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Mandarinka [93]
3 years ago
14

which equation represents a line that passes through (4,1/3) and has a slope of 3/4? A. Y-3/4=1/3 (x-4) B. Y-1/3=3/4 (x-4) C. Y-

1/3=4 (x-3/4) D. Y-4=3/4 (x-1=3)
Mathematics
2 answers:
Zolol [24]3 years ago
7 0
First you need to understand the slope-intercept form y = mx +b m = the slope of the lineb = the y-axis intercept y and x represent the coordinates of a point on the line So for the equation that you listed we know that the slope, m , is (3/4).  We also know a given point on the line.  therefore we also have a y value (1/3) and a x value (4). So plug in the numbers: (1/3)=(3/4)*4 + b So to find the equation of this line we must solve for b Multiply (3/4) and 4 to get 3 (1/3) = 3 + b Now subtract 3 from both sides in order to isolate b -2 2/3 = b or -8/3 = b Now rewrite the equation with the y-intercept, b. y = (3/4)x - (8/3) From the wording I am assuming you are given a list of equations to chose from.  It is possible that the some of all of the equations are listed in standard form.  In that case, we need to find the equation: Ax + By = C To do that we simply take the slope intercept equation and manipulate it algebraically   y = (3/4)x - (8/3)  First subtract (3/4)x from both sides -(3/4)x + y = -(8/3)  This is technically standard form but we can clean it up a bit by multiplying both sides of the                                          equation by -4. So -4 * -(3/4)x = 3x     -4 *y = -4y    -4 *-(8/3) = 32/3 So 3x - 4y = 32/3 I hope this helps 
omeli [17]3 years ago
3 0
Passes through (4, 1/3) and has a slope of 3/4

y-y₁=m(x-x₁)

Plug everything in :)

y - 1/3 = 3/4(x - 4)

B) y - 1/3 = 3/4(x - 4)

~Hope I helped!~
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Write a rule in function notation for each situation:
algol [13]

Answer:

1. \bold{S=f(P) = 0.07P}

2. x = 16

3. Part 1: P is the independent variable and S is the dependent variable.

Part 2: x is the independent variable and y is the dependent variable.

Step-by-step explanation:

1. To write the function notation for:

Sales tax is 7% of the total price.

Let the total price be P.

And sales tax be S.

As per the given statement:

S = 7\% \ of\ P\\\Rightarrow S =\dfrac{7}{100}P\\\Rightarrow S=0.07P

Writing it in the function notation:

\bold{S=f(P) = 0.07P}

2. To find the value of x such that f(x) = 14 and

f(x) = \dfrac{1}4x + 10

Putting the value of f(x) = 14

14 = \dfrac{1}4x + 10\\\Rightarrow \dfrac{1}4x =14-10\\\Rightarrow \dfrac{1}4x =4\\\Rightarrow x =4\times 4\\\Rightarrow \bold{x =16}

3. To find the dependent and independent variable.

Independent variables are those whose value is not dependent on the other variable's values.

Dependent variables are dependent on the value of other variables.

In question 1:

\bold{S=f(P) = 0.07P}

P is the independent variable.

S is the dependent variable.

In question 2:

If we write it as follows:

y=f(x) = \dfrac{1}4x + 10

x is the independent variable and y is the dependent variable.

5 0
3 years ago
What are the x- and y- intercepts of the graph of 9x-3y = 18?
sineoko [7]

Step-by-step explanation:

9x - 3y = 18

Solve for y:

1. 3y= 9x + 18

2. y= 3x + 6 (This is the equation you will graph)  

To graph:  

Make a table for y = 3x +6.

If x =0, y=6

If x =1, y=9

If x =-1, y=3

You could get as many points as you like, however you need at least TWO, to be able to draw the line.

3 0
2 years ago
Write2.1 as a mixed number and as an improper fraction.<br> Do not try to simplify your answers.
Elden [556K]

Answer:

2 1/10 and 21/10

Step-by-step explanation:

2.1 is 2 + 0.1 when expanded.

2 is just 2 and then 0.1 as a fraction is 1/10. The mixed number would be                 2 1/10.

The improper fraction  is just 21/10 (convert the mixed number into improper form).

Converting from mixed number to improper: <u>Multiply the number in the front (in this case 2) by the denominator. </u>

<u />

<u>That is 2 x 10 which is 20. Then add that number (20) to the numerator. 20 + 1 is equal to 21. </u>

<u />

<u>21 would be our numerator and the denominator would stay the same (10). </u>

21/10 is the improper form.

8 0
2 years ago
Caroline is making some table decorations.
eduard

Answer:

there are 8 candles

Step-by-step explanation:

(i) In order to obtain an equal amount of candle to candle holders Caroline has to buy enough packs to obtain a 1:1 ratio.  

Therefore to obtain a 1:1 ratio:

=30 candles/18 candle holders * (18/30)

Therefore she needs to buy 18 packs of candles and 30 packs of candle holders to have exactly the same number of candles and holders

(ii) Caroline can make = 30*18 = 540 table decorations  

Click to let others know, how helpful is it

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3 years ago
Find the value of x.<br> (3x+20) º<br> 12°
PolarNik [594]

Answer:

x=32°

Step-by-step explanation:

2x+3x+20=180 co interior angle

5x=180-20

x=160/5=32°

7 0
2 years ago
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