Answer:
x=0 y=-4
Step-by-step explanation:
Kayla was asked to rewrite the polynomial expression x ^ 2 + 5x + 9 she rewrite the polynomial ? How could she rewrite with the polynomial?
Answer:
x²+6x+9
x²+3x+3x+9
x(x+3)+3(x+3)
=(x+3)(x+3)
Alice and Bob play a game involving a circle whose circumference is divided by 12 equally-spaced points. The points are numbered clockwise, from 1 to 12. Both start on point 12. Alice moves clockwise and Bob, counterclockwise. In a turn of the game, Alice moves 5 points clockwise and Bob moves 9 points counterclockwise. The game ends when they stop on the same point. How many turns will this take
Answer:
Step-by-step explanation:
2005 AMC 8 Problems/Problem 20
Problem
Alice and Bob play a game involving a circle whose circumference is divided by 12 equally-spaced points. The points are numbered clockwise, from 1 to 12. Both start on point 12. Alice moves clockwise and Bob, counterclockwise. In a turn of the game, Alice moves 5 points clockwise and Bob moves 9 points counterclockwise. The game ends when they stop on the same point. How many turns will this take?
$\textbf{(A)}\ 6\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 12\qquad\textbf{(D)}\ 14\qquad\textbf{(E)}\ 24$
Solution
Alice moves $5k$ steps and Bob moves $9k$ steps, where $k$ is the turn they are on. Alice and Bob coincide when the number of steps they move collectively, $14k$, is a multiple of $12$. Since this number must be a multiple of $12$, as stated in the previous sentence, $14$ has a factor $2$, $k$ must have a factor of $6$. The smallest number of turns that is a multiple of $6$ is $\boxed{\textbf{(A)}\ 6}$.
See Also
2005 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 19 Followed by
Problem 21
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.
What is the equation of the line that passes through the point (-4, 2) and has a
slope of -5/4?
Answer:
[tex]y=-\frac{5}{4} x-3[/tex]
Step-by-step explanation:
Use the slope formula equation to plug in values. Slope formula equation is y=mx+b. The known values are y=2, m=-5/4, x=-4. [tex]2=(-\frac{5}{4} )(-4)+b[/tex]. Multiply -5/4 times -4 to get 5. 2=5+b. Subtract 5 from each side to isolate b. b=-3.
What is the volume of a rectangular prism with a length of 2x, a width of x−2, and a height of x + 2?
Therefore, 2x³ - 8x units³ is the volume of a rectangular prism.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
(2x³ - 8x) is the volume of a rectangular prism.
What is volume?
Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.
Given that, a rectangular prism with a length of 2x, a width of (x−2), and a height of (x + 2)
Volume: L x B x H
= (2x) × (x - 2)(x + 2)
= (2x) × (x² - 4)
= 2x(x² - 4)
= 2x³ - 8x units³
Hence, 2x³ - 8x units³ is the volume of a rectangular prism.
For more references on volume, click;
https://brainly.com/question/13338592
#SPJ2
Anyone know how to solve 28?
Answer:
i need help too
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
x = - 3 is a vertical line parallel to the y- axis.
A line perpendicular to it will therefore be a horizontal line parallel to the x- axis with equation
y = c
where c is the value of the y- coordinates the line passes through.
The line passes through (6, - 4 ) with y- coordinate - 4 , then
y = - 4 ← equation of perpendicular line
Anu and Aji solve an equation. In solving Anu commits a mistake in constant term and finds the roots 8 and 2. Aji commits a mistake in the coefficient of x. The correct roots are (a) 9,1 (b)-9,1 (c) 9, -1 (d) -9.-1
The correct roots of the equation are (a) 9 and 1
From the complete question, their mistakes are:
Anu
Roots: 8 and 2Wrong constant termAji
Roots: -9 and -1Wrong coefficientA quadratic equation is represented as:
[tex]ax^2 + bx + c = 0[/tex]
Where:
[tex]\alpha\beta = \frac ca[/tex] --- product of roots
[tex]\alpha + \beta = -\frac ba[/tex] --- sum of roots
Anu made a mistake in the constant term, so we consider the sum of roots
[tex]Sum = 8 + 2[/tex]
[tex]Sum = 10[/tex]
Aji made a mistake in the coefficient, so we consider the product of roots
[tex]Product = -9 \times -1[/tex]
[tex]Product = 9[/tex]
The possible equations from the above sum and products are:
[tex]x^2 + 10x + 9 =0[/tex].[tex]x^2 - 10x + 9 =0[/tex].[tex]x^2 + 10x - 9 =0[/tex].[tex]x^2 - 10x - 9 =0[/tex]Of all the above equations, the most likely equation is [tex]x^2 - 10x + 9 =0[/tex], and it has a root of 9 and 1
Hence, the correct roots are (a) 9 and 1
Read more about roots of equations at:
https://brainly.com/question/3923172
. .. . . . . . .. . .. . so easy
Answer: 7
Step-by-step explanation: if it's so easy, why do you need brainly? (not judging, just confused why you'd waste points)
use the mutipler method to increase £88 by 14%
Answer:
£100.32
Step-by-step explanation:
An increase of 14% on the original amount (100%) is
100 + 14 = 114% = [tex]\frac{114}{100}[/tex] = 1.14 , then
£88 × 1.14 = £100.32
DON'T SEND A LINK AND JUST ANSWER IT PLZ
Answer:
height = 10 , area = 240 units²
Step-by-step explanation:
The diagonal splits the rectangle into 2 right triangles.
Using Pythagoras' identity in the right triangle formed
with hypotenuse h = 26 and legs 24 and height x , then
x² = 26² - 24² = 676 - 576 = 100 ( take square root of both sides )
x = [tex]\sqrt{100}[/tex] = 10
Height = 10 units
area of rectangle = 24 × 10 = 240 units²
A cone has a volume of 94.2 cubic feet and a height of 10 feet. What is its radius?
Answer:
3 ft
Step-by-step explanation:
The formula for the volume of a cone is ...
V = 1/3πr²h
Solving for r, we find ...
r = √(3V/(πh))
r = √((3×94.2)/(π×10)) ≈ √9 = 3 . . . . ft
The radius of the cone is 3 ft.
A small van holds 8 students and a large van holds 12 students. There are a total of 48 students who plan to go on the field trip.
14. Which transformation from the graph of a function f(x) describes the graph of 10f(x)? 2. ( Responses: horizontal, vertical) 2. ( Responses: shift, stretch) 2. ( Responses: up, down, left, right, by a factor of) 10 units. 2. Answer it and then explain it please
Answer: Your mom
Step-by-step explanation:
HEHEHEHA
What is an equation for the linear function whose graph contains the points (2, 5) and (3, 0)?
Enter your answers in the boxes.
y−
=
(x−2)
Answer:
y = -5x + 15
Step-by-step explanation:
We'll look for a linear function of the form y = mx + b, where m is the slope and b is the y-intercept.
We can determine a slope from the two given points by calculating a Rise/Run. Starting at (2,5) and going to (3,0):
Rise = (0 - 5) = -5
Run = (3-2) = 1
Rise/Run = Slope, m) = -(5/1) or -5
Now we have y = -5x + b
To find b, enter either of the two points and solve for b. I'll use (3,0), because I know my zero multiplication and addition tables by heart.
y = -5x + b
0 = -5(3) + b
b = 15
The equation becomes y = -5x + 15
See attachment.
Does anyone know how to answer?
Answer:
A, D, F
Step-by-step explanation:
It is convenient to let a calculator or spreadsheet evaluate the function for you. Reflection over the y-axis means x is replaced by -x in the original function definition.
The values that show up on the reflected graph are ...
(-7, -10.206)
(0.5, -0.221)
(9, -0.003)
y=-1/2x+5/2 Find the slope
Answer:
Here is a pic hope this helps! <3
Step-by-step explanation:
Answer:
-1/2
Step-by-step explanation:
y=-1/2x+5/2
y=mx+b
m=slope
m=-1/2
Which expression is equivalent to log Subscript 5 Baseline (StartFraction x Over 4 EndFraction) squared? 2 log Subscript 5 Baseline x log Subscript 5 Baseline 4 2 log Subscript 5 Baseline x log Subscript 5 Baseline 16 2 log Subscript 5 Baseline x 2 log Subscript 5 Baseline 4 2 log Subscript 5 Baseline x log Subscript 5 Baseline 4.
The required equivalent expression for [tex]{log}_{5} \ (\frac{x}{4} ) ^{2}[/tex] is [tex]2 \ log_{5}\ x-2\ log_{5}\ 4[/tex].
Given expression,
[tex]{log}_{5} \ (\frac{x}{4} ) ^{2}[/tex].
We have to find the Equivalent fraction of [tex]{log}_{5} \ (\frac{x}{4} ) ^{2}[/tex].
We know that from the properties of logarithm, the following identities
[tex]log\ m^{n} =n\ log\ m[/tex] .....(1)
[tex]log\ \frac{m}{n} = log\ m- log\ n\\[/tex].......(2)
Now, [tex]{log}_{5} \ (\frac{x}{4} ) ^{2}= 2 \ log_{5} \ \frac{x}{4}[/tex] ( using 1 identity)
Again using 2 identity, we get
[tex]{log}_{5} \ (\frac{x}{4} ) ^{2}= 2[ log_{5}\ x-log_{5}\ 4 ][/tex]. (using 2 identity)
[tex]{log}_{5} \ (\frac{x}{4} ) ^{2}= 2 \ log_{5}\ x-2\ log_{5}\ 4[/tex]
Hence the required equivalent expression for [tex]{log}_{5} \ (\frac{x}{4} ) ^{2}[/tex] is [tex]{log}_{5} \ (\frac{x}{4} ) ^{2}= 2 \ log_{5}\ x-2\ log_{5}\ 4[/tex].
For more details on logarithm follow the link:
https://brainly.com/question/163125
Answer:
C on edge
Step-by-step explanation:
(a) The area of a rectangular garden is 5658 m?.
If the width of the garden is 69 m, what is its length?
(b) The perimeter of a rectangular window is 262 cm.
If the length of the window is 73 cm, what is its width?
A) Length is 82 m
B) Width is 58 cm
Hope this is helpful!
Evaluate the expression 4(2x + 6) when x = 4.5 *
122
60
42
12
Answer:
The solution to the expression with x = 4.5 is 60.Step-by-step explanation:
Given:
x = 4.5Work:
4(2x + 6)=> 8x + 24=> 8(4.5) + 24=> 36 + 24=> 60Hence, the solution to the expression with x = 4.5 is 60.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
what is the answer in simplest form and is it real or imaginary?
Answer:
12.292 or 1.708
Step-by-step explanation:
1#60 - (2 • (x + 7)2 + 4) = 0
2# -2x2 - 28x - 42 = -2 • (x2 + 14x + 21)
3#x2 + 14x + 21 = -2 • (x2 + 14x + 21) = 0
[tex]\\ \sf\longmapsto -60=2(h+7)^2+4[/tex]
[tex]\\ \sf\longmapsto 2(h^2+14h+49)=-64[/tex]
[tex]\\ \sf\longmapsto h^2+14h+49=-66[/tex]
[tex]\\ \sf\longmapsto h^2+14h+115=0[/tex]
h has imaginary roots- 3m + 7 - 2n
Can I get the answer
Answer:
3m + 5
Step-by-step explanation:
uhmm i think 2n is i cant solve here hope it helps
Why are scarcity and choice basic economic questions faced by every society?
A square fence has an area of 81 cm sq. What is the length of each side?
Answer:
9 cm
Step-by-step explanation:
[tex]\sqrt{81} = 9[/tex]
Complete the table for this equation.
y=x−3
Enter your answers by filling in the boxes.
x y
5
6
7
8
9
Answer:
5 => 2
6 => 3
7 => 4
8 => 5
9 => 6
Answer:
2,3,4,5,6
Step-by-step explanation:
y = 5 - 3 = 2
y = 6 - 3 = 3
y = 7 - 3 = 4
y = 8 - 3 = 5
y = 9 - 3 = 6
help please! a is wrong, that was my initial answer.
Answer:
D -1
Step-by-step explanation:
[tex]-6(3a+4)=3a-3[/tex]
[tex]-18a-24=3a-3[/tex]
[tex]-18a-3a=-3+24[/tex]
[tex]-21a=21[/tex]
a = [tex]\frac{21}{-21} =-1[/tex]
Hope this helps
8. What number should come in the box to make the following statement true?
34 + 32 = 9 × ___
[tex]\huge\boxed{\sf{Hello\:there!}}[/tex]
First of all, we should add 34 and 32:
34+32=66
Now, let's divide both sides by 9:
66÷9=7.3333...
[tex]\huge\boxed{\sf{Hope\:it\:helps.\:Please\:mark\:Brainliest.}}[/tex]
[tex]\huge\bold{Good\:luck!}\\\huge\mathfrak{LoveLastsAllEternity}[/tex]
The diagram shows a cube with sides of length 8 meters. A smaller cube with
sides of length 3.5 meters has been out out of the larger cube.
a) Find the volume, in cubic centimeters of the large aube before the
small cube is out out. Write your answer in scientific notation
Find the volume of the solid after the small cube is removed. Write your
answer in scientific notation. Round the coefficient to the nearest tenth
Answer:
a) 512 cm^3
b) 469.125 cm^3
Step-by-step explanation:
8*8*8 = 512 cm^3
or
8^3 = 512 cm^3
3.5^3 = 42.875
512 - 42.875 = 469.125 cm^3
You can round the second answer down
Toya has a car loan of $8500. Over the course of the loan, she paid a total of $5526 in interest at a rate of 13%. How many months was the car loan?
Answer:
42 months
Step-by-step explanation:
What is the opposite number of -5.23
Answer:
5.23
Step-by-step explanation:
The opposite of a number is the opposite signs,
the opposite of negative is positive and the opposite of positive is negative,
so the opposite of negative 5.23 is positive 5.23.
Which function is represented by the graph?
The parent absolute value function is translated
3 units and Y 1 unit.
The function that is graphed is f(x) =
The parent absolute value function is translated 3 units left and 1 unit up.
The function that is graphed is [tex]f(x) = |x + 3| +1[/tex]
The parent absolute function is given as:
[tex]y =|x|[/tex]
When a function is translated 3 units left, the rule of transformation is:
[tex](x,y) \to (x + 3,y)[/tex]
So, we have:
[tex]y = |x + 3|[/tex]
When a function is translated 1 unit uo, the rule of transformation is:
[tex](x,y) \to (x,y+1)[/tex]
So, we have:
[tex]y = |x + 3| +1[/tex]
Express as a function
[tex]f(x) = |x + 3| +1[/tex]
Hence, the function that is graphed is [tex]f(x) = |x + 3| +1[/tex]
Read more about transformation at:
https://brainly.com/question/1548871
Answer:
left,up, lx+3l+1
Have fun
Math help please
Thanks
A lot
Answer:
2 hours: 3968 [I don't understand the $ sign in the answer box]
At midnight: 12137
Step-by-step explanation:
The bacteria are increasing by 15% every hour. So for every hour we will have what we started with, plus 15% more.
The "15% more" can be represented mathematically with (1 + 0.15) or 1.15. Let's call this the "growth factor" and assign it the variable b. b is (1 + percent increase).
Since this per hour, in 1 hour we'll have (3000)*(1.15) = 3450
At the end of the second hour we're increased by 15% again:
(3450)*(1.15) = 3968.
Each additional hour add another (1.15) factor, If we assign a to be the starting population, this can be represented by:
P = a(1.15)^t for this sample that increase 15% per hour. t is time, in hours.
If a represents the growth factor, and P is the total population, the general expression is
P = ab^t
Using this for a = 3000 and b = 1.15, we can find the total population at midnight after starting at 2PM. That is a 10 hour period, so t = 10
P = (3000)*(1.15)^10
P = 12137