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pashok25 [27]
4 years ago
8

A conjecture and the paragraph proof used to prove the conjecture are shown.

Mathematics
1 answer:
aleksklad [387]4 years ago
6 0

Observe the figure given.

Let us complete the given paragraph:

It is given that E is the midpoint of DF. So, DE \cong EF by the definition of midpoint.

As, midpoint divides the line segment into two equal halves.

Therefore, DE  =EF by the segment congruence postulate. DE+EF = DF by the segment addition postulate and so DE+DE = DF by substitution.

Segment Addition Postulate states that given 2 points P and Q, a third point S lies on the line segment PQ if and only if the distances between the points satisfy the equation PS + SQ = PQ.

Simplifying gives 2DE = DF.



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Factor the polynomial.
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3x4+6x3+9x2
Factored: (3x2)(x2+2x+3)

Answer:
C) 3x2(x2+2x+3)

Hope this helps! :)

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3 years ago
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9. Write the missing addend. 46 + = 52​
Alex73 [517]

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6

Step-by-step explanation:

To find the missing number, subtract: 52 - 46 = 6

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Mr. Hamilton has 60,000 to invest in a tax-free fund and in a money market fund. The tax-free fund pays 7.5%, and the money mark
Valentin [98]

Answer:

He should invest $31,000 in tax-free to get a return of $4,790

Step-by-step explanation:

Let the amount he will invest in tax-free be $x while the amount in money market be $y

Adding both we have the total;

x + y = 60,000 ••••••••(i)

Then let’s work with the percentages;

7.5% of x + 8.5% of y = 4,790

7.5/100 * x + 8.5/100 * y = 4,790

7.5x/100 + 8.5y/100 = 4790

multiply through by 100

7.5x + 8.5y = 479000 ••••••(ii)

From i, y = 60,000 - x

Put this into ii

7.5x + 8.5(60,000-x) = 479000

7.5x + 510,000 -8.5x = 479000

8.5x - 7.5x = 510,000 - 479,000

x = $31,000

6 0
3 years ago
A fish tank holds 10450ml of water. The water is leaking at a rate of 270ml per minute. What is the function to model this situa
bogdanovich [222]

Answer:

The function is given f(t) = 10450 - 270t

3 0
4 years ago
Find two different planes whose intersection is theline:x = 6 + 3ty = -8 - 3tz = -1 - tWrite equations for each plane in the for
alina1380 [7]

Answer:

x+y=-2 and 3z-y=5 are two such planes.

Step-by-step explanation:

To find the two planes whose intersection is the line

x=6+3t\\ y=-8-3t\\ z=-1-t

You can say that <em>t</em> is equal to this expression

t=\frac{x-6}{3} =\frac{y+8}{-3}=-z-1

Next,

\frac{x-6}{3} =\frac{y+8}{-3}\\ \frac{y+8}{-3}=-z-1

Then,

x+y=-2 and 3z-y=5 are two such planes.

You can see in the image attached that the intersection of this planes is the line

x=6+3t\\ y=-8-3t\\ z=-1-t

7 0
4 years ago
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