Consider the following system of linear inequalities and corresponding graph:
y ≥ 2x - 4
x > -3
y < 5
Which of the following points is a solution to this system of linear inequalities?

Answer:

x = 3  rounded to the nearest whole number (actually 2.735)

Step-by-step explanation:

The triangle formed by the sides of length 7x, 12x and 32 form a right triangle with the side of length 32 as they hypotenuse

By the Pythagorean theorem

c² = a² + b² where c = hypotenuse, a and b being the other two sides

Plugging in values we get

38² = (7x)² + (12x)²

1,444 = 49x² + 144x² = 193x²

Switching sides:

193x² = 1444

x² = 1444/193 = 7.48

x = √7.48= 2.735 = 3  rounded to the nearest whole number

Answer:-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0  1  2  3  4  5  6  7  8  9 10

-5 -4 -3 -2 -1 0  1  2  3  4  5  6  7  8  9 10

Step-by-step explanation:

The vertices of triangle J'K'L' after a reflection of the triangle JKL over the x-axis is given as follows:

The original vertices of the figure are given as follows:

J(-5,5), K(5,7) and L(2,3).

For a reflection over the x-axis, the reflection rule is defined as follows:

(x,y) -> (x,-y).

Meaning that the x-coordinate remains constant while the y-coordinate has the sign exchanged.

Then the vertices of the reflected figure are given as follows:

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The probability of success at the second mall is 3/4 which mall should be chosen in order to maximize the expected profit $135,000.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

First mall:

Profit if successful = $300,000

Loss if otherwise = $100,000

Probability of success = 1/2

Second mall:

Profit if successful = $200,000

Loss if otherwise = $60,000

Probability of success = 3/4

If probability of profit 'P(profit)' = 3/4

Then,

Probability of loss P(loss) = 1 - P(profit)

P(loss) = 1 - 3/4 = 1/4

Expected profit:

= [P(profit) x profit] + [P(loss) x loss])

= (0.75 x $200,000) + (0.25 x (-$60,000))

= 150,000 - 15000

= $135,000

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The solution graph is given in the attached image.

The solution is x = 2 and y = 70.

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:

Robert and Tony love to read.

Robert reads 30 pages the first day and 20 pages each day after that.

Tony reads 40 pages the first day and 15 pages each day after that.

We have a system of equations,

y = 20x + 30

y = 15x + 40

Subtracting the equations, we get,

5x = 10

x = 2

And y = 70.

And the graph is given in the attached image.

Therefore, the solution is x = 2 and y = 70.

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Answer: 588π = 1846.32

Step-by-step explanation:

Volume of cylinder = πr²h

Volume = (7)²*12*π = 588π = 1846.32

Answer:

1. The unit price for a doll is three dollars. The unit price for a purse is six dollars.

2. One doll costs three. One purse costs six.

3. Polly spends $24 on the 2 dolls and 3 purses.

Step-by-step explanation:

Doing some calculations, 1 doll costs three dollars and 1 purse costs six dollars.

5 x 3 + 6 = 21

7 x 3 + 1  = 27

If Polly buys 2 dolls and 3 purses, that means she spends six dollars on the dolls and eighteen dollars on the purses.

(2 x 3) + (3 x 6) = $24

Polly spends $24 on 2 dolls and 3 purses.

The absolute inequality 3/4 * |(1/3)x + 2| < 6 has a solution of (d) x > -30 and x < 18

To solve the inequality, we'll start by isolating the absolute value expression on one side of the inequality.

3/4 * |(1/3)x + 2| < 6

We'll first distribute the 3/4 across the absolute value:

|(1/3)x + 2| < 8

To simplify this, we'll split the inequality into two cases:

(1/3)x + 2 < 8

(1/3)x + 2 > -8

First, let's consider the case where (1/3)x + 2 < 8

(1/3)x < 6

x < 18

Now let's consider the case where (1/3)x + 2 > -8

(1/3)x > -10

x > -30

So, the solution set is x > -30 and x < 18

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Complete question

Solve the inequality three-fourths times the absolute value of the quantity one third times x plus 2 end quantity is less than 6. x > −8 and x < −4 x > −30 and x < 2 x < −30 and x < 18 x > −30 and x < 18

Counting of numbers by 5's end with 0, 5, 0, 5, 0, .....

Counting in mathematics is defined as the process of finding the number of objects in a set which is finite.

Counting numbers are the natural numbers.

The question is how to count by 5's.

In order to count by 5's, we have to add 5 to each of the preceding number  to get the next number.

So the pattern will be,

5, 10, 15, 20, 25, 30, 35, ........

So the numbers end either in 0 or 5.

Hence the pattern of counting by 5's are the numbers which ends in either 0 or 5.

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Answer: 5.49 × 10-4

Step-by-step explanation:

When you move the decimal over move it over to the right by 4 units.

When you move right it is (-) negative. So you get 5.49 x 10-4.

Answer:

The possible formula for the linear function h(x) is h(x) = -7x + 190. This can be determined by using the information from numerade.com, which states that the formula for a linear function is y = mx + b. Applying this formula to the given values of h(-30) = 90 and h(20) = -160 gives a formula of h(x) = -7x + 190.

Step-by-step explanation:

The duration of the task is 2.5 days

The task duration if Mr. Bean gets sick is 1.5 days

An equation is an expression showing two or more numbers and variables linked together by a mathematical operation. Types of equations are linear, quadratic, cubic and so on depending on the degree of the variable.

Mr. Hummer works on the task for 3 hours, Mr. Cold works on the task 9 hours, and Mr. Bean works 8 hours on the task

Total time spent on task = 3 hours + 9 hours + 8 hours = 20 hours

Working day has 8 hours, therefore:

1 working day = 8 hours

20 hours = 20 hours * 1 working day per 8 hour = 2.5 days

If Mr. Bean is sick:

Total time spent on task = 3 hours + 9 hours = 12 hours

12 hours = 12 hours * 1 working day per 8 hour = 1.5 days

The task duration if Mr. Bean gets sick is 1.5 days

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The value of y when x = 28 is given as follows:

y = 0.5.

A direct proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

An inverse proportional relationship is defined as follows:

y = k/x.

When x = 7, y = 2, hence the constant k is obtained as follows:

2 = k/7

k = 14.

Hence the equation is:

y = 14/x.

When x = 28, the value of y is obtained as follows:

y = 14/28

y = 0.5.

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The salary of each of specialist, manager and director are $62,000, $75,000 and $90,000.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Linear equations may include one or more variables.

Let x, y and z be the salary of specialist, manager and director respectively.

From the given information, we have three linear equations.

5x + 2y + z = 550,000

6x + 3y + 2z = 777,000

8x + 0y + 2z = 676,000

From the third equation,

2z = 676,000 - 8x

z = 338,000 - 4x

Substituting the value of z in the first equation,

5x + 2y + 338,000 - 4x = 550,000

x + 2y = 212,000

2y = 212,000 - x

y = 106,000 - (1/2) x

Substituting z = 338,000 - 4x and y = 106,000 - (1/2) x in the second equation 6x + 3y + 2z = 777,000,

6x + 3(106,000 - (1/2) x) + 2(338,000 - 4x) = 777,000

6x + 318,000 - (3/2)x + 676,000 - 8x = 777,000

(6x - 3/2 x - 8x) + (318,000 + 676,000) = 777,000

-(7/2) x = -217,000

x = 62,000

y = 106,000 - (1/2) x = 75,000

z = 338,000 - 4x = 90,000

Hence the salary of each specialist is $62,000, each manager is  $75,000 and each director is $90,000.

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The sum of 5 of the interior angles of a regular octagon is 675°.

Angles inside a polygon are referred to as interior angles. A triangle, for instance, has three internal angles. Interior angles are sometimes defined as "angles confined in the interior area of two parallel lines when they are crossed by a transversal."

A regular octagon has equal interior angles.

And one interior angle is equal to 135°.

The sum of 5 of the interior angles of a regular octagon,

= 135 x 5

= 675°

Therefore, the sum is 675°.

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Answer:

Step-by-step explanation:

As an example, let's say I have a pond 7 feet long, 6.5 feet wide, and 3 feet deep. That gives me approximately 1,000 gallons of water. The average recommended gallons per inch of fish is 10. To calculate how many inches of fish I can fit in my pond I would divide 1,000 by 10: 1,000/10 = 100.

I know it is not the answer but I hope this helps you.

The least common denominator for each pair of fractions is as follows:

33.) = 6

33.) = 634.) = 7

33.) = 634.) = 735.) = 30

The least common denominator is defined as the lowest number that can divide a given set of numbers.

28= 2×2×7

7 = 7

The least common denominator would be 7

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The amount of money that Joe needs to pay would be = $15,918.50

In the year 2018, the percentage of social security = 6.2%

Joe's taxable income= $128,400.00

The annual salary of Joe = $256,750.00

The amount of money that joe should not pay is 6.2% of $256,750.00.

That is;

= 6.2/100 × 256,750.00

= 1591850/100

= $15,918.50

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The measure of the largest exterior angle is 96°.

Heptagon is a two-dimensional shape with seven angles, seven vertices, and seven edges. This seven-sided polygon “heptagon” is made up of two words ‘Hepta’ and ‘Gonia’, which means seven angles. Another name given to it is septagon or 7-gon.

In heptagon, the sum of the interior angles is equal to 900 degrees. The sum of exterior angles of a heptagon is 360 degrees.

Here, x°+2x°+3x°+4x°+5x°+7x°+8x°=360°

30x°=360°

x°=12°

So, 8x°= 96°

Therefore, the measure of the largest exterior angle is 96°.

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Solution is in the attachment!!

The situation can be described by the equation x - 3 = 13 = x = 13 + 3 = x = 16.

A mathematical phrase with two equal sides and an equal sign is called an equation. An example of an equation is 4 + 6 = 10. 4 + 6 can be seen on the equal sign's left side, and 10 can be seen on the equal sign's right side. A relationship between two terms on either side of an equal sign is represented by a simple equation. The four mathematical operations of addition, subtraction, multiplication, and division are also used in simple equations, either singly or in combination.

no of egg is decreased e= x - 3

equation to represent the situation

x - 3 = 13

x = 13 + 3

x = 16

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3 pounds of grapes she buy grapes in the market.

A division is a process of splitting a specific amount into equal parts.

Given that each pound of grapes cost 0.85.

Clarissa buys grapes and pays a total of 2.55.

We have to find the number of pounds of grapes does she buy.

To find this we have to divide 2.55 by 0.85.

Two point five five by zero point eight five.

2.55/0.85

3 pounds of grapes.

Hence, 3 pounds of grapes she buy grapes in the market.

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The cost of each popcorn is $0.75 while the cost of each drink is $1.25

An equation is an expression that shows the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on

Let p represent the number of popcorn and d represent the number of drinks that Liliana bought.

Liliana spends $4.00 on 2 boxes of popcorn and 2 drinks, hence:

2p + 2d = 4       (1)

Nadette spends $5.25 on 2 boxes of popcorn and 3 drinks, hence:

2p + 3d = 5.25    (2)

To solve using elimination method, subtract equation 1 from 2, hence:

d = $1.25

substitute the value of d in equation 1 to get p:

2p + 2(1.25) = 4

p = $0.75

The value of p and d are $0.75 and $1.25 respectively

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The solution is Option A.

The sum of the infinite geometric progression is S = -( 9/5 )

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.

The nth term of a GP is aₙ = arⁿ⁻¹

The general form of a GP is a, ar, ar2, ar3 and so on

Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

Given data ,

Let the sum of the geometric progression be represented as S

Now , the equation will be

∑ n = 1 to ∝ ( -3 ( 3/8 )ⁿ )   be equation (1)

The sum of the infinite GP is S = a / ( 1 - r ) , where r is the common ratio

Substituting the values in the equation , we get

when n = 1

a₁ = -3 ( 3/8 )

a₁ = -9/8

when n = 2

a₂ = -3 ( 3/8 )²

a₂ = -27/64

So , the common ratio r = a₂ / a₁

The common ratio r = 3/8

Substituting the values in the equation , we get

The sum of the infinite GP is S = a / ( 1 - r )

The sum of the infinite GP is S = ( -9/8 ) / ( 1 - 3/8 )

The sum of the infinite GP is S = ( -9/8 ) / ( 5/8 )

The sum of the infinite GP is S = - ( 9/5 )

Hence , the sum of GP is - ( 9/5 )

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a) The measure of angle 3 is given as follows: m < 3 = 3x + 105.

b) The value of x is given as follows: x = 10.

c) It is not possible for a triangle to have side lengths 5, 8 and 14, as the sum of the lengths of the two smaller sides would be less than the length of the larger side.

The measure of angle 1 is given as follows:

m<1 = 3x + 15.

As the sum of the measures of the internal angles of a triangle is of 180º, and there is a right triangle, we have that angles 1 and 2 are complementary, hence:

m < 1 + m < 2 = 90

3x + 15 + m < 2 = 90

m < 2 = 75 - 3x.

An angle is always supplementary with it's exterior angle, hence the measure of angle 3 is obtained as follows:

m < 2 + m < 3 = 180

75 - 3x + m < 3 = 180

m < 3 = 180 - 75 + 3x

m < 3 = 3x + 105.

For an isosceles right triangle, the two non-right angles measure 45º, hence the value of x is obtained as follows:

3x + 15 = 45

3x = 30

x = 30/3

x = 10.

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The value of x are:

2) x = 18.87

3) x = 26.68

5) x = 35.52

6) x = 13.75

9) x = 3.69

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

2)

Tan 48 = x / 17

1.11 = x / 17

x = 17 x 1.11

x = 18.87

3)

Sin 67 = x / 29

0.92 = x / 29

x = 0.92 x 29

x = 26.68

5)

Cos 16 = x / 37

0.96 = x / 37

x = 0.96 x 37

x = 35.52

6)

Tan 58 = 22/x

1.6 = 22 / x

x = 22/1.6

x = 13.75

9)

Sin 24 = x / 9

0.41 = x / 9

x = 0.41 x 9

x = 3.69

Thus,

The value of x is given above.

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Answer:

a. Point C is at (8,8)

b. See image/expl

c. AngleABC = 140°

Step-by-step explanation:

You can just count squares to find the slope of AD. To find points along AD, go

UP1 and OVER4

UP1 and OVER4 is the slope 1/4.

Start from B and go

UP1 and OVER4.

Parallel lines have the same slope. Perpendicular lines have slopes with opposite sign and "flipped". To make CD perpendicular to AD the slope should be -4/1 or 4/-1 is the same thing. To find C go from D

UP4 and BACK1

this is the slope 4/-1

1/4 and 4/-1 are negative reciprocals (opposite sign and flipped over) so the lines will be perpendicular.

You cab use this explanation for part b. Or you the slope calculations using the coordinates. See image.

part c, see image.

Answer:If the radius of the cone is equal to one half the height, we can write the radius as r = h/2. Substituting this expression into the formula for the volume of a cone, we get:

V = 1/3 * (h/2)^2 * h = 1/3 * h^3 / 4

So, the volume of a cone in terms of the height, if the radius is equal to one half the height, is V = 1/3 * h^3 / 4.

Step-by-step explanation:

If the radius of the cone is equal to one half the height, we can write the radius as r = h/2. Substituting this expression into the formula for the volume of a cone, we get:

V = 1/3 * (h/2)^2 * h = 1/3 * h^3 / 4

So, the volume of a cone in terms of the height, if the radius is equal to one half the height, is V = 1/3 * h^3 / 4.