Use the table to determine the appropriate model of the function, x       1             2             3             4             5       f(x)       15             12             9             6             3       linear quadratic cubic exponential

A ramp leading to the freeway overpass is 200 feet long and rises 37 feet. The measure of the angle formed between the ramp and the freeway is

[tex]\mathbf{ \theta = sin^{-1} \Big ( \dfrac{37}{200} \Big)}[/tex]

From the information given:

The  measure of the angle formed θ between the ramp and the freeway overpass can be determined by using the sine angle which is:

[tex]\mathbf{sin \theta = \dfrac{opposite}{hypotenuse}}[/tex]

[tex]\mathbf{sin \theta = \dfrac{37}{200}}[/tex]

[tex]\mathbf{ \theta = \dfrac{1}{sin} \Big( \dfrac{37}{200}\Big)}[/tex]

[tex]\mathbf{ \theta = sin ^{-1} \Big( \dfrac{37}{200}\Big)}[/tex]

Therefore, the measure of the angle formed between the ramp and the freeway is

[tex]\mathbf{ \theta = sin^{-1} \Big ( \dfrac{37}{200} \Big)}[/tex]

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Correct Answer:

p: The tire is flat. q: I will have to change it. p -> q

The expression x³ + 27 can be rewritten as (x + 3) (x² - 3x + 9).

The expression x³ + 27 can be rewritten using the formula for the sum of cubes, which is

a³ + b³ = (a + b) (a² - ab + b²)

In this case, we can recognize that 27 is equivalent to 3³

Therefore, we can set 'a' to be 'x' and 'b' to be '3' and apply the formula.

So, the expression x³ + 27 rewrites to:

x³ + 3³ = (x + 3)(x² - 3x + 9)

The expression x³+27 is rewritten as the sum of cubes by identifying a as x and b as 3, then applying the formula a³ + b³ = (a + b)(a² - ab + b²) to get (x + 3)(x² - 3x + 9).

The expression x³+27 can be rewritten using the sum of cubes formula. The sum of cubes formula is a³ + b³ = (a + b)(a² - ab + b²). In this case, x³ can be viewed as a^3 and 27 (which is 3³) as b³. Thus, to express x³ + 27 as a sum of cubes, we identify a as x and b as 3, and then apply the formula.

Using the sum of cubes formula:

Identify a = x and b = 3.

Substitute a and b into the sum of cubes formula: (x + 3)(x² - 3x + 9).

Simplify if necessary.

Therefore, x³ + 27 is rewritten as (x + 3)(x² - 3x + 9).

Answer:

A

Step-by-step explanation:

The solution is 3x+2y is less than or equal to 3 and 3x+4y is greater than or equal to 2

How to solve the inequality

Given the inequalities:

1. [tex]\( y < -\frac{3}{2}x + \frac{3}{2} \)[/tex]

2. [tex]\( y > -\frac{3}{4}x + \frac{1}{2} \)[/tex]

The inequality [tex]\( y < -\frac{3}{2}x + \frac{3}{2} \)[/tex] represents a dashed line with a slope of [tex]\( -\frac{3}{2} \)[/tex] and a y-intercept of [tex]\( \frac{3}{2} \)[/tex]. It does not include the points on the line (hence the dashed line).

3x + 4y = 2

The inequality [tex]\( y > -\frac{3}{4}x + \frac{1}{2} \)[/tex]

slope of [tex]\( -\frac{3}{4} \)[/tex]

y-intercept of [tex]\( \frac{1}{2} \)[/tex].

The region where both inequalities are simultaneously true

[tex]\( y > -\frac{3}{4}x + \frac{1}{2} \)[/tex]

and below the line

[tex]\( y < -\frac{3}{2}x + \frac{3}{2} \)[/tex]

This confirms the solution as the point (-2, 3) and the region it falls into on the graph.

"Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one".

For the given situation,

The sample space for rolling two cubes,

s = { (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6) }

⇒[tex]n(s)=36[/tex]

The event is getting the sum 8,

[tex]e=[/tex] { [tex](2,6), (3,5), (4,4), (5,3), (6,2)[/tex] }

⇒[tex]n(e)=5[/tex]

The formula to find the probability of event, [tex]P(e)=\frac{n(e)}{n(s)}[/tex]

⇒[tex]P(e)=\frac{5}{6}[/tex]

⇒[tex]P(e)=13.8\%[/tex] ≈ [tex]14\%[/tex]

Hence we can conclude that the probability that the sum is 8 is          5/36 ≈ 14%.

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The domain of the function is x ≤ 40, representing the maximum number of weeks Natalie can take to repay the loan.

The situation can be modeled by the function f(x) = 1800 - 45x, where x represents the number of weeks. The domain of this function represents the possible values for x. Since Natalie borrowed $1800 and agrees to repay $45 per week, the maximum number of weeks she can take to repay the loan is given by:

Therefore, the inequality that represents the domain of the function is x ≤ 40. This means that Natalie can take up to 40 weeks to repay the loan without exceeding the borrowed amount.

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The total distance covered by her is 0.81 miles.

Alyssa is jogging near Central Park.

She runs along 65th Street for about 0.19 miles, turns right, and runs along Central Park West for about 0.28 miles.

She then turns right again and runs along Broadway until she reaches her starting point.

We have to determine

How long is her total run to the nearest hundredth of a mile?

According to the question

She runs along 65th Street for about 0.19 miles, turns right, and runs along Central Park West for about 0.28 miles.

Alyssa's route can be considered a right triangle with legs of length 0.19 and 0.28 (hundredths).

The total distance run is determined by using the Pythagoras theorem.

Pythagorean theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Therefore,

The distance run by her is,

[tex]\rm x^2 = (0.19)^2 +(0.28)^2\\\\ x^2=0.0361 + 0.784\\ \\ x^2 = .1145\\ \\ x= \sqrt{.1145} \\\\ x= 0.34[/tex]

Therefore,

The total distance covered by her is,

= .34 + .19 + .28

= 0.81 miles

Hence, the total distance covered by her is 0.81 miles.

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No-Solution implies an inconsistent equation, while infinitely many solutions indicate a condition that holds true for any value of variable.

When an equation has No-Solution, it means that there is no value of variable that satisfies equation. In other words, equation represents an inconsistent condition, and solution set is empty. For example, equation 2x + 5 = 2x + 7 has no solution because the variable x cancels out, leaving an inconsistency (5 ≠ 7),

When an equation has infinitely many solutions, it means that any value of variable will satisfy equation. The equation represents a condition that is always true, regardless of chosen value.

For example, the equation x + 5 = x + 5 has infinitely many solutions because any value of x will make the equation true (such as x = 1, x = 2, x = 3, and so on).

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Answer:

Saturn has about 2,000 times more mass.

 Part A you would use 200-L ( since you have 400 feet total 200 feet would equal length plus width)

Part B 200 - 80 = 120

Part C 200-90 = 110

area = 90 x 110 = 9900 square feet

A vertical stretch in the context of graphing functions occurs when the function is multiplied by a positive constant greater than 1, resulting in the graph being stretched vertically by that factor without affecting the y-intercept.

A vertical stretch occurs when we multiply the function by a positive constant greater than 1. For example, if we have y = a f(x) and a is greater than 1, this results in the graph being stretched vertically by a factor of a. This type of transformation doesn't affect the y-intercept since the behavior of the graph at x=0 remains unchanged. Multiplying the independent variable by a constant such as 1/2 would result in a horizontal stretching or compression, but this is different from the vertical stretching effect we are discussing here.

Additionally, suppose the vertical stretch factor is a natural number. In that case, we can think of the stretched function as being the sum of the original function added to itself repeatedly that number of times. This additive property also extends to the derivative, as the derivative of the vertically stretched function is the original derivative multiplied by the stretch factor. This is known as the vertical stretch property in the context of derivatives and calculus.

Answer:

3

Step-by-step explanation:

.

.

.

The number of vertices will be 24. The correct option is D.

A prism is a polyhedron in geometry that has n parallelogram faces that connect the n-sided polygon basis, the second base, which is a translated duplicate of the first base, and the n faces. The bases are translated into all cross-sections that are parallel to them.

It is given that the number of vertices in a prism is twice the number of vertices of one of the bases. The number of the vertices of a regular prism with 14 faces and 36 edges is calculated as below:-

Use Euler's formula:-

V + F = E + 2

V + 14 = 36 + 2

V + 14 = 38

V = 38 - 14

V = 24

Therefore, the number of vertices will be 24. The correct option is D.

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Using Euler's formula, V + F = E + 2, with the given values for the faces (F = 14) and edges (E = 36), we determine there are 24 vertices in the prism. Considering a prism has twice as many vertices as one of its bases, it follows that one base has 12 vertices.

The question asks about the number of vertices on one of the bases of a regular prism that has 14 faces and 36 edges.

First, we use Euler's formula, which is V + F = E + 2, where V, F, and E represent the number of vertices, faces, and edges, respectively.

In this case, we have F = 14 and E = 36, so plugging these into Euler's formula gives us V + 14 = 36 + 2, therefore V = 24 vertices in total for the prism.

Since the prism has two congruent bases and the remainder of the faces are parallelograms connecting the bases, we can say that the number of vertices of the prism is twice the number of vertices of one of its bases.

So if V is 24, the number of vertices for one base is V/2, which is 12. That means each base of the prism has 12 vertices.

Final answer:

To calculate the mailing cost for an 8-pound package sent first class, convert to ounces, then apply the charges for the first ounce and each subsequent ounce. The total cost is $25.84.

Explanation:

The question involves calculating the total cost of mailing a package that weighs 8 pounds, first class, with specific charges for the first ounce and each additional ounce. To calculate the cost, we first need to convert the package's weight from pounds to ounces. There are 16 ounces in 1 pound, so an 8-pound package is equivalent to 8 x 16 = 128 ounces.

The post office charges $0.44 for the first ounce. Thereafter, it charges $0.20 for each additional ounce. The cost for the additional ounces is $0.20 x (128 - 1) = $25.40. Now, add the cost for the first ounce, so the total cost is $0.44 + $25.40 = $25.84.

The solution to the equation is y = 2 + 2x.

We have,

To solve the equation 6x - 3y = -6 for y, we can isolate the term with y by performing the following steps:

Start with the equation: 6x - 3y = -6.

To isolate the term with y, subtract 6x from both sides of the equation:

6x - 3y - 6x = -6 - 6x.

This simplifies to: -3y = -6 - 6x.

Next, divide both sides of the equation by -3 to solve for y:

(-3y) / -3 = (-6 - 6x) / -3.

This simplifies to: y = 2 + 2x.

Therefore,

The solution to the equation is y = 2 + 2x.

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Answer: Hello!

In the figure, Q and P are on opposite ends of the circle, and the same is for R and S, which means that the line that connects Q and P, or R and S, divides the circle in two equal halves. From this, we know that the angle between QoP is 180°, and the same for the angle RoS = 180°.

We also know that the angle RoP = 125°, then the angle between Q and R is the same as the angle between Q and P minus the angle between R and P.

this is : QoR = QoP - RoP = 180° - 125° = 55°

then QoR and RoP are supplementary angles, wich means that the addition adds up to 180°.

And is easy to see that the angles SoQ and PoS are reflexes of RoP and QoR respectively, then:

SoQ = 125° and PoS = 55°, where this angles also are supplementary.