Let f(x)=x^2+3x-4. Find the number b such that the average rate of change of f on the interval [2,b] is 13.

For the dot plot

We have the next data

11,16,11,15,9,10,11,13,15,17,10,14,17,10,13,15,11,12,12,12,11,12,14,15,15,13,10,15,12,11

we have 30 numbers

in order to create a dot plot we need to add a point every time a value is repeated

Then the frequency table is how many times the values are repeated

values frequency

9-10 5

11-12 11

13-14 5

15-16 7

17-18 2

Answer:

B.  -414,720 x⁷y⁶

Step-by-step explanation:

To find the 4th term of the expansion of (2x - 3y²)¹⁰, we can use the binomial theorem.

The binomial theorem states that for an expression of the form (a + b)ⁿ:

\(\displaystyle (a+b)^n=\binom{n}{0}a^{n-0}b^0+\binom{n}{1}a^{n-1}b^1+...+\binom{n}{r}a^{n-r}b^r+...+\binom{n}{n}a^{n-n}b^n\\\\\\\textsf{where }\displaystyle \rm \binom{n}{r} \: = \:^{n}C_{r} = \frac{n!}{r!(n-r)!}\)

For the expression (2x - 3y²)¹⁰:

Therefore, each term in the expression can be calculated using:

\(\displaystyle \boxed{\binom{n}{r}(2x)^{10-r}(-3y^2)^r}\quad \textsf{where $r = 0$ is the first term.}\)

The 4th term is when r = 3. Therefore:

\(\begin{aligned}\displaystyle &\;\;\;\;\:\binom{10}{3}(2x)^{10-3}(-3y^2)^3\\\\&=\frac{10!}{3!(10-3)!}(2x)^7(-3y^2)^3\\\\&=\frac{10!}{3!\:7!}\cdot2^7x^7(-3)^3y^6\\\\&=120\cdot 128x^7 \cdot (-27)y^6\\\\&=-414720\:x^7y^6\\\\ \end{aligned}\)

So the 4th term of the given expansion is:

\(\boxed{-414720\:x^7y^6}\)

Using the height and radius given, the surface area of the cylinder is 408.2m²

The surface area of a cylinder is the combined area of its curved surface (lateral surface) and its two circular bases. The formula for the surface area of a cylinder is:

A = 2πrh + 2πr²

where:

In the given question, the data are;

Substituting the value into the formula

A = 2π(5 * 8) + 2π(5)²

A = 408.2m²

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The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.

To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

For the line containing (1,2) and (5,3), the slope is:

slope1 = (3 - 2) / (5 - 1) = 1 / 4

To find the slope of the line containing (x,4) and (3,0), we use the same formula:

slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

So, we can set up the equation:

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

Simplifying this equation:

-4 = -4 / (3 - x)

To remove the fraction, we can multiply both sides by (3 - x):

-4(3 - x) = -4

Expanding and simplifying:

-12 + 4x = -4

Adding 12 to both sides:

4x = 8

Dividing both sides by 4:

x = 2

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Answer:

2

Step-by-step explanation:

divide 34 gallons by 14 gallons

Answer:

7c+3

Step-by-step explanation:

Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

\(\boxed{I = \frac{P \times R \times T}{100}}\),

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

\(6180 = \frac{P \times 6.12 \times 28}{100}\)

⇒ \(6180 \times 100 = P \times 171.36\)     [Multiplying both sides by 100]

⇒ \(P = \frac{6180 \times 100}{171.36}\)    [Dividing both sides of the equation by 171.36]

⇒ \(P = \bf 3606.44\)

Therefore, James needs to invest $3606.44.

Point H is the ortho-center of our given triangle and option c is the correct choice.

We have been given an image of a triangle. We are asked to find the term that describes point H.

We can see that point H is the point, where, all the altitudes of our given triangle EFF are intersecting.

We know that ortho-center of a triangle is the point, where all altitudes of triangle intersect. Therefore, point H is the ortho-center of our given triangle and option c is the correct choice.

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Answer:

36 square inches.

Step-by-step explanation:

volume is given by 1 by 3, into base into height is based. His height and volume and area of the base is given by area of the ashe area of the base is given by 3 into 60 by 5. As given in the question on solving it, we get it equals to 36 square inches.

The value of x is equal to 15.1 units.

In Mathematics and Geometry, the measure of each interior angle of a regular polygon can be calculated by using this mathematical equation:

Interior angle = [180 × (n - 2)]/n

Where:

n represents the number of sides of a regular polygon.

Since this regular polygon can be decomposed into 46 triangles, it ultimately implies that it has 46 x 3 = 138 sides.

Therefore, the value of each interior angle can be calculated as;

Interior angle = [180 × (n - 2)]/n

Interior angle = [180 × (138 - 2)]/138

Interior angle = 169.6⁰

For the value of x, we have:

9.5x + 26.2 = 169.6

9.5x = 143.4

x = 15.1 units.

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Complete Question:

Suppose there is a regular polygon that can be decomposed into 46 triangles. The measure of one of its interior angles is (9.5x+26.2).

What is the value of x?

Answer:

27/8 or 3.375 or 3 3/8

Step-by-step explanation:

Answer:

DQ = \(\frac{5}{(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}-\sqrt{x+h})}\)

Step-by-step explanation:

Given function is f(x) = \(\frac{5}{2-\sqrt{x}}\)

f(x + h) = \(\frac{5}{2-\sqrt{x+h} }\)

Therefore, indicated difference quotient will be,

DQ = \(\frac{f(x+h)-f(x)}{h}\)

Now we substitute the values in the difference quotient,

DQ = \(\frac{\frac{5}{2-\sqrt{x+h} }-\frac{5}{2-\sqrt{x}}}{h}\)

      = \(\frac{5(2-\sqrt{x})-5(2-\sqrt{x+h})}{h(2-\sqrt{x})(2-\sqrt{x+h})}\)

      = \(\frac{10-5\sqrt{x}-10+5\sqrt{x+h}}{h(2-\sqrt{x})(2-\sqrt{x+h})}\)

      = \(\frac{-5\sqrt{x}+5\sqrt{x+h}}{h(2-\sqrt{x})(2-\sqrt{x+h})}\)

      = \(\frac{5(-\sqrt{x}+\sqrt{x+h})}{h(2-\sqrt{x})(2-\sqrt{x+h})}\)

      = \(\frac{5(-\sqrt{x}+\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}{h(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}\)

      = \(\frac{5[(x+h)-x]}{h(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}\)

      = \(\frac{5h}{h(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}\)

      = \(\frac{5}{(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}\)

Answer:

The area of the rectangle is increasing at a rate of 54 cm2/s.

Step-by-step explanation:

Answer:

\( \sqrt{2} \: \: \: \: \: \: \frac{ \pi}{2} \: \: \: \: are \: \: \: \: the \: \: \: \: answers\)

Step-by-step explanation:

To determine if the bank would lend Bill and Terry $210,000 to purchase their house, we need to calculate their debt-to-income (DTI) ratio, which is a measure of their total monthly debt payments compared to their monthly income. Banks typically use DTI as a factor in determining how much they will lend to borrowers.

First, we need to calculate their total monthly debt payments:

Monthly mortgage payment: $1,644

Monthly property taxes: $9,888 / 12 = $824

Monthly homeowner's insurance premium: $1,070 / 12 = $89

Car loan payment: $610

Credit card bill: $4,200

Total monthly debt payments = $1,644 + $824 + $89 + $610 + $4,200 = $7,367

Next, we need to calculate their monthly income:

Adjusted gross income: $175,988 / 12 = $14,666

Now we can calculate their DTI ratio:

DTI = Total monthly debt payments / Monthly income

DTI = $7,367 / $14,666

DTI = 0.502 or 50.2%

A DTI ratio of 50.2% is quite high, and many banks may be hesitant to lend to borrowers with such a high DTI. Generally, banks prefer borrowers to have a DTI ratio of 43% or lower.

Therefore, based on their current debt and income situation, it is unlikely that the bank would lend Bill and Terry $210,000 to purchase their house. They may need to consider reducing their debt payments or increasing their income to improve their chances of being approved for a mortgage loan.

Answer:

153.86

Step-by-step explanation:

Do 3.14 times 7 to the power of 2

Hope this helps

Answer:

152.86

Step-by-step explanation:

To find the area of a circle you have to find the radius for this circle we have the diameter so to find the radius we divide the diameter: 14 by 2

14 / 2 = 7

Then we have to square 7

7^2 = 49

Then we multiply 49 by 3.14 or pi

3.14 * 49 = 153.86

Answer:

p=228/5

Step-by-step explanation:

2/3p-7=1/4p+12

12(2/3p-7)=12(1/4p+12)

8p-84=3p+144

5p-84=144

5p=228

p=228/5

Check:

2/3(228/5)-7=1/4(228/5)+12

30.4-7=11.4+12

23.4=23.4

Because the angles add up to 180°, we conclude that the shelves are parallel.

Two adjacent angles always should add up to 180°. The top shelve and middle shelve will be parallel only if:

∠1 = ∠5

∠2 = ∠6

And we know that:

∠1 + ∠2 = 180°

Then we could rewrite this as:

∠5 + ∠2 = 180°

Replacing the measures we will get:

60° + 120° = 180°

180° = 180°

That equation is true, this, the shelves are parallel.

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Answer:

x ≥ 3

Step-by-step explanation:

- 3(2x - 1) ≤ x - 18 ← distribute parenthesis on left side

- 6x + 3 ≤ x - 18 ( subtract x from both sides )

- 7x + 3 ≤ - 18 ( subtract 3 from both sides )

- 7x ≤ - 21

divide both sides by - 7, reversing the symbol as a result of dividing by a negative quantity.

x ≥ 3

Answer:

1:10 AM

Step-by-step explanation:

The 4th eruption of the day as at 12:22 PM. And since the time between each eruption gets 12 minutes added, the next eruption is going to happen in 48 minutes, which is at 1:10 AM. After that eruption, the time will reset and the next eruption will happen at 1:22 AM

a) There are 2400 animals on the farm.

b) The number of sheep on the farm is 700.

c) The percentage of rabbits in relation to the total number of animals is 37.5%.

d) The angle that represents the number of pigs is 75 degrees.

a) To determine the total number of animals on the farm, we add up the number of rabbits, sheep, cattle, and pigs:

Total number of animals = 900 (rabbits) + 700 (sheep) + 300 (cattle) + 500 (pigs) = 2400 animals.

b) The number of sheep on the farm is given as 700.

c) To calculate the percentage of rabbits in relation to the total number of animals, we divide the number of rabbits by the total number of animals and multiply by 100:

Percentage of rabbits = (900 / 2400) * 100 = 37.5%.

d) To calculate the angle that represents the number of pigs, we need to find the proportion of the total number of animals that pigs make up, and then convert it to an angle on the pie chart.

Proportion of pigs = 500 / 2400 = 0.2083.

To find the angle in degrees, we multiply the proportion by 360 degrees:

Angle representing pigs = 0.2083 * 360 = 75 degrees.

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The intersection of sets M and F contains the elements "c" and "d".

To find the intersection of sets M and F, we need to identify the elements that are common to both sets.

M = {a, b, c, d}

F = {c, d, e, f}

The intersection of M

and F is denoted by M ∩ F, which represents the set containing elements that are present in both M and F.

Looking at the elements in M and F, we can see that the common elements between the two sets are "c" and "d".

Therefore, the intersection of M and F can be expressed as:

M ∩ F = {c, d}

So, the intersection of sets M and F contains the elements "c" and "d".

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Answer:

-60 ? At least that's if you meant like

\(5 \times ( - 12) = - 60\)

Answer:

Cannot simplify As a decimal 0.41.6 Explanation: 512 does not cancel down

Step-by-step explanation:

Answer:

1. it will be a

2. It will be c

Answer:False

Step-by-step explanation:

Failed vertical line test

Answer:

where are you from me

Step-by-step explanation:

:philipines

btw ty sayo

Answer:

Given:

Today,  he studies 15 minutes math and 75 minutes science

and from now on, 50 minutes math and 30 minutes science

Step-by-step explanation:

so if he studies for 1 day total time for math and  science will be

math=15+50            science=75+30

       =65 minutes                =105 minutes

2nd day,

math=65+50           science=105+30

       =115 minutes               =135 minutes

3rd day,

math=115+50         science=135+30

       =165 minutes             =165 minutes

So, after three days Thurber will have studied the same total amount of time for both math and science and the time is 165 minutes for both.

In this exercise we have to use interpretation skills to calculate the total time that studied the two subjects:  

\(165 \ both \ subjects\)

Today,  he studies 15 minutes math and 75 minutes science and from now on, 50 minutes math and 30 minutes science. So if he studies for 1 day total time for math and  science will be:

2nd day:  

3rd day:  

So, after three days Thurber will have studied the same total amount of time for both math and science and the time is 165 minutes for both.

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Answer:

3/4

Step-by-step explanation:

Parallel lines have same slopes.

The method that determines the volume of the prism is simply multiply the area of the base by the height, and the result is 12.5 cm³. (option-a)

To determine the volume of the prism shown in the diagram, we need to multiply the area of the base by the height.

The base of the prism is a rectangle with dimensions 5 cm by 2 cm. Therefore, the area of the base is:

A = length x width = 5 cm x 2 cm = 10 cm²

The height of the prism is 2-¹ cm, which is equivalent to 5/4 cm.

Therefore, the volume of the prism is:

V = A x h = 10 cm² x 5/4 cm = 12.5 cm³

The expressions involving unit cubes and one-quarter cubes are not relevant to this problem and do not provide a method for finding the volume of the prism.

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