Referring to the figure, match the system of linear inequalities
with its graph.
a. -x + y < 2 b. -x + y > 2
-x + y ≥ -2 x + y ≤ -2
c. -x + y > -2 d. -x + y ≤ 2
x + y ≤ 2 x + y < 2

Answer:

(2/3)^3

8/27 in^3

Step-by-step explanation:

Answer:

3

0.29629629629in³

Step-by-step explanation:

To find the volume of a cube you multiply the length by the width by the height. Since all the sides of the cube are the same, its the same measure multiplied three times, ie. to the power of three.

(2/3)³=0.29629629629in³

-- least common multiple of 36, 6, 3 = 36

- it is the smallest number divisible by all three.

Answer:

(19228.737 ; 20771.263)

Step-by-step explanation:

Given that:

Sample size, n = 17

Sample mean, m = 20,000

Sample standard deviation, s = 1500

α = 95%

The confidence interval,

Mean ± margin of error

Margin of Error : Tcritical * s/sqrt(n)

Tcritical at α = 0.05 ; df = n-1 = 17 - 1 = 16 ; 2 - tailed test = 2.120

Margin of Error = 2.120 * 1500/sqrt(17) = 771.263

Lower boundary :

20,000 - 771.263 = 19228.737

Upper boundary :

20,000 + 771.263 = 20771.263

Confidence interval :

(19228.737 ; 20771.263)

The equation that models the taxi fare F as a function of the number of miles driven is F = 2.40 + 0.40m

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, the Topology Taxi Company charges 2.40 for the first fifth of a mile and 0.40 for each additional fifth of a mile.

The function will be:

F = 2.40 + (0.40 × m)

F = 2.40 + 0.40m

where m = number of miles

F = taxi fare.

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Answer:

where?

Step-by-step explanation:

The main belt is not located between these all planets.

What is orbit?

A route that an object in space follows around another is known as an orbit. A satellite is a thing that orbits the earth. An Earth- or moon-like natural satellite is one possibility. Moons are satellites that orbit many planets. A man-made satellite is also possible, such as the International Space Station.

The belt of asteroids is located between the orbits of Mars and Jupiter. The asteroids in this region, known as the main belt, are made up of small rocky bodies that orbit the sun in a region between about 2.2 and 3.2 astronomical units (AU) from the sun.

The distance from the sun to the Earth is about 1 AU, and the distance from the sun to Venus is about 0.7 AU, so the main belt is located beyond the orbits of both Venus and Earth.

The orbits of Saturn and Uranus are much farther out from the sun, at distances of about 9.5 and 19.2 AU, respectively, so the main belt is not located between these planets.

Hence, The main belt is not located between these all planets.

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Formulating an equation with a trigonometric ratio we have:

tan(17)=opposite/adjacent

tan(17)=x / 131 (Replacing the values)

tan(17)*131 = x (Multiplying on both sides by 131)

40.05 = x (Multiplying)

The answer is 40.05 ft.

Answer:

Step-by-step explanation:

4/x = x/9

1 = \(x^{2}\) / (9*4)

1 = \(x^{2}\) / 36

36 = \(x^{2}\)

6 =X

Answer: 26129.6

Step-by-step explanation:

6721 x 381 = 2560701

14 + 84 = 98

2560701  / 98 = 26129.6

Answer:

Final mixture is 120 gm

x = 10%      then   (120-x) = 25%

.25(120-x)    + .1 (x)    =  .15 (120)       solve for x= 10% amount

                                                                 then  25% amount = 120-x

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

180 - 120 = 60

An example of a function that models a linear relationship between two quantities, x and y is y = mx + b

We need to use the equation of a straight line, which is commonly expressed in slope-intercept form as:

y = mx + b

In this function, x represents the independent variable, m is the slope of the line, and b is the y-intercept. To use this function, we simply plug in the values of x, m, and b that correspond to the specific relationship we are modeling.

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The volume of the of box is derived to be 12 cubic inches, which makes option B correct.

The volume of the box also known as a cuboid can be calculated using the formula:

V = l x w x h

where:

V is the volume of the cuboid

l is the length of the cuboid

w is the width of the cuboid

h is the height of the cuboid

We shall evaluate for the volume of the box as follows:

Volume of the box = 3 in × 2 in × 2 in

Volume of the box = 12 in²

Therefore, the volume of the of box is derived to be 12 cubic inches.

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The volume of the of box is derived to be 12 cubic inches, which makes option B correct.

The volume of the box also known as a cuboid can be calculated using the formula:

V = l x w x h

where:

V is the volume of the cuboid

l is the length of the cuboid

w is the width of the cuboid

h is the height of the cuboid

We shall evaluate for the volume of the box as follows:

Volume of the box = 3 in × 2 in × 2 in

Volume of the box = 12 in²

Therefore, the volume of the of box is derived to be 12 cubic inches.

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The correct answer is C. $ 3,666.30 is in the savings account.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

Let's calculate how much money you have in the CD after 5 months, this way:

Gross Income = $ 4,520

Total deductions on taxes = 27.9% (11.75 + 7.65 + 8.50) * 4,520 = $ 1,261.08

Realized income = Gross income - Total deductions on taxes

Realized income = 4,520 - 1,261.08

Realized income = $ 3,258.92

Fixed expenses = 3,258.92 * 0.3 = $ 977.68

Emergency fund = 977.68 * 5 = $ 4,888.40

Certificate of Deposit = 4,888.40 * 0.75 = $ 3,666.30

The correct answer is C. $ 3,666.30

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Step-by-step explanation:

\underline{\textsf{Given:}}

Given:

\mathsf{Polynomial\;is\;x^3+7x^2+7x-15}Polynomialisx

3

+7x

2

+7x−15

\underline{\textsf{To find:}}

To find:

\mathsf{Factors\;of\;x^3+7x^2+7x-15}Factorsofx

3

+7x

2

+7x−15

\underline{\textsf{Solution:}}

Solution:

\textsf{Factor theorem:}Factor theorem:

\boxed{\mathsf{(x-a)\;is\;a\;factor\;P(x)\;\iff\;P(a)=0}}

(x−a)isafactorP(x)⟺P(a)=0

\mathsf{Let\;P(x)=x^3+7x^2+7x-15}LetP(x)=x

3

+7x

2

+7x−15

\mathsf{Sum\;of\;the\;coefficients=1+7+7-15=0}Sumofthecoefficients=1+7+7−15=0

\therefore\mathsf{(x-1)\;is\;a\;factor\;of\;P(x)}∴(x−1)isafactorofP(x)

\mathsf{When\;x=-3}Whenx=−3

\mathsf{P(-3)=(-3)^3+7(-3)^2+7(-3)-15}P(−3)=(−3)

3

+7(−3)

2

+7(−3)−15

\mathsf{P(-3)=-27+63-21-15}P(−3)=−27+63−21−15

\mathsf{P(-3)=63-63}P(−3)=63−63

\mathsf{P(-3)=0}P(−3)=0

\therefore\mathsf{(x+3)\;is\;a\;factor}∴(x+3)isafactor

\mathsf{When\;x=-5}Whenx=−5

\mathsf{P(-5)=(-5)^3+7(-5)^2+7(-5)-15}P(−5)=(−5)

3

+7(−5)

2

+7(−5)−15

\mathsf{P(-5)=-125+175-35-15}P(−5)=−125+175−35−15

\mathsf{P(-5)=175-175}P(−5)=175−175

\mathsf{P(-5)=0}P(−5)=0

\therefore\mathsf{(x+5)\;is\;a\;factor}∴(x+5)isafactor

\underline{\textsf{Answer:}}

Answer:

\mathsf{x^3+7x^2+7x-15=(x-1)(x+3)(x+5)}x

3

+7x

2

+7x−15=(x−1)(x+3)(x+5)

\underline{\textsf{Find more:}}

Find more:

Answer:

The answer would be 1.0005 x 10^12

Or, 1,000,500,000,000

Step-by-step explanation:

You take the first number, 1.0005 then move the decimal to the right 12 times.

Add zeros the the empty spots. Then you get your answer.

Answer:

what we have to find or to prove.

The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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The total surface area of the prism is determined as  216 cm².

The surface area of the prism is calculated by applying the following formula.

The area of the two triangular faces is calculated as follows;

Area of the two triangles = 2 (¹/₂ x base x height )

Area of the two triangles = 2 (¹/₂ x 6 cm x 4 cm )

Area of the two triangles = 24 cm²

The area of rectangular faces is calculated as follows;

A = ( 5 cm x 12 cm ) + (5 cm x 12 cm ) + ( 6 cm x 12 cm )

A = 192 cm²

The total surface area of the prism is calculated as follows;

Area = 24 cm² + 192 cm²

Area = 216 cm²

The sketch of the triangular prism is in the image attached.

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Answer:

x sells x

Step-by-step explanation:

$$$$$$$

Equation using slope intercept form is 3y = x + 18

An intercept in mathematics is a location on the y-axis through which the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses. This is reflected in the equation for a line, which is written as y = mx + b, where m denotes slope and c denotes the y-intercept. Y = mx + b is the general formula for the slope-intercept form, where m stands for the line's slope and b for the y-value of the line's y-intercept. We may more easily determine a line's slope and its y-axis intersection using the slope-intercept form of a linear equation.

Given Data

Points(0,6) and (-2,0)

The slope formula = \(\frac{y_{2}-y_{1 } }{x_{2}-x_{1} }\)

y₂= 0

y₁=6

x₂=-2

x₁=0

Slope = (-2-0)/(0-6)

Slope = -2/ -6

Slope = 1/3

Slope intercept form

y = mx + b

y = (1/3)x + 6

y = (x+18)/3

3y = x + 18

Equation using slope intercept form is 3y = x + 18

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The intermediate step in the form (x+a)²=b as a result of completing the square for the equation x² + 2x = 319 is (x+1)² = 320.

To use completing the square to solve the equation x² + 2x = 319, we have to write the left-hand side of the equation as a perfect square.

Add the square of half of the coefficient of x to both sides of the equation:

x² + 2x + (2/2)² = 319 + (2/2)²

x² + 2x + 1 = 320

The left-hand side of the equation can now be factored as a perfect square:

(x+1)² = 320

This is the equation in the form (x+a)²=b, where a=1 and b=320.

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The complete question is as follows:

What is the intermediate step in the form (x+a)²=b as a result of complementing the square for the following equation?

x² + 2x = 319

Where the above relations are given, note that Options A,  D, and E are the relations that represents a function. The others are just relations.

To distinguish a function from a relation, look to see if any of the x values are repeated; if not, the relationship is a function. If some x values are repeated but the accompanying y values differ, we have a relation rather than a function.

Note that where you are given domain and range, only the range is represented on the x-axis.

Some of the x values may be seen repeated in B, and C.

How is this so?

B) In a coordinate system, values are represented as (x, y). so

In relations, B 2 is repeated twice to in connection with -5, and -6. That is:

(2, -5) , (2, -6)

Since two is x, then its repetition nullified the relation as a function.

C) On table indicated on C, it is much easier to identify the x and y values. As is seen, -3 is repeated twice in connection with 4 and 2. Thus, its repetition nullified the relation as a function.

As a result, Options A,  D, and E are the relations that represent a function.

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Answer:

\(\frac{7}{11} * \frac{1}{4}\) = \(\frac{7}{44}\).

Cannot reduce it. Then it will make the numerator a decimal

Which cannot happen.

\(\frac{7}{44}\) is the answer then

Answer:

7/11 x 1/4 = 0.015

I hoped it helped you.

According to the information we can infer that the total yardage traveled from 0 to 120 seconds is 140 yards.

To calculate the total yardage traveled we have to consider the movement of the O'Connor Panthers. In this case we have to consider that the movement in the y axis.

In this case we can conclude that the total yardage traveled was 140 yards because:

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Answer:

43.15

Step-by-step explanation:

See attachment below

The equation that represents the total number of black and white squares on the chess board is 8 * 2² = 32

From the question, we have the following parameters that can be used in our computation:

The chess board

From the chess board, we have

Black squares = 32

White squares = 32

When factorized, we have

Black squares = 32 = 8 * 2²

White squared = 32 = 8 * 2²

Hence, the equation that represents the squares on the chess board is 8 * 2² = 32

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