there are 300 pages in a workbook. every chapter has 25 pages. which equation can be solved to find how many chapters are in the workbook?

[tex]\displaystyle\\Answer:\ y=\frac{7}{16}x^2 -\frac{7}{4}x-\frac{5}{4}[/tex]

Step-by-step explanation:

The vertex is also the symmetry point of the parabola. The formula for finding the x-coordinate of the parabola: x = -b/2a  (2,-3)

Hence,

[tex]\displaystyle\\2=\frac{-b}{2a} \\[/tex]

Multiply both parts of the equation by -2a:

[tex]\displaystyle\\-4a=b\ \ \ \ \ (1)[/tex]

[tex]y=ax^2+bx+c\ \ \ \ \ -\ \ \ \ \ the\ quadratic\ equation\\\\Thus,[/tex]

You can make a system of equations on two points belonging to the quadratic equation:

[tex]-3=a(2)^2+b(2)+c\\4=a(6)^2+b(6)+c\\\\-3=4a+2b+c\ \ \ \ (2)\\4=36a+6b+c\ \ \ \ (3)\\\\[/tex]

Substitute (1) into equations (2) and (3):

[tex]-3=4a+2(-4a)+c\\4=36a+6(-4a)+c\\\\-3=4a-8a+c\\4=36a-24a+c\\\\-3=-4a+c\ \ \ \ (4)\\4=12a+c \ \ \ \ (5)\\\\\\[/tex]

Subtract equation (4) from equation (5):

[tex]7=16a[/tex]

Divide both parts of the equation by 16:

[tex]\displaystyle\\\frac{7}{16} =a\ \ \ \ (6)[/tex]

Substitute (6) into equations (1):

[tex]\displaystyle\\-4(\frac{7}{16} )=b\\\\-\frac{4*7}{4*4}=b\\\\-\frac{7}{4}=b[/tex]

Substitute values a and b into equation (2):

[tex]\displaystyle-3=4(\frac{7}{16})+2(-\frac{7}{4})+c\\\\ -3=\frac{7}{4} -\frac{14}{4}+c\\\\ -3=-\frac{7}{4}+c \\\\-3+\frac{7}{4}=-\frac{7}{4}+c+\frac{7}{4} \\\\ \frac{-3*4+7}{4} =c\\\\\frac{-12+7}{4}=c\\\\ -\frac{5}{4}=c[/tex]

Thus,

[tex]\displaystyle\\y=\frac{7}{16}x^2 -\frac{7}{4}x-\frac{5}{4}[/tex]

Answer:

Step-by-step explanation:

The sides of the triangle are:

Its perimeter is the sum of the three sides:

Answer:

12 dogs

Step-by-step explanation:

Ratios are scaleable, so let's look at all of the equivalent ratios of 3:2. However it needs to add up to 20 (the sum will be in parenthesis)

3:2 (Sum of 5)

6:4 (Sum of 10)

9:6 (Sum of 15)

12:8 (Sum of 20) ----> Correct Answer

By using the concept of linear equations, amount of driving when two of these plans cost the same will be at x = 100.

The cost when two plans cost the same is $67.

The linear equation in one variable is written as ax + b = 0, where a and b are two integers and x is a variable. This equation has only one solution.

Given data:

First plan has it in initial fee of $55 and cost an additional $0.12 per mile.

Second plan has an initial fee of $50 in cost an additional $0.17 per mile.

Linear Equation for first plan: f(x) = 55+0.12x

Linear Equation for second plan: s(x) = 50+0.17x

Here, x is a variable.

To find out the distance when the two plans cost the same, we'll need to solve:

55 + 0.12x = 50 + 0.17x

55 - 50 = 0.17x- 0.12x

5 = 0.05x

x = 5/0.05

x = 100

The cost when the two plans cost the same :

f(100) = 55 + 0.12(100)

f(100) = $67

s(100) = 50 + 0.17(100)

s(100) = $67

Hence, two of the plans will cost the same at x=100 and cost will be $67.

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Answer:

The two in the middle?

The slope between (4, 30) and (12, 90) and between (4, 30) and (10, 75) is the same.

Slope is the 'steepness' of the line, also commonly known as rise over run. slope is dividing the change in the y-value between two points over the change in the x-value.

given co-ordinates:

(4, 30), (10, 75), (12, 90), (22, 165)

Now, the slope between (4, 30) and (12, 90)

m= ( 90-30)/ (12-4)

m= 60 / 8

m = 7.5

and, the slope between (4, 30) and (10, 75)

m= ( 75-30)/ (10-4)

m=45 / 6

m= 7.5

Hence, The slope between (4, 30) and (12, 90) and between (4, 30) and (10, 75) is the same.

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Step-by-step explanation:

we are calculating miles.

when we have speed, which is mph or miles/hour. what do we have to multiply it with to get miles ? hours !

miles/hour × hour = miles

so, in the function D(x) the speed 60 mph has to be multiplied by the hours spent driving to get the driven miles.

x = hours spent driving

the domain is the interval or set of all valid x (input) values. the range is the interval or set of all valid y (function result) values.

so what are valid x (number of driving hours) values ?

it starts with 0, if course (before actually driving). and it goes up to 4 (after 4 hours the 240 miles are "done").

the domain is

0 <= x <= 4

and the range ? that is all the function result values for the valid x values.

for x = 0 this starts at 240.

and goes down for x = 4 to 0.

the range is

0 <= y (= D(x)) <= 240

Answer:

theres a 25% you will grab an apple (work shape is suppose to be circle)

Step-by-step explanation:

Hope this helps

Greetings from Brasil...

The total length will be: 10+10+10+10 = 40

and

(3/4)m = 0.75m

Then, Rule of 3:

QTD             m

  1     ------    3/4

  X     ------   40

X = 53.333

Soon 53 posts will be needed

Answer: 10

Step-by-step explanation: 1 1 1 1 1+ 1 1 1 1 1= 1 1 1 1 1 1 1 1 1 1 or 10

The mass of 3 mangoes and 5 oranges together is 5x kg.

Let the mass of mangoes be 'x'

Given the total mass that pawpaw has = a total mass of 8 mangoes

                                                       = 8x

mass of an orange = 2/5 the mass of a mango

                               = 2/5 * x

Now, the mass of 3 mangoes and 5 oranges together as

= 3 * mass of mangoes + 5 * mass of orange

= 3 * x + 5 * 2/5 * x

= 3x + 2x

= 5x kg

The mass of 3 mangoes and 5 oranges together is 5x kg.

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We know that an arc is a part of the entire perimeter of a circle.

Radian is defined as a unit of plane angular measurement that is equal to the angle subtended by the circle at the center by an arc that is of the length equal to the radius

We also know that the circle as a whole contains 2π radians

we know that s=rΘ

S=rθ represents the central angle in radians and r is the length of the radius.

Thus we can say that radian measure of an angle theta is the length of the arc.

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Answer:

5/4 Quotient[24/5] and 6

Step-by-step explanation:

5/4 Quotient[24/5]

Simplify the following:

(4 + 4/5)/(4/5)

Multiply the numerator of (4 + 4/5)/(4/5) by the reciprocal of the denominator. (4 + 4/5)/(4/5) = ((4 + 4/5)×5)/4:

((4 + 4/5)×5)/4

Put 4 + 4/5 over the common denominator 5. 4 + 4/5 = (5×4)/5 + 4/5:

(((5×4)/5 + 4/5) 5)/4

5×4 = 20:

((20/5 + 4/5)×5)/4

20/5 + 4/5 = (20 + 4)/5:

(((20 + 4)/5)×5)/4

20 + 4 = 24:

(24/5×5)/4

24/5×5 = (24×5)/5:

((24×5)/5)/4

((24×5)/5)/4 = (24×5)/(5×4):

(24×5)/(5×4)

(24×5)/(5×4) = 5/5×24/4 = 24/4:

24/4

The gcd of 24 and 4 is 4, so 24/4 = (4×6)/(4×1) = 4/4×6 = 6:

Answer: 6

Answer:

Step-by-step explanation:

You want to find f(6) and f(a) when f(x) = 15/(x -3).

To evaluate a function, put the argument where the variable is and simplify as needed.

Put 6 where x is:

  f(6) = 15/(6 -3) = 15/3

  f(6) = 5

Put 'a' where x is:

  f(a) = 15/(a -3) . . . . . . cannot be simplified

Answer:

−3 < x ≤ 0

Step-by-step explanation:

1 < x + 4 ≤ 4

Add -4 to all parts

1 + −4< x + 4 + −4 ≤ 4 + −4

Put pairs in bracket to avoid confusion

(1 + −4) < x (+ 4 + −4) ≤ (4 + −4)

−3 < x ≤ 0

It should be noted that solving the system of equations. -5a + 7b = 2 -15a + 21b = 6 will give 0 and this implies that it has no solution

It should be noted that we simply want to solve the equations given:

-5a + 7b = 2 ................ i

-15a + 21b = 6 ............. ii

Divide equation ii through by 3. This will give:

-5a + 7b = 6

Therefore, the equations will be:

5a + 7b = 2 ................ i

5a + 7b = 2 ................ ii

Subtract equation ii from i

This will be (5a + 7b = 2) - (5a + 7b = 2) = 0

Therefore, it should be noted that solving the system of equations. -5a + 7b = 2 -15a + 21b = 6 will give 0 and this implies that it has no solution

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Earning of each = $33.75

Let's take the earnings of each person to be x.

Total person working at the theater = 16 + 4 + 12

                                                          = 32

Now the total earnings of the people = 32x

Which is given = $1080

So we get an equation

              32x = 1080

                 x = $33.75

Hence we get the earnings of each person = $33.75

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Answer:

if you just want to simplify, -6a^2 m^7 n

Step-by-step explanation:

Answer:

3/5

Step-by-step explanation:

500 is the money she started with if you put that over the money she spent on vegetables it would be 300/500 when simplified it's 3/5

Answer: 3 miles

Step-by-step explanation:

Total = 30 miles per week

Weekly runs in the morning= 3*5 = 15 miles per week

Bikes= 30-15 = 15 miles per week

Bikes each day= 15/5 = 3 miles

Solving a system of equations, we conclude that the largest number on a hat is 14.

We have 3 hats, each one with a number that we will define as:

x, y, and z.

We know that by adding pairs of these numbers we get 11, 17 and 22, then we can write a system of equations:

x + y = 11

x + z = 17

y + z = 22

Clearly z is the largest number, so we want to find z.

First, we can isolate x on the first equation so we get:

x = 11 - y

Replacing that in the second equation giveS:

x + z = 17

(11 - y) + z = 17

Now our system is:

y + z = 22

(11 - y) + z = 17

Isolating y in the first one we get:

y = 22 - z

Now we can replace that in the other equation:

(11 - (22 - z)) + z = 17

Now we can solve this for z.

11 - 22 + z + z = 17

-11 + 2z = 17

2z = 17 + 11 = 28

z = 28/2 = 14

z = 14

We conclude that the largest number on a hat is 14.

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Answer:

a) y = 6

b) y = 3x + 3

Step-by-step explanation:

a.)

plug 1 into x in the equation:

[tex]-12+4y=12[/tex]

add 12 to both sides to isolate 4y:

[tex]4y=24[/tex]

divide both sides by 4 to simplify x:

[tex]y=6[/tex]     [24/4=6]

b.)

add 12x to both sides to isolate 4y:
[tex]4y=12x+12[/tex]

divide both sides by 4x to simplify x:

[tex]y=3x+3[/tex]

The time at which the truck will pass the car is 2.5 hours and the distance at which the car and truck meet is 200km.

Velocity is defined as the ratio of the distance moved by the object at a particular time. The velocity is a vector quantity so it needs both the magnitude and the direction.

Given that at 2 p.m., a car is 100 km east of Toronto, driving eastward at 80 km/h. A truck leaves Toronto at 2 p.m. and is driving eastward at 120 km/h.

The time will be calculated as:-

Relative velocity = Distance / Time

Time = Distance /  Relative velocity

Time = 100 / 120 - 80

Time = 2.5 Hours

Distance of car = Speed x time = 80 x 2.5

Distance of car = 80 x 2.5

Distance of car = 200 Km

Therefore, the time at which the truck will pass the car is 2.5 hours and the distance at which the car and truck meet is 200km.

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Statistical power is influenced by all of the following except observed test value.

If there is a real effect present to detect, the statistical power of a hypothesis test is the likelihood of finding it. When an experiment is complete, power may be calculated and presented to make comments about how confident one could be in the conclusions taken from the study's results. It may also be employed as a tool to calculate the sample size or the number of observations needed to detect an effect in an experiment. You will learn the significance of a hypothesis test's statistical power in this lesson, and you'll learn how to compute power analyses and power curves as part of an experimental design.

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The new volume of the right circular cylinder is 44 cubic centimeter.

The formula for the volume of the cylinder is given as

         V = Πr^2h              (1)

We have been given that,   V = 22 cubic centimeters

Now we need to find the volume of the cylinder which is denoted by V’ whose,

                  r = 2r

          and, h = h/2

Now putting the required values in equation (1) we get

 V’ = Π(2r)^2(h/2)

 V’ = Π4r^2(h/2)

V’ = 4/2(Πr^2h)

V’ = 2V   [as V = Πr^2h]

V’ = 2*22 cubic centimeter

V’ = 44 cubic centimeter

Hence the new volume of the right circular cylinder is 44 cubic centimeter

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Answer:

Following is the answer for your question your question can be done in this manner.

Answer:

The answer is D.

Step-by-step explanation:

Answer:

in this case the answer is D

Step-by-step explanation:

your welcome

The correct form of the partial fraction decomposition for given expression 7x+18/x^2+9x is A/x + B/(x + 9)

The correct answer is an option(B)

In this question, we have been given an expression x² + 9x = x (x + 9),

We need to write the correct form of the partial fraction decomposition for given expression.

Suppose, (7x + 18) / (x² + 9x) = A/x + B/(x + 9)

where A and B are some constants.

To find them, multiply both sides by x² + 9x :

7x + 18 = A (x + 9) + Bx

and then we solve for A and B.

Therefore, the correct form of the partial fraction decomposition for given expression 7x+18/x^2+9x is A/x + B/(x + 9)

The correct answer is an option(B)

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Answer:

The correct answer is option B

Step-by-step explanation: