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3 years ago

Figure EFGHK is to be transformed to Figure E'F'G'H'K' using the rule (x, y)→(x + 8, y + 5):

Mathematics

2 answers:

IceJOKER [234]3 years ago

8 0

The rule that has been given means that x coordinate of some point we increase by 8 and y coordinate of some point we increase by 5.

Coordinates of K point on original Figure are:
(-2,-3)

once we implement rule on this we get K':

K' ( -2+8,-3+5)
or
K' ( 6,2)

Answer is third option.

quester [9]3 years ago

3 0

The awnser is c I hope I helped u

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Rewrite (y x 6) x 5 using the associative property.

nasty-shy [4]

Answer:

y * ( 6*5)

Step-by-step explanation:

(y x 6) x 5

We can change the order of multiplication by changing where the parentheses are placed using the associative property

y * ( 6*5)

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3 years ago

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Lesechka [4]

Answer:

Step-by-step explanation:

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3 years ago

What is the nth term rule of the quadratic sequence below?<br> 8,14,22,32 ,44, 58, 74...

DanielleElmas [232]

Answer:

y=n^2+3n+4

Step-by-step explanation:

Sequence,S: 8,14,22,32 ,44, 58, 74...

First differences of S: 6,8,10,12,14,16,...

Second differences of S: 2,2,2,2,2,2,....

It is indeed a quadratic since the 1st differences that are the same are the second differences.

So the 1st term is 8. If the 0th term was listes it would be 4 since 8-4=4 and 6-4=2.

This means our quadratic it is in the form

y=an^2+bn+c where c=4.

So we have y=an^2+bn+4.

Now we can find a and b using two points from our sequence to form a system of equations to solve.

(1,8) gives us 8=a(1)^2+b(1)+4

Simplifying gives 8=a+b+4

Subtracting 4 on both sides gives: 4=a+b

(2,14) gives us 14=a(2)^2+b(2)+4

Simplifying gives 14=4a+2b+4

Subtracting 4 on both sides gives 10=4a+2b

So we have the following system to solve:

4=a+b

10=4a+2b

I'm going to solve using elimination/linear combination style.

Dividing second equation by 2 gives the system as:

4=a+b

5=2a+b

Subtract the 2nd equation from the first gives:

-1=-1a

This implies a=1 since -1=-1(1) is true.

If a+b=4 and a=1, then b=3. Because 3+1=4.

So the equation is y=1n^2+3n+4 or y=n^2+3n+4.

8 0

2 years ago

Write an equation in slope intercept form for the line that passes through (-1, -2) and (3, 4)

LenaWriter [7]

Answer:

The slope-intercept form of the line equation is:

$y=\:\frac{3}{2}x\:-\frac{1}{2}$

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where

m is the slope

b is the y-intercept

Given the points

(-1, -2)

(3, 4)

Determining the slope between (-1, -2) and (3, 4)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(-1,\:-2\right),\:\left(x_2,\:y_2\right)=\left(3,\:4\right)$

$m=\frac{4-\left(-2\right)}{3-\left(-1\right)}$

$m=\frac{3}{2}$

Thus, the slope of the line is:

m = 3/2

substituting m = 3/2 and the point (3, 4) in the slope-intercept form of the line equation

y = mx+b

$4=\frac{3}{2}\left(3\right)+b$

switch sides

$\frac{3}{2}\left(3\right)+b=4$

$\frac{9}{2}+b=4$

subtract 9/2 from both sides

$\frac{9}{2}+b-\frac{9}{2}=4-\frac{9}{2}$

$b=-\frac{1}{2}$

now substituting m = 3/2 and b = -1/2 in the slope-intercept form of the line equation

$y = mx+b$

$y=\:\frac{3}{2}x\:+\:\left(-\frac{1}{2}\right)$

$y=\:\frac{3}{2}x\:-\frac{1}{2}$

Therefore, the slope-intercept form of the line equation is:

$y=\:\frac{3}{2}x\:-\frac{1}{2}$

8 0

2 years ago

Which of the following equations is equivalent to log(y)= 3.994 ?

Kisachek [45]

Answer:

The correct answer is option D: $y = 10^{3.994}$

Step-by-step explanation:

Given:

log(y)= 3.994

Solution:

A logarithm base b of a positive number x satisfies the following definition:

$y =log_b(x) => b^y =x$

For $x > 0, b >0, b \neq 1$

Also if no base b is indicated, the base of the logarithm is assumed to be 10 .

Thus, in log(y)= 3.994 base b is not indicated. so its base is assumed to be 10

now

$log_{10}(y)= 3.994$

Then

$y = 10^{3.994}$

4 0

2 years ago