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3 years ago

If D is the midpoint of EG, find the length of EG

Mathematics

1 answer:

Brrunno [24]3 years ago

7 0

ED = x - 5 given

DG = 4x - 38 given

ED = DG definition of midpoint

x - 5 = 4x - 38 substitution

-5 = 3x - 38 subtraction property of equality (subtracted x from both sides)

33 = 3x addition property of equality (added 38 to both sides)

11 = x division property of equality (divided 3 from both sides)

ED = x - 5 → ED = 11 - 5 → ED = 6 substitution

since ED = DG, then DG = 6 transitive property

ED + DG = EG segment addition property

6 + 6 = EG substitution

12 = EG simplified like terms

Answer: 12

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Given: <SPT = <RQT, ST = RT Prove: PR = QS

andrey2020 [161]

Answer:

See explanation

Step-by-step explanation:

Consider triangles PTS and QTR. In these triangles,

$ST=RT$ - given;
$\angle SPT=\angle RQT$ - given;
$\angle STP=\angle RTQ$ - as vertical angles when lines PR and SQ intersect.

Thus, $\triangle PTS\cong \triangle QTR$ by AAS postulate.

Congruent triangles have congruent corresponding sides, so

$PT=QT$

Consider segments PR and QS:

$PR=PT+TR\ [\text{Segment addition postulate}]\\ \\QS=QT+TS\ [\text{Segment addition postulate}]\\ \\PT=QT\ [\text{Proven}]\\ \\ST=RT\ [\text{Given}]$

So,

$PR=SQ\ [\text{Substitution property}]$

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2 years ago

In the 30-60-90 triangle below, side s has a length of _ and side q has a length of _.

gregori [183]

Answer: F

Step-by-step explanation:

For a 30-60-90 triangle, we know that the hypotenuse is 2x. Since we know the hypotenuse is 10, we can solve for x.

2x=10

x=5

Now that we know x is 5, we can use this to solve for s and q. The side across from 30° is just x. Since we know x, s is 5.

The side across from 60° is x√3. Since we know what x is, we can just plug in. q is 5√3.

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3 years ago

|x-5|<20 What is the solution

postnew [5]

Your solution would be x<25

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Solve 3x + k = cfor x.

Ghella [55]

First, subtract k from both sides. That means c - k is in the left side and 3x is on the right. Then, divide by 3 on both sides. So, the answer is x = (c - k) / 3.

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statuscvo [17]

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