To solve the sustem of equations below, kira isolated variable y in the first equation then sybstituted it into the second equation.what was the resulting equation? 3y=12x, x^2+y^2=81

Answer:

Option D)

Step-by-step explanation:

Given:

x= {2,3,4}

y={49,343,2401}

Points with coordinates (x,log(y)) are required to be plotted

Finding (x,log(y)):

log(y)= {log(49),log(343),log(2401)}

Log(49)=1.69020

log(343)=2.53529

log(2401)=3.38039

Now the transformed data set will be written in coordinates form:

(2,1.690),(3,2.535),(4,3.380)

Which is option D !

when the two books were published

Answer: It would be (B) because you don't actually have to know the date unless it is a part of the equation which you dont have to know in this question :)

Hope this will help you out :)

the standard form of the equation of a parabola that opens up or down is (x - h)^2 = 4p(y - k)  

Answer: y=ax^2+bx+c

Step-by-step explanation:

Answer:

r = - 6

Step-by-step explanation:

Given

6r + 7 = 13 + 7r ( collect terms in r on the left and numbers on the right )

Subtract 7r from both sides

- r + 7 = 13 ( subtract 7 from both sides )

- r = 6 ( multiply both sides by - 1 )

r = - 6

6r+7=13+7r

-6r -6r

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

7=13+1r

flip the equasin to make it easier

13+1r= 7

-13 -13

---------

1r= -6

Answer:

The answer is yes , k = -2 and y = -2x ⇒ first answer

Step-by-step explanation:

* To prove the variation

- Check the constant change in the values of x and y

- Lets check that from the table

# At x = 1 ⇒ y = -2

# At x = 3 ⇒ y = -6

# At x = 5 ⇒ y = -10

* -6 - -2 = -6 + 2 = -4 ⇒ 3 -1 = 2

 -10 - -6 = -10 + 6 = -4 ⇒ 5 - 3 = 2

∴ y decreased by 4 when x increased by 2

* This is a constant change

∴ y is varies directly with x

∴ y ∝ x

∴ y = k x ⇒ where k is the constant of the variation

* Lets find the value of k

- You can use one value of x and y from the table

∵ x = 3 and y = -6

∴ -6 = k (3) ⇒ divide two sides by 3

∴ k = -2

∴ The equation of the variation is = y = -2x

* The answer is yes , k = -2 and y = -2x

Answer:

Yes, k=-2 and y=-2x

Step-by-step explanation:

Using (1,-2) and (3,-6)

[tex]k=\frac{-6--2}{3-1}=-2[/tex]

This implies that

y=-2x

check for the 3rd point;

When x=5,

y=-2(5)=-10

Hence y varies directly as x. The constant of variation is k=-2

Answer:

4: 376   8: -708  12: -59  16: 0  18: -1,884

Step-by-step explanation:

I have really bad eyesight so, I hope I read all the numbers correctly. I hope you get caught up, it sucks to be behind in class.

Dividend Divisor = Quotient + Remainder is the formula for dividing two numbers. The answer is follows:

Therefore,

4) -2632/-7 = 376

Use the fraction rule.: [tex]$\frac{-a}{-b}=\frac{a}{b}$[/tex]

-2632/-7

Divide the numbers as follows:

2632/7 = 376

8) -7080/10 = - 708

12) 4956/-84 = -59

16) 0/-600 = 0

18) (-3768/-6) (-3) = 18

Within parentheses, compute (-3768 /-6) : -6

= -6(-3)

Divide and multiply (left to right) -6(-3 ) : 18

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Nope, it aint there. False

Answer:16

Step-by-step explanation:

original price

100

=  

new price

new percent

;

64.5

100

=  

75

x

64.5x = 7500 → x ≈ 116.3

Subtract 100 from the new percent (116.3 − 100 = 16.3) → 16%

The approximate percentage of the tip is 14%.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Dinner at your favorite restaurant cost $64.50 with tax for you and your family.

You give the waiter $75 to pay the bill and a tip.

That means,

the tip amount = 75 - 64.50

= 10.50

The tip percentage,

= 10.50 x 100 / 75

= 14%

Therefore, 14% is the required percentage.

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Answer:

47.5 miles

Step-by-step explanation:

So, every morning, you travel 4.75 miles to get to school... and another 4.75 miles in the afternoon to return.

So, each day, you travel a total of 9.5 miles (4.75 + 4.75) to go school and back.

On a typical school week, you'll go to school 5 times... so you'll need to travel a total of 47.5 miles (5 * 9.5).

Answer:

(0, 7]

Step-by-step explanation:

Let's call the width W and the length L.  The length is 18 feet more than the width, so:

L = W + 18

The area can be no more than 175, so:

A ≤ 175

LW ≤ 175

Since L = W + 18:

(W + 18) W ≤ 175

W² + 18W ≤ 175

W² + 18W - 175 ≤ 0

(W - 7) (W + 25) ≤ 0

-25 ≤ W ≤ 7

However, the width of the table can't be nonpositive, so:

0 < W ≤ 7

Or in interval notation, (0, 7].

Answer:

About 68 or 68.03

Step-by-step explanation:

Answer:

it is 68.0388555 Kg when you convert it to Kg.

Step-by-step explanation:

1 pound is 0.45359237 Kg

Answer:

The probability that there were 3 males is 1/4.

Step-by-step explanation:

Total Number of kitten = 4

Probability of a kitten to be male = 1/2

Probability of a kitten to be female = 1/2

Probability that out of 3 were male = 4 × 1/2 × 1/2 × 1/2 × 1/2

                                                          = 1/4

Therefore, The probability that there were 3 males is 1/4.

Answer:

a is 800

b is 13

c is 61.5

Step-by-step explanation:

for a you add all of the given data together

b you count how many data points there are

c you get the answer from the a  and divided by 13

By adding all of Jill's quiz scores (totaling 800) and dividing by the number of quizzes (13), we find that Jill's average score is approximately 61.54.

To determine the mean score for Jill's quizzes, we will follow these steps:

Total the quiz scores: Add all individual scores together.

Count the number of quizzes: Determine how many quizzes Jill took.

Calculate the average score: Divide the total score by the number of quizzes.

A. Total of Quiz Scores

20 + 40 + 40 + 40 + 60 + 60 + 60 + 60 + 80 + 80 + 80 + 80 + 100 = 800

B. Number of Quizzes

Jill took 13 quizzes.

C. Average Score

The mean score is calculated by dividing the total score by the number of quizzes:

Mean Score = Total Score / Number of Quizzes = 800 / 13 ≈ 61.54

Answer:

y = - 6x - 57

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 )

here m = - 6, thus

y = - 6x + c ← is the partial equation

To find c substitute (- 9, - 3) into the partial equation

- 3 = 54 + c ⇒ c = - 3 - 54 = - 57

y = - 6x - 57 ← equation of line

Answer:

y + 3 = –6(x + 9)

Step-by-step explanation:

Answer:

$135.70

Step-by-step explanation:

First step is to calculate the daily consumption for this family of four.  We'll assume they're all in age to use and flush the toilet themselves (no babies).

So, one person flushes 9.1 gallons a day, a family of 4 would then flush 4 times that:

daily family flushes = 9.1 gal/person * 4 persons/family = 36.4 gal/family

That's for one day... now for a year...

yearly = 36.4 gal/day * 365 days/yr = 13 286 gal/year

Let's convert those gallons into cubic feet:

13 286 gal / 7.48 gal/ft³ = 1,776.2 ft³

Then we multiply the gallons by the price for 100 cubic feet and divide by 100:

1,776.2  ft³ * $7.64 /100 ft³ = $135.70

Answer:

12

Step-by-step explanation:

We know that 15/20 students voted in the StuCo election on the first go around.

Using this ratio for 16 student is as simple as multiplying 15/20 by 16

(15/20)*16=12

Based on the voting ratio of 3:4 from Monday's election, we predict that 12 out of the 16 students present on Tuesday voted.

The question asks to predict the number of students who voted in Tuesday's election based on the ratio of students who voted on Monday. On Monday, 15 out of 20 students voted, which establishes a voting ratio of 15:20, or 3:4 when simplified. To predict Tuesday's voter turnout, we apply this ratio to the 16 students present on Tuesday.

Using the simplified ratio of 3:4, for every 4 students, 3 vote. Since 16 students were in class on Tuesday:

Therefore, we predict that 12 students voted in Tuesday's election.

Answer:

[tex]b=40.01\ units[/tex]

Step-by-step explanation:

we know that

Applying the law of sines

[tex]\frac{b}{sin(B)}=\frac{a}{sin(A)}[/tex]

[tex]b=\frac{a}{sin(A)}(sin(B))[/tex]

we have

[tex]a=25\ units[/tex]

[tex]A=32.5\°[/tex]

Find the measure of angle B

Remember that the sum of the interior angles of a triangle must be equal to 180 degrees

so

[tex]A+B+C=180\°[/tex]

substitute the given values

[tex]32.5\°+B+26.8\°=180\°[/tex]

[tex]B=180\°-59.3\°=120.7\°[/tex]

Find the length side b

[tex]b=\frac{a}{sin(A)}(sin(B))[/tex]

substitute the values

[tex]b=\frac{25}{sin(32.5\°)}(sin(120.7\°))[/tex]

[tex]b=40.01\ units[/tex]

Answer:

C

Step-by-step explanation:

We can point plot to get graph of both the functions.

** Attached is the graph of both the functions. f(x) is in RED & g(x) is in BLUE.

From the graph shown, it is clear that the point of intersection is x = 4, y = 2

So f(x) = g(x) at the point x = 4

Answer choice C is right.

Answer:

[tex]\frac{901}{999}[/tex]

Step-by-step explanation:

we know that

A Recurring Decimal, is a decimal number with a digit (or group of digits) that repeats forever.

In this problem we have

0.901 recurring

that means

0.901901901..

Let

[tex]x=0.901901901..[/tex]

Multiply x by a power of  [tex]10[/tex], one that keeps the decimal part of the number the same:  

[tex]1,000x=901.901901..[/tex]

Subtract [tex]x[/tex] from [tex]\\1000x[/tex]

[tex]1,000x-x=901.901901..-0.901901..=901[/tex]

The repeating decimals should cancel out

[tex]\\999x=901[/tex]

solve for x

Divide by [tex]999[/tex] both sides

[tex]990x/990=135/990[/tex]

[tex]x=\frac{901}{999}[/tex]

Answer:

many answers,

Step-by-step explanation:

she could make 9 mugs, (3/4 x 9 = 12)

she could make 1 small bowl, 1 small plate, 2 large bowls and 2 mugs. (2.5 + 1.5 = 4, 3.25 x2 = 6.5  .75 x 2 = 1.5; 4+ 6.5= 10.5  10.5 + 1.5 = 12) etc

Answer:

4 x^(3/2)         + 5x -32

Step-by-step explanation:

This problem involves definite integration (anti-derivatives).

If dy/dx = 6x^(1/2) - 5, then dy = 6x^(1/2)dx - 5dx.

                                        (1/2) + 1

This integrates to y = 6x                        

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

                                      (1/2) + 1             x^(3/2)

                                                      =  6 ------------ + C

                                                                 3/2

or:        4 x^(3/2) + C

and the ∫5dx term integrates to 5x + C.

The overall integral is:  

4 x^(3/2) + C + 5x + C. better expressed with just one C:

4 x^(3/2)         + 5x + C

We are told that the curve represented by  this function goes thru (4, 20).

This means that when x = 4, y = 20, and this info enables us to find the value of the constant of integration C:

20 = 4 · 4^(3/2)         + 5·4 + C, or:

20  =  4  (8)           + 20 + C

Then 0 = 32 + C, and so C = -32.

The equation of the curve is thus   4 x^(3/2)         + 5x -32

                                      (1/2 + 1)

The equation of the curve is [tex]y=6x^2-5x+7$.[/tex]

From the given information, we know that the gradient of the curve is [tex]$dy/dx=6x-5[/tex]

This means that the equation of the curve is of the form [tex]$y=6x^2-5x+C$[/tex]  for some constant C.

We can find the value of C by substituting the point (4,20) into the equation of the curve.

This gives us [tex]20=6\cdot4^2-5\cdot4+C[/tex]  so C=7.

Therefore, the equation of the curve is [tex]y=6x^2-5x+7$.[/tex]  

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ANSWER

[tex]\frac{ {x}^{2} }{ 16} + \frac{ {y}^{2} }{ 9} = 1[/tex]

EXPLANATION

The given ellipse has a vertex at (4,0), a co-vertex at (0,3), and a center at the origin.

The equation of an ellipse with vertices on the x-axis and center at the origin is:

[tex] \frac{ {x}^{2} }{ {a}^{2} } + \frac{ {y}^{2} }{ {b}^{2} } = 1[/tex]

The ellipse has vertex at (4,0) , hence a=4.

Also the co-vertex is at (0,3) , b=3

We substitute the values into the equation to get:

[tex] \frac{ {x}^{2} }{ {4}^{2} } + \frac{ {y}^{2} }{ {3}^{2} } = 1[/tex]

[tex] \frac{ {x}^{2} }{ 16} + \frac{ {y}^{2} }{ 9} = 1[/tex]

The equation of the ellipse centered at the origin with a vertex at (4,0) and a co-vertex at (0,3) is (x/4)² + (y/3)² = 1.

The ellipse in question has a vertex at (4,0) and a co-vertex at (0,3), with a center at the origin. The standard form equation for an ellipse with a center at the origin is given by (x/a)² + (y/b)² = 1. In this case, 'a' represents the distance from the center to a vertex, and 'b' represents the distance from the center to a co-vertex. Since our vertex is at (4,0), 'a' equals 4, and  since our co-vertex is at (0,3), 'b' equals 3.

So in this case the standard form equation of the ellipse would be (x/4)² + (y/3)² = 1.

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Answer:

The length of the formed by these vertices is 11 units.

Step-by-step explanation:

We are given the following coordinates of two vertices of a right angled triangle and we are to find the length of the side formed by these vertices:

[tex](-2, 5)[/tex] and [tex](9,5)[/tex]

Using the distance formula to find the side length:

Side length = [tex] \sqrt { ( 9 - ( - 2 ) ) ^ 2 + ( 5 - 5 ) ^ 2 } [/tex] = [tex]\sqrt{121}[/tex] = 11 units

Answer:

11

Step-by-step explanation:

Note that the horizontal line y = 5 goes through both vertices, and that the length of the side formed by those vertices is the distance between the vertices in this case.  That distance would be 9 - (-2), or 11.

Answer:

b

Step-by-step explanation:

Given K is the midpoint of JL, then

JK = KL ← substitute values

6x = 3x + 3 ( subtract 3x from both sides )

3x = 3 ( divide both sides by 3 )

x = 1

Hence

JK = 6x = 6 × 1 = 6

KL = 3x + 3 = (3 × 1) + 3 = 3 + 3 = 6

JL = 6 + 6 = 12

Divide bags of sand by gallons of water:

14 /6 = 2.33

21/9 = 2.33

The ratio is the same, so this means for every gallon of water you need 2.33 bags of sand.

Convert the fractions into decimals and you will get 7/3 = 2.33

The answer for Part 1 is D) 7/3

For part 2, multiply the gallons of water by 2.33 to get the number of sand bags needed:

12 x 2.33 = 27.99, which rounds to 28.

The answer is C) 28 bags.

Answer:

A) [tex]\frac{3}{7}[/tex]

C) 28 bags

Step-by-step explanation:

Part 1 :

By the given table,

[tex]\frac{\text{Gallon of water}}{\text{bags of sand}}=\frac{6}{14}=\frac{9}{21}=\frac{15}{35}=\frac{3}{7}[/tex]

Hence, the proportion of gallons of water to bags of sand is same,

Which is [tex]\frac{3}{7}[/tex]

OPTION A) is correct.

Part 2 : Let x bags of sand should be mixed with 12 gallon of water,

Then the ratio of gallon of water and number of bags of sand = [tex]\frac{12}{x}[/tex]

By part 1,

[tex]\frac{12}{x}=\frac{3}{7}[/tex]

[tex]84 = 3x[/tex] ( by cross multiplication )

[tex]\implies x = \frac{84}{3}=28[/tex]

Hence, 28 bags of sand should be mixed.

OPTION C) is correct.

44%

1. We assume, that the number 375 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 100% equals 375, so we can write it down as 100%=375.

4. We know, that x% equals 165 of the output value, so we can write it down as x%=165.

5. Now we have two simple equations:

1) 100%=375

2) x%=165

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

100%/x%=375/165

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 165 is what percent of 375

100%/x%=375/165

(100/x)*x=(375/165)*x       - we multiply both sides of the equation by x

100=2.27272727273*x       - we divide both sides of the equation by (2.27272727273) to get x

100/2.27272727273=x

44=x

x=44

Answer: Option B

16.8 minutes

Step-by-step explanation:

Machine A produces 75 fishing lures per minute.

Machine B produces 50 fishing lures per minute.

Let's call t time in minutes.

So we want to know how long it will take to produce 2100 fishing lures

We propose the following equation

[tex]75t + 50t = 2100[/tex]

Now we solve for t

[tex]125t = 2100[/tex]

[tex]t = 16.8\ min[/tex]

The answer is Option B

The answer is 243 27×9 is 243 and area is length times width

ANSWER

243 square feet.

EXPLANATION

The rectangular flower bed has length,

l=27 ft

and width, w=9ft.

The area of a rectangle is

Area=length x width

Since the flower bed is rectangular, we use this formula to find its area.

[tex]Area = 27 \times 9 = 243 {ft}^{2} [/tex]

Therefore the area of the flower bed is 243 square feet.

Answer:

8x² + 4x - 5

Step-by-step explanation:

M - N

= 5x² - (- 3x² - 4x + 5) ← distribute parenthesis by - 1

= 5x² + 3x² + 4x - 5 ← collect like terms

= 8x² + 4x - 5

Answer:

slope = 5

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y - 3 = 5(x - 4) ← is in point- slope form

with slope m = 5