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3 years ago

Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.

Mathematics

1 answer:

max2010maxim [7]3 years ago

3 0

Answer:

<1 ,1>..., square root of two

Step-by-step explanation:

Component of vector PQ...,

; Q - P...where you subtract the x coordinate of Q by the x coordinate of P and the same for the y coordinate

; <(6-5),(9-8)>

; < 1,1 >

And the magnitude of PQ...,

;square root of( 1^2 + 1^2 )

;square root of 2

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The smaller triangle is a pre-image of the bigger triangle the center dilation is (1,-1) What is the scale factor used to create

kozerog [31]

Answer:

B. -4

Step-by-step explanation:

When dilation is not about the origin then in order to find the scalar factor, we need to find the ratio of the corresponding lengths.

2 Vertices of smaller triangle (Pre-image):

$(1,-1),(1,1)$

Length of side:

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$\sqrt{((1-1)^2+1-(-1))^2}=\sqrt{0+(1+1)^2} = \sqrt{4} =\pm2$

Since distance is always positive so its 2 units.

2 Vertices of bigger triangle(Image):

$(1,-1),(1,-9)$

Length of side:

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$\sqrt{((1-1)^2+(-9-(-1))^2}=\sqrt{0+(-9+1)^2} = \sqrt{(-8)^2}= \sqrt{64} =\pm8$

Since distance is always positive so its 8 units.

For the given figure we see that the dilated image is rotated 180° from the original position. Thus, for such dilation the scalar factor is taken negative.

Thus the scalar factor can be calculated as:

Scalar factor = $-\frac{length\ of \ image}{length\ of\ pre-image} =-\frac{8}{2} = -4$

Scalar factor =-4

5 0

3 years ago

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raketka [301]

Answer:

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Step-by-step explanation:

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3 years ago

Chapter 5, Review Exercise 11 (5 points) One term, about 700 Statistics 2 students at the University of California, Berkeley, we

g100num [7]

Answer:

The histograms are missing, but ill try to answer it nonetheless.

Here we have that the standard deviation is bigger than the mean, this means that we will not see one of the ends (the smaller one) of our bell.

And we have a normal distribution, so we have a gaussian bell.

We will have that the peak of our bell is at the value x = 1.1

The histogram will start with a kinda high value at x = 0, it will get to the maximum at x = 1.1 and it will decrease as a normal bell, and knowing that the distance between the mean value and the point where the bell almost is almost zero, is equal to 3 standard deviations, we can expect to see this at x = 1.1 + 3*1.5 = 1.1 + 4.5 = 5.6

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3 years ago

Can someone please help me on this question?

yan [13]

Answer: q³⁰

Explanation:

First just solve the first part using the exponent rules

p²q⁵ becomes 1/p-⁸q-²⁰ then we flip the fraction so the exponents become positive. Now we have p⁸q²⁰.

Before multiplying the other equation, we must simplify. p-⁴q⁵ becomes 1/p⁴q-⁵ and since it's the exponents being raised to a power we simply multiply the inner exponents times the outer exponent which yields 1/p⁸q-¹⁰. We must make q-¹⁰ positive so we will then bring it to the numerator of the fraction which gives us: q¹⁰/p⁸.

Multiply q¹⁰/p⁸ * p⁸q²⁰/1 = p⁸q³⁰/p⁸ divide the p exponents by each other which yields 0 since when u divide exponents you just subtract them so 8 - 8 = 0. Your answer is now q³⁰/1 or just q³⁰

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3 years ago

Can someone help me with this problem?

Tanya [424]

Answer:

9(3+5)

Step-by-step explanation:

GCF is 9, because thats the highest <u>common</u> number that both numbers can be divided by.

27/9 = 3

45/9 = 5

so,

9(3+5)

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2 years ago