Solve the following systems of 3-variable linear equations.​



50 points

Answer:

the circle is shifted -5 on the x and +6 on the y. Center is (-5,6). Radius = 2.

Step-by-step explanation:

Answer:

45/4

Step-by-step explanation:

Volume = h x w x l

First multiply the numbers you have

16 2/3 x 2 4/5= 140/3

Then divide the volume.

525 ÷ 140/3 = 45/4

45/4

Answer:

x > (c - a)/b

Step-by-step explanation:

a > -bx + c

We need to make x the subject of the inequality so, first remove c from the right hand side of the inequality by adding -c to both sides. So,

a - c > -bx

Now, we need to remove -b from the right hand side. So, we will divide both sides of the inequality with -b. Multiplying the inequality with a negative number will also change the sign of the inequality. So,

-(a-c)/b < x

x > (c - a)/b

Answer:

C on edge

Step-by-step explanation:

Answer:

3.75

Step-by-step explanation:

3.75 you couldve used calculator :/

Answer:

3.75.

Step-by-step explanation:

15/4 = 3 with a remainder of 3. (3 3/4)

Then you make that into a decimal...

--> 3/4 is equal to 75 percent.

So 3.75..

Answer:

The stereo is now being sold for $227.80.

Step-by-step explanation:

To calculate percentage discounts, multiply the original price (268) by the discount percentage (.85). Make sure to put move the percentage value two places to the right before multiplying, as percentages are percentages of a whole.

268 * .85 = 227.8

Answer:

Quadrant 2

Step-by-step explanation:

Here's how you distinguish which points are in which quadrants.

Quadrant 1: (+x, +y)

Quadrant 2: (-x, +y)

Quadrant 3: (-x, -y)

Quadrant 4: (+x, -y)

(-3,6) has a negative x and a positive y. All the points in Quadrant 2 have a negative x and positive y.

Answer:

  (x, y) = (1/2, -2)

Step-by-step explanation:

Many people find it convenient to work these problems by eliminating fractions as a first step.

Here, you can do that by multiplying the first equation by 4

  4(1/2x +2y) = 4(-15/4)

  2x +8y = -15

From here, there are a number of possibilities for arriving at a solution.

__

Multiply the first equation by 2 and you have ...

  4x +16y = -30

The second equation says you can replace the first term with -y:

  -y +16y = -30

  15y = -30

  y = -30/15 = -2

Substituting this value into the second equation gives ...

  4x = -(-2) = 2

  x = 2/4 = 1/2

The solution is (x, y) = (1/2, -2).

__

Alternate solution

You can rearrange the second equation to give an expression for y:

  y = -4x

Then, substitute this into the first equation:

  (1/2)x +2(-4x) = -15/4

  (-15/2)x = -15/4

  x = (-15/4)/(-15/2) = 2/4 . . . . . . divide by the coefficient of x

  x = 1/2

  4(1/2) = -y = 2 . . . . . substitute for x in the second equation

  y = -2 . . . . . . . . . . . . multiply by -1

_____

Additional comments on problem solving

I find the key to working troubling problems is to be very meticulous. Make certain you follow the rules of algebra: anything you do to one side of the equation must also be done to the other side. I find it easier to think in those terms when moving stuff around.

Some folks would say, "move this term over there and ...". I like to think of it as "subtract this term from both sides of the equation."

It also helps to be careful when dealing with fractions. Make sure you know how to add, subtract, multiply, and divide fractions. You should be just as able to handle that arithmetic as with integers or decimals. Use a calculator if your skills are shaky.

As you may notice, a graphing calculator can help you verify your answer.

Answer:

it is repeating decimal.

Answer: repeating

Step-by-step explanation:

Step-by-step explanation:

Given : If the hypotenuse of a 30-60-90 triangle has length 15 then the shorter leg has length  5.5 , 6.5 , 7.5.

To find : What is the length of the other leg and hypotenuse ?

Solution :

For a  30-60-90 triangle, sides are in the ratio  [tex]1:\sqrt{3}:2[/tex]

where, 1 is the shorter side,  

[tex]\sqrt{3}[/tex] the other side

and 2 the hypotenuse.

Short leg = 5.5

Other leg = [tex]5.5\times \sqrt3=5.5\sqrt3[/tex]

Hypotenuse = [tex]5.5\times 2=11[/tex]

Short leg = 6.5

Other leg = [tex]6.5\times \sqrt3=6.5\sqrt3[/tex]

Hypotenuse = [tex]6.5\times 2=13[/tex]

Short leg = 7.5

Other leg = [tex]7.5\times \sqrt3=7.5\sqrt3[/tex]

Hypotenuse = [tex]7.5\times 2=15[/tex]

Final answer:

In a 30-60-90 triangle with a hypotenuse of 15, the shorter leg has a length of 7.5, based on the ratio 1:√3:2.

Explanation:

If the hypotenuse of a 30-60-90 triangle has length 15, then to find the length of the shorter leg, we can use the properties of this special right triangle. In a 30-60-90 triangle, the ratio of the lengths of the sides is 1:√3:2. In other words, if the shorter leg is 'x', the longer leg is 'x√3', and the hypotenuse is '2x'.

Since the hypotenuse is 15, we set '2x' equal to 15 and solve for 'x':

2x = 15

x = 15 / 2

x = 7.5

The shorter leg of the triangle has a length of 7.5.

Answer:

8 in

Step-by-step explanation:

The ratio of sides and perimeter in similar figures are equal.

let x be the perimeter of the smaller figure, then by proportion

[tex]\frac{7}{28}[/tex] = [tex]\frac{2}{x}[/tex] ( cross- multiply )

7x = 56 ( divide both sides by 7 )

x = 8

The perimeter of the smaller pentagon is 8 in

Answer:

7)

a. a=5

b. b=7

c. y=10

d. z=6

Step-by-step explanation:

hope this helps:)

Answer:

625 miles

Step-by-step explanation:

This is because, since each 25 miles takes one gallon 25 gallons would mean you would go 25 times 25 miles which is 625 miles in all.

To find the surface area of a 10-quarter stack, calculate the surface area of each quarter and then multiply by the number of quarters.

To find the surface area of a 10-quarter stack, we need to calculate the surface area of each quarter and then multiply it by the number of quarters in the stack. The surface area of a quarter can be calculated using the formula for the surface area of a cylinder: SA = 2πr^2 + 2πrh.

Since the diameter of a quarter is 2.2 cm, the radius (r) is half of that, which is 1.1 cm. The approximate height (h) of a quarter is 0.17 cm.

Substituting these values into the formula, we get: SA = 2π(1.1 cm)^2 + 2π(1.1 cm)(0.17 cm). Calculating this gives us the surface area of a single quarter. Then, multiplying it by 10 gives us the surface area of a 10-quarter stack.

Step-by-step explanation:

BC is tangent to the circle with center A at point C and AC is radius.

[tex] \therefore AC \perp BC\\

\therefore \angle ACB =90°\\[/tex]

Now by Pythagorean theorem:

[tex] AB^2 = AC^2 + BC^2 \\

\therefore AC^2 = AB^2-BC^2\\

\therefore x^2 = 17^2-14^2\\

\therefore x^2 =289-196\\

\therefore x^2 =93\\

\therefore x =\sqrt{93}\\

\therefore x =9.64365076\\

\huge \purple {\boxed {\therefore x = 9.64\: units}} [/tex]

message me! i have made an edited file of it finished <3

Answer: 1/2

Step-by-step explanation: The scale factor of the dilation is 1/2 because it's 1/2 of the other triangle. As you can see it used to be 10, but now it's 5.

Have a good day :D

Answer:

From Triangle ABC to Triangle A'B'C', the scale factor is 1/2

b) 1/2

Step-by-step explanation:

Side Length of Line Segment AC is 8 units

Side Length of Line Segment AB is 6 units

Side Length of Line Segment of BC is 10 units

Side Length of Line Segment A'C' is 4 units

Side Length of Line Segment A'B' is 3 units

Side Length of Line Segment B'C' is 5 units

Checking:

A'C'/AC=4/8=1/2 simplified

Hence, the answer is 1/2 as the scale factor for the dilation.

Answer:-24

explain how you know:

Since xy = 4, we have y=4/x. Substituting in (1) we get f(x) = 4x+(36/x) …….(2)

Differentiating we get f ' (x) = 4 - (36/x^2)…..(2)

For maxima or minima, f ‘ (x) = 0

=> 4 - (36/x^2) =0 => (4x^2 - 36)/x^2 = 0 which gives x= +/- 3

Differentiating (2), f ‘’ (x) = 72/x^3

When x= +3 , f ‘’ (x) is clearly +ve. Therefore f(x) at (2) gives minima and the minimum value is 24.

When x= -3, f ‘’ (x) is -ve. Therefore, f(x) has maxima at x= -3. The maximum value is -24.

Note: You may be surprised to observe that the minima is more than the maxima. This is due to the fact that the function is discontinuous at x= 0, the graph of f(x) comprising of two branches, one in the first quadrant giving the minima (= +24) and another in the third quadrant that gives maxima (= -24)

Answer:

its 125 on edg2020 ;)

Step-by-step explanation:

Answer:

135 grams

Step-by-step explanation:

Since there are 15 grams of powder in a 22oz serving, if you divide 198 by 22 you will get 9 total servings. If you multiply 15 by 9 you will get 135 total grams.

Answer:

8 possibilities

Step-by-step explanation:

The pies we have to choose from are 1)Apple 2)Cherry 3)Blueberry or 4)Peach.

The beverages we have to choose from are 1)Milk and 2)Juice.

Here are the possibilities:

Apple + Juice

Apple + Milk

Cherry + Juice

Cherry + Milk

Blueberry + Juice

Blueberry + Milk

Peach + Juice

Peach + Milk

So we have a total of 8 possibilities for one pie and one beverage.

Answer:

8 outcomes

Step-by-step explanation:

Answer:

A =180 in^2

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh

The base is 12 and the height is 30

A = 1/2 *12*30

A = 1/2 *360

A =180 in^2

Answer:

8, 9

Step-by-step explanation:

Since x > 7

This means that x cannot equal 7 but must be greater values than 7.

Thus 8 and 9 are solutions

Answer:

4 days

Step-by-step explanation:

268-112= 156    

156 divided by 39 = 4

Answer:

i think it is 4

Step-by-step explanation:

bc you do 268-112=156 then you take 156 and divide it by 39 and you end up getting 4.

Answer:

Part A

Months, Pounds

3,5

4,9

5,13

6,17

7,21

8,25

9,29

Part B

1 year = 12 months

If we continue the chart it would look like this:

10,33

11,37

12,41

Lucky will weigh 41 pounds by 1 year.

Hope this helps!

Final answer:

Lucky will weigh 41 pounds by the time he is one year old.

Explanation:

To complete the table representing Lucky’s current weight as a function of his age, we'll calculate Lucky's expected weight at each month by using the growth rate of four pounds per month. Starting with Lucky's current weight at three months old, which is five pounds:

Age 4 months: 5 pounds + (1 month * 4 pounds/month) = 9 pounds

Age 5 months: 5 pounds + (2 months * 4 pounds/month) = 13 pounds

Age 6 months: 5 pounds + (3 months * 4 pounds/month) = 17 pounds

Age 7 months: 5 pounds + (4 months * 4 pounds/month) = 21 pounds

Age 8 months: 5 pounds + (5 months * 4 pounds/month) = 25 pounds

Age 9 months: 5 pounds + (6 months * 4 pounds/month) = 29 pounds

Continuing with the growth rate of four pounds per month, by the time Lucky is one year old, which is 12 months, the calculation would be:

Lucky's weight at one year old = initial weight + (growth over months)

12 months old: 5 pounds + (9 months * 4 pounds/month) = 41 pounds.

Answer:

The answer is x-5 or "B" on edge

Answer:

b

Step-by-step explanation:

use slope intercept form

Answer:

2

Step-by-step explanation:

Since you need it fast, I am not going to explain.

(2, 4) - (6, 12) = (-4, -8)

-8/-4 = 2

Answer:

3

Step-by-step explanation:

The average rate of change of g(x) in the closed interval [ a, b ] is

[tex]\frac{g(b)-g(a)}{b-a}[/tex]

Here [ a, b ] = [ - 3, 2 ], thus

g(b) = g(2) = - 2² + 2(2) + 8 = - 4 + 4 + 8 = 8

g(a) = g(- 3) = - (- 3)² + 2(- 3) + 8 = - 9 - 6 + 8 = - 7

average rate of change = [tex]\frac{8-(-7)}{2-(-3)}[/tex] = [tex]\frac{15}{5}[/tex] = 3

Answer:

Yes

Step-by-step explanation:

The mean octane rating will be 90.3

Hope this helps!

Answer:

Yes

Step-by-step explanation:

The mean is just the average, and it's calculated by adding up all the data set numbers and dividing that sum by the number of numbers:

(90.1 + 88.8 + 89.5 + 91.0 + 92.1) / 5 = 451.5 / 5 = 90.3

Our average/mean is 90.3%, which is clearly greater than 90%. So, yes, we can conclude that the mean octane rating is greater than 90%.

Hope this helps!

Answer:

- the angles in the smaller prism measure 90 degrees

- the perimeter of the rectangular bases changes by a factor of 2

-the area of the rectangular bases changes by a factor of 4

Step-by-step explanation:

I just got it right

Answer:

the angles in the smaller prism measure 90 degrees

the perimeter of the rectangular bases changes by a factor of 2

the area of the rectangular bases changes by a factor of 4

Step-by-step explanation: