Answer:
71, 72, 73
Step-by-step explanation:
So we want to find three consecutive integers that equal 216.
Let the first integer be n.
Then the second integer is n+1, and the third integer is n+2.
Thus:
[tex]n+(n+1)+(n+2)=216[/tex]
Combine like terms:
[tex]3n+3=216[/tex]
Subtract 3 from both sides:
[tex]3n=213\\[/tex]
Divide 3 from both sides:
[tex]n=71[/tex]
So, the first term is 71.
And the other two is 72 and 73.
And we are done :)
What is the degree of
the polynomial below?
I
x2 + 2x - 3x4 +5 + 3x?
Let p be a prime number. The following exercises lead to a proof of Fermat's Little Theorem, which we prove by another method in the next chapter. a) For any integer k with 0 ≤ k ≤ p, let (p k) = p!/k!(p - k)! denote the binomial coefficient. Prove that (p k) 0 mod p if 1 ≤ k ≤ p - 1. b) Prove that for all integers x, y, (x + y)^p x^? + y^p mod p.c) Prove that for all integers x, x^p x mod p.
Hello,
a) We know the binomial coefficients are all integers, so
[tex]\dfrac{p!}{k!(p-k)!}[/tex]
is an integer.
And we can notice that the numerator p! is divisible by p.
If we take [tex]1\leq k\leq (p-1)[/tex]
It means that k! does not contain p, and we can say the same for (p-k)!
So, we have no p at the denominator so the binomial coefficient is divisible by p, meaning this is 0 modulo p.
b) We can write that
[tex]\displaystyle (x+y)^p=\sum_{i=0}^{p} \ {\dfrac{p!}{i!(p-i)!}x^{p-i}y^i[/tex]
We use the result from question a) and the binomial coefficients are 0 modulo p for i=1,2 , ... p-1 so there are only two terms left and then,
[tex](x+y)^p=x^p+y^p \text{ modulo p}[/tex]
c) Let's prove it by induction.
step 1 - for x = 0
This is trivial to notice that
[tex]0^p=0 \text{ modulo p}[/tex]
Step 2 - we assume that this is true for k
meaning [tex]k^p=k \text{ modulo p}[/tex]
and we need to prove that this is true for the k+1
We use the results of b)
[tex](k+1)^p=k^p+1^p=k^p+1 \text{ modulo p}[/tex]
and we use the induction hypothesis to say
[tex](k+1)^p=k^p+1^p=k^p+1=k+1 \text{ modulo p}[/tex]
And it means that this is true for k+1
Step 3 - conclusion
We have just proved by induction the Fermat's little theorem.
p a prime number, for for all x integers
[tex]\Large \boxed{\sf \bf x^p=x \textbf{ modulo p}}[/tex]
Thank you
How many ounces of a 30% alcohol solution must be mixed with 18ounces if a 35% alcohol solution to make a 33% alcohol solution
Answer:
12 ounces
Step-by-step explanation:
0.30 x + 0.35 (18) = 0.33 (x + 18)
0.30 x + 6.3 = 0.33 x + 5.94
0.36 = 0.03 x
x = 12
5(x - 10) = 30 - 15x
Answer:
x = 4
Step-by-step explanation:
We can first expand 5(x-10), getting 5x - 50.
Thus, 5x - 50 = 30 - 15x
We can then isolate x, getting (5+15) x = 30 + 50
20 x = 80
x = 4.
Answer:
5(x - 10) = 30 - 15x
We distribute 5 (x-10)
So 5x-50 = 30 -15x
5x+15x=50+30
(-15x became 15x because we brought it back to the other side and -50 became 50 because we brought it back to the other side to put the x's with the x's and the digits with the digits.)
So 20x=80
x= 50/20
We simplify 80/20
So x=4
Solve x+9=7 show work
Answer: x = -2
x + 9 = 7, Move the constant to the right.
x =7 -9 now calculate that.
then you get x = -2
Hope that helps ya out :D
Answer:
x+9=7
So x= 7-9
( 9 became -9 because we brought it back to the other side to have the x alone and the digits alone )
So x= -2
The measure of ZAOC is 90 degrees. Find the value of x.
Answer:
14 + 3x + 46 = 90
3x + 60 =90
3x = 30
x = 10
Answer:
Step-by-step explanation:
If u see it is right angle so 90 - 14 u will get an or bc 76
3x+46=76
3x=76-46
3x=30
X=30/3
10
The width of a rectangle is 4 inches (in) and the area of the rectangle is 32 in2? Which of the following represents the length of the rectange?
a. 8 in
b. 128 in
c. 28 in
d. 36 in
Answer:
A. 8
Step-by-step explanation:
32 divided by 4 = 8
The answer is a. 8 in.
Since the width of the rectangle is 4 inches (in) and the area of the rectangle is 32 in², we need to find the length of the rectangle.
We know that the area of a rectangle with length, L and width, W is A = LW.
Since we need to find the length of the rectangle, we make the length, L subject of the formula.
Since A = LW,
L = A/W
Given that A = 32 in² and W = 4 in
Substituting the values of the variables into the equation, we have
L = 32 in²/4 in
L = 8 in
So, the length of the rectangle is 8 in
So, the answer is a. 8 in.
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Someone help!! Need answer fast!
Answer:
the area of the triangle is 20 units, and the answer to the expression is also 20, so its equal to each other. 20=20
the area of the trapezoid is 38.5 units
Step-by-step explanation:
roll two standard dice and add the numbers. what is the probability of getting a number larger than 8 for the first time on the third roll
Answer:
[tex]Probability = \frac{845}{5832}[/tex]
Step-by-step explanation:
Given
Two standard dice
Required
Probability that the outcome will be greater than 8 for the first time on the third roll
First, we need to list out the sample space of both dice
[tex]S_1 = \{1,2,3,4,5,6\}[/tex]
[tex]S_2 = \{1,2,3,4,5,6\}[/tex]
Next, is to list out the sample when outcome of both dice are added together[tex]S = \{2,3,4,5,6,7,3,4,5,6,7,8,4,5,6,7,8,9,5,6,7,8,9,10,6,7,8,9,10,11,7,8,9,10,11,12\}[/tex]
Next, is to get the probability that an outcome will be greater than 8
Represent this with P(E)
[tex]P(E) = \frac{Number\ of\ outcomes\ greater\ than\ 8}{Total}[/tex]
[tex]P(E) = \frac{10}{36}[/tex]
[tex]P(E) = \frac{5}{18}[/tex]
Next, is to get the probability that an outcome will noy be greater than 8
Represent this with P(E')
[tex]P(E) + P(E') = 1[/tex]
[tex]P(E') = 1 - P(E)[/tex]
[tex]P(E') = 1 - \frac{5}{18}[/tex]
[tex]P(E') = \frac{18 - 5}{18}[/tex]
[tex]P(E') = \frac{13}{18}[/tex]
Now, we can calculate the required probability;
Probability of a number greater than 8 first on the third attempt is:
Probability of outcome not greater than 8 on the first attempt * Probability of outcome not greater than 8 on the second attempt * Probability of outcome greater than 8 on the third attempt
Mathematically;
[tex]Probability = P(E') * P(E') * P(E)[/tex]
Substitute values for P(E) and P(E')
[tex]Probability = \frac{13}{18} * \frac{13}{18} * \frac{5}{18}[/tex]
[tex]Probability = \frac{13 * 13 * 5}{18 * 18 * 18}[/tex]
[tex]Probability = \frac{845}{5832}[/tex]
Bodie Raptor's Iphone 11 has 4/5 of the battery still remaining. His phone battery drains at a rate of 1/3 every hour. If he uses his phone continuously, how many more hours will his phone last. Please give your answer as a mixed number in simplest form in the form of A . b/c
Answer:
[tex]2\frac{2}{5}[/tex] hours, or 1 hours and 24 minutes
Step-by-step explanation:
4/5 battery remaining
drains at rate of 1/3 per hour
[tex]\frac{1}{3}h=\frac{4}{5}\\\frac{3}{1}(\frac{1}{3}h)=\frac{3}{1}*\frac{4}{5}\\h=\frac{3*4}{1*5}=\frac{12}{5}=2\frac{2}{5}[/tex]
He has 2 2/5 hours or 2 hours and 24 minutes left until his phone dies. (A fifth of an hour is 12 minutes and we have 2/5 to deal with, so 12 times 2 is 24 mins.)
Integral- Volumes by Slicing and Rotation About an Axis..Volume of a Pyramid... Could you help me solving this question, please?
Answer: volume is 9 cubic units
===================================================
Explanation:
Each cross section is a square with side length x, so the area of this cross section is x^2
We're integrating from x = 0 to x = 3
So we have
[tex]\displaystyle f(x) = x^2\\\\\\\displaystyle g(x) = \int x^2 dx = \frac{1}{3}x^3+C\\\\\\\displaystyle \int_{a}^{b} f(x) dx = g(b) - g(a)\\\\\\\displaystyle \int_{0}^{3} x^2 dx = g(3) - g(0)\\\\\\\displaystyle \int_{0}^{3} x^2 dx = \left(\frac{1}{3}(3)^3+C\right) - \left(\frac{1}{3}(0)^3+C\right)\\\\\\\displaystyle \int_{0}^{3} x^2 dx = 9\\\\\\[/tex]
Solve the given initial-value problem by finding, as an appropriate integrating factor.
(x2 + y2 − 3) dx = (y + xy) dy, y(0) = 1
Answer:
hello attached below is the detailed solution
answer : In |x+1| + [2/(x+1)] + [1/(1+x)^2] - [y^2/2(1+x)^2] = 5/2
Step-by-step explanation:
Given
(x^2 + y^2 - 3) dx = ( y + xy ) dy, y(0) = 1
solving the given initial-value problem
14. Line AD is parallel to line EG. If
m<3 is 70°, what is m 24?
F 10°
H 110°
G 20°
| 290°
15. Which angle is congruent to Z 3?
H 22
C 26
B 24
D 28
Answer:
14. H. 110°
15. D. <8
Step-by-step explanation:
14. Given that line AD and line EG are parallel as shown above, m<3 and m<4 are linear pairs and are supplementary. That is, m<3 + m<4 = 180°.
If m<3 = 70°, therefore, m<4 = 180° - 70°
m<4 = 110°
15. <3 corresponds with <8. Corresponding angles are congruent. Therefore, <3 = <8.
How many quarts of pure antifreeze must be added to 5 quarts of a 10 % antifreeze solution to obtain a 20 % antifreeze solution?
Considere as mesas com 4 cadeiras, com 6 cadeiras e com 8 cadeiras. ©Shutterstock/jenjira Com base nessa sequência de imagens, qual expressão indica a quantidade de cadeiras utilizadas ao colocarmos n mesas lado a lado?
Responder:
C. Tₙ = 2n + 2Explicación paso a paso:
De la pregunta, la secuencia de imágenes, cuya expresión indica es 4 cadeiras, 6 cadeiras, 8 cadeiras ...
Se puede ver la secuencia una progresión aritmética de la forma 4, 6, 8 ... Para obtener la expresión que indica la cantidad de cadenas utilizadas o colocaremos n tablas una al lado de la otra, tendremos que encontrar el enésimo término de la secuencia que usa la fórmula para encontrar el enésimo término de una secuencia aritmética.
El enésimo término de un AP se expresa como Tₙ = a + (n-1) d donde;
a es el primer término
n es el número de términos es la diferencia común
De la secuencia generada, a = 4, d = 6-4 = 8-6 = 2
Tₙ = 4+ (n-1) 2
abre el paréntesis
Tₙ = 4 + 2n-2
Tₙ = 2n + 4-2
Tₙ = 2n + 2
Por lo tanto, la expresión que indica la cantidad de cadenas utilizadas o colocaremos n tablas una al lado de la otra es 2n + 2
Which of the following are solutions to the equation below?
Check all that apply.
9x^2- 6x + 1 = 7
The answer is C and D
First we must make one side of the equation zero, so we subtract 7 on both sides of the equation, making the equation 9x^2 - 6x - 6 = 0
Then we will use the quadratic formula to find the answers.
using the Quadratic Formula where:
a = 9, b = -6, and c = -6
and the formula is 6 +- [tex]\sqrt{6^{2} } -4 (9)(6) /2 (9)[/tex]
Simplify 55/66 to lowest terms ?
Answer:
5/6
Step-by-step explanation:
To simplify this fraction, we need to find the GCF (greatest common factor) of the numerator and denominator. In this case, the GCF of 55 and 66 is 11. Now, all we have to do is divide both the numerator and denominator by the GCF. The numerator will become 55 / 11 = 5 and the denominator will become 66 / 11 = 6 so the simplified fraction is 5 / 6.
0 to 100 miles per hour in a mere 0.8 seconds. Calculate its acceleration. Show your work and include units.
Answer:
Answer: so the answer is 80 miles per 0.8 Step-by-step explanation: consistence
What is the equation of the slant asymptote of the rational function? f(x)=6x3−15x2+x−43x2−1 y=x−5 y=2x−5 y=x−17/3 y=2x−17/3
Answer:
2x − 5
Step-by-step explanation:
To solve, divide the numerator by the denominator. The result (not including the remainder) will be the equation of the slant asymptote.
We can tell the first term of the quotient will be 2x, so the answer will be either 2x − 5 or 2x − 17/3.
The easiest method here is to simply multiply these by denominator.
(3x² − 1) (2x − 5) = 6x³ − 15x² − 2x + 5
(3x² − 1) (2x − 17/3) = 6x³ − 17x² − 2x + 17/3
So the answer must be 2x − 5.
Alternatively, you can use long division.
Answer:
2x-5
Step-by-step explanation:
f(x)=(6x^3−15x^2+x−4 )/(3x^2−1)
To find the slant asymptote,divide the numerator by the denominator
2x +(-15x^2+3x-4)/ (3x^2-1)
-5 + (3x-9)/(3x^2-1)
The divisor is (2x-5) and the remainder is ( 3x-9)
Round 72.46387 to the nearest whole number
Answer:
72Step-by-step explanation:
[tex]72.46387 = 72[/tex]
4 is not up to 5
x+z-w/r=1 solve for z
Answer: z=1−x+w/r
Step-by-step explanation:
Subtract x from both sides.
z-w/r=1-x
Add w/r to both sides.
z=1−x+w/r
hope i helped
-lvr
Find three positive integers x, y, and z that satisfy the given conditions. The product is 125, and the sum is a minimum.
Answer:
Step-by-step explanation:
Given 3 positive integers x, y and z, if their product is 125, then;
xyz = 125 .......... 1
Sum of the integers S(x, y, z) = x+y+z ........... 2
From equation 1; x = 125/yz ........3
Substitute equation 3 into 2
S(x, y, z) = 125/yz+y+z
Sy = -125/y²z + 1
Sz = -125/z²y + 1
For the sum to be minimum, Sy = Sz = 0
-125/y²z + 1 = 0
-125/y²z = -1
-125 = -y²z
125 = y²z
Also; is Sz = 0
-125/z²y + 1 = 0
-125/z²y = -1
-125 = -z²y
125 = z²y
Hence y²z = z²y = 125
From y²z = 125, z = 125/y²
Substitute z = 125/y² into the equation 125 = z²y
125 = (125/y²)²× y
125 = 125²/y⁴ × y
125 = 125²/y³
1 = 125/y³
y³ = 125.
y = 5
Since 125 = y²z
5²z = 125
25z = 125
z = 5
From the product xyz = 125
x(5)(5) = 125
25x = 125.
x = 5
Hence x = y = z = 5
Find the sum of -6x^2-1−6x 2 −1 and x+9x+9.
Answer:-6x^2+10x-5.
Step-by-step explanation: -6x^2-1−6x 2−1+x+9x+9 -6x^2-1−6x 2−1+10x+9 -6x^2-1-12−1+10x+9 -6x^2+10x-1-12-1+9 6x^2+10x-5
The sum of the two expressions are -6x²+22x+9
What are like and unlike terms in an expression?In Algebra, the like terms are defined as the terms that contain the same variable which is raised to the same power. In algebraic like terms, only the numerical coefficients can vary. We can combine the like terms to simplify the algebraic expressions.
Given here the expressions here as -6x²+1+6x ×2-1, x+9x+9
The sum is -6x²+1+6x ×2-1 +x+9x+9=-6x²+22x+9
Hence, The sum of the two expressions are -6x²+22x+9
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Solve for x in the equation 3x-5=2x²
Answer:
[tex]3x - 5 = 2 {x}^{2} \\ = > 3x = 2 {x}^{2} + 5 \\ = > x = \frac{2 {x}^{2} + 5 }{3} [/tex]
Represent the following expression using an exponent.
12 x 12 x 12 x 12
Answer:
12<4 (12 to the power of 4)
Step-by-step explanation:
an exponet is used when a number is repeated multiplied against itself. sinec 12 is being multiplied against itself 4 times, we can use the exponent of 4
Answer: [tex]12^4[/tex]
Step-by-step explanation:
Concept to know: for exponents, the amount of same number that is multiplied together will be the number of exponents
--------------------------------------
12×12×12×12
There are in total 4 [12]'s multiplied together, so we will get [tex]12^4[/tex]
Hope this helps!! :)
Please let me know if you have any question or need further explanation
Jessica always uses the same ratio of green beads to blue beads when she makes necklaces. The graph shows these equivalent ratios. Which table shows the same data?
Answer:
table 2
Step-by-step explanation:
see attached
Answer:
table no. 2
Step-by-step explanation:
Question 1 (1 point) How many terms are in the polynomial? 3x3 + 4x2 - 8x - 5 3 4 7
Answer:
4
Step-by-step explanation:
The polynomial 3x^3 +4x^2 -8x -5 has 4 terms. A term is a product or single variable or constant separated from other terms by a plus or minus sign.
The four terms are ...
3x^34x^2-8x-5Determine algebraically whether f(x)=3x-2 and g(x)=(x+2)/3 are inverse functions. Show all work.
Answer:
Yes
Step-by-step explanation:
f(x)=3 x-2
y= 3 x-2
x= 3y - 2
3 y -2 = x
3 y -2 + 2 = x + 2
3 y = x + 2
3 3 3
3 y = x + 2
3 3 3
y = x + 2 replace y with f ^ -1(x)
3 3
f ^-1 (x) = x + 2
3 3
The map shows the route for a race.You are at X, 6000 ft from the first checkpoint C.The second checkpoint D is located at the midpoint between C and the end of the race Y.The total race is 3 miles how far apart are the 2 checkpoints? I know the answer is 4920 but i don’t know how to work it out
Answer:
Distance between the two check point (C and D) is 4920 ft.
Step-by-step explanation:
From the question given above, we obtained the following information:
X is 6000 ft from C (1st check point)
D (2nd check point) is the midpoint point between C and Y ( the end of the race)
Total race = 3 miles
1 mile = 5280 ft
Next, we shall express the total race in feet (ft).
This is illustrated below:
1 mile = 5280 ft
Therefore,
3 miles = 3 × 5280 = 15840 ft
Next, we shall determine the distance between the 1st check point (C) and the end of the race (Y)
This can be obtained as follow:
Total distance = 15840 ft
Distance between X and C = 6000 ft
Distance between C and Y =?
Distance between C and Y = (Total distance) – (Distance between X and C)
Distance between C and Y = 15840 – 6000
Distance between C and Y = 9840 ft
Finally, we shall determine the distance between the two check point (C and D) as follow:
Since D is midpoint between C and Y, therefore, we shall we shall divide the distance between C and Y by 2 in order to obtain the distance between the two check point (C and D).
This is illustrated below:
Distance between C and Y = 9840 ft
Distance between the two check point (C and D) = 9840/2 = 4920 ft
Therefore, the distance between the two check point (C and D) is 4920 ft
Rounding whole number which number could round to 80,600 80,532 80,549 80,617 80, ,651
Answer:
80,617
Step-by-step explanation:
the 1 in the tens place puts the number back down to 600