Enter an inequality that represents the description, and then solve.
Nine more than seven times a number (x) is at least thirty.
Inequality:
The solution to the inequality is

Answer:

[tex]\large\boxed{\dfrac{f(x+h)-f(x)}{h}=4x+2h}[/tex]

Step-by-step explanation:

[tex]f(x)=2x^2+4\\\\f(x+h)=2(x+h)^2+4\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\f(x+h)=2(x^2+2xh+h^2)+4\qquad\text{use the distributive property}\\\\f(x+h)=2x^2+4xh+2h^2+4\\\\\text{Substitute to}\ \dfrac{f(x+h)-f(x)}{h}\\\\\dfrac{f(x+h)-f(x)}{h}=\dfrac{2x^2+4xh+2h^2+4-(2x^2+4)}{h}\\\\\dfrac{f(x+h)-f(x)}{h}=\dfrac{2x^2+4xh+2h^2+4-2x^2-4}{h}\\\\\text{combine like terms}\\\\\dfrac{f(x+h)-f(x)}{h}=\dfrac{4xh+2h^2}{h}\qquad\text{distribute}\\\\\dfrac{f(x+h)-f(x)}{h}=\dfrac{h(4x+2h)}{h}\qquad\text{cancel}\ h[/tex]

[tex]\dfrac{f(x+h)-f(x)}{h}=4x+2h[/tex]

Final answer:

After arranging the data for each company and calculating the first and third quartiles, we found that the interquartile range for Company A's students (IQR = 2) is 1 more than the interquartile range for Company B's students (IQR = 1).

Explanation:

The interquartile range (IQR) is a measure of the middle spread of a data set, calculated as the difference between the third quartile (Q3) and the first quartile (Q1). To find the interquartile range for each group of students, we will first need to arrange each company's data in ascending order and then find the values of Q1 and Q3 for each group.

For Company A, the data in ascending order is: 1, 1, 1, 2, 2, 3, 3, 4, 5. Q1 is the median of the first half (1), and Q3 is the median of the second half (3). Thus, IQR is 3 - 1 = 2.

For Company B, the data in ascending order is: 1, 1, 2, 2, 2, 2, 2, 3, 3. Q1 is the median of the first half (1.5), and Q3 is the median of the second half (2.5). So, IQR is 2.5 - 1.5 = 1.

Comparing the IQRs, we find that the interquartile range for Company A's students is 1 more than the interquartile range for Company B's students.

Answer:

The answer to your question is letter A.

Step-by-step explanation:

A. This graph shows that is the sine graph, but it was moved to units up.

B. This is not the equation of the graph because the sine is negative then the graph should be inverted.

C. This is not the equation of the graph because the cosine graph starts in 1.

D. This is not the equation of the graph because it is cosine negative and the graph is different.

Answer:

[tex]y=sinx +2[/tex]

Step-by-step explanation:

We have to choose the function whose graph is given.

A.[tex]y=sinx+2[/tex]

Substitute x=0 then

[tex]y=0+2=2[/tex]

Therefore, y- intercept is at y=2.

Substitute [tex]x=\frac{\pi}{2}[/tex]

[tex]y=sin\frac{\pi}{2}+2=1+2=3[/tex] because ([tex]\sin\frac{\pi}{2}=1[/tex])

Substitute  [tex]x=-\frac{\pi}{2}[/tex]

Then we get

[tex]y=sin(-\frac{\pi}{2})+2=-sin\frac{\pi}{2}+2=-1+2=1[/tex]

[tex] sin (-x)=-sinx[/tex]

Therefore, given graph is [tex]y=sinx +2[/tex]

B.[tex]y=-sinx+2[/tex]

When Substitute  [tex]x=-\frac{pi}{2}[/tex]

Then, [tex]y=-sin(-\frac{\pi}{2})+2=sin\frac{pi}{2}+2=1+2=3[/tex]

But  in graph at [tex]x=-\frac{pi}{2}[/tex] , y=-1

So,It is not true.

C.[tex]y=cosx+2[/tex]

When x=0

then we get [tex]y=cos0+2=1+2=3[/tex] (cos 0=1)

But in graph  y - intercept at y=2

So, it is false.

D.[tex]y=-cosx+2[/tex]

Substitute x=0

Then, we get

[tex]y=-cos 0+2=-1+2=1[/tex]

So, it is false.

Answer: [tex]y=sinx +2[/tex]

Answer: 4 is 12.5% of 32

Step-by-step explanation:

12.5/100 = 0.125

4/0.125 = 32

Unknown number in the question is [tex]32.[/tex]

Let the unknown number is [tex]n[/tex].

It has been given in the question that 4 is 12.5% of the unknown number,

Therefore, expression for the statement will be,

12.5% of [tex]n[/tex] = 4

[tex]\frac{12.5}{100}\times n=4[/tex]

[tex]\frac{1}{8}\times n=4[/tex]

[tex]n=8\times 4[/tex]

[tex]n=32[/tex]

       Hence, unknown number is [tex]32[/tex].

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To show your work for the subtraction [tex]\(50.04 - 1.103\)[/tex], follow these steps:

1. Line up the Decimals:

  Align the decimal points of both numbers, ensuring they are in the same vertical position.

[tex]\[ &50.040 \\ - &1.103 \end{align*} \][/tex]

2. Subtraction:

  Begin subtracting from the rightmost column. Subtract 3 from 0, borrow 1 from 4, subtract 0 from 10, subtract 1 from 4, and subtract 1 from 5.

[tex]\[50.040 \\ - &1.103 \\ \underline{-} \end{align*} \][/tex]

[tex]\[ 48.937 \][/tex]

3. **Final Result:**

  The result of [tex]\(50.04 - 1.103\)[/tex] is [tex]\(48.937\).[/tex]

By displaying each step of the subtraction process, you provide a clear and organized representation of your work.

Answer:

80 + 18i

Step-by-step explanation:

i² = -1

x = i + 9

x² = (i + 9)²

Applying; (a + b)² = a² + 2ab + b² concept,

x² = i² + 18i + 81

We know that i² = -1

So x² = -1 + 18i + 81

x² = 81 - 1 + 18i = 80 + 18i

The square of the complex number x = i + 9 is computed by squaring each term and combining the results, giving us 80 + 18i as the final squared value.

To square the complex number x = i + 9, we use the formula for squaring a binomial:

Square the first term: i² = -1.

Square the second term: 9² = 81.

Multiply the first term by the second term and by 2 for the middle term: 2 times i times 9 = 18i.

Sum all the terms together -1 + 81 + 18i = 80 + 18i.

So, the result of squaring x is 80 + 18i.

Answer:

D. x² + y² = 4²

Step-by-step explanation:

The general equation of a circle is given in the attached  graphic.

In this case, we can see that the center of the circle is at the origin i.e (0,0) and that the radius is 4 units.

the values for h, k and r in the general equation are as follows:

h = 0, k=0, r = 4

putting this into the general equation:

(x-h)² + (y-k)² = r²

(x-0)² + (y-0)² = 4²

x² + y² = 4²

The equation of the circle centered at the origin with a radius of 4 is:

x² + y² = 4².

Option D is the correct answer.

We have,

The equation of a circle centered at the origin (0, 0) with a radius of 4 can be written in the form:

[tex]x^2 + y^2 = r^2[/tex]

where (x, y) represents any point on the circle and r is the radius.

Substituting the given radius of 4 into the equation, we have:

x² + y² = 4²

x² + y² = 16

Therefore,

The equation of the circle centered at the origin with a radius of 4 is:

x² + y² = 4².

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The total cost f(x), in dollars, for renting a car for a day and driving it x miles is shown:

f(x) = 90 + 0.11x

What does f(30) represent?

Answer:

The number of dollars it costs to drive the car 30 miles

option C. The number of dollars it costs to drive the car is 30 miles.

The total cost f(x), in dollars, for renting a car for a day and driving it x miles is shown:

f(x) = 90 + 0.11x.

What does f(30) represent?

It represents the number of dollars it costs to drive the car 30 miles.

1.5 gallons

Good luck on your trip. We hope that our "How much gas to drive 30 miles?" page made the trip planning a little easier for you.

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Answer:

k=12

Step-by-step explanation:

60÷5=12

5+5+5+5+5+5+5+5+5+5+5+5=60

↑=12 5's

Hope this helps!!!

Brady

Answer:

It's 12

Step-by-step explanation:

60 = 5k

or, 60/5 =k

or, k=12

Hence, 60 is 5 times great as 12

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the smaller and the larger number are

17 and 22 respectively

Step-by-step explanation:

let the numbers be x and y

from the expression; The sum of two numbers is 39 means that

x + y=39

let y be the smaller number and x be larger number.

but from the expression

The larger number is 5 more than the smaller is written as

x=5+y

put it in the first equation to get

5+y+y=39

5+2y=39

2y=39-5

2y=34

y=34/2

y=17

put the y value in the equation to get the x value

thus

x=5+y

x=5+17

x=22

assuming that the bases are placed correctly, the bases connected draw a square, each side being 90 ft long. We multiply 90 by the amount of sides(4) to find the total distance/perimeter = 360.

The distance around the bases in meters will be 27.432 meters.

In one feet there are 0.3048 meters.

Given is a baseball field measures 90 feet between each base.

Distance between each base in feet = [d] = 90 feet

The distance between each base in meters will be -

D [meters] = 90 x 1 ft

D [meters] = 90 x 0.3048 meters

D [meters] = 27.432 meters

Therefore, the distance around the bases in meters will be 27.432 meters.

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Answer:

24 months or 2 years

Step-by-step explanation:

For every 6 months it costs $500 then 1 year would be $1000 because there are 12 months in a year. Then just multiply that times 2 because they have $2000 then you would get 24 :)

Answer:

Yes.

Step-by-step explanation:

You can divide both the numerator (18) and the denominator (10) by 2 (also called simplifying) in order to get 9/5.

Answer:

The slope of the line is ⅓.

The y-intercept is at (0,3).

The linear equation for the line is:

y=⅓x+3

The linear function represented by the graph has a slope of 3 and a y-intercept of 9. The equation of the linear function is y = 3x + 9.

The linear function represented by the graph has a slope of 3 and a y-intercept of 9. The slope of a line represents the rate of change of the y-values with respect to the x-values, while the y-intercept is the value of y when x=0. In this case, for every increase of 1 on the horizontal axis, the vertical axis increases by 3 units. The equation of the linear function is y = 3x + 9.

Answer: 32÷4+3=11

Step-by-step explanation:

24÷3=8

Answer:

4 + 5x = x - 2

Answer:

4 + 5x = x - 2

x=-1.5

Step-by-step explanation:

4 + 5x = x - 2

subtract 4 from both sides (or add negative whichever you prefer)

5x=x-6

now subtract x from both sides

4x=-6

now divide by 4

x=-1.5

Answer: Hello there!

we know that on Tuesday, Jennie finished her sprint 0.305 seconds faster than on Monday, and we want to model this with math.

If we define x as the time in which she finished ger sprint on Monday, we can write the time for Tuesday as x - 0.305s

this is because she finished her sprint 0.305 seconds "faster", this means that she finished it in less time, so you need to subtract this number to the previous time.

Then the meaning of 0.305 is the amount of time that you need to subtract from the previous time, in order to get the actual time that she needs to finish the sprint.

12 inches= 1 foot

We have 4 feet

12*4=48

Therefore 48 cubic inches is the answer

Hope this helps!!!

A hot tub pump that circulates 4 cubic feet of water per minute circulates 6912 cubic inches of water per minute, as 1 cubic foot equals 1728 cubic inches.

This question involves a conversion from cubic feet to cubic inches. 1 cubic foot is equivalent to 1728 cubic inches. Therefore, if the hot tub pump circulates 4 cubic feet of water per minute, we need to multiply 4 by 1728 to find out how many cubic inches that would be.

Using the multiplication rule for units, we get:

4 cubic feet x 1728 cubic inches/cubic foot = 6912 cubic inches

Therefore, the hot tub pump circulates 6912 cubic inches of water per minute>.

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Answer:

39. 29

36. 50

33. 7

30. 33

Step-by-step explanation:

39. According to the Order of Operations, in this case, Subtraction & Addition are evaluated after Division & Multiplication:

[tex]6 \times 4 + 5 = 24 + 5 = 29[/tex]

36. Evaluate everything since everything is wrapped in parentheses:

[tex](3 + 2) \times (4 + 6) = 5 \times 10 = 50[/tex]

33. Evaluate everything inside of parentheses FIRST:

[tex]14 - (8 - 2) - 1 = 14 - 6 - 1 = 7[/tex]

I am joyous to assist you anytime.

Answer:

The answer is -7

Step-by-step explanation:

-5 - 3 = -8

-8 + 1 = -7

Hope I helped :)

Answer:

-7

Step-by-step explanation:

The rule for subtraction, in this case it is -5-3, you change the subtraction sign to addition and use the opposite of the second number, making it -5+(-3) which is -8. Then, you add 1 to -8, and the rule for this specific expression is to take the absolute value of both -8 and 1, then subtract the two, making the expression as of now 8-1. Subtract them, and get 7, but you take the sign of whichever number had the greatest absolute value, which was -8, so now the answer is -7. That's how you get your answer

-5-3+1= -5+(-3)+1

-8+1= |-8|-|1|

8-1= -7 (because you take the sign with the greatest absolute value, which is -8.)

Answer:

Carmen would have to sell 8 cars in a month to get the same pay from either dealership.

Step-by-step explanation:

Let c = cars sold

Dealership #1 = 2500 + 125c

Dealership #2 = 2700 + 100c

2500 + 125c = 2700 + 100c

125c - 100c = 2700 - 2500

25c = 200

c = 8

Answer:

16

Step-by-step explanation:

7/16 = 7/16

1/4 = 4/16

The cost of each bottle of mineral water is $0.87.

To find the cost of each bottle of mineral water, we need to divide the total cost of the case by the number of bottles in the case. A case contains 2 boxes and each box contains 4 bottles, so there are 2 x 4 = 8 bottles in a case. The cost of a case is $6.96, so the cost of each bottle is $6.96 divided by 8, which equals $0.87.

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The cost of each bottle of mineral water is $0.87.

To find the cost of each bottle of mineral water, we need to divide the total cost of the case by the number of bottles.

The case of mineral water contains 2 boxes, and each box contains 4 bottles.

So, the total number of bottles in the case is 2 x 4 = 8.

Since the cost of the case is $6.96,

we can divide it by the number of bottles to find the cost of each bottle: $6.96 / 8 = $0.87.

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Answer:

No

Step-by-step explanation:

The reflection (R) around the line y = 1 is not the point illustrated.

Notice that the original point M (5,-2) is THREE (3) units below the line y=1, therefore when doing the reflection, it should end up THREE units above the y=1 line.

That is, it should end up at the point (5,4 ) and not at (5,3) as is shown in the picture.

Answer:

[tex]17x = y[/tex]

Step-by-step explanation:

Since we know that you write 17 text messages a week. 17 will be our constant number, now then after you said for x weeks.

Meaning that x would be our variable cause we can put an input of any number, then put it next to 17 because that is how many times you text a week.

17x = y

17 (how many times you text per week) x (how many weeks) = y (texts in total)

Answer: x = z/(m-1).

Step-by-step explanation: xm - x = z

x (m - 1) = z ; x = z/(m-1).

Answer:C

Step-by-step explanation: The probability of choosing a girl is the number of girls over the total number of students. Since there are 16 girls and 16+18 students, 16/34=8/17. Hope this helps! (Could I please have brainliest?)

The probability of the teacher choosing a girl to answer the question is 8/17. The correct option is C.

To calculate the probability of the teacher choosing a girl to answer the question, we need to determine the ratio of the number of girls to the total number of students.

In the given class, there are 16 girls and 18 boys, making a total of 16 + 18 = 34 students.

The probability of selecting a girl is the number of favourable outcomes (girls) divided by the total number of possible outcomes (students).

Therefore, the probability is 16 (number of girls) / 34 (total number of students).

Simplifying this fraction, we have 8/17.

Hence, the correct option is C. 8/17, which represents the probability of the teacher choosing a girl to answer the question.

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Answer:

14+12=26

Step-by-step explanation:

i worked it pls give brainliest

Answer:

jacob is 12 and his sister is 14. this is the correct answer.

Step-by-step explanation:

hope this helps.