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3 years ago

Find DE 13x-37 2x+13

Mathematics

1 answer:

stiks02 [169]3 years ago

4 0

Answer:

DE = 27

Step-by-step explanation:

From the picture attached,

Points D and E are the midpoints of the segments AC and BC and DE is the mid-segment joining these points.

By the mid-segment theorem,

A segment joining midpoints of the two sides of a triangle is parallel to the third side. length of mid-segment is half of the 3rd side in measure.

DC = $\frac{1}{2}\text{AB}$

(2x + 13) = $\frac{1}{2}(13x-37)$

2(2x + 13) = (13x - 37)

4x + 26 = 13x - 37

13x - 4x = 26 + 37

9x = 63

x = 7

DE = 2x + 13

= 2(7) + 13

= 14 + 13

= 27

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Students who attend Washington Middle School are either in seventh or eighth grade. At the end of the first semester 25% of the

Irina18 [472]

Answer:

There are 1240 students who attended Washington Middle School.

Step-by-step explanation:

Given:

Students who attend Washington Middle School are either in seventh or eighth grade.

At the end of the first semester 25% of the students at Washington Middle School were on the honor roll.

Seventh graders represented 60% of the students on the honor roll.

If 124 students on the honor roll were in eighth grade.

Now, to find the students attend Washington Middle School.

Let the total number of students be $x.$

So, the students at Washington Middle School were on the honor roll:

25% of $x$

$=\frac{25}{100} \times x$

$=\frac{25x}{100}$

$=\frac{x}{4}$

As, given seventh graders represented 60% of the students.

So, the students on the honor roll represented as seventh graders:

$60\%\ of\ \frac{x}{4}$

$=\frac{60}{100} \times \frac{x}{4}$

$=0.6\times \frac{x}{4}$

$=\frac{0.6x}{4}$

As, 124 students on the honor roll were in eighth graders.

Thus,

According to question:

$\frac{x}{4} -\frac{0.6x}{4} =124$

$\frac{x-0.6x}{4} =124$

$\frac{0.4x}{4} =124$

Multiplying both sides by 4 we get:

$0.4x=496$

Dividing both sides by 0.4 we get:

$x=1240.$

Therefore, there are 1240 students who attended Washington Middle School.

6 0

4 years ago

PLEASE HELP

muminat

o.83

Step-by-step explanation:

Conversion a mixed number 3 1/

to a improper fraction: 3 1/4 = 3 1/

= 3 · 4 + 1/

= 12 + 1/

= 13/

To find new numerator:

a) Multiply the whole number 3 by the denominator 4. Whole number 3 equally 3 * 4/

= 12/

b) Add the answer from previous step 12 to the numerator 1. New numerator is 12 + 1 = 13

c) Write a previous answer (new numerator 13) over the denominator 4.

Three and one quarter is thirteen quarters

Conversion a mixed number 2 1/

to a improper fraction: 2 1/3 = 2 1/

= 2 · 3 + 1/

= 6 + 1/

= 7/

To find new numerator:

a) Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/

= 6/

b) Add the answer from previous step 6 to the numerator 1. New numerator is 6 + 1 = 7

c) Write a previous answer (new numerator 7) over the denominator 3.

Two and one third is seven thirds

Add: 13/

+ 7/

= 13 · 3/

4 · 3

+ 7 · 4/

3 · 4

= 39/

+ 28/

= 39 + 28/

= 67/

5 0

3 years ago

Read 2 more answers

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Evgesh-ka [11]

Answer: 10

Step-by-step explanation: The diameter is twice the radius

3 0

2 years ago

If option A is 20 dollar payment and option B requires 50 dollar payment. The opportunity cost of option A would be ------- and

Alecsey [184]

Answer:

a) nothing and 30 dollars.

Step-by-step explanation:

Opportunity cost usually arises when faced with choices or alternatives such that one has to be chosen, while the other is forgone. The benefits forgone by choosing a certain option of the available choices is called opportunity cost.

Given that :

Option A requires $20 payment

Option B requires $50 payment

Opportunity cost of choosing A = nothing (since payment required for the other alternative is higher than the chosen option)

Opportunity cost of Choosing B = ($50 - $20) = $30 (By choosing option B over option A, $30 was forgone as the other option (option A requires $30 lesser payment)

3 0

3 years ago

suzanne is running a 5km race. so far she has ran 1,250m. how many more meters does she need to run to complete the race?

natita [175]

Answer: 3750 m

Step-by-step explanation:

Remember that there are different units; one is in km and the other is in m

I’ll go from km to m

1 km = 1000 m

Therefore 5 km = 5 x 1000 m

5km = 5000 m

Now, we just subtract to find how much more Suzanne have to run

5000 m - 1250 m = 3750 m

6 0

3 years ago