QuestionFind $x$ and $F H$ given that $G$ is the midpoint of $\overline{F H}$ , $F G = 14x + 25$ , and $G H = 73 - 2x$ .

Studdy Solution

STEP 1

Assumptions1. $G$ is the midpoint of $\overline{ H}$ . The length of segment $G$ is represented by the expression $14x +25$
3. The length of segment $G H$ is represented by the expression $73 -x$

STEP 2

Since $G$ is the midpoint of $\overline{ H}$ , the lengths of $G$ and $G H$ are equal. We can set up the equation $14x +25 =73 -2x$ to find the value of $x$ .
$14x +25 =73 -2x$

STEP 3

To solve for $x$ , we first need to get all terms involving $x$ on one side of the equation and the constant terms on the other side. We can do this by adding $2x$ to both sides and subtracting $25$ from both sides.
$14x +2x =73 -25$

STEP 4

implify both sides of the equation to get $16x =48$ .
$16x =48$

STEP 5

Finally, divide both sides of the equation by $16$ to solve for $x$ .
$x = \frac{48}{16}$

STEP 6

Calculate the value of $x$ .
$x = \frac{48}{16} =3$

STEP 7

Now that we have the value of $x$ , we can find the length of $H$ by adding the lengths of $G$ and $G H$ . Since $G = G H$ , we can just multiply the length of $G$ by2.
$H =2(F G)$

STEP 8

Substitute the expression for $G$ and the value of $x$ into the equation.
$H =2(14x +25)$

STEP 9

Substitute $x =3$ into the equation.
$H =2(14(3) +25)$

STEP 10

implify the equation to find the length of $H$ .
$H =2(42 +25)$

STEP 11

Calculate the value of $H$ .
$H =(67) =134$ The value of $x$ is3 and the length of $H$ is134.

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QuestionFind $x$ and $F H$ given that $G$ is the midpoint of $\overline{F H}$ , $F G = 14x + 25$ , and $G H = 73 - 2x$ .

Studdy Solution

STEP 1

Assumptions1. $G$ is the midpoint of $\overline{ H}$ . The length of segment $G$ is represented by the expression $14x +25$
3. The length of segment $G H$ is represented by the expression $73 -x$

STEP 2

Since $G$ is the midpoint of $\overline{ H}$ , the lengths of $G$ and $G H$ are equal. We can set up the equation $14x +25 =73 -2x$ to find the value of $x$ .
$14x +25 =73 -2x$

STEP 3

To solve for $x$ , we first need to get all terms involving $x$ on one side of the equation and the constant terms on the other side. We can do this by adding $2x$ to both sides and subtracting $25$ from both sides.
$14x +2x =73 -25$

STEP 4

implify both sides of the equation to get $16x =48$ .
$16x =48$

STEP 5

Finally, divide both sides of the equation by $16$ to solve for $x$ .
$x = \frac{48}{16}$

STEP 6

Calculate the value of $x$ .
$x = \frac{48}{16} =3$

STEP 7

Now that we have the value of $x$ , we can find the length of $H$ by adding the lengths of $G$ and $G H$ . Since $G = G H$ , we can just multiply the length of $G$ by2.
$H =2(F G)$

STEP 8

Substitute the expression for $G$ and the value of $x$ into the equation.
$H =2(14x +25)$

STEP 9

Substitute $x =3$ into the equation.
$H =2(14(3) +25)$

STEP 10

implify the equation to find the length of $H$ .
$H =2(42 +25)$

STEP 11

Calculate the value of $H$ .
$H =(67) =134$ The value of $x$ is3 and the length of $H$ is134.

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QuestionFind xxx and FHF HFH given that GGG is the midpoint of FH‾\overline{F H}FH, FG=14x+25F G = 14x + 25FG=14x+25, and GH=73−2xG H = 73 - 2xGH=73−2x.

Studdy Solution

STEP 1

Assumptions1. GGG is the midpoint of H‾\overline{ H}H . The length of segment G GG is represented by the expression 14x+2514x +2514x+253. The length of segment GHG HGH is represented by the expression 73−x73 -x73−x

STEP 2

Since GGG is the midpoint of H‾\overline{ H}H, the lengths of G GG and GHG HGH are equal. We can set up the equation 14x+25=73−2x14x +25 =73 -2x14x+25=73−2x to find the value of xxx.14x+25=73−2x14x +25 =73 -2x14x+25=73−2x

STEP 3

To solve for xxx, we first need to get all terms involving xxx on one side of the equation and the constant terms on the other side. We can do this by adding 2x2x2x to both sides and subtracting 252525 from both sides.14x+2x=73−2514x +2x =73 -2514x+2x=73−25

STEP 4

implify both sides of the equation to get 16x=4816x =4816x=48.16x=4816x =4816x=48

STEP 5

Finally, divide both sides of the equation by 161616 to solve for xxx.x=4816x = \frac{48}{16}x=1648​

STEP 6

Calculate the value of xxx.x=4816=3x = \frac{48}{16} =3x=1648​=3

STEP 7

Now that we have the value of xxx, we can find the length of H HH by adding the lengths of G GG and GHG HGH. Since G=GH G = G HG=GH, we can just multiply the length of G GG by2.H=2(FG) H =2(F G)H=2(FG)

STEP 8

Substitute the expression for G GG and the value of xxx into the equation.H=2(14x+25) H =2(14x +25)H=2(14x+25)

STEP 9

Substitute x=3x =3x=3 into the equation.H=2(14(3)+25) H =2(14(3) +25)H=2(14(3)+25)

STEP 10

implify the equation to find the length of H HH.H=2(42+25) H =2(42 +25)H=2(42+25)

STEP 11

Calculate the value of H HH.H=(67)=134 H =(67) =134H=(67)=134The value of xxx is3 and the length of H HH is134.

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QuestionFind $x$ and $F H$ given that $G$ is the midpoint of $\overline{F H}$ , $F G = 14x + 25$ , and $G H = 73 - 2x$ .

Assumptions1. $G$ is the midpoint of $\overline{ H}$ . The length of segment $G$ is represented by the expression $14x +25$
3. The length of segment $G H$ is represented by the expression $73 -x$

Since $G$ is the midpoint of $\overline{ H}$ , the lengths of $G$ and $G H$ are equal. We can set up the equation $14x +25 =73 -2x$ to find the value of $x$ .
$14x +25 =73 -2x$

To solve for $x$ , we first need to get all terms involving $x$ on one side of the equation and the constant terms on the other side. We can do this by adding $2x$ to both sides and subtracting $25$ from both sides.
$14x +2x =73 -25$

implify both sides of the equation to get $16x =48$ .
$16x =48$

Finally, divide both sides of the equation by $16$ to solve for $x$ .
$x = \frac{48}{16}$

Calculate the value of $x$ .
$x = \frac{48}{16} =3$

Now that we have the value of $x$ , we can find the length of $H$ by adding the lengths of $G$ and $G H$ . Since $G = G H$ , we can just multiply the length of $G$ by2.
$H =2(F G)$

Substitute the expression for $G$ and the value of $x$ into the equation.
$H =2(14x +25)$

Substitute $x =3$ into the equation.
$H =2(14(3) +25)$

implify the equation to find the length of $H$ .
$H =2(42 +25)$

Calculate the value of $H$ .
$H =(67) =134$ The value of $x$ is3 and the length of $H$ is134.