QuestionFind $b$ and $Y Z$ given $X Y=6b$ , $Y Z=8b$ , and $X Z=154$ with $Y$ between $X$ and $Z$ .

Studdy Solution

STEP 1

Assumptions1. The length of segment XY is $6b$ . The length of segment YZ is $8b$
3. The length of segment XZ is $154$
4. $Y$ is a point between $X$ and $Z$

STEP 2

Since $Y$ is between $X$ and $Z$ , the sum of the lengths of segment XY and segment YZ should be equal to the length of segment XZ. We can express this relationship as an equation.
$XY + YZ = XZ$

STEP 3

Now, plug in the given values for XY, YZ, and XZ to form the equation.
$6b +8b =154$

STEP 4

Combine like terms on the left side of the equation.
$14b =154$

STEP 5

To find the value of $b$ , divide both sides of the equation by14.
$b = \frac{154}{14}$

STEP 6

Calculate the value of $b$ .
$b = \frac{154}{14} =11$

STEP 7

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

STEP 8

Plug in the value of $b$ to calculate the length of YZ.
$YZ =8 \times11$

STEP 9

Calculate the length of segment YZ.
$YZ =8 \times11 =88$ So, the value of the variable $b$ is11 and the length of segment $YZ$ is88.

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QuestionFind $b$ and $Y Z$ given $X Y=6b$ , $Y Z=8b$ , and $X Z=154$ with $Y$ between $X$ and $Z$ .

Studdy Solution

STEP 1

Assumptions1. The length of segment XY is $6b$ . The length of segment YZ is $8b$
3. The length of segment XZ is $154$
4. $Y$ is a point between $X$ and $Z$

STEP 2

Since $Y$ is between $X$ and $Z$ , the sum of the lengths of segment XY and segment YZ should be equal to the length of segment XZ. We can express this relationship as an equation.
$XY + YZ = XZ$

STEP 3

Now, plug in the given values for XY, YZ, and XZ to form the equation.
$6b +8b =154$

STEP 4

Combine like terms on the left side of the equation.
$14b =154$

STEP 5

To find the value of $b$ , divide both sides of the equation by14.
$b = \frac{154}{14}$

STEP 6

Calculate the value of $b$ .
$b = \frac{154}{14} =11$

STEP 7

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

STEP 8

Plug in the value of $b$ to calculate the length of YZ.
$YZ =8 \times11$

STEP 9

Calculate the length of segment YZ.
$YZ =8 \times11 =88$ So, the value of the variable $b$ is11 and the length of segment $YZ$ is88.

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QuestionFind bbb and YZY ZYZ given XY=6bX Y=6bXY=6b, YZ=8bY Z=8bYZ=8b, and XZ=154X Z=154XZ=154 with YYY between XXX and ZZZ.

Studdy Solution

STEP 1

Assumptions1. The length of segment XY is 6b6b6b . The length of segment YZ is 8b8b8b3. The length of segment XZ is 1541541544. YYY is a point between XXX and ZZZ

STEP 2

Since YYY is between XXX and ZZZ, the sum of the lengths of segment XY and segment YZ should be equal to the length of segment XZ. We can express this relationship as an equation.XY+YZ=XZXY + YZ = XZXY+YZ=XZ

STEP 3

Now, plug in the given values for XY, YZ, and XZ to form the equation.6b+8b=1546b +8b =1546b+8b=154

STEP 4

Combine like terms on the left side of the equation.14b=15414b =15414b=154

STEP 5

To find the value of bbb, divide both sides of the equation by14.b=15414b = \frac{154}{14}b=14154​

STEP 6

Calculate the value of bbb.b=15414=11b = \frac{154}{14} =11b=14154​=11

STEP 7

Now that we have the value of bbb, we can find the length of segment YZ by substituting bbb into the expression for YZ.YZ=bYZ =bYZ=b

STEP 8

Plug in the value of bbb to calculate the length of YZ.YZ=8×11YZ =8 \times11YZ=8×11

STEP 9

Calculate the length of segment YZ.YZ=8×11=88YZ =8 \times11 =88YZ=8×11=88So, the value of the variable bbb is11 and the length of segment YZYZYZ is88.

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QuestionFind $b$ and $Y Z$ given $X Y=6b$ , $Y Z=8b$ , and $X Z=154$ with $Y$ between $X$ and $Z$ .

Assumptions1. The length of segment XY is $6b$ . The length of segment YZ is $8b$
3. The length of segment XZ is $154$
4. $Y$ is a point between $X$ and $Z$

Since $Y$ is between $X$ and $Z$ , the sum of the lengths of segment XY and segment YZ should be equal to the length of segment XZ. We can express this relationship as an equation.
$XY + YZ = XZ$

Now, plug in the given values for XY, YZ, and XZ to form the equation.
$6b +8b =154$

Combine like terms on the left side of the equation.
$14b =154$

To find the value of $b$ , divide both sides of the equation by14.
$b = \frac{154}{14}$

Calculate the value of $b$ .
$b = \frac{154}{14} =11$

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

Plug in the value of $b$ to calculate the length of YZ.
$YZ =8 \times11$

Calculate the length of segment YZ.
$YZ =8 \times11 =88$ So, the value of the variable $b$ is11 and the length of segment $YZ$ is88.