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klio [65]
3 years ago
11

ABC is isosceles with AB=AC=8 units and BC=6 units. D and E are midpoints of AB and BC respectively. Calculate the length of DE?

Mathematics
1 answer:
Allushta [10]3 years ago
6 0
The triangle is drawn and is shown in the image attached with.

We get two similar triangles. Triangle ABC and Triangle ADE. Since the triangles are similar the ratio of their corresponding sides will be the same. 

D and E are the midpoints of AB and BC, therefore, AD and AE are both 4 units in length. Using the property of similar triangles, we can say:

AD : DE= AB : BC
AD = 4 units
AB = 8 units
BC = 6 units
DE = unknown = x units

So,

4 :x = 8 : 6 \\  \\ 
 \frac{4}{x} = \frac{8}{6}  \\  \\ 
x=4* \frac{6}{8}=3 


Therefore, the length of DE will be 3 units

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Write each of the following expressions without using absolute value. |z−6|−|z−5|, if z<5
Andre45 [30]

Answer: 6 - 5

<u>Step-by-step explanation:</u>

|z - 6| - |z - 5|    ; z < 5

Since z < 5, then

|z - 6| will be the absolute value of a negative number. Replace the absolute value with a negative and parentheses:

-(z - 6) =  -z + 6

|z - 5| will be the absolute value of a negative number. Replace the absolute value with a negative and parentheses:  

-(z - 5) = -z + 5

Now subtract them without the absolute value signs:

-z + 6 - (-z + 5)

Distribute the negative sign:

-z + 6 + z - 5

-z + z = 0 which leaves:

6 - 5

3 0
4 years ago
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How long is a guy wire reaching from the top of a 6ft. Pole to a point on the ground 4ft. From the pole
dlinn [17]

Answer:

the guy wire is 7.211 ft long

Step-by-step explanation:

Notice that we are in the presence of a right angle triangle formed by: the height (the standing 6 ft pole), the base (the distance from the pole to the anchoring point on the ground), and the actual guy wire. See attached image for reference.

Notice that since pole and ground are perpendicular to each other (at 90 degrees) , the guy wire forms what is called the "hypotenuse" (longest side) of the right angle triangle. We can therefore use the Pythagorean Theorem to solve this problem with the formula for the hypotenuse:

Hypotenuse=\sqrt{side1^2 +side2^2} \\Hypotenuse= \sqrt{6^2+4^2}\\Hypotenuse=\sqrt{36+16} \\Hypotenuse=\sqrt{52} \\Hypotenuse=7.2111\, ft

4 0
3 years ago
Jackie already owns 19 necklaces, and additional necklaces are priced at 1 for a dollar. How
Marianna [84]

Answer: 13 dollars

Step-by-step explanation: if she already has 19, you just need to subtract that from 32.

5 0
4 years ago
Volume:Question 8
SSSSS [86.1K]

Answer:

84.82 inches squared

Step-by-step explanation:

Volume of a sphere formula

Volume=4/3(pi)r^2

r=4.5

therefore

4/3*pi*(4.5)^2=84.8230016469244 inches squared

round to whatever many decimal places

84.82 inches squared

3 0
4 years ago
Account A and Account B both have a principal of $2,000 and an annual interest rate of 2%. No additional deposits or withdrawals
GuDViN [60]

Answer:

Account B earns more interest.

After 20 years, account B will have earned $171.89 more.

Step-by-step explanation:

Let's calculate the total for each account.

Account A:

Account A earns simple interest. We know that the principal value is $2000 and the interest rate is 2% or 0.02. We can use the simple interest formula:

A=P(1+rt)

Where A is the future value, P is the principal, r is the rate, and t is the time in years.

So, let's substitute 2000 for P, 0.02 for r, and 20 for t. This yields:

A=2000(1+0.02(20))

Multiply and add:

A=2000(1+0.4)=2000(1.4)

Multiply. So, the total amount of money in Account A after 20 years is:

A=\$2800

Since we initially deposited $2000 and our total is now $2800, this means that we earned an interest of 2800-2000=\$ 800

Account B:

Account B earns compound interest. Like Account A, Account B has a principal value of $2000 and the interest rate is 2% or 0.02. We also know that it's compounded annually, so once per year. We can use the compound interest formula:

B=P(1+\frac{r}{n}})^{nt}

Where B is the future value, P is the principal, r is the rate, n is the times compounded per year, and t is the time in years.

So, let's substitute 2000 for P, 0.02 for r, n for 1 (since it's compounded annually), and t for 20. This yields:

B=2000(1+\frac{0.02}{1})^{(1)(20)}

Simplify this to acquire:

B=2000(1.02)^{20}

Evaluate. Use a calculator. So, after 20 years, the amount of money in Account B is:

B\approx\$2971.89

Since our principal was $2000, this means that we earned an interest of approximately  2971.89-2000=\$ 971.89.

So, Account A earned an interest of $800 and Account B earned an approximate interest of $971.89.

So, Account B earned more interest.

And it earned 971.89-800=\$ 171.89 more than Account A.

And we're done!

5 0
3 years ago
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