All categories

3 years ago

Solve for x. (Geometry)

Mathematics

1 answer:

GaryK [48]3 years ago

4 0

Hello from MrBillDoesMath!

Answer: 9

Discussion

By the Pythagorean theorem, the length of the third side (the hypotenuse) in the triangle with sides 4 and 6 is sqrt ( 4^2 + 6^2) = sqrt (52)

Applying Pythagoras to the left most triangle (sides, x and 6) gives:

x^2 + 6^2 = m^2 (I am calling the unknown side "m)

Finally, in the big right triangle (the one containing the two right triangles)

(x + 4) ^2 = (sqrt(52)) ^2 + m^2

OK! Subtract the first equation from the second:

(x+4)^2 = 52 + m^2

x^2 + 36 = m^2

-----------------------------------------------------

( x+4)^2 - x^2 - 36 = 52 + (m^2 - m^2) =>

x^2 + 8x + 16 - x^2 -36 = 52 =>

x^2 - x^2 + 8x + 16 -36 = 52 =>

0 + 8x - 20 = 52 =>

8x = 72 =>

x = 9

Thank you,

MrB

You might be interested in

Please help and get points

stich3 [128]

2/4 and 1/4, 2x3=6 4x2=8, 3x1=3 3x4=12

7 0

3 years ago

With three boys on a large scale, it read 170 pounds. When Adam stepped off, the scale read 100 pounds. When both Adam and Ben s

Elden [556K]

Answer:

Adam = 70 pounds

Ben = 40 pounds

C = 60 pounds

Step-by-step explanation:

We can work out some equations based on the given information:

We can call the boys A, B and C

so,

when all three boys are standing on the scale, it reads 170 pounds.

$A + B + C = 170$ - Eq(1)

when Adam stepped off, the scale reads 100. This means that the combined weight of the remaining two boys is 100.

$B + C = 100$ - Eq(2)

when both Adam and Ben stepped off, the weight of the remaining boy is shown on the scale.

$C = 60$

So we already knew the weight of boy C. (it was in the question all along)

$C = 60$ pounds

Now to find the individual weights of the remaining boys, we can work our way backwards

we can put this value back in Eq(2), to find the weight of boy B.

$B + C = 100$

$B + 60 = 100$

$B = 100 - 60$

$B = 40$

the

the weight of boy B (Ben) is $B = 40$ pounds

now we can put all of the known weights of the boys in Eq(1) to find the weight of Boy A.

$A + B + C = 170$

$A + 40 + 60 = 170$

$A + 100 = 170$

$A = 170 - 100$

$A = 70$

the weight of boy A (Adam) is $A = 70$ pounds

The Answer:

Adam = 70 pounds

Ben = 40 pounds

C = 60 pounds

7 0

4 years ago

How do you graph Y equals -1/3 X +6 and Y equals 3X +6

elena-s [515]

Step-by-step explanation:

step 1. so you want to graph 2 linear equations?

step 2. y = (-1/3)x + 6. put a dot on the y intercept (0, 6).

step 3. draw the line through (0, 6) with a slope of -1/3 (down 1 and to the right 3).

step 4. y = 3x + 6. put a dot on the y intercept (0, 6).

step 5. draw the line through (0, 6) with a slope of 3/1 (up 3 and to the right 1).

4 0

4 years ago

Convert 2/5 into a percent. a 25% b 40% c 50% d 52%

Lady_Fox [76]

Answer: B. 40%

~hope this helps!~

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Please help with this asappppppppll

Alenkinab [10]

We are given with a circle and we need to find the equation of the circle , but first let's recall that , the equation of a circle with radius 'r' and centre at (h,k) is given by ${\bf{(x-h)^{2}+(y-k)^{2}=r^{2}}}$

Now , here as as the circle cuts the +ve x-axis at (9,0) . So , it's radius is 9 units or the 2nd way is to measure the distance from centre of the circle to the point where the circle cuts the graph , as the centre is at Origin , so here (h,k) = (0,0) .Which means that the centre is located at the point whose coordinates are (0,0) which is also known as origin . Now , finding the equation of the circle :-

${:\implies \quad \sf (x-0)^{2}+(y-0)^{2}=(9)^{2}}$

${:\implies \quad \bf \therefore \quad \underline{\underline{x^{2}+y^{2}=81}}}$

This is the required equation of Circle

7 0

3 years ago