Find the equation of the line that is parallel
to the line y = 3x + 9 and passes
through the point (2,1) Write the
equation in slope-intercept form.

Answers

Answer 1

Answer:

y = 3x - 5

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 )

y = 3x + 9 ← is in slope- intercept form

with slope m = 3

Parallel lines have equal slopes, then

y = 3x + c ← is the partial equation

To find c substitute (2, 1) into the partial equation

1 = 6 + c ⇒ c = 1 - 6 = - 5

y = 3x - 5 ← equation of parallel line


Related Questions

From an 80ft building the angle of elevation of the top of a taller building is 59 degrees and the angle of depression of the base of this building is 65 degrees determine the height of the taller building

Answers

Answer:

First we find the distance between the two buildings =

Step-by-step explanation:

[tex] \frac{80}{ \tan(65) } = 37.3 ft[/tex]

then the upper part of the taller building =

[tex]37.3 \times \tan(59) = 62 \: ft[/tex]

Now the total height of the taller building

[tex]80 + 62 = 142 \: ft[/tex]

Five consecutive multiples of 7 have a sum of 350. What is the smallest of these numbers?
A. 70
B. 56
C. 77
D. 84

Answers

Answer:

B. 56

Step-by-step explanation:

x + (x + 7 ) + ( x + 14 ) + ( x + 21 ) + ( x + 28 ) = 350

( x + x + x + x + x ) + ( 7 + 14 + 21 + 28 ) = 350

5x + 70 = 350

     - 70    - 70

_____________

5x = 280

x = 56

Hope this helps!

The smallest number is 56, the correct option is B.

What is Sum?

The sum is the output of the mathematical operation, Addition.

Let the first number is x, they are multiples of 7,

As they are multiples of 7, the consecutive numbers will be added by 7 for next term.

The 5 consecutive numbers can be written as x, (x+7), (x+14), (x+21), (x+28).

The equation can be formed for the numbers that are given as,

An equation is a mathematical statement that relates an algebraic expression with other expression by an equal sign.

The sum of the multiples is 350

x + (x + 7 ) + ( x + 14 ) + ( x + 21 ) + ( x + 28 ) = 350

Grouping the variables and the constants separately

( x + x + x + x + x ) + ( 7 + 14 + 21 + 28 ) = 350

5x + 70 = 350

Adding (-70) to both sides of the equation

5x = 280

Dividing both sides by 5

x = 56

The value of the first number of the series is obtained.

The first value is the smallest number of the series.

To know more about Sum

https://brainly.com/question/13013054

#SPJ2

Please help !!!!!!!!!!!

Answers

Answer:

98°+62°+6x = 180

160+6x = 180

6x = 180 - 160

6x = 20

x= 20/6

x= 3.33

therefor your answer is 3.33

Jeanette ice cream shop sold 10 sundaes with nuts and 7 sundaes without nuts to the total number of sundaes

Answers

The answer to the question is 17
There are 10 sundaes with nuts, and 7 without nuts. Our task is to find the total number of sundaes. We can find this by adding 10 + 7. This gives us 17 sundaes.

PLzzZZHELPPPP


The angle between the top of a building and a point 80 feet away from the base (on level ground) is 70° . To the nearest foot, how tall is the building?

Answers

Answer:

220ft tall

Step-by-step explanation:

From the question we are given the following:

Adjacent side of the triangle = 80feet

Angle of elevation = 70°

Required

Height of the building (Opposite)

Using the SOH CAH TOA identity:

tan theta = opp/adj

tan 70 = H/80

H = 80tan70

H = 80(2.7474)

H = 219.79ft

Hence the building is 220ft tall

A train travels a distance of 60 km at uniform speed. If the speed of the train was reduced by 10 kmh-1, the time taken to travel the 60km will increase by 1/2h. Find the speed of the train at the beginning.

Answers

Answer:

Initial speed is 32 m/s

At uniform speed, acceleration is 0, (a = 0).

When speed reduced, (v - u) = 2.78 ms-¹, t = 1800 sec, s = 60 ,000 metres.

From first equation of motion:

[tex]{ \boxed{ \bf{v = u + at}}} \\ { \tt{(v - u) = at}}[/tex]

substitute:

[tex]{ \tt{2.78 = (a \times 1800)}} \\ { \tt{acceleration = 0.0015 \: {ms}^{ - 2} }}[/tex]

from second equation of motion:

[tex]{ \boxed{ \bf{s = ut + \frac{1}{2} a {t}^{2} }}}[/tex]

substitute:

[tex]{ \tt{60000 = 1800u + ( \frac{1}{2} \times 0.0015 \times {1800}^{2}) }} \\ { \tt{1800u = 57570}} \\ { \tt{u = 32 \: m {s}^{ - 1} }}[/tex]

Will mark brainlest helppppppp​

Answers

Answer:

6

Step-by-step explanation:

again ?

7 = (3x - 4)/2

14 = 3x - 4

18 = 3x

x = 6

y is inversely proportional to V1+x.
When x = 8, y = 2.
Find y when x = 15.

Answers

Answer:

y = 1.5

Step-by-step explanation:

Given x is inversely proportional to [tex]\sqrt{1+x}[/tex] , then the equation relating them is

y = [tex]\frac{k}{\sqrt{1+x} }[/tex] ← k is the constant of proportion

To find k use the condition when x = 8, y = 2

2 = [tex]\frac{k}{\sqrt{1+8} }[/tex] = [tex]\frac{k}{\sqrt{9} }[/tex] = [tex]\frac{k}{3}[/tex] ( multiply both sides by 3 )

6 = k

y = [tex]\frac{6}{\sqrt{1+x} }[/tex] ← equation of proportion

When x = 15 , then

y = [tex]\frac{6}{\sqrt{1+15} }[/tex] = [tex]\frac{6}{\sqrt{16} }[/tex] = [tex]\frac{6}{4}[/tex] = [tex]\frac{3}{2}[/tex] = 1.5

help me with the picture please

Answers

Answer:  115

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

Explanation:

Refer to the diagram below. I've drawn diagonal that slopes upward. This diagonal cuts the quadrilateral into two triangles: One is equilateral and the other is isosceles.

The equilateral triangle marked in blue has all three angles 60 degrees each.

Note that the 60 and y angles combined to form 130, so,

60+y = 130

y = 130-60

y = 70

Then focus on the isosceles triangle (angles y, w and w). These three interior angles must add to 180

y+w+w = 180

70+2w = 180

2w = 180-70

2w = 110

w = 110/2

w = 55

This adds onto its adjacent neighbor of 60 to get w+60 = 55+60 = 115 degrees which is the value of x.

if line y bisects line AC, AB = 4 - 5x, and BC = 2x+25, find AC

Answers

Answer:

4-5x = 2x+25

-5x+4 = 2x+25

-7x = 21

x = -3

4 - 5(-3)

4 + 15

19

AC = 2 x 19

AC = 38

Let me know if this helps!

Math models helpppp plss if you know about math models answer this pls

Answers

Answer:

A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences and engineering disciplines, as well as in non-physical systems such as the social sciences.

How do I solve part c

Answers

Answer:

A possible answer could be 2√2. It depends where points B and C would be. I guess this information was given in the parts A and B.

Step-by-step explanation:

See picture attached

Nina is making pink candles to use as decorations on Valentine's Day. She melts red and white wax together and pours them into a heart-shaped mould. Then, she melts double the amount of red wax and double the amount of white wax together and pours them into a flower-shaped mould. Which candle is a lighter shade of pink?

Answers

Answer:

answer is neither, they are both the same shade.

Step-by-step explanation:

if she doubled the colors exactly then it wouldn't be any different. Also IXL told me I'm right :)

Answer:

Neither.

Step-by-step explanation:

Originally, she used the same amount. For the second one, she used double the same amount, but it was still the amount of red wax as of white wax. So, they both had the same amount, which means it is neither.

To wash a window that is 4 meters off the ground, Rafi leans a 5-meter ladder against the side of the building. To reach the window, how far away from the building should Rafi place the base of the ladder?

Answers

Answer:

Base of the ladder is 3 meters away from the building.

Step-by-step explanation:

Let's use Pythagoras theorem to solve.

Pythagoras theorem says,

[tex]a^{2} +b^{2} =c^{2}[/tex]

Here let horizontal distance is "a''

Vertical distance of window is 4 m

So, b=4

The Rafi leans 5 m ladder against the wall. So, c=5.

[tex]a^{2} +4^{2} =5^{2}[/tex]

Simplify it

[tex]a^{2} +16=25[/tex]

Subtract both sides 16

[tex]a^{2} =9[/tex]

Take square root on both sides

a=±3

So, base of the ladder is 3 meters away from the building.

write an equation for a line that is perpendicular to 2x - 4y = 10

Answers

Answer:

5

The correct answer is Y= - __

4

A small bird can flap its wings 120 times in 30 s. What is the rate of change of wing flaps?

Answers

Answer:

4 Flaps per second

Step-by-step explanation:

M = 120/30

Answer:

4 times per second

Step-by-step explanation:

120 ÷ 30 = 4

30 ÷ 30 = 1

4 flaps per 1 second

so basically 4

To win the annual read-a-thon at his school, Scott has to read more books than any of his classmates over winter break. He starts by reading a lot of sports books. Then, he reads 10 mystery books. In all, Scott reads 23 books for the read-a-thon.

Answers

Answer:

13 sports books and 10 unknown books is 23 books

Step-by-step explanation:

we already know scott read 23 books total, we also know that he read 10 mystery books.

subtracting 10 unknown books from 23 total books, we get 13 sports books as your answer

find the lcm of 10a²b,15ab²c and 20bc²​

Answers

Answer:

jsjuuusjus??dujj??uu?jw?wuw?jjdj

Step-by-step explanation:

e

q

iwsj

l

What is the value of the expression 3y−z
y+5z
when y = 6 and z = 2?

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{Question \#1}[/tex]

[tex]\huge\textsf{3y - z}[/tex]

[tex]\huge\textsf{= 3(6) - 2}[/tex]

[tex]\huge\textsf{= 18 - 2}[/tex]

[tex]\huge\textsf{= 16}[/tex]

[tex]\boxed{\boxed{\huge\textsf{Answer: 16}}}\huge\checkmark[/tex]

[tex]\huge\text{Question \#2}[/tex]

[tex]\huge\textsf{y + 5z}[/tex]

[tex]\huge\textsf{= 6 + 5(2)}[/tex]

[tex]\huge\textsf{= 6 + 10}[/tex]

[tex]\huge\textsf{= 16}[/tex]

[tex]\boxed{\boxed{\huge\textsf{Answer: 16}}}\huge\checkmark[/tex]

[tex]\huge\textsf{\boxed{\star\underline{\underline{16 = 16}}\star}\star}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

hi, please solve these three questions for me, i have to shoe solving steps.​

Answers

question 3

Step-by-step explanation:

i only able to show you the step of question 3..so sorry

I NEED HELP WITH THIS QUESTION ASAP ITS REALLY REALLY URGENT!!!!


Two kids, Albert and Bhara, are 20.0 m apart. Albert sees a soccer ball 25.0 m away. If the angle between the line formed by Albert and Bhara and the line from Albert to the soccer ball is 25 degrees, how far is Bhara from the soccer ball? Correctly round your answer to the nearest tenth of a meter.

Answers

Step-by-step explanation:

I can give you a formula SOH-Sinø=Opposite\Hypotenuse

CAH-Cos=Adjacent\Hypotenuse

TOA-Tan=Opposite\Adjacent

Write the equation in slope-intercept form. y = 6(x + 2) + 5x

Answers

Answer:

y=11x+12

Step-by-step explanation:

y = 6(x + 2) + 5x

y=6x+12+5x

y=11x+12

in slope interception form=  y=mx+c

                                                y=11x+12

Y=11x + 12 my brother

Which inequality is represented by the graph?

Answers

Answer:

It will be -5≤×≤4

help please I'm doing some math homework ​

Answers

Answer:

Slope is 5/2

Step-by-step explanation:

[tex]{ \boxed{ \bf{slope = \frac{y _{2} - y _{1} }{x _{2} - x _{1}} }}}[/tex]

Substitute the terms:

[tex]{ \tt{slope = \frac{7 - ( - 3)}{4 - 0} }} \\ = \frac{5}{2} [/tex]

I suck at math ik but i need anyones help please

Answers

Answer:

f(2)= 1

f-¹(1)= 2

f-¹(f(2))= 2

I hope I helped you^_^

Please help explanation if possible

Answers

Answer:

Step-by-step explanation:

Subtract 3x from both sides

3x - 3x - 2y = -3x + y

Combine

-2y = - 3x + 7  

Divide by - 2

-2y/-2 = -3x/-2 + 7/-2

y = 3x/2 - 7/2

(PICTURE) Im really struggling with questions like these at the moment, if you could please help me out thank you

Answers

Answer:

Arthur should select the Mount Joy Pool when there are less than 10 people at the party

Step-by-step explanation:

The initial fee to rent the Woodbridge Pool = $50

The additional fee per person after renting = $5

The initial fee to rent at Mount Joy Pool = 0 (no initial fee)

The fee per person at Mount Joy Pool = $10

The equation of a straight line is y = m·x + c

Ley y  represent the total cost of renting the pool, x, represent the number of persons in the pool, m represent the fee per person and c represent the initial charges, we get;

The total cost of renting Woodbridge Pool, y = 5·x + 50

The total cost of renting the Joy Pool, y = 10·x

Equating both values of y gives;

5·x + 50 = 10·x

∴ 5·x = 50

x = 50/5 = 10

x = 10

From the above equations, the cost of renting the pool is lower for the Joy Pool when there are less than 10 persons at the pool

It will cost the same amount to rent the pool when the number of persons in the pool are 10 persons and the cost of renting the Mount Joy Pool  will be more than the cost of renting the Woodbridge Pool, when there are more than 10 persons

Therefore, Arthur should select the Mount Joy Pool when there are less than 10 people at the party.

A bus has velocity 20m/s towards east and another bus has velocity 15m/s in West direction.If they start to move from a point simultaneously.What distances do they covered in 2 minutes.​

Answers

Answer:

4,200 m or 4.2 km.

First bus: 2400 m

2nd bus: 1800 m.

Step-by-step explanation:

Their combines speed is 20+15 = 35m/s.

Distance = speed * time

2 minutes = 120 seconds so

D = 35 * 120

= 4200 m.

Splitting the distances:

The first bus covers 20 * 120 = 2400m

The second bus covers 15*120 = 1800m.

Answer:

4200m

Step-by-step explanation:

If two objects A and B are moving in the opposite direction with speed xm/s and ym/s respectively,then;

Relative speed =(x+y)m/s

: Relative speed = 20+15=35m/s

time =2min=160sec

DISTANCE=SPEED ×TIME

D=35×120=4200

4200m

A 60 foot monument casts a 25-foot shadow How long is the shadow of a 4.5 tall person?
A) 1.875 feet (it’s this one)
B) 5.555 feet
C) 2456 feet
D) 13334 feet

Answers

Answer:

A

Step-by-step explanation:

Using similarities we have

(Actual size)/(Shadow length)=60/25=4.5/x

x=4.5*25/60=1.875

Answer:

A) 1.875 feet

Step-by-step explanation:

What is the number when 4is subtracted from the Sum of 4 and 7 multiplied by one-fourth of 20?



Answers

Answer:

one fourth of 20 = 5

(4+7)-4*5

11-4*5

11-20

-9

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