Mathematics High School

Find the equation of the linear function represented by the table below in slope-intercept form.

Answers

Answer 1

Answer:

y = x + 2

Step-by-step explanation:

Use any two points.

For example, let's use (-3, -1) and (1, 3).

First, we find the slope.

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

We have slope = m = 1.

Now we use the equation:

y = mx + b

We plug in the slope we found above.

y = 1x + b

y = x + b

Now we use one of the given points to find b.

We'll use point (1, 3).

3 = 1 + b

b = 2

Now that we know m and b, we write the equation:

y = x + 2

Related Questions

Part A: Without calculating the values, compare the expressions using <, >, or =.
Write the correct symbol. Draw a model if it helps you.
(5+15)x13
31×(15+5)
The difference between 15 fours and
6 fours.
The sum of 4 fours and 5
fours
Part B: Explain how you compared the expressions without calculating.

Answers

The amount of cookies baked was 28 cookies

Solution for how many cookies your mother bake altogether

let the number of pumpkin cookies be x

half of them on a plate for your brother and you

= x - x/2 = x/2

Your dog Gobbles ate six

= x/2 - 6

Your brother ate half of what was left

= (x/2 - 6)) / 2

= x/4 - 3

you ate the last four means that what was left is equal to 4

x/4 - 3 = 4

x - 12 = 16

x = 16 + 12

x = 28

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In the diagram below of triangle
F
G
H
FGH,
I
I is the midpoint of
F
H
‾
FH
and
J
J is the midpoint of
G
H
‾
GH
. If m
∠
H
F
G
=
57
−
6
x
∠HFG=57−6x, and m
∠
H
I
J
=
−
4
x
+
49
∠HIJ=−4x+49, what is the measure of
∠
H
I
J
∠HIJ

Answers

Applying the corresponding angles theorem, the measure of ∠HIJ = 33°.

What is the Corresponding Angles Theorem?

If two triangles are similar to each other, their corresponding angles would be equal. Also, based on the corresponding angles theorem, corresponding angles are equal to each other.

Triangles IHJ and FGH are similar to each other, therefore, angles HFG and HIJ are corresponding angles.

Therefore:

The measure of angle HFG = the measure of angle HIJ

m∠HFG = 57 − 6x

m∠HIJ = −4x + 49

Thus:

57 − 6x = -4x + 49

Combine like terms

4x - 6x = -57 + 49

-2x = -8

Divide both sides by -2

-2x/-2 = -8/-2

x = 4

m∠HIJ = −4x + 49 = -4(4) + 49

m∠HIJ = 33°

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Complete Question:

In the diagram below of triangle FGH, I is the midpoint of FH and J is the midpoint of GH. If m∠HFG = 57 − 6x, and m∠HIJ = −4x + 49, what is the measure of ∠HIJ?

suppose weights of the checked baggage of airline passengers follow a nearly normal distribution with mean 45 pounds and standard deviation 3.2 pounds. most airlines charge a fee for baggage that weigh in excess of 50 pounds. determine what percent of airline passengers incur this fee.

Answers

In most of the cases airlines charges a fees for baggage weigh in excess of 50 pounds. Then about 94.06% passengers incur this fees.

When the distribution is normal, we use the z-score formula.

In a set with mean and standard deviation , the z-score of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Given That,

Mean (μ) = 45 pounds and Standard Deviation (σ) = 3.2

This means that μ = 46 , σ = 3.2

Since, Most airlines charges a fee for baggage that weigh in excess of 50 pound.

Then, As a proportion this is 1 subtracted by the P - value of Z when

X =50. So,

Z = X - μ / σ

⇒ Z = 50 -45/ 3.2

⇒ Z = 5/3.2

⇒ Z = 1.56

when Z = 1.56 has a P- value of 0.9406

Now, 0.9406 × 100%

= 94.06%

Therefor, 94.06% of airline passengers incur this fees.

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What is the answer to 4r - 9r - 11r + 7r

Answers

Answer:

-11r

Step-by-step explanation:

4r - 9r = -5r

-5r - 11r = -16r

-16r + 7r = -11r

4r - 9r - 11r + 7r
= (+4r - 9r) - 11r + 7r
= (-5r) - 11r + 7r
= (-5r - 11r) + 7r
= (-15r) + 7r
= (-15r + 7r)
= -8r

PLEASE HELP, QUESTION IN THE PICTURE

Answers

Step-by-step explanation:

AC is the combination of AB and BC.

so, AB + BC = AC

(2n - 1) + (4n + 5) = 10n - 12

2n - 1 + 4n + 5 = 10n - 12

6n + 4 = 10n - 12

4 = 4n - 12

16 = 4n

n = 4

What is the answer to this question

Answers

Answer:

soda: 97

Hot dogs: 56

Step-by-step explanation:

S-sodas

H- hot dogs

S+H=153

41+H=S

Substitute equation

(41+H)+H=153

41+2H=153

-41. -41

2H=112

/2. /2
H=56

S+56=153

-56. -56

S=97

Hopes this helps please mark brainliest

: in a random sample of 20 people, what is the probability that 2 are 65 years or older, 5 are 55-64 years old, 6 are 25-54 years old, 4 are 15-24 years old and 3 are 0-14 years old?

Answers

the probability that 2 are 65 years or older, 5 are 55-64 years old, 6 are 25-54 years old, 4 are 15-24 years old and 3 are 0-14 years old IS 0.24243

the complete question is:

The demographic profile of Ecuador in 2018 is • 27.08% of the population are 0–14 years old • 18.35% are 15–24 years old • 39.59 are 25–54 years old • 7.53% are 55–64 years old • 7.45% are 65 years and older. In a random sample of 20 people, what is the probability that 2 are 65 years or older, 5 are 55–64 years old, 6 are 25–54 years old, 4 are 15–24 years old and 3 are 0–14 years old?

answer:

P(x) = P(x=2) + P(x=5) +p(x=6) +p(x=4) +p(x=3)

=20[tex]C_{2}[/tex][tex](7.45)^{2}[/tex][tex](2.55)^{18}[/tex]+20[tex]C_{5}[/tex][tex](7.53)^{5}[/tex][tex](2.47)^{15}[/tex]+20[tex]C_{6}[/tex][tex](39.59)^{6}[/tex][tex](0.41)^{14}[/tex]+20[tex]C_{4}[/tex][tex](18.35)^{4}[/tex][tex](1.65)^{16}[/tex]+20[tex]C_{3}[/tex][tex](27.08)^{3}[/tex][tex](2.92)^{17}[/tex]

P(x) = 0.2424

the probability that 2 are 65 years or older, 5 are 55-64 years old, 6 are 25-54 years old, 4 are 15-24 years old and 3 are 0-14 years old IS 0.24243

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if a farm has 30 chickens and cows and there are 82 chicken and cows legs all together then how many chickens and how many cows could the farm have?

Answers

Answer: 11 cows and 19 chickens

Step-by-step explanation:

The farm could have 5 cows and 32 chickens

Does the function y=x have an inverse? If so does it pass the horizontal line test?

Answers

Yes, y=x has an inverse.

Yes, y=x passes the horizontal line test.

If it didn't pass the horizontal line test, it would not have an inverse.

polynomial function

Answers

Answer: (2x+1)(x−3) ( 2 x + 1 ) ( x - 3 )

Step-by-step explanation:

To write a polynomial in standard form, simplify and then arrange the terms in descending order. Expand (2x+1)(x−3) ( 2 x + 1 ) ( x - 3 ) using the FOIL Method.

A cubic polynomial function f has a leading coefficient of 2 and a constant term of -5. When f(1) is zero and f(2) is three what is f(-5). Explain?

Answers

The value of f(-5) = -130

A cubic equation is an equation with degree three. All cubic equations have either one real root and two imaginary roots or three real roots. When polynomials have degree three, they are referred to as cubic polynomials.

A Cubic polynomial function is a polynomial function with the highest degree of exponents as 3. A cubic polynomial function has the following standard form:

Ax3 + bx2 + cx +d = 0

For the given question the cubic equation will be:

2x3 + bx2 + cx - 5 = 0

Given

Leading coefficient (a) = 2

Constant (T) = -5

f(1) = 0

f(2) = 9

Therefore the equation formed will be:

2x3 + bx2 + cx - 5 = 0

Now f(1) = 0

2(1)3 + b(1)2 + c(1) - 5 = 0

2 + b + c -5 = 0

b + c = 3

b = 3-c -----(1)

On solving f(2) = 3

2(2)3 + b(2)2 + c(2) - 5 =3

16 + 4b + 2c – 5 =3

4b +2c = 3 – 11

4b + 2c = -8 ----(2)

Now substitute the b value in equation (2)

4(3-c) + 2c = -8

12 – 4c +2c = -8

-2c = -20

C =10

Now substitute the c value in equation (1)

b= 3 – c

b = 3 -10

b = -7

Now substitute the b and c values in the cubic equation

2x3 - 7x2 + 10x - 5 = 0

Now calculate f(-5)

2(-5)3 - 7(-5)2 + 10(-5) - 5

= -250 + 175 – 50 -5

= -130

Therefore the value of f(-5) = -130

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Please help F(-1/2)=1 and f(0)=-4

Answers

Question:

Write a linear function f with f (- 1/2) = 1 and f (0) = -4

The linear function f with f (- 1/2) = 1 and f (0) = -4 would be ; y = -5x -4.

What is a linear equation?

A linear equation is an equation in which each term has at max one degree. Linear equations in variables x and y can be written in the form

y = mx + c

Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.

We are asked to write the linear function f with f (- 1/2) = 1 and f (0) = -4

Let the equation in variables x and y can be written in the form y = mx + c

So f (- 1/2) = 1

this gives, 1 = -1/2m+c -----------eq 1

Also f (0) = -4

This gives -4 = c. --------------eq2

Now Putting the value of c in the equation in eq1 we get m=0.

So 1 = -1/2m+c

1 = -1/2m - 4

m = -5

Then we get;

y = -5x -4.

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what's the slope of 6x+13y= -18

Answers

Answer:

slope is the coefficient of x

so it is 6

good luck!!

sarah gets pocket money every week from the age of 5 until her 21st birthday and is given a choice of 2 options options .
option 1:get the same number of pounds each week as her age.
option 2 : get 5 pounds a week aged 5 and increasing by 15% a year.
which option should Sara choose ?

please help

Answers

The option that Sarah should choose is option 2.

Which option should Sarah choose?

Sarah would choose the option that give her the higher amount of money at her 21st birthday.

The amount that Sarah would earn each year with option 1 would increase at a linear rate. This is because she gets the same amount of money each year.

The form of a linear equation is y = mx + b

Where:

m = slope b = intercept

The amount that Sarah would earn each year with option 2 would increase at an exponential rate.

The general form of exponential equation is f(x) = [tex]e^{x}[/tex]

Where:

x = the variable e = constant

The rate of growth with an exponential function is faster than that of a linear function. It is for this reason that option 2 is the better option.

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A family buys a studio apartment for 150,000. They pay a down payment of $22,500. a.Their down payment is what percent of the purchase price?
b. What percent of the purchase price would a $60,000 down payment be?
please help!!!

Answers

a. The down payment is 15% of the
purchased price
b. A $60,000 down payment would be 40%
of the purchase price

Help please
I need this by tomorrow

Answers

Answer:

I hope this will help. Tip: reuse the formula!

algebra 2 please help :)!

Answers

the answer to your question is D

find the middle side of each triangle. round your answers to the nearest tenth if necessary.

Answers

Step-by-step explanation:

using Pythagoras theorem.

37,

x² = 6² + 8²

x = √6²+8² = 10ft

38.

13²=12²+x²

169 = 144 + x²

√169 - 144 = x = 5cm

hope it helps. :)

Answer:

x = 10 and x = 5

Step-by-step explanation:

using Pythagoras' identity

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

(36)

x² = 6² + 8² = 36 + 64 = 100 ( take square root of both sides )

x = [tex]\sqrt{100}[/tex] = 10

(38)

13² = x² + 12²

169 = x² + 144 ( subtract 144 from both sides )

25 = x² ( take square root of both sides )

[tex]\sqrt{25}[/tex] = 5 = x

x = 5

Which of the following represents the series?

–12 + (–5) + 2 + 9 + 16

sum from k equals 0 to 4 of negative 19 plus 7 times k
sum from k equals 1 to 5 of negative 19 minus 7 times k
sum from k equals 0 to 4 of negative 12 plus 7 times k
sum from k equals 1 to 5 of negative 12 minus 7 times k

(image includes proper visuals for each option)

Answers

The expression that represents the sum of the arithmetic series that has a first term of -12, a common difference of +7 and a number of terms of 5 is the option with the following;

[tex]\sum\limits_{k = 0}^4-12+7\cdot k[/tex]

What is an arithmetic series?

An arithmetic series one that consists of the sum of an arithmetic sequence, such that each term of the series is obtained from the previous term by the addition or subtraction of a constant.

The series in the question is; -12 + (-5) + 2 + 9 + 16

Each term in the series is obtained from the previous term by the addition of a 7

The series in therefore a series of an arithmetic sequence

The equation of the series when the first term is -12 can therefore be presented as follows;

-12 + 7·k

Where;

-12 is the first term, 7 is the common difference, n is the number of terms, and k = n - 1

When n = 1, k = 0, which gives;When k = 0, the expression, -12 + 7·k = -12 + 7 × 0 = -12When k = 1, -12 + 7·k = -12 + 7 × 1 = -5When k = 2, -12 + 7·k = -12 + 7 × 2 = 2When k = 3, -12 + 7·k = -12 + 7 × 3 = 9When k = 4, -12 + 7·k = -12 + 7 × 4 = 16

The above values for the terms of the series is obtained by using values of k that range from k = 0 to k = 4

The expression that represents the series is therefore the option;

[tex]\sum\limits_{k = 0}^4-12+7\cdot k[/tex]

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You have $18 and earn $0.25 for each cup of orange juice you sell. Write an equation that represents the total amount A (in dollars) you have after selling j cups of orange juice.

Answers

Answer:

A = 0.25*j + 1

Step-by-step explanation:

Answer:

[tex]A = 18 + \frac{j}{4}[/tex]

Step-by-step explanation:

A = 18 + j/4

A = Amount in $

Starting amount is 18 and a 1/4 dollar is earned for every cup of juice sold.

HWLP ASPP PLEASE SHOW UR WORK

Answers

Answer: 1. 3

5. -3

Step-by-step explanation:

I hope this helps. !!

which of the following fractions is smaller 4/9 or 1/5

Answers

Answer:

1/5

Step-by-step explanation:

these fractions are proper fractions

Answer: 1/

Step-by-step explanation:

If a gallon of paint costs $18 and covers 180 ft²,
how much does it cost to paint a 900 ft² wall

Answers

Okay with this problem you just divide 900/180 to figure out how many gallons of paint are needed and then multiply it by $18
900/180=5
5•$18=$90
So the answer is $90

Answer:

$90

Step-by-step explanation:

180x5 equal 00

$18x5 equals $90

Image is the equation

Answers

Answer:

y = [tex]\frac{3}{4}[/tex] x + 8

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 )

here m = [tex]\frac{3}{4}[/tex] , then

y = [tex]\frac{3}{4}[/tex] x + c ← is the partial equation

to find c substitute (- 4, 5 ) into the partial equation

5 = - 3 + c ⇒ c = 5 + 3 = 8

y = [tex]\frac{3}{4}[/tex] x + 8 ← equation of line

Wyatt says that both red lines are lines of symmetry. Is he correct? Why or why not?

Answers

Answer:

Step-by-step explanation:

There is only one line of symmetry:

because the one that is vertical is not representing symmetry.

Find the surface area and volume of each triangular prism (base is a right triangle).
triangle legs are 3 ft and 4 ft, hypotenuse is 5 ft, height of prism is 8 ft

Answers

The surface area of a triangular prism = 108cm2

The volume of the triangular prism = 48cm3

The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area.

Given that

The Triangle legs are 3 and 4 feet long, the hypotenuse is 5 feet long, and the prism height is 8 feet tall.

We have to determine the surface area and volume of each triangular prism

here a = 3ft b = 4ft c = 5ft and height h = 8ft

Surface area of triangular prism = ab + h(a+b+c)

= 3x4 + 8(3+4+5)

= 12 + 8(12)

= 12 + 96

= 108cm2

Volume of triangular prism = ½(abh)

= ½ (3x4x8)

=1/2(96)

= 96/2

= 48cm3

Therefore

The surface area of a triangular prism = 108cm2

The volume of the triangular prism = 48cm3

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what is the vertex of -2x^2 +12x -10

Answers

The vertex of the function f(x) = x^2 + 12x is (-6, -36).

How can the vertex be expressed?

The concept that will be used here is the concept of Standard equation of a curve in vertex form.

The standard equation can be written as

f (x) = ax^2 + bx + c

Then the Vertex is the (h,k)

Then the X-coordinate of the vertex can be written as (h = -b/2a) where k = f(h)

If we compare the given equation with the standard form, then we have

a = 1, b = 12 and c = -10

Then we can input the values into the (h = -b/2a)

h =[ -12/2(1)] = - 6

Then we can substitute the value of h in f (x) which is f(x) = x2 + 12x

k = f(h)= f (-6) =[ (-6)2 + 12 (-6)]

= [36 - 72] = -36

In conclusion the vertex is (-6, -36).

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the 6th term of an arithmetic progreion i 35 and the 13th term i 77. find the 20th term

Answers

The 20th term of the given arithmetic progression is 119.

What is arithmetic progression?

An arithmetic progression is a set of integers with a fixed difference between any two succeeding numbers (A.P.).

3,6,9,12,15,18, and 21 are A.P. examples.

So, the formula for the nth term:

a+(n-1)d, where d is the common difference

Now, take out the equation:

6th term = 35

a+(6-1)d= 35

a+5d=35 ....(1)

13th term = 77

a+12d= 77 .....(2)

Then, subtract equation (1) from equation (2):

a+12d-(a+5d)= 77-35

a+12d-a-5d= 42

7d=42

d=6

Calculate from equation (1):

a= 35-5d= 35-5(6)= 35-30 = 5

20th term= a+19d= 5+19(6)= 119

Therefore, the 20th term of the given arithmetic progression is 119.

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the united nations stores data about the kilowatt-hours of wind power produced around the world. the following data set gives information of the united states for 25 years, from 1990 to 2014, in units of million kilowatt-hours. using a calculator or statistical software, find the linear equation of the first 11 years of data, from 1990 to 2000. round the slope to two decimal places and the y-intercept to the nearest whole number. provide your answer below:

Answers

The value that the linear equation predicts for the year 2001 is 4652.15

The discrepancy between the actual and anticipated value is 2173.85

Given data;

Here, we present the dataset from the United Nations, which contains information on the number of kilowatt-hours of wind energy generated globally. The data set provides statistics on the US for 25 years, from 1990 to 2014, in millions of kilowatt-hours.

The linear equation for the first 11 years of data, from 1990 to 2000, must be determined.

To determine how much the actual value and anticipated value for the year 2001 differ in Quantity, we must first forecast the value for the year 2001 using our fitted equation with y-intercept.

It will be written as y = m(x) + c.

where,

The dependent variable is y. (in our example is quantity)

The independent variable is x. (in our example is the year)

'm' is equal to the slope of the variable X.

'C' is a constant.

The fitted equation is provided as follows:

Quantity = 186.87 (year) - 369274.72

Now that the value for the year 2001 has been provided,

Quantity = -1868.87 -369274.72

Quantity = 4652.15

The value that the linear equation predicts for the year 2001 is 4652.15.

The precise figure for 2001 is 6806.

For the year 2001, the discrepancy between the actual and anticipated values is

6806 - 4652.15 = 2173.85

The distinction is 2173.85.

(2173.85/6806)*100 is the percentage difference.

As a result, the difference between the actual value and the forecasted value for the year 2001 is 31.94%.

Hence,

The value that the linear equation predicts for the year 2001 is 4652.15

The discrepancy between the actual and anticipated value is 2173.85

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i really need help. Strawberries cost $2.13 per pound and Annie purchased 1.2 pounds. How much did she pay for strawberries if her answer is rounded to the nearest cent?

Answers

Annie paid a total of $2.6 for 1.2 pounds of strawberries

How to determine the amount paid?

In this question, we have the following parameters:

Unit cost per pound = $2.13 per pound

Number of pounds = 1.2 pounds

The amount paid for the number of pounds is represented by the equation

Amount paid = Unit cost per pound x Number of pounds

Substitute the known values in the above equation So, we have the following equation

Amount paid = 2.13 * 1.2

Evaluate the products

Amount paid = 2.556

Approximate

Amount paid = 2.6

Hence, the amount is $2.6