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DaniilM [7]
3 years ago
13

Triangle VXW is similar to triangle ZXY. Triangle V X W. Side V W is 12 miles and side V X is 14 miles. Triangle Z X Y. Side Y Z

is 72 miles and side X Z is x miles. Kara finds the value of x. Her work is shown below. Step 1 StartFraction 14 Over 72 EndFraction = StartFraction 12 Over x EndFraction Step 2 14 x = (72) (12) Step 3 14 x = 864 Step 4 x = 61.7 What is Kara’s first error? Kara should have written the proportion in step 1 as StartFraction 12 Over 72 EndFraction = StartFraction 14 Over x EndFraction. Kara should have written the cross-product in step 2 as 12 x = (72) (14). Kara did not correctly divide 864 by 14 going from step 3 to step 4. Kara did not find the correct product of 72 and 12 going from step 2 to step 3.v
Mathematics
2 answers:
amid [387]3 years ago
5 0

Answer: Kara should have written the proportion in step 1 as;

Start Fraction 12 Over 72 End Fraction = Start Fraction 14 Over x End Fraction (that is 12/72 = 14/x)

Step-by-step explanation: The two similar triangles are given with the following dimensions;

Triangle VXW with side VW = 12 and side VX = 14. Also Triangle ZXY with side YZ = 72 and side XZ = x.

For two triangles to be similar, then there must be a similarity ration that is consistent with all sides in both triangles. This means if in the first triangle a side measures  1 unit and the similar side in the other triangle measures 5 units, then the ratio of similarity of corresponding sides shall be ratio 1 : 5. So for every corresponding side in the second triangle the measurement shall be times five of the side that corresponds in the first triangle.

Therefore, in triangle VXW and triangle ZXY, the corresponding sides are as follows;

VX = ZX

VW = ZY

XW = XY

What Kara did was as follows;

VX/ZY = VW/ZX

Which translates to 14/72 = 12/x

This was a wrong calculation because the side that corresponds to VX is ZX and not ZY.

The correct step should therefore have been;

VW/ZY = VX/ZX

12/72 = 14/x (Step 1)

12x = (72) (14) {Step 2}

x = 1008/12 (Step 3)

x = 84 (Step 4)

tia_tia [17]3 years ago
5 0

Answer:

its a

Step-by-step explanation:

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ikadub [295]

Answer:

d. 20+10+5+2.5+...

Step-by-step explanation:

No geometric series with a common ratio of magnitude greater than 1 will have a finite sum. Nor will any arithmetic series.

Those descriptions exclude answer choices a, b, c. Choice d is a geometric series with a common ratio of 1/2, so will have a finite sum. (It is 40.)

7 0
3 years ago
Simplify the expression state any excluded values<br> 2a^2-4a+2<br> ---------------<br> 3a^2-3
chubhunter [2.5K]

Answer:

The simplified form is \dfrac{2(x-1)}{3(x+1)}.

x =1 is the excluded value for the given expression.

Step-by-step explanation:

Given:

The expression given is:

\dfrac{2a^2-4a+2}{3a^2-3}

Let us simplify the numerator and denominator separately.

The numerator is given as 2a^2-4a+2

2 is a common factor in all the three terms. So, we factor it out. This gives,

=2(a^2-2a+1)

Now, a^2-2a+1=(a-1)(a-1)

Therefore, the numerator becomes 2(a-1)(a-1)

The denominator is given as: 3a^2-3

Factoring out 3, we get

3(a^2-1)

Now, a^2-1 is of the form a^2-b^2=(a-b)(a+b)

So, a^2-1=(a-1)(a+1)

Therefore, the denominator becomes 3(a-1)(a+1)

Now, the given expression is simplified to:

\frac{2a^2-4a+2}{3a^2-3}=\frac{2(x-1)(x-1)}{3(x-1)(x+1)}

There is (x-1) in the numerator and denominator. We can cancel them only if x\ne1 as for x=1, the given expression is undefined.

Now, cancelling the like terms considering x\ne1, we get:

\dfrac{2a^2-4a+2}{3a^2-3}=\dfrac{2(x-1)}{3(x+1)}

Therefore, the simplified form is \dfrac{2(x-1)}{3(x+1)}

The simplification is true only if  x\ne1. So, x =1 is the excluded value for the given expression.

8 0
3 years ago
Which expression should you simplify to find the 90% confidence interval,
Alex787 [66]

Answer:

0.45 - 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.287

0.45 + 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.613

And we can conclude at 95% of confidence that the true proportion of interest for this case is between 0.287 and 0.613

Step-by-step explanation:

The estimated proportion of interest is \hat p=0.45

We need to find a critical value for the confidence interval using the normla standard distributon. For this case we have 95% of confidence, then the significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value is:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The confidence interval for the true population proportion is interest is given by this formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

Replacing the values provided we got:

0.45 - 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.287

0.45 + 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.613

And we can conclude at 95% of confidence that the true proportion of interest for this case is between 0.287 and 0.613

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Answer:

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Step-by-step explanation:

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