For the function f(x) = x + 7, construct and simplify the difference quotient


f(x+h)-f(x) Over h
H

The Linear inequality holds true for 21 ≥ x;

What is Linear Inequality?

The mathematical expression with unequal sides is known as inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to a symbol (), less than or equal to a symbol (), or not equal to a symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics. The symbols "" and ">" signify tight inequalities, while "" and "" signify slack inequalities.

In the given question, the given inequality given is:

-3(2x-11) ≥ 8x-9;

Solving the Inequality:

⇒-6x + 33 ≥ 8x - 9;

⇒33 + 9 ≥ 8x - 6x;

⇒ 42 ≥ 2x;

⇒ 21 ≥ x;

Hence,

The Linear inequality holds true for 21 ≥ x;

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The equation for the nth term of the arithmetic sequences are:

a_n = -11 + 4n and a_n = -10 + 2n where n is an positive integer.

What is the arithmetic sequence?

A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms.

The formula of nth term of an arithmetic sequence is a_n = a + (n-1) d

The arithmetic sequence is -7, -3, 1, ....

The first term is a = -7.

The common difference is d = (-3)-(-7) = 1 - (-3) = 4.

The nth term of an arithmetic sequence is

a_n = -7 + (n-1) 4

a_n = -7 + 4n -4

a_n = -11 + 4n

The arithmetic sequence is -8, -6, -4, ....

The first term is a = -8.

The common difference is d = (-6)-(-8) = -4 - (-6) = 2.

The nth term of an arithmetic sequence is

a_n = -8 + (n-1) 2

a_n = -8 + 2n - 2

a_n = -10 + 2n

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256 805 - 136.667 ≈ 256 668.333

The difference is approximately 256 668.333

The length of side CA is right triangle ABC, 8.86 centimeters

In this question, we have been given triangle ABC has a right angle at C.

This means, AB is the hypotenuse of right triangle ABC.

measure of angle A = 41 degrees

and the length of side BC = 7.7 centimeters

We need to find length of CA

Consider sine of angle A.

sin(A) = opposite side/hypotenuse

sin(41°) = BC/AB

0.6561 = 7.7 / AB

AB = 7.7/0.6561

AB = 11.74

Applying Pythagoras theorem,

AB² = BC² + AC²

11.74² = 7.7² + AC²

AC² = 11.74² - 7.7²

AC = √(78.53)

AC = 8.86 centimeters

Therefore, the length of side CA is right triangle ABC, 8.86 centimeters

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Answer:

Red paint  = 12.5 gallons

Blue paint = 7.5 gallons

Step-by-step explanation:

The given ratio of red paint to blue paint is:

Let x be the number of gallons of purple paint.

Therefore, the expression for each color of paint needed per x gallons of purple paint is:

[tex]\implies \textsf{Red\;paint $=\dfrac{5}{8}x$}[/tex]

[tex]\implies \textsf{Blue\;paint $=\dfrac{3}{8}x$}[/tex]

To calculate the number of gallons of red and blue paint needed to make 20 gallons of purple paint, substitute x = 20 into the found expressions:

[tex]\implies \textsf{Red\;paint $=\dfrac{5}{8} \times 20=\dfrac{100}{8}=12.5$}[/tex]

[tex]\implies \textsf{Blue\;paint $=\dfrac{3}{8}\times 20=\dfrac{60}{8}=7.5$}[/tex]

Therefore, the number of gallons of paint that should be used are:

Answer:

[tex] \huge{ \bold{ \orange{ - \frac{4}{3} }}}[/tex]

Step-by-step explanation:

The slope of a line passing through two points can be found by using the formula

[tex]m = \frac{y2 - y1}{x2 - x1} \\ [/tex]

where

(x1, y1) and (x2, y2) are the points

From the question

The points are (4, 8) and (7, 4)

We have

[tex]m = \frac{4 - 8}{7 - 4} = - \frac{4}{3} \\ [/tex]

We have the final answer as

[tex] \bold{ - \frac{4}{3} }[/tex]

Hope this helps you

Answer:

Median: 5.5

Mean: 5.1

The y-intercept is y = 3, and this is the initial height of the ball, and the maximum height is y = 19

The y-intercept is what we get when we evaluate in x = 0, then:

y = -0.25*x² + 4x + 3

replacing x by zero we get:

y = -0.25*0² + 4*0 + 3 = 3

The y-intercept is y = 3.

The maximum height is at the vertex, we know this because the leading coefficient is negative, which means that the parabola opens down.

The vertex is at:

x = -4/(2*-0.25) = 8

Evaluating there:

y = -0.25*8² + 4*8 + 3 = 19

that is the maximum height.

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The gradient will only be equal to 3 if the value of d is 7.

If we have two points (a, b) and (c, d), the gradient of the segment with these endpoints is:

G = (d - b)/(c - a)

Here the endpoints are (5, 9) and (d, 15), and the gradient is 3, so we can write the equation:

3 = (15 - 9)/(d - 5)

3*(d - 5) = 6

3d - 15 = 6

3d = 15 + 6 = 21

d = 21/3

d = 7

The value of d is 7.

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The estimated sum of the given numbers using the range method is 20.1.

We are given three numbers. The numbers are 8.94, 2.16, and 9.02. All the given numbers are decimal numbers. We need to estimate the sum of all the numbers. The approximate value of each number is calculated below.

8.94 ≈ 8.9

2.16 ≈ 2.2

9.02 ≈ 9.0

Let the estimated sum of the given number be represented by the variable "E".

E = 8.9 + 2.2 + 9.0

E = 20.1

The actual sum of the given numbers is given below.

A = 8.94 + 2.16 + 9.02

A = 20.12

We can see that the estimated sum is very accurate as compared to the actual sum.

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1. The unpaid balance after 12 months of paying $546.61 for borrowing $81,000 for 27 years at 6.8% is $79,915.29.

2. During this period, the interest she paid was $5,474.61.

The total payment made, including interest and principal, for 12 months is the product of the monthly payments and 12 months.

From the amortization schedule from an online finance calculator at month 12, we can deduce that the loan balance is $79,915.29.

When this balance is subtracted from the loan, the difference is the principal repayment so far.

N (# of periods) = 324 months (27 years x 12)

I/Y (Interest per year) = 6.8%

PV (Present Value) = $81,000

PMT (Periodic Payment) = $-546.61

Results:

Sum of all periodic payments = $-6,559.32 ($546.61 x 12)

Total Interest for six months = $5,474.61

1 $81,000.00 $-546.61 $459.00 $-80,912.39

2 $80,912.39 $-546.61 $458.50 $-80,824.28

3 $80,824.28 $-546.61 $458.00 $-80,735.68

4 $80,735.68 $-546.61 $457.50 $-80,646.57

5 $80,646.57 $-546.61 $457.00 $-80,556.96

6 $80,556.96 $-546.61 $456.49 $-80,466.84

7 $80,466.84 $-546.61 $455.98 $-80,376.21

8 $80,376.21 $-546.61 $455.47 $-80,285.06

9 $80,285.06 $-546.61 $454.95 $-80,193.40

10 $80,193.40 $-546.61 $454.43 $-80,101.22

11 $80,101.22 $-546.61 $453.91 $-80,008.52

12 $80,008.52 $-546.61 $453.38 $-79,915.29

Total payment at $546.61 x 12 months = $6,559.32

Principal repayment for 12 months = $1,084.71 ($81,000 - $79,915.29)

Interest paid for 12 months = $5,474.61 ($6,559.32 - $1,084.71)

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Answer:  Tommys dispacement 17 miles

Step-by-step explanation:

pyhagorean theorem

he went 15 up (leg 1)

and then right 8 (leg 2)

and Tommy's displacement is the hypotenuse

15^2+8^2=c^2

c^2 = 289

c = 17

If  each week it grow by 4% more than it did the previous week by  it grow in 9 week is  17.67cm.

Now let find the growth in 9 week

Growth in 9 week = 1.67cm × [( 1+ 0.04)^9 -1] ÷ [(1+0.04)-1]

Growth in 9 week = 1.67cm × [( 1.04)^9 -1] ÷ (1.04)-1]

Growth in 9 week = 1.67cm ×  [( 1.4233 -1) ÷ 0.04

Growth in 9 week = 1.67cm ×  [0.4233 ÷  0.04

Growth in 9 week = 1.67cm × 10.5825

Growth in 9 week = 17.67cm

Therefore 17.67cm is the 9 week growth.

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Answer:

Step-by-step explanation:

Answer: 500 + 30 + 1 + 0.2 + 0.04 + 0.006

The sides and angles of the right triangle are as follows:

A right tangle triangle is a triangle that has on e of its angles as 90 degrees. The sides of a right triangle can be named based on the position of the angles.

The sides includes opposite side, adjacent side and hypotenuse side. The longest side of a right angle triangle is the hypotenuse side.

The sides of the right angle triangle can be found using trigonometric ratios as follows:

sin 85 = opposite / hypotenuse

sin 85 = a / 8

a = 8 sin 85

a = 7.96955758473

a = 8.0

cos 85 = adjacent / hypotenuse

cos 85 = b / 8

b = 8 cos 85

b = 0.69724594198

b = 0.7 units

Angle B = 180 - 90 - 85 = 5 degrees.

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Answer:

x < - 4 or x > 4

Step-by-step explanation:

given an inequality of the type| x | > a , then the solution is in the form

x < - a or x > a

thus

- 2x < - 8

divide both sides by - 2, reversing the symbol as a result of dividing by a negative quantity.

x > 4

OR

- 2x > 8

divide both sides by - 2, reversing the symbol

x < - 4

solution is x < - 4 or x > 4

Answer:

The answer can be expressed in two types of forms.

INEQUALITY FORM:  x < -4  or  x > 4

INTERVAL NOTATION:  ( –∞, –4) (4, ∞ )

Step-by-step explanation:

1. Isolate the variable "x" by dividing each side by factors that do not contain the variable "x."

2. Write |-2x|>8 as a piece:

TOP: {-2x > 8    x ≤ 0  / BOTTOM: {2x > 8   x > 0}

3. Divide each term by -2, then simplify.

x < -4

4. Divide each term by 2, then simplify.

x > 4

5. Find the union of the solutions.

Answer: x>-1

Step-by-step explanation:i just did that question

Answer:

Step-by-step explanation:

add 4 to -15 then divide that  by 11x the answer should be x=-1.

If one card is drawn randomly from a deck, then the probability that it is not a face card is 76.9%

Probability

Probability refers the possible way of getting the required event.

Given,

A standard deck of cards has 52 cards of four different suits (diamonds, spades, hearts, clubs). Each suit consists of numbered cards 1 (Ace) to 10, followed by Jack, Queen and King (face cards).

Here we need to find the probability of getting not a face card and we have to round off the resulting value to the tenth percent.

We know that,

Total number of cards = 52

Number of suits = 4

Number of cards in each suit = 13

Number of face cards in each suit = 3

Therefore, the total number of face cards in the deck is calculated s,

=> 3 x 4

=> 12

Therefore, the probability of getting not a face card is

=> (52 - 12)/52

=> 40/52

When we simplify this one then we get,

=> 0.7692

When we convert this into percent and round of to the nearest tenth then we get the probability of getting not a face card is

=> 76.9%.

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The value of the angles that are intersected by BC are m/ABC is 35° and m/DBC is 43°

In the given figure the angle ∠ABD is intersected by the straight line BC such that two new angles are formed ,∠ABC and ∠ADC  .

Now from the properties of angles on a 2-dimensional plane we can see that :

m ∠ABC + m ∠ADC  = m ∠ABD

The values of the angles given are:

m ∠ABC = 5x - 5

m ∠ADC = 5x + 3

m ∠ABD = 78°

now we put these above values in the equation:

(5x - 5) + (5x + 3) = 78

or, 10 x - 2 = 78

or, 10 x = 80

or , x = 8

m ∠ABC = 5×8 - 5 = 35°

m ∠ADC = 5×8 + 3 = 43°

The value of the angles that are intersected by BC are m/ABC is 35° and m/DBC is 43° .

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The additional number of days that is required to complete the rest of the work in mixed fraction is equal to 4 4/11 days.

First of all, we would determine the number of work left for Ann after two (2) working days:

In one (1) day, the amount of work that would be done by Ann alone is given by 1/10 days. Therefore, the amount of work that would be done by Ann alone in two (2) days is given by 2/10 or 1/5 days.

For the number of work left, we have:

Work left = 1 - 1/5

Work left = 4/5 days.

Similarly, the amount of work that would be done by Ben alone in one (1) day is given by 1/12 days.

Therefore, the combined work rate of both Ann and Ben is given by:

Combined work rate = 4/5 + 1/12

Combined work rate = 11/60

For the additional number of days required to complete the rest of the work, we have:

Additional days = 4/5 ÷ 11/60

Additional days = 4/5 × 60/11

Additional days = 4 × 12/11

Additional days = 48/11

Additional days = 4 4/11 days.

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Between the previous balance method and the daily balance method, the method of calculating Yvonne's June finance charge that will result in a greater finance charge is:

Using the previous balance method to compute the finance charge, the beginning balance is added to purchases minus payments.  Then the APR is applied to the sum.

The daily balance method ensures that an average daily balance is computed for the billing cycle and then the APR is applied to the average to compute the finance charge.

Date   Transaction             Amount ($)   Balance     Daily Balance

6/1      Beginning balance    925.43      $925.43  $5,552.58 ($925.43 x 6)

6/7     Payment                       62.74      $862.69     3,450.76 ($862.69 x 4)

6/11    Purchase                      28.27      $890.96     8,909.60 ($890.96 x 10)

6/21   Purchase                      50.00      $940.96    9,409.60 ($940.96 x 10)

Total                                                        $27,322.54

Average daily balance = $910.75 ($27,322.54)

APR = 17.79%

MPR = 1.4825% (17.79%/12)

Previous balance method = $13.95 ($940.96 x 1.4825%)

Average daily balance = $13.50 ($910.75 x 1.4825%)

Difference = $0.45 ($13.95 - $13.50)

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The following table details her credit card transactions in the month of June.

Date   Transaction             Amount ($)

6/1      Beginning balance    925.43

6/7     Payment                       62.74

6/11    Purchase                      28.27

6/21   Purchase                      50.00

Between the previous balance method and the daily balance method, which method of calculating Yvonne's June finance charge will result in a greater finance charge, and how much greater will it be?

a. The daily balance method will have a finance charge $0.21 greater than the previous balance method.

b. The daily balance method will have a finance charge $0.53 greater than the previous balance method.

c. The previous balance method will have a finance charge $0.45 greater than the daily balance method.

d. The previous balance method will have a finance charge $0.40 greater than the daily balance method.

The equation of the line passing through y = 3x-1 and (3,2) is y = 3x-7.

According to the question,

We have the following information:

y = 3x-1 and the point through which line is passing is (3,2)

We know that the slope of the given line (denoted by m) is 3.

Now, the following formula is used to find the equation of the line passing through a point:

y-y' = m(x-x')

In this case, we have x' = 3 and y' = 2.

y-2 = 3(x-3)

y-2 = 3x-9

Moving 2 from the left hand side to the right hand side will result in the change of the sign from minus to plus:

y = 3x-9+2

y = 3x-7

Hence, the equation of the line passing through y = 3x-1 and (3,2) is y = 3x-7.

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The pressure at an altitude of 5000 m if The atmospheric pressure at sea level is about 101 kilopascals. For every 1000-m increase in altitude, the pressure decreases by about 11.5% is  58.08 kPa.

A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.

Given:

The atmospheric pressure, P = 101 kPa,

For every 1000 meters, the pressure decreases by 11.5%,

So at the height of 5000 meter, the % decrease will be 5 × 11.5 = 57.5%,

Now let the 57.5% of 101 kPa be x then,

x = 57.5/100 × 101  kPa,

x = 58.08 kPa,

Therefore, the pressure at an altitude of 5000 m if The atmospheric pressure at sea level is about 101 kilopascals. For every 1000-m increase in altitude, the pressure decreases by about 11.5% is  58.08 kPa.

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When the radius is 9cm, it increases at a rate of 0.06 cm per second.

We assume the ballon is a perfect sphere. Remember that the volume of a sphere as a function of the radius is given by:

V = (4/3)*3.14*(R)³

When the radius is R = 9cm, the volume is:

V =  (4/3)*3.14*(9cm)³ = 3,052.08 cm³

Isolating the radius as a function of the volume, we get:

R = ∛((3/4*3.14)*V)

And we know that the volume increases at a constant rate of 6cm³/s, if we assume that the initial volume is 3,052.08 cm³ then we can write the radius as a function of time as:

R(t) = ∛((3/4*3.14)*(3,052.08 cm³ + 6cm³/s*t))

Where t is the time in seconds.

Now we need to differentiate this and evaluate in t = 0.

R'(t) = (1/3)*(3/4*3.14)*(3,052.08 cm³ + 6cm³/s*t)^(-2/3)* (6cm³/s*3/4*3.14)

Evaluating in t = 0 we get:

R'(0) = (1/3)*(3/4*3.14)*(3,052.08 cm³ + 6cm³/s*0)^(-2/3)* (6cm³/s*3/4*3.14)

       =  (1/3)*(3/4*3.14)*(3,052.08 cm³)^(-2/3)* (6cm³/s*3/4*3.14) = 0.06 cm/s

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The z-score for this amount of advertising time is z = -4.17 so option B is correct.

Given:

Average = 13 minutes

Standard deviation = 1.2 minutes.

Advertising time x = 8 minutes.

z = x - mean / standard deviation.

= 8 - 13/1.2

= -5/1.2

= -5/12/10

= -50/12

= -4.17.

Therefore the z-score for this amount of advertising time is z = -4.17 so option B is correct.

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The time period of the given waveform is 2 units time

From the waveform,

Each units represent one units

The time period is the time taken for waveform to complete one cycle.

Here we have to find the time taken for the given wave to complete one cycle.

Here at t = 0 the wave reaches its positive peak point

At t = 1, the wave reaches its negative peak point

At t = 2, the wave reaches its positive peak point again

Therefore, in this waveform, the wave took 2 units time to complete one cycle

The time period = 2 units time

Hence, the time period of the given waveform is 2 units time

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Answer:

350 in. squared

Step-by-step explanation: