Find the equation of the graph in function notation. Name your function "f" and use x as your variable. ​

Find The Equation Of The Graph In Function Notation. Name Your Function "f" And Use X As Your Variable.

Answers

Answer 1

the equation of the graph should be

f(x)= 1/2x -1

Answer 2

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (2, 0) ← 2 points on the line

m = [tex]\frac{0+1}{2-0}[/tex] = [tex]\frac{1}{2}[/tex]

Note the line crosses the y- axis at (0, - 1) ⇒ c = - 1

y = [tex]\frac{1}{2}[/tex] x - 1 ← in slope- intercept form

f(x) = [tex]\frac{1}{2}[/tex] x - 1 ← in functional notation


Related Questions

ANSWER ASAP! 25 POINTS! WILL GIVE BRAINLIEST!
Rewrite the expression in the form k * x^n (k times x to the n power)


(4x)^2

Answers

Answer:

[tex]16(x^{2})[/tex]

Step-by-step explanation:

we know that

[tex](4x)^{2} =(4^{2})(x^{2})=16(x^{2})[/tex]

therefore

The expression in the form [tex]k(x^{n})[/tex] is equal to

[tex]k(x^{n})=16(x^{2})[/tex]

where

k=16

n=2

What is the exact circumference of the circle?
Show work

2π cm
4π cm
8π cm
16π cm

Answers

C=2πr

25.13 cm is the conference

Answer:

8π cm

Step-by-step explanation:

The diameter is 8 cm

We know the circumference is  pi times diameter

C = pi * d

C = pi *8

C = 8pi cm

We leave it in terms of pi since we want the exact value.

Find the number of positive three-digit even integers whose digits are among 9, 8, 7, 5, 3, and 1.

Answers

Answer:

8

Step-by-step explanation:

Answer:

The number of positive three-digit even integers whose digits are among 9, 8, 7, 5, 3, and 1 are:

                               36

Step-by-step explanation:

We are asked to find the number of positive three-digit even integers whose digits are among 9, 8, 7, 5, 3, and 1.

We know that a number is even if the last digit of the number is divisible by 2 i.e. even.

Hence, the only digits among the given digits which is even is: 8

Now, at the first place any of the 6 digits could come up.

( Since, the digits could be repeated)

Also, at the second palace any of the 6 digits could come up.

Hence, the total number of such numbers possible are:

                 6×6×1=36

What missing angle of the figure

Answers

Answer:

138

Step-by-step explanation:

152+125=277

277-135=142

around 138

Find the value of d. 2d -5=17

Answers

Answer: [tex]d=11[/tex]

Step-by-step explanation:

To find the value of "d" you need to solve for "d" from the equation given

[tex]2d -5=17[/tex]

First, you have to apply the Addition property of equality and add 5 to both sides of the equation. Then:

[tex]2d -5+(5)=17+(5)\\2d=22[/tex]

And finally, you have to apply the Division property of equality and divide both sides of the equation by 2.

Therefore, you get that the value of "d" is:

[tex]\frac{2d}{2}=\frac{22}{2}\\\\d=11[/tex]

Please give Brainliest!

Answer: The value of d is 11

Step-by-step explanation:

To find the value of "d" you need to subtract five from 2d or 2•11 which would give you 17.

2d -5=17

First you would add five to each side.

2d -5 + 5=17+5

This would show you that whatever you multipy 2 by would have to equal 22.

2d=22

The only thing times 2 that equals 22 is 11, so that would have to be your answer.

Hope this helps :)

Have a blessed evening!

I also need help with this one, simplifying this radical expression. This ones weird.

Answers

Answer:

1

Step-by-step explanation:

Factorise numerators/ denominators where possible

3x² - 4x + 1 = (x - 1)(3x - 1)

x² - 1 ← is a difference of squares and factors as

x² - 1 = (x - 1)(x + 1)

Expressing the product in factored form

[tex]\frac{(x-1)(3x-1)}{(x-1)(x+1)}[/tex] × [tex]\frac{x+1}{3x-1}[/tex]

Cancel common factors on numerator/denominator, that is

Cancel (x - 1) , (x + 1) and (3x - 1), leaving the simplified form 1

Answer: 1

Step-by-step explanation:

Help!! ASAP!!!!!! plz answer asap!!!!

Answers

Answer:

50.265

Step-by-step explanation:

HELP ASAP
The first triangle is dilated to form the second triangle . 4.4 arrow point to 4.4 is bigger to 1.1 small select true or false for each statement. The scale factor 0.25 the scale factor is 4

Answers

Answer:

You have to scale the bigger triangle to a small one with ratio of 1.1 to 4.4,  [tex]\frac{1.1}{4.4\\}[/tex]

the ratio is 1/4

the scale factor is 0.25 , so the statement is true

Find the discriminant and the number of real roots for this equation.
x^2+3x+8=0
Apex

Answers

Answer:

You got it right.

Step-by-step explanation:

Answer:

The discriminant is -23 and the equation has no real roots.

Step-by-step explanation:

Since, the discriminant of the quadratic equation [tex]ax^2+bx+c=0[/tex]

is,

[tex]D=b^2-4ac[/tex]

If D > 0, then the equation has two distinct real roots,

if D = 0, then the equation has two equal real roots,

if D < 0 then the equation has no real roots,

Here, the quadratic equation is,

[tex]x^2+3x+8=0[/tex]

Discriminant,

[tex]D=3^2-4\times 1\times 8=9-32 = -23 < 0[/tex]

Therefore, the discriminant is -23 and the equation has no real roots.

Which of the following increases at the fastest rate for larger values of x?

1) f(x)=5^x + 2
2) f(x)=5x + 2
3) f(x)=5x^3 + 2
4) f(x)=5x^2 + 2

Answers

The fastest rate for larger values of x will be observed in the function  f(x)=5^x + 2.

What is an exponential function?

An exponential function is one in which a term has been raised to a particular power as we can see in the options given.

The fastest rate for larger values of x will be observed in the function  f(x)=5^x + 2.

Learn more about exponential function:https://brainly.com/question/11487261

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an energy bar contains 9000 milligrams of protein. how much protein does it contain in grams

Answers

Answer:

9 Grams

Step-by-step explanation:

You would move the decimal over 3 times to the left  from the end of 9000

To convert milligrams to grams, you should know that 1 gram is equal to 1000 milligrams. This is because "milli" in milligrams means one-thousandth of a gram.
If an energy bar contains 9000 milligrams of protein, to convert this amount to grams, you divide the milligrams by 1000 (because 1000 milligrams equals 1 gram).
Here's the calculation:
\( 9000 \text{ milligrams} \div 1000 = 9 \text{ grams} \)
So, an energy bar that contains 9000 milligrams of protein has 9 grams of protein.

Select the two values of x that are roots of this equation x^2+3x-3=0
Apex

Answers

Answer:

C, and D are both roots of this equation

Answer:

The two values of x that are roots are:

[tex]x_{1} = \frac{-3 + \sqrt{21} }{2}[/tex]

[tex]x_{2} = \frac{-3 - \sqrt{21} }{2}[/tex]

Step-by-step explanation:

A cuadratic function has the form [tex]ax^{2} + bx +c = 0[/tex]

To calculate the roots of the cuadratic equation [tex]x^{2} + 3x -3 = 0[/tex] you have to solve the formula:

[tex]x = \frac{-b}{2a}[/tex] ±[tex]\frac{\sqrt{b^{2} -4ac} }{2a}[/tex]

In this case, a =1, b=3 and c= -3

Replacing the values of a,b and c in the formula:

[tex]x = \frac{-3}{(2)(1)}[/tex] ± [tex]\frac{\sqrt{(3)^{2} - (4)(1)(-3) } }{(2)(1)}[/tex]

Solving the mathematic operations:

x = [tex]\frac{-3}{2}[/tex] ± [tex]\frac{\sqrt{9 + 12 } }{2}[/tex]

The two roots are:

[tex]x_{1} = \frac{-3 + \sqrt{21} }{2}[/tex]

[tex]x_{2} = \frac{-3 - \sqrt{21} }{2}[/tex]

given vector u = (6,-4) and the graph of vector v, find v - 2u and express the result of terms in i and j

Answers

Answer:

0i + 10j, or just 10j

Step-by-step explanation:

Vector u = <6, -4> and vector v = <12, 2>.

We are to find v - 2u, which is:

<12, 2> - 2<6, -4>.  We combine x components and y components to obtain:

<12-12, 2+8>, or <0, 10>.

In terms of i and j, that'd be 0i + 10j, or just 10j.

Answer:

v-2u=10j

Step-by-step explanation:

The component of vector v, are

u=<6,-4>

From the graph; vector u, has components.

v=<12,2>

We perform the subtraction;

v-2u=<12,2>-2<6,-4>

We multiply out the scalar to get:

v-2u=<12,2>-<12,-8>

This implies that;

v-2u=<12-12,2--8>

v-2u=<0,10>

v-2u=0i+10j

v-2u=10j

When solving a system of equations, Jared found y = x + 10 for one equation and substituted x + 10 for y in the other equation. Nicole found x = y – 10 for the same equation and substituted y – 10 for x in the other equation. Who is correct? Explain.

Answers

Jared is correct because if you substitute a random number in for x 2 for example

2+10=12

2-10 doesn’t =12

Answer:

Both Jared and Nicole are correct. You can solve for either variable and use the equivalent expression to create a one-variable equation. Then you can solve. Jared would have created a one-variable equation that can be used to solve for x, whereas Nicole would have created a one-variable equation that can be used to solve for y.

Step-by-step explanation:

The angles in a triangle are in the ratio 1:2:3. Show that the triangle is a right - angled triangle.

Answers

Answer:

Angles in a triangles add up to 180°

Respectively 1 : 2 : 3 is going to be 1 x , 2 x and 3 x so,

1 x + 2 x + 3 x = 180°

⇒ Simplify

6 x = 180°

⇒ Divide by 6 on both sides to isolate x

x = 30°

Since the ratio was 1 x : 2 x : 3 x and x is 30°,

30 : 60 : 90

And since there is a 90° angle, it is a right - angled triangle

Determine if each set of ordered pairs represents a function.

Answers

Answer: Choices 1, 3, and 5 are functions

Step-by-step explanation:

To be a function, the x value can only be used once. In choices 2 and 4, the x value is repeated; therefore they are not functions.

Answer:

Step-by-step explanation:

A rectangular prism with a volume of 6 cubic units is filled with cubes with side lengths of 1/2. How many 1/2 unit cubes does it take to fill the prism


Answers

Answer:

48 cubes

Step-by-step explanation:

[tex]V_p=6\\\\\text{Calculate the volume of a cube:}\\\\V_{c}=\left(\dfrac{1}{2}\right)^3=\dfrac{1}{8}\\\\\text{Calculate how many times the volume of the prism is greater}\\\text{than the volume of the cube:}\\\\\dfrac{V_p}{V_c}=\dfrac{6}{\frac{1}{8}}=6\cdot8=48[/tex]

Describe the error in the work below.

Solve –6.1 > x + 11.3

–6.1 – 11.3 > x + 11.3 – 11.3

–17.4 > x

Answers

x should be the subject

Answer:

x should be the subject

Step-by-step explanation:

a sweater was on sale at 40% off regular price. ellasaved 20$ by buying the sweater on sale. What was the regular price of the sweater

Answers

Answer:

$50

Step-by-step explanation:

So that means 40 percent is equal to $20 do

40:20

Divided by 2

20:10

Times 5

100:50

Answer:

$50

Step-by-step explanation:

Sale on sweater = 40% .

Money saved = $20 .

Let original price be x then ,

=> 40% of x = $20

=> 40x/100 = $20

=> x = $20 *100/40

=> x = $ 50

The given line passes through the points (0, -3) and (2, 3).
on
What is the equation, in point-slope form, of the line that is
parallel to the given line and passes through the point
(-1,-1)?
y+1= (x + 1)
(23)
-
N
54-3-2-1
2
3 4
5
(0, -3)
Mark this and return
Save and Frit

Answers

Answer:

[tex]y+1=3(x+1)[/tex]

Step-by-step explanation:

step 1

Find the slope of the given line

[tex]m=(3+3)/(2-0)[/tex]

[tex]m=3[/tex]

step 2

Find the slope of the line that is  parallel to the given line

we know that

If two lines are parallel, then their slopes are the same

therefore

the slope is equal to [tex]m=3[/tex]

step 3

Find the equation in point slope form

we have

[tex]m=3[/tex]

[tex]point (-1,-1)[/tex]

The equation of the line into point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

substitute

[tex]y+1=3(x+1)[/tex] ----> equation of the line into point slope form

Which statement is true about figure DEF?​

Answers

Side DF is congruent (the = and ~ symbol) to side DE

Answer:

The correct option is A) [tex]\overline{DF}\cong \overline{DE}[/tex]

Step-by-step explanation:

Consider the provided figure.

The coordinates of E is (-2,3)

The coordinates of D is (-5,1)

The coordinates of F is (-3,-2)

Now use the distance formula to find the length of line segment:

[tex]\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

The distance between (-2,3) and (-5,1) is:

[tex]\overline{DE}=\sqrt{\left(-5-\left(-2\right)\right)^2+\left(1-3\right)^2}=\sqrt{13}[/tex]

The distance between (-5,1) and (-3,-2) is:

[tex]\overline{DF}=\sqrt{\left(-3-\left(-5\right)\right)^2+\left(-2-1\right)^2}=\sqrt{13}[/tex]

The distance between (-3,-2) and (-2,3) is:

[tex]\overline{EF}=\sqrt{\left(-2-\left(-3\right)\right)^2+\left(3-\left(-2\right)\right)^2}=\sqrt{26}[/tex]

Hence the length of line segment DE and DF is same.

Thus the correct option is A) [tex]\overline{DF}\cong \overline{DE}[/tex]

7 is what percent of 56?

Answers

Answer:

12.5

Step-by-step explanation:

7:56*100 =

(7*100):56 =

700:56 = 12.5

A 3-gallon bottle of bleach costs $13.92. What is the price per cup?

Answers

Final answer:

To calculate the cost per cup of bleach, first convert the quantity from gallons to cups. A 3-gallon bottle equals 48 cups. Divide the total cost ($13.92) by the total number of cups (48) to determine the cost per cup, which is $0.29.

Explanation:

This problem involves finding out the unit cost or, in this case, the cost per cup of bleach. One gallon is equivalent to 16 cups, hence a 3-gallon bottle is equivalent to 48 cups.

So, if $13.92 buys you 48 cups, you can calculate the cost per cup by dividing the total cost by the number of cups.

Proceed with the following calculation: $13.92 costs /48 cups = $0.29 per cup of bleach costs.

In conclusion, each cup of bleach from this 3-gallon bottle would cost you $0.29.

Learn more about Unit costs here:

https://brainly.com/question/31310172

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Final answer:

To find the price per cup of bleach from a 3-gallon bottle costing $13.92, we multiply 3 gallons by 16 cups per gallon to get 48 cups, and then divide $13.92 by 48 to find the cost per cup, which is approximately $0.29.

Explanation:

To calculate the price per cup of bleach when given the price per gallon, we need to know how many cups are in a gallon and then divide the total cost by the total number of cups.

First, we establish that there are 16 cups in a gallon. Since we are dealing with a 3-gallon bottle, the total number of cups will be 3 gallons times 16 cups per gallon, which equals 48 cups.

Next, we take the total cost of the 3-gallon bottle, which is $13.92, and divide it by the total number of cups, 48. Performing this division gives us the cost per cup. So, $13.92 divided by 48 cups equals approximately $0.29 per cup.

This method demonstrates how to break down bulk costs into more manageable unit prices and can be applied across various products and measurements.

If g(x) = x2 + 3, find g(4).

Answers

Answer:

g(4) = 11

Step-by-step explanation:

x = 4

4(2) + 3 = 11

Answer:

19

Step-by-step explanation:

Replace the x with four

What is 2 1/6 ft= to inches as a mixed number?

Answers

Answer: 26

Step-by-step explanation:

because...

Feet result: 0.18055555556 ft.

Calculation: 2.1666666666666665" / 12

= 0.18055555556ft

But at the end your answer is going to 26.

So 2.1666666666666665 = 26

* Hopefully this helps:)

* Mark me the brainliest:)!!

Answer:

Step-by-step explanation:

2  1/6 ft = 24 inches plus (1/6)(12 in), or 24 inches plus 2 inches, or 26 inches.

2  1/6 is ALREADY a mixed number, in feet.

Use the function below to find f(3) f(x)= (1/6)^x

Answers

Hello!

The answer is:

[tex]f(3)=(\frac{1}{216})[/tex]

Why?

To find the required function f(3), we need to use the given function f(x) and evaluate "x" equal to 3 (input).

We are given the function:

[tex]f(x)=(\frac{1}{6})^{x}[/tex]

Then, evaluating "x" equal to 3, we have:

[tex]f(3)=(\frac{1}{6})^{3}[/tex]

[tex]f(3)=(\frac{1}{6})^{3}=(\frac{1}{6})*(\frac{1}{6})*(\frac{1}{6})=(\frac{1}{6*6*6})[/tex]

[tex]f(3)=(\frac{1}{6*6*6})=(\frac{1}{216})[/tex]

Hence, we have that the answer is:

[tex]f(3)=(\frac{1}{216})[/tex]

Have a nice day!

The graph below shows the transformation from triangle 1 to triangle 2.
-
Which sequence of steps would transform triangle 1 to triangle 2?
reflect across the y-axis; rotate 180° counterclockwise about the origin
reflect across the x-axis; rotate 270° counterclockwise about the origin
reflect across the y-axis; rotate 90° counterclockwise about the origin
rotate 90° counterclockwise about the origin; rotate 270° counterclockwise about the origin

Answers

Answer:

reflect across the y-axis; rotate 180° counterclockwise about the origin - first choice

Answer:

Option A.

Step-by-step explanation:

The graph below shows the transformation from triangle 1 to triangle 2 as below.

1). To understand the transformation we will take a point A. Present coordinates of point A are (1, -1).

When point A is reflected across y - axis, coordinates of A' become (1, 1).

2). Now we see that triangle 2 is in 3rd quadrant having coordinates A"(-1, -1)

which reveals that A'(1, 1) has been rotated by 180° counterclockwise.

Therefore, option A. is the correct choice.

Choose the slope _intercept form of 3x+2y=5

Answers

Answer:

3x+2y=5

2y=5-3x

y=5/2-3/2x

Or you can write as:

y=2.5-1.5x

Answer: y=3/5x+5/2

Step-by-step explanation:

Use the data set below to answer the following question.
2, 4, 7, 2, 3, 7, 9, 3, 1,7
What is the mode of this data set?

Answers

Arranging it in ascending order:

1, 2, 2, 3, 3, 4, 7, 7, 7, 9

Mode is most frquently occuring observation..

i.e. Here ,7 Occurs the most(thrice)

So mode= ,7

Hello There!

Mode: The number that occurs most often in a set of numbers.

Although it's optional, I like to put the numbers from least to greatest because it can be easier to see what number occurs the most.

-Least To Greatest-

1 - 2 - 2 - 3 - 3 - 4 - 7 - 7 - 7 - 9

When we look at our set of data, we can notice that the number 7 appears the most so the mode for out set of data is 7.

Mode =  7

identify the relative maximum value of g(x) for the function shown below

g(x) = 2/ x^2 +3

Answers

Answer:

The relative maximum value is [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

The given function is

[tex]g(x)=\frac{2}{x^2+3}[/tex]

We differentiate to obtain;

[tex]g'(x)=-\frac{4x}{(x^2+3)^2}[/tex]

At turning points [tex]g'(x)=-\frac{4x}{(x^2+3)^2}=0[/tex]

[tex]\implies x=0[/tex]

[tex]g''(x)=\frac{16x^2}{(x^2+3)^3}- \frac{4}{(x^2+3)^2}[/tex]

We apply the second derivative test to obtain:

[tex]g''(0)=\frac{16(0)^2}{((0)^2+3)^3}- \frac{4}{((0)^2+3)^2}=-\frac{4}{9}[/tex]

Since the second derivative is negative, there is a relative maximum at x=0.

We substitute x=0 into the original function to obtain the relative maximum value.

[tex]g(0)=\frac{2}{(0)^2+3}=\frac{2}{3}[/tex]

To find the relative maximum value of g(x) = 2/(x² + 3), one should evaluate the function at x = 0, giving the relative maximum value as 2/3.

The question is asking to identify the relative maximum value of the function g(x) = 2/(x² + 3).

To find the relative maximum, we need to find the critical points by taking the derivative of g(x) and setting it to zero. However, this function does not have a simple expression where the derivative is zero.

Instead, we note that because the denominator x² + 3 is always positive and has a minimum when x = 0, the function g(x) will have a maximum value when x = 0.

Thus, the relative maximum value of g(x) is obtained by plugging x = 0 into the function: g(0) = 2/(0² + 3) = 2/3.

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