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NeTakaya
1 year ago
15

In a rectangle, a diagonal forms a 36° angle with a side. Find the measure of the angle between the diagonals, which lies opposi

te to a shorter side.
Mathematics
1 answer:
bezimeni [28]1 year ago
8 0

Answer:

The answer is 72 degrees

Step-by-step explanation:

The picture that Helpmetnx showed does work. But they made a mistake and assumed that the diagonal is a angle bisector, and it's not.

1. rectangle ABCD, BD & AC are the diagonals. ∠ABD =36 degrees

2. ∠ABD= ∠BDC = 36 - alternate interior angles

3. ∠DBC = 90 - 36 = 54. ∠DBC =∠ADB = ∠BCA = 54

4. Now we know that the triangle formed between the two diagonals is a isosceles triangle because of base angle theorem.

5. 180 - 54*2 = 72 degrees

I hope this helps!

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You save $5,000.00 and invest 60% of it in stocks while leaving the rest in a savings account earning a 4.9% APR. The stock incr
Angelina_Jolie [31]

Answer:

5,340

Step-by-step explanation:

Hi there:)

Amount invested in stock

=5000×0.6=3000

Amount invested in a saving account

5000-3000=2000


The stock increases 9% in the first year

3,000×(1+0.09)=3,270

and loses 4% of its value the second year

3,270×(1−0.04)=3,139.2

Amount of a saving account after two years

2,000×(1+0.049)^(2)=2,200.8


the total amount gained during the 2 years

3,139.2+2,200.8=5,340...answer


Hope it helps




8 0
2 years ago
Read 2 more answers
A manager wants to build 3-sigma x-bar control limits for a process. The target value for the mean of the process is 10 units, a
lubasha [3.4K]

Answer: Third option is correct.

Step-by-step explanation:

Since we have given that

Mean = 10

Sample size = 9

Standard deviation = 6

We need to find the upper and lower control limits.

so, Lower limit would be

\bar{x}-3\dfrac{\sigma}{\sqrt{n}}\\\\=10-3\times \dfrac{6}{\sqrt{9}}\\\\=10-6\\\\=4

Upper limit would be

\bar{x}+3\dfrac{\sigma}{\sqrt{n}}\\\\=10+3\times \dfrac{6}{\sqrt{9}}\\\\=10+6\\\\=16

Hence, Third option is correct.

3 0
2 years ago
A company that manufactures small canoes has a fixed cost of $ 18 comma 000$18,000. It costs $ 120$120 to produce each canoe. Th
Scilla [17]
If the company makes 1 canoe only, then the cost is, the fixed cost plus how much it costs for the 1 canoe, or
180,000 + 1*120

if it makes 2 canoes
180,000 + 2*120
3 canoes   180,000 + 3*120
4canoes   180,000 + 4*120
x canoes  180,000 + x*120

so... we dunno what "x" is, but whatever "x" maybe, the cost ends up as 180,000 + x*120, or 180,000 + 120x

now, let's see the revenue
1 canoe 1 * 240
2 canoes 2*240
3 canoes 3*240
x canoes x*240

so.. whatever "x" maybe, the Revenue is x*240 or 240x

break-even point is when, the amount of expenses and earnings cancel each other out, or, there's no profit, but there's no loss either, same amount that's spent is also earned back

so, the break-even point occurs when Revenue = Cost

180,000 + 120x = 240x     <--- solve for "x"
4 0
1 year ago
A researcher carefully calculates the correlation coefficient and gets a value of r=1.23. What does this value mean?
Vaselesa [24]
Answer: An error was made! All correlation coefficients: -1 ≤ r ≤ 1.
4 0
1 year ago
Abbey wants to use her savings of $1,325 to learn yoga. The total charges to learn yoga include a fixed registration fee of $35
Brums [2.3K]
So for this, this can be written into the equation y=50x+35 (x = number of months, y = total cost).

To solve this problem, we need to plug in 1325 into the y-variable and solve from there.

1325=50x+35

Subtract 35 on each side to get 1290=50x

Then just divide by 50 on each side, and your answer should be 25.8=x


And because we cannot go past budget, we will have to round down to 25. In context, the maximum amount of months Abbey can do is 25 months.
8 0
2 years ago
Read 2 more answers
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