Evaluate the expression for x=3 and y=5:(3y - 6)/x

Answers

Answer 1

Let's evaluate the expression by applying the Substitution Method.

Let's substitute x = 3 and y = 6 to the expression:

[tex]\text{ }\frac{3y\text{ - 6}}{x}[/tex]

We get,

[tex]\text{ }\frac{3y\text{ - 6}}{x}\text{ = }\frac{3(5)\text{ - 6}}{3}[/tex][tex]\text{ = }\frac{15\text{ - 6}}{3}\text{ = }\frac{9}{3}[/tex][tex]\text{ = }3[/tex]

Therefore, the expression (3y - 6)/x at x = 3 and y = 5 will give you a value of 3.


Related Questions

Santino tried to find the median from the following table, which shows the number of internet users in 2012 20122012 for the highest using countries. However, he made a mistake. Country China United States Japan India Brazil Number of internet users (in millions) 568 568568 254 254254 101 101101 152 152152 100 100100 Here is Santino's work: "The numbers are 568 568568, 254 254254, 101 101101, 152 152152, and 100 100100. There are 5 55 values, so the middle value is the 3 rd 3 rd 3, start superscript, start text, r, d, end text, end superscript value, 101 101101. The median is 101 101101 million internet users." What mistake did Santino make?

Answers

The median of the data set is 152 . Santino made the mistake of not arranging the numbers in the set.

The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory.

It could be referred to as "the middle" value for a data set. The fundamental difference between the mean and the median when describing data is that the median is more representative of the "normal" value because it is not skewed by a tiny fraction of exceptionally big or small values. Due to the fact that income distribution can be very skewed, the median income, for instance, might be a better indicator of what is considered a "normal" income. Given that it is the most resilient statistic, the median is crucial to strong statistics.

the numbers of the data when arranged are :

100 ,101 , 152 ,254 ,568

Here n =5

Median =(n+1)/2 th data

or , median = 3rd data

or, median =152

Therefore Santino did not arrange the data in ascending order to find the median. the correct median is 152.

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Answer:

Santino should have ordered the numbers from least to greatest before picking the middle number.

Step-by-step explanation:

She earns $12 per hour working at a store.
She earns $30 per lawn mowed working for a landscaper.
Her goal is to earn $1,800 to pay her monthly expenses.

The situation can be modeled by the formula below, where represents the hours Tina works in the grocery store and represents the number of lawns mowed.

Answers

Answer:

Change Mixed fraction to improper fraction 2/9

(Laws of Exponents with Integer Exponents LC) Create an equivalent expression for 9−7 • 95.

Answers

The expression 9⁻⁷ • 9⁵ when simplified is 9⁻²

How to evaluate the expression?

The expression is given as

9−7 • 95.

Rewrite properly

9⁻⁷ • 9⁵

The base of the above expression are the same

i.e. Base = 9

This means that we can apply the law of indices

When the law of indices is applied, we have the following equation:

9⁻⁷ • 9⁵ = 9⁻⁷ ⁺ ⁵

Evaluate the sum in the above equation

So, we have

9⁻⁷ • 9⁵ = 9⁻²

Hence, the simplified expression of the expression given as 9⁻⁷ • 9⁵ is 9⁻²

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Use the information to find and compare ∆y and dy (Round your answers to three decimal places.)
y=4x^3 x=2 ∆x=dx=0.1

Answers

The values of derivatives Δy and dy are given as 0.48 and 4.8

The values of Δy and dy will be calculated using the formula Δy = f(x + Δx) - f(x) and dy = f'(x)dx. For calculating the values, we put the values which are given in the question that is

Δy = f(x + Δx) - f(x)

Δy = f(2 + 0.1) - f(2)

Δy = f(2.01) - f(2)

Δy = 4(2.01)³ - 4(2)³

Δy = 32.48 - 32

Δy = 0.48

Now, we have f(x) = 4x³, so we have f'(x) = 12x²

Now, dy = f'(x)dx

dy = 12x²dx

dy = 12(2)²(0.1)

dy = 4.8

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I need help figuring out what angle these degrees are

Answers

1) Looking at the picture we can state that

m∠1 = 57º and m∠2 = 180-57

m∠2 = 123º

We can state that according to the Same side interior angles that states that those angles ∠1 , and ∠2 are supplementary since those angles belong to lines that have been crossed by a transversal line t.

Yoshi has played in 6 basketball games so far this season. Her points in each game aredisplayed in the table below.GamePoints181234562420142224What is the median of Yoshi's points per game?O 21None of the other answers are correctO 221920

Answers

Let us revise how to find the median

At first you must arrange the numbers from small to big

Let us do that

14, 18, 20, 22, 24, 24

We have 6 numbers we need to find the middle one because the median means middle number in a set of data

But there are 6 numbers the middle numbers are 20 and 22

So the median will be the average of the two number

[tex]\text{Median}=\frac{20+22}{2}=\frac{42}{2}=21[/tex]

There is a very important note for the median

If the number of data is even the median will be the average of the middle two numbers as our question, but if the number of data is odd then the median will be the middle number.

The answer is the first choice

Determine whether each pair of polygons is similar. OPTIONSSimilar, sides are proportional and angles are corresponding Similar, sides are proportional and angles are congruent Not similar, sides are not proportional and angles are congruent Not similar, sides are proportional and angles are not congruent

Answers

From the figure it can be observed that angles of both figure are equal to 90 degrees. So angles are congurent of polygons are conurent to each other.

Determine the ratio of corresponding sides of two polygon.

[tex]\frac{3}{4}[/tex]

And

[tex]\frac{6}{9}=\frac{2}{3}[/tex]

As sides of the polygons are not proportional to each other. So figure are not similar.

Thus correct option is,

Not similar, sides are not proportional and angles are congruent .

Kaitlyn wants to buy Nikes but only brought $156.50 with her to the store. If the Nikes cost $209, what percent discount would she need in order to be able to afford the Nikes? Round your answer to the nearest whole percent.

Answers

Kaitlyn's money =$156.50

Nike's cost = $209

We have to write an equation:

The cost of the Nikes (209) multiplied by the percentage(x) in decimal form (divided by 100) must be equal to the money available (209)

209 x = 156.50

x = 156.50/209

x= 0.75

0.75 x 100 =75%

1- 75 = 25%

Percent discount= 25%

Find the solution set of the inequality
\qquad5x + 13 \geq -37.5x+13≥−37.

5x + 13 ≥ -37

Answers

The solution set of the inequality 5x + 13 ≥ -37 is represented by x≥-10

and internal notation is [-10,∞).

Given the inequality equation is 5x + 13 ≥ -37.

Now solve the equation.

⇒ 5x + 13 ≥ -37

Arrange the constant terms on one side.

⇒ 5x ≥ -37 - 13

Subtract the terms.

⇒ 5x ≥ -50

Now solve for x.

⇒ x ≥ -50/5

⇒ x ≥ -10

Hence the solution set is x ≥ -10.

So, the internal notation is  [-10,∞).

Therefore, the solution set of the inequality is  x ≥ -10.

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A train leaves Little Rock, Arkansas, and travels north at 90 kilometers per
hour. Another train leaves at the same time and travels south at 60 kilometers
per hour. How long will it take before they are 300 kilometers apart?

Answers

Answer: 240 ft to be sure

Step-by-step explanation:

The display shows the data set from a survey about time spent on social media in a day. Vertical box plot titled average time spent on social media in a day, with minutes labeled on the vertical axis. The minimum is at 5, and the maximum is at 80. The lower quartile is at 30, the median is at 50, and the upper quartile is at 60. Which of the following describes the data set? Categorical and bivariate Categorical and univariate Numerical and bivariate Numerical and univariate

Answers

The data-set in this problem is classified as follows:

Numerical and univariate.

What are the classification of variables?

The variables can be classified as categorical or numerical as follows:

Categorical: The possible values assumed by the variable are labels, such as yes/no, good/bad, and so on...Numerical: The values assumed by the variable are numbers.

In the context of this problem, the minimum, the maximum and the quartiles of the variable all assume numeric values, hence the variable is classified as numerical.

From the text, the variable under study is the time spent on social media in a day, as a function of minutes. Since the output of the study is a single variable, the study is called univariate.

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Answer:

Numerical and univariate.

Step-by-step explanation:

f(x) = 2x2 + 6x - 4 9(2) = 573 – 6x2 – 3 Find (f +9)(2). O A. (f +g)(x) = -523 + 8x2 + 6x – 1 O B. (f +9)(x) = 5x3 + 2x2 – 7 O C. (f+g)(x) =1723 – 7 O D. (f + g)(x) = 5x3 - 4x2 + 6x - 7

Answers

Answer:

The function (f+g)(x) is:

[tex](f+g)(x)=5x^3-4x^2+6x-7[/tex]

Explanation:

Given the functions;

[tex]\begin{gathered} f(x)=2x^2+6x-4 \\ g(x)=5x^3-6x^2-3 \end{gathered}[/tex]

We want to find the function (f+g)(x);

[tex]\begin{gathered} (f+g)(x)=f(x)+g(x) \\ (f+g)(x)=(2x^2+6x-4)+(5x^3-6x^2-3) \\ (f+g)(x)=5x^3+2x^2-6x^2+6x-4-3 \\ (f+g)(x)=5x^3-4x^2+6x-7 \end{gathered}[/tex]

Therefore, the function (f+g)(x) is:

[tex](f+g)(x)=5x^3-4x^2+6x-7[/tex]

What is the total volume of all four gum balls?

Answers

[tex]\begin{gathered} De\text{ volume of each gumball is} \\ Volume_{\text{gumball}}=\frac{4}{3}\pi r^3 \\ \\ \text{ we get 3 gumballs, thus the total volume is} \\ V=4(\frac{4}{3}\pi r^3) \\ V=\frac{16}{3}(3.14)(6)^3 \\ V=\frac{50.24\cdot216}{3} \\ V=\frac{1131.84}{3} \\ \\ V=377.28 \\ \\ \text{The answer is 377.24 mm}^3 \end{gathered}[/tex]

Explain how to simplify ( (a*)") using the properties of exponents.

Answers

Simplifying ((a*)"),

In this type of expression, we apply the properties of exponents under Power Rules.

Under the power rule property of exponents,

[tex]((A^x)^y)=A^{x\text{ }\cdot\text{ y}}[/tex]

This says that to raise a power to a power you need to multiply the exponents.

Let's apply this rule to simplify the given expression,

((a*)") = a*"

solve for the unknown angle measure given that f || g

Answers

The measure of the unknown angle is 75°

What is an angle?

An angle is a shape in Euclidean space created by two rays, termed the ends of the angle, that share a common termination, called the vertex of the angle. Angles produced by two rays are located in the longitudinal plane the rays. Angles are also generated when two planes overlap. These are known as dihedral angles. An angle defined by two intersecting curves is the angle of the rays lying tangent to the respective curves at their point of junction. Angle can also refer to the measurement of an angle or of a rotation. In the case of a geometric angle, the arc is defined by the sides and is centered at the vertex.

From figure,

x+70+25 = 180 (angle sum property of a triangle)

x = 180 - 95 = 75°

Hence, the measure of the unknown angle is 75°

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solve the following equation. express your answer as both an exact expression and a decimal approximation rounded to two decimal places. use e = 2.71828182845905.

Answers

SOLUTION:

Case: Exponential equations

Given:

[tex]e^{3x-8}=102^{5x+5}[/tex]

Required: To solve for x

[tex]\begin{gathered} e^{3x-8}=102^{5x+5} \\ Take\text{ }natural\text{ }logarithm\text{ }of\text{ }both\text{ }sides \\ ln(e^{3x-8})=ln(102^{5x+5}) \\ (3x-8)lne^=(5x+5)ln(102) \\ 3x-8=(5x+5)4.624972 \\ 3x-8=23.12x+23.12 \\ Collecting\text{ }like\text{ }terms \\ -23.12-8=23.12x-3x \\ -31.12=20.12x \\ x=-\frac{31.12}{20.12} \\ x=-1.54658754284 \end{gathered}[/tex]

Final answer:

Exact value

[tex]x=-1.54658754284[/tex]

To 2 decimal places

[tex]x\approx-1.55[/tex]

Use the transformations of the graph of f(x) = x^2 to determine the graph of the function. h(x) = -(x+2)^2

Answers

Answer:

Step-by-step explanation:

The graph f(x) = x^2 is shifted along the OX axis to the left by 2 and reflected relative to this axis:

If 3m+5=27, then the value of m is

Answers

Answer:

m=7 1/3 in mixed number or 22/3 in improper fraction

Step-by-step explanation:

3m+5=27 is your equation

You will have to subtract 5 on both sides and you will be left with

3m=22

After that you will divide three on both sides

Therefore the answer is m=7 1/3 or 22/3

Hugo averages 41 words per minute on a typing test with a standard deviation of 7.5 words per minute. Suppose Hugo's words per minute on a typing test are normally distributed. Let X= the number of words per minute on a typing test. Then, X∼N(41,7.5).

Suppose Hugo types 45 words per minute in a typing test on Wednesday. The z-score when x=45 is ________. This z-score tells you that x=45 is ________ standard deviations to the ________ (right/left) of the mean, ________.

Correctly fill in the blanks in the statement above.

Answers

At x = 30, the result is -1.57. According to this z score, x = 30 is 1.57 standard deviations away from the mean. 41 At x = 30, the result is -1.57. According to this z score, x = 30 is 1.57 standard deviations away from the mean.

What is the z score and standard deviation?

In essence, standard deviation represents the degree of variability present in a given data collection. To compute the standard deviation, first, get the distance between each data point and the mean. After that, the discrepancies are squared, added up, and averaged. The variance is caused by this. The variance's square root yields the standard deviation.The Z-score, in contrast, indicates how far a given data point deviates from the mean. The Z-score is adverse for data points that are below the mean. 99% of the values in most sizable data sets have a Z-score between -3 and 3, which denotes that they are within three standard deviations of the mean either above or below.

Given, the Normal distribution with,

     mu  =  41

sigma  =   7

The z-score formula is

z score = (X -  mu) / sigma

So , z score at X = 30 is

z score =  (X -  mu) / sigma = (30 - 41) / 7 = -1.57

At x = 30, the result is -1.57. According to this z score, x = 30 is 1.57 standard deviations away from the mean. 41 At x = 30, the result is -1.57. According to this z score, x = 30 is 1.57 standard deviations away from the mean.

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What is the value of 24 - 5²?Record your answer and fill in thebubbles on your answer document.Be sure to use the correct placevalue.

Answers

24 - 5²

24 - 25 (Raising 5 to the power of 2)

-1 (Subtracting)

The answer is -1.

-12- (-35)

convert each fraction to its equivalent using the least common denominator 3/7 , 3/4

Answers

The least common denominator of 3/7 and 3/4 is 7*4=28, therefore:

[tex]\begin{gathered} \frac{3}{7}=\frac{3\cdot4}{7\cdot4}=\frac{12}{28}, \\ \frac{3}{4}=\frac{3\cdot7}{4\cdot7}=\frac{21}{28}. \end{gathered}[/tex]

Answer:

3/7, option e.

3/4, option c.

What is 13^c^11?
O A. 91
OB. 105
C. 78
D. 120

Answers

78

1) Since we have a Combination, we can write out the following formula:

[tex]_{13}C_{11}=\frac{13!}{11!(13-11)!}=\frac{13\times12\times11!}{11!\text{ 2!}}=\frac{13\times12}{2}=78[/tex]

Note that we canceled 11! on the numerator by the factorial of 11! on the denominator. And notice this is only possible when the order does not matter.

2) Hence, the answer is 78 because there are 78 combinations of 13 choosing 11.

what fraction of a day is 45 minutes

Answers

To be able to determine what fraction of a day is 45 minutes, let's first determine how many minutes are there in a day.

1 day

Martina is driving on a highway. She uses one gallon of gas every 30 miles she drives. The distance, D (in miles), she travels on g gallons of gas is given
by the following function.
D (g) = 30g
How far does Martina drive if she uses 3 gallons of gas?

Answers

Answer:

90 miles

Step-by-step explanation:

First the formula is solving for distance in miles. and is says distance = 30 x gallons. So if it's asking for how far she drives with 3 gallons, it's asking for her distance driven when using 3 gallons of gas. So the formula would be D = 30g. D = 30 x 3 is the  formula, we have to put in 3 for g. When we do 30 x 3 we would get our answer as 90. Therefore our final answer is 90 miles.

What’s the equation passing threw the points? And is parallel to the line 3x+y=3

Answers

The parallel line 3x + y =3, can be write on y-intercept form:

Solve for y the equation:

3x + y = 3

y = 3 -3x

Now, two lines are parallel when they have the same slope. In this case for line y= 3 -3x, the slope is the number with the x.

Therefore, the slope is -3.

Use the slope intercept-form using slope=m=3 and the point (1,-7):

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

Replace these values and solve for y:

[tex]y-(-7)=-3(x-1)[/tex][tex]y+7=-3x+3[/tex]

Solving for x:

[tex]y=3x+3-7[/tex]

The equation that passes through the point (1,-7) and is parallel to the line3x + y =3 is :

[tex]y=-3x-4[/tex]

A customer wants to put in a concrete driveway that is 10″ thick. How much concrete would it take to pour a driveway that measures 18′ by 42′? Express your answer in cubic yards.

Answers

The volume of concrete it would it take to pour a driveway that measures 18′ by 42′ and 10″ thick is equal to 23.33 cubic yard.

What is a conversion factor?

In Mathematics, a conversion factor simply refers to a number that is typically used to convert a number in one (1) set of units to another, either by multiplying or dividing.

Additionally, an appropriate conversion factor to an equal unit of value must be chosen and used when it is necessary to perform any mathematical conversion.

Note: The double quotation mark " is a notation that represent inches while the apostrophe mark ' represents foot.

Next, we would convert the unit in inches to feet:

1 inch = 0.0833333 feet.

10 inches = 10 × 0.0833333 = 0.833333 feet.

For the volume of concrete required, we have:

Volume of concrete = Length × Width × Thickness

Volume of concrete = 18 × 42 × 0.833333

Volume of concrete = 629.999748 cubic feet.

Also, we would convert cubic feet to cubic yard:

1 cubic feet = 0.037037 cubic yard

629.999748 cubic feet = x cubic yard

Cross-multiplying, we have:

Volume of concrete = 629.999748 × 0.037037

Volume of concrete = 23.33 cubic yard.

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Suppose Latoya borrows$4000.00 at an interest rate of 18% compounded each year.Assume that no payments are made on the loan.Find the amount owed at the end of 1 year.Find the amount owed at the end of 2 years.

Answers

Answer:

[tex]\begin{gathered} A=\text{ \$4,720 at the end of 1 year} \\ A=\text{ \$5,570 at the end of 2 year} \end{gathered}[/tex]

Step-by-step explanation:

The compound interest is represented by the following equation:

[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ where, \\ P=\text{ principal borrowed} \\ r=\text{ rate} \\ n=\text{ number of times compounded per time ''t''} \\ t=\text{ time in years} \end{gathered}[/tex]

Therefore, if Latoya borrows $4000 at an interest rate of 18% compounded each year;

[tex]\begin{gathered} A=4000(1+\frac{0.18}{1})^1 \\ A=\text{ \$4,720 at the end of 1 year} \end{gathered}[/tex]

Now, at the end of 2 years:

[tex]\begin{gathered} A=4000(1+\frac{0.18}{2})^2 \\ A=\text{ \$5,569.6 at the end of 2 year} \end{gathered}[/tex]

I need help with this Struggling It asks to answer (a) and (b) Put these separately ^ so I know which is which

Answers

We are given that:

[tex](3x^5-\frac{1}{9}y^3)^4[/tex]

a) We know that binomial theorem in summation form

[tex](a+b)^n=\sum ^{r=n}_{r\mathop=0}\begin{bmatrix}{n} \\ {r}\end{bmatrix}a^{n-r}\cdot b^r[/tex]

Using the formula and substitute

[tex]a=3x^5,b=-\frac{1}{9}y^3\text{ and n=4}[/tex]

Therefore,

[tex](3x^5-\frac{1}{9}y^3)^4=\sum ^{r=4}_{r\mathop=0}\begin{bmatrix}{4} \\ {r}\end{bmatrix}(3x^5)^{4-r}\cdot(-\frac{1}{9}y^3)^r[/tex]

Hence, the sum in summation notation that he uses to express the expansion is

[tex](3x^5-\frac{1}{9}y^3)^4=\sum ^{r=4}_{r\mathop{=}0}\begin{bmatrix}{4} \\ {r}\end{bmatrix}(3x^5)^{4-r}\cdot(-\frac{1}{9}y^3)^r[/tex]

b) Let us now write the simplified terms of the expansion.

Therefore,

Using Combination formula to expand the expression above

The combination formula is,

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Where,

[tex]n!\text{ = n(n-1)(n-2)}\ldots3.2.1[/tex]

Hence,

[tex]\begin{gathered} =\frac{4!}{0!\left(4-0\right)!}\mleft(3x^5\mright)^4\mleft(-\frac{1}{9}y^3\mright)^0+\frac{4!}{1!\left(4-1\right)!}\mleft(3x^5\mright)^3\mleft(-\frac{1}{9}y^3\mright)^1+\frac{4!}{2!\left(4-2\right)!}\mleft(3x^5\mright)^2\mleft(-\frac{1}{9}y^3\mright)^2 \\ +\frac{4!}{3!\left(4-3\right)!}\mleft(3x^5\mright)^1\mleft(-\frac{1}{9}y^3\mright)^3+\frac{4!}{4!\left(4-4\right)!}\mleft(3x^5\mright)^0\mleft(-\frac{1}{9}y^3\mright)^4 \end{gathered}[/tex]

Simplifying the above, we have

[tex]=81x^{20}-12x^{15}y^3+\frac{2x^{10}y^6}{3}-\frac{4x^5y^9}{243}+\frac{y^{12}}{6561}[/tex]

Hence, the simplified terms of the expansion are

[tex]81x^{20}-12x^{15}y^3+\frac{2x^{10}y^6}{3}-\frac{4x^5y^9}{243}+\frac{y^{12}}{6561}[/tex]

The radius of a circle is 11ft. Find its area in terms of pi

Answers

Answer:   A≈380.13ft²

Step-by-step explanation:

1. Anna is saving up for a new laptop. She currently has 2x² - 2x dollars saved in her bank account. After working at her part-time job, she is able to deposit another 11x + 15 dollars. She finally has enough money to buy the laptop, and so she withdraws x²- 5x + 3 dollars. How much money does she have left in her bank account after buying her laptop? SHOW ALL WORK!

Answers

1) Gathering the data

Anna currently has 2x² -2x dollars

Then She adds: 11x +15 dollars

And withdraw x²-5x +3 dollars

2) Let's rewrite that

2x² -2x

+11x +15

---------------------

2x² +9x +15 - (x² -5x +3)

2x² +9x +15

-x² +5x -3

---------------------

x² +14x +12

That's the amount of money Anna has left for her laptop: x² +14x +12 dollars

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