Solved on Nov 07, 2023

Solve for $h$ in the equation $2(15)(85)+2(10)(65)=2(9 \sqrt{8}) h$ .

STEP 1

Assumptions1. We are given the equation $(15)(85)+(10)(65)=(9 \sqrt{8}) h$ . We are asked to solve for $h$

STEP 2

First, let's simplify the left side of the equation.
$2(15)(85)+2(10)(65)$

STEP 3

Calculate the multiplication in the brackets.
$2 \times1275 +2 \times650$

STEP 4

Perform the multiplication.
$2550 +1300$

STEP 5

Add the two values together.
$3850$ So, the left side of the equation simplifies to3850.

STEP 6

Now, let's simplify the right side of the equation.
$2(9 \sqrt{8}) h$

STEP 7

Calculate the multiplication in the brackets.
$2 \times9 \times \sqrt{} \times h$

STEP 8

Perform the multiplication.
$18 \sqrt{8} h$ So, the right side of the equation simplifies to $18 \sqrt{8} h$ .

STEP 9

Now, we can rewrite the equation with the simplified left and right sides.
$385 =18 \sqrt{8} h$

STEP 10

To solve for $h$ , we need to isolate $h$ on one side of the equation. We can do this by dividing both sides of the equation by $18 \sqrt{8}$ .
$h = \frac{3850}{18 \sqrt{8}}$

STEP 11

implify the right side of the equation.
$h = \frac{3850}{18 \times \sqrt{}}$

STEP 12

Perform the multiplication in the denominator.
$h = \frac{3850}{36 \sqrt{2}}$

STEP 13

To rationalize the denominator, multiply both the numerator and the denominator by $\sqrt{2}$ .
$h = \frac{3850 \sqrt{2}}{36 \times2}$

STEP 14

Perform the multiplication in the denominator.
$h = \frac{3850 \sqrt{2}}{72}$ So, the solution to the equation is $h = \frac{3850 \sqrt{2}}{72}$ .

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Solve for $h$ in the equation $2(15)(85)+2(10)(65)=2(9 \sqrt{8}) h$ .

STEP 1

Assumptions1. We are given the equation $(15)(85)+(10)(65)=(9 \sqrt{8}) h$ . We are asked to solve for $h$

STEP 2

First, let's simplify the left side of the equation.
$2(15)(85)+2(10)(65)$

STEP 3

Calculate the multiplication in the brackets.
$2 \times1275 +2 \times650$

STEP 4

Perform the multiplication.
$2550 +1300$

STEP 5

Add the two values together.
$3850$ So, the left side of the equation simplifies to3850.

STEP 6

Now, let's simplify the right side of the equation.
$2(9 \sqrt{8}) h$

STEP 7

Calculate the multiplication in the brackets.
$2 \times9 \times \sqrt{} \times h$

STEP 8

Perform the multiplication.
$18 \sqrt{8} h$ So, the right side of the equation simplifies to $18 \sqrt{8} h$ .

STEP 9

Now, we can rewrite the equation with the simplified left and right sides.
$385 =18 \sqrt{8} h$

STEP 10

To solve for $h$ , we need to isolate $h$ on one side of the equation. We can do this by dividing both sides of the equation by $18 \sqrt{8}$ .
$h = \frac{3850}{18 \sqrt{8}}$

STEP 11

implify the right side of the equation.
$h = \frac{3850}{18 \times \sqrt{}}$

STEP 12

Perform the multiplication in the denominator.
$h = \frac{3850}{36 \sqrt{2}}$

STEP 13

To rationalize the denominator, multiply both the numerator and the denominator by $\sqrt{2}$ .
$h = \frac{3850 \sqrt{2}}{36 \times2}$

STEP 14

Perform the multiplication in the denominator.
$h = \frac{3850 \sqrt{2}}{72}$ So, the solution to the equation is $h = \frac{3850 \sqrt{2}}{72}$ .

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Solve for hhh in the equation 2(15)(85)+2(10)(65)=2(98)h2(15)(85)+2(10)(65)=2(9 \sqrt{8}) h2(15)(85)+2(10)(65)=2(98​)h.

STEP 1

Assumptions1. We are given the equation (15)(85)+(10)(65)=(98)h(15)(85)+(10)(65)=(9 \sqrt{8}) h(15)(85)+(10)(65)=(98​)h . We are asked to solve for hhh

STEP 2

First, let's simplify the left side of the equation.2(15)(85)+2(10)(65)2(15)(85)+2(10)(65)2(15)(85)+2(10)(65)

STEP 3

Calculate the multiplication in the brackets.2×1275+2×6502 \times1275 +2 \times6502×1275+2×650

STEP 4

Perform the multiplication.2550+13002550 +13002550+1300

STEP 5

Add the two values together.385038503850So, the left side of the equation simplifies to3850.

STEP 6

Now, let's simplify the right side of the equation.2(98)h2(9 \sqrt{8}) h2(98​)h

STEP 7

Calculate the multiplication in the brackets.2×9××h2 \times9 \times \sqrt{} \times h2×9×​×h

STEP 8

Perform the multiplication.188h18 \sqrt{8} h188​hSo, the right side of the equation simplifies to 188h18 \sqrt{8} h188​h.

STEP 9

Now, we can rewrite the equation with the simplified left and right sides.385=188h385 =18 \sqrt{8} h385=188​h

STEP 10

To solve for hhh, we need to isolate hhh on one side of the equation. We can do this by dividing both sides of the equation by 18818 \sqrt{8}188​.h=3850188h = \frac{3850}{18 \sqrt{8}}h=188​3850​

STEP 11

implify the right side of the equation.h=385018×h = \frac{3850}{18 \times \sqrt{}}h=18×​3850​

STEP 12

Perform the multiplication in the denominator.h=3850362h = \frac{3850}{36 \sqrt{2}}h=362​3850​

STEP 13

To rationalize the denominator, multiply both the numerator and the denominator by 2\sqrt{2}2​.h=3850236×2h = \frac{3850 \sqrt{2}}{36 \times2}h=36×238502​​

STEP 14

Perform the multiplication in the denominator.h=3850272h = \frac{3850 \sqrt{2}}{72}h=7238502​​So, the solution to the equation is h=3850272h = \frac{3850 \sqrt{2}}{72}h=7238502​​.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Solve for $h$ in the equation $2(15)(85)+2(10)(65)=2(9 \sqrt{8}) h$ .

Assumptions1. We are given the equation $(15)(85)+(10)(65)=(9 \sqrt{8}) h$ . We are asked to solve for $h$

First, let's simplify the left side of the equation.
$2(15)(85)+2(10)(65)$

Calculate the multiplication in the brackets.
$2 \times1275 +2 \times650$

Perform the multiplication.
$2550 +1300$

Add the two values together.
$3850$ So, the left side of the equation simplifies to3850.

Now, let's simplify the right side of the equation.
$2(9 \sqrt{8}) h$

Calculate the multiplication in the brackets.
$2 \times9 \times \sqrt{} \times h$

Perform the multiplication.
$18 \sqrt{8} h$ So, the right side of the equation simplifies to $18 \sqrt{8} h$ .

Now, we can rewrite the equation with the simplified left and right sides.
$385 =18 \sqrt{8} h$

To solve for $h$ , we need to isolate $h$ on one side of the equation. We can do this by dividing both sides of the equation by $18 \sqrt{8}$ .
$h = \frac{3850}{18 \sqrt{8}}$

implify the right side of the equation.
$h = \frac{3850}{18 \times \sqrt{}}$

Perform the multiplication in the denominator.
$h = \frac{3850}{36 \sqrt{2}}$

To rationalize the denominator, multiply both the numerator and the denominator by $\sqrt{2}$ .
$h = \frac{3850 \sqrt{2}}{36 \times2}$

Perform the multiplication in the denominator.
$h = \frac{3850 \sqrt{2}}{72}$ So, the solution to the equation is $h = \frac{3850 \sqrt{2}}{72}$ .