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astra-53 [7]
1 year ago
5

In the accompanying diagram of parallelogram ABCD,diagonals AC and DB intersect at E, AE = 3x - 4, andEC = x + 12.What is the va

lue of x?

Mathematics
1 answer:
skelet666 [1.2K]1 year ago
4 0

x = 8

Explanation:

AE = 3x - 4

EC = x + 12

SInce diagonals AC and DB intersect at E

it means the lines which meet at the intersection E are equal. A and C meet at E which gives AE and EC

AE = EC

3x - 4 = x + 12

collect like terms:

3x - x = 12 + 4

2x = 16

divide both sides by 2:

2x/2 = 16/2

x = 8

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The endpoints of DE and D(-3, y) and x, 6). The midpoint of DE is M(4,2). What is the length of DE.
Natasha_Volkova [10]

If the endpoints of DE where D(-3, y) and E(x, 6) with the midpoint M(4, 2), the length of DE is 16.12 units

The formula for calculating the midpoint is expressed as;

M(x,y)=(\frac{x_1+x_1}{2}, \frac{y_1+y_2}{2})

For the x-coordinate points:

X = -3+x/2

4 * 2 = -3 + x

8 = -3 + x

x = 8 + 3

x = 11

Get the value of y;

2 = y+6/2

y+6 = 2 * 2

y + 6 = 4

y = 4 - 6

y = -2

Hence the coordinates of D and E are D(-3, -2) and E(11, 6)

D=\sqrt{(6-(-2))^2+(11-(-3))^2}\\D=\sqrt{8^2+14^2}\\D=\sqrt{64 + 196}\\D=   \sqrt{260}\\D= 16.12units

Hence the length of DE is 16.12 units

Learn more here; brainly.com/question/22624745

3 0
2 years ago
A base angle of an isosceles triangle measures 30, and the length of one of the legs is 12. What is the length of the altitude d
AfilCa [17]

Answer: 6

Step-by-step explanation:

From the question, a base angle of isosceles triangle is 30°.We are also informed that one of the legs is 12. The altitude is opposite to the angle having a measure of 30°. The hypoteneous in the right angled triangle which is formed by drawing the altitude is 12. This will be calculated as:

Sin = opposite/hypotenuse

Sin 30°=length of the altitude/12

Note that sin 30° = 0.5

0.5 = length of the altitude/12

length of the altitude = 12 × 0.5

Hence, length of altitude = 6

5 0
3 years ago
Plz answer no fake stuff plz
Assoli18 [71]
<h3>3 Answers:</h3>
  • A) The product of the area model is 3055
  • D) The missing number is 200
  • E) The model shows 47 x 65

=======================================================

Explanation:

The first number along the top is 40, and it multiplies with the second number along the side to get 40 x 5 = 200

You can think of it as 4 x 5 = 20, then you tack on an extra 0 to the '4' and to the '2' as well, so it keeps things balanced.

So this explains how choice D is one of the answers.

-------------------------

After 200 fills in that question mark, we'll have these four numbers inside the table: 2400, 420, 200, and 35

Those four values add up to: 2400+420+200+35 = 3055

This shows that choice A is one of the answers.

--------------------------

Finally, choice E is the third answer because along the top we have 40+7 = 47, and along the side we have 60+5 = 65

Put another way, the total top length is the sum of the two smaller pieces of 40 and 7, which explains how the total top length is 47 units long. A similar argument happens for the left side values as well.

We ultimately have a rectangle that is 47 units across in the horizontal direction, and 65 units tall in the vertical direction.

With your calculator, you should note that 47*65 = 3055 to help confirm everything lines up.

--------------------------

Extra info:

Choice B is false because this contradicts choice D.

Choice C is false because it contradicts choice E

3 0
2 years ago
Which of these graphs represents a function
vagabundo [1.1K]

Answer:

There is no picture though :/

4 0
3 years ago
Read 2 more answers
An IPod Nano has 2 gigabytes of storage and can hold about 500 songs. The iPod Plus has 80 gigabytes of storage. How many songs
jasenka [17]
80 * 250 =20,000

The iPod can hold 250 songs per gigabyte.
4 0
3 years ago
Read 2 more answers
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