All categories

3 years ago

In the parallelogram shown, AE = t + 2, CE = 3t − 14, and DE = 2t + 8.

Mathematics

2 answers:

zalisa [80]3 years ago

6 0

Answer: 48 units

Given,
ABCD is a parallelogram
The diagonals bisect at E
Line segment AE = t + 2
Line segment CE = 3t – 14
Line segment DE = 2t + 8

Line segment DB is unknown

Since ABCD is a Parallelogram, Midpoint AC = Midpoint DB
The midpoint is E
Therefore
AE = CE … (Equation I)
DE = BE … (Equation II)

DB = DE + BE
Since DE = BE (Equation II),
DB = 2DE = 2BE

Given, DE = 2t + 8
DB = 2(2t + 8)
DB = 4t + 16 … (Equation III)

To solve for the value of ‘t’
AE = CE … (Equation I)
Line segment AE = t + 2
Line segment CE = 3t – 14
Therefore, t + 2 = 3t – 14

Subtract t from both sides of the equation
3t – 14 – t = t + 2 – t
2t – 14 = 2

Add 14 to both sides of the equation
2t – 14 + 14 = 2 + 14
2t = 16
t = 8

Substitute 8 for t in Equation III to solve for the length of line segment DB
DB = 4t + 16 … (Equation III)
DB = (4*8) + 16
DB = 32 + 16
DB = 48

Therefore, the length of line segment DB is 48 units

Dennis_Churaev [7]3 years ago

6 0

The answer is 48 units

You might be interested in

A superhero recently asked his nemesis how many cats she has. She answered with a riddle: "Five dash sixths of my cats plus tw

pochemuha

1 1/6
I think
Or 2 5/6

3 0

3 years ago

A dolphin is 9 feet below the surface of the ocean. If its position can be recorded as −9 feet, what would the position of 0 rep

bearhunter [10]

Answer:

the sea line

I am guessing

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

An angle measures 64° more than the measure of a complementary angle. What is the measure of each angle?

GarryVolchara [31]

Complementary angles are 90 degrees,so if the angle is 64 degrees more,you just only have to add 90+64=154.

The measure of the angle is 154 degrees

Hope i helped.

Remember:complimentary angles add up to 90 while supplementary angles add up to 180.

6 0

3 years ago

Question 3 (1 point) Co-60 has a half life of 5.3 years. If a pellet that has been in storage for 26.5 years contains 14.5g of C

Zarrin [17]

Answer:

464 grams.

Step-by-step explanation:

Amount of substance:

The amount of substance after t years is given by an equation in the following format:

$A(t) = A(0)(1-r)^t$

In which A(0) is the initial amount and r is the decay rate, as a decimal.

Co-60 has a half life of 5.3 years.

This means that:

$A(5.3) = 0.5A(0)$

We use this to find r. So

$A(t) = A(0)(1-r)^t$

$0.5A(0) = A(0)(1-r)^{5.3}$

$(1-r)^{5.3} = 0.5$

$\sqrt[5.3]{(1-r)^{5.3}} = \sqrt[5.3]{0.5}$

$1 - r = 0.5^{\frac{1}{5.3}}$

$1 - r = 0.8774$

$A(t) = A(0)(0.8774)^{t}$

If a pellet that has been in storage for 26.5 years contains 14.5g of Co-60, how much of this radioisotope was present when the pellet was put in storage?

We have that $A(26.5) = 14.5$ , and use this to find A(0). So