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ZanzabumX [31]
3 years ago
11

Which reflection rule, if any, can be used to prove that rectangle A(-8, -3), B(-2, -3), C(-2, -6), D(-8, -6) and rectangle A'(8

, -3), B'(2, -3), C'(2, -6), D'(8, -6) are congruent?
A) (x, y) → (-x, y)
B) (x, y) → (x, -y)
C) (x, y) → (-x, -y)
D) The rectangles are not congruent.
Mathematics
1 answer:
JulijaS [17]3 years ago
7 0
A, Y doesn’t change and X becomes negative
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The line tangent to the graph of g(x) = x^{3}-4x+1 at the point (2, 1) is given by the formula
Usimov [2.4K]

well, about A and D, I just plugged the values on the slope formula of

\bf \begin{array}{llll} g(x)=x^3-4x+1\\ L(x) = 8(x-2)+1 \end{array} \qquad \begin{cases} x_1=1.9\\ x_2=2.1 \end{cases}\implies \cfrac{f(b)-f(a)}{b-a}

for A the values are 8.01 and 8.0, so indeed those "slopes" are close. \textit{\huge \checkmark}

for D the values are -2.25 and 8.0, so no dice on that one.

for B, let's check the y-intercept for g(x), by setting x = 0, we end up g(0) = 0³-4(0)+1, which gives us g(0) = 1.

checking L(x) y-intercept, well, L(x) is in slope-intercept form, thus the +1 sticking out on the far right is the y-intercept, so, dice. \textit{\huge \checkmark}

for C, well, the slope if L(x) is 8, since it's in slope-intercept form, the derivative of g(x) is g'(x) = 3x² - 4, and thus g'(0) = -4, so no dice.

for E, do they intercept at (2,1)?  well, come on now, L(x) is a tangent line to g(x), so that's a must for a tangent. \textit{\huge \checkmark}

for F, we know the slope of the line L(x) is 8, is g'(2) = 8?  let's check

recall that g'(x) = 3x² - 4, so g'(2) = 3(2)² - 4, meaning g'(2) = 8, so, dice. \textit{\huge \checkmark}

6 0
3 years ago
Larry sold twice as many magazines as Jan. Henry sold 8 more magazines than Jan did. Larry and Henry sold the same amount of mag
Pavlova-9 [17]

Answer:

16 magazines jan sold

6 0
3 years ago
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I need help for a major grade quiz !!
arsen [322]

Answer: The answer would be D.

Step-by-step explanation: I put down the points then simply reflected it over the y-axis. I did this by using the the opposite of the x number and the same y number. Hope this helps!

5 0
3 years ago
What is the equation, in slope-intercept form, of the line parallel to -5x + y = 2 that passes through the point
larisa [96]

Answer:

y = 5x + 11

Step-by-step explanation:

- first rearrange -5x + y = 2 and you'll have y = 5x + 2

- the slopes of parallel lines are equal so the slope of the line is 5

so far we have y = 5x + b

- to get b, replace the values in the equation by the values of the given point

(1) = 5(-2) + b

- rearrange and calculate, b = 11

y = 5x + 11

8 0
3 years ago
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helpppp! The population of a town is 20,000 people in the year 2000. How many people with live in the town in 2016 if the popula
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Answer:

31877 people with live in the town in 2016 if the population increases at a rate of 6% every 2 years

Step-by-step explanation:

The formula used will be

A(t) = P(1+r)^t

A(t) = Future value

P = population

r = rate

t = time

P= 20,000

r =6% or 0.06

t = 16

Since population is increased every 2 years, so t = 16/2 = 8

Putting value:

A(16) = 20,000(1+0.06)^8

A(16)= 20,000(1.06)^8

A(16) = 31876.9 ≈ 31877

So, 31877 people with live in the town in 2016 if the population increases at a rate of 6% every 2 years

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