Answer:
g(k + 1) = k² - 2k - 3
Step-by-step explanation:
Step 1: Plug in (k + 1) in for x
g(k + 1) = (k + 1)² - 4(k + 1)
Step 2: FOIL
g(k + 1) = k² + 2k + 1 - 4(k + 1)
Step 3: Distribute
g(k + 1) = k² + 2k + 1 - 4k - 4
Step 4: Combine like terms
g(k + 1) = k² - 2k - 3
If x - 10 is a factor of x2 - 8x - 20, what is the other
factor?
X +
Answer:
(x + 2)
Step-by-step explanation:
When we factor the expression x² - 8x - 20, we should get (x + 2)(x - 10).
Alternatively, we can use synthetic division or long division to get our answer.
Answer:
x + 2
Step-by-step explanation:
got it right edg '22
Plz help me. Jose travels 34 miles from home to work on a daily basis. If she takes up a job that is 1 and 1/2 times as far as her old job, how many miles would she be traveling? Solve the problem. You MUST explain your reasoning.
Answer:
I think it is either 85 or 51 because the question was not specific
Step-by-step explanation:
I am not entirely sure if you mean Jose changed jobs or added a new job on top but i will do both.
34/2=17
17+34=51
OR
51+34=85
Answer:
51 miles.
Step-by-step explanation:
That would be 34 * 1 1/2
= 34 * 3/2
= 17 * 3
= 51 miles.
The recipe for beef stew calls for 1/4 teaspoon of pepper for every 3 potatoes. If 9 potatoes are used, how much pepper is needed? Solve the proportion StartFraction one-fourth over 3 EndFraction = StartFraction p over 9 EndFraction to answer the question. Explain your steps.
Answer:
3/4 teaspoons of pepper
Step-by-step explanation:
1/4 teaspoons : 3 potatoes = x teaspoons : 9 potatoes
(1/4)/3 = x/9
3x = 9 * 1/4
x = 3 * 1/4
x = 3/4
Answer: 3/4 teaspoons of pepper
Answer:
B
step-by-step explanation:
1/4 over 3 p/9
PLEASEEEEEE HELP MEEEEE 100 points!!!!!!!!!!!! The map shows the location of a mall, library, and school in a city: Coordinate grid shown from negative 12 to positive 12 on x axis at intervals of 2, and negative 12 to positive 12 on y axis at intervals of 2. A triangle is shown with vertices labeled Library, Mall, and School. Library is the ordered pair negative 10, 10 , Mall is the ordered pair 10, 10, and School is the ordered pair 10 and negative 11. Sarah traveled from the school to the mall and then from the mall to the library. Bret traveled from the school to the library. How many miles did Sarah and Bret travel altogether? (1 point) Select one: a. 12 miles b. 29 miles c. 41 miles d. 70 miles
Sarah: School to mall = 21
mall to library = 20
Total distance for Sarah = 20 + 21 = 41 miles.
Use the Pythagorean theorem to find the distance Bret traveled:
Distance = SQRT(21^2 + 20^2)
= sqrt(441 + 400)
= sqrt(841)
= 29 miles
Total distance = 41 + 29 = 70 miles
Answer is D. 70 miles.
Answer:
70
Step-by-step explanation:
i took the test
Two terms of an arithmetic sequence are a7 = 32 and a19 =140. . Find n such that Sn = 511
In an arithmetic sequence, consecutive terms differ by a fixed number d :
[tex]a_8=a_7+d[/tex]
[tex]a_9=a_8+d=a_7+2d[/tex]
[tex]a_{10}=a_9+d=a_7+3d[/tex]
and so on up to
[tex]a_{19}=a_7+12d[/tex]
Solve for d :
[tex]140=32+12d\implies12d=108\implies d=9[/tex]
Work backwards to find the first term in the sequence, and hence the n-th term:
[tex]a_6=a_7-d[/tex]
[tex]a_5=a_6-d=a_7-2d[/tex]
and so on down to
[tex]a_1=a_7-6d[/tex]
So the first term is
[tex]a_1=32-6\cdot9=-22[/tex]
which means the n-th term is
[tex]a_n=a_1+(n-1)d=-22+9(n-1)=9n-31[/tex]
[tex]S_n[/tex] denotes the n-th partial sum of the sequence, i.e. the sum of the first n terms. We want to find the number of terms such that this sum is 511:
[tex]\displaystyle S_n=\sum_{i=1}^na_i=\sum_{i=1}^n(9i-31)=511[/tex]
Distribute the summation and recall the formulas,
[tex]\displaystyle\sum_{i=1}^n1=n[/tex]
[tex]\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2[/tex]
[tex]\implies S_n=\displaystyle9\sum_{i=1}^ni-31\sum_{i=1}^n1[/tex]
[tex]\implies511=9\cdot\dfrac{n(n+1)}2-31n[/tex]
[tex]\implies1022=9n^2-53n[/tex]
[tex]\implies9n^2-53n-1022=0[/tex]
[tex]\implies(n-14)(9n+73)=0[/tex]
[tex]\implies n=14\text{ or }n=-\dfrac{73}9[/tex]
n must be a positive integer, so we the sum is obtained from the first n = 14 terms.
The summer has ended and it’s time to drain the swimming pool. 20 minutes after pulling the plug, there is still 45 000L of water in the pool. The pool is empty after 70 minutes.
Calculate the rate that the water is draining out of the pool. (Hint: remember this line is sloping down to the right)
Answer:
900L per minute
Step-by-step explanation:
1- 70 - 20 = 50
2- in this 50 min the 45000L has been drawned
3- 45000L / 50 = 900L
.. ..
Erin gets her exercise by running. The graph shows the distances she covers in a given amount of time. How many hours does it take for Erin to run 25 miles?
The correct answer is c. 2 [tex]\frac{1}{2}[/tex] hours
Explanation:
The graphic shows the relationship between the distance Erin covers by running and the time this requires. Additionally, to know the specific time that takes for Erin to run a specific distance or vice versa it is necessary to observe at which point the two variables intersect in the line of the graph.
According to this, Erin runs 25 miles (y-axis) in 2.5 hours (x-axis), which you can know because in the line shown by the graph the distance 25 miles that is in the middle of 20 and 30 miles intersects with 2.5 hours or the middle between 2 and 3. Additionally, this number can be expressed as 2 and a half hours, 2.5 or even 2 [tex]\frac{1}{2}[/tex] hours because the fraction represents half. This makes option C the answer.
Find the difference in area between the large circle and the small circle. Click on the answer until the correct answer is showing.
A=4[tex]\pi -8[/tex]
that is your answer :-)
Answer:
[tex]A = 4\pi - 8[/tex]
Step-by-step explanation:
ody
use the bionomial theorem to write the binomial expansion
[tex]( \frac{1}{2}x + 3y) ^{4} [/tex]
Answer:
[tex]$\left(\frac{x}{2} + 3 y\right)^{4}=\frac{x^{4}}{16} + \frac{3}{2} x^{3} y + \frac{27}{2} x^{2} y^{2} + 54 x y^{3} + 81 y^{4}$[/tex]
Step-by-step explanation:
[tex]$\left(\frac{1}{2}x+3y \right)^4=\left(\frac{x}{2}+3y \right)^4\\$[/tex]
Binomial Expansion Formula:
[tex]$(a+b)^n=\sum_{k=0}^n \binom{n}{k} a^{n-k} b^k$[/tex], also [tex]$\binom{n}{k}=\frac{n!}{(n-k)!k!}$[/tex]
We have to solve [tex]$\left(\frac{x}{2} + 3 y\right)^{4}=\sum_{k=0}^{4} \binom{4}{k} \left(3 y\right)^{4-k} \left(\frac{x}{2}\right)^k$[/tex]
Now we should calculate for [tex]k=0, k=1, k=2, k=3 \text{ and } k =4;[/tex]
First, for [tex]k=0[/tex]
[tex]$\binom{4}{0} \left(3 y\right)^{4-0} \left(\frac{x}{2}\right)^{0}=\frac{4!}{(4-0)! 0!}\left(3 y\right)^{4} \left(\frac{x}{2}\right)^{0}=\frac{4!}{4!}(81y^4)\cdot 1 =81 y^{4}$[/tex]
It is the same procedure for the other:
For [tex]k=1[/tex]
[tex]$\binom{4}{1} \left(3 y\right)^{4-1} \left(\frac{x}{2}\right)^{1}=54 x y^{3}$[/tex]
For [tex]k=2[/tex]
[tex]$\binom{4}{2} \left(3 y\right)^{4-2} \left(\frac{x}{2}\right)^{2}=\frac{27}{2} x^{2} y^{2}$[/tex]
For [tex]k=3[/tex]
[tex]$\binom{4}{3} \left(3 y\right)^{4-3} \left(\frac{x}{2}\right)^{3}=\frac{3}{2} x^{3} y$[/tex]
For [tex]k=4[/tex]
[tex]$\binom{4}{4} \left(3 y\right)^{4-4} \left(\frac{x}{2}\right)^{4}=\frac{x^{4}}{16}$[/tex]
You can perform the calculations, I will not type everything.
The answer is the sum of elements calculated.
Just organizing:
[tex]$\left(\frac{x}{2} + 3 y\right)^{4}=\frac{x^{4}}{16} + \frac{3}{2} x^{3} y + \frac{27}{2} x^{2} y^{2} + 54 x y^{3} + 81 y^{4}$[/tex]
Answer: [tex]\bold{\dfrac{1}{16}x^4 + \dfrac{3}{2}x^3y + \dfrac{27}{2}x^2y^2 +54xy^3+81y^4}[/tex]
Step-by-step explanation:
Binomial Tree
n=0 1
n=1 1 1
n=2 1 2 1
n=3 1 3 3 1
n=4 1 4 6 4 1
Using the Binomial Theorem
[tex]\bigg(\dfrac{1}{2}x+3y\bigg)^4\\\\\\=1\bigg(\dfrac{1}{2}x\bigg)^4(3y)^0\quad \rightarrow \quad \dfrac{1}{16}x^4\\\\+4\bigg(\dfrac{1}{2}x\bigg)^3(3y)^1\quad \rightarrow \quad \dfrac{3}{2}x^3y\\\\+6\bigg(\dfrac{1}{2}x\bigg)^2(3y)^2\quad \rightarrow \quad \dfrac{27}{2}x^2y^2\\\\+4\bigg(\dfrac{1}{2}x\bigg)^1(3y)^3\quad \rightarrow \quad 54xy^3\\\\+1\bigg(\dfrac{1}{2}x\bigg)^0(3y)^4\quad \rightarrow \quad 81y^4[/tex]
______________________
[tex]= \dfrac{1}{16}x^4 + \dfrac{3}{2}x^3y + \dfrac{27}{2}x^2y^2 +54xy^3+81y^4[/tex]
Solve the equation. 12x – 14 = –2
Answer:
X=1
Step-by-step explanation:
12x-14=-2
+14 +14
12x=12
x=1
Answer:
x = 1
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other.
Do the opposite of PEMDAS. PEMDAS =
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
First, add 14 to both sides:
12x - 14 = -2
12x - 14 (+14) = -2 (+14)
12x = -2 + 14
12x = 12
Next, divide 12 from both sides:
(12x)/12 = (12)/12
x = 12/12
x = 1
x = 1 is your answer.
~
Can someone please help me I really need help please help me thank you
Answer:
m = ½; b = 0
Please mark my answer as brainliest
the equation can be written y=mx+d.so
m=1/2 and d=3
Find the value of X in the figure PQ is tangent to O at P
Answer:13
Step-by-step explanation:
The mean age of 10 women in an office is 30 years old. The mean age of 10 men in an office is 29 years old. What is the mean age (nearest year) of all the people in the office?
Answer: 30 years
Step-by-step explanation:
From the question, we are told that the mean age of 10 women in an office is 30 years old. This means that the total ages of the women in the office will be:
= 10 × 30 years
= 300 years
Also, the mean age of 10 men in an office is 29 years old. This means that the total ages of the men in the office will be:
= 10 × 29 years
= 290 years
Since there are 10 men and 10 women in the office, the number of people in the office is: 10 + 10 = 20 people. Also, the total ages will be: 300 + 290 = 590 years.
The mean age (nearest year) of all the people in the office will then be:
= 590/20
= 29.5 years
= 30 years approximately
Can someone help assist me on this Honors Algebra 2 Problem? Challenge Problems #6. The distance from a point on the curve y=√x to the point (2,0) is equal to 2 at what points on the curve? (Hint: Draw a picture.)
Answer: (0, 0) & (3, √3)
Step-by-step explanation:
Since we need a distance of 2, I graphed y = √x and then drew a circle at center (2, 0) and radius of 2 to see where they intersect.
The coordinates of intersection can be determined by solving a system of equations.
Equation 1: y = √x
Equation 2: (x - 2)² + y² = 2²
I will use the Substitution method with Equation 2 to solve for x:
(x - 2)² + (√x)² = 2² substituted y with √x
x² - 4x + 4 + x = 4 expanded binomial
x² - 3x + 4 = 4 added like terms
x² - 3x = 0 subtracted 4 from both sides
x(x - 3) = 0 factored
x = 0 x - 3 = 0 applied Zero Product Property
x = 3
Next, solve for y using Equation 1:
x = 0: y = √0 = 0
x = 3: y = √3
Coordinates of intersection are: (0, 0) & (3, √3)
Answer:
(0, 0) & (3, √3)
Step-by-step explanation:
Which statement explains how the lines x+y=2 and y=x+4 are related?
(1) They are parallel.
(2) They are perpendicular.
(3) They are the same line.
4) They are not related.
Answer:
(2)They are perpendicular.
Step-by-step explanation:
What is the volume of the cylinder to the nearest whole number? a) 942 cm3 b) 3,534 cm3 c)471 cm3 d) 9,420 cm3
Answer:
V = 3534 cm^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
the radius is 7.5 and the height is 20
V = pi ( 7.5)^2 * 20
V =1125 pi cm^3
Using the pi button for pi
V =3534.291735 cm^3
Rounding to the nearest whole number
V = 3534 cm^3
Answer:
b)3534 cm^3
Step-by-step explanation:
To find the area of a cylinder, you first have to find the area of the base which is in the shape of a circle. The area of a circle is given by the equation πr^2. In this case r, the radius, is 7.5 cm. So plugging in 7.5 for r you get 7.5^2 × π. Plugging in 3.1415 for π you get ~176.671. Now all you do is multiply this by the height, 20cm, and get the answer of ~3534 cm^3.
here are the ingredients for making pineapple sorbet for 6 people. 800 g pineapple 4 egg whites 1/2 lemon 100 g caster sugar Dan makes pineapple sorbet. he uses 2 and a 1/2 lemons How many people does he make pineapple sorbet for?
Answer:
30 people
Step-by-step explanation:
If you start off with 1/2 a lemon for 6 people, then 1 whole would be 12. 1 1/2 would be 18 people and 2 whole lemons would be 24. so 2 1/2 is 30 people.
At the science fair, Tanvi uses 8 fluid ounces of vinegar to make her volcano erupt. How many times can she make her volcano erupt with 1 quart of vinegar?
Answer:
4 times
Step-by-step explanation:
1 quart is equivalent to 32 fluid ounces.
If each eruption consumes 8 fluid ounces of vinegar. Assuming that the amount of vinegar required per eruption is constant, the number of times Tanvi can make her volcano erupt is:
[tex]n=\frac{32}{8}\\n=4\ times[/tex]
Tanvi can make her volcano erupt 4 times with 1 quart of vinegar.
Answer:
Step-by-step explanation:
Step 1: -10 + 8x < 6x - 4
Step 2: -10 < -2x - 4
Step 3: -6 <-2x
Step 4:
What is the final step in solving the inequality -2(5-
4x) < 6x - 4?
0x<-3
X > -3
0x<3
x > 3
Answer:
Step-by-step explanation:divide both sides by the coefficient of x that is the number beside x and in inequality, when dividing with a negative sign the sign would change to its opposite sign.
-6<-2x
-6/-2>-2x/-2
3>x
X<3 this is the answer.
When you take a picture with a 35mm camera, the image passes through the camera lens and is rotated and dilated onto the screen for viewing.
Answer:
That is true, but there is no question being asked.
A computer can sort x objects in t seconds, as modeled by the function
below:
t=0.007x2 + 0.003.x
How long, in seconds, will it take the computer to sort 15 objects?
Answer:
it will take 0.056025 seconds to complete
Step-by-step explanation:
Here, we want to know the amount of time it will take. the computer to sort 15 items.
What to do here is simply substitute the value of 15 for x
Thus, we have
t = 0.007(15)^2 + 0.003(15)
t = 0.011025 + 0.045
t = 0.056025
answer: 1.62
step-by-step explanation: apx :)
not quite sure of the answer. help me out???
Answer:
C = pi * d
Step-by-step explanation:
C = 2 * pi *r
We can replace 2 * r with d since the diameter is twice the radius
C = pi * 2*r
C = pi * d
Part 1 of 1 -
Question 2 of 50
2 Points
Solve the equation for x. x/3 -1 = -2
Copyright 2010-2020 edtell, LLC. All rights reserved. Portions of this software are copyrighted by other parties as described in the Acknov
Answer:
x = -3
Step-by-step explanation:
When asked to solve the equation for x, it mean that put x only on one side, and everything else on the other side. So....
x/3 - 1 = -2
x/3 = -1 ( add 1 on both side)
x = -3 (x3 on both side)
Helppp!!!! please!!!
Answer:
A) 52.5 inches²
Step-by-step explanation:
The equation for the area of a trapezoid is a=1/2h(b1+b2). This basically means that you take the height of the trapezoid, multiply it by the top base plus the bottom base and divide that by 2. When you do this, you take 8.5 plus 6.5, which equals 15, and multiply that by 7 to get 105. After you get this, you divide it by 2 to get 52.5 inches².
A car travels the first 50 km of its journey at an average speed of 25 m/s and the next 120 km at an On his outward journey, Ali travelled at a speed of s km/h for 2.5 hours. On his return journey, he increased his speed by 4 km/h and saved 15 minutes. Find Ali's average speed for the whole journey. Speed of 80 km/h. The car completes the last part of its journey at an average speed of 90 km/h in 35 minutes. Find the average speed for its entire journey, giving your answer in km/h.
Answer:
The car's average speed for the entire journey = 84.315 km/h
Step-by-step explanation:
Correct Question
A car travels the first 50km of its journey at an average speed of 25m/s and the next 120 km at an average speed of 80km/h. the car completes the last part of its journey at an average speed of 90km/h in 35 minutes. Find the average speed for its entire journey, giving your answer in km/h.
Solution
Average speed is given as total distance travelled divided by total time taken.
So, we will compute the distance covered for each part of the journey and the corresponding time it takes to cover each of these distances.
- The car travels the 50 km first part of the journey at a speed of 25 m/s.
25 m/s = 90 km/h
We have the distance covered in the first part of the journey, now, we need the time taken to cover the distance.
Speed = (Distance/Time)
Time = (Distance/Speed)
Distance = 50 km, Speed = 90 km/h
Time = (50/90) = 0.5556 hr
- The next part, the car covers 120 km at a speed of 80 km/h
Time = (Distance/Speed) = (120/80) = 1.5 hr
- For the last part of the journey, the car travels with an average speed of 90 km/h for 35 minutes.
35 minutes = (35/60) hr = 0.5833 hr
Here, we need to calculate the distance covered for the last part.
Speed = (Distance/Time)
Distance = (Speed) × (Time) = 90 × 0.5833 = 52.5 km
Total distance covered = 50 + 120 + 52.5 = 222.5 km
Total time taken = 0.5556 + 1.5 + 0.5833 = 2.6389 hr
Average Speed = (222.5/2.6389) = 84.315 km/h
Hope this Helps!!!
I need help with this problem ASAP please i have until tmrw to finish my course entirely so if anyone can help it would be greatly appreciated
Answer:
Equation: f(x) = -x² + 3
Step-by-step explanation:
If we want to find the roots/solve for x, we can either graph the problem or use quadratic formula to find when f(x) = 0:
To get the equation of the graph, our parent function is: f(x) = a(x - h)² + k, or f(x) = x². Since we are reflecting over the x-axis with a vertical stretch and vertically moving up to (0, 3), we are modifying a and k only.
Kevin cuts lawns during the summer months. He charges $10 plus $5 per hour. The algebraic model is C = 5h + 10, where C represents the total cost and h represents the hours worked. Use pencil and paper to create a table of values for hours worked from 1 to 5, incrementing h by 1 in each row.
Answer:
[tex]\begin{center}\begin{tabular}{ c c c }Hours(h) & Total Cost(C) \\ 1 & 15 \\ 2 & 20 \\ 3 & 25 \\ 4 & 30 \\ 5 & 35 \end{tabular}\end{center}[/tex]
Step-by-step explanation:
Given that:
Kevin charges $10 plus $5 per hours
C = 5h + 10
To find:
The table of values for hours worked from 1 to 5.
Solution:
First of all, let us put h = 1 in the given equation:
C = 5 \times 1 + 10
C = 5 + 10 = $15
Now, let us put h = 2 in the given equation:
C = 5 \times 2 + 10
C = 10 + 10 = $20
Now, let us put h = 3 in the given equation:
C = 5 \times 3 + 10
C = 15 + 10 = $25
Now, let us put h = 4 in the given equation:
C = 5 \times 4 + 10
C = 20 + 10 = $30
Now, let us put h = 5 in the given equation:
C = 5 \times 5 + 10
C = 25 + 10 = $35
So, the table becomes each row incrementing h by 1:
[tex]\begin{center}\begin{tabular}{ c c c }Hours(h) & Total Cost(C) \\ 1 & 15 \\ 2 & 20 \\ 3 & 25 \\ 4 & 30 \\ 5 & 35 \end{tabular}\end{center}[/tex]
3. In the polygon below, what kind of
angle is P?
A Acute
B Obtuse
C Right
D Straight
Answer:a
Step-by-step explanation:
can somebody help me plz
Answer:
126 people
Step-by-step explanation:
9/5 is the ratio tea/coffee
let x be the one who preferred coffee and x+36 preferred tea
9/5=x+36/x
9x=5x+5(36)
9x-5x=180
4x=180
x=180/4=45
x=45 coffee
x+36=45+36=81
45+81=126
check : 81/45= 9/5
EXTRA POINTS The amount of people diagnosed is 3,131,953 and the amount of deaths is 132,056 what is the percentage of people who die from the disease?
2.3%
divide the infected number by the deaths. Then move the decimal points to the left.
Answer:
2.3%
divide the infected number by the deaths. Then move the decimal points to the left.
Step-by-step explanation: