MATHEMATICS HIGH SCHOOL

Which values are within the range of the piecewise-defined function?f(x) =
2 x + 2 x < - 3
X x = -3
- x - 2 X > -3
y = -6
y=-4
y=-3
y = 0
y = 1
y = 3

Answers

Answer 1
Answer:

-6, -4, -3, and 0 are the values which are within the range of the piecewise-defined function.

Correct options: a) y = -6, b) y = -4, c) y = -3, d) y = 0

Here, we have, to determine which values are within the range of the piecewise-defined function, we need to evaluate the function for each given value of y.

Given piecewise-defined function:

f(x) =

2x, x < -3

x, x = -3

-x - 2, x > -3

Let's evaluate the function for each value of y:

a) y = -6

For y = -6, we need to find x such that f(x) = -6.

-6 is in the range of the function if there exists an x such that f(x) = -6.

For x < -3: f(x) = 2x

2x = -6

x = -3

For x = -3: f(x) = x

x = -3

For x > -3: f(x) = -x - 2

-x - 2 = -6

x = 4

Since there is a value of x (-3) that satisfies f(x) = -6, option a) y = -6 is correct.

b) y = -4

For y = -4, we need to find x such that f(x) = -4.

-4 is in the range of the function if there exists an x such that f(x) = -4.

For x < -3: f(x) = 2x

2x = -4

x = -2

For x = -3: f(x) = x

x = -3

For x > -3: f(x) = -x - 2

-x - 2 = -4

x = 2

Since there is a value of x (-3) that satisfies f(x) = -4, option b) y = -4 is correct.

c) y = -3

For y = -3, we need to find x such that f(x) = -3.

-3 is in the range of the function if there exists an x such that f(x) = -3.

For x < -3: f(x) = 2x

2x = -3

x = -1.5

For x = -3: f(x) = x

x = -3

For x > -3: f(x) = -x - 2

-x - 2 = -3

x = 1

Since there is a value of x (-3) that satisfies f(x) = -3, option c) y = -3 is correct.

d) y = 0

For y = 0, we need to find x such that f(x) = 0.

0 is in the range of the function if there exists an x such that f(x) = 0.

For x < -3: f(x) = 2x

2x = 0

x = 0

For x = -3: f(x) = x

x = -3

For x > -3: f(x) = -x - 2

-x - 2 = 0

x = -2

Since there is a value of x (-3) that satisfies f(x) = 0, option d) y = 0 is correct.

e) y = 1

For y = 1, we need to find x such that f(x) = 1.

1 is in the range of the function if there exists an x such that f(x) = 1.

For x < -3: f(x) = 2x

2x = 1

x = 0.5

For x = -3: f(x) = x

x = -3

For x > -3: f(x) = -x - 2

-x - 2 = 1

x = -3

Since there is no value of x that satisfies f(x) = 1, option e) y = 1 is incorrect.

f) y = 3

For y = 3, we need to find x such that f(x) = 3.

3 is in the range of the function if there exists an x such that f(x) = 3.

For x < -3: f(x) = 2x

2x = 3

x = 1.5

For x = -3: f(x) = x

x = -3

For x > -3: f(x) = -x - 2

-x - 2 = 3

x = -5

Since there is no value of x that satisfies f(x) = 3, option f) y = 3 is incorrect.

Correct options: a) y = -6, b) y = -4, c) y = -3, d) y = 0

The correct values within the range of the piecewise-defined function are -6, -4, -3, and 0.

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Answer 2
Answer:

Answer:

-6, -4, -3, 0

Step-by-step explanation:

I just did this question and got it right.

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An equivalent fraction for 2/3 is
1. 2/6
2. 1/3
3. 8/15
4. 10/15

Answers

As the given and answers are all fractions, this is merely a trial-and-error method to simplify and see which answers are equivalent to the given fraction. So let us try with all them:

1.) 2/6 = 1/3 (X)
2.) 1/3 is already simplified and is not equivalent to 2/3. (X)
3.) 8/15 is already simplified and is not equivalent to 2/3. (X)
4.) 10/15 = 2/3 (by dividing 5 from both numerator and denominator)

Therefore, the correct answer is 10/15

Help the image says it all

Answers

Answer:

use distance formula and solve it

Step-by-step explanation:

this formula is in co ordinate geometry class 10 ncert book

Answer:

5 sqrt(10) square units

Step-by-step explanation:

The coordinates of the points A, B, and C are (-6,-2), (2,-8), and (-4,-6), respectively.

To find the area of a triangle, we can use the following formula:

Area of a triangle = 1/2 * base * height

We can use the distance formula to find the length of the base, which is AB:

d(A,B) = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of A and B, we get:

d(A,B) = sqrt((2 - (-6))^2 + (-8 - (-2))^2) = sqrt(64 + 36) = 10

Now, we need to find the height of the triangle. The height of a triangle is the perpendicular distance from a vertex to the opposite base. In this case, we can draw a perpendicular line from C to AB:

[Image of triangle ABC with line segment CD drawn perpendicular to AB]

The length of CD is the height of the triangle. We can use the distance formula to find the length of CD:

d(C,D) = sqrt(((-7) - (-4))^2 + (-5) - (-6))^2) = sqrt(9 + 1) = sqrt(10) \n

Now, we can find the area of the triangle:

Area of triangle ABC = 1/2 * base * height = 1/2 * 10 * sqrt(10) = 5 * sqrt(10)

Therefore, the area of triangle ABC is 5 square roots of 10 square units.

NOTEIFYOUFINDTHISANSWERUSEFULLINANYWAYTHENPLEASECONSIDERGIVE5STARTANDNOTFORGETTOMAEKASBRAINIST.THISSMALLSTEPSEEMSEASYBUTHAVEAGREATIMPACTONSOMEONE.

There will be 175 guests at a wedding. Instead of a wedding cake, the bride wants to serve cheesecake. If each cheesecake serves 12 people, how many should she order?_____________cheesecakes

Answers

175/12 = 14.58 or 15 cheesecakes

Explanation

Thus, you have 175 visitors. = 175gst

12 GST for one cheesecakes

A ratio should be set up so that the units cancel.

1 cheesecakes x 175gst c

————————

12 gst

Here, the GST is cancelled, leaving you with cheese cake, making 175/12 equal to 14.58 or 15.

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So you have 175 guests. = 175gst

1 cheeseck= 12 gst

Set up you ratio so that your units cancel.

175gst x 1 cheese c
----------------
12 gst

Here the gst cancel and you are left with cheese cake so

175/12 = 14.58 or 15

Divide 6/13 by 6/12 .

Answers

6/13÷6/12=
6/13×reciprocal of 6/12=
6/13×12/6=
6 will get cancelled and so remaining...12/13=0.92307 or. 92

The fence along the length of a ranch measures 4,450.5 meters and the fence along the width of a ranch measures 2,890 meters.The length of the fence is how many kilometers longer than the width?



_______ km

Answers

Given:
Length = 4,450.5 meters
Width = 2,890 meters

1 kilometer = 1,000 meters

Length: 4,450.5 meters * 1km/1,000 meters = 4,450.5 km/1,000 = 4.4505km

Width: 2,890 meters * 1km/1,000 meters = 2,890 km/1,000 = 2.89 km

4.4505 km - 2.89 km = 1.5605 km

The length of the fence is 1.5605 km longer than the width of the fence.

This system has one solution. What is the y-coordinate of the solution? y = 5x - 9
y = x^2 - 3x + 7

Answers

set 5x-9 = x^(2) - 3x + 7
⇒ 0 = x^(2) - 8x + 16
⇒ factoring we get... 0 = (x-4)² so the x-coordinate for the solution is x = 4
To find the y-coordinate, plug x = 4 into one of the equations (you can plug it into both just to make sure you're right).
y = 5x - 9 plug in x = 4 ⇒ y = 5(4) - 9 = 20 - 9 = 11
y = x^(2) - 3x + 7 plug in x = 4 ⇒ y = (4)² - 3(4) + 7 = 16 - 12 + 7 = 11
∴ The solution to the system is (4, 11) which has y-coordinate 11.
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