3. The triangles are similar. Find the value of x.

Step-by-step explanation:

     graphing.

substitution method.

elimination method.

We will use as an example the following system of inequalities:

3x +2y ≥ 5x -4

y < (1/2)x +3

For each inequality, do the following:

1. If it is not this way already, arrange the inequality so that each variable appears on only one side of the inequality. Putting the inequality into any of the standard forms will do this. It will be helpful later if you arrange the inequality so that at least one variable has a positive coefficient. (You may have to multiply by -1 (and change the sense of the inequality) to do this.)

Our example inequalities are now ...

-2x +2y ≥ -4 . . . . . or divide by 2 to get . . . . -x +y ≥ -2

y < (1/2)x +3

2. Notice the inequality symbol, and whether it includes the "or equal to" case.

the first inequality is ≥, so includes "or equal to"

the second inequality is <, so does not include "or equal to"

3. Replace the inequality symbol with an equal sign and graph the resulting equation. If the "or equal to" case is included, the line is graphed as a solid line. If it is not, then the line is graphed as a dashed line.

the first equation (-x +y = -2) is graphed with a solid line

the second equation (y = (1/2)x +3) is graphed with a dashed line

4. It is not necessary, but is less confusing, to choose a variable in the inequality (after step 1) that has a positive coefficient. Notice whether this variable is "less than" or "greater than" the stuff on the other side of the inequality.

y ≥ . . . . for the first inequality

y < . . . or . . . x > . . . . for the second inequality

If it is less than, shade the portion of the graph below (for y <) or to the left (for x <) of the line you graphed in step 3.

the second inequality has y < , so the graph will be shaded below the dashed line. It also has x > , so will be shaded to the right of the dashed line. (These are the same shading.)

If it is greater than, shade the portion of the graph above (for y >) or to the right (for x >) of the line you graphed in step 3.

the first inequality has y ≥ , so the graph will be shaded above the solid line.

5. The solution set is where the shaded areas overlap. Any point on a dashed line is not in the solution set.

_____

The graph for the example inequalities is attached. The first one is graphed and shaded in red; the second one is graphed and shaded in blue.

A system has no solutions if the lines are parallel. When solving the system, if you get a false statement (a number equal to a different number) this means there are no solutions.

Three methods of solving inequalities are the graphing method, substitution method, and elimination method.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.

We will use as an example the following system of inequalities:

3x +2y ≥ 5x -4

y < (1/2)x +3

For each inequality, do the following:

If it isn't already set up this way, organize the inequality so that each variable only appears on one side. This can be accomplished by putting inequality into any of the accepted formats. If you set up the inequality so that at least one variable has a positive coefficient, it will be useful later. To accomplish this, you might need to multiply by -1 (and alter the inequality's sense).

Our example inequalities are now ...

-2x +2y ≥ -4 . . . . . or divide by 2 to get . . . . -x +y ≥ -2

y < (1/2)x +3

Take note of the inequality sign and whether the "or equal to" instance is present.

The first inequality is, so "or equal to" is included. The second inequality is, so "or equal to" is not included.

Create a graph of the equation that results from replacing the inequality symbol with the equal sign. The line is graphed as a solid line if the "or equal to" scenario is present. If not, a dashed line is used to represent the line on the graph.

Graphing the first equation (-x + y = -2) using a solid line

Graphing the second equation (y = (1/2)x + 3) uses a dashed line.

Choosing a variable in the inequality that has a positive coefficient after step one is not required, but it is less ambiguous. If there is an inequality, pay attention to whether this variable is "less than" or "greater than" the items on the other side.

For the initial inequality, y

In the case of the second inequality, y or x >

Shade the area of the graph below (for y) or to the left (for x) of the line you graphed in step 3 if it is smaller than.

The graph will be darkened below the dashed line since the second inequality has the value y. It will be tinted to the right of the dashed line because it also has x >. The shading here is the same.

Shade the area of the graph above (for y >) or to the right (for x >) of the line you graphed in step 3 if it is bigger than.

The graph will be shaded above the solid line because the first inequality has y.

The overlap of the colored areas is the solution set. The solution set does not include any points on a dashed line.

When the lines are parallel, a system cannot have a solution. If you get a false statement after solving the system (a number that is equal to a different number), there are no solutions.

Learn more about inequalities here:

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Answer:

x=4

x=17.9

Step-by-step explanation:

For the first diagram.

cos(45°)=x/4√2

x=4√2cos(45°)

x=4

For the second diagram

tan(38°)=14/x

0.781=14/x

x=14/0.781=17.9

Answer:

4.5

Step-by-step explanation:

60/20=3

3*1.5=4.5

Answer:

p(4)=3

Step-by-step explanation:

p(4)=3(4)-9=12-9=3

Answer:

4400*7.5%=330+315=$645 a week

Step-by-step explanation:

Answer:

the answer is (1,31)

Step-by-step explanation:

As the x value increases by the y value increases by 8

Answer:

C. 1, 31

Step-by-step explanation:

Slope: Y= -9/2x+45/2 or Y= -4.5x+22.5

Midpoint: (4, 4.5)

Distance: √85 or 9.219544

Step-by-step explanation:

These are the Formulas:

Answer:

it is A

Step-by-step explanation:

you line up the numbers and the horizonal line first

Answer:

3 : 7

Step-by-step explanation:

make sure the three of on the left

The number of boxes of cashews to the total number of boxes sold is expressed as 3:7 in ratio.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other. The general form of expressing a ratio between two quantities say 'a' and 'b' is a: b

Margo finds that 3 out of every 7 boxes of nuts are cashews.

In order to calculate the ratio of two quantities, we can use the following steps

First, we must determine the quantities for both scenarios for which we are calculating the ratio. In this situation, there are three cashews and seven boxes.

Write it as a fraction, a/b. As a result, we write it as 3/7.

Therefore, the number of boxes of cashews to the total number of boxes sold is expressed as 3:7 in ratio.

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Answer: B. D. E. F.

Step-by-step explanation:

Answer:

16.64 m

Step-by-step explanation:

Subtract the depth of the water from the height of the tank (0.6) and use this measurement for height instead. then calculate l•h•2+w•h•2+l•w

(we multiplied the length and height and the width and height by two since there’s two sides with the same measurement for each)

Answer:

Mary have £ 0.7

and Eleanor 1.05

because

Mary 10/ 10 +15 × 1.75= .7

Eleanor 15 /10+15× 1.75 =1.05

1/3 of 18 = 6

the song dropped $6 each day

Answer: -6

Step-by-step explanation:

The value of a stock dropped a total of $18 over a 3-day period meaning -6 dollars each day.

-18/3

Answer:

1) According to your choices, 3.

2) The other two points must be critical points/undefined (imaginary according to your choices)

3) Synthetic division  

4) I don't see why the quadratic formula is a choice, but it's the last remaining option.

Answer:

I completed my angel is a line what's the angels has to be alive but B is not an angel cuz it's her Reddit Iran has to be the right has not as Justin Bieber allusions in the Seas Angel against a little angel has to be a line but you got to put it up one line up so that's how you can do it $8 and a symbol

Step-by-step explanation:

i hope it work

Answer:

n= -2

Step-by-step explanation:

5n=-4-6

5n=-10

n=-2

Answer:

d. 250π/3

Step-by-step explanation:

A = πr²

A = 3.14(10)² = 314.159

A = 314.159*(5/6) = 261.799

A = 261.799 = 250π/3

Answer:

D

Step-by-step explanation:

You need to set up a ratio between the area of the sector & the area of the circle vs the angle of the sector & 360 degrees.

[tex]\frac{SectorAngle}{360} =\frac{SectorArea}{CircleArea}[/tex]

That above is your formula you need to remember for these equations.

Now let's solve. You've been given the sector angle, which is 300 degrees, and you've been given the radius of the circle, 10 feet.

The area of a circle is the formula: A = πr²

Given that formula and you know the radius. You plug in 10 feet for r and solve for the area.

[tex]A=\pi10^2\\A=314.159[/tex]

Now lets solve for the missing variable (Sector Area).

[tex]\frac{300}{360} = \frac{x}{100\pi }\\100\pi * \frac{300}{360} = \frac{x}{314.159}*100\pi\\100\pi* \frac{300}{360} = x\\\frac{250\pi }{3} = x[/tex]

I kind of messed up since I didn't realize the answer choices were simplified, make sure for the area you don't completely solve the area, keep the pi simple if the answer choices include pi.

Answer:

20

Step-by-step explanation:

[tex]\frac{10^{2} }{5^{1}}[/tex]

[tex]\frac{100}{5}[/tex]

[tex]\frac{20}{1}[/tex]

[tex]20[/tex]

Answer:

the first one

Step-by-step explanation:

in the first one it says there are no common numbers between x and y which is false.

in the second one its the union of x and y which means that you must list all numbers in x and y without repetition

the third one states that 15,33,1025 are the only numbers that are common between x and y.

so as a breif the first one is wrong

Answer:

first choice

Step-by-step explanation:

Answer:

d.2

Step-by-step explanation:

because if you have 1 blue bead then ur friend gives you another blue bead that makes 2 blue beads.

hope this helps

Answer:

10%

Step-by-step explanation:

The answer is 10% because when you multiply 20 by 10% you get 2 and if you multiply 2 by 10 you get 20.

Answer:

10%, remember to hit that thanks button

Step-by-step explanation:

Step-by-step explanation:

don't tell no one but you should install math.way it help so much

Answer:

260 gallons

Step-by-step explanation:

Hope it's correct

Answer:

the answer is 3

Step-by-step explanation:

Answer:

your in highschool and you cant do that?

i worry for you 3

Step-by-step explanation:

Answer:

[tex]2\sqrt{10}[/tex]

Step-by-step explanation:

To find the distance between points, we can use the following formula:

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

We have two coordinates; (1, 4) and (3, 7)

Let's plug these values into the equation

[tex]d = \sqrt{(3 - 1)^2 + (7 - 1)^2} = 2\sqrt{10}[/tex]

Good luck!

Answer:

A. 45 + 42p

Step-by-step explanation:

Step-by-step explanation:

which questions you were asking