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WARRIOR [948]
3 years ago
9

If M is the midpoint of

Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
6 0

Answer:

A. 10

Step-by-step explanation:

Based on the midsegment theorem, thus:

2x + 7 = ½(7x - 16)

Multiply both sides by 2

2(2x + 7) = 7x - 16

4x + 14 = 7x - 16

Combine like terms

4x - 7x = -14 - 16

-3x = -30

Divide both sides by -3

x = 10

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3 years ago
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In the diagram below DE is the midsegment of AABC.<br> Find the length of DE and BC.
baherus [9]

Answer:

DE = 5

BC = 10

Step-by-step explanation:

ΔAED is a right triangle with legs of 4 and 6/2 = 3

Use the Pythagorean theorem to find DE

4^{2}  + 3^{2} = DE^{2}

16 + 6 = 25 = DE^{2}

DE = 5

The midsegment of a triangle is 1/2 the length of the corresponding side.

Therefore, BC = 2 DE = 2(5) = 10 = BC

4 0
3 years ago
Bill reads 1/5 of a book on Monday he reads 2/3 of the book on Tuesday if he finishes reading the book on Wednesday or fraction
ratelena [41]

Answer:

\frac{2}{15}

Step-by-step explanation:      

We have been given that Bill reads 1/5 of a book on Monday he reads 2/3 of the book on Tuesday.

Let x be the part of book that Bill read on Wednesday. We can find x by equating the sum of parts of book read on each day by 1.  

\frac{1}{5}+\frac{2}{3}+x=1

First of all we will find a common denominator.

\frac{1\times 3}{5\times 3}+\frac{2\times 5}{3\times 5}+x=1

\frac{3}{15}+\frac{10}{15}+x=1

\frac{3+10}{15}+x=1

\frac{13}{15}+x=1

x=1-\frac{13}{15}

x=\frac{15-13}{15}  

x=\frac{2}{15}

Therefore, Bill read \frac{2}{15} of the book on Wednesday.  

7 0
3 years ago
Read 2 more answers
Determine whether or not f is a conservative vector field. If it is, find a function f such that f = ∇f. (if the vector field is
Likurg_2 [28]

A function assigns the values. The function f = xy²-2x² satisfies a conservative vector field F = ∇f.

<h3>What is a Function?</h3>

A function assigns the value of each element of one set to the other specific element of another set.

Given F(x,y) = (y² - 4x) i + 2xy j, and it is needed to be known that,

f_x(x,y)=y^2-4x\\f_y(x,y) = 2xy

Let's look for a primitive of y²-4x with regard to x. Because we regard y (and y²) as constants, a primitive of y² is xy², just as a primitive of k is xk (because we treat y² as a constant). Because a primitive of x equals x²/2, a primitive of 4x is 2x². As a result, a primitive of y²-4x is xy²-2x². We can get any other primitive by adding constants, but because we considered y as a constant, we have that.

f(x,y) = xy²-2x²+c(y)

where c(y) only depends on y (thus, it is constant respect with x).

To learn more about c(y), we shall deduce the formula in terms of y.

2xy=f_y(x,y)

      =\dfrac{d}{dy}(xy^2-2x^2+c(y))\\\\=2xy-0+\dfrac{d}{dy}c(y)\\\\=2xy+\dfrac{d}{dy}c(y)

Thus, d/dy is constant. We can take f(x,y)=xy²-2x². This function f satisfies that  F = ∇f.

Learn more about Function:

brainly.com/question/5245372

#SPJ4

3 0
2 years ago
What is the simplified form of the rational expression below?<br> SX<br> c. 8( Yun?<br> D. 8(**)
frez [133]

Answer: The answer is (5(x-1))/3x

Step-by-step explanation:

5x² - 5/ 3x² + 3x

= 5(x+1)(x-1) all over 3x(x+1)

= 5x - 5 over 3x

Hope this info helps

5 0
3 years ago
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