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2 years ago

Which is a possible turning point for the continuous function f(x)?

Mathematics

1 answer:

babymother [125]2 years ago

5 0

Answer:

We are given coordinates of a continuous function f(x)

(–2, 0)

(0, –2)

(2, –1)

(4, 0).

We need to find the possible turning point for the continuous function.

Note: Turning point is a point on the graph where slope of the curve changes from negative to positive or positive to negative.

A turning point is always lowest or highest point of the curve (where bump of the graph seen).

For the given coordinates we can see that (–2, 0) and (4, 0) coordinates are in a same line, that is on the x-axis.

But the coordinate (0, –2) is the lowest point on the graph.

Therefore, (0, –2) is the turning point for the continuous function given.

hoped this was helpful!

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Point A has coordinates (3,4). After a translation 4 units left, a reflection across the x-axis, and a translation 2 units down,

jeka94

Answer:

The coordinates of the image of point A are (-1, -6)

Step-by-step explanation:

Let us revise the rule of translation to the left, down, and reflection across the x-axis

If the point (x, y) translated horizontally to the left by h units then its image is (x - h, y) ⇒ T (x, y) → (x - h, y)

If the point (x, y) translated vertically down by k units then its image is (x, y - k) ⇒ T (x, y) → (x, y - k)

If the point (x, y) reflected across the x-axis, then its image is (x, -y), the rule of reflection is rx-axis (x, y) → (x, -y)

∵ The coordinates of point A are (3, 4)

∵ It is translated 4 units left

∴ h = 4

→ By using the 1st rule above

∴ Its image is (3 - 4, 4)

∴ Its image is (-1, 4)

∵ Its is reflected across the x-axis

→ By using the 3rd rule above change the sign of its y-coordinate

∴ The new image is (-1, -4)

∵ It is translated 2 units down

∴ k = 2

→ By using the 2nd rule above

∴ The final image is (-1, -4 - 2)

∴ The final image is (-1, -6)

∴ The coordinates of the image of point A are (-1, -6).

6 0

3 years ago

How do i solve 9j-8=8+9j

SIZIF [17.4K]

9j-8=8+9j

+8 to each side:
9j=16+9j

-9j from each side:
0=16
Which is false.

Hope this helps :)

7 0

3 years ago

a punch recipe says to mix 4 cups pineapple juice,8 cups orange juice,and 12 cups seltzer in order to make 18 servings of punch.

patriot [66]

2/3 cups of pineapple juice, 4/3 cups of orange juice and 2 cups of seltzer for 3 servings.

8 0

2 years ago

A single die is rolled twice. Find the probability of rolling an even number the first time and a number greater than 3 the seco

IceJOKER [234]

Events

• A: an even number is rolled in the first time

• B: a number greater than 3 is rolled the second time

The probability of rolling an even number is:

$\begin{gathered} P(A)=\frac{\text{ number of favorable outcomes}}{\text{ total possible outcomes}} \\ P(A)=\frac{3}{6} \\ P(A)=\frac{1}{2} \end{gathered}$

The probability of rolling a number greater than 3 is:

$\begin{gathered} P(B)=\frac{\text{ number of favorable outcomes}}{\text{ total possible outcomes}} \\ P(B)=\frac{3}{6} \\ P(B)=\frac{1}{2} \end{gathered}$

Events A and B are independent, then the probability of one happening after the other is:

$\begin{gathered} \text{ P(A and B) = }P(A)\cdot P(B) \\ \text{ Substituting with the values previously found:} \\ \text{ P(A and B) = }\frac{1}{2}\cdot\frac{1}{2} \\ \text{ P(A and B) = }\frac{1}{4} \end{gathered}$

8 0

1 year ago

Thank you very much anh you

Neko [114]

Hello from MrBillDoesMath!

Answer:

See discussion below

Discussion:

The sum of the interior angles of a polygon of n sides is (n-2)* 180. As the polygon in #4 has 7 sides , the sum of the interior angles is (7-2)*180 = 5 * 180 = 900.

We can also compute the sum of the interior angles by adding up each of the angles (expressed in terms of x) shown in #4. Starting at the top of the polygon and proceeding counterclockwise gives:

900 = (8x +34) + (10x+21)+(9x+30)+(7x+45)+(5x+44)+(12x+13)+(6x+29) =>

(8x + 10x+9x+7x+5x+12x+6x) + (34+21+30+45+44+13+29) =

57x + 216

This simplifies to

900 = 57x + 216 => subtract 216 from both sides

900-216 = 57x => 900-216= 684

684= 57x => divide both sides by 57

684/57 = x => as 684/57 = 12

x = 12

The diagram has makes repeated use of the same variable for vertices. That is, the diagram shows 4 P's, 1 Q, 2 R's, 0 S's, and 1 T making it impossible to determine the values of some angles. For example, consider m RST -- whatever that means.

#5 uses the same ideas but the vertices are properly labeled (I'll leave the grunt of determining the individual angles to you but here are the main points).

Sum of interior angles = (7 -2) * 180 = 5 * 180 = 900.

900 = (8x+62) + (7x+66)+(5x+83)+(6x+55)+(10x+42)+(8x+45)+(4x+67) =>

900 = (8x + 7x +5x+6x+10x+8x+4x) + (62+66+83+55+42+45+67)

900= 48x + 420 =>

900 -420 = 48x => subtract 420

480 = 48x => divide by 48

x = 480/48 = 10

Thank you,

MrB

6 0

3 years ago