What is the best description of the relation?

Answer:

The solutions to the system of the equations are:

\(y=1,\:x=3\)

Step-by-step explanation:

Given the equations

\(y=\frac{2}{3}x-1;\:y=-x+4\)

solving the system of equation

\(\begin{bmatrix}y=\frac{2}{3}x-1\\ y=-x+4\end{bmatrix}\)

Arrange equation variables for elimination

\(\begin{bmatrix}y-\frac{2}{3}x=-1\\ y+x=4\end{bmatrix}\)

\(y+x=4\)

\(-\)

\(\underline{y-\frac{2}{3}x=-1}\)

\(\frac{5}{3}x=5\)

\(\begin{bmatrix}y-\frac{2}{3}x=-1\\ \frac{5}{3}x=5\end{bmatrix}\)

solving for x

\(\frac{5}{3}x=5\)

\(5x=15\)

Divide both sides by 15

\(\frac{5x}{5}=\frac{15}{5}\)

\(x=3\)

\(\mathrm{For\:}y-\frac{2}{3}x=-1\mathrm{\:plug\:in\:}x=3\)

\(y-\frac{2}{3}\cdot \:3=-1\)

\(y-2=-1\)

Add 2 to both sides

\(y-2+2=-1+2\)

\(y=1\)

Therefore, the solutions to the system of the equations are:

\(y=1,\:x=3\)

Answer:

28,000

Step-by-step explanation:

Answer:

28,000

Step-by-step explanation:

if u multiply 6,827 by 4 u get 27,303  and 208, 000 is way off so is 240, 000 24,000 is off by 3,303 and 28, 000 is off by 697. so it's 28,000.

Answer:

Step 1: Divide both sides by 2

Step 2: Subtract both sides by 3

Step-by-step explanation:

Step 1: 2(x + 3) = 14

Step 2: x + 3 = 7

x = 4

x = 50, y = 25 are  the values of x and y that maximize P.

Part 1: Find a × b, where d = (5, −2, 4) and b = (0, 2, −3).

So, we have to use cross product of the two vectors to find a × b;     a × b = |i  j  k|    |5  -2  4|    |0   2  -3|

On taking the cross product, we get;     a × b = -15i + 12j + 10k

Therefore, the answer is D. (−2,−15,10).

Part 2: If P = xy and x + 2y = 100, find the values of x and y that maximize P.

To maximize P, we have to use the concept of differential calculus.

Let's solve the given equation; x + 2y = 100 ⇒ x = 100 − 2y

Now, substitute this value of x in the given expression; P = xy ⇒ P = (100 − 2y) y

Differentiating w.r.t y to get the value of y for which P is maximum; dP/dy = 100 - 4y

Now, equate dP/dy to zero and solve for y; 100 - 4y = 0 ⇒ y = 25

When y = 25, P will be maximum.

Substituting the value of y in x = 100 − 2y, we get the value of x;x = 100 − 2(25) ⇒ x = 50

Therefore, the correct answer is A. x = 50, y = 25.

Learn more about cross product

brainly.com/question/29097076

#SPJ11

The value of y co-ordinate of point Q is found to be -20 or 10 by using the distance formula.

What does the coordinate geometry distance formula mean?

In coordinate geometry, the distance formula is used to compute the distance between two specified points.

The distance formula is D=

It is used to determine the distance between two locations (x1,y1)(x1,y1)) and (x2,y2)(x2,y2).

Given: Points P and Q are separated by 17 units. The coordinates of point P are (5, 5) and point Q are (-3,y).

Using the distance formula,

PQ = \(\sqrt{(x2-x1)^{2} +(y2 - y1)^{2} }\)

17²  = 64 - y² +25 +10y

289-64-25 = - y² + 10y

y² + 10y - 200 = 0

On solving the quadratic equation we get,

y = -20, 10

Therefore, the value of y co-ordinate of point Q is found to be -20 or 10 by using the distance formula.

Learn more about distance formula here:

brainly.com/question/23120005

#SPJ1

The constant of proportionality for the proportional equation is 36.

Option A is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 9 is an equation.

We have,
Box = b

Number of pencils in one box.

p = 36

Now,

The proportional equation for b and p.

p ∝ b

p = mb

where m is the constant of proportionality.

Now,

b = 1

p = 36

p = mb

36 = m x 1

m = 36

Thus,

The constant of proportionality is 36.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

\(the \: answer \: is \: \frac{1}{10} \)

\(\blue{———hope it helps———}\)

\(\large{ \pink{ \underline{ { \sf{Answer}}}}}\)

\(the \: answer \: is \: \frac{1}{10} \)

Answer:

y = 5/2x

60 ft tall

Step-by-step explanation:

Answer:

its 40

Step-by-step explanation: 65+75= 140     180-140=40

give brainliest plz lol

The dimensions are 3 inches, 10 inches, and 13 inches.

It should be noted that the diagonal is the longest side. This will be solved by using Pythagoras theorem.

Therefore,

(2x + 6)²

4x²+ 24x + 36

Reduce to lowest term

x² + 6x + 9

x² + 3x + 3x + 9

x(x + 3) - 3(x + 3)

(x - 3) = 0

x = 0 + 3 = 3

Therefore x = 3

Therefore the dimensions will be:

x = 3

2x + 4 = 2(3) + 4 = 10

2x + 6 = 2(3) + 6 = 12

Learn more about rectangles on:

brainly.com/question/25292087

#SPJ1

The factored forms of the equations and the intercepts would be:

g(x) = x² - 4x - 21:

h(x) = x² + 8x + 12:

For g(x) = x² - 4x - 21:

To find the factored form, we need to factor the quadratic expression:

g(x) = (x - 7)(x + 3)

To find the x-intercepts, we set g(x) = 0 and solve for x:

(x - 7)(x + 3) = 0

x = 7 or x = -3

To find the y-intercept, we set x = 0 and evaluate g(x):

g(0) = (0 - 7)(0 + 3) = -21

Therefore, the y-intercept of g(x) is (0,-21).

For h(x) = x² + 8x + 12:

h(x) = (x + 2)(x + 6)

To find the x-intercepts, we set h(x) = 0 and solve for x:

(x + 2)(x + 6) = 0

x = -2 or x = -6

To find the y-intercept, we set x = 0 and evaluate h(x):

h(0) = (0 + 2)(0 + 6) = 12

Therefore, the y-intercept of h(x) is (0,12).

Find out more on factored forms at https://brainly.com/question/28139549

#SPJ1

Answer:

Step-by-step explanation:

Domain means what are all the x's. Range means what are all the y's. In this case we have m and c(m) instead of x and y. You can think of domain as inputs and range as outputs. Here you need to know months in order to find cost, so months are the input and cost is the output. You can't have negative months. So the domain is m>=0. The range is the output. From Month 0 when the cost is $100, the expense just goes up from there. So the range is c(m) >=100. The slope is the 28, so that is the monthly fee. And the y-intercept is how much you've spent at month 0, which is the $100 that you have to spend before you even start.

Answer:

awnser is 28m +100 interprept 28 per month

Answer: 1/4

Step-by-step explanation:

2-1/2 ==> 1/2

3-1/3 ==> 2/3

4-1/4 ==> 3/4

1/2 x 2/3 x 3/4 = 6/24

*Reduce 6/24*

1/4

Part A: A reasonable domain to plot the growth function, considering the context, would be d ≥ 0, indicating that we are interested in studying the growth of the algae from the initial time onwards.

Part B: The y-intercept of the graph represents the initial radius of the algae when the study began, which is 11 mm.

Part C: The average rate of change of the function from d = 2 to d = 7 represents the average rate at which the radius of the algae is increasing per day over that time period.

Part A: To determine a reasonable domain to plot the growth function, we need to consider the context of the problem. In this case, the biologist is studying the growth of algae over time. The equation provided, \(f(d) = 11(1.01)^d\), represents the radius of the algae after d days.

Since time cannot be negative and the biologist concluded her study when the radius was approximately 11.79 mm, it implies that the radius cannot be negative as well.

Therefore, we can infer that the domain of the function should be limited to non-negative values of d.

Part B: The y-intercept of the graph of the function f(d) represents the value of the function when d = 0. Substituting d = 0 into the equation, we have \(f(0) = 11(1.01)^0 = 11(1) = 11.\)

Part C: To find the average rate of change of the function f(d) from d = 2 to d = 7, we need to calculate the slope of the secant line connecting the points (2, f(2)) and (7, f(7)).

Using the given equation, we can find the values of f(2) and f(7) as follows:

\(f(2) = 11(1.01)^2 \approx 11.2221 mm\\f(7) = 11(1.01)^7 \approx 11.6897 mm\)

The average rate of change (slope) is given by (f(7) - f(2))/(7 - 2) = (11.6897 - 11.2221)/(7 - 2) ≈ 0.0931 mm per day.

In this case, it indicates that, on average, the radius of the algae is increasing by approximately 0.0931 mm per day between days 2 and 7.

For more such questions on average rate

https://brainly.com/question/11627203

#SPJ8

Answer:

y = 5x

Step-by-step explanation:

slope intercept form is y=mx+b

m = slope

b = the y-intercept

so you just have to plug in those values

Answer:

1200$

Step-by-step explanation:

All right, you usually pay 160 dollars but with the extra 25% off sale, you pay 120(160 ÷ 4 = 40, 160 - 40 = 120). BUT you have the extra VAT charge you will pay 150 dollars every day. You stay for 8 nights so 150 × 8 = 1200

Answer:

Yes

Step-by-step explanation:

KL=ST(GIVEN)

ANGLE(K)=ANGLE(U)(GIVEN)

ANGLE(M)=ANGLE(S)(GIVEN)

By SAS Triangle KLM Is Congruent to Triangle TUS....

Apply The Same Rules For Next One , Feel Free to ask any queries.

DEFINITIONS and APPLICATION:
1A short answer is a concise response that directly addresses the question or prompt. It typically consists of a few sentences or a paragraph and is focused on providing a specific answer without unnecessary details or elaboration.

Example: When asked "What is the capital of France?", a short answer would be "Paris."

A 100-word response refers to providing a written explanation or description within a specific word limit of 100 words. This limitation requires the writer to be concise and selective with their information while still conveying a comprehensive understanding of the topic.

Example: If asked to describe the water cycle in 100 words, a response could include information about evaporation, condensation, precipitation, and how water moves between the Earth's surface, atmosphere, and bodies of water.

A conclusion is the final part of a written piece that summarizes the main points and provides a closing statement. It serves to wrap up the information discussed in the body of the text and leave a lasting impression on the reader.

Example: In an essay about the benefits of exercise, the conclusion may restate the key advantages, such as improved physical and mental health, increased energy levels, and reduced risk of chronic diseases, while also encouraging the reader to prioritize regular physical activity.

4. Application: In the context of these concepts, application refers to the practical use or implementation of a particular idea, theory, or skill in real-life situations. It involves taking what has been learned and using it to solve problems, make decisions, or accomplish specific tasks.

Example: If learning about the Pythagorean theorem, applying it would involve using the formula to find the length of the hypotenuse in a right triangle when given the lengths of the other two sides.

These are four of the eight concepts related to definitions and applications. Remember to provide clear explanations, relevant examples, and use a step-by-step approach when addressing each concept.

To know more about Pythagorean theorem , visit ;

https://brainly.com/question/28361847

#SPJ11

Answer:

Let the width of the rectangle be w.

Then the length of the rectangle is w+2.

The perimeter of the rectangle is the sum of all its sides, so it is 2(w) + 2(w+2) = 60.

Expanding the parentheses and combining like terms, we get:

2w + 2w + 4 = 60

4w + 4 = 60

4w = 56

w = 14

The width of the rectangle is 14.

The length of the rectangle is 14+2 = 16.

Therefore, the length of the rectangle is 16 and the width is 14.

Answer:

B.23-14i

Step-by-step explanation:

(3x5)+(3x2i)-(4ix5)-(4ix2i)

15+6i-20i-8(-1)

15+6i-20i+8

23-14iฟ

Answer:

The x-intercept is (2.25,0).

The y-intercept is (0,18)

Mandy's actual direct labor rate per hour (AP), rounded to two decimal places, is approximately $42.00.

To find Mandy Company's actual direct labor rate per hour (AP), we need to use the given information and apply the formula for direct labor efficiency variance:

Direct Labor Efficiency Variance = (AQ - SQ) × AP

We are given the following information:

Standard direct labor hours allowed for units produced (SQ) = 3,800

Actual direct labor hours worked (AQ) = 3,650

Direct labor efficiency variance, favorable (F) = $6,300

We can rearrange the formula to solve for AP:

AP = Direct Labor Efficiency Variance / (AQ - SQ)

Substituting the values:

AP = $6,300 / (3,650 - 3,800)

AP = $6,300 / (-150)

AP ≈ -$42 per hour

However, a negative value of direct labor rate variance is called favorable direct labor rate variance, which is the result of the actual rate being less than the standard rate.

Therefore, Mandy's actual direct labor rate per hour (AP), rounded to two decimal places, is approximately $42.00.

Learn more about actual direct labor rate per hour click;

https://brainly.com/question/17198407

#SPJ4

Complete question =

Mandy Company has the following information from last month:

Standard direct labor hours allowed for units produced (SQ) 3,800

Actual direct labor hours worked (AQ) 3,650

Direct labor efficiency variance, favorable (F) $ 6300

Total payroll $ 190530

What was Mandy's actual direct labor rate per hour (AP), rounded to two decimal places?

Answer: a and b

Step-by-step explanation: lol it obvious

Answer: Quadrilateral, Parallelogram

Step-by-step explanation:

A Quadrilateral is any closed 4 sided figure

A Parallelogram is a quadrilateral with two sets of parallel and opposite sides.

Answer:

1,3,4,5 (2 and four I can't make out what the notations are)

Step-by-step explanation:

Any equation that has a constant slope is a linear equation.

1 has a slope of 8/3

3 has a slope of 5

4 and 5 have a slope of 0

2 looks to be some form of absolute value equation and therefore is in the shape of a V and not a straight line.

6 looks to be an equation with an exponent as part of a term and will have a gradually decreasing slope (decreasing because of the negative 4)

The simplification of the expression (3√-5 + 2)(4√-5 -1) gives 5√-5 - 62

Simplification is a way of determining an answer for a complex calculation that may involve numbers on division, multiplication, square roots, cube roots, plus and minus, etc.

Given: the expression (3√-5 + 2)(4√-5 -1)

(3√-5 + 2)(4√-5 -1)

Clear the parenthesis:

(3√-5 + 2)(4√-5 -1) = 3√-5(4√-5) + 3√-5 (-1) + 2(4√-5) + 2(-1)

                             = -60 - 3√-5 + 8√-5 -2

                            = 5√-5 - 62

Therefore, the expression (3√-5 + 2)(4√-5 -1) simplifies to 5√-5 - 62

Learn more about simplification on:

brainly.com/question/29458827

#SPJ1

it's easier b or d I'm not sure

Answer:  

It would be D

Step-by-step explanation:

By mathematical induction we know that P(n) is true for all integers n > 4

We have proven that \(2^n > n^2\) for all integers n > 4.

=> Let P(n) be the proposition that \(2^n > n^2\), n > 4

Put n = 5

\(2^5 > 5^2\)

32 > 25

It is true for n = 5

=> For the inductive hypothesis we assume that P(k) holds for an arbitrary integer k > 4

Let P(k) be true where k is greater than 4

That is, we assume that

\(2^k > k^2\), k > 4

Under this assumption, it must be shown that, it is true for p(k+1).

\(= > 2^k^+^1=2.2^k\\\\=2^k+2^k > k^2+k^2\\\\=k^2+k.k > k^2+4k\\\\=(k+1)^2\\\\\)

This shows that P(k + 1)  is true under the assumption that P(k) is true.

This completes the inductive step.

Learn more about Integers at:

https://brainly.com/question/15276410

#SPJ4

Answer:

(-41)/6 or -6 5/6 as a mixed fraction

Step-by-step explanation:

Simplify the following:

1 + 2/3 - (8 + 1/2)

Put 8 + 1/2 over the common denominator 2. 8 + 1/2 = (2×8)/2 + 1/2:

1 + 2/3 - ((2×8)/2 + 1/2)

2×8 = 16:

1 + 2/3 - (16/2 + 1/2)

16/2 + 1/2 = (16 + 1)/2:

1 + 2/3 - ((16 + 1)/2)

16 + 1 = 17:

1 + 2/3 - 17/2

Put 1 + 2/3 - 17/2 over the common denominator 6. 1 + 2/3 - 17/2 = 6/6 + (2×2)/6 + (3 (-17))/6:

6/6 + (2×2)/6 + (3 (-17))/6

2×2 = 4:

6/6 + 4/6 + (3 (-17))/6

3 (-17) = -51:

6/6 + 4/6 + (-51)/6

6/6 + 4/6 - 51/6 = (6 + 4 - 51)/6:

(6 + 4 - 51)/6

6 + 4 = 10:

(10 - 51)/6

10 - 51 = -(51 - 10):

(-(51 - 10))/6

| 5 | 1

- | 1 | 0

| 4 | 1:

Answer:  (-41)/6

The five-number summary is:

Minimum: 9

First Quartile: 16.5

Median: 25.5

Third Quartile: 39

Maximum: 51

3. Range = 42

4. Interquartile range = 22.5

Given the data for the lengths as, 36, 15, 9, 22, 36, 14, 42, 45, 51, 29, 18, 20, to find the five-number summary of the data set, we would follow the steps below:

1. The numbers in ordered from the smallest to the largest would be:

9, 14, 15, 18, 20, 22, 29, 36, 36, 42, 45, 51

2. The five-number summary for the lengths in minutes would be:

3. Range of the data = max - min = 51 - 9 = 42

4. The interquartile range for the data set = Q3 - Q1 = 39 - 16.5

Interquartile range for the data set = 22.5

Learn more about the five-number summary on:

https://brainly.com/question/24809873

#SPJ1

Answer:

Cost of each football ticket=$41.56

Cost of each  basketball ticket=$43.56

Step-by-step explanation:

Let

Cost of each football ticket=x

Cost of each basket ball ticket=y

According to question

\(2x+y=126.77\)...(1)

\(x+2y=128.86\) ....(2)

We have to find  the cost of each ticket.

Equation (1) multiply by 2 then we get

\(4x+2y=253.54\)  .....(3)

Now, subtract equation (2) from (3)

\(3x=124.68\)

\(x=124.68/3\)

\(x=41.56\)

Now, using the value of x in equation (2)

\(41.56+2y=128.86\)

\(2y=128.86-41.56\)

\(2y=87.3\)

\(y=87.3/2=43.65\)

Hence, cost of each football ticket=$41.56

Cost of each  basketball ticket=$43.56