The solution to an inequality is graphed on the number
ne.
-5 -4 -3 -2 -1 0 1 2 3 4 5
Mark this and return
What is another way to represent this solution set?
{xx<4.5}
Ox|x≤4.5}
Oxx> 4.5)
O{x|x24.5)
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The y-intercept of a line is the point at which the line crosses the y-axis. This means that the x-coordinate of the point is 0.

To find the equation of a line passing through two points, we use the slope-intercept form of the equation of a line: y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the y-intercept of a line passing through two points, we can use the slope-intercept form of the equation of a line and the coordinates of the two points:

(y1, y2) = m(x1, x2) + b

m = (y2-y1)/(x2-x1)

In this case, the two points are (-1,-5) and (6,0)

m = (0-(-5))/(6-(-1)) = 5/7

We can substitute the slope in the slope-intercept form of the equation of a line:

y = mx + b

so we can substitute point (-1,-5) in the equation and solve for b

-5 = (5/7)*(-1) + b

b= -5 + (5/7) = -5 + 0.7142857142857143

So, the y-intercept of the line passing through the two points (-1,-5) and (6,0) is -4.2857142857142865

The rate of change for the Carol with respect to time is 3/16 miles per minute.

The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time. When discussing momentum, the term "rate of change" (ROC) is frequently used. It is typically defined as the ratio of a change in one variable to a matching change in another; visually, the rate of change is represented by the slope of a line.

Given The table shows the distance Carol traveled after various numbers of minutes,

Input        Output

 2            1/6

 3          17/48

 4          13/24

 5          35/48

 6          11/12

Here, the output values from 1/6 to 11/12 indicate the distance in miles whereas the input values from 2 to 6 describe the time in minutes.

by utilizing the first two sets of input-output numbers, calculating the rate of change

Relative change = change in distance/change in time

(17/48 - 1/6)/(3-2) = (17/48 - 8/48) /1 = 9/48 = 3/16 miles per minute

Hence the rate of change is 3/16 miles per minute.

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The difference after the subtraction is: 2a³ +  10a² - 5a - 4

A polynomial is an expression which has one or more of its variables with a power of at least 2 degrees. It can be expressed in form of a term.

Therefore, a polynomial equation is a means of expressing an expression with terms and on variable with a degree of 2 or more.

To find the difference by subtracting the polynomials, we have:

4a³ + 6a² - 11a - 3 - (2a³ - 4a² - 6a + 1) = 4a³ + 6a² - 11a - 3 - 2a³ + 4a² + 6a - 1

collecting like terms,

4a³ - 2a³ +  6a² + 4a²  - 11a + 6a - 3 - 1 = 2a³ +  10a² - 5a - 4

Therefore, the difference by subtracting the two polynomials is:

2a³ +  10a² - 5a - 4

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Step-by-step explanation:

the surface area of a half-cylinder is, surprise, surprise, half of the surface area of a whole cylinder ...

the surface area of a cylinder is

A=2×pi×r×h + 2×pi×r²

r being the radius, h being the height of the cylinder.

the formula simply adds

the sidewall area (which is a rectangle of

circle circumference × height)

+

the top and base circle areas

half of this area calculation for a half-cylinder is

A/2 = pi×r×h + pi×r²

Meters and seconds are the two units of measurement required to describe speed.

A ball freely falling at 20 m/s will in the next second have a speed of 30 m/s.This is because the speed of a freely falling item rises by 9.8 m/s per second owing to gravity's acceleration. The ball begins at a speed of 20 m/s and adds 9.8 m/s to its initial speed after one second, ending in a final speed of 20 + 9.8 = 29.8 m/s (approx. 30 m/s).

Meters and seconds are the two units of measurement required to describe speed. These units are used to calculate the distance travelled by an item as well as the time it takes to traverse that distance. In this scenario, the ball's speed is measured in metres per second (m/s), which is the distance the ball travels in one second.

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Answer:

89

Step-by-step explanation:

The angles are congruent since they are alternate interior angles of parallel lines cut by a transversal.

30x - 1 = 29x + 2

x = 3

30x - 1 = 30 × 3 - 1 = 89

Answer:

Kinda Hard to explain hope this helps

Step-by-step explanation:

Lets say molly is 6 and parker bought 4 times as many then he bought 24 marbles.Then cole bought 5 fewer then parker so 24-5=19

the equation is 4(6)m=p(24) Cole p(24)-5=Cole

M=6

The correct answer is done by Curran,the equation is an example for Inequality Equations. X = -1\2

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols.

Examples,

Symbol Name               Symbol                          Example

Not equal                            ≠                                     x ≠ 3

Less than                            (<)                           x + 7 < √2

Greater than                       (>)                        1 + 10x > 2 + 16x

Less than or equal to         (≤)                            y ≤ 4

Greater than or equal to     (≥)                             -3 - √3x ≥ 10

Let's solve your inequality step-by-step.

−4(x−6)<22

Step 1: Simplify both sides of the inequality.

−4x+24<22

Step 2: Subtract 24 from both sides.

−4x+24−24<22−24

−4x<−2

Step 3: Divide both sides by -4.

−4x/4<= -2/-4x

x-1/2

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If in the party there are 5 different appetizers and 6 different desserts , then the number of different ways the 3 appetizers and 2 desserts can be selected is 150  ways .

the number of different appetizers in dinner party is = 5 ;

the number of different desserts in dinner party is = 6 ;

the number of ways of selecting 3 appetizers from 5 is = ⁵C₃ = 10 ;

number of ways of selecting 2 desserts from 6 is = ⁶C₂ = 15 ;

the number of ways of selecting 3 appetizers and 2 desserts is

= 15 × 10

= 150 ways .

Therefore , 3 appetizers and 2 desserts can be selected in 150 ways .

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The simplified form of the polynomial ( x + 6 )( x² - 3x - 4 ) is x³ + 3x² - 22x - 24

Given the polynomial in the question;

( x + 6 )( x² - 3x - 4 )

Apply distributive property.

x( x² - 3x - 4 ) + 6( x² - 3x - 4 )

x³ - 3x² - 4x + 6x² - 18x - 24

Collect like terms

x³ - 3x² + 6x² - 18x - 4x - 24

Add like terms

x³ - 3x² + 6x² - 18x - 4x - 24

Add -3x² and 6x²

x³ + 3x² - 18x - 4x - 24

Add -18x and -4x

x³ + 3x² - 22x - 24

Therefore, the simplified form is x³ + 3x² - 22x - 24.

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Answer:

18

Step-by-step explanation:

see attached

The total monthly premium for all her insurance is 6249 .

What is percentage ?

Percentage can be defined as the product of ratio of given value , total value and hundred.

Given ,

Donna Wagner is a self-employed musician. She pays 100 percent of the PPO insurance premium of 5,824 annually.

She also has a dental plan that costs 600 annually and a vision plan that costs 365 annually.

The total monthly premium for all her insurance = 5284+600+365

= 6249.

So, The total total monthly premium for all her insurance is 6249 .

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Answer:

4th option

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (3, 6 ) and (x₂, y₂ ) = (8, 4 )

m = [tex]\frac{4-6}{8-3}[/tex] = [tex]\frac{-2}{5}[/tex] = - [tex]\frac{2}{5}[/tex] , then

y = - [tex]\frac{2}{5}[/tex] x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (8, 4 ) , then

4 = - [tex]\frac{2}{5}[/tex] (8) + c = - [tex]\frac{16}{5}[/tex] + c ( add [tex]\frac{16}{5}[/tex] to both sides )

[tex]\frac{20}{5}[/tex] + [tex]\frac{16}{5}[/tex] = c , that is

c = [tex]\frac{36}{5}[/tex]

y = - [tex]\frac{2}{5}[/tex] x + [tex]\frac{36}{5}[/tex] ← equation of line

Using the laws of exponents to simplify the expression, we have; 5 1/3

When the power of one or more terms of an expression is greater than 1, then the expression is in an exponential form. Thus some laws can be require to simplify an exponential expression.

In the given question,

2^7/ 2^5 + (4^5)^0 + 3^-1

Thus applying the division law of indices to the first term, we have;

2^7/ 2^5 = 2^(7 - 5)

              = 2^2

In the second term, anything to the power of zero is 1. So that;

(4^5)^0 = (1024)^0

            = 1

In the third term, applying the inverse law of indices. We have;

3^-1 = 1/ 3

Therefore,

2^7/ 2^5 + (4^5)^0 + 3^-1 = 2^2 + 1 + 1/3

                                        = 4 + 1 + 1/3

                                        = 5 + 1/3

                                        = 16/ 3

                                        = 5 1/3

The value of the expression is 5 1/3.

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9.43 inches is the measure of the longest segment

We are aware that the diagonal connecting the two opposing corners at the top and bottom will be the longest segment.

We know how to find the diagonal of a right triangular prism using the following formula:

d = [tex]\sqrt{w^2 + l^2+h^2} \\\\[/tex]

where w = width = 1.4

l = length = 4.8

h = height = 8

We would put these values in the formula above

[tex]d = \sqrt{1.4^2 + 4.8^2+8^2} \\\\[/tex]

d = [tex]\sqrt{1.96+23.04+64}[/tex]

d = 9.43

The measure of the longest line segment is given as 9.43 inches

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Answer:

462

Step-by-step explanation:

do 6x77 which is 462.       alternative forms: 4.62 x 10^2

Answer:

Step-by-step explanation:

x=4
x=-3/2

hope this helps !! :)

Answer:

370.1 [tex]units^{2}[/tex]

Step-by-step explanation:

Square

a = [tex]s^{2}[/tex]

a = [tex]12^{2}[/tex] = 144

Semi - Circle:

a = 1/2([tex]\pi r^{2}[/tex])

a = 1/2(3.14)(36)     The radius is 1/2 the diameter of 12 (6) [tex]6^{2}[/tex] = 36

a = 1/2(113.04)

a = 56.52

144 + 4(56.52)

144 + 226.08

370.08  rounded to the nearest tenths place 370.1

The area for the given figure by using distributive property is 5y+35.

What is Area of rectangle?

Area of rectangle can be defined as the product of length and breadth .

From the Given figure,

We have to find the area of rectangle

so,

There is one small rectangle inside that,

So,

total area = area of small rectangle + area of larger rectangle

area = 5*y + 7*5

So by summing up the area of two rectangles

we get,

Total area = 5y+ 35

Therefore, The area for the given figure by using distributive property is 5y+35.

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A population is the entire group of items of interest in a particular study, and it is not necessarily the same size as the sample. It is not the same as a sample, which is a subset of the population chosen for the study.

A population is the complete set of items of interest in a study. It could be people, animals, plants, objects, or anything else being studied. A population can be large or small, and it is not always the same size as the sample. A sample is a subset of the population that is chosen to represent the entire population. It is important to choose a sample that accurately reflects the population. Sampling techniques, such as random sampling, are used to ensure that the sample is representative of the population. Once the sample is chosen, data is collected from the sample to infer information about the population. This data can then be used to draw conclusions about the population as a whole.

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Answer:6/5 or 1 1/5

Step-by-step explanation:

1. Add 2 on each side

2. Then divide 1/5 and 6

Answer:

X = 30

Step-by-step explanation:

Add 2 on both sides, cancelling the -2. Divide 1/5 by 6 (4+2) and you'll get 30

60 students chose chocolate ice cream If 84 students chose vanilla ice cream.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, Elmhurst School organized an ice cream social for the incoming sixth graders. At the social, 7 students chose vanilla ice cream for every 5 that chose chocolate ice cream.

Since,

The ratio of students who choose vanilla ice cream to chocolate ice cream is: 7/5

Thus,

for every students choose chocolate ice cream = 5/7 student who chooses vanilla ice cream

If 84 students chose vanilla ice cream

Thus, students choose chocolate ice cream = 5/7 * 84

students choose chocolate ice cream = 12* 5

students choose chocolate ice cream = 60

Therefore, If 84 students chose vanilla ice cream, 60 students chose chocolate ice cream.

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Answer:

pls see attached

Step-by-step explanation:

Answer:

Triangle ABC is being enlarged using a scale factor of 2 and the origin as the center to give triangle A'B'C'. To find the coordinates of A' and B', we will have to multiply each of the x and y coordinates of A and B by the scale factor of 2.

The coordinates of A are (-5, -6) and the coordinates of B are (2, 3)

The coordinates of A' will be (-52, -62) = (-10, -12)

The coordinates of B' will be (22, 32) = (4, 6)

So the coordinates of A' are (-10, -12) and the coordinates of B' are (4, 6).

Answer:ugy8f67

Step-by-step explanation: yessss

The sum of the numbers on the three chosen slips of paper is either 21 or 23 in both the given cases.

We are given that one of the slips chosen is numbered 7, so the only possible sums of the remaining two slips are:

16 = 7 + 9

14 = 7 + 7

In the statement (1), the sum of two of the numbers chosen is 16, which means that the remaining two slips are 7 and 9. So the sum of the numbers on the three chosen slips of paper is 7 + 9 + 7 = 23.

In the statement (2), the sum of two of the numbers chosen is 14, which means that the remaining two slips are 7 and 7. So the sum of the numbers on the three chosen slips of paper is 7 + 7 + 7 = 21.

Hence, we get that in both cases, the sum of the numbers on the three chosen slips of paper is either 21 or 23.

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Answer:

450 cupcakes

Step-by-step explanation:

Let x be the number of cupcakes sold for John's total pay to be the same for both companies

For the first company

Salary = $800/week

Commission is $0.30 per cupcake

For sales of x cupcakes, total commission = 0.30x

Total pay = Weekly salary + Total commission from sales

Total Pay = 800+ 0.3x

For the second company
Salary = 350 /week

Commission: $1.30 per cupcake

For sales of x cupcakes, total commission = 1.30x

Total Pay = Weekly salary + Total commission from sales

Total Pay = 350 + 1.3x

If both pay must be he same,
800 + 0.3x = 350 + 1.3x

800-350 = 1.3x - 0.3x

450 = 1x

x = 450 cupcakes ANSWER

Answer: 450

Step-by-step explanation:

    If we let x and y represent the number of cupcakes John sells and his total weekly income, respectively, we get the following system of equations.

=0.35x+845

=1.4x+372.5

​

Since both equations are solved for y​, any substitution for y​ will result in the following

211.4 x+372.5&=0.35

x+845

1.4x+372.5

​

=0.35x+845

​

Solving for x will give us the number of cupcakes John needs to sell weekly for each paycheck to be the same. Doing so, we get

1.4 x+372.5&=0.35     x+845

1.05 x&=472.5x=450

1.4x+372.5

1.05x

x

=0.35x+845

=472.5

=450

Therefore, John needs to sell 450450​ cupcakes each week for both salaries to be the same.

Total amount in Ruby's account after doing one time investment of $6200 for 12 years with rate of interest 4.3% is equal to $10,300 ( nearest hundreds dollars )

Principal 'P' amount in Ruby's account is equal to $6200

Rate of interest 'r' compounded continuously is 4.3%

Time 'N' = 12 years

Let 'A' be the final amount in Ruby's account after 12 years

Amount 'A' = P × ( 1 + (r/100) )ⁿ

Substitute the value in the formula we get,

⇒ A = 6200 × [ 1 + ( 4.3/100) ]¹²

⇒ A = 6200 × [ 1 + 0.043 ]¹²

⇒ A = 6200 × [ 1.043 ]¹²

⇒ A = $10,275.5

⇒ A = $10,300 ( nearest hundreds dollars )

Therefore , the total money in Ruby's account after depositing $6200 with rate of interest 4.3% compounded continuously for 12 years is equal to

$10,300 ( nearest hundreds dollars ).

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Answer:

A

Step-by-step explanation:

Any equation with a single independant variable (often an 'X') that is not ( x2,x3 ) is linear.

1). To eliminate variable x,

we subtract the equation 2 to equation 1

And 2). The solution of the system is x = 16 and y = 20.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

Each of 36 students at a school play bought either a cup of orange juice or a sandwich.

A cup of orange juice costs $1 and a sandwich costs $3.

The total amount collected was $76.

Let x represent the number of students who bought a cup of orange juice and y represents the number of students who bought a sandwich.

Then the problem can be represented by this system of equations:

x + 3y = 76   {equation 1}

x + y = 36     {equation 2}

1). To eliminate variable x,

we subtract the equation 2 to equation 1,

2y = 40

y = 20.

And x = 16.

2). The solution of the system is x = 16 and y = 20.

To check the solution, substituting the values to the equation 2,

16 + 20 = 36

36 = 36

Therefore, all the required values are given above.

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