For this question, use the information given in the situation, as well as your answers to the previous questions.

After looking through different hotel options, Gabriela and Luis decided to estimate a budget of $1,200 for hotel costs. They want to stay 6 nights at a hotel. In addition, they know they should plan to pay $240 in taxes and tips. Let c represent the total cost per night they should plan for the hotel.

1. How do you know that the solution you found in the previous question is correct?
2. What does the solution to the equation mean for the Morales family?

Write 2 or 3 sentences to answer the two questions. Be sure to use clear, correct math language. Number your responses (1 and 2) so that your teacher knows which question you are answering.Your response will be automatically saved. So, once you finish your response, wait a few seconds, and then move on to the next activity.

Answers

Answer 1

According to the information given, the equation that represents the situation is 6c - 1200 = 240.

What is a quadratic equation?

Any equation of the form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

The total costs are:

 $240 in taxes and trips.

 6 nights at the hotel, each night with a cost of c, hence 6c

Then:

T = 6c + 240

The budget is of $1200, hence, since the total cost is equals to the budget:

T = 1200

6c + 240 = 1200

Rearranging:

6c - 1200 = 240

Hence, according to the information given, the equation that represents the situation is 6c - 1200 = 240.

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Related Questions

slope: 3; y-intercept: -8

Answers

Answer:

Use desmos to help with slopes and finished equations its a graphing calculator and its very helpful

Step-by-step explanation:

Answer:

y=3x-8

Step-by-step explanation:

slope, or m (3), is always next to an x. y-intercept (-8) goes always after the mx

What is the coefficient of the x¹y³ term in the expansion of (x - 2y)'?
X
-8
560
-280
35

Answers

-280 Sorry I just need to answer

10pts and whoever gets this right gets brainliest✅️​

Answers

Answer:

Step-by-step explanation:

Your second option is your answer;

Arrow pointing to the right with circle filled. Your arrow would start at the 2.

5. Write the following Arithmetic Sequence using an Explicit Formula: a₁ = 8, an = an-1-2
an = 8+2(n-1)
an=8-2(n-1)
an=2-8(n-1)
an=2+8(n-1)

Answers

The explicit formula of the sequence is (b) a(n) = 8 - 2(n - 1)

How to determine the explicit formula

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

a₁ = 8,

aₙ = aₙ₋₁ - 2

In the above sequence, we can see that the 2 is subtracted from the previous term to get the current term

This means that

first term, a = 8

common difference, d = -2

The nth term is then represented as

a(n) = a + (n - 1)d

Substitute the known values in the above equation, so, we have the following representation

a(n) = 8 + (n - 1) * -2

Evaluate

a(n) = 8 - 2(n - 1)

Hence, the explicit is (b) a(n) = 8 - 2(n - 1)

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Hello can i get a little help giveing 20 points to who ever help and bralyles so yeh help

Answers

Answer:

a) n less than or equal to 21

b) n greater than or equal to 5

c) n > 3/5

Step-by-step explanation:

i hope this helps!!

Answer:

A.) n ≤ 21

B.) n  ≥ 5

C.) n > 3/5

Step-by-step explanation:

For the first question it says that the number is no more than 21, so it could be equal to or less than 21

For the second question, it says that the number is at least 5, so it could be equal to or greater than 5

Finally, for the last question it says that the number is more than 3/5, so greater than would be the correct inequality symbol to use

let f=(y2+z3,x3+z2,xz). evaluate ∬∂wf⋅ds for each of the following regions w:

Answers

For ∬∂WF⋅dS differentiable each of the following regions is 0, [tex]\frac{18 \sqrt{2}}{15}, -\frac{16 \sqrt{2}}{15}[/tex]

Let the f=[tex]\left(y^2+z^3, x^3+z^2, x z\right) \\[/tex],

Differentiability of Function: For a function to be differentiable at any point x=a in its domain, it must be continuous at that particular point but vice-versa is not always true. In complex analysis, complex-differentiability is defined using the same definition as single-variable real functions. This is allowed by the possibility of dividing complex numbers

Solution: For checking the continuity, we need to check the left hand and right-hand limits and the value of the function at a point x=a.

This means that f'(a) must exist, or equivalently:

[tex]$$\lim _{x \rightarrow a^{+}} f^{\prime}(x)=\lim _{x \rightarrow a^{-}} f^{\prime}(x)=\lim _{x \rightarrow a} f^{\prime}(x)=f^{\prime}(a)$$[/tex]

(A).

[tex]& x^{2 / t} y^2 \leq z \leq 2 \\\\& \int_{\theta=0}^{2 \pi} \int_{\gamma=0}^{\sqrt{2}} \int_{z=\gamma^2}^2 \gamma \cos \theta d z d \gamma d \theta \\\\&=\int_{\theta=0}^{2 \pi} \int_{\gamma=0}^{\sqrt{2}}[\gamma \cos \theta][z]_{\gamma^2}^2 d \gamma d \theta \\[/tex]

[tex]&=\int_{\theta=0}^{2 \pi} \int_{\gamma=0}^{\sqrt{2}}\left(2-\gamma^2\right) \gamma \cos \theta d \gamma d \theta \\\\&=\int_{\theta=0}^{2 \pi}\left[\gamma^2-\frac{\gamma^4}{4}\right]_0^{\sqrt{2}} \cos \theta d \theta \\\\&=\int_{\theta=0}^{2 \pi} \cos \theta d \theta \\\\&=[\sin \theta]_0^{2 \pi} \\&=0[/tex]

(B).

[tex]& \ x^2+y^2 \leq 2 \leq 2 . \quad, x \geqslant 0 \\[/tex]

[tex]& \int_{0=-\frac{\pi}{2}}^{\frac{\pi}{2}} \int_{\gamma=0}^{\sqrt{2}} \int_{z=\gamma^2}^2 \gamma^2 \cos \theta d z d \gamma d \theta . \\\\& =\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \int_0^{\sqrt{2}} \gamma^2 \cos \theta[z]^2 \gamma^2 \cdot d \gamma d \theta \text {. } \\[/tex]

[tex]& =\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \int_0^{\sqrt{2}} \cos \theta\left(2-\gamma^2\right) \gamma^2 d \gamma d \theta . \\\\& =\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos \theta\left[\frac{2}{3} \gamma^3-\frac{\gamma^5}{5}\right]_0^{\sqrt{2}} d \theta \text {. } \\[/tex]

[tex]& =\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos \theta\left[\frac{4}{3} \sqrt{2}-\frac{4 \sqrt{2}}{5}\right] d \theta . \\\\& =[\sin \theta]_{-\frac{\pi}{2}}^{\frac{\pi}{2}} d \theta\left[\frac{4}{4} \sqrt{2}-\frac{4 \sqrt{2}}{5}\right] \\\\& =\left[\frac{4 \sqrt{2}}{3}-\frac{4 \sqrt{2}}{5}\right] \\[/tex]

[tex]& =\left[\frac{4 \sqrt{2}}{3}-\frac{4 \sqrt{2}}{5}\right] \\\\& =\left[\frac{20 \sqrt{2}-12 \sqrt{2}}{15}\right]=2\left[\frac{8 \sqrt{2}}{15}\right] \\\\& =\frac{18 \sqrt{2}}{15}[/tex]

(C).

[tex]x^2+y^2 & \leqslant z \leqslant 2, x \leq 0 \\[/tex]

A+B+C

0=B+C

B=-C or C=-B

C=[tex]-\frac{16 \sqrt{2}}{15}[/tex]

Therefore, the differentiable of each function is 0, [tex]\frac{18 \sqrt{2}}{15}, -\frac{16 \sqrt{2}}{15}[/tex].

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Let F=[tex]\left(y^2+z^3, x^3+z^2, x z\right) \\[/tex]) . Evaluate ∬∂WF⋅dS for each of the following regions W:

A.[tex]& x^{2 / t} y^2 \leq z \leq 2 \\\\ \\[/tex]

B. [tex]& \ x^2+y^2 \leq 2 \leq 2 . \quad, x \geqslant 0 \\[/tex]

C. [tex]x^2+y^2 & \leqslant z \leqslant 2, x \leq 0 \\[/tex]

Given the inequality -6 (1 + 2x) ≥ 6 (2x - 1) + 2, which of the following are included in the solution? Select ALL that apply.



Ps. I chose just the answer 0 and only received a 1/3

Answers

Answer:

  A, C, E

Step-by-step explanation:

You want the values from the list that are included in the solution set of -6(1 + 2x) ≥ 6(2x - 1) + 2x.

Solution

Simplifying the inequality, we get ...

  -6 -12x ≥ 12x -6 +2x

  0 ≥ 26x . . . . . . . . . . . . . add 12x+6

  x ≤ 0 . . . . . . . . . . . . divide by 26

The solution set includes 0 (choice C) and all negative values (choices A and E).

help me solve this please

Answers

The inequality or number of units produced per hour is 15.50<10+0.50x.

What is Inequality?

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

According to the question the inequality can be

15.50<10+0.50x

15.50-10<0.50x

5.50<0.50x

5.50/0.50x

x> 11

For checking the Inequality

Let x=12.

15.50<10+.50*12

15.50+10+6

15.50<16

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Write the equation for a parabola with a focus at (-2, 5) and a directrix at x = 3.

Answers

First, we must find the distance from the focus to the vertex and the vertex to the directrix. There is a special property about parabolas: any point (x, y) on the parabola to the focus is equidistant from that point (x, y) to the directrix. Therefore, this means that from the vertex to the focus and from the vertex to the directrix, the lengths to these two features are equidistant. Generally, this equal distance is called “p.”

Let’s find “p:”

We know the parabola is opens to the left because the directrix is always below the vertex. So, we must find the distance between the two x-coordinates of -2 and 3 and divide that in half

-2+3/2=.5

Because the directrix and focus lie on the same y-coordinate, we can use that coordinate to determine the y-coordinate of the vertex. In this case, y=5.

This means the vertex is at (.5, 5) or (1/2, 5).

Now, we must determine how wide or stretched the parabola is, which is known as the “a” value in a(x-h)^2+k

The formula for a is:

a=1/4p

We know that p=.5

a=1/4(.5)

a=1/2

So, we have all the information to come the equation:

f(x)=1/2(x-1/2)^2+5

However, the function is inverted, so it is reflected across the line y=x. This means we must swap all x and y coordinates:

x=1/2(y-5)^2+1/2 is the equation

Solid chance this is way above your knowledge level



A parabola is a curve in the shape of a U that is defined as the set of all points that are equidistant to a fixed point (called the focus) and a fixed line (called the directrix).

To write the equation of a parabola with a focus at (-2, 5) and a directrix at x = 3, we can use the standard form of the equation of a parabola, which is:

y = (1/(4f))x^2 + k

Where f is the distance between the focus and the vertex (the point where the parabola changes direction), and k is a constant that determines the position of the parabola along the y-axis.

To find the value of f, we can use the distance formula:

f = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Where (x1, y1) is the coordinate of the focus and (x2, y2) is the coordinate of the vertex.

Since the focus is at (-2, 5) and the directrix is at x = 3, we can use the y-coordinate of the focus as the y-coordinate of the vertex, and the x-coordinate of the directrix as the x-coordinate of the vertex. Therefore, the coordinate of the vertex is (3, 5).

Substituting these values into the distance formula, we get:

f = sqrt((3 - (-2))^2 + (5 - 5)^2)

= sqrt((5)^2 + (0)^2)

= sqrt(25)

= 5

Now that we have the value of f, we can substitute it into the standard form of the equation of a parabola to get:

y = (1/(4*5))x^2 + k

= (1/20)x^2 + k

This is the equation for a parabola with a focus at (-2, 5) and a directrix at x = 3. The constant k determines the position of the parabola along the y-axis.

The length of the Bolden
Boat is 5.2 x 102 inches
long. The length of Riggin
is double the length of the
Bolden. How long is the
Riggin boat?

Answers

Answer:

This is answer of 530.4 Q

The dimensions of a rectangle are StartRoot 50 a cubed b squared EndRoot and StartRoot 200 a cubed EndRoot. A student found the perimeter as follows: 2 StartRoot 50 a cubed b squared EndRoot + StartRoot 200 a cubed EndRoot = 2 times 5 a b StartRoot 2 a EndRoot times 10 a StartRoot 2 a EndRoot. = 10 a b StartRoot 2 a EndRoot + 20 a StartRoot 2 a EndRoot. = 30 a b StartRoot 2 a EndRoot.

What is the student’s error?

Answers

The correction made by the student is incorrect simplification of 30ab√2a+20a√2a

What is perimeter?

The perimeter of a polygon is the sum of its, all the side lengths.

Given that, the dimension of a rectangle is given by, √50a³b² and √200a³

The perimeter of the rectangle is = 2(length + width)

Solving for the perimeter,

2(√50a³b²+√200a³)

= 2(5ab√2a+10a√2a)

= 10ab√2a+20a√2a

The student solved it as 30ab√2a,

Which is incorrect, because 'b' is not there in both the expressions, hence, we cannot add them.

Hence, The correction made by the student is incorrect simplification of 30ab√2a+20a√2a

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Answer:

Step-by-step explanation:

Answer is D on Edge,

The student incorrectly simplified 10ab sqrt 2a + 20a sqrt 2a

Which expression finds enzo’s net worth? 127,100 dollars minus 88,500 dollars 127,100 dollars divided by 88,500 dollars 88,500 dollars 127,100 dollars 88,500 dollars minus 127,100 dollars

Answers

An expression that finds Enzo's net worth is:

$ 127100 - $ 88500.

What is the net worth?

The amount by which the value of the assets exceeds the liabilities is the net worth (equity) of the business. The net worth reflects the amount of ownership of the business by the owners. The formula for computing net worth is. Assets - Liabilities = Net Worth.

Enzo's net worth is the difference between the amount of money he has and the amount of money he owes. Therefore, the correct expression is: 88,500 dollars minus 127,100 dollars.

net worth = Assets - liabilities

net worth = 127100 - 88500

net worth = 38600.

This expression would give us the difference between the two amounts, which is the net worth.

The other expressions are not correct because they do not represent the difference between the two amounts.

127,100 dollars minus 88,500 dollars would give us the difference between the two amounts, but this difference would be the opposite of the net worth.

127,100 dollars divided by 88,500 dollars would give us the ratio of the two amounts, which is not the same as the net worth.

88,500 dollars is just the amount of money that Enzo has, and it does not take into account the amount of money he owes.

127,100 dollars is just the amount of money that Enzo owes, and it does not take into account the amount of money he has.

Hence, An expression that finds Enzo's net worth is:

$ 127100 - $ 88500

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Find the dimensions of a right triangle if it’s area is 40m^2 where the height is 2 meters less than the base.


base = _ meters
height= _ meters

Answers

Answer:

The dimensions of the right triangle are 9 meters by 7 meters.
or
The base of the triangle is 9 meters, and the height is 7 meters (since the height is 2 meters less than the base).

Step-by-step explanation:

To find the dimensions of the right triangle, we can use the formula for the area of a triangle, which is:

A = 1/2 * b * h

Where b is the base and h is the height of the triangle. In this case, we know that the area of the triangle is 40 square meters, and the height is 2 meters less than the base, so we can write the equation as:

40 = 1/2 * b * (b - 2)

To solve for b, we can rearrange the equation to get b by itself:

40 = 1/2 * b^2 - b

Then, we can move all the terms involving b to the left-hand side of the equation and all the constants to the right-hand side:

1/2 * b^2 - b - 40 = 0

Next, we can use the quadratic formula to solve for b:

b = (-(-1) +/- sqrt((-1)^2 - 4 * (1/2) * -40)) / (2 * (1/2))

Which simplifies to:

b = (1 +/- sqrt(1 + 80)) / 1

Since b must be a positive number, we take the positive solution:

b = (1 + sqrt(81)) / 1

Therefore, the base of the triangle is 9 meters, and the height is 7 meters (since the height is 2 meters less than the base). Thus, the dimensions of the right triangle are 9 meters by 7 meters.

Factor the perfect-square trinomial in y = (x2 2x 1) − 1− 1. y = (x )2 − 1 −1

Answers

The perfect square trinomial in y = ( [tex]x^{2} + 2x + 1[/tex] ) -1 - 1 will be

[tex](x+1)^{2}[/tex]

The perfect square trinomial in y = (x + 2)2 - 1 - 1 will be

⇒ Null

A perfect square trinomial can be expressed as the square of a binomial,

We can write the first expression as,

y = [tex]x^{2} + 2x + 1[/tex]

y = [tex]x^{2} + 2x + 1 - 2[/tex]

⇒ [tex]x^{2} + x + x + 1[/tex]

⇒ [tex]x(x + 1) + 1(x + 1)[/tex]

⇒ (x + 1) (x + 1)

⇒ [tex](x + 1)^{2}[/tex]

Therefore, according to the first expression, [tex](x^{2} + 2x + 1) -1 - 1[/tex] is a perfect square binomial with the factor = [tex](x + 1)^{2}[/tex]

According to the second expression, y = (x +2)2 − 1 −1

This expression does not show any factors

Therefore, this second expression doesn't have any perfect square trinomial factors.

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Factor the perfect-square trinomial in y = (x2 + 2x + 1) − 1− 1, y = (x +2)2 − 1 −1

Answer: 1

Step-by-step explanation:

got it right

I'll give brainliest for the correct answers!!

Answers

Using proportions and constant of proportionality, the train always move the same distance and the cost is always the same

What is Proportions

Proportion can defined as the comparison between two numbers or ratios. Using proportions, when two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

The proportional relationship between two numbers can be represented as

y = kx

k = constant of proportionality

i)

In this question, let's determine if they have the same constant of proportionality.

y = kx

6 = k(2)

k = 3

12 = k(4)

k = 3

Since they have the same constant of proportionality, the train always go the same distance each minute.

ii)

The time travelled in 10 minutes

y = 3x

y = 3(10)

y = 30

The distance in 10 minutes is 30km

b)

Using constant of proportionality to determine if they have a proportional relationship;

y = kx

21 = k(3)

k = 7

42 = k(6)

k = 7

The equation is y = 7x and the constant of proportionality is 7.

The cost for each person is always the same

ii) From y = 7x

63 = 7x

x = 63 / 7

x = 9

The predicted number for a cost of $63 is 9

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Increase by
50%
Decrease by
5%
A number went into this machine and 57 came out.
What number went in?

Answers

Answer:

Step-by-step explanation:

Let x be the number that went in,

[x(1+50%)]x(1-5%)=57
x(1+50%)=60

x=40

The solution is, the number went in is 40.

What is percentage?

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,

given that,

when a number Increase by 50% & Decrease by 5%,

then, A number went into this machine and 57 came out.

Let x be the number that went in,

so, using the given condition, we get,

[x(1+50%)]x(1-5%)=57

x(1+50%)=60

x=40

Hence, The solution is, the number went in is 40.

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A kangaroo chae a rabbit that tart 150 feet ahead of the kangaroo. For every 12-foot leap of the kangaroo, the rabbit leap 7 feet. How many leap would the kangaroo have to make to catch up to the rabbit?

Answers

Rabbit leaps two feet. Kangaroo leaps sixteen feet. sEight time as far as the rabbit, the kangaroo jumps.

What is unitary method?

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. what kinds of values and units

Let's say you go to the store to buy six apples.

You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples. Recognizing the units and values is crucial when using the unitary technique to a problem.

Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.

We are aware of the quantity of apples and the amount of money in the aforesaid problem.

According to our question-

A bunny leaps two feet. The kangaroo leaps 16 feet. The kangaroo leaps eight times farther than the rabbit.

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Find the Area of the figure below, composed of a rectangle and a semicircle. The radius of the circle is shown. Round to the nearest tenths place.

Answers

Answer:

13 × 10 = 130 ( it's a rectangle)

5² π /2 ≈ 12.5 × 3.14 = 39.25 ( semicircle)

130 + 39.25 = 169.25 ≈ 170

(7×107)(8 x 10²) what is the anwser

Answers

Answer:

The correct answer would be 5000 x ^108

Step-by-step

show that f is continuous on (−[infinity], [infinity]). f(x) = 1 − x2 if x ≤ 1 ln(x) if x > 1

Answers

The function f is continuous on (-∞, ∞).

What are Continuous Functions?

A function f is said to be continuous at a point 'a' if,

lim ₓ→a f(x) = f(a).

f(x) = [tex]\left \{ {{1-x^2 if x\leq 1} \atop {ln x if x > 1}} \right.[/tex]

That is, if x ≤ 1, f(x) = 1 - x² and if x > 1, f(x) = ㏑ x

Taking interval (-∞, 1], f(x) is a polynomial 1 - x².

Polynomials are continuous everywhere. So f is continuous at (-∞, 1].

Now take the interval (1, ∞).

[tex]\lim_{x \to \infty} f(x)[/tex] = [tex]\lim_{x \to \infty} lnx[/tex] = ㏑ ∞ = ∞ = f(∞)

So f is continuous at the interval (1, ∞)

To check for continuity at 1,

lim x → 1⁻ f(x) = lim x → 1⁻ [1 - x²] = 1 - 1² = 0

lim x → 1⁺ f(x) = lim x → 1⁺ ㏑ x = ㏑ 1 = 0

So, lim x → 1⁻ f(x) = lim x → 1⁺ f(x)

So f is continuous in the whole interval (-∞, ∞).

Hence the function f(x) = [tex]\left \{ {{1-x^2 if x\leq 1} \atop {ln x if x > 1}} \right.[/tex] is continuous on the interval  (-∞, ∞).

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What is the circumference of a circle whose radius is 16 feet leave answer in term of pi please show ur work Bc I have too !!

Answers

Answer:

Step-by-step explanation:

Formula for Circumference of a circle is 2* pi * radius

If r=16

C= 2*π*16

C=32π

imagine that we rolled a fair, six-sided die 1,000 times. out of 1,000 rolls, how many times do you think the die would come up even (2, 4, or 6)?

Answers

Probability of Number of outcome is an even in likely situation is given as 512

Given that;

Number of time die roll = 1,000

Find:

Probability of Number of outcome is an even

Computation:

Probability of an even = 3 / 6

Probability of an even = 1 / 2

Probability of Number of outcome is an even = [Probability of an even]1000

Probability of Number of outcome is an even = [1/2]1000

Probability of Number of outcome is an even = 500

So most likely outcome is 512

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marquis has some quarters and dimes. he has 26 coins worth a total of $ 3.80 . how many of each type of coin does he have?

Answers

Each type of coin marquis have is 18

The value of a dime is ten cents. The value of a quarter is 25 cents. Dimes are smaller than quarters. Fun fact: Copper and nickel, the metal used to create quarters and dimes, are the same. One dime is equal to ten cents. The value of a penny, often known as a one-cent coin, is one cent.

A dime coin is equivalent to 10 one-cent coins in value (pennies). The word "dime" derives from the Latin word "decimus," which means "one tenth." When they came up with the concept of money being split into ten parts in the 1500s, the French adopted the word "disme." The spelling was altered from "disme" to "dime" in America.

Here  d  =  number of dimes

Here  q  =  number of quarters and

Number equation:  d + q  =  26

Value equation:  0.10d + 0.25q  =  3.80

Here the value for the equation is multiplied by 100:  10d + 25q  = 380

the two equations:

d + q  +  26   --->   multipling by -10   --->    -10d - 10q  =  -260

10d + 25q  =  380                                --->   10d + 25q  = 380

Adding the columns:                                   15q  =  120

                                                                            q = 120/15

                                                                            q  =  8

                                                                             d + q  =  26

                                                                             d+8=26 ;        

                                                                             d=26-8    

                                                                              d  =  18

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Given mn, find the value of x.
149⁰

Answers

X = 31

Hope this helps

find the area enclosed by the curve x = t2 − 3t, y = t and the y-axis.

Answers

The area enclosed by the curve x = t2 − 3t, y = t and the y-axis is 9/2

In this question we have been given parametric equations x = t^2 − 3t, y = t

In this question we need to find the area enclosed by the curve x = t2 − 3t, y = t and the y-axis.

The curve has intersects with y-axis.

Consider x = 0

So, t^2 − 3t =  0

t(t - 3) = 0

t = 0   or  t = 3

Let f(t) =  t^2 − 3t and g(t) = t

Now we have to draw the graph,

Differentiate the curve f(t) with respect to t.

f'(t) = 2t - 3

Now, find the area under the curve using the above formula

A = ∫[a to b] g(t)f'(t) dt

so, A = ∫[0 to 3] t (2t - 3) dt

A = ∫[0 to 3] (2t^2 - 3t) dt

A = [2/3 t^3 - 3/2 t^2]_[t = 0, t = 3]

A = 2/3 3^3 - 3/2 3^2

A = 18 - (3^3)/2

A = 18 - 27/2

A = 9/2

Therefore,  the area of the curve is 9/2.

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Work out the area of a rectangle with base B= 38mm and perimeter, P = 88mm

Answers

Answer:  the area of the rectangle is 456 square millimeters.

Step-by-step explanation:

the perimeter is 88 mm, so if we let L be the length of the rectangle and W be the width, we can write the following equation to find the perimeter:

2L + 2W = 88 mm

Since the base of the rectangle is 38 mm, we know that the width of the rectangle is 38 mm, so we can substitute that value into the equation above to get:

2L + 2(38 mm) = 88 mm

Solving for L, we get:

2L = 88 mm - 2(38 mm)

2L = 88 mm - 76 mm

2L = 12 mm

Therefore, the length of the rectangle is 12 mm. Now that we know both the length and the width, we can find the area by multiplying the length and the width:

Area = L * W

Area = 12 mm * 38 mm

Area = 456 mm^2

Thus, the area of the rectangle is 456 square millimeters.

Answer:

A=228mm

Step-by-step explanation:

What formulas do we know?

Parameter= 2(length)+2(width)

Area= length x width

We can just substitute in values for parameters so,

88=2(length) + 2(38)

88=2L + 78 ------> 12=2L -------> L=6

Now we know width (which is just B) and Length (what we calculated)

Now we use area ----> Area= length x width

Area= (38)(6)-----> 228mm

Determine wheather the graphs of y=2x+1 and y=-1/2x-7 are parallel, perpendicular, coincident, or none of these. PLEASE HELP ASAP!!!! will mark brainlest.

Answers

Answer:

b

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x + 1 ← is in slope- intercept form

with slope m = 2

y = - [tex]\frac{1}{2}[/tex] x - 7 ← is in slope- intercept form

with slope m = - [tex]\frac{1}{2}[/tex]

• Parallel lines have equal slopes

the slopes are not equal thus not parallel

• the product of the slopes of perpendicular lines is equal to - 1

2 × - [tex]\frac{1}{2}[/tex] = - 1

Thus the 2 lines are perpendicular to each other.

Hello help please

14+2n - -4(n-5)

Answers

Answer:8

Step-by-step explanation:

The drama club i elling ticket to their play to raie money for the how' expene. Each tudent ticket ell for $5 and each adult ticket ell for $7. 50. The auditorium can hold at mot 125 people. The drama club mut make no le than $790 from ticket ale to cover the how' cot. If 73 adult ticket were old, determine all poible value for the number of tudent ticket that the drama club mut ell in order to meet the how' expene. Your anwer hould be a comma eparated lit of value. If there are no poible olution, ubmit an empty anwer

Answers

This means that in order to make at least $790, the drama club must sell 47 number of student tickets. 47,48,49,50,51

The first equation is 5x + 7(73) = 790, where x is the number of student tickets. We can solve this equation to determine that x = 47. This means that in order to make at least $790, the drama club must sell 47 student tickets. Then, we can check the other possible values of x to see how many tickets they must sell. The other possible values are 48, 49, 50, and 51. Therefore, the answer is 47, 48, 49, 50, 51.

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Helpppppp pleaseeee thank you

Answers

The first NO

The second YES

The third NO

The forth YES
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