Please use statement and reason, not sin cos or tan. In rectangle ABCD the diagonals intersect each other at point O and ABD = 30. Find BC if AC = 16 in. Include a picture if you can, but you don't have to.
Answers
Answer:
- 8 in
Step-by-step explanation:
- Rectangle has properties:
- Diagonals are congruent
- Opposite sides are congruent
- All angles are right
Given
- m∠ABD = 30°
- AC = 16 in
- BC = ?
Solution
As per properties mentioned above we have:
- BC = AD
- BD = AC = 16 in
ΔABD is right triangle with ∠B - 30°, ∠A- 90°, ∠D - 60°
Side opposite to 30 is half of the length of the hypotenuse
AD is opposite to ∠B and BD is the hypotenuse, then:
- AD = 1/2*BD
- AD = 1/2(16)
- AD = 8 in
and
- BC = AD = 8 in
Related Questions
Consider the sequence below. 3, 1, 1/3, 1/9,... select the explicit function which defines the sequence. A.) f(n) = 1/3 • 2^(n - 1) B.) f(n) = 2 • (1/3)^(n - 1) C.) f(n) = 1/3 • 3^(n - 1) D.) f(n) = 3 • (1/3)^(n - 1)
For each of the following four statements, indicate whether it is possible or not according to probability theory. Explain your answer. (1) The probability that a customer will buy 5 items in a single purchase is 30% ___________________________ (2) The probability that a customer will buy 3 items in a single purchase is 101% ___________________________ (3) The probability that a customer will buy 3 items in a single purchase is 99% ___________________________ (4) The probability that a customer will buy 8 item
Jenny drove 715 miles in 11 hours.At the same rate, how long would it take her to drive 325 miles?
Breyers is a major producer of ice cream and would like to test if the average American consumes more than 17 ounces of ice cream per month. A random sample of 25 Americans was found to consume an average of 19 ounces of ice cream last month. The standard deviation for this sample was 5 ounces. Breyers would like to set LaTeX: \alpha = 0.025 α = 0.025 for the hypothesis test. It is known that LaTeX: z_{\alpha}=1.96 z α = 1.96 and LaTeX: t_{\alpha}=2.06 t α = 2.06 for the df = 24. Also, it is established that the ice cream consumption follows the normal distribution in the population. The conclusion for this hypothesis test would be
Answers
Given
Jessie has 5 dogs
2 are male
3 are female
Procedure
What percent of the dogs are male?
Male dogs
40 % of dogs are male
longer side yd
What is this area?
yd2
Answers
Answer:
Shorter side = 755 yd
longer side = 1510 yd
A(max) = 1140050 yd²
Step-by-step explanation:
The owner has 3020 yd of fencing
Lets assume:
x the shorter side of the rectangle ( we will use fencing in two sides of length x )
y the longer one
A area of the rectangle and P the perimeter of the rectangle ( we have only three sides covered by fencing material)
We have: A = x * y P = 2 * x + y ⇒ y = P - 2*x ⇒ y = 3020 - 2* x
A (x) = x * ( 3020 - 2*x) ⇒ A(x) = 3020 * x - 2* x²
Taken derivative
A´(x) = 3020 - 4 * x
If A´(x) = 0 3020 -4*x = 0 ⇒4*x = 3020 x = 755 yd
If we take second derivative A´´(x) = -4
so A´´(x) < 0 so there is a maximun in point x = 755
Then
Rectangle dimensions :
x = 755 yd ⇒ y = 3020 - 2 * x ⇒ y = 3020 - 2 * (755) y = 1510 yd
Maximum area is : A(max) = 1510 * 755 ⇒ A(max) = 1140050 yd²
Final answer:
To get the largest area, 3020 yards of fencing is divided equally to form a rectangular grazing piece. Each side is 1510 yards, leading to a total area of 2,280,100 square yards.
Explanation:
We are given a total of 3020 yards of fencing which is used to fence two sides of a rectangle, with a river enclosing the third side. The largest area of a rectangle is obtained when the rectangle is a square. However, since one of the sides is the river, and hence not fenced, the rectangle is not square but should be as close to a square as possible to give the maximum area.
The optimum distribution is dividing the fence into two equal parts for both sides of the rectangle, so each side will be 3020 / 2 = 1510 yds. The dimensions of the largest area he can enclose are: shorter side = yd, longer side = 1510 yds.
The area of this rectangular grazing land would then be 1510 yd * 1510 yd = 2,280,100 yd2.
Learn more about Maximum Area here:
#SPJ3
Answers
Answer:
i think its 85
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Answers
Here we will show you step-by-step with detailed explanation how to calculate 48 divided by 32 using long division.
Before you continue, note that in the problem 48 divided by 32, the numbers are defined as follows:
48 = dividend
32 = divisor
Step 1:
Start by setting it up with the divisor 32 on the left side and the dividend 48 on the right side like this:
3 2 ⟌ 4 8
Step 2:
The divisor (32) goes into the first digit of the dividend (4), 0 time(s). Therefore, put 0 on top:
0
3 2 ⟌ 4 8
Step 3:
Multiply the divisor by the result in the previous step (32 x 0 = 0) and write that answer below the dividend.
0
3 2 ⟌ 4 8
0
Step 4:
Subtract the result in the previous step from the first digit of the dividend (4 - 0 = 4) and write the answer below.
0
3 2 ⟌ 4 8
- 0
4
Step 5:
Move down the 2nd digit of the dividend (8) like this:
0
3 2 ⟌ 4 8
- 0
4 8
Step 6:
The divisor (32) goes into the bottom number (48), 1 time(s). Therefore, put 1 on top:
0 1
3 2 ⟌ 4 8
- 0
4 8
Step 7:
Multiply the divisor by the result in the previous step (32 x 1 = 32) and write that answer at the bottom:
0 1
3 2 ⟌ 4 8
- 0
4 8
3 2
Step 8:
Subtract the result in the previous step from the number written above it. (48 - 32 = 16) and write the answer at the bottom.
0 1
3 2 ⟌ 4 8
- 0
4 8
- 3 2
1 6
You are done, because there are no more digits to move down from the dividend.
The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 48 divided by 32 calculated using Long Division is:
1
16 Remainder
Answers
Answer:
oh well thanks
Step-by-step explanation:
Answers
Step-by-step explanation: