Determine the linear function for a graph that is a line with a slope of 1/7
and contains the point
(−4, 1).

Answers

Answer 1

The linear equation is y = (1/7)*x + 11/7.

How to get the linear equation?

The general linear equation is:

y = a*x + b

Where a is the slope.

Here we know that a = (1/7), then the line is:

y = (1/7)*x + b

We also know that the line contains the point (-4, 1), this means that when x = -4, we must have y = 1.

Replacing that, we get:

1 = (1/7)*(-4) + b

1 + 4/7 = b

7/7 + 4/7 = b

11/7 = b

So the linear equation is:

y = (1/7)*x + 11/7.

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Answer 2

The equation of the linear function of the line is: y = 1/7x + 11/7.

What is a Linear Function Equation?

A linear function equation is modelled as, y = mx + b, where m is the slope and b is the y-intercept.

Slope (m) = 1/7, and the line passes through (-4, 1), therefore, substitute (x, y) = (-4, 1) and m = 1/7 into y = mx + b:

1 = 1/7(-4) + b

1 = -4/7 + b

1 + 4/7 = b

11/7 = b

b = 11/7

Plug in the values of m and b into y = mx + b:

y = 1/7x + 11/7

The equation of the linear function is: y = 1/7x + 11/7

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Related Questions

A small dairy farm writes a business plan. It includes a graph showing the estimated amount of feed used each day in thousands of pounds, y, compared to the number of years since the farm began operating, x.



What does the y-intercept represent?

the estimated amount of years the farm can afford feed
the maximum feed per day estimated for the life of the farm
the estimated amount of feed per day for the start of the farm
the maximum years the farm needs the originally estimated feed per day

Answers

The y intercept means , the estimated amount of feed per day for the start of the farm , Option C is the right answer.

What is a function ?

A function is a law that relates two variables , independent and dependent variable.

It is given that

On y axis , amount of feed used each day in thousands of pounds,

On x axis,  number of years since the farm began operating

The y intercept means x = 0 , which means at the starting of the farm , the feed needed per day.

Therefore Option C is the right answer , the estimated amount of feed per day for the start of the farm.

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2 triangles are shown. The first triangle has side lengths 35, 20, and 20. The second triangle has side lengths x, 44, 44.
What value of x will make the triangles similar by the SSS similarity theorem?

Answers

The value of x is 77 cm which will make the triangles similar by SSS similarity theorem

Given length of the three sides of one triangle are  35 , 20 and 20

and length of the three sides of another triangle are  x, 44,44

We need to find the values of x by using SSS Similarity theorem

We know that triangles are are similar by side - side - side similarity creation and hence the sides are in the same ratio

As both the triangles are isosceles triangles

Therefore ,

x/35 = 44/20=44/20 (Using ratio)

Solving the equation we get

x=44*35/20

x= 77

Hence the value of x is 77cm

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answer?.......................

Answers

When we mark the coordinates (0, 2), (1, 1), (x, 0), (9, -1) on graph we obtain option C.

The given function is [tex]y=2-\sqrt{x}[/tex].

We need to find which is the graph of the given function from the options.

What are coordinates?

In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

Take, x=0, 1, 4, 9, 16, 25, 36,....

Now, when x=0, y=2.

When x=1, y=1.

When x=4, y=0.

When x=9, y=-1

So, when we mark the coordinates (0, 2), (1, 1), (x, 0), (9, -1) on graph we obtain option C.

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Please Help me!!!!!!!!!

Answers

Answer:

(2,-3) (3,-3)

Step-by-step explanation:

f(x) is y

x² - 5x + 3 = -3

x² - 5x + 6 = 0

ask yourself

which 2 numbers when multiplied give you

+6 and when added give you -5

they are -3 and -2

(x-3)(x-2)

x=3 x=2

when you put x=3 and x=2

in x² - 5x + 3 it's gives -3 which is y

(3,-3) (2,-3)

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Simplify the expression when j = 5 and k = 3
*
1 point
Captionless Image
3
-9/5
41/3
6

Answers

Answer:

1 7

_

8

Step-by-step explanation:

5 x 3 = 15

5 + 3 = 8

=1 7

_

8

3n-5p+2n=10 solve for n

Answers

Answer:

n=3p

Isolate the variable by dividing each side by factors that don't contain the variable.



3n - 5p + 2n = 10
5n - 5p = 10
5n = 10 + 5p
n = 2 + p

Solve: |2x − 1| < 11.

Answers

STEP 1 : Rearrange this Absolute Value Inequality

Absolute value inequalitiy entered

|2x-1| < 11

STEP 2 : Clear the Absolute Value Bars

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |2x-1|

For the Negative case we'll use -(2x-1)

For the Positive case we'll use (2x-1)

STEP 3 : Solve the Negative Case

-(2x-1) < 11

Multiply

-2x+1 < 11

Rearrange and Add up

-2x < 10

Divide both sides by 2

-x < 5

Multiply both sides by (-1)

Remember to flip the inequality sign

x > -5

Which is the solution for the Negative Case

STEP 4 : Solve the Positive Case

(2x-1) < 11

Rearrange and Add up

2x < 12

Divide both sides by 2

x < 6

Which is the solution for the Positive Case

STEP 5 : Wrap up the solution

-5 < x < 6

Solution in Interval Notation

(-5,6) .

answer?.............

Answers

Answer:

-21

Step-by-step explanation:

My guess would be -21 Im not sure but that is my guess because x=5 the normal answer would be negative 25 so my guess would negative 21

Multiply (5z + 6)(2z + 1)(2z - 1)
Pls help and explain WELL ty

Answers

Answer:

[tex]\huge\boxed{\sf 20z\³ + 24z\² - 5z - 6}[/tex]

Step-by-step explanation:

Given expression:

= (5z + 6)(2z + 1)(2x - 1)

Using formula (a + b)(a - b) = a² - b²

= (5z + 6)[(2z)² - (1)²]

= (5z + 6)(4z² - 1)

Distributing

= 5z (4z² - 1) + 6(4z² - 1)

= 20z³ - 5z + 24z² - 6

Arrange

= 20z³ + 24z² - 5z - 6

[tex]\rule[225]{225}{2}[/tex]

Write the quadratic equation whose roots are 3 and 1, and whose leading coefficient is 1

Answers

Answer:

x² - 4x + 3 = 0

Step-by-step explanation:

given roots x = a and x = b then the corresponding factors are

(x - a) and (x - b)

the equation is then the product of these factors , that is

(x - a)(x - b) = 0

given

roots x = 3 and x = 1 , then factors are (x - 3) and (x - 1) , then

(x - 3)(x - 1) = 0 ← expand factors using FOIL

x² - 4x + 3 = 0

Find the value of x,y and z​

Answers

Answer:

x = 95°

y = 40°

z = 95°

Step-by-step explanation:

a = 45° (Vertical angles)

y = 40° (corresponding angles)

z = 180° - (45° + 40°) (Interior angle sum theorem of a triangle)

-> z = 180° - 85°

-> z = 95°

x = z (vertical angles)

-> x = 95°

Simplify this expression.
[tex]\\\\(\sqrt{2} + \sqrt{3})(\sqrt{5} - \sqrt{7} \\A: \sqrt{5} + \sqrt{-2} \\B: \sqrt{10} + \sqrt{15} - \sqrt{14} - \sqrt{21} \\C: 2\sqrt{5} - 2\sqrt{7} \\D: 2\sqrt{5} + 3\sqrt{5} - 2\sqrt{7} - 3\sqrt{7}[/tex]

Answers

By applying algebra, radical and power properties, we find that the simplified form of (√2 + √3) · (√5 - √7) is equal to √10 + √15 - √14 - √21. (Correct choice: B)

How to simplify a product of two binomials with radical numbers

Herein we need to apply algebra and radical and power properties to simplify the expression described in the statement, whose procedure is shown below:

(√2 + √3) · (√5 - √7)     Given(√2 + √3) · √5 + (√2 + √3) · (- √7)     Distributive property√2 · √5 + √3 · √5 + √2 · (- √7) + √3 · (- √7)     Distributive property√10 + √15 - √14 - √21     (- a) · b = - a · b/ √a · √b = √a · b/Result

By applying algebra, radical and power properties, we find that the simplified form of (√2 + √3) · (√5 - √7) is equal to √10 + √15 - √14 - √21. (Correct choice: B)

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Answer:

B is correct

Step-by-step explanation:

Cus I said so

please help me. I really need to get this right. I appreciate the hard work

Answers

A function assigns the values. The value of g(x) can be filled as 4, 6, 9, and 13.5, respectively.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

The value of g(x) can be found by substituting the value of x as given in the function. Therefore, the values will be,

A.) x = -1

[tex]g(-1) = 6(\dfrac32)^{-1}\\\\g(-1) = 4[/tex]

B.) x = 0

[tex]g(0) = 6(\dfrac32)^0\\g(0) = 6[/tex]

C.) x = 1

[tex]g(1) = 6(\dfrac32)^1\\\\g(1) = 9[/tex]

D.) x = 2

[tex]g(2) = 6(\dfrac32)^2\\\\g(2) = 13.5[/tex]

Hence, the value of g(x) can be filled as 4, 6, 9, and 13.5, respectively.

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Solve 6x+7=3x+16
X=6
X=3
X=4
X=2

Answers

Answer:

x=3

Step-by-step explanation:

6x-3x=16-7

3x=16-7

3x=9

x=3

Games Made x
(in 1000s)
Profit y
(in $1000s)
4
6
8
10 12
118 142 150 142 118
Which type of function best models the data in the
table? Justify your choice.

Answers

The type of function that best models the data in the table is the quadratic function

How to determine the function type?

The table of values is represented as:

x: 4 6 8 10 12

y : 118 142 150 142 118

From the above table, we can see that:

The y values increase from 118 to 150The y values then decrease to 118The x values increase

This is only possible in a quadratic function

Hence, the type of function that best models the data in the table is the quadratic function

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ST
6
9
10
Which phrase best describes the translation from the graph y = 2x² to the graph of y = 2x² + 5?
O 5 units up
O 5 units down
O 5 units right
O 5 units left

Answers

The answer to the question is 5 units up.

Chris wants to create a rectangular rose garden in a yard. he has 40 meters of fencing to go around the garden and he has to use it all. pick two ways he could construct the garden

Answers

Answer:

4x10 8x5

Step-by-step explanation:

Answer
1st way = 8W x 12L
2nd way = 6W x 14L
Reason
Using W as width and L length
We know Perimeter is 2w + 2L
1st way
8m width x 12m length =
2(8) + 2(12) =
16 + 24 = 40
2nd way
6m width x 14 length
2(6) + 2(14)=
12 + 28 = 40

how to round to 4 decimal places using calculator with the given number of tan 30

Answers

Answer:

0.5774

Step-by-step explanation:

1) Input tan(30) into a calculator to get 0.5773502692...

2) To count 4 decimal places, we start after the decimal point. This means that we end it at the first 3. Additionally, we round 3 up to 4 because of the digit after it which is 5.

[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]

What is the tangent of 30, rounded to 4 decimal places?

.

[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]

First, let's focus on this phrase - "tan 30"

.

What in the world could that possibly mean?

"tan" is the tangent, which is one of the six trig ratios.

.

The simplest way to find the tangent of 30 degrees is ... with a calculator!

[tex]\bf tan\quad 30 \approx 0.5774[/tex]

The answer has been rounded to 4 decimal places, like you asked.

Since the fifth decimal place was more than 5, I added 1 to the fourth decimal place - 0.5774, and not 0.5773.

[tex]\rule{300}{1.7}[/tex]

[tex]\bf tan 30\approx 0.5574. \quad Hope\;you\;will\;have\;a\;fantabulous\;day![/tex]

~ [tex]\boxed{\bf aesthetic\;\not{101}}[/tex]~

What is the range of the given data set?

Answers

Answer:

6

Step-by-step explanation:

21 - 15 = 6

if each interior angle of a regular polygon measures 180° how many sides does it have

Answers

Answer:

This is impossible.

Step-by-step explanation:

The interior angle of a regular polygon is equal to

[tex] \frac{180(n - 2)}{n} [/tex]

where n is the number of sides.

Setting this equal to 180°,

[tex] \frac{180(n - 2)}{n} = 180 \\ \\ \frac{n - 2}{n} = 1 \\ \\ n = n - 2 \\ \\ 0 = - 2[/tex]

which is false.

The pieces of a puzzle are placed half by Giulio, one fifth by Marco and Fabrizio in equal parts, while Michele arranges on the 90 pieces of the frame. how many pieces does Marco place?

Answers

The number of pieces that Marco places is given as follows:

30 pieces.

How to obtain the number of pieces that Marco places?

The number of pieces that Marco places is obtained applying the proportions in the context of the problem.

The fractions of each person are given as follows:

Giulio: 1/2.Marco and Fabricio: 1/5.

Hence the fraction composed by these three people is given as follows:

1/2 + 1/5 = (5 + 2)/10 = 7/10 = 0.7.

Hence Michele's fraction is given as follows:

1 - 0.7 = 0.3.

As Michele arranges 90 pieces, the total number of pieces is given as follows:

0.3x = 90

x = 90/0.3

x = 300.

Marco arranged one tenth, hence the number is:

0.1 x 300 = 30.

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Which expression has a value of 16 when n = 5?
StartFraction 25 Over n EndFraction + 7
30 minus 3 n
7 + StartFraction 45 Over n EndFraction
n cubed minus 114

Answers

An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is C.

What is an Expression?

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

To solve the problem substitute the value of n as 5 in each expression and then simplify to check if it equals to 16 or not.

A.) (25/n) + 7

      = (25/5) + 7

      = 12

This is not the required expression.

B.) 30 - 3n

      = 30 - 3(5)

      = 15

This is not the required expression.

C.) 7+ (45/n)

       = 7 + (45/5)

       = 7 + 9

       = 16

This is the required expression.

D.) n² - 114

       = (5)³ - 114

       = 125 - 114

       = 11

This is not the required expression.

Hence, the correct option is C.

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Which of the following equations have exactly one solution?
Choose all answers that apply:

Answers

the equations that will have only one solution are:

19x - 18 = -19x + 18  (option c)19x + 18 = -19x + 18  (option d)

When we have only one solution?

An equation of the form:

a*x + b = c*x + d

Has one solution only if a ≠ c.

With that in mind, we can see that the equations that will have only one solution are:

19x - 18 = -19x + 18  (option c)

19x + 18 = -19x + 18  (option d)

In the other two cases, the slopes of the linear equations are equal, so these equations have no solutions or infinite solutions.

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HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
write and solve a proportion to complete the statement. Round to the nearest hundredth if necessary.
1. 6km ≈ ?mi
2. 2.5 L≈ ?gal
3. 90lb ≈ ?kg
pls help

Answers

Using proportion, the equivalent units of the following units rounded to the nearest hundredth are as follows:

6km =  3.73 miles2.5 Litres = 0.66 gallons90 pounds = 40.82 kg

How to use proportion to find equivalent units?

Using proportion,

1.60934 km = 1 miles

6 km = ?

cross multiply

distance(m) = 6 / 1.60934 = 3.7282364199 = 3.73 miles

1 litre = 0.264172 gallons

2.5 litres = ?

volume(gallons) = 2.5 × 0.264172 = 0.66 gallons

1 pounds = 0.453592 kg

90 pounds  = ?

cross multiply

weight(kg) = 40.82328 = 40.82 kg

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convert the following numbers into scientific notation
3,400=
0.000023=
4.50=
1,000,000=
0.00671=

Answers

The Scientific notation of given numbers are  [tex]3400=3.4 \times 10^{-3}[/tex], [tex]0.000023=2.3 \times 10^{5}[/tex], 4.50, [tex]1,000,000=1 \times 10^{6}[/tex] and [tex]0.00671=6.71 \times 10^{-3}[/tex].

The given numbers are 3400, 0.000023, 4.50, 1,000,000 and 0.00671.

What is scientific notation?

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.

Now, [tex]3400=3.4 \times 10^{-3}[/tex], [tex]0.000023=2.3 \times 10^{5}[/tex], 4.50, [tex]1,000,000=1 \times 10^{6}[/tex] and [tex]0.00671=6.71 \times 10^{-3}[/tex].

Therefore, the Scientific notation of given numbers are  [tex]3400=3.4 \times 10^{-3}[/tex], [tex]0.000023=2.3 \times 10^{5}[/tex], 4.50, [tex]1,000,000=1 \times 10^{6}[/tex] and [tex]0.00671=6.71 \times 10^{-3}[/tex].

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Find the expected value of the winnings
from a game that has the following
payout probability distribution:
Payout ($) 2
4 6 8 10
Probability 0.5 0.2 0.15 0.1 0.05
Expected Value = [?]
Round to the nearest hundredth.
Enter

Answers

The expected value of the winnings from the game is $4

How to determine the expected value?

The payout probability distribution is given as:

Payout ($) 2 4 6 8 10

Probability 0.5 0.2 0.15 0.1 0.05

The expected value is then calculated as:

[tex]E(x) = \sum x * P(x)[/tex]

This gives

E(x) = 2 * 0.5 + 4 * 0.2 + 6 * 0.15 + 8 * 0.1 + 10 * 0.05

Evaluate the expression

E(x) = 4

Hence, the expected value of the winnings from the game is $4

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Write the next 3 numbers in each sequence.

Answers

Answer:

The next 3 numbers will be 1 3/4, 2, and 2 1/4

Step-by-step explanation:

The numbers in the sequence are increase by 1/4. So to find the next number in the sequence and 1/4 to the previous number. Don't foget to simplify your answers. Ex.) Rather than saying 2 2/4 you would say 2 1/2.

TIME REMAINING
57:11
Solve the equation for a.

K = 4a + 9ab

a = K(4 + 9b)
a = 4(K + 9b)
a = a equals StartFraction 4 plus 9 b Over K EndFraction equals h.
a = a equals StartFraction K Over 4 plus 9 b EndFraction equals h.

Answers

An equation is formed of two equal expressions. The given equation can be solved for 'a' as a = K/(4+9b). Thus, the correct option is D.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The given equation, K = 4a + 9ab can be solved for a as shown below,

K = 4a + 9ab

K = a(4+9b)

a = K/(4+9b)

Hence, the given equation can be solved for 'a' as a = K/(4+9b). Thus, the correct option is D.

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Convert the following common fractions to decimals. Round to three decimal places if necessary. You may use a
calculator. 3/4

1. 0.75
2. 3.4
3. 0.34
4. 7.5

Answers

1. 3/4
2.3 2/5
3. 34/100
4. 7 1/2

A charity bingo game costs $2 per round and has a $13 entry fee for an adult. It costs $3 per round and a $10 entry fee for a child. For how many rounds of bingo are the costs the same for an adult and a child?.

Answers

The number of rounds of bingo when the two costs would be the same is 3.

When would the two costs be the same?

The equation that represents the total cost for adults is : 13 +2r

The equation that represents the total cost for children: 10 + 3r

where r is the number of rounds

When the two costs are the same, the two above equations would be equal: 13 + 2r = 10 + 3r

13 - 10 = 3r - 2r

r = 3

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