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Bad White [126]
3 years ago
13

What is the length of CD in the figure below? Show your work.

Mathematics
1 answer:
Nata [24]3 years ago
3 0

Answer:

5

Step-by-step explanation:

First, notice that these two triangles are similar using AA.

Because sides BC and EC are corresponding, you can divide 24 by 8, to determine that the ratio of similitude is 3.

That means that because sides AC and DC are corresponding, 25 - 2x divided by x is 3.

25 - 2x / x = 3

25 - 2x = 3x

25 = 5x

x = 5

x is the same as side CD, so CD = 5.

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Dawn is ordering 1 veggie sandwich for every 3 ham sandwiches. She needs 12 sandwiches in all. Veggie sandwiches cost 4.00 dolla
NISA [10]

Answer:

$52.50

Step-by-step explanation:

Lets use V for Veggie, and H for Ham.

V=4

H=4.50

She is getting 12 sandwiches, and Every 3 H, she buys one V.

So, the order of her buying the sandwiches would be:

H H H V H H H V H H H V

9 H and 3 V

9*H=40.5

3*V=12

40.5+12= $52.50

5 0
3 years ago
Solve the following System of Three Equations:<br> x−3y+z=−15<br> 2x+y−z=−2<br> x+y+2z=1
SashulF [63]

Answer:

x = -3 , y = 4 , z = 0

Step-by-step explanation:

Solve the following system:

{x - 3 y + z = -15

2 x + y - z = -2

x + y + 2 z = 1

Hint: | Choose an equation and a variable to solve for.

In the first equation, look to solve for z:

{x - 3 y + z = -15

2 x + y - z = -2

x + y + 2 z = 1

Hint: | Solve for z.

Subtract x - 3 y from both sides:

{z = 3 y + (-x - 15)

2 x + y - z = -2

x + y + 2 z = 1

Hint: | Perform a substitution.

Substitute z = -15 - x + 3 y into the second and third equations:

{z = -15 - x + 3 y

15 + 3 x - 2 y = -2

x + y + 2 (-15 - x + 3 y) = 1

Hint: | Expand the left hand side of the equation x + y + 2 (-15 - x + 3 y) = 1.

x + y + 2 (-15 - x + 3 y) = x + y + (-30 - 2 x + 6 y) = -30 - x + 7 y:

{z = -15 - x + 3 y

15 + 3 x - 2 y = -2

-30 - x + 7 y = 1

Hint: | Choose an equation and a variable to solve for.

In the second equation, look to solve for x:

{z = -15 - x + 3 y

15 + 3 x - 2 y = -2

-30 - x + 7 y = 1

Hint: | Isolate terms with x to the left hand side.

Subtract 15 - 2 y from both sides:

{z = -15 - x + 3 y

3 x = 2 y - 17

-30 - x + 7 y = 1

Hint: | Solve for x.

Divide both sides by 3:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

-30 - x + 7 y = 1

Hint: | Perform a substitution.

Substitute x = (2 y)/3 - 17/3 into the third equation:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

(19 y)/3 - 73/3 = 1

Hint: | Choose an equation and a variable to solve for.

In the third equation, look to solve for y:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

(19 y)/3 - 73/3 = 1

Hint: | Isolate terms with y to the left hand side.

Add 73/3 to both sides:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

(19 y)/3 = 76/3

Hint: | Solve for y.

Multiply both sides by 3/19:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

y = 4

Hint: | Perform a back substitution.

Substitute y = 4 into the first and second equations:

{z = -x - 3

x = -3

y = 4

Hint: | Perform a back substitution.

Substitute x = -3 into the first equation:

{z = 0

x = -3

y = 4

Hint: | Sort results.

Collect results in alphabetical order:

Answer:  {x = -3 , y = 4 , z = 0

4 0
3 years ago
Simplify the expression
natka813 [3]

Answer:

its B bro come on

Step-by-step explanation:

ok good

4 0
3 years ago
True or False? If two lines are crossed by a transversal and corresponding angles are equal, the lines are parallel.
svetoff [14.1K]
TRUE

To visualize this property, you can draw two parallel lines and cross them by a third line.

Corresponding angles are those that are in the same relative position, between the crossing line and the parallel lines. You can see that those (corresponding) angles are equal if and only if the lines are parallel.

4 0
3 years ago
Read 2 more answers
Find the values of p and q
VashaNatasha [74]

Answer:

p = 2 and q = 14

Step-by-step explanation:

Evaluate f(g(x)) by substituting x = g(x) into f(x), that is

f(px + 4)

= 3(px + 4) + p = 3px + 12 + p

f(g(x)) = 3px + 12 + p and f(g(x)) = 6x + q

Equating the 2 expressions gives

3px + 12 + p = 6x + q

Compare the coefficients of like terms and the constant term

For the 2 expressions to be equal then

3p = 6 ⇒ p = 2 , and

q = 12 + p = 12 + 2 = 14

6 0
3 years ago
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