The expression 45h +225 represents the total cost in dollars of
renting a large party tent from a local rental store for h hours. Jamal's
parents are willing to spend between $500 and $750 for the tent.
Part A. Write an inequality to represent the possible lengths of time
the tent can be rented.
Part B. Using your inequality in Part A, what is one possible length of
time the tent could be rented? Give your answer in number of hours.

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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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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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.

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

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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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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Answer:

Step-by-step explanation:

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: 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! :)

Using mathematical operations of addition and subtraction, Rodrigo needs to buy additional 2⁷/₂₄ pounds of vegetables.

The basic mathematical operations are addition, subtraction, division, and multiplication.

These mathematical operations can be used to determine the results of mathematical expressions.

The total pounds of vegetables required for a stew = 3 pounds

Available pounds of vegetables:

Onions = 3/8 pounds

Tomatoes = 1/3 pounds

The total available pounds = 17/24 pounds

Additional pounds required = 3 - 17/24 pounds

= 2⁷/₂₄ pounds

Thus, based on addition and subtraction, Rodrigo needs additional 2⁷/₂₄ pounds of vegetables.

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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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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)

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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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:

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

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:

65c

Step-by-step explanation:

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 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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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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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:

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: 1) C- the survey participants should be randomly selected

2) C- how interested would you be in purchasing a blue car?
3) C- the stadiums front gate

Step-by-step explanation: I took the quick check.

Answer:

1. c

2. d

3. c

Step-by-step explanation:

[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]

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:

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

The equation of the line perpendicular to the given line is, y = 3x + 1.

What is slope of the line?

The change in y coordinate relative to the change in x coordinate is referred to as a line's slope in mathematics. The symbols Δy and Δx stand for the net change in the y-coordinate and the net change in the x-coordinate, respectively. where "m" denotes a line's gradient. tanθ then represents the slope of a line.

Consider, the given equation of line

[tex]y = -\frac{1}{3}x+4[/tex]

We have to find the equation of line passes through the point (-2, -5) and perpendicular to the given line.

Here, the point is (-2, 5).

First to find the slope of the line.

Since, the slope of the line, perpendicular to the given line is negative reciprocal of the slope of given line.

Here, the slope of given line is, -1/3.

So, the slope of perpendicular line is [tex]-(\frac{1}{(-\frac{1}{3}) }) = 3[/tex]

Therefore, the slope of the line is 3.

Now to find the equation of the line.

Consider, the point - slope form of the line

[tex]y-y_1=m(x-x_1)[/tex]

Plug [tex](x_1, y_1) = (-2, -5) , m = 3[/tex]

⇒

[tex]y-(-5)=3(x-(-2))\\y+5=3(x+2)\\y+5=3x+6\\y=3x+6-5\\y=3x+1[/tex]

Hence, the equation of line in slope - intercept form, is y = 3x + 1.

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