page will be = 11 x 11 = 121 square inches.

Area of three pictures will be = 15 x 3 = 45 square inches.

So the remaining area will be = 121 - 45 = 80 square inches.

Therefore the remaining area of the page will be 80 square inches.

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Answer: So you want to convert 5 cubic meters into cubic centimeters? If you're in a rush and just need the answer, the calculator below is all you need. The answer is 5000000 cubic centimeters.

Step-by-step explanation:

Answer: QN=19

Step-by-step explanation:

Diagonals of an isosceles trapezoid are congruent, so NQ=PM.

By the segment addition postulate, NQ=QR+RN=3x+7.

So,

[tex]6x-5=3x+7\\\\3x-5=7\\3x=12\\\\x=4[/tex]

So, [tex]QN=3(4)+7=\boxed{19}[/tex]

Answer:

the answer is 64

Step-by-step explanation:

now atleast mark me brainliest answer

Answer:

[tex] \frac{1}{4} (3a + 2b)[/tex]

The expression from the given condition is 1/4(3a+4b).

We have given that,

The product of a quarter of 3 more than a number a and 2 times a number b.

The quarter means divided into four equal or corresponding parts.

Therefore we get the expression from the given condition is

1/4(3a+4b).

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Answer:

29/60

Step-by-step explanation:

probability of playing is 290/600 which when simplified is29/60

Answer:

the answer above the image

Answer:

a=-4/3, 14/3

Step-by-step explanation:

absolute value only makes the answer become positive whether the value inside is negative or positive.
so -3a+5=9 or -3a+5=-9 all works

-3a+5=9

-3a=4

a=-4/3

If -3a+5=-9

-3a=-14

a=14/3

The smallest interior angle of the given regular polygon with 36 sides is; 170°

The formula for calculating the sum of interior angles of a regular polygon is; S = (n − 2) × 180°

where n is number of sides of the polygon

We are told that number of sides of ploygon is 36. Thus;

S = (36 - 2) × 180°

S = 6120°

Thus;

Smallest possible angle of polygon = 6120/36 = 170°

Sum of external angles of a regular polygon is;

S = 360/n

S = 360/36

S = 10°

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Answer:

Step-by-step explanation:

it equal 925 tins in total when you multiply 37 times 25. Hope that helps

Yes it is

Step-by-step explanation:

it is a linear function as it is written in the standard form Y=MX+C

We will need to shade the region above f(x) and the region below the function g(x)…

We have:

f(x) = x² - 1

g(x) = -x² + 4

Both of these are already graphed, and we want to transform it into:

y > f(x)

y ≤ g(x)

The first inequality means that we need to graph f(x) with a dashed line, because f(x) is not part of the solution, and then we shade all the region above f(x)…

For the other inequality, we use a solid line (because the points on the line are solutions) and then we shade the part below the curve…

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Answer:

[tex] \frac{3}{2} n {}^{2} + \frac{9}{2} n - 12[/tex]

Step-by-step explanation:

This sequence is a quadratic sequence meaning that we should find the difference and the constant second difference.

The difference between the 4 terms is in the sequence:

9;12;15

The constant second difference is 3.

Use your method of finding the general term:

2a=3 3a+b=9 a+b+c=-6

a=3/2 3(3/2)+b=9 3/2+9/2+c=-6

b=9/2 c=-12

Standard form for quadratic sequence:

[tex] {an}^{2} + bn + c[/tex]

Therefore your general term is the one stated above in the answer.

Hope that helps!

Given that [tex]f(x) = 3x^2 + 5[/tex], we have

[tex]f(x + 3) = 3 (x + 3)^2 + 5 \\\\= 3 (x^2 + 6x + 9) + 5 \\\\= 3x^2 + 18x + 32[/tex]

so that

[tex]f(x+3) - (f(x) + 3) = (3x^2 + 18x + 32) - (3x^2 + 8) \\\\= \boxed{18x + 24}[/tex]

======================================================

Explanation:

The white rectangle is 3 by 6 with area of 3*6 = 18 square inches.

The larger rectangle is 8 by 5 with area of 8*5 = 40 square inches.

The difference of these will get us the shaded area:

40 - 18 = 22 square inches

The probability you will draw a blue marble on your first draw and then draw a blue marble on your second draw is 0.063.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

Total marbles = 20

Number of blue marbles = 5

P(blue) = 5/20

P(blue∩blue) = P(blue)×P(blue)

= (5/20)(5/20)

= 25/400

= 1/16

= 0.0625 ≈ 0.063

Thus, the probability you will draw a blue marble on your first draw and then draw a blue marble on your second draw is 0.063.

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An example of independent events is P(Police Officers and choose cars).

When one event's occurrence or non-occurrence doesn't affect the occurrence or non-occurrence of another event, then such events are called independent events.

Symbolically, we have:

Two events A and B are said to be independent if we have:

P(A ∩ B) = P(A)P(B)

                    Police Officers         Firefighters

Cars               12                             3

Trucks            9                              4

SUVs              15                             2

Let  P(A) = Firefighters choose cars

P(B) = Firefighters choose Trucks

P(A ∩ B)  =  Police Officers choose cars

Thus,

P(A ∩ B) = P(A)P(B)

12 = (4) ( 3)

Hence,  an example of independent events is P(Police Officers and choose cars).

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Answer:

-4

Step-by-step explanation:

x^2+4x+5=0

a=1,b=4^1 C=5

4^2-4×1×5

-4

No. of pounds of seed it takes to plant an 8-acre field = 70 pounds.

No. of acres can be planted per pound of seed = 70/8

= 8.75.

thus, 8.75 acres can be planted per pound of seed.

Step-by-step explanation:

hope you can understand

Answer:

Samantha is 8 years and Maurice is 17 years

Step-by-step explanation:

First represent Samantha's brother's age with a variable, x.

Secondly, find Samantha's age. since shes 9 years younger, then it will be her brother's age which is x minus 9

Thirdly, in ten years, they will all age hence 10 will be added to all their ages.

Fourthly, once 10 has been added to their after 10 years, rhen we realise Maurice age will be 1.5 timess Samantha's age... Then you solve the resulting equation.

Answer:

Domain = x ≥ 0

Range = y ≥ 20

Step-by-step explanation:

The equation in slope-intercept form would look like this:

y = 4x + 20

The slope is $4 because that is the money that can be made depending on the week. Because he received a random $20 at the beginning, this is just an additional income.

                     ---------------------------------------------------------------------------

In this scenario, the domain (x-values) represent the number of weeks. The range (y-values) represent the total money made.

So the domain is asking, what is the lowest/highest amount of weeks he can save for? We know the number of weeks cannot be negative because he can't save for negative weeks. However, he could save for zero weeks. He can be saving for theoretically infinite weeks. Therefore, the domain is x ≥ 0.

The range is asking, how much money can he save? Since he starts out with a baseline of $20, this is the lowest amount of money he can have. If he were to save for an infinite amount of weeks, he could make an infinite amount of money. Therefore the range is y ≥ 20.