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Goshia [24]
3 years ago
5

Point P is at (3,-3) it undergoes the transformation (x - 2, y + 3). Where is P' at?​

Mathematics
1 answer:
Vanyuwa [196]3 years ago
5 0

Answer:

The coordinates of P' are P'(x,y) = (1, 0).

Step-by-step explanation:

The coordinates of the point P' is determined by the following expression:

P'(x, y) = P(x,y) + T(x,y) (1)

Where:

P(x,y) - Original point.

P'(x,y) - Translated point.

T(x,y) - Translation vector.

If we know that P(x,y) = (3, -3) and T(x,y) = (-2, 3), then the coordinates of point P':

P'(x,y) = (3, -3) + (-2, 3)

P'(x,y) = (1, 0)

The coordinates of P' are P'(x,y) = (1, 0).

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Find the area of the region that lies under the parabola y=5x - x^2, where 1≤x≤4. I would definitely like to see some work :)
Elena L [17]

Answer:

  16.5 square units

Step-by-step explanation:

You are expected to integrate the function between x=1 and x=4:

  \displaystyle\text{area}=\int_1^4{(5x-x^2)}\,dx=\left.\left(\dfrac{5}{2}x^2-\dfrac{1}{3}x^3\right)\right|_{x=1}^{x=4}\\\\=\dfrac{5(4^2-1^2)}{2}-\dfrac{4^3-1^3}{3}=37.5-21=\boxed{16.5}

__

<em>Additional comment</em>

If you're aware that the area inside a (symmetrical) parabola is 2/3 of the area of the enclosing rectangle, you can compute the desired area as follows.

The parabolic curve is 4-1 = 3 units wide between x=1 and x=4. It extends upward 2.25 units from y=4 to y=6.25, so the enclosing rectangle is 3×2.25 = 6.75 square units. 2/3 of that area is (2/3)(6.75) = 4.5 square units.

This region sits on top of a rectangle 3 units wide and 4 units high, so the total area under the parabolic curve is ...

  area = 4.5 +3×4 = 16.5 . . . square units

4 0
2 years ago
Joni earned $0.625 per day for two days as interest on her $1,000.00 investment. What percent interest did she earn in total? Gi
Kitty [74]

Joni’s total interest earned is 0.125% of her investment.

<u>Solution:</u>

Given that

Interest earned by Joni per day = $0.625

Investment done by Joni = $1000

Duration of earning interest = 2 days  

Total interest earned = interest earned by Joni \times duration of interest earned.

= 0.625 \times 2 = $1.25

\text { Percentage of interest earned }=\frac{\text {total interest earned}}{\text {investment done}} \times 100

=\frac{125}{1000} \times 100=0.125 \%

So Joni’s total interest earned is 0.125% of her investment.

4 0
3 years ago
The function y = -x - 1 and y = ½x + k intersect at the point (-2,1). Find the value of k.
horrorfan [7]

Answer:

  k = 2

Step-by-step explanation:

Fill in the given point values and solve for k.

  y = (1/2)x + k

  1 = (1/2)(-2) +k . . . . . . for x = -2, y = 1

  1 = -1 +k . . . . simplify; next, add 1

  2 = k

5 0
4 years ago
Translate the word into a equation 15 is equal to 9 more than a number
WITCHER [35]

Answer:

Step-by-step explanation:

We'll go part by part.

"15 is equal to" so simple enough 15= now what is it equal to?

9 more than a number.  Well what does that mean?  it might help if we try out an actual number.  What is 9 more than 3?  12, so another way of writing that is +9.  It's not telling us the number we are adding 9 to so it's a variable.  So we'll say x + 9.

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3 0
4 years ago
What is 9y5−4y3−8y7−5y6+3y4 written in standard form?
Bingel [31]

Answer:

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Step-by-step explanation:

Please be sure to use " ^ " to indicate exponentiation.  Then,

your 9y5−4y3−8y7−5y6+3y4 becomes 9y^5 - 4y^3 - 8y^7 - 5y^6 + 3y^4.

We must now write that in descending order by powers of y:

-8y^7 - 5y^6 + 9y^5 + 3y^4 - 4y^3

4 0
3 years ago
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