Answer:
The properties and characteristics of the sum of two cubes
1) In the sum of two cubes, the middle sign of the binomial factor on the right hand side of the equation is positive
2) The trinomial factor has a middle sign that is opposite to the middle sign in the question on the sum of two cubes
The properties and characteristics of the difference of two cubes
1) In the difference of two cubes, the middle sign of the binomial factor on the right hand side of the equation is always negative
2) The trinomial factor has a middle sign that is opposite to the middle sign in the question on the difference of two cubes
Step-by-step explanation:
The sum and difference of two cubes are;
a³ + b³, and a³ - b³
Factorizing the expressions for the sum and difference of two cubes can be shown as follows;
Sum of two cubes; a³ + b³ = (a + b) × (a² - a·b + b²)
Difference of two cubes; a³ - b³ = (a - b) × (a² + a·b + b²).
You want to borrow three rock CDs from your friend. She loves math puzzles and she always makes you solve one before you can borrow her stuff. Here's the puzzle: Before you borrow three CDs, she will have 39 CDs. She will have half as many country CDs as rock CDs, and one-fourth as many soundtracks as country CDs. How many of each type of CD does she have after you borrow three rock CDs?
Answer:
Rock CD's=21
Country CD's=12
Soundtrack CD's=3
Step-by-step explanation:
let
r= rock CD's
c = country CD's
s = soundtrack CD's
Total CD's=r + c + s =39
2c=r
c/4=s
2c+c+c/4=39
8c+4c+c=156
13c=156
c=12
Substitute c=12 into 2c=r
2c=r
3(12)=r
24=r
r=24
Substitute c=12 into c/4=s
c/4=s
12/4=s
3=s
s=3
Therefore, she has
c=12
s=3
r=24
before she borrowed you 3 rock CD's
Sha has
r=21
s=3
c=12
after you borrowed 3 rock CD's
At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 16 computer chips is taken. What is the probability of thesample mean
THIS IS COMPLETE QUESTION
computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.2 centimeters. A random sample of 16 computer chip is taken. What is the probability that the sample mean will be below 0.95?
Answer:
the probability is P=0.045
Step-by-step explanation:
We were given mean of computer chips as 1 centimeter and a standard deviation of 0.1 centimeter
We were given
σ=0.1
n=16
We calculate:
Z=(0.95-1)/0.1 √16
Z=-0.125
Using the standard z- tables. to get the probability we have
P(X<0.95)=P(z<-0.115)=0.045
Therefore, probability is P=0.045
How many times does 5 go into 1,200??
240 times.
Explanation:
24 times because,
If you divide 5 with 12k that's,
= 1200/5
= 240
Hence proved, 240 times.
Finding which number supports the idea that the rational numbers are dense in the real numbers.
Answer:A terminating decimal between -3.14 and -3.15.
Step-by-step explanation:
A natural number includes non-negative numbers like 5, 203, and 18476.
It is encapsulated by integers, which include negative numbers like -29, -4, and -198.
Integers are further encapsulated by rational numbers, which includes terminating decimals like 3.14, 1.495, and 9.47283.
By showing a terminating decimal between -3.14 and -3.15, you are showing that rational numbers include integers (because integers include negative numbers.
I need help bc I am not smart
Answer:
1) one and two-thirds hour
2) 2.4 miles
Which of these is NOT discrete data:
A. number of home-runs hit in a professional baseball game
B. air pressure in a car tire
C. cars per household in a town
D. number of pills in a container of vitamins
Answer:
B, air pressure in a car tire.
Step-by-step explanation:
Discrete data is data which come in intervals, and isn't continuous.
The number of home runs can only go 0 -> 1 -> 2 -> 3, you can't have 2.5 or 3.2 home-runs.
The number of pills in a container can also only go 0 -> 1 -> 2. Again, can't have 0.7 pills.
The number of cars per household is also discrete. The number of cars in a household goes 0 -> 1 -> 2, you can't have half a car!
However, the air pressure is continuous. If you're increasing the air pressure, it'll (in theory) go from 0 -> 0.000...001 -> 0.000..002 etc. It doesn't "jump" from 0 pressure -> 1 pressure like the others, it goes smoothly. It can be any value.
So the air pressure isn't discrete data.
Marta esta poniendo sus libros en una estantería. Le faltan 7 libros para poder poner 12 en cada estante; sin embargo, si pone 10 libros en cada estante, se quedan 5 libros sin poner. ¿Cuantos es antes tiene la estantería?
Answer:
x = 6 la cantidad de estantes
y = 65 cantidad de libros
Step-by-step explanation:
LLamemos "x" la cantidad de estantes que tiene Marta, y llamaremos "y" la cantidad de libros.
La primera condición que se debe cumplir es que cuando Marta coloca 12 libros en cada estante entonces le faltan 7, esto lo expresamos así:
y + 7 = 12*x (1)
La segunda condición establece que si Marta coloca los libros en número de 10 por estante le quedan 5 sin colocar, luego esto en lenguaje matemático se expresa así:
y - 5 = 10*x (2)
Ahora hemos obtenido un sistema de dos ecuaciones con dos incógnitas que se resuelve por cualquiera de los métodos conocidos, usaremos el método de sustitución.
Despejamos y en la primera ecuación y lo sustituimos en la segunda, de esa forma obtendremos el valor de x
y = 12*x - 7
(12*x - 7 ) - 5 = 10*x
2*x -12 = 0
2*x = 12
x = 6 la cantidad de estantes, y
y = 12*x -7
y = 72 - 7
y = 65 cantidad de libros
zero of the function f(x)=3x/x2-9
Answer:
It should equal zero or seven. I think is zero
Write an equation of the line that passes through the point (5, –8) with slope 5. A. y−5=5(x+8) B. y+8=−5(x−5) C. y−5=−5(x+8) D. y+8=5(x−5)
Answer:
D
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = 5 and (a, b) = (5, - 8 ), thus
y - (- 8) = 5( x - 5), that is
y + 8 = 5(x - 5) → D
2. A person's height is 73 inches. How
would you convert this height to feet
using a conversion factor?
a.
73in 12 in
ift
1
b.
73in ift
1
12in
Answer:
6.08 ftStep-by-step explanation:
In this problem we are expected to do unit conversion from inches to feet.
from table we can see that
if 1 inches is 0.0833333 ft
then 73 inches will be x ft
By cross multiplication we can solve for the value of x which is
]x= 6.08 ft
Hence the person is 6.08 ft tall
Chen is baking muffins and banana bread for a brunch buffet. He needs 3 and one-fifth cups of flour to make the muffins and 3 and two-thirds cups of flour to make the banana bread. Which is the best estimate of the number of cups of flour that Chen needs to bake both recipes?
Options :
A. 6 cups of flour
B.7 cups of flour
C.8 cups of flour
D.9 cups of flour
Answer:
B.7 cups of flour
Step-by-step explanation:
Given the following :
Cups of flour required to make muffins = 3 1/5
Cups of flour required to make banana = 3 2/3
Number of cups of flour required to make both recipe :
(cups of flour required to make muffins + cups of flour required to make bread)
(3 1/5 + 3 2/3) = 3+3+(1/5 + 2/3)
= 6 + (1/5 + 2/3) = (3 + 10)/15 = 6 + (13/15)
6 13/15 = 6.8666666
The best estimate is to round to the nearest whole number = 7
Answer: The answer is 7
Step-by-step explanation:
I got it right in my quiz! Hope this helps (:
Graph the following inequality and then select the correct graph below. x - y - 2 ≥ 0
Answer:
x - y - 2 ≥ 0
Step-by-step explanation:
Plot the value(s) on the number line where this function is equal to zero: f(x) = (x + 5)(x − 1).
Answer:
Step-by-step explanation:
Hope this Helps ;)
It took Amir 2 hours to hike 5 miles. On the first part of the hike, Amir averaged 3 miles per hour. For the second part of the hike, the terrain was more difficult so his average speed decreased to 1.5 mile per hour.
Answer:
Times
first part x = 1,33 h second part y = 0,66 h
distances d₁ (first part ) d₁ = 4 miles d₂ (second part ) d₂ = 0,999 miles
Step-by-step explanation: IMPORTANT NOTE: EVEN PROBLEM STATEMENT DID NOT ASK ANY QUESTION WE WILL ASSUME QUESTION ARE: LENGTH ( IN MILES ) AND SPENT TIME OF EACH PART OF THE HIKE
We formulate a two-equation system according to:
x = time for the first part
y = time for the second part
then x + y = 2 or y = 2 - x
And 3 m/h * x(h) + 1,5 m/h * y (h) = 5
3*x + 1,5*y = 5
3*x + 1,5 * ( 2 - x ) = 5
3*x + 3 - 1,5*x = 5
1,5*x = 2
x = 2/1,5 (h)
x = 1,33 (h)
And y = 2 - 1,33 y = 0,66 (h)
Distances are
first part d₁ = 3*1,33 d₁ = 4 miles
second part d₂ = 1,5*0,66 d₂ = 0,999 miles
Adding
ing and Multiplying Rati
What type of answer would you expect from the problem below? Expla
answer
DONES
witch numbers are domain -3 ,-2 ,-3 ,0 ,-1 ,2 ,1 ,2
Correct Presentation of Question
Which numbers are domain? (-3,-2) (3,0)(-1,2)(1,2)
Answer:
Domain = {-3,-3,-1,1}
Step-by-step explanation:
Given
(-3,-2) (3,0)(-1,2)(1,2)
Required
Determine which numbers are domain
A function is always represented as thus (x,y) in this format (domain, range);
Tabulate the given data
x || y
-3 || -2
3 || 0
-1 || 2
1 || 2
The values under the x column are the domain;
Hence, the domain are {-3,-3,-1,1}
Solve the equation 7b-27=8(6+4b)
Answer:
b = -3
Step-by-step explanation:
7b-27=8(6+4b)
Distribute
7b -27 = 48 + 32b
Subtract 7b from each side
7b-7b-27=48+32b-7b
-27 = 48+25b
Subtract 48 from each side
-27-48 = 48+25b -47
-75 = 25b
Divide each side by 25
-75/-25 =25b/25
-3 =b
Answer: b= -3
Step-by-step explanation:
[tex]7b-27=8\left(6+4b\right)[/tex]
distribute
[tex]7b-27=48+32b[/tex]
add 27 to both sides
[tex]7b-27+27=48+32b+27[/tex]
[tex]7b=32b+75[/tex]
subtract 32b on both sides
[tex]7b-32b=32b+75-32b[/tex]
divide -25 on both sides
[tex]-25b=75[/tex]
[tex]b=-3[/tex]
Based on the graph what are the solutions to ax^2 + bx+c=0 Select all that apply
A. X=-2
B. X=10
C. X=5
D. X=8
Answer:
x=-2 and x = 5
Step-by-step explanation:
The solutions to the equation are where the graph crosses the x axis
We can see that the graph crosses at x=-2 and x = 5
Answer:
x = -2
x = 5
Step-by-step explanation:
The answer is found when the graph crosses the x-axis
Hope this helps :D
2( -4n+ 2)
6n = 4(-2 - 2n)
Answer:
(n^(2)+6n-4)(2n-4)
The graph represents revenue in dollars as a function of greeting cards sold. A coordinate plane showing Greeting Card Revenue, Number of Cards Sold on the x-axis and Revenue in dollars on the y-axis. A line starts at (0. 0) and passes through (2, 8), (4, 16), and ends at (5, 20). Which equation represents the function shown on the graph? y = x y = x y = 2x y = 4x
Answer:
D
Step-by-step explanation:
Just did it
A function assigns the values. The equation that represents the function shown on the graph is y=4x.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given that the graph represents revenue in dollars as a function of greeting cards sold. Therefore, we can write the function as,
Revenue ∝ Number of cards sold
Since the Number of Cards Sold on the x-axis and Revenue in dollars on the y-axis. Therefore, we can write,
y ∝ x
Removing the proportionality, we will get,
y = k x
Now, substitute any point through which the graph of the function passes to get the value of k,
20 = k × 5
20/5 = k
k = 4
Thus, the function can be represented as,
y = kx
y = 4x
Hence, the equation that represents the function shown on the graph is y=4x.
Learn more about Function here:
https://brainly.com/question/5245372
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April typed a 5 page report in 50 mintues. Each page had 500 words at what rate is April typing
Answer:
Amy types at a rate of 50 words per minute
Step-by-step explanation:
In this question, we are interested in calculating the rate at which April is typing.
From the question, we can deduce that she typed a 5 page report, with each page having a total of 500 words.
Now, if each page has 500 words, the total number of words in all of the pages will be 5 * 500 = 2,500 words
Now, from here, we can see that 2,500 words were typed in 50 minutes.
The number of words per minute will be ;
Total number of words/Time taken = 2500 words/50 minutes
That will give a value of 50 words per minute
the volume of a cube is 125cm cubed. The area of a square is 64cm squared. How does the length of one edge of the cube compare to the length of one side of the square? Explain
Answer:
One edge of the cube is 5 cm, one edge of the square is 8 cm, so the edge of the cube is 3 cm shorter than the edge of the square.
Step-by-step explanation:
The volume of the cube is found by the formula
V = s³,
where s is the side length (called the edge in this problem)
Since V = 125 cm³, we can take the cube root of 125 to find the edge length.
The cube root of 125 is 5, ( 5³ = 125)
So the edge of the cube is 5 cm
The are of a square is found by the formula
A = s² ,
where s is the side length (called the edge in this problem)
Since A = 64 cm², we can take the square root of 64 to find the edge length.
The square root of 64 is 8 (8² = 84)
So the edge of the square is 8cm
Comparing the two edges tells us that the edge of the cube is 3cm shorter than the edge of the square.
Jared and Zach are practicing their free throws. Jared attempted x shots and made 75% of them. Zach attempted 10 more shots than Jared did and made 80% of them. Together, they made a total of 101 shots. Which equation represents this situation?
0.75x+0.8(x + 10) = 101
Answer:
0.75x+0.8(x+10)=101
Step-by-step explanation:
Jared attempted x shots and made 75% of them, or 0.75x. Zach attempted 10 more shots than Jared did, which is represented as x + 10. He made 80% of them, or 0.8(x + 10). Together, they made 101 shots. So, add the two expressions and set the sum equal to 101:
0.75x + 0.8(x + 10) = 101.
Solve the equation. Check your solution.
20x-2=36x +10
Answer: [tex]x=-3/4[/tex]
Subtract 36x from both sides
[tex]20x-2-36x=36x+10-36x\\-16x-2=10[/tex]
Add 2 to both sides
[tex]-16x-2+2=10+2\\-16x=12[/tex]
Divide both sides by -16
[tex]\frac{-16x}{16} =\frac{12}{-16} \\x=\frac{-3}{4}[/tex]
Answer:
x = - [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Given
20x - 2 = 36x + 10 ( subtract 36x from both sides )
- 16x - 2 = 10 ( add 2 to both sides )
- 16x = 12 ( divide both sides by - 16 )
x = [tex]\frac{12}{-16}[/tex] = - [tex]\frac{3}{4}[/tex]
As a check
Substitute this value into the equation and if both sides are equal then it is the solution.
left side = 20 × - [tex]\frac{3}{4}[/tex] - 2 = - 15 - 2 = - 17
right side = 36 × - [tex]\frac{3}{4}[/tex] + 10 = - 27 + 10 = - x17
Since both sides are equal then x = - [tex]\frac{3}{4}[/tex] is the solution
A student finds the slope of the line between (8,17,) and (1,4) she writes 17-4/1-8 What mistake did she make?
The first mistake is that she didn't use parenthesis to indicate we're dividing all of one thing (numerator) over all of another expression (denominator)
slope = rise/run = numerator/denominator
So she should write (17-4)/(1-8) to indicate all of "17-4" is divided over all of "1-8"
However, there's another error that your teacher is probably more focused on. Note how 17-4 represents subtracting the y coordinates from left to right. We start with the left point y coordinate 17 and subtract off the right point y coordinate 4
left y - right y = 17 - 4
But then the student swaps the order when they wrote 1-8. Instead it should be 8-1
-----------------
Here's what they should have written (17-4)/(8-1)
This is the same as (4-17)/(1-8)
We can subtract in any order as long as it stays consistent between the numerator and denominator
tan α=2.4, Find: sin α and cot α
Answer:
cot α = 1/tan α = 1/2.4 = 0.42
Step-by-step explanation:
cot α=0.42
sin α = 0.92
we know that cot α = 1/tan α
thus,
cot α = 1/tan α = 1/2.4 = 0.42
we know that
sin(x)=tan(x)1+tan2(x)√
[tex]\ sin(\alpha )=tan(\alpha )/\sqrt{ 1+tan^2(\alpha )} \\sin(\alpha )= 2.4/\sqrt{1+2.4^2} = 2.4/\sqrt{1+5.76}\\sin(\alpha )= 2.4/\sqrt{6.76} = 2.4/2.6 = 12/13 = 0.92[/tex]
sin α = 0.92
5/9 of a piece of metal has a mass of 7 kg. What is
the mass of the piece of metal?
No wrong answer or else I will report
Answer:
The mass of the metal is 12.6 kgStep-by-step explanation:
Let the mass of the metal be x
From the question
5/9 of the metal is 7kg
That's
[tex] \frac{5}{9} x = 7[/tex]
Multiply through by 9
We have
5x = 7 × 9
5x = 63
Divide both sides by 5
[tex] \frac{5x}{5} = \frac{63}{5} [/tex]
We have the final answer as
x = 12.6 kg
The mass of the metal is 12.6 kgHope this helps you
Kari bought 3 boxes of cookies to share with a book club. Each box contains 12 cookies. The expression StartFraction 36 over p EndFraction represents the number of cookies that each person, p, can have if the cookies are divided equally. Which evaluations of the expression are correct? Select three options. If p = 5, then each person would get 6 cookies, with 4 cookies left over. If p = 7, then each person would get 5 cookies, with 1 cookie left over. If p = 8, then each person would get 4 cookies, with 3 cookies left over. If p = 10, then each person would get 3 cookies, with 6 cookies left over. If p = 11, then each person would get 3 cookies, with 3 cookies left over.
Answer:
i). If p = 7, then each person would get 5 cookies, with 1 cookie left over.
ii). If p = 10, then each person would get 3 cookies, with 6 cookies left over.
iii). If p = 11, then each person would get 3 cookies, with 3 cookies left over.
Step-by-step explanation:
First option is wrong because 5 dividing 36 is 7, not 6. It would remain 1, not 4.
Second option is correct because 36 divided by 7 would give you 5 remaining 1.
Third option is correct because 8 dividing 36 is 4, but will remain 4, not 3.
Fourth option is correct because 36 divided by 10 is 3, then will remain 6.
Fifth option is correct because 36 divided by 11 is 3, remaining 3.
Answer:
B,D,E
Step-by-step explanation:
edge
Emergency help will mark brainliest answer
Answer:
Step-by-step explanation:
Use the formula
[tex]A(t)=P(1+r)^t[/tex] where P is the initial investment, r is the interest rate in decimal form, and t is the time in years. Filling in what we are given:
[tex]A(t)=5000(1+.05)^6[/tex] and simplifying a bit:
[tex]A(t)=5000(1.05)^6[/tex] and a bit more:
A(t) = 5000(1.340095641) so
A(t) = 6700.48
Look at the picture and answer the question
Answer:
b
Step-by-step explanation:
Answer:
80 degrees
Step-by-step explanation:
m∠4 is the same as m∠2
I measured it with a protracter
( plz mark me as brainliest, that would be most appreciated! )
