3. In the diagram below of right triangle ACB, altituDB find the length of CD in simplest radical form4,
Answers
For triangle ACB:
7^2=(AC)^2+(BC)^2 (1)
For triangle ACD:
(AC)^2=3^2+(CD)^2 (2)
For triangle DCB:
(BC)^2=(CD)^2+4^2 (3)
To make things simpler, we let
(AC)=x
(BC)=y
(CD)=z
Hence we have:
49=x^2+y^2 (1)
y^2=z^2+16 (2)
x^2=9+z^2 (3)
To solve for the unknown c, let us first substitute equation (2) in (1)
49=x^2+z^2+16
33=x^2+z^2 (4)
Then, we can substitute equation (3) in (4)
33=9+z^2+z^2
24=2z^2
z^2=12
z=2sqrt(3)
Thus, the length of z or (CD) is 2sqrt(3) in simplest radical form.
Related Questions
Solve the system of equations.x - 4y = 5x = 3y - 2( , )
3√x -6=0
Divide 33 photos into two groups so the ratio is 4 to 7, please help!!!!
What is the fraction 28/60 expressed in lowest terms?
Please help me. Thanks~! ^^
A. z = -42
B. z = -34
C. z = 30
D. z = 42
Answers
Multiply both sides by 3 :
3 * 2 - 3 * ( z / 3 ) = 3 * 12
Refine :
6 - z = 36
Subtract 6 from both sides:
6 - z - 6 = 36 - 6
- z = 30
Divide both sides by - 1
- z / - 1 = 30 / - 1
z = - 30
answer C
hope this helps!
Answers
64 / 4 = 16
So for 64 servings of pudding, we will need 16 cups of milk. But that's not what the question wants to know, it wants to know how many gallons of milk it would need.
In order to find that out, we have to know how many cups there are in one gallon. There are 2 cups in one pint, there are 2 pints in a quart, and there are 4 quarts in a gallon, so we just have to multiply those numbers, and we get 4 * 2 * 2 = 8 * 2 = 16
There are 16 cups in one gallon, therefore, 64 servings of pudding will require 1 gallon of milk.
Hope that helped! =)
O (10,--20)
O (10,4)
O (4, 10)
Answers
The value of the solution to the system of equations are, (10, - 20)
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
System of equations are,
y = -5x + 30 .. (i)
x = 10
Now, We can find the solution as;
Plug x = 10 in equation (i);
y = - 5x + 30
y = - 5 × 10 + 30
y = - 50 + 30
y = - 20
Thus, The value of the solution to the system of equations are, (10, - 20)
Learn more about the mathematical expression visit:
#SPJ7
Answers
0.4 is exactly 0.01 less than 0.41 .
Unless it is a trick question and 0.4 was rounded down from a larger number then this should be the correct answer.
b) You want to make a profit of $100. Decide on a price for each size of candle.
c) Did you set the prices so that they are proportional to the volume of each size of candle? Why or why not?
Answers
I decided to have the candles equal in volume. So, 1 cubic foot divided by 8 gives us 0.125 cubic foot, 216 in cubic inches.
With each candle having a volume of 216 cubic inches, I assign a radius to each: 0.5 in, 1.0 in, 1.5 in, 2.0 in, 2.5 in, 3.0 in, 3.5 in, and 4.0 in. Then, using the formula of the volume of a cylinder, which is:
V=pi(r^2)(h)
we then solve the corresponding height per candle. Let us let the value of pi be 3.14.
Hence, we will have the following heights (expressed to the nearest hundredths) for each of the radius: for
r=2.5 in: h=11.01 in
r=3.0 in: h= 7.64 in
r=3.5 in: h= 5.62 in
r=4.0 in: h= 4.30 in
r=4.5 in: h= 3.40 in
r=5.0 in: h= 2.75 in
r=5.5 in: h= 2.27 in
r=6.0 in: h= 1.91 in
b. each candle should sell for $15.00 each
($20+$100)/8=$15.00
c. yes, because the candles are priced according to the volume of wax used to make them, which in this case, is just the same for all sizes
A.4 227/500
B. 4 9/20
C. 4 5/11
D. 4 9/2
Answers
This would be so easy for you to solve, in about 3 minutes with a calculator.
A fraction means division ... (the top number) divided by (the bottom number).
Take the fraction part of each choice, do the division for each one,
and see which one gives you 0.4545... repeating.
A). 227/500 = 0.454 That's not 0.45 repeating.
B). 9/20 = 0.45 That's not 0.45 repeating.
C). 5/11 = 0.4545... THAT's 0.4545... repeating !
D). 9/2 = 4.5 That's not 0.45 repeating.