1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Yuki888 [10]
2 years ago
12

Find the value of x. Leave your answer in simplest radical form.

Mathematics
2 answers:
Ivenika [448]2 years ago
8 0

Step-by-step explanation:

Pythagoras.

c² = a² + b²

c being the Hypotenuse (the side opposite of the right angle).

so, the length of the rectangle is the Hypotenuse of the right-angled triangle on the top :

length² = 7² + 3² = 49 + 9 = 58

length = sqrt(58)

the diagonal of the rectangle is again the Hypotenuse of the right-angled triangle of length (sqrt(58)), width (x) and diagonal (9) of the rectangle.

so, we have

9² = sqrt(58)² + x² = 58 + x²

81 = 58 + x²

23 = x²

x = sqrt(23)

Artyom0805 [142]2 years ago
3 0

Answer:

First you need to find at least two dimensions of the triangle containing a side length of x. The triangle of the top can be used for that. The hypothenuse for the 7,3 triangle is \sqrt{58}.

Now we can use the other triangle with sides of x,\sqrt{58}, and a hypothenuse of 9 to find x.

x^2 + \sqrt{58}^2 = 9^2

simplify

x^2 + 58 = 81

subtract 58 from both sides

x^2 = 23

x = \sqrt{23\\}

and since this radical cannot be simplified further that is your answer.

Step-by-step explanation:

You might be interested in
On a coordinate plane, a shape is plotted with vertices of (3, 1), (0, 4), (3, 7), and (6, 4). what is the area of the shape if
QveST [7]
Let
<span>A (3, 1)
B (0, 4)
C(3, 7)
D (6, 4)

step 1
find the distance AB
d=</span>√[(y2-y1)²+(x2-x1)²]------> dAB=√[(4-1)²+(0-3)²]-----> dAB=√18 cm

step 2
find the distance CD
d=√[(y2-y1)²+(x2-x1)²]------> dCD=√[(4-7)²+(6-3)²]-----> dCD=√18 cm

step 3
find the distance AD
d=√[(y2-y1)²+(x2-x1)²]------> dAD=√[(4-1)²+(6-3)²]-----> dAD=√18 cm

step 4
find the distance BC
d=√[(y2-y1)²+(x2-x1)²]------> dBC=√[(7-4)²+(3-0)²]-----> dBC=√18 cm

step 5
find slope AB and CD
m=(y2-y1)/(x2-x1)
mAB=-1
mCD=-1
AB and CD are parallel and AB=CD

step 6
find slope AD and BC
m=(y2-y1)/(x2-x1)
mAD=1
mBC=1
AD and BC are parallel and AD=BC
and 
AB and AD are perpendicular 
BC and CD are perpendicular

therefore
the shape is a square wit length side √18 cm

area of a square=b²
b is the length side of a square
area of a square=(√18)²------> 18 cm²

the answer is
18 cm²

see the attached figure


6 0
3 years ago
Given a dilation with the origin O (0, 0), by observation determine the scale factor "K."
timurjin [86]
15 is 3 times 5. The point (5, 0) is dilated to the point (15, 0) by using a factor of
  K = 3.
7 0
3 years ago
Read 2 more answers
How does tripling the side lengths of a right triangle affect its area?)
kap26 [50]
The area of the triangle will then be 9 times as great. 

The formula of the area of a triangle is 1/2bh, so if the base has been tripled and the height has been tripled, you're essentially multiplying 3 to the original equation twice (3 x 3 = 9).
6 0
3 years ago
Read 2 more answers
Math question help need it​
Lelechka [254]

Answer:

Dont really understand what the question is saying but i graphed it on Desmos hope this helps

Step-by-step explanation:

3 0
3 years ago
A box of golf balls costs $7.32. At that rate, how much will a box of 15 balls cost?
san4es73 [151]
Your question is vague. There is not enough information. How many balls are in the box? 15 boxes would cost 109.80 thought.
3 0
3 years ago
Other questions:
  • A quantity with an initial value of 870 decays exponentially at a rate of 0.55% every 4 decades. What is the value of the quanti
    11·1 answer
  • Monday's high temperature was six degrees Celsius the low temperature was -3°C
    6·1 answer
  • What does 2/3 * 14/6 equal. Please show work
    12·1 answer
  • PLEASE HELP I'M DESPERATE &lt;3
    11·2 answers
  • A policeman is standing near a highway using a radar gun to catch speeders. He aims the gun at a car that has just passed his po
    7·1 answer
  • What is wrong with the following equation 4+(10/5) equals 6-2
    8·1 answer
  • A technology company recently released two new products and tracked the increase in sales of each product. They were able to mod
    15·2 answers
  • Fycgvhbkjnlmlmjiohugyftdxzs hi
    12·1 answer
  • I need help with #5
    10·2 answers
  • on a distant​ planet, a central angle intercepts an arc of miles. what is the radius of the planet at its​ equator?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!