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3 years ago

Which facts could be applied to simplify this expression? Check all that apply.

Mathematics

2 answers:

Harlamova29_29 [7]3 years ago

4 0

Answer:

Options B, C, and D.

Step-by-step explanation:

We have to simplify the given expression given (5x + 3y + (-x) + 6z).

We will use the process as given below.

1) We will identify the like terms, we have to add or subtract.

2) Like terms are those, which have the same variable of the same degree.

3) We get the simplified expression by combining the same terms.

5x + 3y + (-x) + 6z = 4x + 3y + 6z

Therefore, Options B, C and D will be the correct options.

kykrilka [37]3 years ago

3 0

The answer is B, C, and D. Like terms are terms with all the same variable, so 5x and -x are like terms.

C is correct. If we add -x to 5x, we get 4x. The other numbers remain unchanged because they have no like terms.

D is correct. Applying the rule of like terms, which is that like terms are numbers with the same variable, only add together numbers with the same variable.

Hope this helps!

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Graph the linear equation. 4x+6y=-12

lianna [129]

Answer:

Step-by-step explanation:

To graph an equation using the slope and y-intercept, 1) Write the equation in the form y = mx + b to find the slope m and the y-intercept (0, b). 2) Next, plot the y-intercept. 3) From the y-intercept, move up or down and left or right, depending on whether the slope is positive or negative.

5 0

1 year ago

Simply your expression 4[(12-2) ²÷4]

lina2011 [118]

Answer:

100

Step-by-step explanation:

Simplify the following:

4 (12 - 2)^2/4

Hint: | Express 4 (12 - 2)^2/4 as a single fraction.

4 (12 - 2)^2/4 = (4 (12 - 2)^2)/4:

(4 (12 - 2)^2)/4

Hint: | Cancel common terms in the numerator and denominator of (4 (12 - 2)^2)/4.

(4 (12 - 2)^2)/4 = 4/4×(12 - 2)^2 = (12 - 2)^2:

(12 - 2)^2

Hint: | Subtract 2 from 12.

| 1 | 2

- | | 2

| 1 | 0:

10^2

Hint: | Evaluate 10^2.

| 1 | 0

× | 1 | 0

| 0 | 0

1 | 0 | 0

1 | 0 | 0:

Answer: 100

8 0

2 years ago

Tickets at a play cost $10 or $14. If 800 tickets were sold and $9,040 was collected by the box office, how many $14 tickets wer

pav-90 [236]

STEP 1:
determine equations needed

x= # of $10 tickets
y= # of $14 tickets

QUANTITY EQUATION
x + y= 800

COST EQUATION
$10x + $14y= $9,040

STEP 2:
multiply quantity equation by -14

-14(x + y)= -14(800)
-14x - 14y= -11,200

STEP 3:
add new quantity equation in step 2 to cost equation of step 1 to solve for x using elimination

-14x - 14y= -11,200
10x + 14y= 9040
y term cancels out

-4x= -2160
divide both sides by -4

x= 540 ten dollar tickets

STEP 4:
substitute x value in step 3 into either original equation

x + y= 800
540 + y= 800
subtract 540 from both sides

y= 260 fourteen dollar tickets

ANSWER: There were 540 $10 tickets and 260 $14 tickets sold.

Hope this helps! :)

5 0

2 years ago

The coordinates of the vertices of a regular polygon are given. Find the area of the polygon to the nearest tenth.

alexandr1967 [171]

Answer:

The area is equal to $8\ units^{2}$

Step-by-step explanation:

we have

A(0, 0), B(2, -2), C(0, -4), D(-2, -2)

Plot the figure

The figure is a square (remember that a regular polygon has equal sides and equal internal angles)

see the attached figure

The area of the square is

$A=AB^{2}$

Find the distance AB

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

substitute the values

$AB=\sqrt{(-2-0)^{2}+(2-0)^{2}}$

$AB=\sqrt{(-2)^{2}+(2)^{2}}$

$AB=\sqrt{8}$

$AB=2\sqrt{2}\ units$

Find the area of the square

$A=(2\sqrt{2})^{2}$

$A=8\ units^{2}$

4 0

3 years ago

Four circles of unit radius are drawn with centers $(1,0)$, $(-1,0)$, $(0,1)$, and $(0,-1)$. a circle with radius 2 is drawn wit

Reika [66]

Check the picture 1.

The regions contained in an odd number of these 5 circles are

the pink colored region, contained only in the circle with radius 2,

and the yellow regions, each contained in the intersection of 2 small circles and the third large circle.

So what we need to determine is the "area pink + area yellow".

Consider the second picture.

Let A2 be the area of the right isosceles triangle, and A1 be half of the yellow region.

the region A2 + A1 is called a sector, and it is 1/4 of the area of a unit circle.

$A1=A_{sector}-A2= \frac{1}{4} \pi r^2- \frac{1}{2}.1.1= \frac{1}{4} \pi 1^2- \frac{1}{2}= \frac{1}{4}\pi- \frac{1}{2}$

Thus, the overall yellow region is $8A1=8(\frac{1}{4}\pi- \frac{1}{2})=2\pi-4$

The purple area is:

Area of large circle - 4*(Area of 1 small circle) + yellow region.

(because subtracting all 4 small circles means that each of the 4 separate yellow regions have been subtracted twice)

$A_{purple}=\pi.2^2-4(\pi.1^2)+2\pi-4=4\pi-4\pi+2\pi-4=2\pi-4$

Finally, the total area is : $2\pi-4+2\pi-4=4\pi-8$ (units squared)

Answer: $6\pi-8$ square units

6 0

3 years ago