Solve the quadratic equations in questions 1 – 5 by factoring.1. x2 – 49 = 02. 3x3 – 12x = 03. 12x2 + 14x + 12 = 184. –x3 + 22x2 – 121x = 05. x2 – 4x = 5

From the given, it shows two points that pass through the given graph. These points are:

Point A : x1, y1 = 4, 1

Point B : x2, y2 = 5, 2

We will be using these points in generating the equation of the line.

Step 1: Let's determine the slope m of the line.

Step 2: Let's determine the y-intercept b. Substitute x,y = 4, 1 and m = 1 in y = mx + b.

Step 3: Let's complete the equation. Substitute m = 1 and b = -3 in y = mx + b.

Therefore, the equation of the line is y = x - 3.

The answer is letter B.

1) Gathering the data

3 ¼ cups of sugar------------------ 2 ⅓ cups of flour

x 4

2) Let's set a proportion, and then cross multiply those ratios but before that

let's convert those mixed numbers:

So rewriting it above, we have. 39/7 as 39/7 is >1 then we can rewrite it into a Mixed Number:

3) Hence, I'll need 5 4/7 cups of sugar

Since the temperature rises by 11 degrees we need to add this to the original temperature, then:

Therefore the temperature at 11 pm is 5° Celsius.

Answer

x = 85°

Explanation

The image of this question shows that the two angles 20° and (x - 15)° both sum up to give a right angle (90°). So,

20° + (x - 15)° = 90°

20° + x - 15° = 90°

x° + 20° - 15° = 90°

x + 5° = 90°

x = 90° - 5°

x = 85°

Hope this Helps!!!

Answer:

Explanation:

Given the below set of numbers;

Let's go ahead and reduce the mixed fractions to improper fractions;

Let's begin by listing out the information given to us:

thirteen million = 13,000,000

three hundred and two thousands = 300,000 + 2,000

fifty = 50

13,302,050 = 13,000,000 + 300,000 + 2,000 + 50

Answer:

51.28%

Step-by-step explanation:

since the test is worth 60% of your grade, the rest is worth 40%

calculate your new grade by multiplying each grade percent (as written) by the percent of your grade (as a decimal):

   77.2(0.4) = 30.88

   34(0.6) = 20.4

then add them together: 30.88 + 20.4

To solve an equation for a variable, we mean to "isolate" the variable on one side of the equation ( right or left), in order to solve for the variable we add and subtract constant terms, like 7, 8, 10, or any other constant.

In this case, we have the equation -8-2y=10, so the first step to take is to take the -8 "away" and put it to the other side of the equation ( this is the shortest way but you can take the -2y to the other side of the equation first or perform any other operation that you want that does not alter the equation, but the point is to isolate y), to put -8 in the other side of the equation we have to add it to both sides of the equation because -8+8=0:

Now, notice that y still has a constant next to it, but the goal is to leave y alone, so we check what is it that this constant is doing to y, well -2 is multiplying y so in order to take to the other side of the equation we divide all the equation by -2, because -2/-2=1:

That is how one solves an equation for a variable.

Alternative solution:

Solve x+1=3, for x: first I choose on which side of the equation I want x, I want x on the left side ( could be the right side, it is up to you), second, I observe the equation and notice that there is a number being added to x, the constant is +1, to get rid of the constant I must subtract the constant on both sides of the equation:

The last step is to simplify:

Answer:

13.3

Explanation:

To calculate the mean number of movies, use the formula below:

Substituting the data gives:

The mean number of movies that the students saw is 13.3 (correct to the nearest tenth).

Given:

Function :

Initial deposit =$800

Annual interest rate =8.5%

Where,

When deposit is double of initial deposit .

So after 8.15 year initial amount will be double.

Answer:

which question you want to be answered

Answer:

[tex]\textsf{13.\;a)}\quad d=\dfrac{P}{0.5 \pi +1}[/tex]

[tex]\textsf{13.\;b)}\quad d=14\; \sf inches[/tex]

Step-by-step explanation:

The perimeter, P inches, of a semicircle of diameter, d inches, is represented by the equation:

[tex]\boxed{P=0.5 \pi d+d}[/tex]

Part (a)

To express d in terms of P, rearrange the equation to isolate d.

Factor out the common term d from the right side of the equation:

[tex]\implies P=d(0.5 \pi +1)[/tex]

Divide both sides by (0.5π + 1):

[tex]\implies \dfrac{P}{0.5 \pi +1}=\dfrac{d(0.5 \pi +1)}{0.5 \pi +1}[/tex]

[tex]\implies \dfrac{P}{0.5 \pi +1}=d[/tex]

[tex]\implies d=\dfrac{P}{0.5 \pi +1}[/tex]

Part (b)

Given:

Substitute the given values into the equation derived in part (a) and solve for d:

[tex]\implies d=\dfrac{36}{0.5 \left(\frac{22}{7}\right) +1}[/tex]

[tex]\implies d=\dfrac{36}{\frac{11}{7} +1}[/tex]

[tex]\implies d=\dfrac{36}{\frac{11}{7} +\frac{7}{7}}[/tex]

[tex]\implies d=\dfrac{36}{\frac{18}{7}}[/tex]

[tex]\implies d=36 \times \dfrac{7}{18}[/tex]

[tex]\implies d=\dfrac{252}{18}[/tex]

[tex]\implies d=14[/tex]

Therefore, the diameter is 14 inches.

The solution to the Logarithmic Expression  Log ₅ 8 given that Log 5 = 1.61 And Log 8 = 2.08 is; 1.29

Some of the rules of logarithm are as follows;

Rule 1; Log (M*N) = Log M + Log N

Rule 2; Log (M/N) = Log M - Log N

Rule 3; Log (M)ⁿ = nLog(M)

Rule 4; Log 1 = 0

Rule 5; Logₐ a = 1

Now, we are given that Log 5 = 1.61 And Log 8 = 2.08. We want to find Log ₅ 8.

From the rules of logarithm, we can say that;

Logₐ7 = (Log 7)/(Log a)

Thus;

Log ₅ 8 = (Log 8)/(Log 5)

= 2.08/1.61

= 1.29

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Complete question is;

If Log 5 = 1.61 And Log, 8 = 2.08, Then Log ₅ 8 = O 3.25 O 3.35 10 0.47 O 2.69 O 1.29

Given

Quadratic equation

Find

Explain best method to solve equation

Explanation

I prefer the factorisation method to solve the equation.

to solve the equation with this method we take following steps

1. Put all the terms on one side.

2. then factor

3. now, set every factor equal to zero

4. next, solve the new equation which obtained by taking equal to zero

5. atlast, check the solution by puting values in main equation

Now, let us take an example

now, use step 1st

next, factor

now, put each factor equal to 0 and solve for x

Final Answer

Factorisation is the best method to solve quadratic equation

We make a system of equations from the statement

Alexa will earn $20 every time one of her songs is played in a commercial and she will $110 every time one of her songs is played in a movie.

where T is the total earned, c the number of commercials and m the number of movies

Alexa earned a total of $340 in 8 commercials and movies

we replace the total (340) on the first equation and make and equation for the total of commercials and movies

it is our system

Since the rate in which the balloon ascends is constant this means that we can represent its altitude (the location relative to its starting point) as a linear function.

A linear funtion is given by:

where m is the slope or rate of change and b is the y-intecept (the value of y when x=0).

In our case let x be the time it passes since the balloon started ascending and let y be its altitude. With this definition for the variables we conclude that in our case the rate of change is 4 and, since the ballon started on the ground, the valur of b is zero. Therefore the expression we need is:

Note:

It is important to notice that this expression is only valid for:

This comes from the fact that that the balloon ascends at that rate for 60 seconds and the fact that the time can't be negative.

Answer: The answer to that would be y=4 x 60 or just write it as y= 240

But in expression form it would be 0<_x<_60

Hope this helps.

In order to solve the missing side for a right triangle, we can use the Pythagorean theorem

then, we rewrite the expression for on of the sides different from the hypotenuse

replace with the values

Given:

f(x) = 5x - 2

g(x) = 1 - 2x

Let's find (fg)(x).

To solve the function operation, we have:

(fg)(x) = f(x) * g(x)

Thus, we have:

Solving further:

Expand using FOIL method, then apply distributive property

ANSWER:

Most likely = more probability.

ANSWER

Getting a promotion in the next year.

We will have the following:

First, we construct the exponential decay function, that is:

Now, we will determine the population after 6 years:

So, the population after 6 years will be of approximately 37491 people-

So, for values lesser than -1 and greater than -7 this inequality is true.

In this inequality let's work applying the Absolute Value properties

1) -5ln+4l<15 Dividing both sides by 5

-|n+4|<3

|n+4|>-3

2) Applying Absolute value properties

|n+4|>-3

|n+4|>-3

n+4-4>-4-3

n>-4-3

n>-7

|n+4|>3

n+4>3

n+4-4>3-4

n>-1

3) So n < -1 and >-7

So for values lesser than -1 and greater than -7 this inequality is true.

To find the functions we need to remember that

Then

Therefore

Similarly

therefore

The number of possiblities is given by the combinations of 5 blue block taken at 1

where 5C1 denotes the combinations of 5 blue block taken at 1 time. Then, we have

then, we will expect 5 times form the total of 12.

Similarly, for the other case (number of times = 24), we will get

that is, we will double the number of times.

5)

The given equations are

- 4x - 2y + 3z = 7

- 3x + 5y - 3z = 13

- 5x + y - z = 11

From equation 3, we have

y = 11 + 5x + z

We would substitute y = 11 + 5x + z into equations 1 and 2. For equation 1, we have

- 4x - 2(11 + 5x + z) + 3z = 7

- 4x - 22 - 10x - 2z + 3z = 7

- 4x - 10x - 2z + 3z = 7 + 22

- 14x + z = 29

For equation 2, we have

- 3x + 5(11 + 5x + z) - 3z = 13

- 3x + 55 + 25x + 5z - 3z = 13

- 3x + 25x + 5z - 3z = 13 - 55

22x + 2z = - 42

Dividing both sides of the equation by 2, we have

11x + z = - 21

z = - 21 - 11x

Substituting z = - 21 - 11x into - 14x + z = 29, we have

- 14x - 21 - 11x = 29

- 14x - 11x = 29 + 21

- 25x = 50

x = 50/- 25

x = - 2

z = - 21 - 11(- 2) = - 21 + 22

z = 1

Substituting x = - 2 and z = 1 into y = 11 + 5x + z, we have

y = 11 + 5(-2) + 1

y = 11 - 10 + 1

y = 2

The solutions are

x = - 2, y = 2, z = 1

The quadratic equation for the given points x-intercepts: (-3,0) and (1,0). y-intercept: (0,1) is,

f(x) = (-x² - 2x + 3)/3

Given, an equation having

x-intercepts: (-3,0) and (1,0). Also, y-intercept: (0,1)

Now, as we know that the equation is quadratic then, it is clear that the equation will be in the given form :

f(x) = ax² + bx + c

Now, using the given points,

x-intercepts: (-3,0) and (1,0) and y-intercept: (0,1)

we get,

0 = 9a - 3b + c

0 = a + b + c

1 = c

Now, using the value of c, we get

9a - 3b = -1

a + b = -1

On solving the equations, we get

9a - 3b = -1

3a + 3b = -3

On adding both the equations we get,

12a = -4

a = -1/3

Now, using the value of a, we get

-3 - 3b = -1

-2 = 3b

b = -2/3

So, the quadratic equation, be

f(x) = -x²/3 - 2x/3 + 1

On simplifying, we get

f(x) = (-x² - 2x + 3)/3

Hence, the quadratic equation for the given points x-intercepts: (-3,0) and (1,0). y-intercept: (0,1) is,

f(x) = (-x² - 2x + 3)/3

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In the question, we are given that 6 garbage trucks can collect the trash of 36 homes in a day. We can find how many trucks are needed to collect in 180 houses below.

Explanation

Answer: 30 trucks

The coordinate is starting from the origin

7 units up and 4 units to the left

My coordinate will be (4, 7)

This is because the up is positive y- axis and the left is postive x - axis as well

X = 4 and y = 7

Joining the two points together will end up in the first quadrant

The answer is (4, 7) and First quadrant

In this problem, we are trying to choose between using a permutation and a combination.

The main difference between the two is the order.

In a combination, order doesn't matter, but it does matter in a permutation. Since the coach is choosing people based on how they performed, this will be a permutation.

For the first box on your screen, you should drag and drop the "P" variable for permutation.

Next, we need to apply the permutation formula:

I'm assuming there are a total of 14 players on the team? So we will let

Where n represents the total number of players, and r represents the number of people being chosen based on performance. Then we have:

You can drag the 14! to the numerator and the 11! to the denominator.

Finally, we need to simplify to get the final answer. We can always use a calculator, but I'll show the steps for simplifying here:

Multiply the remaining values:

The coach has 2184 ways to choose a player.

Answer

-3x + 5(x + 2) = 2x + 10

Explanation

The way to find this equivalent is simply to solve the given expression.

-3x + 5(x + 2)

= -3x + 5x + 10

= 2x + 10

Hope this Helps!!!