Write and solve an inequality to find the values of x for which the perimeter of the rectangle is less than 122.
A rectangle has a width of x and a length of x plus 4.

The missing values of the ordered pairs using the given equation are:

x = -1; y = 8

The computed table is:

x  | y  

-3   8

-1,   2

To complete a table of values, we can plug in the known value of each of the ordered pairs that are represented in a table into the given equation that models the relationship, then find the value of the missing variable.

The equation that represents the relationship between x and y is given as y = -3x - 1.

Find the value y in the ordered pair (-3, y) by substituting x = -3 into y = -3x - 1:

y = -3(-3) - 1 = 8

y = 8

Find the value x in the ordered pair (x, 2) by substituting y = 2 into y = -3x - 1:

2 = -3x - 1

Add 1 to both sides

3 = -3x

Divide both sides by -3

x = 3/-3

x = -1

The ordered pairs with the missing values are: (-3, 8) and (-1, 2).

The table would be computed as:

x  | y  

-3   8

-1,   2

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Answer:

65c

Step-by-step explanation:

The runner's speed If a runner traveled a distance of d(h)=/16h4 in time t(h) = 3h^4 - 3h^3 -5h^2 is  4 /3h^2 - 3h -5h.

The concept that will be used to calculate this is the concept of speed which is the ratio of the distance per time which can be expressed as

speed = distance/time

Then we were given distance as d(h)=/16h^4

time as  t(h) = 3h^4 - 3h^3 -5h^2

Speed = [tex]\sqrt{16h^4} /3h^4 - 3h^3 -5h^2[/tex]

Then we will have 4h^2 /3h^4 - 3h^3 -5h^2

then  take h^2 from both the numerator and denominator and then cancel them , then we will have

= 4 /3h^2 - 3h -5h.

Therefore, the first option is correct.

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Step-by-step explanation:

your teacher gave you the solution to the real problem of this question : how many cups are in 1 gallon. 16 cups.

and if you remember that a year has 365 days, then the rest is rant simple and straight forward :

8 cups per day

so

365 × 8 = 2920 cups per year.

2920 cups = 2920/16 = 182.5 gallons

therefore, she drinks 182.5 gallons of water per year.

Answer:

9 m

Step-by-step explanation:

given,

area of floor of play pen = 5 m²

we know, area of a square = (side)² sq units

now according to the question,

5 = (side)²

⇒√(side)² = √5 [taking square root on both sides]

⇒ side = √5 m

now, we know,

perimeter of a square = 4 × side = 4 × √5 = 8.94 m (app.) ≈ 9 m

Step-by-step explanation:

so there sre 104 postcards .so what we do is 104 ÷ 4 post cards on each page , it will then = to 26 pages

[tex]{ \pink{ \boxed{ \purple{ \sf{f(3) = 98}}}}}[/tex]

Step-by-step explanation:

[tex]{ \blue{ \tt{f(x) = 2 {x}^{4} - 8 {x}^{2} + 5x - 7}}}[/tex]

[tex]{ \blue{ \tt{f(3) = 2( {3})^{4} - 8( {3})^{2} + 5(3) - 7}}}[/tex]

[tex]{ \blue{ \tt{f(3) = 2(81) - 8(9) + 15 - 7}}}[/tex]

[tex]{ \blue{ \tt{f(3) = 162 - 72 + 8}}}[/tex]

[tex]{ \blue{ \tt{f(3) = 162 - 64}}}[/tex]

[tex]{ \red{ \boxed{ \green{ \sf{f(3) = 98}}}}}[/tex]

A table of equivalent ratios for the miles and gallons of gas driven is as follows:

Miles        Gallons

39                 1

117                 3

312                8

The data points are plotted in the graph shown in the image attached below.

In Mathematics, a proportional relationship can be modeled or represented by the following mathematical expression:

x = ky

Where:

In order to have a proportional relationship and equivalent ratios, the variables x and y must have the same constant of proportionality.

Next, we would calculate the constant of proportionality (k) as follows:

Constant of proportionality (k) = x/y

Constant of proportionality (k) = 312/8

Constant of proportionality (k) = 39.

When x = 39, the value of y is given by:

y = x/k

y = 39/39

y = 1 gallons.

When y = 3, the value of x is given by:

x = ky

x = 39 × 3

x = 117 miles.

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Considering the given translation, the vertex that is not part of the image is:

H(3,0).

The translations to an image are represented as follows:

The vector notation of a translation is given as follows:

{x ± a, y ± a}

In this problem, this notation is:

{3, -3}.

Hence the rule applied to each vertex of the image is:

(x,y) -> (x + 3, y - 3).

The vertices of the original figure are as follows:

( -7, 3), (- 4,6), ( -1, 3) and (-4, 0)

Applying the translation rule, the vertices of the image are given as follows:

(-4, 0), (-1, 3), (2, 0), (-1, -3).

The lone coordinate without a vertex of the image is H(3,0).

The problem is given by the image at the end of the answer.

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Part A Write an inequality to represent the possible lengths of time

the tent can be rented

[tex]6.11\leq h\leq 11.66[/tex]

Part B. Using your inequality in Part A, what is one possible length of

time the tent could be rented

[tex]6hr 6min\leq h\leq 11hr39min[/tex]

The definition of a linear inequality

The inequality symbol is used to compare two mathematical expressions in what are referred to as linear inequalities. The expression could be both numerical and algebraic, or it could just be one.

What does a linear inequality in mathematics look like?

What Is an Example of Linear Inequality? An example is the linear inequality x - 5 > 3x - 10. The LHS is obviously greater than the RHS because the greater than symbol is being utilized in this inequality. After being resolved, the inequality appears as follows: 2x 5 x (5/2).

Given That

45h+225 is total cost in dollars for renting tent and parents are willing to spend between $500 and $750 for the tent.

Part A

[tex]500\leq 45h+225\leq 750\\500-225\leq 45h+225-225\leq 750-225\\275\leq 45h\leq 525\\\frac{275}{45} \leq h\leq \frac{525}{45} \\6.11\leq h\leq 11.66[/tex]

Part B

[tex]6.11hr\leq h\leq 11.66hr[/tex]

6.11 hr = 366 minute approx.

11.66 hr = 699 minute approx.

[tex]6hr 6min\leq h\leq 11hr39min[/tex]

Hence this is the answer

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Answer:

x > -2

Step-by-step explanation:

3x - 10 < 4x - 8

Collect like terms

3x - 4x < 10 - 8

-1x < 2

Divide both sides by -1

-1x/-1 < 2/-1

x > -2

Yes, the graph shown represents a function for 0 < x < 6 because its domain is true about the given interval.

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

The function is given in the represented graph

According to the given graph, we can see the value of the domain of the given function f(x) when the function includes all possible variables of x values of a function.

Here the domain of the given function is  0 < x < 6

Therefore, the graph shown represents a function for 0 < x < 6 because its domain is true about the given interval.

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Answer:

7

Step-by-step explanation:

13x - 7 + 30 = 30 + 84

13x - 7 + 30 - 30 = 30 - 30 + 84

13x - 7 = 84

13x = 84 + 7

13x = 91

x = 91 / 13

x = 7

Answer:

the slope is 1.75

Step-by-step explanation:

Interpretation: The weight of newborn is 6 lb at birth, and every month baby gained 1.75 lb. You replace x with month you want to know the weight.  For example you can calculate the weight after 4 month : w= 1.75(4)+6= 13 lb

Answer: Yes, Probably

Step-by-step explanation:

there are 18 dogs to choose 1 dog.

therefore, these are 18 options.

for each of these 18 options there are 24 cats to choose from.

so, altogether, there are

18×24 = 432

dog-cat options.

There are are 432 ways to choose dog-cat options are possible for the producer.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.

Total Number of Dogs= 18

Total Number of cats= 24

so, the number easy to select

= 18 x 24

= 432

Hence, there are 432 ways to choose dog-cat options are possible for the producer.

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The equation of a line perpendicular to -5x + y = 9 that passes through the point (0, -9) is [tex]y = -\frac{1}{5}x -9[/tex]

The equation of the line in slope intercept form can be represented as follows:

y = mx + b

where

Perpendicular lines follows the following rules as follows:

m₁ m₂ = -1

Let's find the slope of -5x + y = 9 .

y = 5x + 9

Hence,

slope = 5

Let's find the slope of the equation of the line that passes through (0, -9) and perpendicular to  -5x + y = 9 .

5m₂ = -1

m₂ = -1 / 5

m₂ = - 1 / 5

Therefore, let's find the y-intercept of the line using (0, -9)

-9 = - 1 / 5(0) + b

b = -9

Therefore, the equation of the line is y = - 1 / 5 x - 9

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The factor of the difference of two squares (x + 2)² - (y - 2)² is (x + y)(x - y + 4).

If for any two squares say a² and b², then their difference a² - b² = (a + b)(a - b).

Given the two squares (x + 2)² and (y - 2)²

then their difference will yeild the factors derived as follows;

(x + 2)² - (y - 2)² = [(x + 2) + (y - 2)][(x + 2) - (y - 2)]

open brackets

(x + 2)² - (y - 2)² = (x + 2 + y - 2)(x + 2 - y + 2)

collect like terms

(x + 2)² - (y - 2)² = (x + y + 2 - 2)(x - y + 2+ 2)

so

(x + 2)² - (y - 2)² = (x + y)(x - y + 4)

Thus, by application of the rule of difference of two squares, we have the factors of (x + 2)² - (y - 2)² to be (x + y 2 - 2) and (x - y + 2+ 2).

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The Diameter of the cube would be 3 inches

What is Variation?

A variation is a relationship that exists between a set of values for one variable and a set of values for other variables.

Solution:

We know that,

Horse Power is directly proportional to RPM * Diameter

So, we can write

Horse Power = k * RPM * Diameter

here, k is any constant

From the first case given, we can find the value of k

16 = k * 2 * 120

k = 1/15

Putting the value of k in second case,

30 = 1/15 * 150 * Diameter

Diameter = 3 inches

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Answer:

See below.

Step-by-step explanation:

Each of the graphs shows a line segment, but because of the arrowheads, each situation is different.

Left graph.

The line segment has a point at each end. The graph is of just the line segment shown.

The lowest x-coordinate is -4.

The greatest x-coordinate is 3.

The lowest y-coordinate is 2.

The greatest y-coordinate is 5.

Domain: -4 ≤ x ≤ 3

Range: 2 ≤ x ≤ 5

In interval notation:

Domain: [-4, 3]

Range: [2, 5]

Middle graph.

The line segment has a point at the right endpoint but an arrowhead at the left. The graph is a ray that starts at point (2, 2), goes through point (-4, 5) and keeps going forever past point (-4, 5) in the direction of the segment.

The lowest x-coordinate is -∞.

The greatest x-coordinate is 2.

The lowest y-coordinate is 2.

The greatest y-coordinate is ∞.

Domain: x ≤ 2

Range: x ≥ 2

In interval notation:

Domain: (-∞, 2]

Range: [2, ∞)

Right graph.

The line segment has an arrowhead at each end. The graph is a line that includes the line segment shown. A line has no beginning and no end; therefore, it goes on in both directions forever.

The lowest x-coordinate is -∞.

The greatest x-coordinate is ∞.

The lowest y-coordinate is -∞.

The greatest y-coordinate is ∞.

Domain: all real numbers

Range: all real numbers

In interval notation:

Domain: (-∞, ∞)

Range: (-∞, ∞)

Answer:

1.  Domain: [-4, 3]    Range: [2, 5]

2.  Domain: (∞, 2]    Range: [2, ∞)

3.  Domain: (-∞, ∞)    Range: (-∞, ∞)

Step-by-step explanation:

Domain: The set of all possible input values (x-values).

Range: The set of all possible output values (y-values).

An open circle indicates the value is not included in the interval.

A closed circle indicates the value is included in the interval.

An arrow shows that the function continues indefinitely in that direction.

Note:  Assume that each square on the given graphs is 1 unit.

Question 1

There are closed circles at both endpoints of the line: (-4, 2) and (3, 5).

Therefore, the values are the endpoints of the intervals.

Question 2

There is a closed circle at (2, 2).

There is an arrow at one endpoint, so as x → -∞, y → ∞.

Question 3

There are arrows at the endpoints of the line.

Therefore, the domain and range are unrestricted.

The function is positive and increasing from 0 to 2.5, at negative and decreasing  from 0 to -2.5,  respectively.

How to find returns to scale?

Returns to scale involves an increase in an output more than when all the inputs increase proportionately.

Using the graph, there is a line segment from the origin to a point. at the middle of the third block making 2.5.

This shows an increase which is positive and on the other hand, there is a line segment from the origin towards left hand side on the number line showing a decrease and a negative from 0 to -2.5.

In conclusion, the line pointing upwards towards right hand side shows both positive and increase while the line pointing leftward shows decrease and negative.

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The rational zeros for f(x) = 3x^4 - 4x^3 + x^2 + 6x - 2 are x = -1 and x = 1/3 whereas the linear factors of f(x) are (x + 1) and (3x - 1).

We will use the synthetic division method to determine the rational zeros and linear factors of given polynomials.

Polynomials are divided via synthetic division.

The procedure entails of synthetic division:

Step 1: Create a synthetic divide.

Step 2: Bring the leading coefficient down to the bottom row.

Step 3: Divide this by the value stated in the bottom row.

Step 4: Finally, add the column you defined in step 3.

This can proceed as:

Given: f(x) = 3x⁴- 4x³ + x² + 6x - 2

3x⁴ - 4x³ + x² + 6x - 2 = 0

We will put x = -1 in f(x). In this case, replace x with -1. This will be:

f(-1) = 3 * 1⁴ - 4 * 1³ + 1² + 6 * 1 - 2 = 0

Since f(-1) = 0, so (x + 1) is a factor of f(x).

Using synthetic division:

-1)....3....-4....1....6....-2

.........3.....-7...8....-2..|..0

Remainder = 0

Quotient = 3x³ - 7x² + 8x - 2

For 3x³ - 7x² + 8x - 2,  f(1/3) = 0, so (x - 1/3) is a factor.

1/3)....3....-7....8....-2

..........3.....-6...6...|..0

Remainder = 0

Quotient = 3x² - 6x + 6 = 3(x² - 2x + 2)

Because x² - 2x + 2 has no more rational zeros or linear components. The rational zeros are hence x = -1 and x = 1/3.

Thus, the rational zeros for f(x) = 3x^4 - 4x^3 + x^2 + 6x - 2 are x = -1 and x = 1/3 whereas the linear factors of f(x) are (x + 1) and (3x - 1).

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Answer: See coordinate graph below.

Step-by-step explanation: Again, the black point is the original point and the red point is the reflected point.

Ordered pair of the reflected point:

D': (-6, 5)

Have a great day! :)

Answer: There are 52 cards in a standard deck and half of them, 26 in all, are red.

Suppose that you are drawing 4 cards without replacement from a thoroughly shuffled deck. You have 26 cards choose 4 over 52 choose 4.

∴  P(pulling 4 cards from deck) =  (264)(524)

An amount of $ 92,495.60 must be the initial deposit to become into $ 300,000 by compound interest.

In this problem we must determine the initial deposit that must become into $ 300,000 by compound interest after a period of 30 years. Compound interest model is a model where money gains interest continuously, whose formula is:

C' = C · (1 + r / 100)ⁿ

Where:

If we know that C' = 300,000, r = 4 and n = 30, then the initial deposit is:

C = C' / (1 + r / 100)ⁿ

C = 300,000 / (1 + 4 / 100)³⁰

C = 92,495.60

The initial deposit must be $ 92,495.60.

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Answer:

[tex]\frac{50}{50\\}[/tex] [tex]= \frac{65}{50}[/tex]

Now cross-multiply

Let p represent the percentage

50(50) = 50(65) ; 2500p = 3250

now divide 2500 on both sides to find p

2500p/2500 and 3250/2500

p = 1.3 ; percentage change is equal to %1.3 increase

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

-28,100 if you subtract 29,700.00 - 1,600.00  =  -28,100