Mathematics College

Which graph represents the solution to the inequality 2(b + 2) < 24?

number line with open point at 10 with arrow pointing left
number line with closed point at 10 with arrow pointing left
number line with closed point at 10 with arrow pointing right
number line with open point at 10 with arrow pointing right

Answers

Answer 1

The solution to the inequality shows that the circle will be on 10 and pointing to the left.

Solving inequality

Inequality are expressions not separates by an equal sign.

Given the inequality expression below:

2(b + 2) < 24

Expand

2b + 4 < 24

2b < 24 - 4

2b < 20

Divide both sides by 2

2b/2 < 20/2

b < 10

Hence the number line with open point at 10 with arrow pointing left.

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Related Questions

find all real and complex zeros for f(x)=x^3-x^2+3x-3

Answers

The real and complex zeros for the function given as .f(x) = x³ - x² + 3x - 3 are x = 1 and x = ±i√3, respectively

How to determine the zeros of the function?

The equation of the function is given as

f(x) = x³ - x² + 3x - 3

Group the terms of the function in two's

So, we have the equation

f(x) = (x³ - x²) + (3x - 3)

Factor each group in the function

f(x) = x²(x - 1) + 3(x - 1)

Factor out x - 1

f(x) = (x² + 3)(x - 1)

Set to 0

(x² + 3)(x - 1) = 0

This gives

x² = - 3 and x = 1

Evaluate the roots

x = ±i√3 and x = 1

Hence, the zeros of the equation are x = ±i√3 and x = 1

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find the answer to this problem (15/16) - ( -3/16)

A. 3/4
B. -3/4
C. -1 1/8
D. 1 1/8

Answers

Answer;D.
First you would do change change and it would be (15/16)+3/16,then do 15+3=18,then put it over 16,18/16,then you simplify and it would be 9/8,but you can’t have a bigger numerator over a denominator,so you would divide 9/8 and it would be 1 1/8.

How many months does it take $428 to double at a simple interest rate of 12%

Answers

When $428 doubles, it means that the

Through how many radians does the minute hand of a clock rotate from12:40 PM to 1:10 PM?o10- 10The minute hand rotates through radians.(Simplify your answer. Type an exact answer in terms of Use integers orfractions for any numbers in the expression)-10

Answers

As you can see in the given figure the minute hand of a clock rotate from 12:40 to 1:10 formig a straigth angle.

A straight angle in radians is π radians.

Then, the minute hand rotates π radians

Rewrite the equation in Ax+By=C form. Use integers for A, B, and C. y=-1/6x+3

Answers

The equation y = - 1 / 6 x + 3 in standard form is x + 6y = 18.

How to rewrite equation in standard form?

The standard form for linear equations in two variables is Ax + By = C.

where

A , B and C are constantx and y are the independent and dependent variables respectively

Therefore, let's represent the equation y = - 1 / 6 x + 3 in standard form .

y = - 1 / 6 x + 3

multiply the equation by 6 to eliminate the fraction

6y = 6(- 1 / 6 x) + 6(3)

Therefore,

6y = - x + 18

x + 6y = 18

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Find the equation for the circle with a diameter whose endpoints are (5,5) and (3,−5).

Answers

The equation of the circle in standard form whose center is at (h, k) = (4, 0) is (x - 4)² + y² = 26.

How to derive the standard equation of the circle based on the coordinates of diameter endpoints

In this question we find the coordinates of the endpoints of the diameter of the circle, then, the center of the circle is the midpoint of the line segment. The center of the circle is found by midpoint formula:

(h, k) = 0.5 · (5, 5) + 0.5 · (3, - 5)

(h, k) = (4, 0)

And the radius of the circle is determined by Pythagorean theorem:

r = √[(4 - 5)² + (0 - 5)²]

r = √[(- 1)² + (- 5)²]

r = √26

Then, the equation of the circle in standard form is describe below:

(x - h)² + (y - k)² = r²

If we know that (h, k) = (4, 0) and r = √26, then the equation of the circle is:

(x - 4)² + y² = 26

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1. Write the regression2.r =3. what does the r mean?I predict there will be a [blank] relationship between [blank] and [blank] I think it’s because [blank] and I’m gonna send a photo about my graphing points

Answers

First of all, we have to find the mean of x values.

According to the given graph, the x values are: 0, 1, 2, 2, 3, 3, 4, 5, 6, 7.

So, the mean is

[tex]\bar{x}=\frac{0+1+2+2+3+3+4+5+6+7}{10}=\frac{33}{10}=3.3[/tex]

The mean of x values is 3.3.

The y values are: 2, 2, 3, 4, 4, 4, 5, 6, 8, 9.

The mean would be

[tex]\bar{y}=\frac{2+2+3+4+4+4+5+6+8+9}{10}=\frac{44}{10}=4.4[/tex]

The mean of y values is 4.4.

Now, we find the standard deviation for x values and y values.

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Horatio left a campsite, hiking at a rate of 1 mile per hour. Ivan left 3 hours later, hiking at a rate of 2 miles per hour. How long will it take Ivan to catch up to Horatio?

Answers

Ivan will catch up to Horatio in 3 hours .

In the question ,

it is given that

speed of Horatio is 1 miles per hour

speed of Ivan is 2 miles per hour .

and Ivan leaves 3 hours late than Horatio .

Let "t" be the time ( in hours ) taken for Ivan to meet Horatio ,

So, the distance covered by Ivan will be 2*t .

Since Horatio left 3 hours before so the time taken for Horatio to meet Ivan is (t+3).

So, the distance covered by Horatio will be 1*(t+3) .

The distance covered for Horatio and Ivan will be equal ,

which means

2*t = 1*(t+3)

2t = t + 3

2t - t = 3

t = 3

Therefore , Ivan will catch up to Horatio in 3 hours .

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What is a different common Denominator you could use in problem 2

Answers

Answer:

what is the problem ???

Step-by-step explanation:

Well we need problem 2 to know the answer

7. On February 12th, a fire occurred at a local dry cleaning plant and the inpatient service days for the localhospital (120 beds) was reported to be 130. What is the bed occupancy rate for February 12th? Round toone decimal place.

Answers

We can use the following formula:

[tex]_{\text{ }}Bed_{\text{ }}occupancy_{\text{ }}rate=\frac{\#_{\text{ }}of_{\text{ }}inpatient_{\text{ }}days_{\text{ }}for_{\text{ }}a_{\text{ }}given_{\text{ }}period}{_{\text{ }}avalaible_{\text{ }}beds\times\#_{\text{ }}days_{\text{ }}in_{\text{ }}the_{\text{ }}period}_{}\times100[/tex]

So:

[tex]_{\text{ }}Bed_{\text{ }}occupancy_{\text{ }}rate=\frac{130}{120\cdot365}\times100[/tex]

Answer:

0.3%

A teacher is organizing binders for her students. She has 54 pieces of lined paper, 36 pieces of grid paper, and 72 dividers. What is the greatest number of identical binders that she can make? Please help!

Answers

Using the highest common factor, the greatest number of identical binders that the teacher can make is 18.

What is the highest common factor?

The highest common factor or multiple of the given numbers is the highest number that can divide them without a remainder.

We know that 2, 9, and 18 can divide 54, 36, and 72 without leaving a remainder.

We can see that the highest common factor is 18.

When we divide 54 by 18, the quotient is 3. If you divide 36 by 18, the quotient is 2. When you divide 72 by 18, the result is 4.

The number of lined paper = 54 pieces

The number of grid paper = 36 pieces

The number of dividers = 72 dividers

The common factors of 54, 36, and 72 are 2, 9, and 18.

The highest common factor of 54, 36, and 72 is 18.

Thus, 18 binders containing 3 pieces of lined paper, 2 pieces of grid paper, and 4 dividers can be made from the collection, using their HCF.

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A certain standardized test has a mean of 421 and a standard deviation of 18. For a student to score higher than 30.85% of those who took the exam, what score would be necessary?

Answers

The score required for the exam so that the score is higher than 30.85% is 412 for certain standardized test.

What is defined as the z-score?A Z-Score is a measurable statistic of a score's connection to the mean among a set of scores.A Z-score can tell a trader whether a value is characteristic for a given data set or atypical.In overall, a Z-score of less than 1.8 indicates that a company may be on the verge of bankruptcy, whereas a score nearer to 3 indicates that a company is in good financial standing.

The formula for finding the z-score is;

z = (x - μ)/σ

x = sample size

μ = mean of the population

σ = standard deviation of the population.

The given values are-

μ = 421

σ = 18

Probability = 30.85% = 0.3085

Check the z-score from the negative z table for 0.3085

z score = -0.5

Put the values in z formula and find x.

z = (x - μ)/σ

-0.5 = (x - 421)/18

Simplifying;

x = -9 + 421

x = 412

Thus, the score required for the standardized test is found as 412.

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If a ball is thrown directly upward with a velocity of 88 ft/s, its height (in feet) after t seconds is
given by y = 88t - 16t².
When does the ball reach its maximum height? (Round to two decimal places)

Answers

If a ball is thrown directly upward with a velocity of 88 ft/s, its height (in feet) after t seconds is given by y = 88t - 16t².The ball will reach its maximum height at 121 feet.

Maximum height

Given equation:

y = 88t - 16t²

Maximum height dy/dt = 0

88-32t = 0

32t = 88

t = 88/32sec

t = 2.75sec

Hence,

Maximum height attained by the ball :

Maximum height attained by the ball = 88(2.75)-16(2.75)²

Maximum height attained by the ball = 242 - 121

Maximum height attained by the ball = 121 feet

Therefore the maximum height is 121 feet.

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Solve the equation for x.
6(x + 3) - 8 = 4x + 2(4 + x)

Answers

===============================Solve the Equation - Solution and Explanation===============================

Hello! So...

We are given the following to solve:

Solve for x.

[tex]6(x+3)-8=4x+2(4+x)[/tex]

_______________________________________________________

1. Expand both sides of the equation.

[tex]6(x+3)-8=6x+10[/tex]

[tex]4x+2(4+x)=6x+8[/tex]

[tex]6x+10=6x+8[/tex]

______________________________

2. Subtract 10 from both sides.

[tex]6x+10-10=6x+8-10[/tex]

_______________________________

3. Simplify.

[tex]6x=6x - 2[/tex]

_______________________________

4. Subtract 6x from both sides.

[tex]6x-6x=6x-2-6x[/tex]

_______________________________

5. Simplify.

[tex]0=-2[/tex]

^Notice, the sides are not equal in the solution. This being said, there would be no solution.

___________________________________________________

Hope this helps! If you need anything else, feel free to comment below. Thanks and good luck!

y= −2x+8
x-intercept:
Enter as a coordinate: such as
(a,b)
y
-intercept:
Enter as a coordinate: such as
(a,b)

Answers

For given equation y = -2x + 8, the x-intercept is (4, 0) and the y-intercept is (0, 8)

In this question, we have been given an equation y = -2x + 8

We need to find the x-intercept and y-intercept. Also, we need to write it as a coordinate (a, b)

To find the x-intercept we need to substitute y = 0 in the above equation.

0 = -2x + 8

2x = 8

x = 4

So, the x-intercept is (4, 0)

To find the y-intercept we need to substitute x = 0 in the above equation.

y = -2(0) + 8

y = 0 + 8

y = 8

So, the y-intercept is (0, 8)

Therefore, for given equation y = -2x + 8, the x-intercept is (4, 0) and the y-intercept is (0, 8)

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Provide the correct reason for the statement in line 1. (please help)

Answers

Answer:

d) given

Step-by-step explanation:

nothing has been done yet, the statement is given as stated above the statement

Sarah enrolled $10,000 worth of debt with National Debt Relief. We negotiated with the creditors and reduced the debt by 50%. Sarah’s fee for our services was 25% of the enrolled debt ($10,000). How much did Sarah end up saving after reducing her debt and paying us our fee?*

Answers

Answer:

7500$

Step-by-step explanation:

Find the value of (-3/8) x (+8/15)

A. -1/5
B. -1/3
C. 11/15
D. 11/23

Answers

Answer: [tex]\Large\boxed{A. -\dfrac{1}{ 5}}[/tex]

Step-by-step explanation:

Given expression

[tex]-\dfrac{3}{8} \times \dfrac{8}{15}[/tex]

Combine the fractions

[tex]=\dfrac{-3\times 8}{8 \times 15}[/tex]

Cancel out the 8 on both the numerator and denominator

[tex]=\dfrac{-3}{ 15}[/tex]

Divide 3 on both the numerator and denominator

[tex]=\dfrac{-3\div 3}{ 15\div 3}[/tex]

[tex]=\Large\boxed{-\dfrac{1}{ 5}}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer is A. -1/5

Step by step

Multiply across and simplify

-3/8 x 8/15

-3 x 8 = -24 over 120

Simplified to -1/5

12. The perimeter of a triangle with sides 5x-1, 5x-1, 2.2x +10, and the perimeter of a square with a side length of 6.5x -11.8 are the same. What is the value of x?

Answers

The value of x is 4.

The perimeter of any shape is the sum of lengths of all its sides.

We are provided with the sides of triangle i.e., 5x-1, 5x-1 and 2.2x +10.

So, The perimeter of a triangle = sum of length of all three sides = (5x-1) + (5x-1) + (2.2x +10)

The perimeter of a triangle = 12.2x + 8 equation 1

Also, we are provided with the side of square i.e., 6.5x -11.8.

The perimeter of a square = 4 (side) = 4 (6.5x - 11.8)

The perimeter of a square = 26x - 47.2 equation 2

As per question,

Perimeter of a triangle = Perimeter of a square

12.2x + 8 = 26x - 47.2

13.8x = 55.2

x = 4

So we can write, the value of x is 4.

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Classify the following functions as growth or decay: f(x) = 10 (6/7)^x, g(x)= 1/3e^x, h(x)=5e^-x, k(x)= -10(6/7)^x

Answers

It is known that any exponential function with the form f(x)=a^x is an increasing function while a function of the form g(x)=a^(-x) is a decreasing function.

Furthermore, it a function h(x) is increasing, then the function -h(x) is decreasing. By analogy, if a function k(x) is decreasing, then -k(x) is increasing.

Now let's analyze the functions from the problem.

[tex]\text{ Let }f(x)=10\cdot(\frac{6}{7})^x[/tex]

Since (6/7)^x is increasing and the multiplying factor of 10 is positive, then the function f(x) is also increasing.

Use these rules to find whether each function is increasing or decreasing.

Remember that increasing functions are used to represent growth while decreasing functions are used to represent decay.

the original price of an article was 240.00. The price is increased by 12½%. The new price of the article is?

Answers

Answer:

The new price of the article is $270

Step-by-step explanation:

270-240/240

x 100% = 12.5%

12.5x240/100

= 30

hot-air balloon is floating above a straight road. To calculate their height above the ground, the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be 26∘ and 30∘.
How high (in feet) is the ballon?

Answers

The height of balloon is 1.99 miles above the ground.

What is angle of depression ?

In the event when the line of sight is directed downhill from the horizontal line, an angle is created with it. Angle of depression is the angle produced between the horizontal line and the observer's line of sight when the object being observed is below the level of the observer.

Let's give the balloon's height above the earth and the distance it is from the first milepost horizontally a name.

We can state the following if the angle of this milepost's depression is 24 degrees:

Tan(24)=[tex]\frac{h}{b}[/tex]

b = [tex]\frac{h}{tan(24)}[/tex]

We can state the following for the following milepost as there will be (b+1)miles horizontal distance of and a 20 degree depression at that location.

tan(20)=[tex]\frac{h}{b+1}[/tex]

b +1 = [tex]\frac{h}{tan(20)}[/tex]

Therefore, substituting equation 1

[tex]\frac{h}{tan(24)}[/tex] = [tex]\frac{h}{tan(20)} -1[/tex]

1 = [tex]\frac{h}{tan(20)}[/tex] - [tex]\frac{h}{tan(24)}[/tex]

1 = h× ( [tex]\frac{h}{tan(20)}[/tex] - [tex]\frac{h}{tan(24)}[/tex] )

h = 1.99 miles

Consequently, the height of balloon is 1.99 miles above the ground.

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Can you check work please?

Answers

When rotating a point 180 degrees counterclockwise about the origin our point A(x,y) becomes A'(-x,-y). So all we do is make both x and y negative.

[tex]\begin{gathered} K(-4,-3)\rightarrow K^{\prime}(4,3) \\ L(-3,-1)\rightarrow L^{\prime}(3,1) \\ M(0,-3)\rightarrow M^{\prime}(0,3) \end{gathered}[/tex]

[tex]3-\sqrt{x} 5[/tex]

Answers

The value of the expression given as 3 - √x⁵ is 3 - x^2√x

What are expressions?

Expressions are mathematical statements that are represented by variables, coefficients and operators

How to evaluate the expression?

The expression is given as

3 - √x⁵

Express 5 as the sum of 4 and 1