The equation y=1/5x+3.5 can be used to find the amount of accumulated snow y in inches x hours after 5 P.M. on a certain day. Graph this equation.

1 Yes  the set of rational expressions is closed under subtraction

2. Yes  the set of rational expressions is closed under multiplication

3. No  the set of rational expressions is not closed under division

1. The subtraction of two rational expressions results in another rational expression.

=  p(x)/q(x) - r(x)/s(x)= ((p(x)s(x) - r(x)q(x))/(q(x)s(x)))

this is also a rational expression.

2. The multiplication of two rational expressions results in another rational expression.

=(p(x)/q(x)) * (r(x)/s(x)) = ((p(x)r(x))/(q(x)s(x)))

this is a rational expression.

3. Division of two rational expressions may result in an expression that is not a rational expression.

= (p(x)/q(x)) / (r(x)/s(x)))

= ((p(x)s(x)) / (q(x)r(x)))

this may not be a rational expression if q(x)r(x) equals zero at some point, causing division by zero

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Answer:

12520

Step-by-step explanation:

Firstly , we need to find 25²

25 × 25 = 625

Then let us multiply before we add on ,

20 × 25² = 20 × 625 = 12500

12500 + 20 = 12520

And this is the final answer.

Question

20 + 20 × 25²

Answer:

Step by step explanation:

=20 + 20 × 25²

=20 + 20 × (25 × 25)

=20 + 20 × 625

=20 + 12.500

=12.520

results of 12.500 is 12.520

I hope this helps

Answer:

1/2x-2

Step-by-step explanation:

i might be wrong

The inequality will be 2 < 0.5x. Then the value of x is greater than 4.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Two less than 50% of x.

Then the inequality is written as,

2 < 0.5x

Then the value of x will be

x > 2/0.5

x > 4

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Answer:

c = 6.25

Step-by-step explanation:

We are given the following piecewise function:

\(\left \{ {{cx^{2} + 2x, x < 3} \atop {3x^{3} - cx, x \geq 3}} \right\)

Continuous function:

A function f(x) is continuous, at a point a, if:

\(\lim_{x \to a} f(x)\) exists and \(\lim_{x \to a} f(x) = f(a)\)

In this question:

Piece-wise function, so we have to verify if the limit exists.

The function changes at x = 3. So we verify at a = 3.

It will exist if:

\(\lim_{x \to 3^{-}} f(x) = \lim_{x \to 3^{+}} f(x)\)

To the left:

Less than 3.

\(\lim_{x \to 3^{-}} f(x) = \lim_{x \to 3^{-}} cx^{2} + 2x = c*(3)^{2} + 2*3 = 9c + 6\)

To the right:

Greater than 3.

\(\lim_{x \to 3^{+}} f(x) = \lim_{x \to 3^{+}} 3x^{3} - cx = 3*3^{3} - 3c = 81 - 3c\)

f continuous:

They have to be equal:

\(\lim_{x \to 3^{-}} f(x) = \lim_{x \to 3^{+}} f(x)\)

\(9c + 6 = 81 - 3c\)

\(12c = 75\)

\(c = \frac{75}{12}\)

\(c = 6.25\)

Answer:

981/100

Step-by-step explanation

step: 9.81= 9.81/1

step 2 multiply both too and bottom by 10

9.81/1 = (9.81*100)/(1*100)= 981/100

thus 981/100 is also equal to 9 81/100

The best breakfast that would be best on the morning of a test is cereal with milk and sweet roll. Hence, option B is correct

Breakfast is frequently referred to as "the most important meal of the day," and with good cause. Breakfast, as the name implies, breaks the overnight fast. Along with providing other crucial nutrients needed for optimal health, it replaces your glucose supply to increase your energy and alertness.

There is medical evidence that eating breakfast is beneficial. In addition to helping you control your weight better, reducing your risk of type 2 diabetes and heart disease in the long run, it also boosts your energy levels and concentration capacity in the near term.

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the function that models the inverse variation: y = 48/x. This can be solved using the formula of equation.

The meaning of such an equations in algebra is just a mathematical expression stating the equality between two mathematical terms. For instance, 6x + 5 = 11 is an equation where 6x + 5 and 11 are two expressions separated by the 'equal' sign.

Identity equations and conditional equations are the two types of equations. For just any value of both the variables, an equality remains true. Only such variables have values that make a condition expression true. Two expressions joined by an equals sign ("=") form an equation.

It is given that, x and y vary inversely

x - 12 = 0

therefore, x = 12

y - 4 = 0

therefore, y = 4

Equation of inverse variation is: y = c/x

4 = c/12

c = 48

Thus, equation of inverse variation is: y = 48/x

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Answer:

QR=11

Step-by-step explanation:

Answer:

80 degrees

Step-by-step explanation:

The sum of the angles in a triangle is 180 degrees so we can create the equation 70+30+x=180. This solves out to 80 so x=80 degrees.

A. The mass of the rock in ounce is 22400 ounce.

B. The mass of the rock in ton is 0.7 ton

1 pound = 16 ounce

Therefore,

1400 pound =1400 × 16

1400 pound = 22400 ounce

1 pound = 0.0005 ton

Therefore,

1400 pound =1400 × 0.0005

1400 pound = 0.7 ton

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The values of the trigonometric ratios are: a) - 7/5, b) -75 c ) -1/5  d ) -25/12

Trigonometric ratios are measurements of the lengths of two sides of a triangle. There are three basic trigonometric ratios: sine, cosine, and tangent.  Sine ratios are the ratios of the length of the side opposite the angle they represent over the hypotenuse

the give parameters are:

tanα = -4/3 where π/2 <α<π and sinβ = √3/2, 0<β<π/2

a)  sin(α+β)

Using the trig ratios tan = opp/adj

but from pyth. rule, 4² + 3² = h²

16+9 = h²

h = √25 = 5

Now from trig Sin(α+β)

4/5 + 3/5

=- 7/5

b) cos(α+β)

cos = ad/hypo

4/5 + 3/5

= -7/5

c) Sin(α-β)

4/5 - 3/5

-1/5

d) tan(α-β)

= -4/3 - 3/4

= (-16 - 9)/ 12

-25/12

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Answer:

i think u got it

Step-by-step explanation:

To answer the given questions, let's use conditional probability based on the information provided:

a. To find the probability that the selected student does not get a scholarship, given that they cannot get a job within 2 months after graduation, we can use Bayes' theorem. Let's denote the events as follows:

A: Not getting a scholarship

B: Not getting a job within 2 months after graduation

We want to find P(A|B), which is the probability of not getting a scholarship given that the student cannot get a job within 2 months. According to the given information, 25% of students who cannot get a job within 2 months get at least one university scholarship.

Using Bayes' theorem:

P(A|B) = (P(B|A) * P(A)) / P(B)

P(B|A) is the probability of not getting a job within 2 months given that the student does not get a scholarship. Since this information is not provided, we cannot determine this probability.

b. To find the probability that the selected student gets no university scholarship, we can use the law of total probability. Let's denote the events as follows:

A: Not getting a scholarship

B: Getting a job within 2 months after graduation

C: Not getting a job within 2 months after graduation

We want to find P(A), the probability of not getting a university scholarship. According to the given information, 60% of students get a job within 2 months after graduation, and among those students, 70% get at least one university scholarship. For students who cannot get a job within 2 months, 25% get at least one university scholarship.

Using the law of total probability:

P(A) = P(A|B) * P(B) + P(A|C) * P(C)

We don't have the values for P(A|B) or P(B) and P(A|C) or P(C), so we cannot calculate the exact probability of not getting a university scholarship.

Therefore, without additional information or values for conditional probabilities, we cannot provide specific numerical answers to these questions.

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Answer:

x² - 10x + 2

Step-by-step explanation:

(x - 2)(2x + 3) = 2x² + 3x - 4x - 6

= 2x² - x - 6

(3x² - 11x - 4) - (2x² - x - 6) = x² - 10x + 2

Answer:

24 gallons

Step-by-step explanation:

50% more than 16 is all of the 16 and another 50%.

50% of 16 is 8

You can logic this because 50% is half.

Or do a calculation:

.5 × 16 = 8

So now we nee to know what is all the 16 and plus 8 on top of that. It is 24.

16 + 8 = 24.

Answer:

Mochi

Step-by-step explanation:

Mochi

Each week theres a increase of 4 in Mochi's weight. So you will add 4 twice to get to the 5th week.

4th week : 17

5th week : 21

Kappa

In 4 weeks Kappa weighed 14, which is less that Mochi at the pace Kappa is going at.

on the 3rd week Kappa weighed 11

and 2nd week Kappa weighed 5

and 1st week Kappa weighed 3

Looking at the graph, we can give a rough estimate on the 5th week it's going to be 16 or 17 either way making Mochi heavier.

Answer:

Domain: -5,6,2,1,-3

Range: 13,18,-7,4,-1

Step-by-step explanation:

Domain is the independent value/ x / input

Range is the dependent value/ y / output

Answer:

\( - 8(45) + 482 = - 360 + 482 = 122\)

Answer: No they are the same.

Step-by-step explanation:

Step-by-step explanation:

no it is less due to negative sign if it is positive then we say it is bigger

Answer:

the answer would be 2.15

Step-by-step explanation:

first you would have to divded 64/5 by 30 and you get 2.15

Answer:

x=1

y=-5

P.S. hope it helped. If you have any questions, I'll be glad to answer them.❤

Hello !

Answer :

Explanation :

\( \to \boxed{ ({x}^{a}) {}^{b} = {x}^{ab} } \)

\( \to \boxed{ {x}^{ \frac{1}{n} } {}^{} = \sqrt[n]{x} } \)

\( ({x}^{4} ) {}^{ - \frac{2}{3} } = {x}^{- \frac{2}{3} \times 4} \\ \boxed{= {x}^{ - \frac{8}{3} } } \\ \boxed{= \sqrt[3]{ {x}^{ - 8} }} \\ \boxed{ = \sqrt[3]{ ({x}^{ 4}) {}^{ - 2} }}\)

Have a nice day ;)

Answer:

A

Step-by-step explanation:

The month of June has  40 sweets

Let the number of sweets in the month of June be  P

Given that April,  May and June collectively have 90 sweets

Given that May has three quarters of number of sweets as that of June

So we can write

\(\rm Number\; of \; sweets\; in \; May = \dfrac{3P}{4 } .......(1) \\\)

Similarly it is given that April has two third of sweets as that of May month and hence we can write

\(\rm Number\; of\; sweets \; in \; April = \dfrac{2}{3} \times \dfrac{3P}{4} = P/2 ......(2)\\\)

As the total number of sweets in  April,  May and June is  90

Let the number of sweets in  May be "M" and in April be "A"

We can write the following equation and solve it further

\(\rm M + A + P = 90\\From \;equations \; (1) \; and \; (2) \\\)

\(\rm P + 3P/4 + P/2= 90\\\\2.25 \; P = 90\\P = 40\)

So we can conclude that the month of June has  40 sweets

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Answer:

Step-by-step explanation:

wheres the diagram?

Answer:B

Step-by-step explanation:

Answer:

X = 66

Step-by-step explanation:

A straight line is equal to 180 degrees so if you have one side of that line you can figure out the inside angle.

Now that you have two of the angles inside the triangle add them up. All the interior angles of a triangle will add to 180. So add up 38 and 76 to get 114. Now do 180 - 114, you should get 66

so x = 66

Answer:

the answer should be y=1/3x+8

Solution:

Consider the following equations:

Equation 1:

Equation 2:

Equation 3:

Equation 4:

From equation 1, we get:

this is equivalent to:

this is equivalent to:

solving for A, we get:

then A = 3.

From equation 4, we get:

this is equivalent to:

this is equivalent to:

Thus A = 0.

But this is a contradiction since we had found that A =3. Then, the linear system has no solution (is incongruent).

a) The combined number of $3 carwashes for cars, c, and $5 carwashes for trucks or SUVs, t, needed can be represented by the equation y = c + t.

b) If only 5 cars are washed, the number of trucks or SUVs needed to be washed to raise the full $915 is 180.

An equation is a mathematical statement that shows that two mathematical expressions are equal or equivalent.

Equations use the equation symbol (=) to show the equality of expressions.

The total amount needed for the new equipment = $915

The charge for a car wash per car = $3

The charge for cash wash per truck or SUV = $5

Let the number of cars = c

Let the number of trucks or SUVs = t

c + t = y... Equation 1

3c + 5t = 915... Equation 2

If the number of cars, c = 5

From equation 2:

3c + 5t = 915

3(5) + 5t = 915

15 + 5t = 915

5t = 900

t = 180

Thus, from equation 2, we can determine that if cars are 5, the trucks or SUVs must be 180 to meet the target.

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Putting money into more than one kind of investment at a time is called Diversification.

This a technique which helps to reduce risk through investing in different sectors and opportunities.

It also involves putting money in more than one type of investment which makes Diversification the most appropriate choice.

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