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3 years ago

6

Ming writes a number pattern on a slip of paper and hands it to his friend Jack. 24 21 23 20 22 19 21 18 Jack writes the next nu

mber in the pattern and hands the paper back to Ming. What number should Jack write?

1 answer:

tiny-mole [99]3 years ago

3 0

The rule is -3, then +2

24-3 = 21
21 + 2 = 23
23-3= 20
20+2= 22
22-3= 19
19+2 = 21
21-3= 18
18+2 = 20

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Find the area of the region under the graph of f on [a, b].<br> f(x) = x2 − 8x + 17; [−1, 2]

Harman [31]

Answer:

The area is 42 area units.

Step-by-step explanation:

The area of a function f(x) on an interval [a,b] is given by:

$A = \int\limits^a_b {f(x)} \, dx$

Applying to this question:

$A = \int\limits^-1_2 {x^2 - 8x + 17} \, dx$

Then

$F(x) = \frac{x^{3}}{3} - 4x^{2} + 17x$

$A = F(2) - F(-1)$

$F(2) = frac{2^{3}}{3} - 4*2^{2} + 17*2 = \frac{8}{3} + 18 = \frac{8 + 3*18}{3} = \frac{62}[3}$

$F(-1) = frac{(-1)^{3}}{3} - 4*(-1)^{2} + 17*(-1) = -\frac{1}{3} - 21 = \frac{-1 - 21*3}{3} = -\frac{64}[3}$

$A = F(2) - F(-1) = \frac{62}[3} - (-\frac{64}[3}) = \frac{62+64}{3} = 42$

The area is 42 area units.

5 0

3 years ago

Given a point A(-2,5), find the coordinates of a point B so that the line segment AB has each slope.

Kaylis [27]

Step-by-step explanation:

I understand this that we need to find a point B for each of a) to f).

remember, the slope is the (y coordinate difference / x coordinate difference) when going from one point on the line to the other.

a)

the slope 2/3 means that when going to B x has to increase by 3, and y has to increase by 2.

so, B = (-2 + 3, 5 + 2) = (1, 7)

b)

-2/3 means that either x or y have to decrease and the other to increase.

e.g. x increases by 3, y decreases by 2.

so, B = (-2 + 3, 5 - 2) = (1, 3)

c)

4 stands for 4/1.

so, x increases by 1, y increases by 4.

B = (-2 + 1, 5 + 4) = (-1, 9)

d)

similar to c) -3 stands for -3/1.

and similar to b) either x or y has to decrease and the other to increase.

e.g. x increases by 1, y decreases by 3.

B = (-2 + 1, 5 - 3) = (-1, 2)

e)

that means the y difference is 0. B has the same y coordinate.

e.g. B = (3, 5)

x can be any value.

the line is a horizontal line going through y = 5 or (0, 5) on the y-axis.

f)

that means the x difference is 0. B has the same x coordinate.

e.g. B = (-2, 9)

y can be any value.

the line is a vertical line going through x = -2 or (-2, 0) on the x-axis.

8 0

1 year ago

Simplify the expression <br> (3-i)-(2+6i)

vredina [299]

Answer:5-5i

Step-by-step explanation:(3-i)-(2+6i) (3+2)-(6i-i) =5-5i

8 0

3 years ago

Which expression completes the factored form of this quadratic expression? x2 + 4x – 5

Advocard [28]

Find factors of -5 that, when added together, will give 4

x² + 4x - 5
x 5
x -1

(x + 5)(x -1)

Using the FOIL method (First, Outside, Inside, Last), we can get the question again.

x(x) = x²
x(-1) = -x
5(x) = 5x
5(-1) = -5

x² - x + 5x - 5
x² + 4x - 5

(x + 5) (x - 1) is your answers

however, i believe it is only asking for one. Therefore, because (x - 1) is a choice, (x - 1) should be your answer

hope this helps

5 0

3 years ago

Which graph correctly represents (5/2)x - y < 3?

Setler79 [48]

You can rewrite the inequality as

$y > \cfrac{5}{2}\ x - 3$

Note that

$y = f(x) = \cfrac{5}{2}\ x - 3$

is the equation of the line drawn in the pictures. This means that, for every point on the line, the y coordinate is exactly image of the x coordinate, i.e. $f(x)$

The inequality is satisfied by all points whose y coordinate exceeds the image of the x coordinate. Since the y axis is positively oriented upwards, a greater value for the y coordinate means that the point has to be higher than the line.

Also, since the equality inlves a $>$ and not a $\geq$ sign, the line itself is excluded.

So, the correct graph is the second one.

3 0

3 years ago

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