Given the system of equations.

4x+y=8

6x-9y=12

Which of the options represents the resulting equation after an equivalent expression for y is substituted into the second equation?

6x - 9(4x - 8) = 12

4x + 4x - 8 = 8

6(4x - 8) - 9y = 12

6x - 9(-4x + 8) = 12

Answer:

Step-by-step explanation:

1/40=3/120

Answer:

Thus; Jupiter travels at 480 miles/m and in 6 minutes, it will travel 2880 miles.

Step-by-step explanation:

First to convert it you need to multiply 8 miles per second by 60 seconds because there are 60 seconds in a minute:

 8 miles    x    60 s 

1 second        1 min

The unit of seconds will cancel out so you will get 480 miles/ min

To get how far it travels in 6 min you need to multiply the speed by 6 minutes

480 miles   x  6 min = 2880

  1 min

The unit of minutes will cancel out to get 2880 miles

Answer:

$0.25 per pound.

Step-by-step explanation:

Let us find unit rate for both quantities.

[tex]\text{Price per pound}=\frac{8.75\text{ dollars}}{2.5\text{ pound}}[/tex]

[tex]\text{Price per pound}=3.5\frac{\text{ dollars}}{\text{ pound}}[/tex]  

Therefore, cost of per pound for first given rate is $3.5.

Now let us find unit rate for second quantity.

[tex]\text{Price per pound}=\frac{9.75\text{ dollars}}{3\text{ pound}}[/tex]

[tex]\text{Price per pound}=3.25\frac{\text{ dollars}}{\text{ pound}}[/tex]

We can see that price for second quantity is less than 1st. To find the savings per pound we will subtract 3.25 from 3.5.

[tex]\text{Savings per pound}=3.50-3.25[/tex]

[tex]\text{Savings per pound}=0.25[/tex]

Therefore, we will save $0.25 per pound by buying the least expensive.

Answer:

0.25

Step-by-step explanation:

Answer:

Point R = 8

Step-by-step explanation:

-2.5 r = -20

The solution to this equation is represented by a number line

In the given equation we have only the variable 'r'

We will get the value of 'r' while solving the above equation

That 'r' value is the solution point R on number line

[tex]-2.5r = -20[/tex]

divide by -2.5 on both sides

[tex]r=\frac{-20}{-2.5}[/tex]

r= 8 is our solution

Answer:

280 minutes

Step-by-step explanation:

First, you must find the miles per minute:

112/14 = 8

Then you must multiply the miles per minute by the amount of miles:

35 * 8 = 280

Answer: 11.6 units.

Step-by-step explanation:

1. Plot the points as you can see in the graph attached.

2. As you can see, the lenght TA is 3 units.

3. Apply the formula for calculate the distance between two points, to calculate the length TP and TA. The formula is:

[tex]d=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}[/tex]

4. Therefore, you have:

[tex]TP=\sqrt{(1-3)^{2}+(4-0)^{2}}=4.47units[/tex]

[tex]AP=\sqrt{(4-3)^{2}+(4-0)^{2}}=4.12units[/tex]

5. The perimeter is the sum of the the lenght of each side, therefore:

[tex]Perimeter=3units+4.47units+4.12units\\Perimeter=11.59units[/tex]

6. To the nearest tenth unit:

[tex]Perimeter=11.6units[/tex]

Answer:

130 m

Step-by-step explanation:

Let surface of ocean be at 0 feet (sea level)

The distance from albatross to surface is 100 and the distance from surface to shark is 30 m. The total distance between them is [tex]100+30=130[/tex]

Distance between shark and albatross is 130 m

Answer:

130 m

Step-by-step explanation:

Answer:

78

Step-by-step explanation:

112-18-16=78

Answer:

Correct answer is 2/3.

Step-by-step explanation:

Answer:The answer is mostly C) 10

Step-by-step explanation:

It's C because when you go to day 9, you count after 58 by adding 4 more, which equals 62 and then, since day 10) is 68 people that means that the answer is C.

Answer: c 10

Step-by-step explanation:

Since each day 4 more people sign up, on day 7, 50 will have signed up; on day 8, 54 people; day 9, 58 people; and day 10, 62 people

Answer:

2.  x=-2  y= 2

3. x=3 y=0

Step-by-step explanation:

-2x - 3 y = -2

y = 2x + 6

The first step is to get x and y on the same side

Take the second equation and subtract 2x from each side

-2x+ y = 2x-2x + 6

-2x+y = 6

Multiply this by -1

-1(-2x+y) =-1*6

2x -y =-6

Add this to the first equation  to eliminate x

-2x - 3 y = -2

2x -y =-6

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

-4y = -8

Divide by -4

-4y/-4 = -8/-4

y =2

Now we need to find x

y = 2x + 6

Substituting in y=2

2 = 2x+6

Subtract 6 from each side

2-6 = 2x+6-6

-4 = 2x

Divide by 2

-4/2 = 2x/2

-2 =x

3) -x - 18 y = -3

7x - 9 y = 21

We will eliminate by by multiplying the second equation by -2

-2(7x - 9 y) = -2*21

-14x + 18y = -42

Now we will add this to the first equation

-x - 18 y = -3

-14x + 18y = -42

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

-15x    = -45

Divide by -15

-15x/-15 = -45/-15

x =3

We still need to solve for y

-x -18y = -3

Substituting in x =3

-3 -18y = -3

Add 3 to each side

-3+3 -18y =-3+3

-18y =0

Divide by -18

y= 0

Answer:

54.01

If it’s an less than problem then

49.01<54.01<100

Step-by-step explanation:

100-54.99

= 54.01

Answer:

17+6i

-----------

25

Step-by-step explanation:

2+3i

---------

4+3i

We want to multiply by the complex conjugate of the denominator

4+3i has a complex conjugate of 4-3i

2+3i             4-3i

--------- * --------------

4+3i           4-3i

Lets multiply the numerator

(2+3i) ( 4-3i)

2*4 +4*3i -3i*2 - 3i*3i =

8 +12i -6i - 9i^2

Remember i^2 = -1

8 +6i -9(-1)

17 +6i

Lets multiply the denominator

(4+3i) ( 4-3i)

4*4 +4*3i -3i*4 - 3i*3i =

16 +12i -12i - 9i^2

Remember i^2 = -1

16 -9(-1)

25

Putting numerator over denominator

17+6i

-----------

25

Answer: 7 + 2/3(12) = 15

90/15 = $6 for adult tickets

Answer:

[tex]y=-\frac{7}{18}x^2+\frac{41}{18}x+\frac{64}{9}[/tex]

Step-by-step explanation:

We need to write a quadratic equation so we can use standard quadratic equation:

[tex]y=ax^2+bx+c[/tex]

Plug the given points to get three equations.

for (7,4), we plug x=7 and y=4

[tex]4=a(7)^2+b(7)+c[/tex]

[tex]4=49a+7b+c[/tex] ...(i)

similarly using other two points, we get:

[tex]1=4a-2b+c[/tex] ...(ii)

[tex]9=a+b+c[/tex] ...(iii)

Now we solve those three equations by any method like substitution, or matrices or by any method and get:

[tex]a=-\frac{7}{18},\ b=\frac{41}{18},\ c=\frac{64}{9}[/tex]

Now plug these values into [tex]y=ax^2+bx+c[/tex], we get final equation as:

[tex]y=-\frac{7}{18}x^2+\frac{41}{18}x+\frac{64}{9}[/tex]

Answer:

35.7

Step-by-step explanation:

First, you would calculate how many gallons of gasoline the car gets. To do this, divide your total mileage of 500 miles by the mpg (30). Now you know how many gallons of gasoline will be used by the car. After calculating, you get 16.67. Multiply this by how much it costs per gallon of gasoline, and you get an answer of $35.7.

Answer:

The limit does not exist

Step-by-step explanation:

lim as we approach from below 7

x+5 when x=7  

7+5

12

lim as we approach from above 7

5x-25 when x=7  

5*7 -25

35-25

10

The limit does not exist since these numbers are not the same

Answer:

Limit [tex]7^{-}[/tex] (left hand side limit) is 12

Limit [tex]7^{+}[/tex] (right hand side limit) is 10

Limit at 7 DOES NOT EXIST

Step-by-step explanation:

Limit [tex]7^{-}[/tex]:

When we want to find limit of left side of 7, we take the first part of the function shown (since its defined for [tex]x\leq7[/tex]).

We check values very close to 7 but less than it:

So the limit is approaching 12.

Thus, left hand side limit is 12.

Limit [tex]7^{+}[/tex]:

When we want to find limit of right side of 7, we take the second part of the function shown (since its defined for [tex]x>7[/tex]).

We check values very close to 7 but greater than it:

So the limit is approaching 10.

Thus, right hand side limit is 10.

Limit at 7:

If both right hand side limit and left hand side limit equal, then the limit at that specific number exists and is equal to it.

Since we see that the left hand limit (12) and the right hand limit (10) ARE NOT EQUAL, so we conclude that the limit at 7 for the function given DOES NOT EXIST.

Suppose the polygons have 3 sides, [tex]s_1,s_2,s_3[/tex]. In the smaller polygon, the corresponding sides would have lengths [tex]\dfrac25s_1,\dfrac25s_2,\dfrac25s_3[/tex].

So if the perimeter of the larger polygon is

[tex]s_1+s_2+s_3=85[/tex]

then the perimeter of the smaller polygon would be

[tex]\dfrac25(s_1+s_2+s_3)=\dfrac25\cdot85[/tex]

so its perimeter would be 34 meters.

Final answer:

The perimeter of the smaller similar polygon is 34 meters, calculated by setting up and solving the proportion 2/5 = P/85.

Explanation:

When dealing with similar polygons, the ratio of their corresponding side lengths is the same as the ratio of their perimeters. Given that the ratio of the sides is 2 to 5, and the perimeter of the larger polygon is 85 meters, we can set up a proportion to find the perimeter of the smaller polygon.

Let the perimeter of the smaller polygon be P. The proportion will be 2/5 = P/85. To find P, we cross-multiply and get: 2 * 85 = 5 * P. Simplifying, we find that P equals 34 meters. Hence, the perimeter of the smaller polygon is 34 meters.

Answer:

16 rotations.  

Step-by-step explanation:

We have been given that Shawn is coasting down a 500 cm long ramp on his inline skates. The wheels on his inline skates are 32 cm in circumference.

To find the number of rotations we will divide length of ramp by 32 as distance covered by wheels in one rotation will be equal to 32 cm.

[tex]\text{Number of rotations}=\frac{\text{Total distance}}{\text{Circumference of wheel}}[/tex]

[tex]\text{Number of rotations}=\frac{500}{32}[/tex]

[tex]\text{Number of rotations}=15.625\approx 16[/tex]

Therefore, each wheel must make 16 rotations while Shawn is coasting down the ramp.

Answer:

The regular price was $93.03

Step-by-step explanation:

In order to find the regular price, divide the amount spent by the percentage of which she paid for it. Since it was 25% off, she paid 75% of the overall price.

$69.77/75% = $93.03

Answer:  True, False, True

Step-by-step explanation:

To determine steepness, compare the coefficients of each function:

f(x) = 4x²      coefficient is: 4

g(x) = [tex]\dfrac{15}{4}x^2[/tex]   coefficient is: 4.75

h(x) = [tex]\dfrac{4}{15}x^2[/tex]   coefficient is: 0.27

f(x)  ??? h(x)

 4    >  0.27

f(x) is steeper than h(x)

               h(x) ??? g(x)

               0.27 <   4.75

               h(x) is LESS steep than g(x)

                                              g(x) ??? f(x)

                                              4.75 >   4

                                              g(x) is steeper than f(x)

Answer:

1/9

Step-by-step explanation:

1/3 ÷ 3 is the set-up for the problem we are trying to solve.

Remember when we divide fractions we multiply by the reciprocal. So we have:

1/3 × 1/3 since the reciprocal of 3/1 is 1/3

Multiplying 1/3 x 1/3 we find the product is 1/9

Therefore, each person would receive 1/9 of the watermelon

Answer:

left 3 units

down 1 unit

Step-by-step explanation:

The required transformation is obtained by shifting of 3 units left and 1 unit down. The correct options are (c) and (d).

The graph of a function can be transformed by either shifting it in the right, left, up or down.

When the transformation is rightwards, the function becomes as f(x - a).

The given functions are as below,

f(x) = [tex]2^{x - 6} + 3[/tex]

And, g(x) = [tex]2^{x - 3} + 2[/tex]

It can be rewritten as,

g(x) = [tex]2^{x - 3} + 2[/tex] = [tex]2^{x - 6 + 3} + 3 - 1[/tex]

It clearly shows as per the rule of transformation, f(x) is shifted 3 units left and 1 unit down to get g(x).

Hence, the parent function f(x) is shifted 3 units left and 1 unit down.

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Answer:

The answer is 17 items in 5 groups.

Step-by-step explanation:

If we have 20 pencils + 25 erasers + 40 paper clips; that´s a total of 85 items.

Then we just divide all the items into 5 groups so we can have the same amount of items in each group.

85 items  ÷ 5 groups = 17 items each.

17 x 5 = 85.

Answer:

[tex] \displaystyle y _{ \text{parallel}} = \frac{5}{6} x- 2[/tex]

Step-by-step explanation:

we are given a equation of line

[tex] \displaystyle y = \frac{5}{6} x - 10[/tex]

we want to figure out the line Parallel to the given line and passes through (12,8)

to figure out the parallel line we need to figure out two things one is the Slope of the parallel line another is the y-intercept of the parallel line

figuring out the slope of the parallel line is easy because we know that parallel lines have the same slope therefore,

[tex] \displaystyle m _{ \text{parallel}} = \frac{5}{6} [/tex]

now we need to figure out the y-intercept and the equation to do so we can consider the following formula:

[tex] \displaystyle y - y_{1} = m(x - x_{1})[/tex]

we the point where the parallel line passes i.e [tex](x_1,y_1)=(12,8)[/tex] and we already got that the slope is ⅚ thus substitute:

[tex] \displaystyle y - 8= \frac{5}{6} (x- 12)[/tex]

we can figure out the equation by simplifying the above equation to slope-intercept form in order to do so

distribute:

[tex] \displaystyle y - 8= \frac{5}{6} x- \frac{5}{6} \times 12[/tex]

reduce fraction:

[tex] \displaystyle y - 8= \frac{5}{6} x- 5 \times 2[/tex]

simplify multiplication:

[tex] \displaystyle y - 8= \frac{5}{6} x- 10[/tex]

add 8 to both sides:

[tex] \displaystyle y = \frac{5}{6} x- 2[/tex]

and we are done!

Answer:

767

Step-by-step explanation:

The relationship between the weight of a person on Earth and the

person's weight on the Moon is a  proportional relationship.

Reasons:

The weight of the person on Earth = 120 pounds

Weight of the person on the Moon = 20 pounds

Required:

The weight of a person that weighs 93 pounds on Earth on the Moon

Solution:

Let x represent the factor (acceleration due to gravity) on Earth, let y

represent the factor on the Moon, and let m, represent the mass of the

person, we have;

x·m = 120

y·m = 20

Therefore;

[tex]\displaystyle \mathbf{\frac{x \cdot m}{y \cdot m}} = \mathrm{\frac{x}{y} } = \frac{120}{20} = 6[/tex]

For the person that weighs 93 pounds on Earth, we have;

[tex]\displaystyle \mathrm{\frac{x}{y} } = \mathbf{\frac{93}{Weight \ on \ the \ Moon}} = 6[/tex]

Which gives;

[tex]\displaystyle Weight \ of\ the \ person\ on \ the\ Moon = \frac{93}{6} = 15.5[/tex]

The weight of the person on the Moon = 15.5 pounds

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Answer: B) x = -3

Every point on this line has one thing in common: the x coordinate is -3. This is why x is fixed at -3, so we simply say the equation is x = -3

Some example points on this line are (-3,10) and (-3,2)

The y coordinate can be anything you want, so that is why it doesn't show up at all (because it doesn't affect how x will turn out).

The correct answer is option C - Spanish.

From which language does the underlined phrase originate? When the house guests arrived, Granny said, "Mi casa es su casa."

"mi casa es su casa" is a common Spanish expression which means - "welcome" or "make yourself at home" Mi casa es su casa literally means "my house is your house".

Answer:

you would divide 28 by 8 and get 3.5. so around 3:30 per song

Step-by-step explanation:

Answer:

Step-by-step explanation:28÷8=3.5 , each song is 3 and a half minutes long