Find the solutions of the following equations in the interval [0, 2π).

6W + 7 = 12

to solve this, just isolate W

so, the answer is w=5/6

ANSWER

30 + 15x = 180

EXPLANATION

We have that Gary has read 30 pages of his book.

He wants to read 15 pages every day till he finishes the 180 pages.

Let the number of days it will take him be x.

This means that after reading 15 pages for x days, he will have read:

15 * x = 15x

Therefore, the total number of pages he will have read (180) will be:

30 + 15x = 180

That is the equation that represents the situation.

Answer:

[tex]\frac{4}{20}[/tex] = [tex]\frac{11}{55}[/tex]

Step-by-step explanation:

[tex]\frac{x}{20}[/tex] = [tex]\frac{11}{55}[/tex]  cross multiply and solve for x

55x = 11(22)

55x = 220  Divide both sides by 55

x = 4

A polynomial has the following form:

Therefore, the function is a polynomial

Answer:

It is a polynomial of degree 3.

The standard form of a 3rd degree polynomial is given by:

So:

The polynomial in standard form is:

With the leading term x³ and the constant 0.

in the given image

m it is given that m

120 = 3x - 5 + 2x

120 = 5x - 5

5x = 120 + 5

x = 125/5

x = 25

so the value of x is 25

So, mm

m = 3 (25) - 5

= 75 - 5

mso, m

the, sum of the angles

so,

120 + mmm

For a given function  f(x) = x² + 3x - 2, f(a) is a² + 3a - 2 and f(x - 1) = x² + x - 4

Given,

The function f(x) = x² + 3x - 2

We have to find f(a) and domain f(x - 1)

Here,

f(x) = x² + 3x - 2

Then,

f(a) = a² + 3a - 2

Now,

f(x - 1) = (x - 1)² + 3(x - 1) - 2

f(x - 1) = x² - 2x + 1 + 3x - 3 - 2

f(x - 1) = x² + x - 4

That is,

For a given function  f(x) = x² + 3x - 2, f(a) is a² + 3a - 2 and f(x - 1) = x² + x - 4

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In order to prove that two triangles are congruent using the ASA theorem, it is necessary to show two pairs of congruent angles and one pair of congruent sides of the triangles.

In the given diagram, there is already a pair of congruent triangles and a pair of congruent sides shown.

Then, in order to use the ASA theorem, we need to prove that there is another pair of congruent angles, one from each triangle.

Since the side VX must be adjacent to both angles involved in the procedure, then we need to show that the angle VXW is congruent to the angle YXZ, which is adjacent to the side YX.

This can be proven using the fact that VXW and YXZ are vertical angles.

Therefore, the necessary step in Johnny's proof is shown in option D)

The compound ineqality which the number line represents will be 5x ≥ -15 or 5x ≤ 10 so option (B) must be correct.

What is inequality?

In option (B) given that

5x ≥ -15

⇒ x ≥ -15/5

⇒ x ≥ -3

And

5x ≤ 10

⇒ x ≤ 10/5

⇒ x ≤ 2

By looking at the number line it is clear that the blue line is greater than -3 and less than 2 hence it will be correct.

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a=6

1) Given that we have M (-2, a), N(0, -2), and the gradient -4. Let's start by applying the formula for the gradient.

G = (y_2 - y_1 ) / (x_2- x_1)

2) So "a", the second coordinate of point M is equal to 6, and as the gradient is a negative number indicates a "downhill" a decreasing direction of that line.

we know that

For 2 dozen cookies

we need

1 1/3 cups of sugar

3/4 teaspoon of salt

1 1/4 cups of raisins

To convert 2 dozens to 3 dozens------> multiply by 3/2

but first convert mixed number to improper fractions

1 1/3=1+1/3=4/3 ----> multiply by 3/2

(4/3)*(3/2)=2 cups of sugar

3/4*(3/2)=9/8 ----> convert to mixed number

9/8=8/8+1/8=1 1/8 teaspoon of salt

1 1/4=1+1/4=5/4

5/4*(3/2)=15/8

15/8=8/8+7/8=1 7/8 cups of raisins

ANSWER

Graph D is the correct option

EXPLANATION

The turning points of a function are the points where its derivative changes sign - therefore the slope of the function changes sign. In other words, the turning points are the local maximums and local minimums of the function.

From these options, the one that has a local maximum/minimum at point (-1, 2) and another at point (1, -2) is option D.

Well we just need to do the analise of the function h, so for the first question we need to know what is the value of h when x=0, so if we evaluate we see that

So the first answer is that the start heigth of the rocket is 20.

Now for the second we need to do the derivate and see the critical ponit to know the maximum, we are going to calculate first the derivate, so

now we need to find the critical ponits so for this, we are going to see when h'(x) = 0, this meand when the derivate is equal to zero, so h'(x) = 0 when

to see if this critical poni is a maximum we need to calculate the secon derivate and see that the second derivate valued in 300/32 is smaller than 0, so

now when x= 300/32 we have that h''(x) is -32 because the second derivate is constant, in this case h''(300/32) < 0, because of this the answer is that 300/32 is the maximum, bur 300/32 = 75/8.

Now for the third question, we need to see the roots of h, so we need to see when h is zero, so for wich values of x we have that h(x) = 0, then

we can solve this with the quadratic equation to solve this kind of equations. This equation is

so we have that

the answer is x = (-300 - v/ 91280)/(-32) or x = (-300 + v/ 91280)/(-32) and this is equal to x = (300 + v/ 91280)/(32) or x = (300 - v/ 91280)/(32) if you prefer. We can also write the answer in a simpler way: x = (75 + v/ 5705)/(8) or x = (75 - v/ 5705)/(8), this is

Well we just need to do the analise of the function h, so for the first question we need to know what is the value of h when x=0, so if we evaluate we see that

So the first answer is that the start heigth of the rocket is 20.

Now for the second we need to do the derivate and see the critical ponit to know the maximum, we are going to calculate first the derivate, so

now we need to find the critical ponits so for this, we are going to see when h'(x) = 0, this meand when the derivate is equal to zero, so h'(x) = 0 when

to see if this critical poni is a maximum we need to calculate the secon derivate and see that the second derivate valued in 300/32 is smaller than 0, so

now when x= 300/32 we have that h''(x) is -32 because the second derivate is constant, in this case h''(300/32) < 0, because of this the answer is that 300/32 is the maximum, bur 300/32 = 75/8.

Now for the third question, we need to see the roots of h, so we need to see when h is zero, so for wich values of x we have that h(x) = 0, then

we can solve this with the quadratic equation to solve this kind of equations. This equation is

so we have that

the answer is x = (-300 - v/ 91280)/(-32) or x = (-300 + v/ 91280)/(-32) and this is equal to x = (300 + v/ 91280)/(32) or x = (300 - v/ 91280)/(32) if you prefer. We can also write the answer in a simpler way: x = (75 + v/ 5705)/(8) or x = (75 - v/ 5705)/(8), this is

When an exponent is a fraction, the number of the numerator is the exponent and the number of the denominator is the radical number:

Then, in this case:

Since

(when the number of the radical is 2 we can write it without the 2), then

Then

Answer: III

SOLUTION

Incomplete question

30% are trout, 20% are bass, 10% are perch

what is the chance that one of the next 4 is a bass

20% are bass

100 - 20 = 80

0.8^4 = 0.4096

1 - 0.4096 = 0.5904

of the 20 simulation results, 12 had bass

12/20 = 0.6

B) 60% estimate

59.04% actual

Notice that for the $6.40 package each battery costs:

For the $15.80 package each battery costs:

Therefore, the 20 count pack of AA batteries has a lower unit price of $0.79 per battery.

Answer: Last option.

The given function is:

It is reflected across the x-axis to obtain a new function. This transformation follows the rule:

If we apply this rule, we obtain:

The answer is y=-|x|

The regular pentagon can divide into 5 congruent isosceles triangles

The equal sides of each triangle have length r and vertex angle of measure 72 degrees

Then we will use the sine rule of the area to find the area of each triangle, then multiply it by 5 to get the area of the pentagon

Since the radius is 7mm, then

r = 7

Substitute r by 7

Round it to the nearest whole number

A = 117 mm^2

The area of the pentagon is 117 mm^2

Let the output is y and the input is x, then

output is means y =

9 less than 5 times input means 9 less than 5x

Then

y = 5x - 9

The option D that is "Renting a movie for $2 for the first day and $1 for each day after the first day" shows a proportional relationship as they are in proper ratio.

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportional relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

As they are in the right ratio, option D, "Renting a movie for $2 for the first day and $1 for each day after the first day," demonstrates a proportional relationship.

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Answer:

96

Step-by-step explanation:

let the number be x then

1.2x=32

x=80/3

again

3.6x

3.6×80/3

96

The distance travelled by both Evelyn and Sarah is 30 miles.

Given,

The speed travelled by Evelyn = 30 mph

Time taken by Evelyn to cover a distance = 20 minutes

Speed travelled by Sarah = 60 mph

We have to find the distance travelled by both of them.

Speed = distance / time

Then,

Distance = speed x time

Lets take x as the distance.

Then,

36 × (x + 20) = 60x

36x + 720 = 60x

60x - 36x = 720

24x = 720

x = 720/24

x = 30

That is,

The distance travelled by both Evelyn and Sarah is 30 miles.

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SOLUTION:

Step 1:

In this question, we have that:

Step 2:

Part A:

We are meant to show that the equation:

can be written in the form

Proof:

Re-arranging, we have that:

Part B:

b) Hence, solve for x in the interval:

Hello there. To solve this question, we'll have to remember some properties about rate of change.

Given the points A and B from a line, we want to determine the vertical change and the horizontal change between the points and then, using these values, determine the rate of change of the function (the line passing through them).

For this, we first find the coordinates of the points.

The vertical change is the difference between the y-coordinates of the points, hence

The horizontal change is given by the difference between the x-coordinates of the points, therefore

The rate of change of this function is, finally, given by the ratio between the vertical (rise) and horizontal (run) changes of the function:

This is the rate of change of this function.

before we can dtermone whether it is a function, there must be a relationship between X and y i.e they must have a constannt of proportionality as shown:

From the table:

when x = 9, y = 1

when x = 7, y = 2

when x = 5, y = 2

when x = 3, y = 3

when x = 1, y = 4

let us determine the constant of proportionality from the given values as shown:

k = y2-y1/x2-x1

when x = 9, y = 1

when x = 7, y = 2

k = 2-1/7-9

k = 1/-2

k = -1/2

Also

when x = 5, y = 2

when x = 3, y = 3

k = 3-2/3-5

k = 1/-2

k = -1/2

Also;

when x = 5, y = 2

when x = 3, y = 3

k = 3-2/3-5

k = 1/-2

k = -1/2

Since all the constant of proportionality are the same;

Hence y = kx

y = -1/2 x

This shows that the tabke is a function and X is directly proportional to y. hence the answer is YES, it is function

It is given that she produce print of her photos at a cost of 4 dollar per print and a setup cost of 45 dollar per run.

Let the number of photos produced be x.

Then the equation formed is

The sellling cost given is the unnecessary data given in the question.

The total cost is determined by only the setup cost and cost produce per prints.

The graph formed for the total cost and number of photos produced is

X-axis represent the number of photos produced and Y-axis represent the total cost.

We can calculate a percent change by calculating the difference between the actual state and the previous state and then dividing this difference by the previuos state.

Finally, multypling by 100% gives the percentage change.

Here we have the last state as the future population (4823 thousand people). The actual state (in this case the state to which wew want to compare the variation ir change) is 5700 thousand people.

The difference is 4823 - 5700 = -877.

Then, we can divide it by the actual population and we will have:

This is equivalent to:

If we have to round to nearest tenth, the percent change is 15.4%.

Sarah bought 8 first class tickets and she buy 2 coach ticket .

In the question ,

it is given that

total number of people including Sarah = 10 people .

let the number of first class ticket = f

let the number of coach tickets = c

So , the equation is f + c = 10

f = 10 - c

the cost for first class tickets = $240

the cost for "f" first class tickets = 240f

the cost for coach tickets = $1040

the cost for "c" coach tickets = 1040c

total budget is $4000  .

So , the equation is 240f + 1040c = 4000

On substituting f = 10 - c , we get

240(10 - c) + 1040c = 4000

2400 - 240c + 1040c = 4000

1040c - 240c = 4000 - 2400

800c = 1600

c = 1600/800

c = 2

and f = 10 - 2 = 8 .

Therefore , Sarah but 8 first class tickets and she buy 2 coach ticket .

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Answer:

7/19

Step-by-step explanation: we could get two equations from the question if we set the denominator as x and the numerator as y:

1: x=2y+5

2:(y-3)/(x-3)=1/4

cross multiply

4(y-3)=1(x-3)

4y-12=x-3

x=4y-9

3: Then we can choose one of them and minus by another one

x-x=4y-2y-(9+5)

0=2y-14

2y=14

y=7

Then we only have to plug in

x=2*7+5

x=14+5

x=19