By the binomial theorem,
[tex]\displaystyle (2x+y)^7 = \sum_{k=0}^7 \binom7k (2x)^{7-k} y^k=\sum_{k=0}^7 \binom7k 2^{7-k} x^{7-k} y^k[/tex]
where
[tex]\dbinom nk=\dfrac{n!}{k!(n-k)!}[/tex]
is the binomial coefficient.
We get the x⁴y³ terms with k = 3, for which the coefficient would be
[tex]\dbinom73 2^{7-3}=\dfrac{7!}{3! 4!} 2^4=\boxed{560}[/tex]
How many solutions does the equation have? If there is only one, determine the value.
12
y
−
18
=
6
(
2
y
−
3
)
Answer:
0=0
Step-by-step explanation:
Infinite
The given equation can be rearranged to equate both side of the equation and thus we can get equivalent on both side as 6 (2y-3) = 6 (2y-3). Therefore, y can have any values from 0.
What are algebraic equations?Algebraic equations are expression used to represent the relation between two values by some letters or alphabets whose values are not specified in the equation.
In general, the letters x and y are used in the algebraic equations. They can linear or non-linear equation. By rearranging this equations we can determine the values of x and y.
Given the expression 12 y - 18 = 6 (2y - 3). From the left hand side, divide the part 12 y - 18 by 6. Thus we obtain the expression equivalent to the right hand side as 6 (2y - 3).
Therefore, 6 (2y - 3) = 6 (2y - 3). Which means both sides are equal and have equal value of y. means y can have any values from zero since all the terms including y is zero both side.
Thus, giving any value to y will always remains the same equation.
To find more about algebraic equations, refer the link below:
https://brainly.com/question/953809
#SPJ5
the cost for a pack of 15 pens is $3.15. find the unit price in dollars per pen. if necessary, round to the nearest cent
Right answer is correct
Step-by-step explanation:
3x=6
X=6
_
3
X=2..
3Y=3
Y=3/3
Y= 1
The daily consumption of milk in a house is 3.25 litres. How much milk will be consumed in 30 days?
Answer:
Milk consumed in 30 days = (30 days)(3.25 litres/day) = 97.5 litres
Step-by-step explanation:
You are given a rate at which the milk is consumed (3.25 litres per 1 day). This is just multiplied by the 30 days to get your answer.
Answer:
97.5
Step-by-step explanation:
Daily :3.25
Days: 30
So,
3.25× 30
=97.5
is 55 810 a multiple of 10
Answer:
Yes
Step-by-step explanation:
Any number that ends with a zero is a multiple of 10
To find means to cover. Choose the missing prefix.
1. pre
2. dis
3. in
4. con
it is B: Dis Hope this helps
Convert 3x - 5y = 30 into Slope-Intercept Form
1) y = -3x - 6
2) y = -3x + 5y + 30
3) y = 3/5x - 6
4) y = 5/3x - 6
Giovanni went to the Lowe’s looking for supplies. He bought three pounds of cement for $27.75 per pound. A plant for $12.58. He paid $8.99 is sales taxes. How much did he pay in total at Lowe’s?
Step-by-step explanation:
Hey there! Let's break this answer down.
1. If he bough 3 pounds of cement for $27.75 each, that 3x27.75, which is $83.25. So he spent $83.25 on cement.
2. Next, add $12.58 for the cost of the plant to $83.25, which $95.83.
3. Finally, he paid $8.99 for the sales tax. When adding that to $95.83, we get $104.82.
So, his total was $104.82.
Have a great day!
Answer:
104.82
1Step-by-step explanation:
27.75 times 3 equals 83.25 plus 12.58 equals 95.83 then add 8.99 which is $104.92
(b^2+5) (-b^2+7) I need help asap pleas and thank you if you do
Answer:
42
Step-by-step explanation:
b to the second power thats 1 plus 1 plus 5 times -1to the second power plus seven times 7 and 6 get you the answee 42
The √28 is between which two whole numbers?
Answer:
between 5 and 6
Step-by-step explanation:
Choose 2 perfect squares either side of 28, that is
25 < 28 < 36, then
[tex]\sqrt{25}[/tex] < [tex]\sqrt{28}[/tex] < [tex]\sqrt{36}[/tex] , thus
5 < [tex]\sqrt{28}[/tex] < 6
please please help me!!
Answer:
k=1
Step-by-step explanation:
because the intercept form, y=mx plus b the y intercept changes where the graph is positioned. the line has been translated down to the y intercept 1, therefore that is what k equals
(2+7-1)divided by 2 over 2
Answer:
The answer is 2
Step-by-step explanation:
[tex](2 + 6) \div 2 {}^{2} \\ \\8 \div 4 = 2[/tex]
The graph of a quadratic function creates a curve called a hyperbola. True False
Answer:
its false
Step-by-step explanation:
What congruency theorem would this be : SSS, SAS or ASA ???
Find the slope of a line parallel to the given line:
7x - 3y = -6
Answer:
7/3x
Step-by-step explanation:
parallel lines have the same slope, so you would have to find the slope of the first line.
7/3x
Hope this helps :-)
A contractor bought 12.6 ft2 of sheet metal. He has used 3.7 ft2 so far and has $160.20 worth of sheet metal remaining. The equation 12.6x−3.7x=160.2 represents how much sheet metal is remaining and the cost of the remaining amount. How much does sheet metal cost per square foot?
Answer:$18 per square foot
Step-by-step explanation:
12.6x-3.7x=160.2
8.9x=160.2
x=18
$18 per square foot
Rewrite each geometry formula using function notation. Use the same variables as the formula in your function. Evaluate each function when r=5 feet. Do not round; write answers in terms of pi, if necessary. Explain the meaning of the result.
a. Diameter, d=2r
The formula using function notation is _______; The value when r=5 is _______; The diameter of the circle is ______ feet when the radius is ________ feet.
b. Area, A=pi x r^2
The formula using function notation is _______; The value when r=5 is _______; The area of the circle is ______ feet when the radius is ________ feet.
c. Circumference C=2 x pi r
The formula using function notation is _______; The value when r=5 is _______; The Circumference of the circle is ______ feet when the radius is ________ feet.
Answer:
A) d(r) = 2r
Value when r = 5 is 10 ft.
diameter is 10 ft when the radius is 5ft
B) A(r) = πr²
Value when r = 5 is 25π ft²
Area is 25π ft² when radius is 5 feet
C) C(r) = 2πr
Value when r = 5 is 10π
Circumference is 10π when radius is 5 feet
Step-by-step explanation:
A) Using function notation, since d = 2r
d(r) = 2r
d(5) = 2(5)
d(5) = 10 feet
This means that the diameter is 10 ft when the radius is 5ft
B) Area = πr²
In function notation, its;
A(r) = πr²
When radius is 5 feet,
Area is; A(5) = π(5²) = 25π
It means Area is 25π ft² when radius is 5 feet
C) Circumference is 2πr
In function notation, it's;
C(r) = 2πr
When r = 5 feet,
Circumference is;
C(5) = 2π(5)
C(5) = 10π
help what is the solution for : 5 + |x| = 14
Answer:
9
step by step explanation
5+x=14
14-5=9
x=9
If P*Q = PxQ - 7,
what is 9*5?
Given problem:
What is 9*5;
The formula P*Q = P x Q - 7;
To find 9*5, simply make P = 9 and Q = 5
Input into the equation and solve;
P*Q = P x Q - 7 = 9 x 5 - 7
= 45 - 7
= 38
The solution to this problem is 38.
FRESHMEN MATH PLEASE HELP
Answer:
see below
Step-by-step explanation:
[tex]\sqrt{2}\approx 1.41\\\\\sqrt{3}\approx1.73\\\\\sqrt{4}=2\\\\\sqrt{5}\approx2.23\\\\\sqrt{6}\approx2.44\\\\[/tex]
so we can say
[tex]1.36<\sqrt{2}<2.45\\\\1.65<\sqrt{3}<2.34\\\\1.65<\sqrt{4}<2.34\\\\2.16<\sqrt{5}<3.45\\\\2.41<\sqrt{6}<3.56[/tex]
that's the smalles possible intervals I could find, i don't know if those are the smalles, but those are what I found
Can you always draw a piecewise function without picking up your pencil.
Answer:
Yes
Step-by-step explanation:
A function is continuous on an interval if the graph has no breaks, jumps, or holes. You can draw it without picking up your pencil.
I need help to solve it
Answer:
to solve what
Step-by-step explanation:
Solve for y; 1/y = a/w + w/a
Answer:
y = aw/(a^2 + w^2)Step-by-step explanation:
Given
1/y = a/w + w/aSolving for y
1/y = a/w + w/a1/y = (a^2 + w^2)/awy = aw/(a^2 + w^2)Lola purchased two pairs of shoes that each cost $20.00. She then purchased a pair of jeans for $14.50 and a shirt for $8.25. What is the total amount of money she spent, before tax?
Answer: $62.75
Step-by-step explanation:
1.)$20.00 x2= $40.00
2.)$14.50 +$8.25= $22.75
3.)$40.00 +$22.75= $62.75
Hope this helps
help me pleaseeee.........
9514 1404 393
Answer:
y = 204^8x = 0Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
a^0 = 1 . . . . for a ≠ 0
__
And, it is convenient to know the cubes of small integers:
1³ = 1; 2³ = 8; 3³ = 27; 4³ = 64; 5³ = 125
6³ = 216; 7³ = 343; 8³ = 512; 9³ = 729; 10³ = 1000
__
1) p^3 × p^5 = p^-12 × p^y
Equating exponents:
3 + 5 = -12 + y
20 = y . . . . . . . . . . . add 12
__
2) 64 × 4^5 = 4^3 × 4^5 = 4^(3+5) = 4^8
__
3) 10^x = 1 = 10^0
x = 0
answer:
okay so i did it and i got these answers
- y = 20
- 4^8
- x = 0
step-by-step explanation:
my work
- p^3 × p^5 = p^-12 × p^y then 3 + 5 = -12 + y so: 20 = y
64 × 4^5 = 4^3 × 4^5 = 4^(3+5) so: its 4 over 8
10^x = 1 = 10^0 so: its 0
hope this helped :) pls give me brainliest <3
Estimate: 10 + 24.73 A 25 B 15 C 125 D 35
Answer: 35
To estimate, we can remove the decimal points and numbers.
So, now we have 10 and 24. Count on by tens since we have one 10.
24, 34 (24 + 10 = 34)
34 is closest to the number 35, it is one away.
The answer is 35. Hope this helps you!
-1/2 = m -7/4
solve for m
Answer:
[tex]\boxed {m = \frac{5}{4}}[/tex]
Step-by-step explanation:
Solve for the value of [tex]m[/tex]:
[tex]-\frac{1}{2} = m - \frac{7}{4}[/tex]
-Switch sides:
[tex]m - \frac{7}{4} = -\frac{1}{2}[/tex]
-Add both sides by [tex]\frac{7}{4}[/tex] and the least common multiple of both [tex]2[/tex] and [tex]4[/tex] is [tex]4[/tex]. So, convert [tex]-\frac{1}{2}[/tex] to a fraction with denominator [tex]4[/tex]:
[tex]m - \frac{7}{4} + \frac{7}{4} = -\frac{1}{2} + \frac{7}{4}[/tex]
[tex]m = -\frac{2}{4} + \frac{7}{4}[/tex]
-Since both [tex]-\frac{2}{4}[/tex] and [tex]\frac{7}{4}[/tex] have the same denominator, then you would add the numerators:
[tex]m = \frac{-2 + 7}{4}[/tex]
[tex]\boxed {m = \frac{5}{4}}[/tex]
Therefore, the value of [tex]m[/tex] is [tex]\frac{5}{4}[/tex].
helpp pleaseee <3 !
Answer:
I belive the first one is 5:7 And the second one is 7:12
Step-by-step explanation:
solve the inequality 2x + 8 < 5x − 4.
Answer:
x>4
Step-by-step explanation:
2x+8<5x-4
4+8<5x-2x
12<3x
4<x
x>4
Answer:
x > 4
Step-by-step explanation:
Write 2^3×2^6 as a single power of 2.
Answer:
The answer is 2^9
Step-by-step explanation:
You add the exponents.
Thats it.
PLEASE HELP WILL GIVE BRAIINLIES AND DONT PUT RANDOM WORDS
Answer:
8a. $432
8b. about 36 2/3 hours
9. %17.50 per article
10. $338.4 after 3 weeks
Step-by-step explanation: