Which of the following equations matches the proportional relationship?
(A) A cell phone rate plan costs 6 cents per minute.
y= 0.06x
(B) A bag of 10 apples costs $6.
y= 60x
(C) A car is driving at an average speed of 60 miles per hour.
y= 0.60x
(D) A person burns 6 calories per minute using a rowing machine.
y= 60x

Answer: 90

Step-by-step explanation: You equation is 4(3*7) + 2(1*3). To solve this, you first solve what is on the inside of the parenthesis. so 3 times 7 is 21. And 1 times 3 is 3. So now your equation looks like this 4(21) + 2(3). 4 times 21 is 84 and 2 times 3 is 6. So now your equation is 84 + 6 which equals 90.

Answer:

90

Step-by-step explanation:

4(3*7)+2(1*3)=4(21)+2(3)=84+6=90

Answer:

The coordinates are x = -1 and y = -2.

Step-by-step explanation:

Given:

Equations are 2x-4y=6 and 3x+y=-5.

Now, to find the coordinates.

[tex]2x-4y=6[/tex]...........(1)

[tex]3x+y=-5[/tex]...........(2)

So, first we solve the equation 1 to get the value of [tex]x[/tex].

[tex]2x-4y=6[/tex]

Subtracting both sides by [tex]-4y[/tex] we get:

[tex]2x=6+4y[/tex]

Dividing both sides by 2 we get:

[tex]x=3+2y[/tex]

Now, we put the value of [tex]x[/tex] in equation 2 to get [tex]y[/tex].

[tex]3x+y=-5[/tex]

[tex]3(3+2y)+y=-5[/tex]

[tex]9+6y+y=-5[/tex]

[tex]9+7y=-5[/tex]

On solving the whole equation we get :

[tex]y=-2[/tex]

And, now putting the value of [tex]y[/tex] in equation (1) we get [tex]x[/tex]:

[tex]2x-4y=6[/tex]

[tex]2x-4(-2)=6[/tex]

[tex]2x+8=6[/tex]

[tex]2x=6-8[/tex]

[tex]2x=-2[/tex]

on solving we get:

[tex]x=-1[/tex]

Therefore, the coordinates are x=-1 and y=-2.

984 members of club would be in favor of used-gear sale based on results of survey.

Step-by-step explanation:

Number of people surveyed = 72

People in favor of sale = 63

Percentage of people in favor = [tex]\frac{People\ in\ favor\ of\ sale}{No.\ of\ people\ surveyed}*100[/tex]

Percentage of people in favor = [tex]\frac{63}{72}*100 = \frac{6300}{72}\\[/tex]

Percentage of people in favor = 87.5%

It means that 87.5% members of club will be in favor of sale.

Total members of club = 1125

Total members in favor = 87.5% of total members

[tex]Total\ members\ in\ favor=\frac{87.5}{100}*1125 = \frac{98437.5}{100}\\Total\ members\ in\ favor=984.3[/tex]

Rounding off to nearest whole number

Total members in favor = 984

984 members of club would be in favor of used-gear sale based on results of survey.

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Answer: B

Step-by-step explanation: The equation of the line in Slope-intercept form is:

Where "m" is the slope of the line and "b" is the intersection of the line with the y-axis.

For the graph of the line, you can identify that:

And for, you can identify that:

Therefore, you can observe that the slope does not change, but now the line cuts the y-axis at . In other words, it was moved from to (3 units on the y-axis)

Then, it is the graph of translated 3 units upward, which means that the graph of g(x) is 3 units above the graph of f(x).

The graph of g is 3 units above the graph of f(x), the correct option is A.

The graph is a mathematical representation of the relation between two objects.

It helps in determining the function that fits best for the data obtained.

A function is a mathematical statement that defines a relationship between a dependent and an independent variable.

A function always has a defined range and domain, domain is all the value a function can have as input and range is all the value that a function can give as output.

The function f(x) = 2x

g(x) = 2x+3

Both functions are a straight line, an equation of a straight line is given by y =mx +c, m is the slope of the line and c is the y intercept.

In the function f(x), the slope is 2 and the intercept is 0

In the function g(x), the slope is 2 and the intercept is 3.

As the intercept is 3, the g(x) is 3 units above the graph f(x).

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The equation of the line that is parallel to y = -5x + 6 and passes through the point (-4, -1) in slope intercept form is y = -5x -21

Given that line passes through the point (-4, -1) and parallel to y = -5x + 6

We have to find the equation of line

Let us first calculate the slope of line having equation as y = -5x + 6

The slope intercept form of line is given as:

y = mx + c ---- eqn 1

where "m" is the slope of line and "c" is the y-intercept

Comparing the given equation of line y = -5x + 6 with slope intercept form y = mx + c,

we get the slope of line "m" = -5

We know that slope of two given parallel lines are always equal

Hence the slope of line which is parallel to line with equation y = -5x + 6 is also -5

Now we have to find the equation of line passing through point (-4, -1) with slope -5

Substitute (x, y) = (-4, -1) and m = -5 in eqn 1 to find "c" intercept

-1 = -5(-4) + c

-1 = 20 + c

c = -21

Substitute c = -21 and m = -5 in eqn 1 to get the equation of line

y = -5x + (-21)

y = -5x -21

Thus the equation of required line is found out as y = -5x -21

Answer:

The y-intercept is (0,-26)

Step-by-step explanation:

Given two points P(a,b) and Q(c,d), the line that passes for both points can be found with the expression

[tex]\displaystyle y-b=\frac{d-b}{c-a}(x-a)[/tex]

We'll take the first two points P(34,-52) and Q(51,-65) to find

[tex]y=-\frac{13}{17}(x-34)-52\\ \\y=-\frac{13}{17}x-26[/tex]

Let's verify if the third point is on the line:

[tex]y=-\frac{13}{17}68-26=-52-26=-78[/tex]

It belongs to the line. To find the y-intercept of the line, we set x to 0

[tex]y=-\frac{13}{17}(0)-26=-26[/tex]

The y-intercept is (0,-26)

Answer:

The length of VW is [tex]25\ m[/tex]

Step-by-step explanation:

we know that

The perimeter of triangle TVW is equal to

[tex]P=VW+TV+TW[/tex]

we have

[tex]P=74\ m[/tex]

so

[tex]74=VW+TV+TW[/tex] -----> equation A

[tex]VW=TV+3[/tex] ----> equation B

[tex]TW=(VW+TV)-20[/tex] ----> equation C

substitute equation B in equation C

[tex]TW=(TV+3+TV)-20[/tex]

[tex]TW=2TV-17[/tex] ----> equation D

substitute equation B and equation D in equation A

[tex]74=(TV+3)+TV+(2TV-17)[/tex]

solve for TV

[tex]74=4TV-14[/tex]

[tex]4TV=74+14[/tex]

[tex]4TV=88[/tex]

[tex]TV=22\ m[/tex]

Find the value of VW

[tex]VW=TV+3[/tex] -----> [tex]VW=22+3=25\ m[/tex]

Find the value of TW

[tex]TW=2TV-17[/tex] -----> [tex]TW=2(22)-17=27\ m[/tex]

Answer:

Part 11) The table represent a direct variation. The equation is [tex]y=18x[/tex]

Part 12) The table represent a direct variation. The equation is [tex]y=0.4x[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Part 11)

For x=0.5, y=9

Find the value of k

[tex]k=y/x[/tex] -----> [tex]k=9/0.5=18[/tex]

For x=3, y=54

Find the value of k

[tex]k=y/x[/tex] -----> [tex]k=54/3=18[/tex]

For x=-2, y=-36

Find the value of k

[tex]k=y/x[/tex] -----> [tex]k=-36/-2=18[/tex]

For x=1, y=18

Find the value of k

[tex]k=y/x[/tex] -----> [tex]k=18/1=18[/tex]

For x=-8, y=-144

Find the value of k

[tex]k=y/x[/tex] -----> [tex]k=-144/-8=18[/tex]

The values of k is the same for each ordered pair

therefore

The table represent a direct variation

The linear equation is

[tex]y=18x[/tex]

Part 12)

For x=-5, y=-2

Find the value of k

[tex]k=y/x[/tex] -----> [tex]k=-2/-5=2/5=0.40[/tex]

For x=3, y=1.2

Find the value of k

[tex]k=y/x[/tex] -----> [tex]k=1.2/3=0.40[/tex]

For x=-2, y=-0.8

Find the value of k

[tex]k=y/x[/tex] -----> [tex]k=-0.8/-2=0.4[/tex]

For x=10, y=4

Find the value of k

[tex]k=y/x[/tex] -----> [tex]k=4/10=0.4[/tex]

For x=20, y=8

Find the value of k

[tex]k=y/x[/tex] -----> [tex]k=8/20=0.4[/tex]

The values of k is the same for each ordered pair

therefore

The table represent a direct variation

The linear equation is

[tex]y=0.4x[/tex]

Answer:

C = [tex]$ \frac{1}{10} $[/tex]

D = [tex]$ \frac{1}{10^2} $[/tex]

Step-by-step explanation:

78.09 = 7 [tex]$ \times A + 8 \times B + 0 \times C + 9 \times D $[/tex]

78.09 = 7 [tex]$ \times 10^1 + 8 \times 10^0 + 0 \times \frac{1}{10} + 9 \times \frac{1}{10^2}[/tex]

⇒ C = [tex]$ \frac{1}{10} $[/tex]

   D = [tex]$ \frac{1}{10^2} $[/tex]

Hence, the answer.

The standard form of a parabola with points through (2, 0) (3, 2) (4, 6)

is y = x² - 3x + 2 ⇒ 3rd answer

Step-by-step explanation:

The standard form of a parabola is y = ax² + bx + c, where a, b , c are constant

To find a , b , c

∵ The standard form of a parabola is y = ax² + bx + c

∵ The parabola passes through points (2 , 0) , (3 , 2) , (4 , 6)

- Substitute the coordinates of each point in the equation

Point (2 , 0)

∵ x = 2 and y = 0

∴ 0 = a(2)² + b(2) + c

∴ 0 = 4a + 2b + c

- Switch the two sides

∴ 4a + 2b + c = 0 ⇒ (1)

Point (3 , 2)

∵ x = 3 and 2 = 0

∴ 2 = a(3)² + b(3) + c

∴ 2 = 9a + 3b + c

- Switch the two sides

∴ 9a + 3b + c = 2 ⇒ (2)

Point (4 , 6)

∵ x = 4 and y = 6

∴ 6 = a(4)² + b(4) + c

∴ 6 = 16a + 4b + c

- Switch the two sides

∴ 16a + 4b + c = 6 ⇒ (3)

Subtract equation (1) from equations (2) and (3)

∴ 5a + b = 2 ⇒ (4)

∴ 12a + 2b = 6 ⇒ (5)

- Multiply equation (4) by -2 to eliminate b

∴ -10a - 2b = -4 ⇒ (6)

- Add equations (5) and (6)

∴ 2a = 2

- Divide both sides by 2

∴ a = 1

Substitute the value of a in equation (4) to find b

∵ 5(1) + b = 2

∴ 5 + b = 2

- Subtract 5 from both sides

∴ b = -3

Substitute the value of a and b in equation (1) to find c

∵ 4(1) + 2(-3) + c = 0

∴ 4 - 6 + c = 0

- Add like terms

∴ -2 + c = 0

- Add 2 to both sides

∴ c = 2

Substitute the values of a , b , c in the standard form above

∵ y = ax² + bx + c

∵ a = 1 , b = -3 , c = 2

∴ y = (1)x² + (-3)x + (2)

∴ y = x² - 3x + 2

The standard form of a parabola with points through (2, 0) (3, 2)

(4, 6) is y = x² - 3x + 2

There is another solution you can substitute the x-coordinate of each point in each answer to find the corresponding value of y, if the value of y gives the same value of the y-coordinate of the point for the three points then this answer is the standard form of the parabola

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Answer:

C. y = x^2 - 3x + 2

Step-by-step explanation:

(4,6)

6 = 4² - 3(4) + 2

6 = 16 - 12 + 2

6 = 6

2 = 2

(3,2)

2 = 3² - 3(3) + 2

2 = 9 - 9 + 2

2 = 2

(2,0)

0 = 2² - 3(2) + 2

0 = 4 - 6 + 2

0 = 0

Answer:

12 km/h

Step-by-step explanation:

Given: Distance covered by boat downstream = 50 km

           Distance covered by boat upstream = 30 km

           Time taken by boat in down stream and upstream are equal.

           Speed of the stream = 3 km/h

Let x be the speed of boat in still water.

∴ Speed of boat in downstream [tex](s_1)[/tex] = [tex](x+3)\ km/h[/tex]

Speed of boat in upstream [tex](s_2)[/tex] = [tex](x-3)\ km/h[/tex]

As we know, [tex]Time = \frac{Distance}{speed}[/tex]

And time remain same for both upstream and downstream

∴ [tex]\frac{50}{(x+3)} = \frac{30}{(x-3)}[/tex]

Now, cross multiply both side

⇒  [tex]50\times (x-3) = 30\times (x+3)[/tex]

⇒ [tex]50x-30x = 150+90[/tex]

∴ [tex]x= 12\ km/h[/tex]

∴ Speed of boat in still water is 12 km/h

For this case we must simplify the following expression:

[tex](2x ^ 3 + 6x-1) + (3x ^ 2-7x)[/tex]

We eliminate the parentheses taking into account that:

[tex]+ * + = +\\+ * - = -[/tex]

So, we have:

[tex]2x ^ 3 + 6x-1 + 3x ^ 2-7x =[/tex]

We add similar terms taking into account that:

Different signs are subtracted and the sign of the major is placed:

[tex]2x ^ 3 + 3x^2-x-1[/tex]

Answer:

[tex]2x ^ 3 + 3x^2-x-1[/tex]

1) Find the solution to each equation.

A) 4(2x - 1) = -3x + 32

The solution to the equation 4(2x - 1) = -3x + 32 is x = 3.273

Need to find the solution of following equation

4(2x - 1) = -3x + 32

Let use BODMAS rule to solve the expression

According to Bodmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right.

On opening the bracket of left hand side we get

[tex]4 \times 2x-4 \times 1=-3 x+32[/tex]

Now perform multiplication,

8x – 4 = -3x + 32

On bringing terms having variable x in left hand side and constant term on right hand side we get

8x + 3x = 32 + 4

=> 11x  = 36

On dividing both sides by 11, we get

[tex]\begin{array}{l}{\Rightarrow \frac{11 x}{11}=\frac{36}{11}} \\\\ {\Rightarrow x=\frac{36}{11}=3.273}\end{array}[/tex]

Hence solution of equation 4(2x - 1) = -3x + 32 is 3.273

Answer:

30x+45

Step-by-step explanation:

5*6x=30x

5*9=45

Answer:

30x + 45

Step-by-step explanation:

We distribute the 5 to the variable 6x and the constant 9:

5(6x+9)

5 x 6x = 30x

5 x 9 = 45

The answer is 30x + 45

Answer:

198

Step-by-step explanation:

-511 + (+709) =

709 - 511 = 198

Answer:

-511 + 709 = 198

Step-by-step explanation:

-511+709 is the same as 709-511

A function that gives the amount that the plant earns per man-hour t years after it opens is [tex]\mathrm{A}(\mathrm{t})=80 \times 1.05^{\mathrm{t}}[/tex]

Given that  

A manufacturing plant earned $80 per man-hour of labor when it opened.

Each year, the plant earns an additional 5% per man-hour.

Need to write a function that gives the amount A(t) that the plant earns per man-hour t years after it opens.  

Amount earned by plant when it is opened = $80 per man-hour

As it is given that each year, the plants earns an additional of 5% per man hour

So Amount earned by plant after one year = $80 + 5% of $80 = 80 ( 1 + 0.05) = (80 x 1.05)

Amount earned by plant after two years is given as:

[tex]=(80 \times 1.05)+5 \% \text { of }(80 \times 1.05)=(80 \times 1.05)(1.05)=80 \times 1.052[/tex]

Similarly Amount earned by plant after three years [tex]=80 \times 1.05^{t}[/tex]

[tex]\begin{array}{l}{\Rightarrow \text { Amount earned by plant after } t \text { years }=80 \times 1.05^{t}} \\\\ {\Rightarrow \text { Required function } \mathrm{A}(t)=80 \times 1.05^{t}}\end{array}[/tex]

Hence a function that gives the amount that the plant earns per man-hour t years after it opens is [tex]\mathrm{A}(t)=80 \times 1.05^{t}[/tex]

Do:

3x6

(3)(6)

6+6+6

Do not:

(3)-(6)

3/6

3+6

Answer:

b. y = 27x

Step-by-step explanation:

When you talk about "per" it means multiplication, and 27 is being multiplied by (x) gallons of gas.

Answer:

16a^4

Step-by-step explanation:

You do 4a^2*4a^2= 16a^4 because area of square is length times width and we know that that length and width in a square is equal.

4*4= 16

a^2*a^2= a^4 (because when you multiply powers with the same base like a in this case, you add the powers up. So in this example it would be 2+2= 4)

Put them together to give you 16a^4

Final answer:

The area of a square with a side length of 4a² is A = 16a⁴, showcasing the area's proportionality to the fourth power of side length a.

Explanation:

The expression for the area of a square with a side length of 4a squared is found by squaring the side length. Since the side of the square is 4a², the area A is given by:

A = (4a²) × (4a²) = 16a⁴

The simplified expression for the area is 16a to the fourth power, which indicates that the area is proportional to the fourth power of the side length a.

Answer:

d.every word in the first sentence of the first page of every chapter.

Step-by-step explanation

Answer:

Step-by-step explanation:

[tex]x^2-3x=28\qquad\text{subtract 28 from both sides}\\\\x^2-3x-28=0\\\\x^2+4x-7x-28=0\qquad\text{distribute}\\\\x(x+4)-7(x+4)=0\\\\(x+4)(x-7)=0\iff x+4=0\ \vee\ x-7=0\\\\x+4=0\qquad\text{subtract 4 from both sides}\\\boxed{x=-4}\\\\x-7=0\qquad\text{add 7 to both sides}\\\boxed{x=7}[/tex]

Answer:

x = -4 or x = 7

Answer:

The error Tara made is she rewrote incorrectly 3 3/8 as 17/8 and 4 1/9 as 13/9,

the corrected number can be rewrote as 3 3/8 as 27/8 and 4 1/9 as 37/9.

Step-by-step explanation:

To find the Product of:

[tex]3\frac{3}{8}\times 4\frac{1}{9}[/tex]

The Number can be rewrote as,

[tex]\frac{3\times8+3}{8}\times \frac{4\times9+1}{9}\\\\\frac{24+3}{8}\times \frac{36+1}{9}\\\\\frac{27}{8}\times \frac{37}{9}[/tex]

Tara made error here she rewrote the number incorrectly 3 3/8 as 17/8 amd 4 1/9 as 13/9.

Now multiplying the fraction we get

[tex]\frac{999}{72}[/tex]

Because she rewrote incorrectly which led her answer to multiplication of fraction, the product too was incorrect which she wrote as 221/72.

The expression x=20-3D will present the amount Amy has left after buying D sodas.

Step-by-step explanation:

Given,

Total amount = 20 quarters

Cost of sodas = $0.75 = 0.75*100 = 75 cents

25 cents = 1 quarter

1 cent = [tex]\frac{1}{25}\ quarter[/tex]

75 cents = [tex]\frac{1}{25}*75[/tex] = 3 quarters

Amount of D sodas = 3D

Let x be the amount left with Amy.

Amount left = total amount - Amount of D sodas

[tex]x=20-3D[/tex]

The expression x=20-3D will present the amount Amy has left after buying D sodas.

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Answer:

he can only buy 5

Step-by-step explanation:

7x5=35

he has 2 bucks left

Answer:

5

Step-by-step explanation:

5 times 7 is 35.  5 times 8 is 40 which is 3 dollars more than he has therefore he can only buy 5.

1. The rate of change is -1 and the initial value is 1.

2. The graph represents Ava’s travel plans is graph (I).

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

1. We have the coordinates as C(3, -2) and D(-2, 3).

So, the rate of change of linear function is

= 3 - (-2) / (-2 -3)

= 3+ 2 / (-5)

= 5/ (-5)

= -1.

and, the initial values is where the independent variable is zero which is (1, 0).

2. The graph represented for Ava journey is (A).

This, is because the speed of Ava car and speed of taxi is equal which is shown in graph 1 clearly.

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1. The rate of change is -1 and the initial value is 1 (Option B). 2. The graph represents Ava’s travel plans is: option A (Graph 1).

The rate of change for a linear function is given by the slope of the line. The slope (m) can be calculated using the formula:

m = change in y / change in x

In this case, using the given points C (3, -2) and D (-2, 3):

[tex]\[ m = \frac{{3 - (-2)}}{{(-2) - 3}} = \frac{{5}}{{-5}} = -1 \][/tex]

So, the rate of change is -1.

The initial value of a linear function is the y-intercept, which is the y-coordinate when x = 0. Substituting (x, y) = (-2, 3) and m = -1 into y = mx + b, find b (initial value):

3 = -1(-2) + b

3 = 2 + b

3 - 2= b

b = 1.

Therefore, the correct answer is:

B. The rate of change is -1, and the initial value is 1.

2. The graph depicting Ava's journey is labeled as (A) because it clearly illustrates that Ava's car and the taxi have the same speed, as shown in Graph 1.

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Answer:

30 hours

Step-by-step explanation:

Let the small pipe take time "t" to fill up the tank alone

Since larger pipe takes 15 HOURS LESS, so it will take "t - 15" time to fill up the tank alone

Let the whole tank be equal to "1" and each pipe fills up a fraction of the tank.

Smaller Pipe fills up 10/t, and

Larger Pipe fills up 10/(t-15)

Totalling "1". So we can write:

[tex]\frac{10}{t}+\frac{10}{t-15}=1[/tex]

Now, we solve for t. First, we multiply whole equation by (t)(t-15), to get:

[tex]t(t-15)*[\frac{10}{t}+\frac{10}{t-15}=1]\\(t-15)(10)+10t=t(t-15)[/tex]

Now we multiply out and get a quadratic and solve by factoring. Shown below:

[tex](t-15)(10)+10t=t(t-15)\\10t-150+10t=t^2-15t\\20t-150=t^2-15t\\t^2-35t+150=0\\(t-30)(t-5)=0\\t=5,30[/tex]

Since, this time is for the smaller pipe (which takes longer than 15 hours), so we disregard t = 5 and take t = 30 as our solution. So,

Smaller pipe takes 30 hours to fill up the tank alone

The smaller pipe takes 30 hours to fill the tank on its own, determined by solving the equation derived from the combined and individual rates at which each pipe fills the tank.

Since they can jointly fill the tank in 10 hours, we can use the rates at which they fill the tank to set up the equation: 1/x + 1/(x - 15) = 1/10. To find the solution, we multiply each term by 10x(x - 15) to clear the denominators, which gives us 10(x - 15) + 10x = x(x - 15). This simplifies to 20x - 150 = x^2 - 15x. Rearranging the terms yields x^2 - 35x + 150 = 0, which can be factored into (x - 30)(x - 5) = 0. Thus, x could be either 30 hours or 5 hours. Since x - 15 must also be positive, x = 30 hours is the correct solution, meaning the smaller pipe takes 30 hours to fill the tank alone.

Answer:

n = -2

Step-by-step explanation:

Distribute first.

-32 - 32n = 8n + 48

Subtract 8n.

-32 - 40n = 48

Add 32

-40n = 80

n = -2

Answer: download Photomath is the best!! The answer is n=-2

Step-by-step explanation: