Answer:
0
Step-by-step explanation:
Hello, please consider the following.
For any a and b real numbers we can write.
[tex](a-b)(a+b)=a^2-b^2[/tex]
We apply this formula two times here, as below.
[tex](x+1)(x^{2}+1)(x-1)=(x+1)(x-1)(x^{2}+1)\\\\=(x^2-1^2)(x^2+1)=(x^2-1)(x^2+1)\\\\=(x^2)^2-1^2=x^4-1[/tex]
We have the coefficient of 1 for [tex]x^4[/tex] and the constant term is -1, so the sum of the coefficients is 0.
Thank you.
Answer:
1
Step-by-step explanation:
(x + 1)(x² + 1)(x - 1)
= (x³ + x + x² + 1)(x - 1)
= x^4 - x³ + x² - x - x³ - x² + x - 1
= x^4 - 1
Coefficient of x^4 = 1
Let f(x) = 8x3 + 16x2 − 15 and g(x) = 2x + 1. Find f of x over g of x
[tex]\dfrac{f(x)}{g(x)}=\dfrac{8x^3+16x^2-15}{2x+1}[/tex]
The average value of a function f(x, y, z) over a solid region E is defined to be fave = 1 V(E) E f(x, y, z) dV where V(E) is the volume of E. For instance, if rho is a density function, then rhoave is the average density of E. Find the average value of the function f(x, y, z) = 5x2z + 5y2z over the region enclosed by the paraboloid z = 9 − x2 − y2 and the plane z = 0.
Answer:
An aluminum bar 4 feet long weighs 24 pounds
Step-by-step explanation:
if a flight to europe takes about 13 hours and you make one round trip flight per month how many total days do you travel in a year
Answer:
13 days
Step-by-step explanation:
Given that a one-way flight to europe will take 13 hours
A round trip will take = 13 hrs x 2 = 26 hours
Also given that we make one round trip per months for 12 months (1 year)
We will take a total of 12 round trips per year
Number of hours taken for 12 round trips
= 26 hours per round trip x 12 round trips
= 26 x 12
= 312 hours
Recall that there are 24 hours in a day, hence to convert 312 hours into days, we have to divide this by 24.
Number of days = number of hours ÷ 24
= 312 ÷ 24
= 13 days
The relative frequency approach to probability uses long term relative frequencies, often based on past data.
a. True
b. False
Answer:
True
Step-by-step explanation:
Relative frequency is the ratio of the occurrence of a singular event and the total number of outcomes. This is a tool that is often used after you collect data. You can compare a single part of the data to the total amount of data collected.
For example, if a particular machine produces 50,000 widgets one at a time, and 5,000 of those widgets are faulty, the probability of that machine producing a faulty widget is approximately 5,000 out of 50,000, or 0.10.
Which of the following equations have infinitely many solutions?
Choose all answers that apply:
A10x- 10 = -10x + 10
B- 10x - 10 = -10x + 10
C-10x – 10 = -10x - 10
D10x - 10 = -10x – 10
Hey there! I'm happy to help!
An equation with infinite solutions has a solution of x=x. You can plug in any x-value and it will equal x, so there are infinitely many solutions.
ANSWER A
10x-10=-10x+10
We add 10 to both sides.
10x=-10x+20
We add 10x to both sides.
20x=20
We divide both sides by 20.
x=1
We have a solution of 1, so this is not an equation with infinitely many solutions.
Answer B
-10x-10=-10x+10
We add 10 to both sides.
-10x=-10x+20
We add 10 x to both sides.
0=20
This has no solutions because the x is gone, so there cannot be a solution.
Answer C
-10x-10=-10x-10
We add 10 to both sides.
-10x=-10x
We divide both sides by -10.
x=x
This has infinitely many solutions.
Answer D
10x-10= -10x-10
We add 10x to both sides.
20x-10=-10
We add 20 to both sides.
20x=0
We divide both sides by 20.
x=0
There is a single solution here, not infinitely many.
Therefore, the answer is C. -10x-10=-10x-10.
Have a wonderful day! :D
more math questions if you would
Answer:
A.
Step-by-step explanation:
So we are given the function:
[tex]f(x)=7x+8[/tex]
To find the inverse of the function, we simply need to flip f(x) and x and then solve for f(x). Thus:
[tex]x=7f^{-1}(x)+8\\x-8=7f^{-1}(x)\\f^{-1}(x)=\frac{x-8}{7}[/tex]
So the answer is A.
Answer:
[tex]\large \boxed{\mathrm{Option \ A}}[/tex]
Step-by-step explanation:
f(x) = 7x+8
Write f(x) as y.
y = 7x + 8
Switch variables.
x = 7y + 8
Solve for y to find the inverse.
x - 8 = 7y
[tex]\frac{x-8}{7}[/tex] = y
Find equations of the tangent plane and the normal line to the given surface at the specified point. x + y + z = 7exyz, (0, 0, 7)
Answer:
Full question is:
Find equations of the tangent plane and the normal line to the given surface at the specified point. x + y + z = 7[tex]e^{xyz}[/tex] at a specified point (0, 0, 7)
Step-by-step explanation:
If we have a level surface, then it will give us
f(x,y,z) = x+y+z = 7[tex]e^{xyz}[/tex]. where f is the function of the x, y, and z coordinates.
Now let us calculate the ∇ gradient of f at point (0,0,7):
∇[tex]f|_{(0,0,7)}[/tex] = (fx,fy,fz) = (1−7yz[tex]e^{xyz}[/tex],1−7xz[tex]e^{xyz}[/tex],1−7xy[tex]e^{xyz}[/tex])[tex]|_{(0,0,7)}[/tex]
= (1, 1, 1)
We get the equation for the tangent plane A:
A: 1(x−0) + 1(y−0) + 1(z−7)=0
This can also be written as:
x+y+z = 7 ------------------------------------------------------------------(a)
The equation for the normal line B gives us :
L: (x,y,z) = (0,0,7) + t(1, 1, 1), t ∈ R --------------------------------(b)
A plot of land has vertices as follows, where each coordinate is a measurement in feet. Find the perimeter of the plot of land. (1,7),(7,7),(7,1),(1,1) please help and explain how to do this type of thing because i am lost
Answer:
Perimeter of ABCD = 36 ft
Step-by-step explanation:
Given:
A (1,7)
B (7,7)
C (7,1)
D (1,1)
Find:
Perimeter of ABCD
Computation:
Distance between two point = √(x1-x2)² + (y1-y2)²
So,
AB = √(1-7)²+(7-7)²
AB = 6 ft
BC = √(7-7)²+(7-1)²
BC = 6 ft
CD = √(7-1)²+(1-1)²
CD = 6 ft
DA = √(1-1)²+(1-7)²
DA = 6 ft
Perimeter of ABCD = AB + BC + CD + DA
Perimeter of ABCD = 6 + 6 + 6 +6
Perimeter of ABCD = 36 ft
The perimeter of the plot is the sum of side length of the plot of land.
The perimeter of the plot is 24 feet.
Represent the vertices as follows:
[tex]W = (1,7)[/tex]
[tex]X = (7,7)[/tex]
[tex]Y = (7,1)[/tex]
[tex]Z = (1,1)[/tex]
First, we calculate the side length using the following distance formula:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
So, we have:
[tex]WX = \sqrt{(1- 7)^2 + (7- 7)^2} = \sqrt{36} = 6[/tex]
[tex]XY = \sqrt{(7- 7)^2 + (7- 1)^2} = \sqrt{36} = 6[/tex]
[tex]YZ = \sqrt{(7- 1)^2 + (1- 1)^2} = \sqrt{36} = 6[/tex]
[tex]ZW = \sqrt{(1- 1)^2 + (1- 7)^2} = \sqrt{36} = 6[/tex]
The perimeter (P) is then calculated as follows:
[tex]P = WX + XY + YZ + ZW[/tex]
So, we have:
[tex]P = 6 + 6 + 6 + 6[/tex]
[tex]P = 24[/tex]
Hence, the perimeter of the plot of land is 24 feet.
Read more about perimeters at:
https://brainly.com/question/394193
need help asap please help let quick eeeeeeeeeeeeeeee
Answer:
5/14
Step-by-step explanation:
1[tex]\frac{3}{4}[/tex] = 7/4
4[tex]\frac{9}{10}[/tex] = 49/10
[tex]\frac{7}{4}[/tex] / [tex]\frac{49}{10}[/tex]
[tex]\frac{7}{4}[/tex] x [tex]\frac{10}{49}[/tex] = [tex]\frac{70}{196}[/tex]
or
[tex]\frac{1}{2}[/tex] x [tex]\frac{5}{7}[/tex] = [tex]\frac{5}{14}[/tex]
Answer:
e
Step-by-step explanation:
e
You are an urban planner assessing the growth of a city. Ten years ago, the city's population was 250,823. Its current population is 325,823. By about what percentage has the city grown over the past ten years? Round to the nearest percent.
Answer:
Here is the answer i got-
Step-by-step explanation:
325823-250823=75000
325823’s 244367250percent is 75000
Find (fºg)(2) and (f+g)(2) when f(x)= 1/x and g(x) = 4x +9
[tex](f\circ g)(2)=\dfrac{1}{4\cdot2+9}=\dfrac{1}{17}\\\\(f+g)(2)=\dfrac{1}{2}+4\cdot2+9=\dfrac{1}{2}+17=\dfrac{1}{2}+\dfrac{34}{2}=\dfrac{35}{2}[/tex]
which polynomial correctly combines the like terms and expresses the given polynomial in standard form? 9xy³ -4y⁴ -10x²y² + x³y + 3x⁴ + 2x²y² - 9y⁴
Answer:
3x^4+(x^3)y-8x^2y^2+9xy^3-13y^4
Step-by-step explanation:
3x^4+(nothing)=3x^4
x^3y+(nothing)=x^3y
-10x^2y^2=2x^2y^2=-8x^2y^2
9xy^3+(nothing)=0
-4y^4-9y^4=-13y^4
Add it all up and write the terms by descending order of exponent value, and u get my answer.
Find the side length, b.
Round to the nearest tenth.
Answer:
b ≈ 9.2
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
b² = a² + c² = 6² +7² = 36 + 49 = 85 ( take the square root of both sides )
b = [tex]\sqrt{85}[/tex] ≈ 9.2 ( to the nearest tenth )
Answer:
9.22
Step-by-step explanation:
Since it's a 90° triangle [tex]c^{2} =a^{2} +b^{2}[/tex].
In this example they labeled the hypotenuse as b instead of c are equation is still the same just put the correct variables in the right places.
[tex]b = \sqrt{6^{2} +7^{2} }[/tex]
b = 9.22
Find the missing coordinate
Answer:
(0, -10a)
Step-by-step explanation:
From the picture attached,
Coordinates of a point have been given as (-10a, 0)
x-coordinate → distance of the point from the origin on x-axis
y-coordinate → distance of the point from the origin on y-axis
Therefore, distance of the given point on x-axis = -10a [(-) sign denotes the negative side of the x-axis]
Distance of the other point with unknown coordinates (x, y) (on y-axis) from the origin = y
And y = 10a
Therefore, coordinates of the unknown point will be (0, -10a).
[Here (-) sign denotes the negative side of the y-axis]
The graph of the function f(x) = (x − 3)(x + 1) is shown.
On a coordinate plane, a parabola opens up. It goes through (negative 1, 0), has a vertex at (1, negative 4), and goes through (3, 0).
Which describes all of the values for which the graph is positive and decreasing?
all real values of x where x < −1
all real values of x where x < 1
all real values of x where 1 < x < 3
all real values of x where x > 3
Answer:
x < -1
Step-by-step explanation:
Since the parabola opens upward, it is positive and decreasing where the left branch is above the x-axis: all points to the left of x=-1.
all real values of x where x < -1
please help solving.
Answer:
right machine first, then left.6 into left machine, then rightStep-by-step explanation:
a) Putting 6 into the first (left) machine will give an output of ...
y = √(6 -5) = √1 = 1
Putting 1 into the second (right) machine will give an output of ...
y = 1² -6 = -5
This answers the second question, but not the first question.
__
If we put 6 into the right machine first, we get an output of ...
y = 6² -6 = 30
Putting 30 into the left machine, we get an output of ...
y = √(30 -5) = √25 = 5 . . . . . the desired output.
The input must go into the right machine first, then its output goes into the left machine to get a final output of 5 from an input of 6.
__
b) The left machine cannot produce negative outputs, so achieving an output of -5 with the arrangement used in part A is not possible. (green curves in the attached graph)
However, as we have shown above, inputting 6 to the left machine first, following that by processing with the right machine, can produce an output of -5. (purple curve in the attached graph)
60 is x% of 12. Find the value of x.
Answer:
20
Step-by-step explanation:
We can set up a percentage proportion to find the value of x.
[tex]\frac{12}{x} = \frac{60}{100}[/tex]
Now we cross multiply:
[tex]100\cdot12=1200\\\\1200\div60=20[/tex]
Hope this helped!
WILL GIVE BRAINILY 5 STARS AND THANKS FOR CORRECT ANSWERLenora wants to buy granola bars for her hiking trip. Eight bars cost $2.40. She wants to buy 12 bars. How much will 12 bars cost?
Answer:
$3.60
Step-by-step explanation:
2.40/8=.30
$.30 per bar
.3 x 12= $3.60
Answer:
$3.60
Step-by-step explanation:
Proportions
8 bars ⇔ $2.4
12 bars ⇔ $W
W = 12*2.4/8
W = $3.6
Find the value of x.
Answer:
6x + 6 = 32
6x = 32 - 6
6x = 26
divide both sides by 6
6x/6 = 26/6
6x + 6 = 4.35
9x - 9 = 24
9x = 24 + 9
9x = 33
divide both sides by 9
9x/9 = 24/9
9x + 9 = 2.66
9x + 9 = 2.66
Answer: x=3
Step-by-step explanation:
[tex]\frac{32}{24} =\frac{4}{3} \\\\\frac{4}{3}=\frac{6x+6}{9x-9}\\ x=3[/tex]
Find the probability of winning a lottery with the following rule. Select the winning numbers from 1, 2, . . . ,34 . (In any order. No repeats.)
Complete Question
Find the probability of winning a lottery with the following rule. Select the six winning numbers from 1, 2, . . . ,34 . (In any order. No repeats.)
Answer:
The probability is [tex]P(winning ) = 7.435 *10^{-7}[/tex]
Step-by-step explanation:
From the question we are told that
The total winning numbers n = 34
The total number to select is r = 6
The total outcome of lottery is mathematically represented as
[tex]t_{outcome}) = \left n } \atop {}} \right. C_r[/tex]
[tex]t_{outcome}) = \frac{n! }{(n-r )! r!}[/tex]
substituting values
[tex]t_{outcome}) = \frac{ 34 ! }{(34 - 6 )! 6!}[/tex]
[tex]t_{outcome}) = \frac{ 34 ! }{28 ! 6!}[/tex]
[tex]t_{outcome}) =1344904[/tex]
The number of desired outcome is
[tex]t_{desired} = 1[/tex]
this is because the desired outcome is choosing the six winning number
The probability of winning a lottery is mathematically represented as
[tex]P(winning ) = \frac{t_{desired}}{t_{outcome}}[/tex]
substituting values
[tex]P(winning ) = \frac{1}{1344904 }[/tex]
[tex]P(winning ) = 7.435 *10^{-7}[/tex]
Find the Vertical asymptotes of the graph of f
[tex]f(x) = \frac{x + 2}{ {x}^{2} - 4}[/tex]
Answer:
x = 2 and x = -2
Step-by-step explanation:
To find the vertical asymptotes, set the denominator equal to zero and solve for x:
vertical asymptotes are x = 2 and x = -2
The table shows the results of a survey in which 10th-grade students were asked how many siblings (brothers and/or sisters) they have. A 2-column table has 4 rows. The first column is labeled Number of siblings with entries 0, 1, 2, 3. The second column is labeled number of students with entries 4, 18, 10, 8. What is the experimental probability that a 10th-grade student chosen at random has at least one, but no more than two, siblings? Round to the nearest whole percent. 65% 70% 75% 80%
Answer:
70%
Step-by-step explanation:
Given
Number of Siblings: || 0 || 1 || 2 || 3
Number of Students: || 4 || 18 || 10 || 8
Required
Determine the probability of a student having at least one but not more than 2 siblings
First, we have to determine the total number of 10th grade students
[tex]Total = 4 + 18 + 10 + 8[/tex]
[tex]Total = 40[/tex]
The probability of a student having at least one but not more than 2 siblings = P(1) + P(2)
Solving for P(1)
P(1) = number of students with 1 sibling / total number of students
From the given parameters, we have that:
Number of students with 1 sibling = 18
So:
[tex]P(1) = \frac{18}{40}[/tex]
Solving for P(2)
P(2) = number of students with 2 siblings / total number of students
From the given parameters, we have that:
Number of students with 2 siblings = 10
So:
[tex]P(2) = \frac{10}{40}[/tex]
[tex]P(1) + P(2) = \frac{18}{40} + \frac{10}{40}[/tex]
Take LCM
[tex]P(1) + P(2) = \frac{18 + 10}{40}[/tex]
[tex]P(1) + P(2) = \frac{28}{40}[/tex]
Divide numerator and denominator by 4
[tex]P(1) + P(2) = \frac{7}{10}[/tex]
[tex]P(1) + P(2) = 0.7[/tex]
Convert to percentage
[tex]P(1) + P(2) = 70\%[/tex]
Hence, the required probability is 70%
Answer:
Step-by-step explanation:
bB
Average of 44.64, 43.45, 42.79, 42.28
Answer:
43.29Step-by-step explanation:
[tex]44.64+ 43.45+42.79+42.28\\\\= \frac{44.64+ 43.45+42.79+42.28}{4} \\\\\\= \frac{173.16}{4} \\\\= 43.29\\[/tex]
According to a survey, typical American spends 154.8 minutes per day watching TV. A survey of 50 Internet users results in a mean time watching TV per day of 128.7 minutes, with a standard deviation of 46.5 minutes. Which appropriate test we should use to determine if Internet users spend less time watching TV
Answer:
Z > ± 1.645
z= 3.968
Step-by-step explanation:
We formulate the null and alternate hypotheses as
H0 =μ2 ≥ μ1 Ha: μ2 <μ1 one sided
Let α= 0.05
Since the sample sizes are large therefore the test statistic used under H0 is
The critical region for α= 0.05 for a one tailed test Z > ± 1.645
Z = (x`2- x`1) /s/ √n
Z= 154.8-128.746.5/√50
z= 26.1/6.577
z= 3.968
Since the calculated value of z lies in the critical region we reject H0 that internet users spend more time or equal time.
Find the center, vertices, and foci of the ellipse with equation 4x2 + 9y2 = 36. Center: (0, 0); Vertices: (-3, 0), (3, 0); Foci: Ordered pair negative square root 5 comma 0 and ordered pair square root 5 comma 0 Center: (0, 0); Vertices: (-9, 0), (9, 0); Foci: Ordered pair negative square root 65 comma 0 and ordered pair square root 65 comma 0 Center: (0, 0); Vertices: (0, -3), (0, -3); Foci: Ordered pair 0 comma negative square root 5 and ordered pair 0 comma square root 5 Center: (0, 0); Vertices: (0, -9), (0, 9); Foci: Ordered pair 0 comma negative square root 65 and ordered pair 0 comma square root 65
Answer:
Option A.
Step-by-step explanation:
The given equation of ellipse is
[tex]4x^2+9y^2=36[/tex]
Divide both sides by 36.
[tex]\dfrac{4x^2}{36}+\dfrac{9y^2}{36}=1[/tex]
[tex]\dfrac{x^2}{9}+\dfrac{y^2}{4}=1[/tex]
[tex]\dfrac{x^2}{3^2}+\dfrac{y^2}{2^2}=1[/tex] ...(1)
The standard form of an ellipse is
[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex] ...(2)
where, (h,k) is center, (h±a,k) are vertices and (h±c,k) are foci.
On comparing (1) and (2), we get
[tex]h=0,k=0,a=3,b=2[/tex]
Now,
Center [tex]=(h,k)=(0,0)[/tex]
Vertices [tex]=(h\pm a,k)=(0\pm 3,0)=(3,0),(-3,0)[/tex]
We know that
[tex]c=\sqrt{a^2-b^2}=\sqrt{3^2-2^2}=\sqrt{5}[/tex]
Foci [tex]=(h\pm c,k)=(0\pm \sqrt{5},0)=(\sqrt{5},0),(-\sqrt{5},0)[/tex]
Therefore, the correct option is A.
Paisley is playing with a yo-yo. The following graph traces the path of the yo-yo while it is in the air, where y is the height of the yo-yo above the
ground, and x is the time, in seconds, from when the yo-yo leaves Paisley's hand Five stages of the yo-yo's path are marked on the graph.
Which of the five stages shows the slowest rate of change in the yo-yo's height above the ground?
А
В
C
D
Answer:
C
Step-by-step explanation:
From the graph we can notice that the yo-yo crosses five positions: A,B,C,D and E.
The path created by the yo-yo has a parabolic form.
● In the area C, the yoyo crosses the vertex in wich the rate of change equals 0.
●In A the parabola decreases dramatically
● In B, the parabola is decreasing but slower than A.
● In D, the parabola is increasing in a fast way
● In E, the parabola is increasing faster than D.
● In the first half of C, the parabola is decreasing slower than B and A.
● At the vertex, the parabola has a null rate of change.
● In the second half of C, the parabola is increasing but slower than D and E.
So we deduce that C has the slowest rate of change.
Answer:
The answer is C i took the test
Step-by-step explanation:
The end of a hose was resting on the ground, pointing up an angle. Sal measured the path of the water coming out of the hose and found that it could be modeled using the equation f(x) = –0.3x2 + 2x, where f(x) is the height of the path of the water above the ground, in feet, and x is the horizontal distance of the path of the water from the end of the hose, in feet. When the water was 4 feet from the end of the hose, what was its height above the ground? 3.2 feet 4.8 feet 5.6 feet 6.8 feet
Answer: 3.2 feet.
Step-by-step explanation:
Given: The end of a hose was resting on the ground, pointing up an angle. Sal measured the path of the water coming out of the hose and found that it could be modeled using the equation[tex]f(x) = -0.3x^2 + 2x[/tex], where [tex]f(x)[/tex] is the height of the path of the water above the ground, in feet, and [tex]x[/tex] is the horizontal distance of the path of the water from the end of the hose, in feet.
At x= 4 , we get
[tex]f(x) = -0.3(4)^2 + 2(4)=-0.3(16)+8 =-4.8+8=3.2[/tex]
Hence, when the water was 4 feet from the end of the hose, its height above the ground is 3.2 feet.
Answer:
3.2 feet.
Step-by-step explanation:
use the product of powers property to simplify the numeric expression.
4 1/3 • 4 1/5 = _____
Answer:
The value of [tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex] is [tex]4^{\dfrac{8}{15}}[/tex] .
Step-by-step explanation:
We need to simplify the numeric expression using property. The expression is as follows :
[tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex]
The property to be used is : [tex]x^a{\cdot} x^b=x^{a+b}[/tex]
This property is valid if the base is same. Here, base is x.
In this given problem, x = 4, a = 1/3 and b = 1/5
So,
[tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}}=4^{\dfrac{1}{3}+\dfrac{1}{5}}\\\\=4^{\dfrac{5+3}{15}}\\\\=4^{\dfrac{8}{15}}[/tex]
So, the value of [tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex] is [tex]4^{\dfrac{8}{15}}[/tex] .
let d equal the distance in meters and t equal the time in seconds. Which is a direct variation equation for this relationship
Answer:
d = s x t
Step-by-step explanation:
The formula for distance.
Evan’s dog weighs 15 3/8 pounds. What is this weight written as a decimal? A. 15.125 Ib B. 15.375 Ib C. 15.385 Ib D. 15.625 Ib Please include ALL work!
Answer:
ok as we know 15 is a whole number by itself and 3/8 is the decimal part
so we know it is 15. something
that something is 3/8 to find decimal you do 3/8
3/8 is = .375
so 15.375 is the answer
hope it helps
brainliest give me pls
