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vekshin1
2 years ago
11

Triangle XYZ has vertices X(0,3), Y(2,0) and Z(4,2). if yo reflect triangle XYZ across the line x=4, what will be the coordinate

s of the vertices of the image Triangle X1,Y1,Z1

Mathematics
1 answer:
Paha777 [63]2 years ago
3 0

As X' is the reflected point of X(0,3) , so the x co ordinate of X' = 0+8 =8 and here y co ordinate remains same.

So, X'= (8,3)

Like that way, Y' is the reflected point of Y(2,0) and Z' is the reflected point of Z(4,2)

As the point Z is lying on the line x=4 and the reflection is also across that line, so both Z and Z' represent same point.

Y'= (2+4, 0) = (6, 0)

Z' = (4, 2)

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Meeko Insurance offers an annuity with a minimum interest rate of 3% for the
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single payment variable annuity

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2 years ago
Babe Ruth's 1931 salary was $80,000, Government statistics show a consumer price index of 15.2 for 1931 and 237 for 2015. Ruth's
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Answer:

Ruth's 1931 salary was equivalent to a 2015 salary of $1,247,368.

Step-by-step explanation:

This question can be solved by a rule of three.

Government statistics show a consumer price index of 15.2 for 1931 and 237 for 2015.

This means that $15.2 in 1931 is equivalent to $237 in 2015. So

$15.2 in 1931 - $237 in 2015

$80,000 in 1931 - $x in 2015

15.2x = 237*80,000

x = \frac{237*80,000}{15.2}

x = 1,247,368

Ruth's 1931 salary was equivalent to a 2015 salary of $1,247,368.

8 0
2 years ago
A psychologist is collecting data on the time it takes to learn a certain task. For 50 randomly selected adult subjects, the sam
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Answer: (15.263,\ 17.537)

Step-by-step explanation:

According to the given information, we have

Sample size : n= 50

\overline{x}=16.40

s=4.00

Since population standard deviation is unknown, so we use t-test.

Critical value for  95 percent confidence interval  :

t_{n-1,\alpha/2}=t_{49, 0.025}= 2.009575\approx2.010

Confidence interval : \overline{x}\pm t_{n-1, \alpha/2}\dfrac{s}{\sqrt{n}}

16.40\pm (2.010)\dfrac{4}{\sqrt{50}}\\\\=16.40\pm1.13702770415\\\\=16.40\pm1.1370\\\\=(16.40-1.1370,\ 16.40+1.1370)\\\\=(15.263,\ 17.537)

Required 95% confidence interval :  (15.263,\ 17.537)

8 0
2 years ago
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section
LUCKY_DIMON [66]

Answer:

y2 = C1xe^(4x)

Step-by-step explanation:

Given that y1 = e^(4x) is a solution to the differential equation

y'' - 8y' + 16y = 0

We want to find the second solution y2 of the equation using the method of reduction of order.

Let

y2 = uy1

Because y2 is a solution to the differential equation, it satisfies

y2'' - 8y2' + 16y2 = 0

y2 = ue^(4x)

y2' = u'e^(4x) + 4ue^(4x)

y2'' = u''e^(4x) + 4u'e^(4x) + 4u'e^(4x) + 16ue^(4x)

= u''e^(4x) + 8u'e^(4x) + 16ue^(4x)

Using these,

y2'' - 8y2' + 16y2 =

[u''e^(4x) + 8u'e^(4x) + 16ue^(4x)] - 8[u'e^(4x) + 4ue^(4x)] + 16ue^(4x) = 0

u''e^(4x) = 0

Let w = u', then w' = u''

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w' = 0

Integrating this, we have

w = C1

But w = u'

u' = C1

Integrating again, we have

u = C1x

But y2 = ue^(4x)

y2 = C1xe^(4x)

And this is the second solution

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2 years ago
What is 576 hundredths in decimal form
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5.76 because the hundredths place is two spaces to the right of the decimal point.
6 0
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