The graph represents the piecewise function:
f(x)= { __, if -1 ≤ x ≤ 1; __, if 3 ≤ x ≤ 5 }

The Graph Represents The Piecewise Function:f(x)= { __, If -1 X 1; __, If 3 X 5 }

Answers

Answer 1

Answer:

4, x-1

Step-by-step explanation:

The first piece of this function goes from -1 to 1. Since that part of the function is a horizontal line at y=4, and has no slope, this first part is just 4.

The second piece of this function goes from 3 to 5. This piece does have a slope that you can either solve or just from reading the graph will give you a slope of 1. Since one of the points is (3, 2), we can figure out that the y-intercept is -1. (You can also just extend the line across the y-axis). When putting this equation together we get x-1 being the second part.

Answer 2

The solution is:

The graph represents the piecewise function:

f(x)= { 4, if -1 ≤ x ≤ 1;

         (x - 1), if 3 ≤ x ≤ 5 }

What is graph?

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

The first piece of this function goes from -1 to 1.

Since that part of the function is a horizontal line at y=4, and has no slope, this first part is just 4.

so, we have,

The second piece of this function goes from 3 to 5.

This piece does have a slope that you can either solve or just from reading the graph will give you a slope of 1.

Since one of the points is (3, 2), we can figure out that the y-intercept is -1. (You can also just extend the line across the y-axis).

When putting this equation together we get x-1 being the second part.

Hence, The solution is:

The graph represents the piecewise function:

f(x)= { 4, if -1 ≤ x ≤ 1;

         (x - 1), if 3 ≤ x ≤ 5 }

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Related Questions

+
(10x+2)

(9X+18) find the value of x

Answers

16

Step-by-step explanation:

10x+2=9x+18

-2 -2

10x=9x+16

-9x -9x

x=16

Hope this helps! :)

Answer:

x = 16°

Step-by-step explanation:

(10x + 2)° = (9x + 18)°

10x + 2 = 9x + 18

10x + 2 - 2 = 9x + 18 - 2

10x = 9x + 16

10x - 9x = 9x - 9x + 16

x = 16°

Find an equation of the circle whose diameter has endpoints (6,4) and (2,-6)

Answers

Answer:

[tex](x-4)^2+(y+1)^2=29[/tex]

Step-by-step explanation:

We want to find a circle whose diameter has the endpoints (6, 4) and (2, -6).

Since this is the diameter, its midpoint will be the center of the circle. Find the midpoint:

[tex]\displaystyle M=\left(\frac{6+2}{2}, \frac{4+(-6)}2}\right)=(4, -1)[/tex]

So, the center of our circle is (4, -1).

Next, to find the radius, we can find the length of the diameter and divide it by half.

Using the distance formula, find the length of the diameter:

[tex]\begin{aligned} d&=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\ &=\sqrt{(2-6)^2+(-6-4)^2}\\\\&=\sqrt{(4)^2+(-10)^2}\\\\&=\sqrt{116}\\\\&=2\sqrt{29}\end{aligned}[/tex]

So, the radius will be:

[tex]\displaystyle r=\frac{1}{2}d=\frac{1}{2}\left(2\sqrt{29}\right)=\sqrt{29}[/tex]

The equation for a circle is given by:

[tex]\displaystyle (x-h)^2+(y-k)^2=r^2[/tex]

Substitute:

[tex](x-4)^2+(y+1)^2=29[/tex]

If line a has a slope of -3 and is perpendicular to line b, what would is the slope of line b?

Answers

Answer:

Slope of line B: 1/3

Step-by-step explanation:

To find a slope perpendicular to another slope, you take its negative reciprocal.

Therefore, line B will have a slope of 1/3 because -3 -> -1/3 -> 1/3

What is the length of leg s of the triangle below?
45
3
1072
90°
45
$

Answers

Can you please repost with the image?

The length of the leg is 9.

What is the Pythagorean theorem?

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

From the triangle,

S = length of the leg.

Now,

Applying the Pythagorean theorem.

√18² = 3² + s²

18 = 9 + s²

s² = 18 - 9

s² = 9

s = 9

Thus,

The length of the leg is 9.

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3/4x × 12/11 ÷ 3x/22​

Answers

Answer:

242/48

Step-by-step explanation:


What is the midpoint of the line segment graphed below?
A. (4,7/2)
B. (8,7/2)
c. (4,3/2)
D (8, 3/2)

Answers

Answer:

a) (4,7/2)

Step-by-step explanation:

Midpoint Formula:

[(-1+9)/2], [(2+5)/2]

(8/2, 7/2) = (4, 7/2)

Can someone help me? It's urgent and thank you!

Answers

(-4, 2) is the mid point
The answer is M=(4,-2)

7X^2+20x=24
X=?
Please answer to 2 d.p

Answers

Answer:

0.76

or

-0.76

hope this helps

Please help?? I have an exam tomorrow

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

x² - 5xy + 6y² = x² - 3xy - 2xy + 6y²

                      = x(x  - 3y) - 2y(x - 3y)

                      = (x - 3y)(x -2y)

x² - 4xy + 3y² = x² -xy - 3xy + 3y²

                      = x(x - y) - 3y(x - y)

                      = (x - y)(x - 3y)

x² - 3xy + 2y² = x² - xy - 2xy + 2y²

                      = x(x - y) - 2y(x - y)

                     = (x - y)(x - 2y)

Least common denominator = (x-y)(x - 2y)(x - 3y)

[tex]RHS = \frac{1*(x-y)}{(x-3y)(x-2y)*(x-y)}+\frac{a*(x-2y)}{(x-y)(x-3y)*(x-2y)}+\frac{1*(x-3y)}{(x-y)(x-2y)*(z-3y)}\\\\= \frac{x- y + ax - 2ay +x -3y}{(x-y)(x-2y)(x-3y)}\\\\= \frac{2x -4y +ax - 2ay}{ x^{3}-5x^{2}y+8xy^{2}-4y^{3}}[/tex]

A rectangle measures 8/3 inches by 9/4 inches. What is its area?

Answers

Answer:

To find the area, you have to multiply the length times the width

Step-by-step explanation:

Answer:

The area of this rectangle is 6 square units.

Step-by-step explanation:

Multiply the width (8/3 inches) by the height (9/4 inches) to get the rectangle area:

 8       9

----- * -----

  3      4

                        8 * 9

This results in ----------    which itself reduces to 6.  

                          4 * 3

The area of this rectangle is 6.

The regular price of an item at a store is p dollars. The item is on sale for 20% off the regular price. Some of the expressions shown below represent the sale price, in dollars,of the item.Expression A: Expression B: Expression C: Expression D: Expression E: Which two expressions each represent the sale price of the item?AExpression A and Expression EBExpression B and Expression CCExpression B and Expression DDExpression C and Expression D

Answers

Answer:

Expression B: 0.8p

Expression D: p - 0.2p

Step-by-step explanation:

The regular price of an item at a store is p dollars. The item is on sale for 20% off the regular price. Some of the expressions shown below represent the sale price, in dollars, of the item.

Expression A: 0.2p

Expression B: 0.8p

Expression C:1 - 0.2p

Expression D: p - 0.2p

Expression E: p - 0.8p

Which two expressions each represent the sale price of the item?

Regular price of the item = $p

Sale price = 20% off regular price

Sale price = $p - 20% of p

= p - 20/100 * p

= p - 0.2 * p

= p - 0.2p

= p(1 - 0.2)

= p(0.8)

= 0.8p

The sale price is represented by the following expressions

Expression B: 0.8p

Expression D: p - 0.2p

A quadrilateral is a parallelogram if each____ divides a parallelogram into two____.​

Answers

Answer:

diagonal, congruent triangles

Step-by-step explanation:

A chef got 9 bags of onions. The red onions came in bags of 6 and the yellow onions came in bags of 7. If the chef got a total of 59 onions, how many bags of each type of onion did he get?

Answers

Answer:

yellow = 5 bags

red = 4 bags

Step-by-step explanation:

two equations can be derived from the question

x + y = 9 equation 1

6x + 7y = 59 equation 2

where x = number of red onion bags

y =  number of yellow onion bags

Multiply equation 1 by 6

6x + 6y = 54 equation 3

subtract equation 3 from 2

y = 5

substitute for y in equation 1

x + 5 = 9

x = 9 - 5

x = 4

Jeremy is conducting a survey about his coworkers’ in-office water consumption to encourage management to install more water dispensers at their location. He found that the population mean is 112.5 ounces with a standard deviation of 37.5. Jeremy has a sample size of 96. Complete the equation that Jeremy can use to find the interval in which he can be 99.7% sure that the sample mean will lie. 37.5 112.5 75 96 150 9.8

Answers

Using the z-distribution, as we have the standard deviation for the population, it is found that the 99.7% confidence interval is given by:

[tex]112.5 \pm 3\frac{37.5}{\sqrt{96}}[/tex]

What is a t-distribution confidence interval?

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.

99.7% confidence level, hence[tex]\alpha = 0.997[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.997}{2} = 0.9985[/tex], so [tex]z = 3[/tex].

The other parameters are:

[tex]\mu = 112.5, \sigma = 37.5, n = 96[/tex]

Hence, the interval is:

[tex]112.5 \pm 3\frac{37.5}{\sqrt{96}}[/tex]

To learn more about the z-distribution, you can check https://brainly.com/question/25890103


A rope is 9 1/2 meters long. How many pieces can be cut from the rope if
each piece is to be 1/4 meter?

Answers

A rope is 9 1/2 m long because 1/4 m that is your answer because I need points

which ratio is equivalent to the ratio 2:52

Answers

Answer:

1:26

Step-by-step explanation:

You can divide both sides by 2.

What is the explicit formula for the geometric sequence 2, 6, 18, 54, …?

Answers

Answer:

3x

Step-by-step explanation:

You multiply the pervious number with 3 to get the next number

For example 2 times 3 = 6

6 times 3 = 18

18 times 3 =54

54 times 3= 162

So on and so forth

The object below is made with six identical cubes. Each cube edge is 3 inches long.
As
3 in.
What is the surface area of the object in square inches?

Answers

Answer:

306 square inches.

Step-by-step explanation:

All surfaces of the cubes are exposed to the outside except 2 ( where 2 of the cubes join).

6 separate cubes have 6 * 6 faces exposed so this object has 36 - 2 = 34 surfaces exposed.

Each face of one cube = 3*3 = 9 in^2.

Therefore the surface area =  9 * 34 = 306 in^2.

The Chang family is on their way home from a cross-country road trip. During the trip, the function D(t)=3260−55t can be used to model their distance, in miles, from home after t hours of driving. find D(12) and interpret the meaning in the context of the problem.

Answers

Answer:

D(12) = 2,600 miles

It means a distance of 2,600 miles is already traveled from home after 12 hours

Step-by-step explanation:

To find D(12); all we have to do is to substitute the value of 12 for D

We have this as;

D(12) = 3260-55(12)

D(12) = 2,600

In the context of this problem, what this mean is that the distance away from home is 2,600 miles after traveling 12 hours

Help pleaseeeeeeeeeeeeeeeeeeeeee

Answers

Answer:

-8 X 3 = -24 + 9 = -15 or you could do    -24+9=-15

Step-by-step explanation:

x = 72
Hope this helps

279 students went on a field trip. Five buses were filled and 9 students traveled in cars. How many students were in each bus? PLEASEEEEE HELPPPPP ME you get 60 points i dont know if anyone cares but hey

Answers

Answer:

90 students.

Step-by-step explanation:

279-9=270, and 270 divided by 9 is 90.

helpppp pleaseee its hard

Answers

Answer:

Ten thousands

Step-by-step explanation:

Replace all other digits with zero

This gives 40,000

Ten thousand (10,000) has the same amount of digits

Find the interior angle sum for each polygon. Round your answer to the nearest tenth if needed
(#4 and #3 are solve for x)

Answers

Answer:

1) 720

2) 540

3) x = -1

4) x = 10

Step-by-step explanation:

The formula for finding the sum of interior angles in a polygon is the following,

[tex]S=180(n-2)[/tex]

Where (S) represents the sum of interior angles, and (n) represents the number of sides.

1)

The given polygon is a hexagon, meaning it has (6) sides. Substitute the number of sides into the formula and solve for the sum of interior angles.

[tex]S=180(n-2)[/tex]

[tex]S=180(6-2)\\\\S=180(4)\\\\S = 720[/tex]

2)

This polygon is a pentagon, meaning it has (5) sides. Substitute the number of sides into the formula and solve for the sum of interior angles.

[tex]S=180(n-2)[/tex]

[tex]S=180(5-2)\\\\S=180(3)\\\\S=540[/tex]

3)

The sum of interior angles in a triangle is (180) degrees. One can see that one of the measures of an angle is (90) degrees (indicated by the box around the angle). One can form an equation by adding up the expressions for the angle measures and setting it equal to (180) degrees.

(55) + (x + 36) + (90) = 180

Simplify,

181 + x = 180

Inverse operations,

181 + x = 180

x = -1

4)

The remote angles theorem states that when one extends one of the sides of a triangle, the angle formed between the side and the extension is equal to the sum of the two non-adjacent interior angles in the triangle. Based on this theorem, one can form an equation and solve for the unknown.

<F + <G = <FEZ

Substitute,

(4x) + (-5 + 7x) = 105

Simplify,

4x - 5 + 7x = 105

11x - 5 = 105

Inverse operations,

11x - 5 = 105

11x = 110

x = 10

A silo in the shape of a cylinder is partially filled with corn to feed cows. The corn fills 25% of the height of the silo. What is the approximate volume of the part of the silo that is filled with corn if the silo is 12 feet in diameter and 60 feet high?

- PLEASE HELP im in the middle of an exam

Answers

Answer:

1695.6 cubic feet

Step-by-step explanation:

Given that,

The corn fills 25% of the height of the silo.

The diameter of silo, d = 12 feet

Radius, r = 6 feet

Height, h = 60 feet

The volume of the part of the silo that is filled with corn is given by :

[tex]V=25\%\ of\ \pi r^2 h\\\\=\dfrac{25}{100}\times 3.14\times 6^2\times 60\\\\V= $$1695.6\ feet^3[/tex]

So, the required volume is equal to 1695.6 cubic feet.

Let z be inversely proportional to the cube root of y. When y =.064, z =3
a) Find the constant of proportionality k.
b) Find the value of z when y = 0.125.​

Answers

Given:

z be inversely proportional to the cube root of y.

When y =0.064, then z =3.

To find:

a) The constant of proportionality k.

b) The value of z when y = 0.125.​

Solution:

a) It is given that, z be inversely proportional to the cube root of y.

[tex]z\propto \dfrac{1}{\sqrt[3]{y}}[/tex]

[tex]z=k\dfrac{1}{\sqrt[3]{y}}[/tex]              ...(i)

Where, k is the constant of proportionality.

We have, z=3 when y=0.064. Putting these values in (i), we get

[tex]3=k\dfrac{1}{\sqrt[3]{0.064}}[/tex]

[tex]3=k\dfrac{1}{0.4}[/tex]

[tex]3\times 0.4=k[/tex]

[tex]1.2=k[/tex]

Therefore, the constant of proportionality is [tex]k=1.2[/tex].

b) From part (a), we have [tex]k=1.2[/tex].

Substituting [tex]k=1.2[/tex] in (i), we get

[tex]z=1.2\dfrac{1}{\sqrt[3]{y}}[/tex]

We need to find the value of z when y = 0.125.​ Putting y=0.125, we get

[tex]z=1.2\dfrac{1}{\sqrt[3]{0.125}}[/tex]

[tex]z=\dfrac{1.2}{0.5}[/tex]

[tex]z=2.4[/tex]

Therefore, the value of z when y = 0.125 is 2.4.

Proportional quantities are either inversely or directly proportional. For the given relation between y and z, we have:

The constant of proportionality k = 1.2, andWhen y = 0.125 , z = 2.4

What is directly proportional and inversely proportional relationship?

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

[tex]p = kq[/tex]

where k is some constant number called constant of proportionality.

This directly proportional relationship between p and q is written as

[tex]p \propto q[/tex]  where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n are two variables.

Then m and n are said to be inversely proportional to each other if

[tex]m = \dfrac{c}{n}[/tex]

or

[tex]n = \dfrac{c}{m}[/tex]

(both are equal)

where c is a constant number called constant of proportionality.

This inversely proportional relationship is denoted by

[tex]m \propto \dfrac{1}{n}\\\\or\\\\n \propto \dfrac{1}{m}[/tex]

As visible, increasing one variable will decrease the other variable if both are inversely proportional.

For the given case, it is given that:

[tex]z \propto \dfrac{1}{^3\sqrt{y}}[/tex]

Let the constant of proportionality be k, then we have:

[tex]z = \dfrac{k}{^3\sqrt{y}}[/tex]

It is given that when y = 0.064, z = 3, thus, putting these value in equation obtained above, we get:

[tex]k = \: \: ^3\sqrt{y} \times z = (0.064)^{1/3} \times (3) = 0.4 \times 3 = 1.2[/tex]

Thus,  the constant of proportionality k is 1.2. And the relation between z and y is:

[tex]z = \dfrac{1.2}{^3\sqrt{y}}[/tex]

Putting value y = 0.0125, we get:

[tex]z = \dfrac{1.2}{^3\sqrt{y}}\\\\z = \dfrac{1.2}{(0.125)^{1/3} } = \dfrac{1.2}{0.5} = 2.4[/tex]

Thus, for the given relation between y and z, we have:

The constant of proportionality k = 1.2, andWhen y = 0.125 , z = 2.4

Learn more about proportionality here:

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is my dad abusive? today he grabbed my ears so hard and they turned so red and he put his arms around my face. then he kicked me really hard to the point where I peed, he also pushed me a lot and started slapping me. he did more which I can't remember but he also smashed my phone :) this all happened within 20 minutes and I could barely breathe after that lol. this may not seem so much but it is. this is too personal ig lol and I started self-harming again bc of him yay.

Answers

Answer:

Step-by-step explanation:

OMG! Don't do that! I am so sorry this is happening to you. Look I don't know how to comfort you. IF he keeps doing this tell your mom or litterally call 911. If he did it just on that day then try confronting him on it. And ask him why he did that! Don't self-harm you deserve so much more than that! You are awesome!

Find the measure of x and y

Answers

Answer:

y - 41°

x - ?

Step-by-step explanation:

use method of Z equation

Z 41° so y is 41° too

make sense

There are 5 red, 4 blue, and 3 green marbles in a bag. What are the odds of randomly pulling a blue marble out of the bag and then randomly pulling a green marble out of the bag? The blue marble is NOT replaced.

A - 7/2
B - 12/24
C - 1/12
D - 1/11

Answers

C -1/12 is the answer

PLS HELP Find the value of x.
A. 4
B. 2
C. 7
D. 14

Answers

Answer:

ANSWER IS B

Step-by-step explanation:

5x - 3 = 3x + 1

5x - 3x = 1 + 3

2x = 4

x = 4/2

x = 2

Answer:

B. 2

Step-by-step explanation:

The sides 5x - 3 and 3x + 1 are the same length, so you can put an equal sign: 5x - 3 = 3x + 1, x = 2:

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

10 - 3 = 6 + 1

7 = 7

So x is 2

what is the answer to this question

Answers

D

Explanation: the b value is the starting point and it starts at positive 2, the graph is positive so the slope is also positive which only leaves answer choice D.

Answer:

[tex]slope = \frac{2 - ( - 1)}{0 - ( - 1)} \\ = 3 \\ y = mx + c \\ 2 = (0 \times 3) + c \\ c = 2 \\ { \boxed{y = 3x + 2}}[/tex]

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