Piecewise Functions
Use the ray tool to graph
g(x)={−2x, x≥3
−1/3x−5, x≤3.

First plot the endpoint of the ray, then plot any point on the ray.

Answer:

V = 460.68

Step-by-step explanation:

V=(lwh)/3

Answer:

\(\huge\boxed{\sf x = 130\°}\)

Step-by-step explanation:

So,

90 + 90 + 50 + x = 360

230 + x = 360

x = 360 - 230

\(\rule[225]{225}{2}\)

Answer:

1 yard = 3 feet: 3.25 yards x 3 feet per yard = 9.75 feet. 1 foot = 12 inches: 9.75 feet x 12 inches per foot = 117 inches.

Step-by-step explanation:

1 yard = 3 feet: 3.25 yards x 3 feet per yard = 9.75 feet. 1 foot = 12 inches: 9.75 feet x 12 inches per foot = 117 inches.

Answer:

4.47 OR,. 4 whole 8/17

4 is the whole 8 is remainder and divisor is 17 as well as dividend is 76

Step-by-step explanation:

\( \frac{76}{17} \)

By dividing;

=4.47

Answer:

See attached

Step-by-step explanation:

Refer to attached

Point B has coordinates of (8, 12) relevant to point P

So the coordinates of the image are

The point is

The domain of the function R(x) is (-∞, -4) U (-4, 3) U (3, ∞).

The vertical asymptote is x = -4 and x = 3

The horizontal asymptote is y = 1.

In Mathematics, a domain refers to the set of all real numbers (x-values) for which a particular function is defined.

In Mathematics, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached below, we can logically deduce the following domain:

Domain = {0, ∞}.

In conclusion, an asymptote is a line which the graph of any given function approaches but would never cross or touch;

Vertical asymptote is x = -4 and x = 3

Horizontal asymptote is y = 1.

Read more on domain here: brainly.com/question/9765637

#SPJ1

Complete Question:

Analyze the graph of the function.

\(R(x)=\frac{x^2}{x^2+x-12}\)

a. What is the domain of R(x)?

b. What is the vertical and horizontal asymptote?

If three points that are provided are not collinear then the only possible polygon that can be formed by connecting these points would be a triangle.

A polygon is a closed two-dimensional shape made up of straight line segments called sides. It is formed by connecting three or more points (vertices) in a specific order. The sides of a polygon do not intersect, and each vertex is connected to exactly two sides. The region enclosed by the sides of a polygon is called its interior, while the points outside the polygon but on the same plane are called its exterior.

If three points are provided and they are not collinear (i.e., they do not lie on the same straight line), then the only possible polygon that can be formed by connecting these points would be a triangle(refer image attached). A triangle is a polygon with three sides and three angles.

The specific type of triangle (e.g., equilateral, scalene, isosceles) would depend on the lengths of the sides and the measure of the angles formed by connecting these points in a specific order. Different orders of connecting the points may result in different types of triangles.

Learn more about Polygons here:

https://brainly.com/question/24464711

#SPJ1

Answer:

y = 10x

Step-by-step explanation:

y = number of sit-ups

x = number of weeks

Equation of that can be used to find the number of sit-ups can be generated using the graph in the slope-intercept form, y = mx + b. Where, slope = m, and y-intercept is b.

Let's find slope using two points on the blue line, (0, 0) and (3, 30):

Slope (m) = change in y/change in x

m = (30 - 0)/(3 - 0)

m = 30/3

m = 10

b = 0 (the point where the line intercepts the y-axis)

✔️To write the equation, substitute m = 10 and b = 0, into y = mx + b

y = 10x + 0

y = 10x

The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

for such more question on temperature

https://brainly.com/question/14820864

#SPJ8

The true statement is now presented: If \(c > 0\) and \(|u| > c\), then \(u > c\) or \(u < -c\).

Mathematically speaking, the absolute value is defined by following expression:

\(|a| = \left \{ {{a,\,a \ge 0} \atop {-a,\,a < 0}} \right.\) (1)

If \(c > 0\) and \(|u| > c\), then \(u > c\) or \(-u > c\). Hence, \(u > c\) or \(u < -c\).

Therefore, if \(c > 0\) and \(|u| > c\), then \(u > c\) or \(u < -c\). (By tricotomy)

We kindly invite to see this question on absolute values: https://brainly.com/question/4691050

Answer:

36720 different desserts

Step-by-step explanation:

(1020x3)x12=36720

Answer:

We know length of one quarter of a circle = 2πr/4 = πr/2

So here we can make the equation for to find thr value of radius r

length of one quarter given = 25 cm

so πr/2 = 25 cm

=> πr = 50 cm

=> r = 50/π cm

So the entire circumference of circle =

2πr

= 2 π 50/π cm

= 100π/π cm (ans)

Here we dont substitute the value of π due to represent the answer in terms of pi.

Hope it helps you

Answer:

Step-by-step explanation:

Probability is defined as the likelihood or chance that an event will occur.

Probability = Expected outcome/Total outcome

probability = n{E}/n{S}

n(E) is the total number of events

n{S} is the total number of sample space.

For a coin that is tossed 3times, the possible outcome are:

S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

The total number of sample space is n(S) = 2³ = 8

n{S} = 8

a) probability of getting two heads.

Events E = {HHH, HHT, HTH, THH}

n(E) = 4

Pr(getting two heads) = 4/8 = 1/2

b) probability of getting one head.

Events E = {HTT, THT, TTH}

n(E) = 3

Pr(getting one head) = 3/8

c) probability of getting at least one head means probability of getting 1 head and more but not less than a head.

Events E = {HHH, HHT, HTH, HTT, THH, THT, TTH}

n(E) = 7

Pr(getting at least one head) = 7/8

d) probability of getting at least two heads means probability of getting 2 head and more but not less than 2 head.

Events E = {HHH, HHT, HTH, THH}

n(E) = 4

Pr(getting at least two head) = 4/8 = 1/2

Find the tree diagram in the attachment below.

Answer:

a = 57 mm is the answer.

Step-by-step explanation:

a = ?

b = 76 mm

c = 95 mm

According to the Pythagoras theorem,

a² + b² = c²

a² + 76² = 95²

a² + 5776 = 9025

a² = 9025 - 5776

a² = 3249

a = 57 mm

∴ a = 57 mm is the length of the missing leg.

Answer:

57 mm

Step-by-step explanation:

To solve for a, we can use the Pythagorean Theorem.

a² + b² = c²

We have to solve for a, and we are given values for b and c, c being the hypotenuse.

This is what we know-

a² + 76² = 95²

We can simplify this to-

a² + 5776 = 9025

To solve for a, we have to isolate the variable on on side of the equals sign. So, we can subtract 5776 from both sides.

a² + 5776 - 5776 = 9025 - 5776

Simplify.

a² = 3249

Finally, to solve for a, find the square root of a².

\(\sqrt{3249^{2}\) = 57

So, a = 57 mm

I hope this is helpful :) Good luck ^^

The vοlume οf the prism is 14 cubic feet.

A three-dimensiοnal structure having six rectangular faces is called a prism. It is alsο knοwn as a rectangular cubοid οr a rectangular parallelepiped.

The prism is cοmpletely filled with 1750 cubes that have an edge length οf 1/5 ft. This means that the vοlume οf each cube is \((1/5)^3 = 1/125\) cubic feet.

Tο find the vοlume οf the prism, we can divide the tοtal vοlume οf the cubes by the number οf cubes:

Vοlume οf prism = (Vοlume οf οne cube) x (Number οf cubes)

Vοlume οf prism = (1/125) x 1750

Vοlume οf prism = 14 cubic feet

Therefοre, the vοlume οf the prism is 14 cubic feet.

To know more about rectangular prism visit:

brainly.com/question/21308574

#SPJ1

The area of the rectangle shown is expressed as 4x² - 2x  - 6

The diagram is attached below:

Area of a rectangle = Length * width

From the diagram;

Length = 4x - 6

Width = x+1

Substitute the given parameters into the formula as shown:

Area = 4x-6(x+1)

Area = 4x(x) + 4x (1) - 6x - 6

Area = 4x² + 4x - 6x - 6

Area = 4x² - 2x - 6

Hence the area of the rectangle shown is expressed as 4x² - 2x  - 6

Learn more here: https://brainly.com/question/20968176

Answer:

D<-20

Step-by-step explanation:

Multiply to remove the fraction, then set equal to  0  and solve.

Answer:

47

Step-by-step explanation:

just keep adding by 5

Your Answer Is 10

Step-by-step explanation:

This One is easy

1500/150=10

The equation X^2/2 - 8 = 2X - 2 has two solutions, X = 6 and X = -2. These are the values of X that satisfy the equation and make both equations Y = X^2/2 - 8 and Y = 2X - 2 intersect on the graph.

To find the solutions to the equation X^2/2 - 8 = 2X - 2, we need to set the two equations equal to each other and solve for X.

The equation is:

X^2/2 - 8 = 2X - 2

To simplify the equation, let's multiply both sides by 2 to eliminate the fraction:

X^2 - 16 = 4X - 4

Next, we rearrange the equation to have all terms on one side:

X^2 - 4X - 12 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use factoring in this case:

(X - 6)(X + 2) = 0

Setting each factor equal to zero gives us two possible solutions:

X - 6 = 0 --> X = 6

X + 2 = 0 --> X = -2

So the solutions to the equation X^2/2 - 8 = 2X - 2 are X = 6 and X = -2.

For more such question on intersect . visit :

https://brainly.com/question/30915785

#SPJ8

Answer:

\(v=46\\\)

Step-by-step explanation:

Simply:

\(-v=-46\)

Answer:

Step-by-step explanation:

$373 - $74 = $299

299 divided by 23 = 13

13 months (?)

Answer:

Step-by-step explanation:

(180 - 127) / 2 = 26.5°

================================================

Explanation:

I'll be using the formula

\(_n C _r = \frac{n!}{r!*(n-r)!}\)

which is the nCr combination formula. We use nCr instead of nPr because the order of coasters doesn't matter. The whole time, the value of n stays fixed at n = 17 which is the total number of coasters to pick from.

While n is constant, the value of r will vary. It ranges from r = 15 to r = 17 inclusive of both endpoints. In other words, r will take on values from the set {15,16,17}. So we have three cases to consider. The r value is how many coasters we select. This is due to the "at least 15" which means "15 or more".

-----------------------

If you ride r = 15 coasters, then we have the following number of combinations

\(_n C _r = \frac{n!}{r!*(n-r)!}\\\\_{17} C _{15} = \frac{17!}{15!*(17-15)!}\\\\_{17} C _{15} = \frac{17!}{15!*2!}\\\\_{17} C _{15} = \frac{17*16*15!}{15!*2!}\\\\_{17} C _{15} = \frac{17*16}{2!}\\\\_{17} C _{15} = \frac{17*16}{2*1}\\\\_{17} C _{15} = \frac{272}{2}\\\\_{17} C _{15} = 136\\\\\)

There are 136 ways to ride exactly 15 coasters (when selecting from a pool of 17 total). The order doesn't matter.

We'll use this result later, so let x = 136.

-----------------------

If r = 16, then we follow the same steps as above. You should get 17C16 = 17

There are 17 ways to ride 16 coasters where order doesn't matter. Effectively this is the same as saying "there are 17 ways of picking a coaster that you won't ride"

Let y = 17 so we can use it later

-----------------------

Lastly, if r = 17, then nCr = 17C17 = 1 represents one way to ride all 17 coasters where order doesn't matter.

Let z = 1

-----------------------

Add up the values of x, y, and z to get the final answer

x+y+z = 136+17+1 = 154

The perimeter and area of the square are; 24√2 units and 12 units² respectively

Given the coordinates of the midpoints of the four sides of a square are S(-4,11), Q(2,5), U(-4,-1), A (-10,5)

But since we have the midpoints of all the sides, we can assume they're equidistant from one another since the figure is a square.

SQ = √(x₂ - x₁)² + (y₂ - y₁)²

SQ = √(2 - (-4)² + (5 - 11)²

SQ = 6√2

Let's find QU

QU = √(-4 - 2)² + (-1 - 5)²

QU = 6√2

Let's find UA ;

UA = √(-10 - (-4))² - (5 - (-1)²

UA = 6√2

And the distance AS = 6√2

The perimeter of the square = 4 (6√2)

Perimeter = 24√2 units

The area of the square = l²

Area of the square = (6√2)²

Area of square = 12 units²

Learn more on perimeter of square here;

brainly.com/question/25092270

#SPJ1