Answers
Related Questions
10 POINTS!!! FULL ANSWER IN STEP BY STEP FORMAT!!
Answers
The sign of the first derivative changes at x=0, at which point the slope is undefined (the curve is vertical). The curve approaches +∞ at x=0 both from the left and from the right, so the other absolute extreme is (0, +∞).
b) The second derivative (g'') changes sign at x=2, so there is a point of inflection there.
c) There is a vertical asymptote at x=0 and a flat spot at x=2. The curve goes through the points (-2, 5) and (4, 1), is increasing to the left of x=0 and non-increasing to the right of x=0. The curve is concave upward on [-2, 0) and (0, 2) and concave downward on (2, 4]. A possible graph is shown, along with the first and second derivatives.
Find the inverse function f^-1(x) for the given function f(x). f(x) =3x-8
Answers
Answer: [tex]y=\dfrac{x+8}{3}=\dfrac{1}{3}x+\dfrac{8}{3}[/tex]
Final answer:
To find the inverse of the function f(x) = 3x - 8, you swap x and y and solve for y, resulting in the inverse function f^-1(x) = (x + 8) / 3.
Explanation:
To find the inverse function f-1(x) for the given linear function f(x) = 3x - 8, we will follow these steps:
Replace f(x) with y: y = 3x - 8.
Swap x and y to make it x = 3y - 8.
Solve for y to get the inverse function.
Starting with x = 3y - 8, we add 8 to both sides to obtain x + 8 = 3y. Then, we divide both sides by 3 to isolate y, resulting in y = (x + 8) / 3. Therefore, the inverse function is f-1(x) = (x + 8) / 3.
A 9 cm tall cone shaped paper cup can hold up to 58.9 cm cubed of water. What is the minimum amount of paper needed to make the paper cup, assuming no overlap in the paper? Use 3.14 for π.
Answers
r = Sqrt 3V/πh = Sqrt [(58.9*3)/(3.14*9)] = 2.5 cm, minimum
Surface area, A = πr [r+ Sqrt (h^2+r^2)] = 3.14*2.5*[2.5+ Sqrt (9^2+2.5^2)] = 92.95 cm^2
Therefore, minimum amount of paper required is 92.95 cm^2
What is the equation of the circle with a diameter of 6 units and a center located at (2, -5) on the coordinate plane?
Answers
[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{2}{ h},\stackrel{-5}{ k})\qquad \qquad radius=\stackrel{3}{ r} \\\\\\\ [x-2]^2+[y-(-5)]^2=3^2\implies (x-2)^2+(y+5)^2=9[/tex]
The equation of a circle centered at (2, -5) with a diameter of 6 units is (x-2)² + (y+5)² = 9.
Explanation:The equation of a circle in the coordinate plane is given by (x-h)² + (y-k)² = r², where (h, k) are the coordinates of the center of the circle, and r is the radius. In this case, the center of the circle is at (2, -5) and the diameter is 6 units. Therefore, the radius (r) is half the diameter, which is 3 units.
Substituting h=2, k=-5, and r=3 into the equation, we get the equation of the circle: (x-2)² + (y+5)² = 9.
Learn more about Circle Equation here:https://brainly.com/question/36026103
#SPJ2
The median is 28; 16,24,x,48
Answers
To find the media, you take the middle number. If there is no discrete middle number, take the sum of the two closest to the middle and divide by 2.
(24 + x)/2 = 28
Multiply by 2 on both sides to get:
24 + x = 56
Subtract 24 from both sides to isolate the variable:
x = 56 - 24
x = 32
Please help me with this question
Answers
◉ Data point (10, 10); Residual = 4.50
_____
Apparently, this question makes no use of the line of best fit.
Multiply the polynomials.
(x – 7)(x2 + 3x – 3)
A. x3 – 4x2 – 3x + 21
B. x3 – 7x2 – 24x + 21
C. x3 – 4x2 – 24x + 21
D. x3 – 7x2 – 3x + 21
Answers
Answer:
C) x³ -4x² - 24x + 21.
Step-by-step explanation:
Given : (x – 7)(x² + 3x – 3).
To find : Multiply the polynomials.
Solution : We have given (x – 7)(x² + 3x – 3).
Distributes x over (x² + 3x – 3) and -7 over (x² + 3x – 3).
Then
x (x² + 3x – 3) -7(x² + 3x – 3).
x³ + 3x² -3x - 7x² - 21x +21.
Combine like terms
x³ + 3x² - 7x² -3x -21x + 21.
x³ -4x² - 24x + 21.
Therefore, C) x³ -4x² - 24x + 21.
Answer:
x³ -4x² - 24x + 21.
Step-by-step explanation:
Ape-x
[Geometry Basics] I'm just checking if this is correct:
~ Endpoint: (-9, -1), midpoint: (8,14)
Answer I got: (25, 31)
~ Endpoint: (10,12), midpoint: (6,9): (2,6)
I will give you brainiest if it's correct :) And 20 pts.
Answers
[tex]\bf -------------------------------\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ x &,& y~) % (c,d) &&(~10 &,& 12~) \end{array}\qquad \\\\\\ \left( \cfrac{10+x}{2}~~,~~\cfrac{12+y}{2} \right)=\stackrel{midpoint}{(6,9)}\implies \begin{cases} \cfrac{10+x}{2}=6\\\\ 10+x=12\\ \boxed{x=2}\\ -------\\ \cfrac{12+y}{2} =9\\\\ 12+y=18\\ \boxed{y=6} \end{cases}[/tex]
For the solids show, choose all the statements that will be true if we can infer the solids' congruence by Cavalieri's Principle. The radii are congruent. The bases are congruent. The altitudes are congruent. The bases are parallel.
Answers
Cavalieri's principle states that if two solids have equal height and if the cross-sections intersected by planes parallel to the bases and equally distant from them have always the same ratio, then the two volumes will have the same ratio.
Therefore, we can say that:
1) the radii are congruent (bases and cross-sections are congruent circles);
2) the bases are congruent;
3) the altitudes are congruent;
4) the bases are parallel.
Hence, all four statements are TRUE.
Answer:
All four are true :)
Step-by-step explanation:
What is the exact area of a circle with a diameter of 20 cm?
400πcm^2
10πcm^2
100πcm^2
20πcm^2
Answers
The radius of a circle can be found by dividing the diameter by 2. In other words : the radius is half of the diameter.
Therefore, the radius of a circle with a diameter of 20 cm is 10 cm.
The exact area of a circle can be found using the following formula:
[tex]a = \pi \times \: {r}^{2} \\ with \\ a = area \\ r = radius[/tex]
In order to find our answer, we need to plug in the data from the question.
[tex]a = \pi \: \times {10}^{2} = 100\pi[/tex]
Hence, the answer is 100πcm^2.
The exact area of a circle with a diameter of 20 cm is 100π cm². This is found using the formula Area = πr², with 'r' being the radius of the circle.
Explanation:The subject of this question falls under the category of Mathematics, specifically geometry. In order to find the area of a circle, we use the formula: Area = πr², where r is the radius of the circle.
The diameter of the circle is given as 20 cm, so the radius, which is half the diameter, would be 10 cm. Substituting the radius value into the formula gives us: Area = π(10 cm)² = 100π cm². Therefore, the exact area of the circle with a diameter of 20 cm is 100π cm².
Learn more about Area of a Circle here:https://brainly.com/question/28642423
#SPJ3
Graph the function y = 6/x . Draw a chart to show the ordered pairs that are on the graph.
Answer:
x y
-3
-2
-1
1
2
3
Answers
Answer:
see the attachment for the graph and chart
Step-by-step explanation:
A spreadsheet or graphing calculator is convenient for making a chart of ordered pairs.
Jon performs 3 transformations on a pentagon. First, he reflects it over the x-axis. Then, he translates it 3 units to the left and 4 units up. Finally, he reflects the image over the line x = 1. Are the original and transformed images congruent? Justify your answer.
Answers
The original and transformed images are congruent.
yes; Reflections and translations are rigid motions. Rigid motions preserve the size of the original image.
does anyone know where to find the poly-graphical point of a circle?
Answers
y = cy + r * sin(a)
A rectangular crate has the dimensions of 32.1 inches by 28.2 inches by 1 foot.What is the volume of the crate? Round your answer to the nearest tenth, if necessary
a)6.3 cubic feet
b)16. cubic feet
c)18.4 cubic feet
d)905.22 cubic feet
Answers
So the answer is D
28.2 inches = 28.2 ÷ 12 = 2.35 feet
32.1 inches = 32.1 ÷ 12 = 2.675 feet
Volume = Length x Width x Height
Volume = 2.35 x 2.675 x 1 = 6.3 ft³ (nearest tenth)
Answer: 6.3 ft³
3 red pens, 9 blue pens, 8 green pens
What is the probability of picking a blue? In a decimal
Answers
the probability of picking a blue is 0.45.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
3 red pens, 9 blue pens, 8 green pens
now, we get,
There are a total of 20 pens.
There are 9 blue pens out of 20 total pens.
In decimal format,
i.e. 9/20
=0.45
you have a chance of 0.45 .
hence, the probability of picking a blue is 0.45.
To learn more on probability click:
brainly.com/question/11234923
#SPJ2
Please help, I need to turn in today
Answers
Please help with geometry
Answers
[tex]A_\Delta=\dfrac{ah}{2}[/tex]
We have:
[tex]a=6.3cm;\ h=8cm[/tex]
therefore
[tex]A_\Delta=\dfrac{6.3\cdot8}{2}=25.2\ cm^2[/tex]
Answer: 25.2 cm².
Chris plants a sunflower that is 6 inches tall. The sunflower is expected to grow at an average rate of 1.5 inches per day during the next month.
A. Create an equation that Chris can use to find the number of days, x, it will take the sunflower to grow to a height of 45 inches.
B. How many days will it take the sunflower to grow to a height of 45 inches?
Answers
B. We will solve the equation to find out how many days it will take to get to 45 inches.
6 + 1.5d = 45
-6 -6
1.5d = 39
1.5 1.5
d = 26
The number of days it would take is 26.
The midpoint of is m(–8, 1). one endpoint is k(–6, 5). find the coordinates of the other endpoint l.
Answers
The midpoint of kl is m(–8, 1). one endpoint is k(–6, 5). find the coordinates of the other endpoint l.
we know that
the formula of midpoint is
Xm=(x1+x2)/2----> 2*Xm=x1+x2------> x2=2*Xm-x1
Ym=(y1+y2)/2----> 2*Ym=y1+y2------> y2=2*Ym-y1
let
(x1,y1)-------> (–6, 5).
(Xm,Ym)-----> (-8,1)
find (x2,y2)
x2=2*Xm-x1-----> 2*(-8)-(-6)----> -10
y2=2*Ym-y1----> 2*(1)-5-----> -3
the point l is (-10,-3)
The price of a gym membership has a one-time sign-up fee and a monthly fee. The price can be modeled by the function y = 10x + 15, where x is the number of months. What is the y-intercept, and what does it represent?
10; it represents the monthly fee
10; it represents the one-time sign-up fee
15; it represents the monthly fee
15; it represents the one-time sign-up fee
Answers
Suppose N represents a power of 10. what is the value of n when 31,100 is rounded to the nearest power of 10?
Answers
We get the approximate value of [n] as 5.
What is logarithm? What is a mathematical equation and expression?A quantity representing the power to which a fixed number (the base) must be raised to produce a given number. We can write -[tex]$\log_{b}({b^x})=x[/tex]
A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have 31,100 is rounded to the nearest power of 10 and [N] represents a power of 10.
We can write -
10ⁿ = 31100
10ⁿ = 311 x 10²
10ⁿ ⁻ ² = 311
log(10ⁿ ⁻ ²) = log(311)
(n - 2) log 10 = log (311)
n - 2 = log(311)/log(10)
n - 2 = 2.5
n = 4.5
n = 5 (approx.)
Therefore, we get the approximate value of [n] as 5.
To solve more questions on Equations, Equation Modelling and Expressions visit the link below -
brainly.com/question/14441381
#SPJ2
When rounding 31,100 to the nearest power of 10, we get the value of n is 4.
To find the value of n when 31,100 is rounded to the nearest power of 10, we first need to determine which powers of 10 are closest to 31,100. The nearest powers of 10 to 31,100 are 104 (10,000) and 105 (100,000). Since 31,100 is closer to 104 than to 105, we round it down to 104.
Therefore, when 31,100 is rounded to the nearest power of 10, the value of n is 4.
The process involves converting the number into scientific notation and then adjusting the exponent, which represents the number of places the decimal point moves. In our case, to convert 31,100 to a number between 1 and 10, we would express it as 3.11 × 104, confirming that the value of n is 4.
How do I find the solution for this quadratic?
Answers
Please, see the attached file.
Thanks.
Find the quotient of 3/5 and 9/10 . Express your answer in simplest form.
Answers
Short answer: 2/3
Why?
When dividing two fractions, you don't divide, you find the reciprocal of the second fraction (9/10) and multiply. So, it's 3*10/9*5. Simplify. {3 * 10 => 30} ~ {9 * 5 => 45} Now we have 30/45. This can be simplified. Simplified, 30/45 reduces down to 2/3.
Hope this helped you! ♥
The quotient of 3/5 and 9/10 is the value obtained by dividing both values, Hence, the quotient of the division is 2/3
The numerator = 3/5 The denominator = 9/10The division operation can be expressed thus :
3/5 ÷ 9/10
Take the reciprocal of the denominator and change the sign to multiplication ;
Reciprocal of 9/10 = 10/9
Hence, we have ;
3/5 × 10/9 = 30/45
In simplest form ; 30/45 = 10/15 = 2/3Therefore, the quotient is 2/3
Learn more : https://brainly.com/question/18112348
Find the slope of the line
-4
-1/4
1/4
4
Answers
run = 8 (from -4 to +4)
rise = 2 (from 0 to 2)
rise 2
slope = ------- = -------- = 1/4 y-intercept is (0,1)
run 8
equation of this line is thus y = mx + b, or y = (1/4)x + 1 (answer)
another geometry file upload
Answers
combining like terms 13x -8x =12 +13
5x= 25 x= 5
x=5
PLEASE HELP! BRAINLIEST!!!!!!! PLEASE
Jade used candle molds, as shown, to make candles that were perfect cylinders and spheres:
What is the approximate difference in the amount of wax needed to make a candle from each of these molds? (Use π = 3.14.)
27.0 cubic inches
47.1 cubic inches
84.78 cubic inches
91.12 cubic inches
Answers
First you have to find the volume of the cylinder
To find the volume of a cylinder you use the equation
[tex]V = \pi r^{2} h[/tex]
V is volume
r is radius
h is height
Put in the values you know and 3.14 for pi
[tex]V = 3.14 * 3^{2} * 7[/tex]
Square the number
V = 3.14 * 9 * 7
Multiply
V = 197.82
------------------------------------------------------------------------------------------------------
Next you find the volume of the sphere
To find the volume of a sphere you use the equation
[tex]V = \frac{4}{3} \pi r^{3} [/tex]
V is volume
r is radius
Put in the values you know and 3.14 for pi
[tex]V = \frac{4}{3} * 3.14 * 3^{3} [/tex]
Cube the number
[tex]V = \frac{4}{3} * 3.14 * 27[/tex]
Multiply
V = 113.04
------------------------------------------------------------------------------------------------------
Finally you subtract the two volumes from each other
197.82 - 113.04 = 84.78
------------------------------------------------------------------------------------------------------
The answer is C)84.78
Hope this helps!
Jonathan opened an auto repair shop. In the first month, 11 cars were serviced at his shop. The number of cars serviced at Jonathan's shop increased at 9 cars per month.
How many total cars were serviced at Jonathan's shop at the end of the 7th month?
329 cars
65 cars
266 cars
201 cars
Answers
Number of cars in second month = 11 + 9 =20
Number of cars in third month = 20 + 9 = 29
If we observe, the number of cars form an Arithmetic sequence with first term as 11 and common difference 7. We are to find the total cars received till the end of 7th term in the shop i.e. we are to find the sum of first 7 terms of the sequence.
So, using the formula of sum Arithmetic series we can write:
Cars received in 7th months = [tex] \frac{7}{2}(2(11)+(7-1)(9)) = 266 [/tex] cars
Thus, 266 cars were received at the end of 7th month at Jonathan's auto repair shop.
He probability of choosing a vowel (a, e, i, o, or u) from a deck of cards containing the 26 letters of the alphabet is shown below. what is the probability of choosing the letters a and e one after the other without replacement?
Answers
There is 1 a out of 26 letters; P(a) = 1/26
There is 1 e out of 26 letters; however, since it comes after drawing the a and is done without replacement, it is out of 25: 1/25
Together, their probabilities are 1/26(1/25) = 1/650
Need help on this asap!!
Answers
Please, see the attached file.
Thanks.
Find the length of the hypotenuse of a right triangle whose legs are 5 and sqare root of 2
Answers
4 + 5 = c²
9 = c²
c = 3
Sorry this is so late and was never answered. I just saw it pop up in the related questions.
Answer:
The length of the hypotenuse is 3√3 units.
Step-by-step explanation:
It is given that the length of the legs of a right triangle are 5 units and √2 units.
According to the Pythagoras theorem, in a right angled triangle
[tex](hypotenuse)^2=(leg_1)^2+(leg_2)^2[/tex]
Substitute leg₁=5 and leg₂=√2 in the above formula.
[tex](hypotenuse)^2=(5)^2+(\sqrt{2})^2[/tex]
[tex](hypotenuse)^2=25+2[/tex]
[tex](hypotenuse)^2=27[/tex]
Taking square root both the sides.
[tex]hypotenuse=\sqrt{27}[/tex]
[tex]hypotenuse=3\sqrt{3}[/tex]
Therefore the length of the hypotenuse is 3√3 units.