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3 years ago

The figure shows a kite inside a rectangle. Which expression represents the area of the shaded region? 2x2 4x2 6x2 8x2

Mathematics

2 answers:

notka56 [123]3 years ago

5 0

The picture in the attached figure

we know that
area of the the shaded region=area of rectangle -area of a kite

area of rectangle=(3x+x)*(x+x)----> 4x*2x---> 8x²

area of a kite=(1/2)*[d1*d2]
where d1 and d2 are the diagonals
d1=4x
d2=2x
so
area of a kite=(1/2)*[4x*2x]----> 4x²

area of the the shaded region=8x²-4x²-----> 4x²

the answer is
4x²

zhuklara [117]3 years ago

3 0

Answer:

B.)4x²

Step-by-step explanation:

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traveled Downstream a distance of 33 Mi and then came right back. If the speed of the current was 12mph and the total trip took

spayn [35]

Traveled Downstream a distance of 33 Mi and then came right back. If the speed of the current was 12 mph and the total trip took 3 hours and 40 minutes.
Let S = boat speed in still water then (s + 12) = downstream speed (s -12) = upstream speed
Given Time = 3 hours 40 minutes = 220 minutes = (220/60) h = (11/3) h Time = Distance/Speed
33/(s +12) + 33/(s-12) = 11/3 3{33(s-12) + 33(s +12)} = 11(s+12) (s -12) 99(s -12 + s + 12) = 11( s^{2} + 12 s -12 s -144) 99(2 s) = 11(s^{2} -144) 198 s/11 = (s^{2} -144) 18 s = (s^{2} -144) (s^{2} - 18 s - 144) = 0 s^{2} - 24 s + 6 s -144 =0 s(s- 24) + 6(s -24) =0 (s -24) (s + 6) = 0 s -24 = 0, s + 6 =0 s = 24, s = -6 Answer) s = 24 mph is the average speed of the boat relative to the water.

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3 years ago

When Scott got his dog Arfus, it weighed

Leokris [45]

It gained 2 lb. because if you subtract 8-6 you would get 2. So Arfus gained 2 lb.

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3 years ago

5^(2x-1)+5^(x+1)=250 how do you solve? thank you

zepelin [54]

Answer:

x = 2

Step-by-step explanation:

Exponential Equations

Solve:

$5^{2x-1}+5^{x+1}=250$

Separate each exponential:

$5^{2x}5^{-1}+5^{x}5^{1}=250$

Operating:

$\displaystyle \frac{5^{2x}}{5}+5^{x}5=250$

Multiplying by 5:

$5^{2x}+25\cdot5^x=1250$

Rearranging:

$5^{2x}+25\cdot5^x-1250=0$

Recall that:

$5^{2x}=(5^{x})^2$

$(5^{x})^2+25\cdot5^x-1250=0$

Calling

$y=5^{x}:$

$y^2+25y-1250=0$

Factoring:

$(y-25)(y+50)=0$

There are two possible solutions:

y=25

y=-50

Since

$y=5^{x}$

y cannot be negative, thus:

$5^{x}=25=5^2$

The solution is:

x = 2

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3 years ago

What is the complete square of y=x^2-16x+17

aliina [53]

Y = x^2 - 16x + 17
-16/2 = (-8)
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y = x^2 - 16x + 64 + 17 - 64
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7 0

3 years ago

A data set lists weights (lb) of plastic discarded by households. The highest weight is 5.31 lb, the mean of all of the weight

a_sh-v [17]

Answer:

a) The difference is of 3.222 lbs.

b) 1.64 standard deviations.

c) Z = 1.64

d) Not significant, as the z-score of 1.64 is between -2 and 2.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The mean of all of the weights is x=2.088 lb, and the standard deviation of the weights is s=1.968 lb.

This means that $\mu = 2.088, \sigma = 1.968$

a. What is the difference between the weight of 5.31 lb and the mean of the weights?

This is $X - \mu = 5.31 - 2.088 = 3.222$

The difference is of 3.222 lbs.

b. How many standard deviations is that [the difference found in part (a)]?

This is the z-score. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{5.31 - 2.088}{1.968}$

$Z = 1.64$

1.64 standard deviations.

c. Convert the weight of 5.31 lb to a z score.

Z = 1.64, as found above.

d. If we consider weights that convert to z scores between −2 and 2 to be neither significantly low nor significantly high, is the weight of 5.31 lb significant?

Not significant, as the z-score of 1.64 is between -2 and 2.

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3 years ago