Mathematics High School

Given the function f(x) = −3x^3 + 9x^2 − 2x + 3, what part of the function indicates that the left end starts at the top of the graph?

A) The degree of the first term
B) The coefficient of the first term

Answers

Answer 1
the coefficient of the first term. 
If it's talking about the left end, then it'll be the first degree. So since it's to the third power, you'll have something that looks like x^3, which starts at the bottom left. The negative sign indicates a swapped axis. So it'll be the coefficient (which is -3). That states it'll start from the top left and go downward. The +3 is just a vertical shift.
Answer 2
The coefficiient of the first term  ( the -3). AS its negative the grph starts at top left.

Related Questions

What is the first step to simplify the expression: [–23 – [5 · (2 – 4)]] ÷ 32

Answers

Hello there, and thank you for posting your question here on brainly.

Short answer: 2 - 4

Why?

When you have an equation with parenthesis, you do those first. When you have parenthesis inside of parenthesis, you do that first.

Hope this helped you! ♥

Answer:

According to PEDMAS , We first simplify the PARENTHESES

[5 · (2 – 4)] = [5· -2] = -10

Step-by-step explanation:

 Given expression  [–23 – [5 · (2 – 4)]] ÷ 32

We have to find the  first step to simplify the given expression.

We apply PEDMAS

P stands for PARENTHESES

E  stands for EXPONENTS

D stands for DIVIDE

M  stands for MULTIPLY

A stands for ADDITION

S stands for SUBTRACTION.

So, according to PEDMAS , We first simplify the PARENTHESES

Thus, [5 · (2 – 4)] = [5· -2] = -10

If 30 fair dice are rolled find the approximate probability that the average number ofo dots is between 2 and 4

Answers

The probability that the average number of dots is between 2 and 4 when rolling 30 fair dice is 0.9441.

what is probability?

Probability is the branch of mathematics that deals with the study of random events or phenomena. It involves the quantification of uncertainty and the measurement of the likelihood of occurrence of an event.

The average number of dots on a fair die is

= (1+2+3+4+5+6)/6

= 3.5.

We can model the sum of the numbers on the 30 dice as a normal distribution with mean

= (30)(3.5) = 105

and, standard deviation √(30)(35/12) ≈ 9.13.

Let X be the sum of the numbers on the 30 dice, and let Y be the average number of dots. Then Y = X/30.

We want to find P(2 ≤ Y ≤ 4). This is equivalent to P(60 ≤ X ≤ 120), since Y = X/30.

Using the normal distribution, we can standardize X to get:

Z = (X - 105) / 9.13

Then we can compute the probability as:

P(60 ≤ X ≤ 120)

= P[(60 - 105) / 9.13 ≤ Z ≤ (120 - 105) / 9.13]

≈ P(-4.93 ≤ Z ≤ 1.64)

Using a standard normal distribution table or calculator, we can find that P(-4.93 ≤ Z ≤ 1.64) ≈ 0.9441.

Therefore, the approximate probability that the average number of dots is between 2 and 4 when rolling 30 fair dice is 0.9441.

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Use the x-intercept method to find all real solutions of the equation. x^3-9x^2+11x+21=0

Answers

We must graph y=x^3-9x^2+11x+21. Please, see the attached file.
Then we see were the graph cuts the x-axis, and these values of x are the real solutions of the given equation:

The real solutions of the given equation are:x = -1, 3, and 7

Answer:

c: x=-1,3,7

Step-by-step explanation:

An automobile manufacturer sold 30,000 new cars, one to each of 30,000 customers, in a certain year. The manufacturer was interested in investigating the proportion of the new cars that experienced a mechanical problem within the first 5,000 miles driven. (a)

A list of the names and addresses of all customers who bought the new cars is available. Describe a sampling plan that could be used to obtain a simple random sample of 1,000 customers from the list.

Each customer from a simple random sample of 1,000 customers who bought one of the new cars was asked whether they experienced any mechanical problems within the first 5,000 miles driven. Forty customers from the sample reported a problem. Of the 40 customers who reported a problem, 13 customers, or 32.5%, reported a problem specifically with the power door locks. (b)

Explain why 0.325 should not be used to estimate the population proportion of the 30,000 new cars sold that experienced a problem with the power door locks within the first 5,000 miles driven. (c)

Based on the results of the sample, give a point estimate of the number of new cars sold that experienced a problem with the power door locks within the first 5,000 miles driven.

Answers

A) In order to create a sampling plan, you need to follow the following 5 steps:
    1) Define the sample population: who are the customers you want to contact?
       The costumers who bought a new car on a certain year.
    2) Define the size of population: how many customers are you going to contact?
       Of the 30000 customers who bought a car, you want to contact 1000 customers.
    3) Define the contact options: how are you going to contact the customers?
       You have a list of names and addresses, therefore you can send a questionnaire via mail.
    4) Form a sampling frame: what is the time or contact frame to get in touch with your customers? 
       You will send the questionnaires and you will wait two months for the answer.
    5) Define the analysis method: is yours a qualitative or quantitative research?
     In your case, you want a quantitative research and therefore a probabilistic sampling.

B) The 32.5% probability refers to customers having issues with the power doors locks among the costumers who had problems, it does not consider the customers who did not have any problem or those who had problems after the first 5000 miles.

C) In order to find the probability of a power door lock problem if there have been problems within the first 5000 miles, we need to consider the whole sample:
P = 13 / 1000
   = 0.013

Therefore, 
N = 0.013 × 30000
   = 390

Hence, the number of new cars sold that experienced a problem with the power door locks within the first 5000 miles will be 390.
         

Analyzing the situation of the automobile industry it will be important that:

A)build a list that attracts buyers to cars, looking for an interested audience, through emails, nearby residents.

B) 0.013

C)390

If it is necessary to analyze how to attract a corresponding public so that a car sale can take place, a list will be created that takes into account:

A) 1) Define the sample population: The costumers who bought a new car on a certain year.

   2) Define the size of population: Of the 30000 customers who bought a car, you want to contact 1000 customers.

   3) Define the contact options: You have a list of names and addresses, therefore you can send a questionnaire via mail.

   4) Form a sampling frame: You will send the questionnaires and you will wait two months for the answer.

   5) Define the analysis method: In your case, you want a quantitative research and therefore a probabilistic sampling.

B) The 32.5% probability refers to customers having issues with the power doors locks among the costumers who had problems, it does not consider the customers who did not have any problem or those who had problems after the first 5000 miles.

C) In order to find the probability of a power door lock problem if there have been problems within the first 5000 miles, we need to consider the whole sample:

[tex]P= \frac{13}{1000} = 0.013[/tex]  

[tex]N=0.013*30000=390[/tex]

Hence, the number of new cars sold that experienced a problem with the power door locks within the first 5000 miles will be 390.

A class is trying to eliminate t from the parametric equations x=t^2+3 and y=4t. Beth says that she can write t=sqrt(x-3) to eliminate the parameter. Why is this wrong?

She should have added 3 to x, not subtracted.
She should always solve for t as a function of y.
She should have taken both the positive and negative square root.
She should first substitute y for t before solving.

Answers

C, She should have taken both the positive and negative square roots,

Because when a number is squared, even if it is negative it can become positive,

so taking square should include + and - to the answer.

Beth says that she can write that she should have taken both the positive and negative square root to eliminate the parameter. Therefore, option (c) is correct.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

We have to find the error which is done by Beth to eliminate the parameter. So, we will take the first equation and do all the steps to find the error and get the desired result.

Given that, x=t²+3 and y=4t

Try find the expression of "t" in terms of "x". We will use equation (1) and we have

x-3=t²

t=√(x-3)

Thus, Beth says that she can write that she should have taken both the positive and negative square root to eliminate the parameter. Therefore, option (c) is correct.

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Two angles whose measures add up to 90º are called?

Answers

Two angles that add up together and equal 90 degrees are called complementary angles.
He is correct I used this answer

Drag and drop the symbols to enter the equation of the circle in standard form with center and radius given. Center (5, -3), radius = 1

Answers

Hi there!

The standard form of the equation of a circle is:
[tex](x - a) {}^{2} + (y - b) {}^{2} = r {}^{2} [/tex]


With (a, b) representing the centre and r representing the radius of the circle. 
Since the centre of the circle is (5, -3) and the radius is 1, we get the following equation:

[tex](x - 5) {}^{2} + {(y + 3)}^{2} = 1[/tex]

Graph f(x)=- square root -x

Answers

Graph in the attachment.

[tex]x=0\to f(0)=-\sqrt0=0\to(0;\ 0)\\\\x=-0.25\to f(-0.25)=-\sqrt{-(-0.25)}=-\sqrt{0.25}=-0.5\to(-0.25;-0.5)\\\\x=-1\to f(-1)=-\sqrt{-(-1)}=-\sqrt1=-1\to(-1;-1)\\\\x=-4\to f(-4)=-\sqrt{-(-4)}=-\sqrt4=-2\to(-4;-2)[/tex]

The graph of function f (x) = - √- x is shown in image.

We have to given that,

Graph the function,

f (x) = - √- x

Here, Function is defined as,

f (x) = - √- x

At x = 0;

f (x) = - √-0

f (x) = 0

Plot the graph of function f (x) = - √- x.

Hence, The graph of function f (x) = - √- x is shown in image.

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complete the general solution to y=cos^-1(1) for K a whole number

Answers

I think that would be 0 +/- 360n  in degrees ans 0 +/- 0 + 2npi  in radians

Answer:  

If the equation is exactly the one you posted then the unique answer is:

[tex]y = 0[/tex]

or  what is the same:

[tex]y=0K[/tex]

Explanation:

If your equation is exactly the one you posted then it has only one solution: y = 0

Because the range of [tex]y=\cos^{-1}(x)[/tex] is the interval [tex][0, \pi][/tex]

The meaning of [tex]\cos^{-1}(1)[/tex] is to find the angle whose cosine is 1.

In the range of the function arccosine the only angle whose cosine is 1 is the angle 0.

But if your equation was the following one:

[tex]\cos(y)=1[/tex]

Then in that case we would have infinite solutions since it will be the set:

[tex]y=\cos^{-1}(1)+2K\pi[/tex]  where K is an integer, since the period of cosine is [tex]2\pi[/tex]

So, in such a case the solution set would be:

[tex]y=0+2K\pi=2K\pi[/tex]  

But for the equation you posted, the unique solution is: y = 0 or what is the same y = 0K

simplify
3 (2x+4y-2z)+7 (x+y-4z)

Answers

6x+12y-6z+7x7y-28z= 13x+19y-34z

Ernie is making a cylinder-shaped container to store his pens. The container has a base on one end and an opening on the other end. He is going to spray paint the outside of the container. The container has a diameter of 3 inches and a height of 18 inches.

Answers

For this case we must calculate the surface area of the container to know the amount of paint that Ernie must use.
 We have then:
 A = pi * r ^ 2 + 2 * pi * r * h
 Where,
 r: cylinder radius
 h: cylinder height
 Substituting values:
 A = 3.14 * (3/2) ^ 2 + 2 * 3.14 * (3/2) * 18
 A = 176.625 in ^ 2
 Answer:
 The amount of paint needed is:
 A = 176.625 in ^ 2

Need help with these 2 problems I’m pretty sure I got the first one right but I don’t know how to do the second one please and thank you!!

Answers

Since APR interest is a simple interest rate, we are going to use the formula for calculating simple interest: [tex]A=P(1+rt)[/tex]
where 
[tex]A[/tex] is the final amount after [tex]t[/tex] years
[tex]P[/tex] is the initial investment 
[tex]r[/tex] is the interest rate in decimal form 
[tex]t[/tex] is the number of years 

Mathematical steps for solving the problem:
We can infer from our problem that you are going to invest $800-$640=$160 in your savings account, so [tex]P=160[/tex]. To convert the interest rate to decimal form, we are going to divide the rate by 100%
[tex]r= \frac{4.5}{100} =0.045[/tex]. Since you are leaving the money in your savings account for a year, [tex]t=1[/tex]. Lets replace those values in our formula:
[tex]A=P(1+rt)[/tex]
[tex]A=160[1+(0.045)(1)][/tex]
[tex]A=160(1+0.045)[/tex]
[tex]A=160(1.045)[/tex]
[tex]A=167.2[/tex]

We can conclude that  your total savings after buying the refurbished laptop are: $167.2

Which summation formula represents the series below? 12 – 24 + 48 – 96

Answers

The summation formula for the series given by:
 12 – 24 + 48 – 96
will be calculated as follows:
first term,a=12
common ratio=+/-2
thus the sum will be:
(i=1)Σ[12(-2)^(i-1)]

Thus the answer:
(i=1)Σ[12(-2)^(i-1)]

Answer: B

Step-by-step explanation:

How to find the length of a rectangle when given the height?

Answers

Height usually refers to three dimensional objects, so I assume you mean height.

The formula for area is:

Area = length • width

If you were given the width and area of the rectangle you would be able to find the length by doing inverse operations. In this case, the opposite of multipication is division

Example: 56 = l • 8

56 / 8 = 7

56 = 7 • 8

The length is 7.

I hope this helps!

The length of a rectangle can be found by dividing the area of the rectangle by its height if the area is known. Without the area, additional information is necessary to calculate the length.

To find the length of a rectangle when given the height, we typically need additional information such as the area or the aspect ratio of the rectangle. However, without that information, directly calculating the length is not possible. Let's explore a scenario where we have the area of the rectangle. In such a case, if we are given the area (A) of the rectangle and the height (h), we can use the formula for the area of a rectangle which is A = length times height. Solving for the length (l), we rearrange the formula to get l = A/h. For instance, if the area of the rectangle is 150 square centimetres and the height is 10 centimetres, the length would be 150 cm2 / 10 cm = 15 cm. It's also important to consider proportions when scaling shapes.

Which value is the 10th term in the sequence:-62,-47,-32,-17,-2?

Answers

The answer is 13
Sure!!!

If Kareem’s living room has an area of 225 square feet, how much will he spend to carpet his living room?

Answers

Answer: $ 568.99

Because 18.99+22 x 225/9 = 568.99

Answer: 568.99

Step-by-step explanation: your mom

The perimeter of a rectangular garden is 43.8 feet. Its length is 12.4 feet. What is the width

Answers

perimeter of rectangle =2(l+b)

43.8 =2(12.4 + w)

21.9=12.4 +w

21.9-12.4 = w

w=9.5 feet
The width is 9.5.

  First you know what the length is. You must find the measurement of both combined.
   12.4 x 2 = 24.8   (Length)

  Subtract this number from the perimeter.  43.8 - 24.8 = 19.

  19 is your width multiplied by two. The total measurement of both, to find just the width divide by 2.

  19 / 2 = 9.5 (WIDTH)

In the coordinate plane line p had slope 8 and y intercept (0,5). Line r is the result of dilating line p by a factor of 3 with (0,3) what is the slope and y intercept of line r?

Answers

The slope of line r is 24 and the y-intercept is (0, 3).

How to find the slope and y-intercept?

To find the slope and y-intercept of line r, which is the result of dilating line p by a factor of 3 with a center at (0,3), we can use the following steps:

The slope of the dilated line r is the product of the dilation factor and the slope of the original line p.

The y-intercept of the dilated line r is the point where the original line p intersects the line of dilation.

Given that line p has a slope of 8 and a y-intercept of (0,5), the slope of line r is:

8 * 3 = 24.

The y-intercept is (0, 3)

Therefore, the slope of line r is 24 and the y-intercept is (0, 3).

according to the U.S. census bureau, the population of Hawaii in 2010 was 1,360,301 and it was growing at an annual rate of 1.2%. Predict the population in Hawaii in 2032

Answers

By applying the formula for the compound interest, [tex]FV_{N} = PV_{N} * (1+r)^{N} [/tex], because of the same logic we could calculate population in 2032. According to the formula, we can write that: 1,360,301 * (1+0.012) ^ [tex] {22} [/tex]   = 1,768,505. 

A lawn roller is 1 m wide and 80 cm high. What area is covered in each revolution

Answers

The area for each revolution is given by:
 A = 2 * pi * r * l
 Where,
 r: roller radius
 l: roller width
 We have then:
 A = 2 * 3.14 * (0.80 / 2) * 1
 A = 2.512 m ^ 2
 Answer:
 The area that is covered in each revolution is:
 A = 2.512 m ^ 2

A bag contains 2 blue, 4 green, and 3 white chips. What is the probability of drawing a white chip then another white chip without replacement?


A.) 7/9


B.) 8/81


C.) 2/3


D.) 1/12

Answers

total number of chips: 2 + 4 +3 = 9

total white chips = 3
 probability of picking white first = 3/9 = 1/3

after taking one chip there would be 9-1 = 8 chips left

and 3-1 2 white chips left

probability of picking 2nd white chip = 2/8 = 1/4

probability of picking both =  1/3 x 1/4 = 1/12
 answer is D


in a cylinder the radius and height was quadrupled. How much bigger would the new surface area be then the original surface area.

Answers

The original surface area is:
 A = 2 * pi * r ^ 2 + 2 * pi * r * h
 Where,
 r: radio
 h: height
 The area when the dimensions are modified is:
 A '= 2 * pi * (4r) ^ 2 + 2 * pi * (4r) * (4h)
 Rewriting we have:
 A '= 16 * 2 * pi * r ^ 2 + 16 * 2 * pi * r * h
 A '= 16 (2 * pi * r ^ 2 + 2 * pi * r * h)
 A '= 16A
 Answer:
 the new surface area would be 16 times bigger than the original surface area
we know that
if in a cylinder the radius and height was quadrupled
so
the scale factor is equal to 4
scale factor=4
and
new surface area=[scale factor]²*original surface area 
new surface area=[4]²*original surface area 
new surface area=16*surface area original

therefore
the new surface area will be 16 times the original surface area.

alternative method
we know that 
surface area of cylinder=2*[area of the base]+perimeter of the base*height
area of the base=pi*r²
perimeter of the base=2*pi*r

original surface area=2*[pi*r²]+[2*pi*r]*h-----> 2*pi*r*[r+h]

if the radius and height was quadrupled
so
new surface area=2*pi*(4*r)*[4r+4h]-----> 2*pi*(4*r)*4*[r+h]
new surface area=16*[2*pi*r*(r+h)]----> 16*[original surface area]

the answer is
the new surface area will be 16 times the original surface area.

Training course a takes 9 weeks and 4 days to complete.training course b takes 54 days to complete.how much longer does training course a take than training coure b to complete

Answers


[tex]7 \times 9 + 4 = 67 \\ 67 - 54 = 13[/tex]
Training course A takes 13 more days than training course B.
Final answer:

Training course A takes 13 days longer than training course B to complete.

Explanation:

To find how much longer training course A takes than training course B to complete, we need to compare the durations of the two given courses with given values.

Training course A takes 9 weeks and 4 days to complete, which is found to be :

9 x 7 + 4 = 67 days in total.

Training course B takes 54 days to complete.

To find the difference, we subtract the duration of course B from the duration of course A:
67 - 54 = 13 days.

Therefore, training course A takes 13 days longer than training course B to complete.

The sum in a half adder can be represented by what boolean expression (assuming a

Answers

The sum of a half adder is only 1 when ONLY ONE of the two inputs are 1.
If they are both 0, the sum is 0. If they are both 1, the sum is 0 and the carry is 1.

This is the XOR logic gate; either one of the two inputs, but not both. In boolean algebra, XOR can be represented as: ¬AB + A¬B

Simplify the expression.

(–1 + 6i) + (–4 + 2i)

Answers

(-1+6i)+(-4+2i) =====> -5+8i (simplified)
( -1 + 6i ) + ( -4 + 2i )
= -1 + 6i - 4 + 2i
= -5 + 8i

Hope it helped!

this will be worth ten points

Answers

First, you can write that 1260 ÷ 15 = 84.

To prove this one way, you can show the multiplication of the quotient and divisor.  If the division was correct, it would end up as the value of the dividend:

84 * 15 = 1260
1260 = 1260

To prove this another way, you can show 84 being added 15 times and seeing if it totals 1260:

84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 = 1260
1260 = 1260

Answer:

1260/15=84

Step-by-step explanation:

1200/15=80 and 60/15=4

80 + 4 = 84.

Another way is 15 + 15 + 15 and keep counting 84 times and you would get 84

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Barbara is making bracelets to sell on her Etsy site. It costs her $0.79 per bead and she needs 22 beads per bracelet. She sells her bracelets for $28 each. What is the percent markup per bracelet?

Answers

the answer is 10.62 please give brainliest

The table below shows the number of hours some college athletes in two states spend on indoor sports each week:

State A 7 9 5 4 25 21 6 6 8
State B 14 12 10 13 15 14 11 15 16

Part A: Create a five-number summary and calculate the interquartile range for the two sets of data. (6 points)

Part B: Are the box plots symmetric? Justify your answer. (4 points)

Answers

State A: 7 9 5 4 25 21 6 6 8
State B: 14 12 10 13 15 14 11 15 16

When arranged in order,
State A: 4 5 6 6 7 8 9 21 25
State B: 10 11 12 13 14 14 15 15 16

Part A:
For state A, Q1 = minimum number = 4, Q2 is the lower quartile = 6, Q3 is the middle number = 7, Q4 is the upper quartile = (9 + 21)/2 = 15, Q5 = maximum number = 25
Interquatile range = upper quatile - lower quatile = 15 - 6 = 9

For state B, Q1 = minimum number = 10, Q2 is the lower quartile = 11.5, Q3 is the middle number = 14, Q4 is the upper quartile = 15, Q5 = maximum number = 16
Interquatile range = upper quatile - lower quatile = 15 - 11.5 = 3.5



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what is the measure of the angle?

Answers

Remember that the x-axis is a straight angle, so is measure is 180°. To find the measure of our angle, we are going to add the right angle, 180°, and the smaller angle 55°:

Measure of the angle=55°+180°=235°

We can conclude that the measure of the angle in the picture is 235°

saidhari bought a toaster oven for $60. this price was 1/4 off the list price. What was the list price

Answers

Final answer:

The list price of the toaster oven was $80.

Explanation:

To find the list price, we need to determine the price of the toaster oven before the discount. Let's call the list price 'x'. The discount is 1/4 off the list price, so the discounted price is 3/4 of the list price. We can set up the equation 3/4 * x = $60 to find the value of 'x'. To solve for x, we can multiply both sides of the equation by 4/3: (3/4 * 4/3) * x = $60 * 4/3. Simplifying the equation gives us x = $80.

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