QuestionFind $Y$ and $Y Z$ given $X Y=11$ , $Y Z=4c$ , and $X Z=83$ .

Studdy Solution

STEP 1

Assumptions1. The length of segment XY is11. The length of segment YZ is4c3. The length of segment XZ is834. Point Y is between points X and Z5. The lengths of segments XY, YZ, and XZ are related by the equation XY + YZ = XZ

STEP 2

First, we need to set up the equation that relates the lengths of the segments XY, YZ, and XZ. $XY + YZ = XZ$

STEP 3

Now, plug in the given values for the lengths of the segments XY, YZ, and XZ into the equation.
$11 +c =83$

STEP 4

Next, we need to isolate the variable c in the equation. We can do this by subtracting11 from both sides of the equation.
$4c =83 -11$

STEP 5

Calculate the right side of the equation.
$4c =72$

STEP 6

To solve for c, divide both sides of the equation by4.
$c =72 /4$

STEP 7

Calculate the value of c.
$c =18$

STEP 8

Now that we have the value of c, we can find the length of segment YZ by substituting c into the expression for YZ.
$YZ =4c$

STEP 9

Plug in the value of c into the expression for YZ.
$YZ =4 \\times18$

STEP 10

Calculate the length of YZ.
$YZ =72$ The value of the variable c is18 and the length of segment YZ is72.

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QuestionFind $Y$ and $Y Z$ given $X Y=11$ , $Y Z=4c$ , and $X Z=83$ .

Studdy Solution

STEP 1

Assumptions1. The length of segment XY is11. The length of segment YZ is4c3. The length of segment XZ is834. Point Y is between points X and Z5. The lengths of segments XY, YZ, and XZ are related by the equation XY + YZ = XZ

STEP 2

First, we need to set up the equation that relates the lengths of the segments XY, YZ, and XZ. $XY + YZ = XZ$

STEP 3

Now, plug in the given values for the lengths of the segments XY, YZ, and XZ into the equation.
$11 +c =83$

STEP 4

Next, we need to isolate the variable c in the equation. We can do this by subtracting11 from both sides of the equation.
$4c =83 -11$

STEP 5

Calculate the right side of the equation.
$4c =72$

STEP 6

To solve for c, divide both sides of the equation by4.
$c =72 /4$

STEP 7

Calculate the value of c.
$c =18$

STEP 8

Now that we have the value of c, we can find the length of segment YZ by substituting c into the expression for YZ.
$YZ =4c$

STEP 9

Plug in the value of c into the expression for YZ.
$YZ =4 \\times18$

STEP 10

Calculate the length of YZ.
$YZ =72$ The value of the variable c is18 and the length of segment YZ is72.

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QuestionFind YYY and YZY ZYZ given XY=11X Y=11XY=11, YZ=4cY Z=4cYZ=4c, and XZ=83X Z=83XZ=83.

Studdy Solution

STEP 1

Assumptions1. The length of segment XY is11. The length of segment YZ is4c3. The length of segment XZ is834. Point Y is between points X and Z5. The lengths of segments XY, YZ, and XZ are related by the equation XY + YZ = XZ

STEP 2

First, we need to set up the equation that relates the lengths of the segments XY, YZ, and XZ.XY+YZ=XZXY + YZ = XZXY+YZ=XZ

STEP 3

Now, plug in the given values for the lengths of the segments XY, YZ, and XZ into the equation.11+c=8311 +c =8311+c=83

STEP 4

Next, we need to isolate the variable c in the equation. We can do this by subtracting11 from both sides of the equation.4c=83−114c =83 -114c=83−11

STEP 5

Calculate the right side of the equation.4c=724c =724c=72

STEP 6

To solve for c, divide both sides of the equation by4.c=72/4c =72 /4c=72/4

STEP 7

Calculate the value of c.c=18c =18c=18

STEP 8

Now that we have the value of c, we can find the length of segment YZ by substituting c into the expression for YZ.YZ=4cYZ =4cYZ=4c

STEP 9

Plug in the value of c into the expression for YZ.YZ=4times18YZ =4 \\times18YZ=4times18

STEP 10

Calculate the length of YZ.YZ=72YZ =72YZ=72The value of the variable c is18 and the length of segment YZ is72.

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QuestionFind $Y$ and $Y Z$ given $X Y=11$ , $Y Z=4c$ , and $X Z=83$ .

First, we need to set up the equation that relates the lengths of the segments XY, YZ, and XZ. $XY + YZ = XZ$

Now, plug in the given values for the lengths of the segments XY, YZ, and XZ into the equation.
$11 +c =83$

Next, we need to isolate the variable c in the equation. We can do this by subtracting11 from both sides of the equation.
$4c =83 -11$

Calculate the right side of the equation.
$4c =72$

To solve for c, divide both sides of the equation by4.
$c =72 /4$

Calculate the value of c.
$c =18$

Now that we have the value of c, we can find the length of segment YZ by substituting c into the expression for YZ.
$YZ =4c$

Plug in the value of c into the expression for YZ.
$YZ =4 \\times18$

Calculate the length of YZ.
$YZ =72$ The value of the variable c is18 and the length of segment YZ is72.