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2 years ago

Which set of measures can represent the lengths of a right triangle?

Mathematics

1 answer:

Ivanshal [37]2 years ago

4 0

Answer:

A and B are correct, but A is most correct.

Step-by-step explanation:

just do Pythagorean theorem and see which numbers add up to each other. if you do them for all 4 answers, you see d and c do not equal to each other. b is almost correct, and a comes out exact.

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Solve for x x2 - 3|x - 2| - 4x = - 6

SashulF [63]

X=2

2
−
3
(
|
x
−
2
|
)
−
4
x
=
−
6
−
3
(
|
x
−
2
|
)
−
4
x
+
2
=
−
6
Step 1: Add 4x to both sides.
−
3
(
|
x
−
2
|
)
−
4
x
+
2
+
4
x
=
−
6
+
4
x
−
3
(
|
x
−
2
|
)
+
2
=
4
x
−
6
Step 2: Add -2 to both sides.
−
3
(
|
x
−
2
|
)
+
2
+
−
2
=
4
x
−
6
+
−
2
−
3
(
|
x
−
2
|
)
=
4
x
−
8
Step 3: Divide both sides by -3.
−
3
(
|
x
−
2
|
)
−
3
=
4
x
−
8
−
3
|
x
−
2
|
=
−
4
3
x
+
8
3
Step 4: Solve Absolute Value.
|
x
−
2
|
=
−
4
3
x
+
8
3
We know either
x
−
2
=
−
4
3
x
+
8
3
or
x
−
2
=
−
(
−
4
3
x
+
8
3
)
x
−
2
=
−
4
3
x
+
8
3
(Possibility 1)
x
−
2
+
4
3
x
=
−
4
3
x
+
8
3
+
4
3
x
(Add 4/3x to both sides)
7
3
x
−
2
=
8
3
7
3
x
−
2
+
2
=
8
3
+
2
(Add 2 to both sides)
7
3
x
=
14
3
(
3
7
)
*
(
7
3
x
)
=
(
3
7
)
*
(
14
3
)
(Multiply both sides by 3/7)
x
=
2
x
−
2
=
−
(
−
4
3
x
+
8
3
)
(Possibility 2)
x
−
2
=
4
3
x
+
−
8
3
(Simplify both sides of the equation)
x
−
2
−
4
3
x
=
4
3
x
+
−
8
3
−
4
3
x
(Subtract 4/3x from both sides)
−
1
3
x
−
2
=
−
8
3
−
1
3
x
−
2
+
2
=
−
8
3
+
2
(Add 2 to both sides)
−
1
3
x
=
−
2
3
(
3
−
1
)
*
(
−
1
3
x
)
=
(
3
−
1
)
*
(
−
2
3
)
(Multiply both sides by 3/(-1))
x
=

2
−
3
(
|
x
−
2
|
)
−
4
x
=
−
6
−
3
(
|
x
−
2
|
)
−
4
x
+
2
=
−
6
Step 1: Add 4x to both sides.
−
3
(
|
x
−
2
|
)
−
4
x
+
2
+
4
x
=
−
6
+
4
x
−
3
(
|
x
−
2
|
)
+
2
=
4
x
−
6
Step 2: Add -2 to both sides.
−
3
(
|
x
−
2
|
)
+
2
+
−
2
=
4
x
−
6
+
−
2
−
3
(
|
x
−
2
|
)
=
4
x
−
8
Step 3: Divide both sides by -3.
−
3
(
|
x
−
2
|
)
−
3
=
4
x
−
8
−
3
|
x
−
2
|
=
−
4
3
x
+
8
3
Step 4: Solve Absolute Value.
|
x
−
2
|
=
−
4
3
x
+
8
3
We know either
x
−
2
=
−
4
3
x
+
8
3
or
x
−
2
=
−
(
−
4
3
x
+
8
3
)
x
−
2
=
−
4
3
x
+
8
3
(Possibility 1)
x
−
2
+
4
3
x
=
−
4
3
x
+
8
3
+
4
3
x
(Add 4/3x to both sides)
7
3
x
−
2
=
8
3
7
3
x
−
2
+
2
=
8
3
+
2
(Add 2 to both sides)
7
3
x
=
14
3
(
3
7
)
*
(
7
3
x
)
=
(
3
7
)
*
(
14
3
)
(Multiply both sides by 3/7)
x
=
2
x
−
2
=
−
(
−
4
3
x
+
8
3
)
(Possibility 2)
x
−
2
=
4
3
x
+
−
8
3
(Simplify both sides of the equation)
x
−
2
−
4
3
x
=
4
3
x
+
−
8
3
−
4
3
x
(Subtract 4/3x from both sides)
−
1
3
x
−
2
=
−
8
3
−
1
3
x
−
2
+
2
=
−
8
3
+
2
(Add 2 to both sides)
−
1
3
x
=
−
2
3
(
3
−
1
)
*
(
−
1
3
x
)
=
(
3
−
1
)
*
(
−
2
3
)
(Multiply both sides by 3/(-1))
x
=
2

3 0

2 years ago

Angelina_Jolie [31]

9514 1404 393

Answer:

x = 8

Step-by-step explanation:

Corresponding segments are proportional.

(3x +1)/10 = (7x -1)/22

11(3x +1) = 5(7x -1) . . . . . . multiply by 110

33x + 11 = 35x -5 . . . . . . eliminate parentheses

16 = 2x . . . . . . . . . . . add 5-33x to both sides

8 = x . . . . . . . . . . divide by 2

3 0

3 years ago

Read 2 more answers

Calculate the volume of the rectangular prism below

Svetradugi [14.3K]

Answer:

210 in

Step-by-step explanation:

3 0

2 years ago

hich property would be used first to simplify the expression 2(x + 5y + 1) - 4(3x - y - 2)? A Inverse B Commutative C Distributi

nika2105 [10]

The first to simplify the expression would be C. Distributive

8 0

3 years ago

Read 2 more answers

Worth 17 points! Help me please!!! Look in the picture

ivanzaharov [21]

Answer:

Part A

1. After 4 weeks of work, Jeremy has saved 300

2. Jeremy worked 8 weeks in order to save $600

3. For every one week of work, Jeremy saved 75 dollars

4. If Jeremy works 15 weeks, then he can expect to save 1,125 dollars

Part B

1. Saeed orders 15 meals and his total cost of delivery is $24

2. Saeed paid $32 to have 20 meals delivered

3. For every meal delivered, Saeed is charged $1.6

4. If Saeed pays $19.20 in delivery fees then he ordered 12 meals

Step-by-step explanation:

Part A

The given graph gives the proportional relationship between total amount saved and the number of weeks worked

1. Reading from the graph, at the point where the vertical line from point 4 touches the line of the graph, an horizontal line to the vertical y-axis touches the y-axis at 300

Therefore;

After 4 weeks of work, Jeremy has saved 300

2. The point where an horizontal line from point 600 on the vertical y-axis touches the line of the graph, a vertical line drawn to the horizontal, x-axis touches the x-axis at 8

Therefore;

Jeremy worked 8 weeks in order to save $600.

3. The rate of change of the amount saved to the number of weeks worked, 'm', for the given proportional relationship (straight line relationship, passing through the origin) is given as follows;

Rate of change, m = Constant = y/x

∴ Rate of change of the amount saved to the number of weeks worked = (300-0)/(4 weeks- 0 week) = 75/week

Therefore;

For every one week of work, Jeremy saved 75 dollars

4. The amount Jeremy would have saved in 15 weeks, 'A', is given as follows;

A = m × n

Where;

m = The rate of change of the amount saved to the number of weeks worked = 75/week

n = The number of weeks worked

∴ A = 75/week × 15 = $1,125

Therefore;

If Jeremy works 15 weeks, then he can expect to save 1,125 dollars

Part B

From the graph, we have;

1. From the graph there is a proportional relationship between the total cost of delivery and the number of meals

At the point a vertical line drawn to the line of the graph from 15 on the horizontal axis (number of meals), a horizontal line drawn to the vertical y-axis touches the y-axis at 24

Therefore;

1. Saeed orders 15 meals and his total cost of delivery is $24

2. From the point where the horizontal line from 32 on the vertical axis touches the linear graph of the relationship between the total cost of delivery and the number of meals, a vertical line drawn down to the horizonal axis touches the horizontal x-axis at 20

Therefore;

Saeed paid $32 to have 20 meals delivered

3. The rate of change of the total cost of delivery to the number of meals, 'm', is given as follows;

m = y/x (for proportional relationships)

Taking any corresponding 'x' and y-values

m = 16/10 = 32/20 = 24/15 = 1.6 Dollars/meal

Therefore;

For every meal delivered, Saeed is charged $1.6

4. From m = y/x = 1.6

When y = $19.20

x = y/m = $19.20/($1.6/meal) = 12 meals

Therefore;

If Saeed pays $19.20 in delivery fees then he ordered 12 meals.

3 0

3 years ago