Mathematics High School

I need step by step instructions on how to get the y-intercept for the following function:

f(x)=x^3-18x^2+107x-210.

Answers

Answer 1
luktdkilfdiykfg;oizxkuilouyk7it8rl,kvkuc kugc ulv lug 

Related Questions

Find the surface area of the cylinder in terms of π.

See picture

a) 1008π in.2

b) 522π in.2

c) 360π in.2

d) 396π in.2

Answers

[tex]\bf \textit{total surface area of a cylinder}\\\\ SA=2\pi r(h+r)~~ \begin{cases} r=radius\\ h=height\\ -----\\ r=9\\ h=20 \end{cases}\implies SA=2\pi (9)(20+9) \\\\\\ SA=18\pi (29)\implies SA=522\pi [/tex]

This is a question about inverse/transcendental functions. Can anyone confirm that the answer is D? The question is asking which statement is FALSE, and I'm bouncing back and forth a bit.

Answers

Your choice is correct. The slope of the function on the interval is negative. The slope of the inverse function is the reciprocal of that, still negative.

It is NOT true that [tex]\dfrac{d}{dx} \left( f^{-1}(x) \right) \ge 0[/tex]

I really need help

What is the equation of a circle with its center at(10,−4) and a radius of 4?

(x−10)2+(y+4)2=4

(x+10)2+(y−4)2=16

(x−10)2+(y+4)2=16

(x+10)2+(y−4)2=2

(x−10)2+(y+4)2=2

(x−10)2+(y+4)2=8

(x+10)2+(y−4)2=8

(x+10)2+(y−4)2=4

Answers

The answer should be
(x-10)²+(y+4)²=16


The equation of any circle is
(x – h)² + (y – k)² = r²

(h,k) is the center point and r is the radius

what is the sum of the geometric series E (-2)(-3)^n-1

Answers

Sum of the geometric series: S=?
S=(-2)(-3)^(1-1)+(-2)(-3)^(2-1)+(-2)(-3)^(3-1)+(-2)(-3)^(4-1)
S=(-2)[(-3)^0+(-3)^1+(-3)^2+(-3)^3]
S=(-2)[1+(-3)+9+(-27)]
S=(-2)(1-3+9-27)
S=(-2)(-20)
S=40

Answer: Third option 40

Answer:

The sum is 40.

Step-by-step explanation:

Given,

[tex]\sum_{n=1}^{4} (-2)(-3)^{n-1}[/tex]

We know that,

[tex]\sum_{n=1}^{4} (-2)(-3)^{n-1}=(-2)(-3)^{1-1}+(-2)(-3)^{2-1}+(-2)(-3)^{3-1}+(-2)(-3)^{4-1}[/tex]

[tex]=(-2)(-3)^{0}+(-2)(-3)^1+(-2)(-3)^2+(-2)(-3)^3[/tex]

[tex]=-2\times 1 - 2\times - 3 - 2\times 9-2\times -27[/tex]

[tex]=-2+6-18+54[/tex]

[tex]=40[/tex]

Hence,

[tex]\sum_{n=1}^{4} (-2)(-3)^{n-1}=40[/tex]

Calculate the total cost of the order: Veggiburger with cola and soup, sales tax 4%, tip 15.

Veggiburger: $3.25
Cola: $1.50
Soup: $2.25

A $8.33
B $7.28
C $7.00
D $5.50

Answers

Add the prices of the food together to get $7. Then you calculate the sales tax, which is 1.04 * $7 = $7.28. The tip is 15% I am assuming, and not 15, so it would be $7 * 0.15 = $1.05. Add $1.05 with $7.28 to get $8.33, so the answer is A.
Final answer:

The cost of the order, including the sales tax of 4%, comes out to be $7.28. However, the tip is unclear in the question. If it's 15%, the cost rises to $8.37, but none of the provided options match this result.

Explanation:

The first step is to calculate the total cost of the Veggiburger, cola, and soup by adding them together. So, $3.25 (Veggiburger) + $1.50 (cola) + $2.25 (soup) = $7.00. Next, apply the 4% sales tax on this amount which is $7.00 * 4/100 = $0.28. So the subtotal now is $7.28 ($7.00 + $0.28). Finally, the tip mentioned in the problem is not clear whether it is a percentage or a fixed amount. If it is a 15% tip, then calculate 15% of the subtotal, i.e $7.28 * 15/100 = $1.09 (Approx). Adding this to the subtotal we get $8.37 which is not an option in the given answers. If $15 is a fixed tip amount, the total cost would be substantially larger. Please ensure the tip amount is correct.

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Henry has a defined benefit plan that promises a 2.5% annual retirement benefit based on the average of his last five years of salary. At retirement Henry has 21 years of service and an average salary over the last five years of $95,000. What will his annual benefit be?

Answers

Henry's annual retirement benefit will be $2,375.

We have,

To calculate Henry's annual retirement benefit, we need to find 2.5% of his average salary over the last five years.

First, let's calculate 2.5% of $95,000:

2.5% = 2.5/100 = 0.025

Annual benefit = 0.025 * $95,000

Annual benefit = $2,375

Therefore,

Henry's annual retirement benefit will be $2,375.

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Compute the stock turnover in dollars for a product that has sales of $6,000 and an average value of inventory investment of $1,500.

Answers

Question: It should be inventory turnover.

Solution:
Inventory turnover = Cost of goods sold/Average inventory

Substituting the values given for cost of goods and average inventory;
 Inventory turnover = 6,000/1,500 = 4

Answer: 4

Step-by-step explanation:

Given: Cost of product sold = $6,000

Average value of inventory= $1,500

We know that the inventory turnover formula is given by :-

[tex]\text{Inventory turnover}=\frac{\text{ Cost of product sold}}{\text{Average value of inventory}}[/tex]

[tex]\\\Rightarrow\ \text{Inventory turnover}=\frac{\$6,000 }{\$1500}\\\\\Rightarrow\ \text{Inventory turnover}=4[/tex]

Therefore, the stock turnover for a product that has sales of $6,000 and an average value of inventory investment of $1,500 = 4

Solve each of the following right triangles. Round angle measures to the nearest degree and segment lengths to the nearest tenth. Angle C is the right angle of the triangle

Answers

6. C=67
AC=23.
BA=55.2

Help needed soon. please

Answers

For this case we first define variables:
 x = daisies flowers
 y = roses flowers
 We write the system of equations:
 x + 2y = 33
 x = y + 3
 Solving the system we have:
 x = 13
 y = 10
 Therefore, the cost of roses is:
 2 * y = 2 * 10 = 20 $
 Answer:
 Roses = $ 20

The unt informs club has 16 members. they need to elect a president, a vice president, a secretary and a treasurer. how many different ways can this group of 4 officers be formed? (order is important)

Answers

If they needed to elect just the president there could be 16 possible combination. If they needed to elect the president and the vice there could be 16×15 possible combination, because each president could have 15 possible vice. So the possible combination are 16×15×14×13=43 680.

Hope this helped!

Suppose that a small town has seven burger shops whose respective shares of the local hamburger market are (as percent- ages of all hamburgers sold): 23 percent, 22 percent, 18 percent, 12 percent, 11 percent, 8 percent, and 6 percent. what is the four-firm concentration ratio of the hamburger industry in this town

Answers

SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS

what is the value of the expression?

Answers

To solve this we are going to use the unitary circle and the fact that [tex]tan \alpha = \frac{sin \alpha }{cos \alpha } [/tex]

From our circle we can infer that [tex]sin\frac{5 \pi }{3}= \frac{- \sqrt{3} }{2} [/tex] and [tex]cos\frac{5 \pi }{3}= \frac{1}{2} [/tex].

Since [tex]tan \alpha = \frac{sin \alpha }{cos \alpha } [/tex], [tex]tan\frac{5 \pi }{3}= \frac{\frac{- \sqrt{3} }{2}}{\frac{1}{2} } [/tex]
[tex]tan\frac{5 \pi }{3}=- \sqrt{3} [/tex]

We can conclude that [tex]tan\frac{5 \pi }{3}=- \sqrt{3} [/tex].

Please help me, if you'd be so kind.

A right rectangular prism is shown.

What is the length of DH¯¯¯¯¯¯ to the nearest tenth of an inch?

Drag and drop the answer into the box.

Answers

[tex]\overline{DH}=\sqrt{3^2+1.5^2+1^2}=\sqrt{9+2.25+1}=\sqrt{12.25}=\boxed{3.5}[/tex]

HELP!!!!!!What is the equation of the graph below?

Answers

The answer to your question is y = sin(x + 90) as we have a sine graph phase shifted 90 units left

Tina can paint a room 1.5 times faster than Joey can. If they work together, they can paint a room in 6 hours. How long would it take the slower person working alone to paint the room?

Answers

So, the rate is 1 job / hours, so:
1/n + 1/1.5n = 1/6
We'll make the denominator 3n:
3/3n + 2/3n = 1/6
5/3n = 1/6
Cross multiply:
3n = 30
n = 10
It will take the slower person 10 hours to complete the room.

Factor the trinomial below.

9x2 + 6x + 1

A. (3x + 1)(3x – 1)
B. (9x + 1)(x – 1)
C. (9x + 1)(x + 1)
D. (3x + 1)(3x + 1)

Answers

Answer: D. (3x + 1)(3x+1)

Step-by-step explanation:

9x² + 6x + 1

find two factor of 9 such that its product gives 9 and its sum gives 6 (3 and 3, 3×3 = 9 , also 3+ 3=6)

we are going to replace 6x by 3x + 3x

9x² + 6x + 1

9x² + 3x +3x + 1

3x(3x + 1) + 1(3x+ 1)

(3x + 1)(3x+1)

The correct factorization of the trinomial 9x² + 6x + 1 is (3x + 1)(3x + 1) or (3x + 1)². option D.

How do we identify the correct option when the trinomial is factorized?

The trinomial 9x² + 6x + 1 is a perfect square trinomial, which can be factored as the square of a binomial.

Let's find the correct answer from your options:

(A) (3x + 1)(3x - 1): The difference of squares isn't the correct form for our trinomial.

(B) (9x + 1)(x - 1): Expanding this will not give us the original trinomial.

(C) (9x + 1)(x + 1): Expanding this will not give us the original trinomial.

(D) (3x + 1)(3x + 1): When expanded, this gives us 9x^2 + 3x + 3x + 1, which simplifies to 9x² + 6x + 1.

Therefore option D (3x + 1)(3x + 1) is correct

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Four golf balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 4cm.

What is the volume of the cylinder rounded to the nearest cubic centimeter?

What is the total volume of the four balls rounded to the nearest cubic centimeter?

What percent of the volume of the container is occupied by the four balls?

Answers

Hello,
Please, see the attached files.
Thanks. 

Multiply: (2x2 − 5x)(4x2 − 12x + 10)

Answers


The answer is 60x^2 - 138x + 72

Hope this helps!

Answer:

[tex]8x^4-44x^3+80x^2-50x[/tex]

Step-by-step explanation:

The given expression is

[tex](2x^2-5x)(4x^2-12x+10)[/tex]

Using distributive property we get

[tex]2x^2(4x^2-12x+10)-5x(4x^2-12x+10)[/tex]

[tex]2x^2(4x^2)+2x^2(-12x)+2x^2(10)-5x(4x^2)-5x(-12x)-5x(10)[/tex]

On simplification we get

[tex]8x^4-24x^3+20x^2-20x^3+60x^2-50x[/tex]

On combine like terms.

[tex]8x^4+(-24x^3-20x^3)+(20x^2+60x^2)-50x[/tex]

[tex]8x^4-44x^3+80x^2-50x[/tex]

Therefore the product of two polynomials is [tex]8x^4-44x^3+80x^2-50x[/tex].

a triangle with a base of 6cm and a height of 8cm is similar to a triangle with base 21cm. What is the height of the second triangle

Answers

Make a proportion.

Do base over height; [tex] \frac{base}{height}[/tex].

[tex] \frac{6}{8} = \frac{21}{h} [/tex]
h is the height of the second triangle. Solve for h.

Cross multiply.
[tex] \frac{6}{8} = \frac{21}{h} [/tex] 
6h = 168
h = 28

The height of the second triangle is 28 cm.

Cans of juice cost 25p each to produce
There are 6 cans in a pack.
12 packs are sold at £3.60 each.
What is the profit?

Answers

 the profit is 1.60 beacuse at 25  cents times 6 is two dollars and since it is 3.60 the profit is 1.60 and 1.60 times twelve is 19.20 so the answer is 19 dollars  and twenty cents

How many arrangements are possible using the letters in the word fuzzy if each letter "z" is distinctly different than the other? how many arrangements are possible if the letter "z" is interchangeable with the other? explain your reasoning?

Answers

If the letter z's are distinctly different, there are P(5,5) arrangements. That is 
    [tex]P\left(5,5\right)=5!=5\cdot 4\cdot 3\cdot 2\cdot 1=120[/tex]

If the z's are interchangeable, the number of different arrangements is given by 
     [tex]\frac{5!}{2!}=5\cdot 4\cdot 3=60[/tex]

When each letter "z" is distinctly different, there are 60 possible arrangements.
When the letter "z" is interchangeable with the others, there are 24 possible arrangements.

1. When each letter "z" is distinctly different from the others:
- The word "fuzzy" has 5 letters in total, including 2 "z" letters.
- To calculate the number of arrangements, we use the formula for permutations with repeated elements:
- The formula is: n! / (n1! n2! ... * nk!)
- n is the total number of letters in the word (5 in this case).
- n1, n2, ... are the number of repetitions of each distinct letter.
- Calculating: 5! / (1! 2! 1! * 1!) = 120 / 2 = 60 arrangements.

2. When the letter "z" is interchangeable with the other letters:
- In this case, there are 4 distinct letters in the word "fuzzy" (f, u, z, y).
- The total number of arrangements can be calculated using the formula for permutations of distinct items.
- Calculating: 4! = 24 arrangements.
In summary:
- When each letter "z" is distinctly different, there are 60 possible arrangements.
- When the letter "z" is interchangeable with the others, there are 24 possible arrangements.

|-x-2y| for x =-3 and y=3

Answers

[tex]|-x-2y|\ for\ x=-3\ and\ y=3.\\\\substitute:\\\\|-(-3)-2\cdot3|=|3-6|=|-3|=3[/tex]

Tom has been given 35 chores to complete today this morning he finished seven of them how many chores does he now have left to do

Answers

Simple equation: 35-7=28 chores left to do
He should only have 28 left to do.

PLS HELP! Tanisha is planning a party. She will serve hamburgers, potato salad, strawberry shortcake, and lemonade. Including Tanisha, 28 people will be at the party. Tanisha expects that each person will drink two 8−ounce glasses of lemonade at the party, and makes 448 ounces of lemonade. Tanisha's mother buys 38 lemons. They know it takes 8 lemons to make 80 ounces of lemonade. Does Tanisha need more lemons?

Answers

Shee needs 448 ounces of lemonade.

448 ÷ 80 =5.8
⇒ There are 5.6 80-ounce of lemonade.

80 ounces of lemonade needed 8 lemons.
448 ounces of lemonade needed 8 x 5.6 = 44.8 lemons.

Tanisha has 38 lemons. 
She does not have enough lemons.
She needs 44.8 - 38 = 7 more lemons.

Answer: Tanisha needs more lemons. She needs 7 more.

Answer: 7 more lemons

Step-by-step explanation:

Since she needs 448 ounces of lemonade you have to divide which is 5.6 . As a result there are 5.6 80 ounces of lemonade. 80 ounces needs 8 lemons.  448 ounces of lemonade are needed 8 x 5.6 = 44.8 lemons.  Tanisha only has 38 lemons, which isn't enough. 44.8 - 38 =  is about 7 more lemons.

HEEEELLLPP!!!!!!!!!!!!!!!WILL GIVE THE BRAIN!!!!!POINTS!!!!!!!
plz

Answers

If you observe the graph, it has a minimum point at x = -2

It is the local minimum as it is the minimum point in the neighboring. The term local is used, as it is the lowest point within a short interval and not for the entire function. 

The interval which correctly shows the local minimum is [-3, -1]

So, the correct answer is option Third

What is the slip of the line given by the equation y=-1/3 x

Answers

the slip?  I don't think it has any slip, but as far as the slope goes, well, the equation is in slope-intercept form, thus

[tex]\bf y=\stackrel{slope}{-\cfrac{1}{3}}x~~\stackrel{y-intercept}{+0}[/tex]

Which additional information is needed to solve this problem?



John wants to buy a new game for his computer. He can save $12 a week if he mows his neighbor's lawn and $10 a week if he babysits his nephew. How many weeks will it take John to save enough money to buy the computer game?


A.
total amount John can save in 1 week

B.
the cost of the game

C.
amount John earns per hour babysitting

Answers

Hi there!

The answer is B.
the cost of the game.

We need to know the cost of the game in order to find out how many weeks John has to save money. If we don't know this price, we'll never know whether John has saved enough money.

We can find out the total amount of money John can save in 1 week (so A. is not the answer). The amount of money John earns per hour doesn't matter to answer the question (so C. is wrong).

~ Hope this helps you!
the answer is B he won't know how much to save if he does not know the cost of the game

which transformation can verify congruence by flipping a triangle over the y-axis?

A. Dilation
B. Translation
C. Reflection
D. Rotation

Answers

Reflection. Reflection is when you flip an object over an axis. Flipping the triangle over axis wouldn't change the triangles properties.

Answer:  C.  Reflection

Step-by-step explanation:

There are three rigid transformations which create congruent figures :  

a)reflections, b) rotations, c) translations

A reflection is a transformation that flips a figure on the coordinate plane across a given line without changing the shape or size of the figure.

A translation moves a shapes by a particular distance.

A rotation rotates a shape around a fix point by an angle .

Therefore, the transformation can verify congruence by flipping a triangle over the y-axis is reflection.

someone please help asap! Which statement is most likely true for this distribution?

Answers

Answer:

C) The mean is greater than the median.

Step-by-step explanation:

This distribution is right skewed; that means it has a longer tail to the right and the data is "bunched up" at the left.

In a right skewed distribution, the majority of data points are at the smaller end; for this reason, the median will be towards the left side of the graph.

The higher numbers in the "tail" will bring the mean up, making it larger than the median.

The correct statement for the distribution is the mean is greater than the median.

What is mean and median?

The mean is the average of a data set. The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.

The median is the middle term of a distribution.

It measure determines the middle value of a dataset listed in ascending order.

Therefore, from the distribution the data are rightly skewed. The higher numbers in the "tail" will bring the mean up, thereby making it larger than the median.

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A license plate has 3 letters and 3 digits in that order. a witness to a hit-and-run accident saw the first 2 letters and the last digit. if the letters and digits can be repeated, how many license plates must be checked by the police to find the culprit?

Answers

26×10×10=2600

Hope this helped!

The police must check 2600 possible license plates, calculated by multiplying 26 possibilities for the third letter not seen by the witness with 100 possibilities for the two digits also not seen.

To determine how many license plates the police must check to find the culprit, we consider the information that the witness saw the first two letters and the last digit. Since letters can be repeated, there are 26 possibilities for each of the two letters the witness saw. For the last digit, which the witness also saw, there are 10 possibilities (0 through 9). The third letter and the other two digits, which the witness did not see, each have the following number of possibilities: 26 for the third letter, and 10 for each of the two remaining digits.

Calculating the number of possible combinations:

First two letters (seen by the witness): 26 * 26 = 676 possibilitiesLast digit (seen by the witness): 10 possibilitiesThird letter (not seen by the witness): 26 possibilitiesThe two remaining digits (not seen by the witness): 10 * 10 = 100 possibilities

Therefore, the total number of license plates the police must check is the product of the possibilities for the parts the witness did not see:

26 (third letter) * 100 (two remaining digits) = 2600 possible license plates.

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