Evaluate this expression:

| b + 1 | + 8

Answer: x < 2

Step-by-step explanation:

    To solve this, we will isolate the variable c.

   Given:

4c < 14 - 3c

   Add 3c to both sides of the equation:

7x < 14

   Divide both sides of the equation by 7:

x < 2

The line that passes through the pair of points has the given slope. ( − 2 , 8 ) , ( r , 4 ) , m = − 1 2, then the intersection with the domain is r = -5/3.

The line that passes through the pair of points has the given slope is,

( − 2 , 8 ) , ( r , 4 )  and m = -12

Slope, numerical measure of a line's inclination relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).

m = rise/run

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

Where,

m = slope

[tex](x_{1} ,y_{1} )[/tex] = coordinates of first point in the line

[tex](x_{2} ,y_{2} )[/tex] =  coordinates of second point in the line

Then, we can find the [tex]m_{1}[/tex]

We can use these two values, ( − 2 , 8 ) , ( r , 4 )

x1 = -2

y1 = 8

x2 = r

y2 = 4

m = [tex]\frac{4-8}{r-(-2)}[/tex]

[tex]m = \frac{-4}{r+2}[/tex]

We can substitute m= -12 value into m= -(4/r+2)

So,

We can write,

-12 =  [tex]\frac{-4}{r+2}[/tex]

We can find the domain,

If the fraction is defined, the dominator can not be equal to zero.

2 + r ≠ 0

Rearrange variables to the left side of the inequality,

r ≠ -2

Append the inequality as the domain,

r ≠ -2

We can solve the equation,

-12 =  [tex]\frac{-4}{r+2}[/tex]

Multiply both sides of equation by the common denominator,

-12 (r+2) =  -4(r+2)/ (r+2)

Reduce the fractions,

-12 (r+2) = -4

Apply the distributive property,

-12r - 24 = -4

Rearrange variable to the left side of the equation,

-12r = -4 + 24

Calculate the sum or difference,

-12r = 20

Divide both sides of the equation by the coefficient of variables,

r = - 20/12

r = -5/3

Therefore,

The intersection with the domain is r = -5/3, so  the line that passes through the pair of points has the given slope. ( − 2 , 8 ) , ( r , 4 ) , m = − 12.

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Probability of three youngest student are selected is [tex]\frac{1}{816}[/tex]

The field of mathematics known as probability concerns with numerical representations of the possibility that an event will occur or that a statement is accurate. An event's probability is a number between 0 and 1, where, roughly speaking, 0 indicates the event's impossibility and 1 represents certainty.

Given data

Total number of students available = 17

Number of students selected = 3

C₍₁₈₋₃₎ = [tex]\frac{18!}{3!(18-3)!}[/tex]

C₍₁₈₋₃₎ = [tex]\frac{18(17)(16)}{3(2)(1)}[/tex]

C₍₁₈₋₃₎ = [tex]\frac{4896}{6}[/tex]

C₍₁₈₋₃₎ = 816

Number of ways where students selected are youngest = 1

Probability of three youngest student are selected

= [tex]\frac{1}{C}[/tex]₍₁₈₋₃₎

= [tex]\frac{1}{816}[/tex]

Probability of three youngest student are selected is [tex]\frac{1}{816}[/tex].

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Answer:

7.719

Step-by-step explanation:

The value of the numbers 3√5•√10+11√5•√10-√5 based on the information is D. 14✓50 - ✓5

It should be noted that based on the information given, we simply want to simplify 3√5•√10+11√5•√10-√5.

This will be illustrated as:

= 3√5•√10+11√5•√10-√5

It should be noted that the numbers inside the square roots will be multiplied. This will be:

= (3√5•√10) + (11√5•√10) -√5

= 3✓50 + 11✓50 - ✓5

= 14✓50 - ✓5

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Answer:

c=-12

Step-by-step explanation:

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

2/3c−2=2+c

Step 1: Simplify both sides of the equation.

2/3c−2=2+c

2/3c+−2=2+c

2/3c−2=c+2

Step 2: Subtract c from both sides.

2/3c−2−c=c+2−c

−1/3c−2=2

Step 3: Add 2 to both sides.

−1/3c−2+2=2+2

−1/3c=4

Step 4: Multiply both sides by 3/(-1).

(3/−1)*(−1/3c)=(3/−1)*(4)

c=−12

Answer:

c=−12

Answer: 21 containers of ice cream

Step-by-step explanation: simple problem, take 126 and divide it by 6 to get your answer

The expression will be given as -4x² + 3x. Thus, option B is correct answer.

Area may be defined as the total amount of space which is covered by an entity. The area for a square will be given by the product of its sides and the area of the rectangle will be given as the product of its length and breadth. It is given that the area of Maria's garden is 8x² - 3x and the length and breadth of Jamal's garden are 4x - 2 and 3x respectively. The area of Jamal's garden is given by A = l×b  = (4x - 2) × 3x = 12x² - 6x.

Now, difference between Maria's garden and Jamal's garden is given by

(8x² - 3x) - (12x² - 6x)

= 8x² - 3x - 12x² + 6x

=> -4x² + 3x which is the required answer.

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We can simplify the numerical expression to get:

(2/5)*(14 - 27) + (2⁵/16) = -16/5

Here we have the expression:

(2/5)*(14 - 27) + (2⁵/16)

Let's simplify the term in the right first, we know that:

2⁵ = 2*2*2*2*2 = 4*4*2 = 16*2 = 32

Replacing that we get:

(2⁵/16) = 32/16 = 2

Then we get:

(2/5)*(14 - 27) + (2⁵/16) = (2/5)*(14 - 27) + 2

Now we can simplify the term in the left:

(2/5)*(14 - 27) = (2/5)*(-13) = -26/5

Replacing that we get:

(2/5)*(14 - 27) + 2 = -26/5 + 2 = -26/5 + 10/5 = -16/5

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The equation to determine the number of hours worked by the plumber is 190 = 35 + 50x and the number of hours is 3.1 hours option (A) is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Jerald is having drain issues at his home and decides to call a plumber.

The plumber charges $35 to come to his house and $50 for every hour they work.

Let x be the number of hours:

190 = 35 + 50x

50x = 155

x = 3.1 hours

Thus, the equation to determine the number of hours worked by the plumber is 190 = 35 + 50x and the number of hours is 3.1 hours option (A) is correct.

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The △ABC is congruent to △DCB (△ABC ≅ △DCB) under the SAS condition.

So, △ABC ≅ △DCB:

So, △ABC ≅ △DCB is under SAS condition.

Therefore, the △ABC is congruent to △DCB (△ABC ≅ △DCB) under the SAS condition.

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The value of x in the equation given as x - 2(x - 6) = -x + 12 is 0

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the equation is given as

x - 2(x - 6) = -x + 12

Open the bracket

So, we have

x - 2x + 12 = -x + 12

Evaluate the like terms

So, we have

x - 2x = -x

This gives

x = 0

Hence, the solution of x in the equation is 0

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Answer: $10.50

Step-by-step explanation:

Cot of 1 slice a pizza = $1.75

Cost of 6 slices of pizza = 6 × $1.75

=$10.50

Hence, Robert will pay $10.50 for the 6 slices of pizza and $20 for the membership.

The exponential function given in this problem represents an exponential decay, and it's asymptote is of y = 0.

An exponential function is modeled according to the rule given as follows:

[tex]y = ab^x + c[/tex]

The parameters of the function are defined as follows:

To verify if the function represents growth or decay, we have to check parameter b as follows:

In the context of this problem, the function is defined as follows:

[tex]y = 14\left(\frac{1}{2}\right)^x[/tex]

Hence the parameters of the given function are as follows:

a = 14, b = 0.5, c = 0.

Then:

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Answer:

Answer down bellow

Step-by-step explanation:

Q's asked: Does the function y equals 14 times the quantity 1 over 2 end quantity to the x power represent exponential growth or decay? What is the equation of the asymptote?

Answer: Decay; y = 0

hope this helps

~~Wdfads~~

7 × 12 = 72 satisfies the closure property of multiplication, the other integer when the sum is - 38 and one integer is - 22 will be - 16 and the total score for Gopi will be 112 marks.

1)

Closure property of multiplication:

It states that if  two real numbers a and b are multiplied, then the product will be a real number as well.

We have 7 × 12 = 72

7, 12 and 72 all are real numbers.

So, it is a closure property under multiplication.

2)

Sum = - 38

a = - 22

We need to find b

a + b = - 38

- 22 + b = - 38

b = - 38 + 22

b = - 16

3)

1 correct answer = 4 marks

1 incorrect answer = - 2 marks

Number of correct answers = 32

Number of incorrect answers = 8

Total score = 32 × 4 + (- 2) × 8

= 128 - 16

= 112 marks.

Therefore, we get that, 7 × 12 = 72 satisfies the closure property of multiplication, the other integer when the sum is - 38 and one integer is - 22 will be - 16 and the total score for Gopi will be 112 marks.

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Due to different rates of change in each case, neither graph shows a proportional relationship.

A graph represents a proportional relationship if the output variable y in the y-axis can be written as a product of the input variable x in the x-axis and the constant of proportionality k, as follows:

y = kx.

For the first case, the rate of change is of:

k = 4/10 = 0.4.

For the second case, the rate of change is of:

k = 8/10 = 0.8.

Different rates, hence cannot be written as proportional relationship.

Hence the rates for each interval are given as follows:

Different rates, hence it is not a proportional relationship.

The graphs are missing and are given by the image inserted at the end of the answer.

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The scissor has intersecting lines with angles 1,2,3,4.The angles are ∠1=159° and ∠3 is 159°. We got the angle ∠2=21° and ∠4=21°.

Given that,

In the picture there is a scissor.

The scissor has intersecting lines with angles 1,2,3,4.

∠1=159° and ∠3 is 159°.

We have to find the angles ∠2 and ∠4.

Two straight lines that intersect at the same location are said to be intersecting lines. The junction point is the place where two intersecting lines meet. Four angles are created when two lines cross. The four angles added together always equal 360 degrees. There is a unique connection between the angles created when lines intersect.

The straight line has 180°

∠1+∠2=180°

159°+∠2=180°

∠2=180°-159°

∠2=21°

Now,

∠3+∠4=180°

159°+∠4=180°

∠4=180°-159°

∠4=21°

Therefore, the angle ∠2=21° and ∠4=21°.

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r and s are the parallel lines, if ∠4 equals ∠5.

Given,

The figure with,

Four lines: Line r, Line s, Line l and Line m.

Angles: ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7 and ∠8

Here, we have to find the parallel lines when ∠4 = ∠5

Lets see:

Angle 1 and angle 4 are the same because the opposite angles created by two crossing lines are identical. As a result, angle 1 also equals angle 5.

The corresponding angles are identical when two parallel lines cross across a line. To put it another way, if r and s are parallel, the angles created when l intersects r and s are same. Angle 1 equals Angle 5, Angle 2 equals Angle 6, etc. We can infer that r and s are parallel since we know that angle 1 Equals angle 5.

So, we can conclude that if ∠4 equals ∠5, then r and s are the parallel lines.

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Answer: 80

Step-by-step explanation:

72.4 = 724/10

9.38=

938/10.

72.4/9.38

= 7.7

=8 approximately

The estimated quotient of 72.4 ÷ 9.38 is 8

Estimation is the process of calculating the approximate value to make the calculation easier and simple.

The rounding off a number is the process of putting a number up or down to the nearest whole number or the nearest tens, hundred, thousand, etc

First number is 72.4

Round the number to the nearest whole number

72.4 = 72

Second number is 9.38

Round the number to the nearest whole number

9.38 = 9

Divide the number 72 by 9

72/9 = 8

The quotient is 8

Hence, the estimated quotient of 72.4 ÷ 9.38 is 8

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Answer:

you could either make the fraction a decimal or my personal like is to make the decimal a fraction

Step-by-step explanation:

convert the fraction to a decimal or decimal to fraction

The diagram prove that  m ║n by the consecutive interior angles converse.

The diagram is to prove line m is parallel to line n.

Therefore,

m ║ n

Hence,

m∠1 = 115°, m∠2  = 65° is given.

m∠1 + m∠2 = m∠1 + m∠2 follows the reflexive property of equality.

The reflexive property of equality means that anything is equal to itself

m∠1 + m∠2 = 115° + 65° is the substitution property of equality

Supplementary angles add up to 180 degrees.

m∠1 + m∠2 = 180 is the definition of supplementary angles

∠1 and ∠2 are supplementary when simplify

m ║ n by consecutive interior angles converse.

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Answer: 3/24 or 1/8 of the pizza

Step-by-step explanation:..

Answer:

x = +/-[tex]\frac{\sqrt{291} }{3} -6[/tex]

Step-by-step explanation: