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4 years ago

In the diagram below QT =7 which additional facts would guarantee that QRST is a parallelogram check all that apply

Mathematics

2 answers:

lions [1.4K]4 years ago

4 0

Answer: A. QT is parallel to RS and C. QR =5, ST=5

nlexa [21]4 years ago

3 0

Answer:

option A and C

QT is parallel to RS

QR = 5 , ST = 5

Step-by-step explanation:

The definition of a parallelogram is as below

A parallelogram is a quadrilateral with 2 pairs of opposite, equal and parallel sides.

To prove a quadrilateral is a parallelogram, one of these five ways is to prove that one pair of opposite sides is both congruent and parallel.

And ways is to prove that both pairs of opposite sides are congruent.

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1. Consider an athlete running a 40-m dash. The position of the athlete is given by , where d is the position in meters and t is

sasho [114]

There is some information missing in the question, since we need to know what the position function is. The whole problem should look like this:

Consider an athlete running a 40-m dash. The position of the athlete is given by $d(t)=\frac{t^{2}}{6}+4t$ where d is the position in meters and t is the time elapsed, measured in seconds.

Compute the average velocity of the runner over the intervals:

(a) [1.95, 2.05]

(b) [1.995, 2.005]

(d) [2, 2.00001]

Answer

(a) 6.00041667m/s

(b) 6.00000417 m/s

(d) 6.00001 m/s

The instantaneous velocity of the athlete at t=2s is 6m/s

Step by step Explanation:

In order to find the average velocity on the given intervals, we will need to use the averate velocity formula:

$V_{average}=\frac{d(t_{2})-d(t_{1})}{t_{2}-t_{1}}$

so let's take the first interval:

(a) [1.95, 2.05]

$V_{average}=\frac{d(2.05)-d(1.95)}{2.05-1.95}$

we get that:

$d(1.95)=\frac{(1.95)^{3}}{6}+4(1.95)=9.0358125$

$d(2.05)=\frac{(2.05)^{3}}{6}+4(2.05)=9.635854167$

so:

$V_{average}=\frac{9.6358854167-9.0358125}{2.05-1.95}=6.00041667m/s$

(b) [1.995, 2.005]

$V_{average}=\frac{d(2.005)-d(1.995)}{2.005-1.995}$

we get that:

$d(1.995)=\frac{(1.995)^{3}}{6}+4(1.995)=9.30335831$

$d(2.005)=\frac{(2.005)^{3}}{6}+4(2.005)=9.363335835$

so:

$V_{average}=\frac{9.363335835-9.30335831}{2.005-1.995}=6.00000417m/s$

$V_{average}=\frac{d(2.0005)-d(1.9995)}{2.0005-1.9995}$

we get that:

$d(1.9995)=\frac{(1.9995)^{3}}{6}+4(1.9995)=9.33033358$

$d(2.0005)=\frac{(2.0005)^{3}}{6}+4(2.0005)=9.33633358$

so:

$V_{average}=\frac{9.33633358-9.33033358}{2.0005-1.9995}=6.00000004m/s$

(d) [2, 2.00001]

$V_{average}=\frac{d(2.00001)-d(2)}{2.00001-2}$

we get that:

$d(2)=\frac{(2)^{3}}{6}+4(2)=9.33333333$

$d(2.00001)=\frac{(2.00001)^{3}}{6}+4(2.00001)=9.33339333$

so:

$V_{average}=\frac{9.33339333-9.33333333}{2.00001-2}=6.00001m/s$

Since the closer the interval is to 2 the more it approaches to 6m/s, then the instantaneous velocity of the athlete at t=2s is 6m/s

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3 years ago

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ExtremeBDS [4]

Answer:

Step-by-step explanation:

Y-intercept is where the line touches the y-axis, in this case it was the origin (0,0) so the y-intercept is 0

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3 years ago

Is (-2, -6) a solution to this system of equations? 3x + 18y = -14 15x − 7y = 12 yes no

soldi70 [24.7K]

Answer:

Step-by-step explanation:

Plug in (-2, -6) to see if it's the solution or not

3(-2) + 18(-6) ? -14

-6 + ( -108) ? -14

-114 ≠ -14

Answer is NO

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4 years ago

Adding polynomial expressions

slamgirl [31]

Answer:Start with: 1.2x2 + 6x + 5 + 3x2 − 2x − 1.

2.Place like terms together:2x2+3x2 + 6x−2x + 5−1.

3.Which is:(2+3)x2 + (6−2)x + (5−1)

4.Add the like terms:5x2 + 4x + 4.

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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