What is the average rate of change of the function f(x)=5(2)xfrom x = 1 to x = 5? Enter your answer in the box.

By Calculating the Constant of Proportionality, we get,

1. 5 cups of yellow paint is required for 1 cup of blue paint.

2. For 4 cups of blue paint, 20 cups of yellow paint is required.

   For 5 cups of blue paint, 25 cups of yellow paint are required.

3. Cups of Yellow Paints = 5* Cups of Blue Paints

4. The constant of Proportionality is 5.

Let the cups of blue paint = x

and cups of yellow paint = y

From the table, we can infer that to make the same shade of green, we need to mix 5 cups of yellow color with 1 cup of blue.

We have, To make the same shade of green,

we need to mix 5 cups of yellow color with 1 cup of blue.

we need to mix 10 cups of yellow color with 2 cups of blue.

we need to mix 15 cups of yellow color with 3 cups of blue.

So, here we can see a relationship between the two colors, blue (x) and green(y)  

Let k be the constant of proportionality, then, we have :

10 = k *2

k =[tex]\frac{10}{2} = 5[/tex]

Hence, For one cup of blue paint, we need 5 cups of yellow paint to make the same shade of green.

And the equation of the same is y =kx, that is y =5x....equation(1)

To make new pair of numbers that would make the same shade of green.

We can use the equation 1,

for x = 4, we need y = 20

foe x =5, we need y = 25

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Answer:

{48, 55,73}

Explanation:

To determine if any three side lengths can form a right triangle, we check if it satisfies the Pythagorean Theorem.

Therefore, the side lengths that could form a right triangle are {48, 55,73}.

The coordinate pair is between the third and fourth quadrants, on the y-axis.

Remember that the quadrants are:

First quadrant: x > 0, y > 0.

Second quadrant: x < 0, y > 0.

Third quadrant: x < 0, y < 0.

Fourth quadrant: x > 0, y < 0.

In this case our coordinate pair is (0, -1/2).

So it will be between the third and fourth quadrants.

And yes, because one of the variables is zero, it is on the y-axis (just between the two quadrants).

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Answer:

B

Step-by-step explanation:

if the number is x then 3 times the number is 3x

the difference is the subtraction of 3x and 4 , that is

3x - 4

Based on the given equivalences, you have:

7 m = 7(100 cm) = 700 cm

700 cm = 700 (2.54 in) = 1,778 in

Hence, there are 1,778 inches in 7 meters

As we can see, there are 8 parts in our circle but 4 parts belong to wedge 2 and 5. Then, the probability of landing on 4 or 6 is given by

because part 4 and part 5 are disjoint sets. Since there are 8 parts in our circle, we have

which gives

which corresponds to option B

Let's begin by identifying key information given to us in the graph:

The reciprocal parent function is given as 1/f(x). This is better written as shown below

When the value for x is greater than zero, the function is positive as shown below:

When the value of x is lesser than zero, the function is negative as shown below:

Therefore, the correct answer is option A (The function is negative when x < 0)

The values in Manu’s list of rational roots he should try in the synthetic division, in light of these findings is

"Manu should try first +1/4,+1/2 and +1."

This is further explained below.

Generally, Because the lower and higher bonds are located between -6 and 1, Manu should have only analyzed the potential rational zeros that fall between those two numbers.

A lower bond indicates that the feasible rational zero cannot be lower than -6, and therefore the higher number that may be achieved cannot be more than 1.

In this manner, Manu will get an opportunity to test. This approach of rationalization based on bonds aims to reduce the number of potential solutions.

Therefore, if Manu discovers through the synthetic division that the possible roots are +1/4,+1/2,+1,+5/4,+2,+5/2,+4,+5,+10,+20, then he should only consider those inside the intervals marked by the lower and upper bounds, which are +1/4,+1/2,+1, because the rest is greater than 1. This is because the rest of the possible roots are higher than 1.

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CQ

Manu determines the roots of a polynomial equation p(x)=0 by applying the theorems he knows. He organizes the results of these theorems. From the fundamental theorems of algebra, Manu knows there are 3 roots to the equation. From Descartes' rule of sign, Manu finds no sign changes in p(x) and 3 sign changes in p(-x). The rational root theorem yields +1/4,+1/2,+1,+5/4,+2,+5/2,+4,+5,+10,+20 as a list of possible rational roots. The lower bound of the polynomial is -6. The upper bound of the polynomial is 1. What values in Manu's list of rational roots should he try in synthetic division in light of these findings?

Answer:

The answer is -23/2 or -11.5

Step-by-step explanation:

Answer:

  (d)  Isosceles right

Step-by-step explanation:

You want to know the classification of a triangle with angles 45°-45°-90°.

The largest angle is 90°, a right angle. Any triangle containing a right angle is a right triangle.

Two of the angles have the same measure. This means the triangle is an isosceles triangle.

The triangle is classified as an isosceles right triangle.

__

Additional comment

A triangle whose largest angle is less than 90° is an acute triangle. If the largest angle is greater than 90°, it is an obtuse triangle.

If no sides are the same length, the triangle is scalene. If two sides are the same length, the triangle is isosceles. If all three sides are the same length, it is an equilateral triangle.

Larger angles are opposite longer sides, so if angles are the same, their opposite sides are the same.

It can be worthwhile to remember that the side length ratios in an isosceles right triangle are 1 : 1 : √2.

Let's call C the weight of the Cashews and B the weight of the Brazil nuts.

Since the professor wants to sel a 32 pound mixture, we have the following equation:

Now, since the price of the mixture will be $5.37 per pound, this means the price of the whole mixture will be

This leads us to the followin equation:

Now we have a system of equations:

To solve it, let's isolate one of the variables in the first equation by subtracting B from both sides of it:

Now, let's use this value of C in the second equation:

To solve this equation, let's subtract 198.4 from both sides of it:

Then, let's divide both sides by -1.9:

Using this value of B in the first equation will give us:

These would be the values of B and C round to two decimals. If we want, we can also write them as integer numbers. so the mix would need to have 18 pounds of cashews and 14 pounds of Brazil nuts.

The years of education as per the given equation, for a person whose father had 14 years of education is 14.966 years.

What is education?

A planned activity, education has objectives like knowledge transmission or character and skill development. The development of understanding, reason, kindness, and honesty may be some of these goals.

As given in the question,

respondent's years of education is represented by y, and

respondent's father years of education is represented by x,

The equation for the least squares regression line for predicting a respondent's years of education is given as:

y = 9.996 + 0.355x

The year of education of respondent's father is given as 14

So putting the value of x in the given equation as 14:

we get,

y = 9.996 + 0.355(14)

y = 14.966

Hence, the years of education for a person whose father had 14 years of education is 14.966 years.

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You have to find a line perpedicular to the line y=1/2x-3 that passes through the point (-5,2)

Given one line, to find another one perpedicular to it, you have to keep in mind that the slope of the perpedicular line is the negative inverse of the slope of the first one, that is:

Let the given line be:

And the perpendicular line

The slope of the perpendicular line will be:

So for the line

The slope is

For the perpedicular line it will be:

Now that the slope of the perpendicular is determined, use the point slope form to find the equation of the perpedicular line:

Replace the with m=-2 and (-5,2)

The equation perpendicular to

is

Now you can draw both lines:

Answer:

Step-by-step explanation:

Starting from tan x, you can find sec x, because of the trigonometric identity 1 + tan2 x = sec2 x.

1 + (-4/3)2 = 1 + 16/9 = 25/9 = sec2 x.

So sec x = ±√(25/9) = ±5/3.  But since x is in Quadrant II, sec x has to be negative.  That's because sec x has the same sign as cos x, because sec x = 1 / cos x.  We know that cos x is negative is Quadrant II, therefore so is sec x.  So sec x = -5/3.

Since sec x and cos x are reciprocals of each other, cos x = 1/sec x = -3/5.

Now use the identity sin2 x + cos2 x = 1, to find sin x:

sin2 x + (-3/5)2 = 1

sin2 x + 9/25 = 1

sin2 x = 16/25

sin x = ±4/5

Again, we know that sin x is positive in Quadrant II, so sin x = 4/5.

Now that we know sin x and cos x, we can use the double angle formulas to find sin 2x and cos 2x.

sin 2x = 2 sin x cos x = 2 (4/5) (-3/5) = -24/25

cos 2x = cos2 x - sin 2 x = (-3/5)2 - (4/5)2 = 9/25 - 16/25 = -7/25

Finally use the identity tan x = sin x / cos x to find tan 2x:

tan 2x = sin 2x / cos 2x = (-24/25) / (-7/25) = -24/-7 = 24/7

The length of AC is given by AE + EC

According to the Pythagorean Theorem, we know that:

AE² = AD² - ED²

AE² = 5² - 3²

AE² = 25 - 9

AE² = 16

AE = 4

EC² = DC² + ED²

Since DC = BC, we have:

EC² = BC² + ED²

EC² = 45 - 9

EC² = 36

EC = 6

Therefore, AC = 4 + 6 = 10

Answer: D. 10

In order to find the center of the circunscribed circle, we can use the midpoint theorem because the center point is in the middle of any two vertices

that is, if we take points (9,23) and (8,16) the midpoint C is given as

which gives

So the center of the circle is the point (8.5,19.5)

On the other hand, the radius is equal to the distance from any vertex to the center. If we take the vertex (8,16), we get

which gives

so, the radius measure 3.54 units.

Now, lets prove that the answer are correct. In order to do that, we can choose the other vertices and apply the same procedure as above.

So the vertices are (5,20) and (12,19). Again, the center is the midpoint between these points and is given as

which is the same center as above.

Now, the distance from the center to vertec (5,20) is

which is the same radius obtained above. Then, the answers are correct.

Answer:

54 x 5

Step-by-step explanation:

the first figure out the brackets, then multiply by 5.

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Answer:

the answer is 6 ^ 15 you are very welcom

She cannot afford to buy the car with monthly instalments of $350. She needs to make a downpayment of $856.44 to afford the car

The total amount of the car loan = 13456.44

Number of instalments = 36 monthly payments

Affordable installment per month = $350

EMI: A fixed payment is made by a borrower to a lender at a specific time each month, known as an equated monthly instalment (EMI). The loan is repaid in full over a predetermined period of time by making equal monthly payments to the principal and interest.

Total payment that can be made using the instalments = Monthly instalments * Number of instalments

= 350*36

Total payment that can be made using the instalments = 12600

The amount remaining after paying instalments = 13456.44 - 12600

= 856.44

Downpayment required = $856.44

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Given:

Set U: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

Set P: {2, 3, 5 7, 9, 11, 13, 17, 19}

Questin 7.

Complement of set P.

The complement of set P will be the set that contains the elements present in set U but not in P.

Hence, we have:

ANSWER:

P' = {1, 4, 6, 8, 10, 12, 14, 15, 16, 18, 20}

The box has 3 white balls and 4 black balls.

Total number of balls = 3 + 4 = 7

First draw:

The probability of getting a white ball is given by

Second draw:

Notice that after the first draw the ball is put back in the box.

The probability of getting a white ball is given by

At least one of the balls is white means that one white ball or two white balls.

We have already found the probability of getting one white ball that is P(x=1) = 3/7

The probability of getting two white balls is

Finally, the probability of at least one white ball is

Therefore, the probability of the event that at least one of the balls is white is 30/49

To make things easier to understand, let's see this figure, which represents the given situation:

According to this diagram, to find x, which is the length of the side of the triangle, we can use pythagorean theorem, this way:

The area of the square is 16 square inches.

The area of a square is calculated by multiplying a side by itself.

In this case, the side S is replaced by 4 in, then:

During a basketball game, you made 11 shots of either 2 or 3 points. You scored a

total of 25 points. How many shots of each point value did you make?

Let

x -----> number of shots of 2 points

y -----> number of shots of 3 points

we have that

x+y=11

x=11-y -----> equation A

and

2x+3y=25 -----> equation B

substitute equation A in equation B

2(11-y)+3y=25

solve for y

22-2y+3y=25

y=25-22

y=3

Find the value of x

x=11-3

x=8

therefore

Answer:

The expression is given below as

Concept:

We will have to explain the options so we can figure out what the final answer is

Sum:

The result is obtained by adding numbers

Quotient:

a quotient is a quantity produced by the division of two numbers.

Product:

A product is the result of multiplication,

Factor:

factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder.

Step 1:

We will then have to deal with the parenthesis

We will then have to multiply 7 by 16 before adding to 10

Hence,

7 in the expression above represents a factor because after adding 3 and 13, you would need to multiply 2 and 5. Then, you will multiply 7 and 16 which shows that 7 in the expression above represents a factor. 7 is a factor common to both 3 and 16

Therefore,

The final answer is OPTION A

Jake's weekly rate of eating of cake slices is 11.6

Given,

Number of equal slices of cake = 12

Number of slices Jake eaten after 3 days = 5

We have to find the weekly rate of eating;

Here,

Number of days in a week = 7

Jake eaten 5 slices in 3 days so, 7 - 3 = 4

Again after 3 days 5 slices.

Then,

4 - 3 = 1

That is, Jake eaten 10 slices of cake in 6 days.

Number of cake slices eaten in 1 day = 5/3 = 1.6

Therefore,

Weekly rate of eating is 10 + 1.6 = 11.6

That is,

Jake's weekly rate of eating of cake slices is 11.6

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The given function is increasing over these following intervals:

B. -2 ≤ x ≤ -1.

C. 0 < x < 1.

Considering the given definitions on the bullet points above, the behavior of the function can be separated as follows:

Items B and C have subsets of the interval -2.5 ≤ x ≤ 2.5, hence the function is increasing on those intervals, and they are the correct options for this problem.

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