All categories

4 years ago

Given: ABCD is a trapezoid, AC ⊥ CD AB = CD, AC=the square root of 75 , AB = 5 Find: AABCD

Mathematics

1 answer:

babymother [125]4 years ago

5 0

Look at the picture.
Use the Pythagorean theorem:
$|AD|^2=5^2+(\sqrt{75})^2\\\\|AD|^2=25+75\\\\|AD|^2=100\to|AD|=\sqrt{100}\to|AD|=10$
The area of a triangle ADC:
$A_\Delta=\dfrac{|DC|\cdot|AC|}{2}\ and\ A_\Delta=\dfrac{|AD|\cdot h}{2}$
Substitute:
$\dfrac{10h}{2}=\dfrac{5\sqrt{75}}{2}\\\\5h=\dfrac{5\sqrt{75}}{2}\ \ \ |:5\\\\h=\dfrac{\sqrt{75}}{2}$
The triangles ADC and DCE are similar. Therefore:
$\dfrac{|ED|}{\frac{\sqrt{75}}{2}}=\dfrac{5}{\sqrt{75}}\\\\\dfrac{2|ED|}{\sqrt{75}}=\dfrac{5}{\sqrt{75}}\ \ \ |\cdot\sqrt{75}\\\\2|ED|=5\ \ \ |:2\\\\|ED|=2.5$
$|BC|=|AD|-2|ED|\\\\|BC|=10-2\cdot2.5=10-5=5$
The area of the trapezoid:
$A=\dfrac{|AD|+|BC|}{2}\cdot h$
Substitute:
$A=\dfrac{10+5}{2}\cdot\dfrac{\sqrt{75}}{2}=\dfrac{15\sqrt{75}}{4}\\\\=\dfrac{15\sqrt{25\cdot3}}{4}=\dfrac{15\cdot5\sqrt3}{4}=\dfrac{75\sqrt3}{4}$

You might be interested in

Given the geometric sequence where a1=1 and the common ratio is 6, what is the domain for n?

kari74 [83]

We have been given that a geometric sequence's 1st term is equal to 1 and the common ratio is 6. We are asked to find the domain for n.

We know that a geometric sequence is in form $a_n=a_1(r)^{n-1}$ , where,

$a_n$ = nth term of sequence,

$a_1$ = 1st term of sequence,

r = Common ratio,

n = Number of terms in a sequence.

Upon substituting our given values in geometric sequence formula, we will get:

$a_n=1\cdot (7)^{n-1}$

Our sequence is defined for all integers such that n is greater than or equal to 1.

Therefore, domain for n is all integers, where $n\geq 1$ .

4 0

4 years ago

Please help I’m really confused and need to learn this

egoroff_w [7]

Answer:

Step-by-step explanation:

For #2, another way to word this question is: For which of the following trig functions is π/2 a solution? Well, go through them one by one. If you plug π/2 into sinθ, you get 1. This means that when x is π/2, y is 1. Try and visualize that. When y is 1, that means you moved off the x-axis; so y = sinθ is NOT one of those functions that cross the x-axis at θ = π/2. Go through the rest of them. For y = cos(π/2), you get 0. At θ = π/2, this function crosses the x-axis. For y = tanθ, your result is undefined, so that doesn't work. Keep going through them. You should see that y = secθ is undefined, y = cscθ returns 1, and y = cotθ returns 0. If you have a calculator that can handle trig functions, just plug π/2 into every one of them and check off the ones that give you zero. Graphically, if the y-value is 0, the function is touching/crossing the x-axis.

Think about what y = secθ really means. It's actually y = 1/(cosθ), right? So what makes a fraction undefined? A fraction is undefined when the denominator is 0 because in mathematics, you can't divide by zero. Calculators give you an error. So the real question here is, when is cosθ = 0? Again, you can use a calculator here, but a unit circle would be more helpful. cosθ = π/2, like we just saw in the previous problem, and it's zero again 180 degrees later at 3π/2. Now read the answer choices.

All multiples of pi? Well, our answer looked like π/2, so you can skip the first two choices and move to the last two. All multiples of π/2? Imagine there's a constant next to π, say Cπ/2 where C is any number. If we put an even number there, 2 will cut that number in half. Imagine C = 4. Then Cπ/2 = 2π. Our two answers were π/2 and 3π/2, so an even multiple won't work for us; we need the odd multiples only. In our answers, π/2 and 3π/2, C = 1 and C = 3. Those are both odd numbers, and that's how you know you only need the "odd multiples of π/2" for question 3.

6 0

4 years ago

What is the answer to this problem?

emmasim [6.3K]

I hope this helps if you need any other help just message me and i will answer

True
True
False

6 0

3 years ago

He buys a suit that was on sale for 25%off. He only paid $125.00. What was the original price? What was the amount of the discou

Citrus2011 [14]

Equation 1):

You want to buy something that costs $166.66, and it's on sale for 25% off. What is the item's sale price?

First, convert the 25% to a real mathematical number. For percent's, this is always done by dividing the 25% by 100%, or 25% / 100% = 0.250.

Second, find out what 25% of $166.66 is. This is the amount of the sale discount. This is always found by multiplying 0.250 by the item's cost $166.66, like this:

0.250 x $166.66 = $41.67.

So for this sale, you'll save $41.67 on this item.

This means, the cost of the item to you is

$166.66 - $41.67 = $125.00.

Alternatively, you can think about it this way. The item is 25% off. This means you'll pay 75.000% of the total cost (100% - 25% = 75.000%).

Now what's 75.000% of the total cost?

0.750 x $166.66 = $125.00.

Answer =====> Just like the result above, the sale price on the item is $125.00.

Equation 2:)

You want to buy something that costs $125, and it's on sale for 25% off. What is the item's sale price?

First, convert the 25% to a real mathematical number. For percent's, this is always done by dividing the 25% by 100%, or 25% / 100% = 0.250.

Second, find out what 25% of $125 is. This is the amount of the sale discount. This is always found by multiplying 0.250 by the item's cost $125, like this:

0.250 x $125 = $31.25.

So for this sale, you'll save $31.25 on this item.

This means, the cost of the item to you is

$125 - $31.25 = $93.75.

Alternatively, you can think about it this way. The item is 25% off. This means you'll pay 75.000% of the total cost (100% - 25% = 75.000%).

Now what's 75.000% of the total cost?

0.750 x $125 = $93.75.

Answer =====> Just like the result above, the sale price on the item is $93.75.

Hope that helps!!! : )

8 0

4 years ago

A rectangular gift box has dimensions that can be represented as shown in the figure. The volume of the box is 56w cubic inches.

suter [353]

Answer:

Step-by-step explanation:

5 0

3 years ago