find the equation of the straight line passing through 4,1 with a gradient of 1

Answers

Answer 1

Answer:

y = x - 3

Step-by-step explanation:

If the gradient (slope) of the line is m, then the point-slope form of the appropriate equation  is y - k = m(x - h).  If the gradient is 1, then

                                         y - k =   x - h

Since this line passes through (4, 1), we have

                                          y - 1 = x - 4, or

                                            y = x - 3


Related Questions

After studying the growing population of a certain species of fish, Dr. Goldthwait has determined that the population will grow
in such a way that the population each year will be 27 less than the square of the previous year's population. If he introduces
this species of fish to a new environment by placing a population of 15 fish, and the population grows according to his results
which of the following recursive formulas can be used to determine the number of fish that will be in the environment in the
future? Assume that the space for the population to grow is unlimited.
OA
NEXT = Now2 - 27 starting at 15
OB. NEXT = (NOW + 27) starting at 15
OC. NEXT = now? + 27 starting at 15
OD. NEXT =
(NOW - 27) starting at 15

Answers

Answer:

OB. NEXT

Step-by-step explanation:

Please help with this question

Answers

Answer:

ans is g=x^3+1

x=(-2-1,0,1,2,3)

again put the value of x

therefore g(x)=(-7,0,1,2,9,28)

Evaluate the function.
f(x) = -x^2 + 6
Find f(-3)

Answers

Answer:

-3

Step-by-step explanation:

You plug the value of -3 into where the x is {-(-3)^2} + 6, resulting in -3.

If f(x) = \XI + 9 and g(x) = -6, which describes the range of (f + g)(x)?
O (f + g)(x) > 3 for all values of x
O (f + g)(x) < 3 for all values of x
O (f + g)(x) < 6 for all values of x
O (f + g)(x) > 6 for all values of x

Answers

Answer:

the first option

Step-by-step explanation:

well, 9 +(-6) = 3

so the equations last part is changed, but the rest stays the same

The  range of (f + g)(x) is (f + g)(x) > 3 for all values of x.

What is a function?

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Gives are two function, f(x) = |XI + 9 and g(x) = -6, we need to find the range of (f + g)(x),

f(x)=|x|+9 and g(x)= -6

Taking the sum of the functions:

f(x) + g(x) = |x|+9  + (-6)

f(x) + g(x) =  |x|+9 - 6

f(x) + g(x) =   |x|+3

Due to the modulus of x which is positive,

Hence (f + g)(x) is greater to 3 for all values of x

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Amit and Aman have a water tank of 44 litres. Amit uses 3/4 part of the water in water
tank and Aman yses 1/4 part of the water and out the quantity of water used by
both also find who is using much water than other and by how much. (3)​

Answers

Answer:

i dont know

Step-by-step explanation:

7th-grade students decided to start fundraising money by selling raffle tickets. The administration promised to contribute $2 extra for each raffle ticket sold. The 7th graders sold 223 tickets and raised a total of $1,115. Write an equation to represent this situation. Remember to define your variable.

Answers

Answer:

Let x be the price of a raffle ticket

(x+2)*223 = 1115

x=3

Step-by-step explanation:

Let x be the price of a raffle ticket

The amount they get is now x+2 since the admin is donating 2 dollars per ticket

The sold 223 tickets

(x+2) *223 = amount raised

(x+2)*223 = 1115

Divide each side by 223

x+2 = 1115/223

x+2 = 5

Subtract 2 from each side

x+2-2 =5-2

x=3

Problem:

7th-grade students decided to start fundraising money by selling raffle tickets. The administration promised to contribute $2 extra for each raffle ticket sold.

The 7th graders sold 223 tickets and raised a total of $1,115. Write an equation to represent this situation. Remember to define your variable.Using variable x:

Let x is equal to,

• (x + 2) 223 = 1,115

Let's Solve it!

[tex] \quad \quad \quad \quad \tt{(x + 2) 223 = 1,115}[/tex]

[tex]\quad \quad \quad \quad \tt{ \huge x + 2 = \frac{1,115}{223} }[/tex]

[tex]\quad \quad \quad \quad \huge\tt{ x + 2 = 5 }[/tex]

Covert the 2 like this:

[tex]\quad \quad \quad \quad \huge\tt{ x = 5 - 2}[/tex]

[tex]\quad \quad \quad \quad\huge \tt{ x = 3 }[/tex]

Hence, the answer is:

[tex]\quad \quad \quad \quad \boxed{ \huge \tt{ \color{green} x = 3 }}[/tex]

_________

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Consider the probability model that allows you to determine probability that there will be X number of successes out of n trials; when the outcomes from each trial (each defined as either a success or a failure), are independent, and subject to the same probability of success from one trial to the next. How will the coefficient of variation for this model change

Answers

Answer:

The probability of number of success = C (n,k)p^kq^(n-k)

Step-by-step explanation:

This is the case of Bernoulli's experiment in which there are n independent trials with X number of success

The probability of number of success = C (n,k)p^kq^(n-k)

Where k = 0,1,2,3...n

Jane and Sophia went to the corner store where packages of gum cost 54¢ each and candy bars cost 88¢ each. They spent $26.38 total and bought 35 items total. How many candy bars did they buy?

Answers

Answer:

22

Step-by-step explanation:

number of gum = x

number of candy bar = y

0.54x + 0.88y = 26.38

x + y = 35

         0.54x + 0.88y = 26.38

(+)      -0.54x - 0.54y = -18.9

-----------------------------------------

                       0.34y = 7.48

y = 7.48/0.34

y = 22

Answer: 22

The number of the gum is 13 and the number of the candy will be 22.

What is linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Jane and Sophia went to the corner store where packages of gum cost 54¢ each and candy bars cost 88¢ each.

They spent $26.38 total and bought 35 items total.

Let x be the number of the gum and y be the number of the candy.

Then the equation will be

x + y = 35 ...1

0.54x + 0.88y = 26.38 ...2

By solving the equations 1 and 2, then we have

x = 13 and y = 22

Then the number of the gum is 13 and the number of the candy will be 22.

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A gas station sold 300.5849 gallons of gas in a day. How many
gallons of gas did the gas station sell, rounded to the nearest
hundredth?

Answers

Answer:

30058.49

Step-by-step explanation:

b/c when u multiply it in hundredth u can get your answer

Frank earned f dollars mowing lawns. Bryce's earnings, b, were $15.25 less than 3.5 times as
much as Frank's earnings. Which of the following equations best represents this situation?
A. b = 3.5f + 15.25
B. f= 3.5b - 15.25
C. b = 3.5f-15.25
D. f = 3.5b + 15.25

Answers

it’s D. f = 3.5b + 15.25

25 divided by 94,056

Answers

Answer:

0.00026579909 is what 25 divided by 94,056 equals

HELP ME FOR 30 POINTS!!
Determine the equation of the circle graphed below.

Answers

Answer:

(x-7)²+y²=9

Step-by-step explanation:

There is a formula used for the equation of a circle:

(x-h)²+(y-k)² = r²

(h, k) is the center of the circle

r is the radius

In this case, (h, k) is (7, 0)

Plug in the values for h and k

∴ (x-7)²+(y-0)²=3² which can be simplified to (x-7)²+y²=9 (No need to expand the brackets)

What is the solution to this equation?
X+ 7 = -8
O A. x= 15
O B. x= 1
O c. x = -15
O D. x= -1

Answers

C. x = -15

Explanation:
Replace x with -15 to check ur answer
-15 + 7 = -8
THIS EQUATION IS TRUE.

Mark me brainliest ty!

Maham has a number of apples. She could share my apples equally among 3, 4, or 5 people. What is the smallest number of apples Maham could have?

Answers

Answer:  60

The value 60 is the LCM of 3, 4 and 5.

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

Explanation:

LCM = lowest common multiple

To find the LCM, we list out the prime factorization of each number

3 = 3*14 = 2*25 = 5*1

Ignoring the factors of 1, we have the unique primes of 2, 3, 5. There are 2 copies of '2', one copy of '3', and one copy of '5'. So we multiply this out to get 2*2*3*5 = 4*15 = 60

----------

If she had 60 apples, and wanted to give them to 3 friends, then each friend gets 60/3 = 20 apples

If instead, she had 4 friends, then each friend gets 60/4 = 15 apples.

Or if she had 5 friends, then each friend gets 60/5 = 12 apples.

For any of those three cases, there are no leftovers or remainders.

Any multiple of 60 will work (eg: 120 or 180), but 60 is the smallest such number that allows her to divide the apples this way without any leftovers.

Answer:

60

Step-by-step explanation:

60 / 3 = 15

60 / 4 = 20

60 / 5 = 12

They all divide evenly.

Which line intersects the parabola y = x^2 + 6x – 2 at two points?
A.y = 6x – 4
B.y = 6x – 3
C.y = 6x – 2
D.y = 6x – 1

Answers

Answer:

C

Step-by-step explanation:

U fisrt find the y intercept where x=0 and deferentiate to find gradient

What is the difference of the polynomials?

(8r6s3 – 9r5s4 + 3r4s5) – (2r4s5 – 5r3s6 – 4r5s4)

6r6s3 – 4r5s4 + 7r4s5
6r6s3 – 13r5s4 – r4s5
8r6s3 – 5r5s4 + r4s5 + 5r3s6
8r6s3 – 13r5s4 + r4s5 – 5r3s6

Answers

Answer:

8r6s3 – 13r5s4 + r4s5 – 5r3s6 it is D

D

Step-by-step explanation:

The value of the difference of the polynomials is,

⇒ 8r⁶s³ - 13r⁵s⁴ + r⁴s⁵ - 5r³s⁶

What is mean by Subtraction?

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

The expression is,

⇒ (8r⁶s³ – 9r⁵s⁴ + 3r⁴s⁵) – (2r⁴s⁵ – 5r³s⁶ – 4r⁵s⁴)

Now, We can find the difference as;

⇒ (8r⁶s³ – 9r⁵s⁴ + 3r⁴s⁵) – (2r⁴s⁵ – 5r³s⁶ – 4r⁵s⁴)

⇒ (8r⁶s³ – 9r⁵s⁴ – 4r⁵s⁴ + 3r⁴s⁵ – 2r⁴s⁵ – 5r³s⁶

⇒ 8r⁶s³ - 13r⁵s⁴ + r⁴s⁵ - 5r³s⁶

Thus, The value of the difference of the polynomials is,

⇒ 8r⁶s³ - 13r⁵s⁴ + r⁴s⁵ - 5r³s⁶

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At age 25, you invest $1,500 that earns 8 percent each year. How much money will you have at age 65? $_____ (no comma) 32586.78 b. At age 40 you invest $1,500 that earns 11 percent per year. How much money will you have at age 65? $______ (no comma) 20378.20 In which case (a or b) would you have more money at age 65? Why?

Answers

Answer:

The Money Invested At age 25 earns more because it earns more Interest As compare to The Money Invested At age 40.

Step-by-step explanation:

According To the Question,

Given, A Person Invested $1,500 at Age of 25, With an 8% Per Annum Interest Rate.

Thus, The Money He will have at age of 65 would be, [tex]$1,500 * (1.08)^{40}[/tex] = 32586.78$ . Here The Interest Earn in 40 Year Is 31086.78$.

And, the Same Person Invested $1,500 at Age of 40, With an 11% Per Annum Interest rate.

Thus, The Money He will have at age of 65 would be, [tex]$1,500 * (1.11)^{25}[/tex] = $20378.20 . Here The Interest Earn in 25 Years Is 18878.20$.

⇒ Now, it is understood that the same amount invested for different periods of time & with a different interest rate, Since The Amount who get more Interest Would earn More. hence, The Money Invested At age 25 earns more because it earns more Interest As compare to The Money Invested At age 40.

Find the aspect ratio of a computer screen that measures 12 inches by 16 inches.

Answers

Answer:

3:4

Step-by-step explanation:

That ratio would be 12:16, or 3:4.

The aspect ratio of a computer screen will be 4: 3.

What are ratio and proportion?

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

The computer screen measures 12 inches by 16 inches.

Then the aspect ratio will be given by the number 16 inches divided by 12 inches.

We know that the aspect ratio will be greater than 1. Then the aspect ratio will be

Aspect ratio = 16 / 9

Aspect ratio = 4/3

Aspect ratio = 4: 3

The aspect ratio of a computer screen will be 4: 3.

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anyone know the answer to this??

Answers

Answer: Choice A) 8/3

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

Explanation:

Use the slope formula to find the slope of the given line through those two points (-3, 4) and (5, 1)

m = (y2-y1)/(x2-x1)

m = (1 - 4)/(5 - (-3) )

m = (1-4)/(5+3)

m = -3/8

The line shown has a slope of -3/8

----------

We do two things from here:

flip the fractionflip the sign

That will have -3/8 turn into +8/3 or simply 8/3 which is the perpendicular slope. That's why the answer is choice A.

Multiplying the original slope -3/8 with the perpendicular slope 8/3 will lead to -1. This is true of any perpendicular pair of lines, as long as neither line is vertical.

Can y’all help me with this ASAP please?

Answers

Answer:

x + 3

5

Explanation:

x+3 is the equation for the first line to the left, and f(x)=5 is the second equation for the second line at the top.

2(1/3x)(2/5y)
i cant solve this one can anyone help me I am stuck over here

Answers

Answer:

4/15xy

step-by-step explanation:

2(1/3x) (2/5y)

= 2/3x × (2/5)y

= 2×2

xy

3×5

= 4/15xy

Hope this answer helps you :)

Have a great day

Mark brainliest

Answer:

4/15xy

Step-by-step explanation:

2(1/3x) (2/5y)

= 2/3x × (2/5)y

= 2×2

xy

3×5

= 4/15xy

Find the area of PQRS. (Hint: Use the Pythagorean Theorem to find the height .)

Answers

Height = sqrt(5^2 - 4^2) = sqrt(9) = 3

Area = length x height
Area = 8 x 3 = 24m^2

Factorise the following
c) x2 – 3x + 2​

Answers

Answer:

(x−1)(x−2)

Step-by-step explanation:

En el autoservicio del barrio reciben al proveedor de gaseosas cada 8 dias,al de lacteos cada 3 dias y al de galletitas cada 12 dias . El 5 de abril fueron los 3. A¿Cuantos dias pasaran para qie se encuentren nuevamente?

Answers

Respuesta:

24 días

Explicación paso a paso:

Para calcular el día en que se volverán a reunir después del 5 de abril; tomamos el mínimo común múltiplo de la cantidad de días de cada visita:

Por lo tanto, tomamos el mínimo común múltiplo de 8, 3 y 12.

Múltiple de:

8: 8, 16, 24, 32, 40, 48

3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

12:12, 24, 36, 48, 60

El mínimo común múltiplo es 24;

Todos se volverán a encontrar después de 24 días.

5 de abril + 24 días = 29 de abril

how do you determine the second deriviative of x^3-7x^2+36​

Answers

Answer:

6x -14

Step-by-step explanation:

x^3-7x^2+36​

Take the first derivative

3x^2 -14x

Now take the derivative again

6x -14

Answer:

6x - 14

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Calculus

Derivatives

Derivative Notation

Basic Power Rule:

f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

Identify

f(x) = x³ - 7x² + 36

Step 2: Differentiate

Basic Power Rule:                                                                                             f'(x) = 3x³⁻¹ - 2 · 7x²⁻¹ + 0Simplify:                                                                                                             f'(x) = 3x² - 14xBasic Power Rule:                                                                                             f''(x) = 2 · 3x²⁻¹ - 1 · 14x¹⁻¹Simplify:                                                                                                              f''(x) = 6x - 14

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

1] Angelo used 425 centimeters of ribbon to trim banners he made. How many meters of ribbon did he use? ***HINT: 1 meter = 100 centimeters*** *

Answers

Answer:

4.25 meters

Step-by-step explanation:

425/100 = 4.25

or move the decimal to the left 2 places. One place for each zero in 100.

3) How could Tyler have made a more specific request for 2 sides and an angle so that his triangle was guaranteed to match Jada's?

Answers

Answer:

His specific request will be any of the following:

A triangle of side lengths 4 and 5, with a measure of 143 degrees between themA triangle of side lengths 5 and 8.5, with a measure of 16 degrees between themA triangle of side lengths 8.5 and 4, with a measure of 21 degrees between them

Step-by-step explanation:

Given

See attachment for complete question

Required

Specific information to match Jada's request

From the attachment, we have the following:

Triangle 1: Jada's request

Triangle 2: The triangle made by Tyler

The two triangles are not congruent because:

The side lengths do not correspond

How did we know this?

On Jada's triangle, the longest side is 8.5

On the triangle, Tyler made; the longest side is 5 and does have a corresponding ratio to Jada's triangle

Having said this; this is what Jada needs to do;

He needs to make his request based on any of the following postulate

[tex]SSS \to Side\ Side\ Side[/tex]

[tex]SAS \to Side\ Angle\ Side[/tex]

[tex]ASA \to Angle\ Side\ Angle[/tex]

However, the best postulate to use in this regard is:

[tex]SAS \to Side\ Angle\ Side[/tex]

So, his specific request will be any of the following:

A triangle of side lengths 4 and 5, with a measure of 143 degrees between themA triangle of side lengths 5 and 8.5, with a measure of 16 degrees between themA triangle of side lengths 8.5 and 4, with a measure of 21 degrees between them

Use the graph that shows the solution to
f(x) = g(x).
f(x) = 1+2x/x=
g(x) = 2+x
What is the solution to f(x) = g(x)?
Select each correct answer.

Answers

Answer:

The solution for f(x) = g(x) are;

x = 1 and x = -1

Step-by-step explanation:

The given equations for the functions, g(x) are;

[tex]f(x) = \dfrac{1 + 2\cdot x}{x}[/tex]

g(x) = 2 + x

The solution for f(x) = g(x), is given by equating the equations of the two functions as follows;

When f(x) = g(x), we have;

[tex]\dfrac{1 + 2\cdot x}{x} = 2 + x[/tex]

By cross multiplication, we have;

1 + 2·x = x × (2 + x) = 2·x + x²

∴ x² + 2·x - 2·x - 1 = 0

x² - 1 = 0

(x - 1)·(x + 1) = 0

x = 1, or x = -1

f(x) = g(x) = 2 + 1 = 3, or 2 - 1 = 1

Therefore, the solution for f(x) = g(x) are;

f(x) = g(x) = 3 or 1 where x = 1 and x = -1.

Answer: a , b

Step-by-step explanation:

Write the following as an inequality.
2 is less than w, and 7 is greater than or equal to w
Use w only once in your inequality.

Answers

Answer:

2 > w ≤ 7

Step-by-step explanation:

Find the length of AB pls and thank you

Answers

Answer:

x=4

AB=19

Step-by-step explanation:

in such a parallelogram the length of AD must be equal to the length of BC.

=>

18x = 17x + 4

x = 4

AB = 4x + 3 = 4×4 + 3 = 19

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