Step-by-step explanation:
Let x = m² and y = 4n.
Then m⁶ - 64n³ = x³ - y³
= (x - y)(x² + xy + y²)
= (m² - 4n)(m⁴ + 4m²n + 16n²).
The container that holds the water for the football team is 1/4 full. After pouring in 10 gallons of water, it is 2/3 full. How many gallons can the container hold?
Answer:
[tex]x =24[/tex]
Step-by-step explanation:
From the question we are told that
Amount of water 1/4x
Gallons added 10
Amount of water after addition 2/3x
Where x is a full container
Generally the parameters above gives the equation
[tex]\frac{1}{4}x +10=\frac{2}{3}x[/tex]
Therefore
[tex]\frac{1}{4}x -\frac{2}{3}x =-10[/tex]
[tex]-\frac{5}{12}x =-10[/tex]
[tex]x =\frac{-10}{-\frac{5}{12}}[/tex]
[tex]x =24[/tex]
Therefore the container can hold 24 gallons of water
How do I find n in the the permutation equation of nP3 = 990
Answer:
n=11
Step-by-step explanation:
Permutations
The formula to calculate permutations is:
[tex]\displaystyle nPm=\frac{n!}{(n-m)!}[/tex]
We know nP3=990. Substituting:
[tex]\displaystyle nP3=\frac{n!}{(n-3)!}=990[/tex]
Expanding the factorial in the numerator:
[tex]\displaystyle \frac{n(n-1)(n-2)(n-3)!}{(n-3)!}=990[/tex]
Simplifying:
[tex]n(n-1)(n-2)=990[/tex]
This equation can be easily solved by inspection. The product of three consecutive numbers resulting 990. Starting from greatest to smallest, those numbers are 11,10, and 9, thus:
[tex]n(n-1)(n-2)=11*10*9[/tex]
It follows that n=11
Which two grids have 25% shaded
Answer:
there's no grid provided
PLEASEE HELP ASAP IM BEGGIMG YOUUUUUU
I WILL GIVE BRAINLIEST ASAP
Answer:
Below
Step-by-step explanation:
Problem 1
Blank 1 = 6
Blank 2 = 17
(5*3)+2
Blank 3 = 4
(4*1)
Problem 2
Blank 1= (-5)^3=-5*-5*-5=-125
Blank 2= 18
(6*3)
Blank 3= 12
(4*3)
~Uh- ~ Hey ~ can ~ someone ~ help ~ me ~ out ~ once ~ again...?~
A circle has a radius of 6 meters. What is the circumference of the circle?
Answer:
The answer is option A
A) Circumference= 12[tex]\pi[/tex] m
Step-by-step explanation:
To find the circumference of a circle the formula you would use is C=2[tex]\pi[/tex]r
if the radius is 6 meters, C is
C = 2*6 [tex]\pi[/tex]r
C= 12[tex]\pi[/tex] m
Plz help!! Meera is researching cruising speeds of different planes. Which airplanes has a greater cruising speed?
Answer:
The one on the graph
Step-by-step explanation:
What is the slope of a line perpendicular to the line whose equation is x−2y=12.
Answer:
-2/x
Step-by-step explanation:
simplified is y = -x/2 - 6
Perpendicular slopes are just reciprocals of the original slope, so just flipp the original slope around to be the complete opposite.
Example if slope= -2, the reciprocal= -1/2
Just flip the numerator with the denominator for perpendicular slope
A culture of bacteria has an initial population of 39000 bacteria and doubles every 9 hours. Using the formula P_t = P_0\cdot 2^{\frac{t}{d}}P t =P 0 ⋅2 d t , where P_tP t is the population after t hours, P_0P 0 is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 2 hours, to the nearest whole number?
Answer:
45495
Step-by-step explanation:
Answer:
10077
Step-by-step explanation:
A culture of bacteria has an initial population of 5400 bacteria and doubles every 10 hours. Using the formula P_t = P_0\cdot 2^{\frac{t}{d}}P
t
=P
0
⋅2
d
t
, where P_tP
t
is the population after t hours, P_0P
0
is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 9 hours, to the nearest whole number?
P_0=5400
P
0
=5400
The initial population
t=9
t=9
Time elapsed
d=10
d=10
The doubling time
P_t = P_0\cdot 2^{\frac{t}{d}}
P
t
=P
0
⋅2
d
t
P_t=5400\cdot 2^\frac{9}{10}
P
t
=5400⋅2
10
9
Plug in
P_t=10076.7563\approx10077
P
t
=10076.7563≈10077
Use parenthesis in the calculator for the exponent
Solve 24≤−6t.
the solution is __
Answer:
t ≤ − 4
Step-by-step explanation:
Answer: t ≤ -4
Step-by-step explanation:
rearrange the problem 24-(-6*t)≤0 Pull out like factors :24 + 6t = 6 • (t + 4)
Divide both sides by 6 Subtract 4 from both sides t ≤ -4
Someone pls pls answer this ill mark u brainliest
Answer:
[tex]m\angle CBD=35^{\circ}[/tex]
Step-by-step explanation:
Since there are [tex]180^{\circ}[/tex] on each side of a line and [tex]\angle ABC[/tex] is marked as a right angle, [tex]m\angle CBE=180-90=90^{\circ}[/tex].
[tex]m\angle CBE=m\angle DBE+m\angle CBD[/tex], and [tex]m\angle DBE[/tex] is given as [tex]55^{\circ}[/tex].
Therefore, we can plug in our values and solve:
[tex]90=55+m\angle CBD,\\m\angle CBD=\fbox{35^{\circ}$}[/tex].
A building is 200 feet high. One end of a wire is attached to the top of the building.
The other end is attached to the group 150 feet away from the base of the building. How
long is the wire?
Answer:
250 feet
Step-by-step explanation:
If you draw out this situation, you would get a right triangle with a height of 200 (feet) and a base of 150 (feet). The wire is the missing length, or the 'hypotenuse' of this right triangle. You use the pythagoras thingie, and the formula is a^2 + b^2 = c^2.
a= 200
b= 150
c= ?
40,000 + 22,500 = c^2
62,500 = c^2
c = √62,500
∴ c = 250
Divide 3 1/2 divided by 1/2 in simplest form
Answer:
7
Step-by-step explanation:
For the problem:
3 1
2
÷
1
2
= ?
Convert any mixed numbers to fractions:
3 1
2
=
7
2
Division of fractions is equivalent to multiplication by the reciprocal of the second fraction:
7
2
÷
1
2
=
7
2
×
2
1
Once rearranged, multiply all of the numerators by each other. Do the same with the denominators and form a new fraction with these values:
7 × 2
2 × 1
=
14
2
The Greatest Common Factor (GCF) of 14 and 2 is 2. The result can be simplified by dividing both the numerator and denominator by 2.
14
2
=
14 ÷ 2
2 ÷ 2
= 7
The result is:
3 1
2
÷
1
2
= 7
expand and simplify (x-3)(2x+1)(3x-2)
Answer:
6x³ - 19x² + x + 6
General Formulas and Concepts:
Algebra I
Terms/CoefficientsExpand by FOIL (First Outside Inside Last)Step-by-step explanation:
Step 1: Define
(x - 3)(2x + 1)(3x - 2)
Step 2: Expand
Expand [FOIL]: (2x² + x - 6x - 3)(3x - 2)Combine like terms: (2x² - 5x - 3)(3x - 2)Expand: 6x³ - 15x² - 9x - 4x² + 10x + 6Combine like terms: 6x³ - 19x² + x + 6m + 7 ≥ 20, if m = 11
Answer:
False;18 ≥ 20
Step-by-step explanation:
Add 11 and 7
The left side 18 is less than the right side 20 , which means that the given statement is false.
12 ÷ 4 x ___ = 12
im so confused on this question can you guys help
Answer:
Step-by-step explanation:
12/4 = 3
3 x 4 = 12
4 is the answer
Which expression is equivalent to 13 - (-21)?
Choose 1 answers
А
13 +21
B
-21 - 13
-13 +21
D
-21 +13
HURRY
Evaluate the power.
0.4 2=____
Answer:
0.2
Step-by-step explanation:
Answer:
0.16
Step-by-step explanation:
Gio wants to serve salad at the party. He will need one head of lettuce for every 6 guests who attend. Write an algebraic expression Gio could use to determine how much lettuce he needs. Gio finds out 18 people are coming to the party. Evaluate the expression for 18 guests
Answer:
a. y = x/6 b. 3 heads of lettuce
Step-by-step explanation:
a. Write an algebraic expression Gio could use to determine how much lettuce he needs
Since Gio needs one head of lettuce for every 6 guests who attend, then, the number of lettuce y needed for x guests is one head of lettuce/6 guests × x guests is y = 1/6 × x
= x/6
b. Gio finds out 18 people are coming to the party. Evaluate the expression for 18 guests
Since 18 guest come to the party, x = 6. So, y = x/6
= 18/6
= 3 heads of lettuce.
Solve the system of equations by the substitution method.
y=5x+8 y=8x+9
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Answer:
whichever one corresponds with the answers you have will be right.
Very confused. Will give 40pts.
Answer:
Y = 10.25 or 10.247
Step-by-step explanation:
Alright So use the Formula A^2 + B^2 = C^2
You have one leg and the hypotenuse so first you are going to find 19 ^2 = 361.
Next, you need to find 16^2 = 256.
Last but not least, you subtract the leg from the hypotenuse, which equals 361-256=105
Finally, you take 105 and find its square root.
And depending on how far you round it down, your answer would be 10.25(that is in tenths), or 10.247(which is rounded to hundredths)
Hope this helps!
Solve for x !!!!!!!!
Mary has a \large 16\frac{1}{2} ounce bag of chocolate chips. She will only use \large \frac{1}{4} of the bag for decorating a cake. How many ounces will she use for decorating
Answer:
4 1/8 ounces
Step-by-step explanation:
Total bag of chocolate chips Mary has = 16 1/2 ounces
She will only use 1/4 of the bag for decorating a cake.
How many ounces will she use for decorating
Ounces used in decoration = 1/4 of 16 1/2
= 1/4 × 33/2
= (1*33)/(4*2)
= 33/8
= 4 1/8 ounces of chocolate chips
She will use 4 1/8 ounces of chocolate chips for decorating a cake
Find X in this picture.
Answer:
x is in the top left of the triangle :)
Step-by-step explanation:
Answer:
its there....
Step-by-step explanation:
plssss help ASAPPP!!!!!!!
Answer:
12
Step-by-step explanation:
you have to times 2 x 6 to find your x
I'm not for sure tho but I hope it's right
Carlota’s smartphone contains 500 megabytes of data. She uses 300 megabytes for applications and the rest for music. If each song takes an average of 4 megabytes, which equations can be used to find the number of songs on Carlota’s smartphone? Select all that apply. A. 500−300=4n B. 500+300=4n C. 4n+300=500 D. 300−4n=500
Answer: A:500-300=4n and C:4n+300=500
Step-by-step explanation:
The angle of elevation of the top of a flagpole from a point on the ground 30 meters
from the base of the flagpole is 18 degrees. What is the height of the flagpole, to the
nearest meter?
I need help
Answer:
[tex]10\:\mathrm{meters}[/tex]
Step-by-step explanation:
We can use trigonometry for a right triangle to solve this problem:
[tex]\tan 18^{\circ}=\frac{h}{30},\\h=30\cdot\tan 18^{\circ},\\h\approx \fbox{$10\:\mathrm{m}$}[/tex].
The height of the flagpole is 10 meters.
What is angle of elevation?"It is the angle from the horizontal upward to an object."
For given question,
Consider the following figure.
The angle of elevation is 18°
⇒ ∠ACB = 18°
Also, BC = 30 meters
We need to find the height of the flagpole i.e., we need to find the distance AB.
Consider a tan(∠ACB )
[tex]\Rightarrow tan(18^{\circ})=\frac{AB}{BC}\\\\ \Rightarrow 0.3249 = \frac{AB}{30}\\\\ \Rightarrow AB=9.747 ~~meters\\\\\Rightarrow AB\approx 10~~meters[/tex]
Therefore, the height of the flagpole is 10 meters.
Learn more about angle of elevation here:
https://brainly.com/question/21137209
#SPJ3
Penny makes $5,400 a month plus commission. She gets 3% of everything she sells. If Penny sold $62,000 worth of items this month, what is her salary for the month?
Answer:
Her salary for the month = $7260
Step-by-step explanation:
Given
Base Salary = $5,400 Amount sold = $62,000Percentage rate = 3%To determine
Salary for month = ?Given that Amount sold = $62,000 and Percentage rate 3%
so
Salary from commission rate = Amount sold × Percentage rate
= $62,000 × (3 / 100) = $1860
Thus, the total salary can be calculated by adding Base salary and Salary from the commission rate.so
Total salary = Base salary + Salary from commission rate
= $5,400 + $1860
= $7260
Hence, her salary for the month = $7260
c=27+10h where c= cost in dollars and h= number of hours rented
Answer:
that help
Step-by-step explanation:
10h+27+−27=c+−27
10h=c−27
10h10=c−2710
h=110c+−2710
Answer:
h=110c+−2710
find the angle p (add a explanation too)
Step 1: Find the sum of the interior angles
Use this formula: 180 x (n - 2)
n is the number of sides of the polygon
Work:
180 x (4 - 2)
180 x 2
360
Step 2: Find the angle right above the 94 degree angle
The entire angle (a circle) is equal to 360 degrees. To find the part we're looking for (inside of the polygon), we need to subtract the angle we already know from 360.
Work:
360 - 94
266
Step 3: Set up an equation to find the missing angle p
We now know every angle except p! And we know the sum of the interior angles. Knowing this information makes it really easy to set up an equation.
360 = 12 + 75 + 266 + p
360 = 353 + p
p = 7 degrees
Does this answer make sense?
Yes! Although the drawing may not be to scale, it is very possible that angle p could be 7 degrees because of how 12 degrees looks on this graph.
Hope this helps!! :)
James is solving a number puzzle that involves three integers, a, b, and c, where c
is a positive integer. The product of A and B is 6. The product of a and c is – 4.
The product of b and c is -6.
Please help!!!
Answer:
a = -2, b = -3, c = 2
Step-by-step explanation:
We have the following three equations.
ab = 6
ac = -4
bc = -6
Multiply equation 2 and 3, we get
abc^2=24
Dividing it by the first equation, we get
c^2=4
c=2 or -2 (rejected since c is a positive integer)
We can then substitute c=2 into the equations, and find out that a = -2 and b = -3.
