Write the equation of the line that passes through points A(6,1) and B(9,4)? simple answers

Given:

The equation of a line is:

[tex]y=-\dfrac{5}{7}x+2[/tex]

A line passes through the point (-5,-3) and perpendicular to the given line.

To find:

The equation of the line.

Solution:

Slope intercept form of a line is:

[tex]y=mx+b[/tex]                 ...(i)

Where, m is the slope and b is the y-intercept.

We have,

[tex]y=-\dfrac{5}{7}x+2[/tex]          ...(ii)

On comparing (i) and (ii), we get

[tex]m=-\dfrac{5}{7}[/tex]

We know that the product of slopes of two perpendicular lines is always -1.

[tex]m_1\times m_2=-1[/tex]

[tex]-\dfrac{5}{7}\times m_2=-1[/tex]

[tex]m_2=\dfrac{7}{5}[/tex]

Slope of the required line is [tex]\dfrac{7}{5}[/tex] and it passes through the point (-5,-3). So, the equation of the line is:

[tex]y-y_1=m_2(x-x_1)[/tex]

[tex]y-(-3)=\dfrac{7}{5}(x-(-5))[/tex]

[tex]y+3=\dfrac{7}{5}(x+5)[/tex]

Using distributive property, we get

[tex]y+3=\dfrac{7}{5}(x)+\dfrac{7}{5}(5)[/tex]

[tex]y+3=\dfrac{7}{5}x+7[/tex]

[tex]y=\dfrac{7}{5}x+7-3[/tex]

[tex]y=\dfrac{7}{5}x+4[/tex]

Therefore, the equation of the line is [tex]y=\dfrac{7}{5}x+4[/tex]. Hence, option A is correct.

Answer:

x = 4/5 is the one x value that is not permitted.  The domain of (fog)(x) is

(-infinity, 4/5) ∪ (4/5, infinity)

Step-by-step explanation:

(fog)(x) is the "composition" of f and g.  We start with f(x) and replace x with g(x), which is 5x - 4:

              3

f(x) = x - ------- becomes

               x

                                          3            

f(5x - 4) =     [5x - 4]  -  ------------

                                      [5x - 4]

To identify the domain, consider the value or values of x for which the denominator shown above is zero:  5x - 4 = 0, or 5x = 4, or x = 4/5

The domain of the composite function (f·g)(x) in interval notation is (-∞,0)∪(0,∞).

The domain and range are defined for a relation and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively.

The given functions are f(x)= x-3/x and g(X)=5x-4.

Now, (f·g)(x)=f(x)×g(x)

= (x-3/x)(5x-4)

(f·g)(x)= 5x²-15-4x+12/x

Find the domain by finding where the expression is defined.

Interval Notation: (-∞,0)∪(0,∞)

Set-Builder Notation:{x|x≠0}

Therefore, the domain of the composite function (f·g)(x) in interval notation is (-∞,0)∪(0,∞).

To learn more about the domain and range visit:

brainly.com/question/28135761.

#SPJ7

Answer:

47 ft

Step-by-step explanation:

3.14 x 15

Answer:

Two line are perpendicular when they are at right angles to each other.

The red line is perpendicular to the blue line in each of these examples:

Perpendicular Example

Step-by-step ex;planation:

The graph is a function. When drawing a vertical line, there will be two circumstances:

For the first circumstance, the graph that has only one intersect with a line - it is a function. For the second circumstance, the graph cannot be a function as it gives more than one y-value for a single x-value.

The conclusion is that if a line only has one intersect on a graph then it is a function. Otherwise, not a function but a relation instead. All functions are relations, but not all relations can be functions.

Answer

Answer:

Value of p is 3

Step-by-step explanation:

One of the root is 1.

So, putting 1 in the place of x in the given equation,

px²-4x+3p-8=0

or, p-4+3p-8=0

or, 4p-12=0

or, 4p=12

or, p=3

Answered by GAUTHMATH

Answer:

I think it is of the last option

Answer:

15×5 =75

Step-by-step explanation:

1 inch reprsnt 5

Answer:

[tex]x\le \:-1[/tex]

Step-by-step explanation:

[tex]3\left(x-1\right)\le \frac{1}{2}\left(x+1\right)-6[/tex]

[tex]3x-3\le \:-\frac{11}{2}+\frac{1}{2}x[/tex]

[tex]3x\le \:-\frac{5}{2}+\frac{1}{2}x\\[/tex]

[tex]\frac{5}{2}x\le \:-\frac{5}{2}[/tex]

[tex]5x\le \:-5[/tex]

[tex]x\le \:-1[/tex]

x = -1

3(-2) ≤ ½(0) - 6

-6 ≤ 0 - 6

-6 ≤ -6

This is true.

x = -2

3(-3) ≤ ½(-1) - 6

-9 ≤ -½ - 6

-9 ≤ [tex]-\frac{13}{2}[/tex]

This is also true.

Therefore, x ≤ -1.

Answer:

Step-by-step explanation:

Compound ratio is the multiplication of the ratios:

Multiply to get:

Given ratios,

2/15 : 3/7 and 5/8 : 14/27

Then to find the compound ratio,

We have to multiply,

→ (2/15 × 5/8) : (3/7 × 14/27)

→ 10/120 : 42/189

Now simplify the ratio,

→ 1/12 : 2/9

Thus, required ratio is 1/12 : 2/9.

Answer:

can you make it a bit clear to understan?

Answer:

We reach at 8.

Step-by-step explanation:

The starting point is 2 .

Jump at the six places, the final point reaches at 8, so the point is 8.

Answer:

Step-by-step explanation:

We could use the Law of Sines if we only knew what angle A was. It just so happens that by the Triangle Angle-Sum Theorem, angle A is equal to

180 - B - C. Therefore,

angle A = 180 - 11 - 75 so

angle A = 94. And the Law of Sines is

[tex]\frac{sin94}{a}=\frac{sin11}{600}[/tex] and cross multiply to get

600sin94 = asin11 and solve for a:

[tex]a=\frac{600sin94}{sin11}[/tex] gives you that

a = 3136.85

Answer:

who is the captain of the football team

Step-by-step explanation:

i might be wrong i havent taken a class that neads this, but all the others need a bunch of values from a group of people. this is just asking who someone is

15. 70° because a right angle is 90° and we have the angle of ADB which is 20°. So 90°-20°=70°.

16. 70° because angle PSQ is 60° and angle QSR is 10°. So 60°+10°=70°.

17. 55° because it says it in the explanation. I assume this is a typo and they meant to ask the measurement of ADC and in that case it would be 130° because angle ADB is 75° and angle BDC is 55°. 75°+55°=130°.

18. 40° because angle PSQ is a right angle which means it's 90°. So 130°-90°=40°.

19. 140° because angle ADB is 120° and angle BDC is 20° so 120°+20°=140°.

20. 125° because again it's in the explanation. But if it's a typo and they meant what is the measurement of PSQ then it is 50° because PSR is 125° and QSR is 75° so 125°-75°=50°.

Hope this helps! :)

There are 6 numbers on the cube.

The probability of getting a 3 would be 1 out of 6, 1/6

The probability of getting heads on a coin toss is 1/2

The probability of getting both a 3 and a head = 1/6 x 1/2 = 1/12

Answer: 1/12

Answer:

d

Step-by-step explanation:

its the correct answer

Hope this helps:)

Answer:

yes

because the descent of the ball is 32m per second

Step-by-step explanation:

To determine if the relationship is proportional, determine the descent of the ball per second

after 2 seconds = 64 / 2 = 32

after3 seconds = 96/3 = 32

after 4 seconds = 128 / 4 = 32

the relationship is proportional

Answer:

2 whole pieces

5/24 feet left

Step-by-step explanation:

divide 5/6 by 5/16 = 2 2/3 pieces

so there are 2 whole pieces and 2/3 small piece.

The 2/3 small short equals to 5/16 x 2/3 = 5/24 ft

Answer:

f(x) = -3x

Step-by-step explanation:

f(x) = -3x

Answer:

x = 4/3

Step-by-step explanation:

[tex]\frac{4}{3x} + \frac{5}{4} = \frac{3}{x}[/tex]

take lcm of the denominator

lcm = 12x

[tex]\frac{4*4 +5*3x}{12x} = \frac{3}{x}[/tex]

[tex]\frac{16+15x}{12x} = \frac{3}{x}[/tex]

do cross multiplication

x(16 + 15x) = 3*12x

16x + 15x^2 = 36x

15x^2 = 36x - 16x

15x^2 = 20x

x^2 = 20x /15

x*x = 4x/3

x = 4x/3/x

x = 4x/3 *1/x

x = 4x/3x

x = 4/3

Answer:

(0.5,3)

Step-by-step explanation:

Hi there!

We are given a line that has the endpoints of (5,9) and (-4,-3); we need to find the midpoint of the line.

The midpoint formula is given as ([tex]\frac{x_{1}+x_{2} }{2}[/tex], [tex]\frac{y_{1}+y_{2}}{2}[/tex]), where [tex]x_{1}[/tex], [tex]x_{2}[/tex], [tex]y_{1}[/tex], and [tex]y_{2}[/tex] are values of coordinate points

to avoid any confusion, we can label the values of the coordinates and then substitute them into the formula to find the midpoint

[tex]x_{1}[/tex]=5

[tex]y_{1}[/tex]=9

[tex]x_{2}[/tex]=-4

[tex]y_{2}[/tex]=-3

now substitute into the formula

so to find the value x in the midpoint, we'll use this part of the formula: [tex]\frac{x_{1}+x_{2} }{2}[/tex]

substitute 5 and -4 into the formula

[tex]\frac{5+-4}{2}[/tex]

do the addition on the numerator

[tex]\frac{1}{2}[/tex] or 0.5

now let's find the value of y in the midpoint. we'll use this part of the formula: [tex]\frac{y_{1}+y_{2}}{2}[/tex]

substitute 9 and -3 into the formula

[tex]\frac{9+-3}{2}[/tex]

do the addition on the numerator

[tex]\frac{6}{2}[/tex] or 3

Therefore the midpoint is (0.5,3)

Hope this helps! :)

Answer:

108.56

Step-by-step explanation:

First find the amount of the tip

92 * 18%

92 * .18

16.56

Add this to the amount of the bill

92+16.56

108.56

Answer:

108.56

Step-by-step explanation:

92$ + .18*92 = 108.56$

Answer:

(y ^2 ) (x ^2)

Step-by-step explanation:

Answer:

So, the difference is 44874.

Step-by-step explanation:

Multiplication of 4986 by 45

= 4986 x 45 = 224370

Multiplication of 4986 by 54

= 4986 x 54 = 269244

So, the difference in results is

= 269244 - 224370 = 44874

Answer:

D

Step-by-step explanation:

there is zero chance of it happening