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Pachacha [2.7K]
3 years ago
12

1.Point E is the midpoint. Find EF. *

Mathematics
1 answer:
Soloha48 [4]3 years ago
5 0

Step-by-step explanation:

Since, Point E is the midpoint of DF

Therefore,

DE = EF

10x = 4x + 12

10x - 4x = 12

6x = 12

x = 12/6

x = 2

EF = 4x + 12 = 4*2+12 = 8 * 12 = 20

EF = 20

AB = BC

6x + 2 = 9x - 10

10 + 2 = 9x - 6x

12 = 3x

12/3 = x

x = 4

BC = 9x - 10 = 9*4 - 10 = 36 - 10 = 26

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What is the length of Line segment B C, rounded to the nearest tenth? 13. 0 units 28. 8 units 31. 2 units 33. 8 units.
Len [333]

The length of the line segment BC is 31.2 units.

<h2>Given that</h2>

Triangle ABC is shown.

Angle ABC is a right angle.

An altitude is drawn from point B to point D on side AC to form a right angle.

The length of AD is 5 and the length of BD is 12.

<h3>We have to determine</h3>

What is the length of Line segment BC?

<h3>According to the question</h3>

The altitude of the triangle is given by;

\rm Altitude = \sqrt{xy}

Where x is DC and y is 5 units.

Then,

The length DC is.

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Squaring on both sides

\rm DC = \dfrac{144}{5}\\&#10;\\&#10;DC = 28.8

Considering right triangle BDC, use the Pythagorean theorem to find BC:

\rm BC^2 = DC^2+BD^2\\\\  BC^2 = (28.8)^2+(12)^2\\&#10;&#10;\\&#10;BC = \sqrt{829.44+144}\\&#10;\\&#10;BC = \sqrt{973.44}\\&#10;\\&#10;\rm BC = 31.2 \ units

Hence, the length of the line segment BC is 31.2 units.

To know more about Pythagoras Theorem click the link given below.

brainly.com/question/26252222

6 0
2 years ago
the perimeter of a rectangle can be found by using the formula P=21+2w. What is the width of the rectangle if the perimeter is 1
mixas84 [53]
\begin{gathered} P=2l+2w \\ \text{If l=50 and P=100, then:} \\ 100=2(50)+2w\Rightarrow0=2w\text{ !!!!} \end{gathered}

Since this can't happen, let's suppose that P=150, then:

\begin{gathered} P=2l+2w \\ \Rightarrow150=2(50)+2w \\ \Rightarrow150=100+2w \end{gathered}

Now we have to move the 100 to the other side of the equation with a negative sign to get this:

\begin{gathered} 150=100+2w \\ \Rightarrow150-100=2w \\ \Rightarrow50=2w \end{gathered}

Finally, to get w, we move the 2 that's multiplying to the other side dividing the 50:

\begin{gathered} 50=2w \\ \Rightarrow\frac{50}{2}=w \\ \Rightarrow w=25 \end{gathered}

Therefore, the width of the rectangle would be 25 ft if the perimeter is 150ft, and we can see how the rectangle would look:

6 0
2 years ago
The boundary line on the graph represents the equation 5x + 2y = 6. Write an
BartSMP [9]

Answer:

The inequality representing the shaded area is y < 3 - 2.5·x

Step-by-step explanation:

The given equation of the graph is 5·x + 2·y = 6

Therefore, we have;

2·y = 6 - 5·x

y = 6/2 - 5/2·x

y = 3 - 2.5·x

Given that the graph is represented by a shaded region on the left and lower side of a broken line, the inequality relationship for the graph is that of a lesser than area inequality with a symbol of < and the inequality for the graph can be represented as follows,

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4 0
3 years ago
sophie will draw one card at random and then roll a number cube. There are four cards. Each card has a picture of a shape. All p
Hunter-Best [27]

Answer:

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The total number of outcomes will be equal to the product between the number of outcomes in each individual event, this is:

C = 4*6 = 24.

Now, suppose that you have a restriction like:

"What is the probability that you have an odd number in the number cube?"

Ok, let's do the same:

Drawing a card ---- 4 outcomes (the restriction does not affect this event)

Rolling a number cube ---- 3 outcomes (because there are only 3 odd numbers)

The number of combinations is:

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Then the probability will be the quotient between the number of outcomes that meet the condition and the total number of outcomes:

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6 0
3 years ago
Daniela painted a photo that was 4/5 afoot by 1 7/8 of afoot. What was the area?​
Ahat [919]

Answer:

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Step-by-step explanation:

The dimensions of the photo is 4/5 by 1 7/8 of a foot.

But,

1 7/8 = \frac{15}{8} feet

So that,

length of the photo = \frac{15}{8} feet

width of the photo = \frac{4}{5} feet

The area of the photo = length x width

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                                     = \frac{3}{2}

Area of the painted photo is \frac{3}{2} square feet.

8 0
3 years ago
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