What is the y-intercept of the liner function? (y=3x-2)

Answers

Answer 1

The y-intercept of the linear function y = 3x - 2 is -2

How to determine the y-intercept?

The function is given as

y = 3x - 2

The above function is a linear function, and the y-intercept is the point on the graph, where x = 0 i.e. the point (0, y)

As a general rule, linear functions are those functions that have constant rates or slopes

Next, we set x to 0, and calculate y to determine the value of the y-intercept

y = 3(0) - 2

Remove the bracket in the above equation

y = 3 * 0 - 2

Evaluate the product of 3 and 0 i.e. multiply 3 and 0

y = 0 - 2

Evaluate the difference of 0 and -2 i.e. subtract 0 from 2

y = -2

The above means that the value of y when x is 0 is -2

Hence, the y-intercept of the linear function y = 3x - 2 is -2

Related Questions

suppose that g is a continuous function, 3_integral^5
g(x)dx=18, and 3_integral^10 g(x)dx =36. Find
5_ integral^10 g(x)dx
those are intergral symbols with numbers on
top and bottom. please show work. thanks

Answers

The value of the definite integral [tex]\int\limits^{10}_5 {g(x)} \, dx = 18[/tex]

The question has to do with definite integrals

What are definite integrals?

Definite integrals are integrals obtained within a range of values (or limits) of the independent variable.

Given that

[tex]\int\limits^5_3 {g(x)} \, dx = 18[/tex] and also [tex]\int\limits^{10}_3 {g(x)} \, dx = 36[/tex] and we require [tex]\int\limits^{10}_5 {g(x)} \, dx[/tex]

For any integral [tex]\int\limits^a_c {g(x)} \, dx = \int\limits^a_b {g(x)} \, dx + \int\limits^b_c {g(x)} \, dx[/tex]

So, [tex]\int\limits^{10}_3 {g(x)} \, dx = \int\limits^5_3 {g(x)} \, dx + \int\limits^{10}_5 {g(x)} \, dx[/tex]

So, [tex]\int\limits^{10}_5 {g(x)} \, dx = \int\limits^{10}_3 {g(x)} \, dx - \int\limits^5_3 {g(x)} \, dx[/tex]

Since

[tex]\int\limits^5_3 {g(x)} \, dx = 18[/tex]and [tex]\int\limits^{10}_3 {g(x)} \, dx = 36[/tex]

Substituting the values of the variables into the equation, we have

[tex]\int\limits^{10}_5 {g(x)} \, dx = \int\limits^{10}_3 {g(x)} \, dx - \int\limits^5_3 {g(x)} \, dx[/tex]

[tex]\int\limits^{10}_5 {g(x)} \, dx = 36 - 18 \\\int\limits^{10}_5 {g(x)} \, dx = 18[/tex]

So, the value of the definite integral [tex]\int\limits^{10}_5 {g(x)} \, dx = 18[/tex]

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Solve 15.9 = 11.3 + b for b

Answers

Answer:

subtract 11.3 from 15.9 and b is 4.6

Step-by-step explanation:

what is the ration between 28000 and 14?

Answers

The ratio between 28,000 and 14 is 2000 : 1

How to determine the ratio?

The numbers are given as:

28,000 and 14

Express as ratio

Ratio = 28000 : 14

Divide each number by 14

Ratio = 2000 : 1

Hence, the ratio between 28,000 and 14 is 2000 : 1

Answers

Answer:

Step-by-step explanation:

Answer:

10 apples

Step-by-step explanation:

20% of 50 = 10

10 apples

Combine like terms to simplify the following polynomial.

5a²b+7ab² +9c+ 11a²b-3ab² - 9c

Answers

Answer:

5a²b + 7ab² + 9c + 11a²b - 3ab² - 9c

= (5a²b + 11a²b) + (7ab² - 3ab²) + (9c - 9c)

= 16a²b + 4ab²

Dan & Alex measure themselves against a tree in their backyard. The tree is 80% taller than Dan and 20% taller than Alex. Which of the following statements is true?

A. Alex is 50% taller than Dan.
B. Dan is 60% taller than Alex.
C. Dan is 40% taller than Alex.
D. Alex is 40% taller than Dan.

Answers

The true statement is that Alex is 50% taller than Dan.

How to solve percentage questions?

They both measured themselves against a tree in their backyard.

Therefore, the tree is 80% taller than Dan and 20% taller than Alex.

Hence,

let

Dan height = x

Tree's height = x + 0.8x

Tree's height = 1.8x

let

Alex height = y

Tree's height = y + 0.2y

Tree's height = 1.2y

Therefore, if we use Dan height as 100, the height of the tree will be 180.

Then,

180 = 1.2y

y = 150

This means Alex is 50 percent taller than Dan.

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Find a polynomial function of degree 7 with -1 as a zero of multiplicity 3, 0 as a zero of multiplicity 3, and 1 as a zero
of multiplicity 1.

Answers

The polynomial function is P(x) = x^3(x + 1)^3(x -1)

How to determine the polynomial function?

The zeros of the polynomial and the multiplicities are given as:

-1 as a zero of multiplicity 3, 0 as a zero of multiplicity 3, 1 as a zero of multiplicity 1

The degree is given as

Degree = 7

The polynomial is represented as:

P(x) = (x - zero)^multiplicity

Using the above format, we have

P(x) = (x + 1)^3(x - 0)^3(x -1)

This gives

P(x) = x^3(x + 1)^3(x -1)

Hence, the polynomial function is P(x) = x^3(x + 1)^3(x -1)

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If a 17-foot ladder makes a 71° angle with the ground, how many feet up a wall will it reach? Round your answer to the nearest tenth.

Answers

Given the length of the ladder and the angle it made with the ground, it will reach 16.7 ft up the wall.

How many feet up the wall will the ladder reach?

Given that;

Angle with the ground θ = 71°Length of the ladder / hypotenuse = 17ftLength of wall = x

To determine the length wall from the tip of the ladder to the ground level, we use trigonometric ratio since the scenario forms a right angle triangle.

Sinθ = Opposite / Hypotenuse

Sin( 71° ) = x / 17ft

x = Sin( 71° ) × 17ft

x = 0.9455 × 17ft

x = 16.1 ft

Given the length of the ladder and the angle it made with the ground, it will reach 16.7 ft up the wall.

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Is this figure a polygon? Explain.

Answers

Yes.

It’s a flat figure (2D), and all of its lines are connected with one another. There aren’t any open points/lines. It’s closed to create a shape. This means it’s a polygon.

a solid sphere is cut into 12 equal wedges. the volume of each wedge is V=1/9πr^3. solve the formula for r.

Answers

The formula, solved for r is r = ∛(9V/π)

Subject of formula

From the question, we are to solve for r is the given formula

The given formula is

V = 1/9πr³

Multiply both sides of the equation by 9 to get

9V = πr³

Now, divide both sides by π

∴ r³ = 9V/π

r = ∛(9V/π)

Hence, the formula, solved for r is r = ∛(9V/π)

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find the difference

Answers

Answer:

141; 6526; 28d.

Step-by-step explanation:

try this option, all the details are in the attachment.

Find t and the terminal point determined by t for each point in the figure, where t is increasing in increments of /4.

Answers

The missing coordinates are listed below:

(x₁, y₁) = (0, 1)(x₂, y₂) = (- √2 /2, √2 /2)(x₃, y₃) = (- 1, 0)(x₄, y₄) = (- √2 /2, - √2 /2)(x₅, y₅) = (0, - 1)(x₆, y₆) = (- √2 /2, √2 /2)(x₇, y₇) = (1, 0)

How to determine the location a terminal point in a unit circle

According to the polar coordinate system, a vector in standard position is defined by this parametric formula:

(x, y) = (r · cos t, r · sin t), where t is in radians.

If we assume that r = 1, then we proceed to determine the location of the seven points remaining:

(x₁, y₁) = (cos π/2, sin π/2)

(x₁, y₁) = (0, 1)

(x₂, y₂) = (cos 3π/4, sin 3π/4)

(x₂, y₂) = (- √2 /2, √2 /2)

(x₃, y₃) = (cos π, sin π)

(x₃, y₃) = (- 1, 0)

(x₄, y₄) = (cos 5π/4, sin 5π/4)

(x₄, y₄) = (- √2 /2, - √2 /2)

(x₅, y₅) = (cos 3π/2, sin 3π/2)

(x₅, y₅) = (0, - 1)

(x₆, y₆) = (cos 7π/4, sin 7π/4)

(x₆, y₆) = (- √2 /2, √2 /2)

(x₇, y₇) = (cos 2π, sin 2π)

(x₇, y₇) = (1, 0)

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Which of the following estimates at 895% confidence level most likely comes from a small sample?
A. 67% (+-7%)
B. 59 % (+-21%)
C. 53 % (+-3%)
D. 48 % (+-5%)

Answers

Option B. The estimate that would most likey come from the small sample is going to be B. 59 % (+-21%).

How to find the sample

The sample space can be gotten rom the margin of error. A smaller sample space would be gotten by dividing with a larger number.

This would give a margin of error that is large. In the second option, we can see that the largest margin of error is ± 21%.

Hence this is the answer to the question.

Answers

Answer:

12 inches

Step-by-step explanation:

Perimeter refers to distance around the 2D shape.

A hexagon is a polygon with 6 sides. The formula for the perimeter of a hexagon is P=6s

72=6s

The hexagon is 12 inches long

A hexagon has 6 sides. This means that 72 divided by 6 sides = 12 in.

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Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle

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two candles of the same height are lighted at the same time. the first is consumed in 4 hrs and the second in 3 hrs. assuming that each candle burns at a constant rate, in how many hours after being lighted was the first candle twice the height of the second?

Answers

The height of candle 4 is twice that of candle B after 2.4 hours.

How many hours after being lighted was the first candle twice the height of the second?

For candle, A time is taken for 100% bearning=4hour.

For 1 hour, it burns for 25%(100/4)

After 1 hr.[tex]\frac{25}{100}[/tex]

After x hours, the amount burnt[tex]=\frac{x}{4}[/tex]

Amount left[tex]=1-\frac{x}{4} =\frac{4-x}{4}[/tex]

Let's not presume that candle B's height will be half that of candle A after x hours.

After x hours, part vemacing [tex]=1-\frac{x}{3} =\frac{3-x}{3}[/tex]

[tex]\frac{4-x}{4} =1\frac{3-x}{3}[/tex]

Height of candle A[tex]=2[/tex]×Height of candle B.

[tex]12-3x=24-8x[/tex]

⇒[tex]5x=12[/tex]

[tex]x=\frac{12}{5}[/tex]

[tex]=2.4[/tex]

The height of candle 4 is twice that of candle B after 2.4 hours.

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In △ OPQ, OP ≅ QO and m∠O=65∘. Find m∠Q

Answers

Answer:

65°

Step-by-step explanation:

Angles opposite congruent sides in a triangle are congruent, so both angle Q and angle P are congruent.

Since angles in a triangle add to 180°, angle Q measures (180-50)/2 = 65°

Someone please help with this math problem.

Answers

I don’t know how to get a pic but I think I’m just trying a little bit more to make it better but I don’t 2 -2 is 0

Evaluate 2x − 2 for x = 0, x = 1, and x = 2. Question 1 options: A) −1, 0, 2 B) −1, 1, 2 C) 0, 1, 2 D) 1, 2, 4

Answers

The value of x in 2^x - 2 when x = 0, x = 1 and x = 2 are -1, 0 and 2 respectively. option A

Algebra

2^x - 2

when x = 0

2^x - 2

= 2^0 - 2

= 1 - 2

= -1

when x = 1

2^x - 2

=2^1 - 2

= 2 - 2

= 0

when x = 2

2^x - 2

= 2^2 - 2

= 4 - 2

= 2

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The nurse must give a patient 9 milligrams of a medication. If the tables are 2 milligrams each, how many tablets are needed?

Answers

Answer:

4.5 tablets.

Step-by-step explanation:

We just divide 9 by 2.

13. The tablets needed is 4 and a half.

14. There are 10 half-gram doses available from the 5 gram vials of medication.

15. Pat's heart beats approximately 58.5 times in 3/4 of a minute.

Given are words problems based on the mixed numbers:

13. To determine the number of tablets needed, we divide the total dosage required by the dosage per tablet.

In this case, the nurse needs to administer 9 milligrams of medication, and each tablet contains 2 milligrams.

So, the number of tablets needed is:

9 milligrams / 2 milligrams per tablet = 4.5 tablets

Hence, the tablets needed is 4 and a half.

14. If the pharmacy has 5 gram vials of medication, we can calculate the number of 1/2 gram doses available by dividing the total amount of medication by the dose size.

The total amount of medication in grams is 5 grams.

To find the number of 1/2 gram doses available, we divide the total amount of medication (5 grams) by the dose size (1/2 gram):

5 grams / (1/2 gram) = 5 grams x (2/1 gram)

= 5 x 2 = 10 doses.

Therefore, there are 10 half-gram doses available from the 5 gram vials of medication.

15. To calculate how many times Pat's heart beats in 3/4 of a minute, you can use a simple proportion:

1 minute = 78 beats

3/4 minute = ? beats

Let's solve for the number of beats in 3/4 of a minute:

Number of beats in 3/4 minute = (3/4) x 78

= 0.75 x 78

= 58.5

So, Pat's heart beats approximately 58.5 times in 3/4 of a minute. Since you can't have half a heartbeat, the closest whole number is 58 beats.

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15) Mr. and Mrs. Rupe and their 4 sons are taking a 2500 mile camping trip across country. They plan to spend $120 for campsites per
day. The camper rental fee is $65 a day. While pulling the camper their car has a fuel economy of 8 miles per gallon. They estimate $85
per day for food for the 5-day trip. If gasoline is $1.92 per gallon how much will their trip cost?
O a.) $1950
Ob.) $1850
Oc.) $2950
Od.) $1750

Answers

Answer:

A $1950

Step-by-step explanation:

Food, camper rental and camp site will cost 1350

(120 + 65 + 85)5 = 1350

The trip is 2500 and the car gets 8 miles per gallon 2500/8 = 31.5. The will need to buy 31.5 gallons of gas at 1.92 a gallon or $600 (31.5 x 1.92).

When we add the cost of gas to the other costs, we get a total of 1950 (1350 + 600)

A train travels 600 kilometers in 1 hour. What is the train's velocity in meters/second?
lunch Then more students joined Jaden's

Answers

Answer:

166 2/3 meters/sec.

Step-by-step explanation:

1/1 =1 12 inches/1 foot =1 you are looking for equivalents that will cancel out the unit until you can get to meters and seconds. See work in the picture.

A focus group study has always been the primary way for ABC Toys Company to gather customers' opinions for marketing strategy. In the past, when a new product was popular in the market, a focus group study had incorrectly indicated that it would be unpopular with a probability of 0.275. When a new product was unpopular, a focus group had incorrectly indicated that it would be popular with a probability of 0.175. Assume that the probability of a new product being popular in the market is 0.60. What is the probability that a new product will be unpopular if a focus group study indicates that it will be unpopular?

Answers

Using conditional probability, there is a 0.6667 = 66.67% probability that a new product will be unpopular if a focus group study indicates that it will be unpopular.

What is Conditional Probability?

Conditional probability is the probability of one event happening, considering a previous event. The formula is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which:

P(B|A) is the probability of event B happening, given that A happened.[tex]P(A \cap B)[/tex] is the probability of both A and B happening.P(A) is the probability of A happening.

For this problem, the events are given as follows:

Event A: Study indicates that the product is unpopular.Event B: Product is unpopular.

The parameters are given as follows:

P(A) = 0.6 x 0.275 + 0.4 x 0.825 = 0.495.[tex]P(A \cap B) = 0.4 \times 0.825 = 0.33[/tex]

Hence the conditional probability is:

[tex]P(B|A) = \frac{0.33}{0.495} = 0.6667[/tex]

0.6667 = 66.67% probability that a new product will be unpopular if a focus group study indicates that it will be unpopular.

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Select the symbol = (equal to) or ≠ (not equal to) to make the expression true.
{0} ? { }

Answers

Answer:

Step-by-step explanation:

{0}={} because 0 means that there is nothing and in null set too, there is no elements.

Following a group of truck drivers and noting the number of miles traveled for one year refers to which type of statistical study?

Answers

Considering that the data is only noted and not changed, this is an example of an observational study.

What are observational and experimental studies?

Experimental study: In an experimental study, there is an intervention in a sample, and it's effect is studied.Observational study: In an observational study, the sample is just analyzed, without any intervention.

In this problem, the data, which is the number of miles traveled, is only analyzed, no interventions are made, hence this is an example of an observational study.

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You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable preliminary estimation for the population proportion. You would like to be 98% confident that you estimate is within 2% of the true population proportion. How large of a sample size is required?

Answers

Using the z-distribution, it is found that a sample size of 3,385 is required.

What is a confidence interval of proportions?

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.

In this problem, we have a 98% confidence level, hence[tex]\alpha = 0.98[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.98}{2} = 0.99[/tex], so the critical value is z = 2.327.

We have no prior estimate, hence [tex]\pi = 0.5[/tex] is used, which is when the largest sample size is needed. To find the sample size, we solve the margin of error expression for n when M = 0.02, hence:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.02 = 2.327\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.02\sqrt{n} = 2.327 \times 0.5[/tex]

[tex]\sqrt{n} = \left(\frac{2.327 \times 0.5}{0.02}\right)[/tex]

[tex](\sqrt{n})^2 = \left(\frac{2.327 \times 0.5}{0.02}\right)^2[/tex]

n = 3,385.

A sample size of 3,385 is required.

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Plot the complex number.
18i

Answers

The point has a real part of 0 and an imaginary part of 18, and thus corresponds to the point (0,18) in the complex plane.

Compute the exact value of the height h of the square-based straight pyramid, given that the base is a square with sides 34 feet long, and all other edges are 50 feet long.

Answers

Answer:

31√2 feet

Step-by-step explanation:

The height can be found using the Pythagorean theorem. The height of the pyramid will be the height of the right triangle whose sides are half the diagonal of the square base, the distance from the base to the peak, and the edge from the peak back to the corner of the base.

Setup

Let h represent the height of the pyramid. The diagonal of the square base will be √2 times the side of the base. So, half the diagonal will be 17√2 ft. The Pythagorean theorem tells us ...

h² +(17√2)² = 50²

Solution

Subtracting the constant on the left gives ...

h² = 2500 -578 = 1992

h = √1992 = 31√2

The height of the square pyramid is exactly 31√2 feet.

__

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A town planner is interested in getting some demographic data about the households in the city. The city has ten wards that vary in size. Which sampling method is most appropriate?

Answers

The best sampling method that Is most appropriate for the town planner is called Stratified Sampling.

What is the Sampling Method used?

The best sampling method that I would recommend for the town planner is called Stratified Sampling.

The reason for using stratified sampling is because it is a method of sampling that involves dividing a population into smaller groups–called strata and in this case, the rows of houses can be used as a strata.

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questions 5 and 6 please!
will give brainliest to whoever answers
90 points

Answers

Answer:

rise over run so

5/5 = 1

-2/4 = -0.5

Type 4 points found on the circumference of the following equation. Exact points only, no approximations.

(x-3)^2 +(y+2)^2+49

Answers

The points on the circumference are (3, 5), (3, -9), (8, -2 + √24) and (8, -2 - √24))

How to determine the points on the circumference of the circle?

The circle equation is given as:

(x-3)^2 +(y+2)^2= 49

Rewrite as:

(y+2)^2= 49 -(x-3)^2

Take the square root of both sides

y+2= ±√[49 -(x-3)^2]

Subtract 2 from both sides

y = -2 ± √[49 -(x-3)^2]

Next, we determine the points

Set x = 3

y = -2 ± √[49 -(3-3)^2]

Evaluate

y = -2 ± 7

Solve

y = 5 and y = -9

So, we have

(x, y) = (3, 5) and (3, -9)

Set x = 8

y = -2 ± √[49 -(8-3)^2]

Evaluate

y = -2 ± √24

Solve

y = -2 - √24 and y = -2 + √24

So, we have

(x, y) = (8, -2 + √24) and (8, -2 - √24)

Hence, the points on the circumference are (3, 5), (3, -9), (8, -2 + √24) and (8, -2 - √24)