Answer:
, or 8.7
Step-by-step explanation:
To solve this problem, you need to use the Pythagorean theorem . The tricky part is visualizing where the right triangle will be in the cube. The diagonal you are trying to find will be the hypotenuse, the diagonal of the base of the cube is one leg, and the edge of the cube is another leg.
First, you need to find the lengths of both legs of the triangle. The first leg is the length of the edge of the cube, which is given as 5 cm.
The next leg is the diagonal of the base of the cube, which is a 5x5 square. To find the diagonal of the 5x5 square, you can cut the square across its diagonal and use the 45-45-90 special right triangle rule. Each leg of the newly formed 45-45-90 triangle is 5 cm, which can be represented by x, and the hypotenuse, which is also the diagonal of the original 5x5 square, can be represented as .
Using 5 as x and substituting, you can find that the diagonal of the 5x5 square is cm, so the second leg of the right triangle is cm.
Now, you can do a final substitution of both legs into the Pythagorean theorem, which turns out as
Solving this equation starts with doing out the squares on the left side as which means . From here you take the square root of both sides of the equation to get or .
The final step is to make this solution rational by rounding it, so plug in into a calculator and round to the nearest tenth to get 8.7.
As always, the sum of the measures of the angles in a triangle is 180°.
(x -5) +(3x +30) +35 = 180
4x +60 = 180 . . . . . . . . . . . . . collect terms
4x = 120 . . . . . . . . . . . . . . . . . subtract 60
x = 30 . . . . . . . . . . . . . . . . . divide by 4
a) The value of x is 30.
7x+40... If you go to mathwarehouse.com you can type your question in and you'll get an answer in less than a second
Answer:
x=8
Step-by-step explanation:
Cross multiply to solve
2/x=4/16
4*x=2*16
4x=32
Divide by 4 on both sides
x=8
So,
2/8=4/16
Hope this helps! :)
Hey there! I'm happy to help!
The domain is all of the possible x-values and the range is all of the possible y-values.
Let's quickly rearrange our equation so we can plug in x to see what y is.
12x+6y=24
We subtract 12x from both sides.
6y=-12x+24
We divide both sides by six.
y= -2x+4
Since there are three domains we can plug into this equation that can give us one output, we will have three numbers in our range! Let's plug in our x-values to get our three y-values.
y=-2(-4)+4
y=12
y=-2(0)+4
y=4
y=-2(5)+4
y= -6
When writing your range, you order the numbers from least to greatest. We can write this range as {-6,4,12}
Have a wonderful day!