Step-by-step answer:
The coefficients of terms of (p+q)^n can be found by the Pascal's triangle for small values of n. Pascal's triangle will start with (1,1) = coefficients of (p,q)^n =1. For n=2, we add successive terms of the previous value of n. Thus for n-2, we have (, 1+1,11=(1,2,1), for n=3, we have (1,3,3,1), giving the following pattern:
(1,1)
(1,2,1)
(1,3,3,1)
(1,4,6,4,1)
(1,5,10,10,5,1)
meaning for n=5, the binomial expansion for (P+Q)^5 is
P^5+5P^4Q+10P^3Q^2+10P^2Q^3+5PQ^4+Q^5
Setting P=2x, Q=y in the term 10P^3Q^2, we get a term
10(2x)^3(y)^2
=10(8x^3)(y^2)
=80x^3y^2
So the required coefficient is K=80.
We can also find the coefficient 10 by binomial expansion of
n=5, x=3 in
C(n,x) = n! / (x! (n-x)!) = 5! / (2!3!) = 5*4*3/(1*2*3) = 10
Then again substituting 10(2x)^3(y)^2 = 80x^3y^2
to get the coefficient K=80.
Answer: 80
Step-by-step explanation: cuz
Convert the improper fraction into a mixed number. 6 1/8 divided by 1 3/4
Answer:
4 19/32
Step-by-step explanation:
convert into improper fractions
6 1/8= 49/8
1 x 3/4= 3/4
49/8 x 3/4 = 147/32
reduce into mixed number
4 19/32
To convert the mixed numbers 6 1/8 and 1 3/4 to improper fractions, resulting in 49/8 and 7/4, respectively. Then, perform the division as multiplication with the reciprocal of the second fraction, which yields 3 1/2.
Explanation:Firstly, it's essential to convert the mixed numbers into improper fractions. The given mixed numbers are 6 1/8 and 1 3/4. We can convert 6 1/8 to an improper fraction by multiplying 6 (the whole number) by 8 (the denominator) and then adding 1 (the numerator) to get 49/8. With 1 3/4, we multiply 1 (the whole number) by 4 (the denominator), then add 3 (the numerator), which gives us 7/4.
Now, the division 49/8 ÷ 7/4 can be performed. To divide fractions, we multiply the first fraction by the reciprocal of the second. Therefore, we will multiply 49/8 by 4/7. The result is 196/56. This simplifies to 3 1/2 when converted back to a mixed number.
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Brayden starts out riding his bike for 5 kilometers. He stops and takes a turn and rides his bike
14 more kilometers. After resting, he takes another road that will lead him back toward his starting
point. He is only on that road for 8 kilometers. Is it possible that he made it back to his starting point
Explain your answer and include a sketch to support your argument.
Part I: Sketch the route that represents Brayden's route. Label the distance traveled for each
portion of his ride.
Part ll: Is it possible that he made it back to his starting point?
Answer:
it is not possible that Brayden made it back to his starting point.
Step-by-step explanation:
Part 1: Step 1: Define the map scale
REAL:MAP
1 km : 1 cm
5 km : 5 cm
14 km : 14 cm
8 km : 8 cm
Step 2: Sketch the map according to the scale.
Shown on the map in the picture attached.
Part 2: As shown on the map, it is not possible that Brayden made it back to his starting point.
!!
Subtract 15mn - 22m +2n from 14mn - 12m +7n.
Answer:
[tex]\large\boxed{-mn+10m+5n}[/tex]
Step-by-step explanation:
[tex](14mn - 12m +7n)-(15mn - 22m +2n)\\\\=14mn-12m+7n-15mn-(-22m)-2n\\\\=14mn-12m+7n-15mn+22m-2n\qquad\text{combine like terms}\\\\=(14mn-15mn)+(-12m+22m)+(7n-2n)\\\\=-mn+10m+5n[/tex]
write the equation of the direct variation that includes the given point (-6,5)
[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (\stackrel{x}{-6},\stackrel{y}{5})~~ \begin{cases} x=-6\\ y=5 \end{cases}\implies 5=k(-6)\implies \cfrac{5}{-6}=k~\hfill \boxed{y=-\cfrac{5}{6}x}[/tex]
If LMNO is a rectangle, and m_MON = 30°, what is the value of x?
Answer:
120
Step-by-step explanation:
a pex
A music store owner noted that CD sales had dropped 29% from one quarter to the next. If the owner sold 570 units in the first quarter, how many did she sell in the next quarter?
Answer:
About 405
Step-by-step explanation:
570 CDs were sold the first quarter.
The second quarter CDs had dropped 29% from the first quarter (570).
Dropped, you should think you are subtracting.
So we need to
simplify 570-.29(570):
570(1-.29)
570(.71)
404.7
404.7 --> 405 (when rounded)
Step-by-step explanation:In order to find the answer to your question, we would need to find how much of 570 is 29%, and subtract that number to 570.
The reason why we would do this is because in the question, it says that the sales dropped 29% for one quarter to the next. This means that the next quarter would drop 29%.
We know that they sold 570 units, so we would use 570 in our calculations.
We know that the sales decrease by 29%, so we would multiply 570 by 0.29 to find how much of 570 is 29%.
[tex]570*0.29=165.3[/tex]
29% of 570 is 165.3
What we would do now is subtract 570 by 165.3 in order to fin how much sales they made in the next quarter.
[tex]570-165.3=404.7[/tex]
Once you're done solving, you would get the answer of 404.7
This means that they sold 404.7 (405 when rounded) CDs in the next quarter.
I hope this helps you out.Good luck on your academics.Have a fantastic day!If p(x)=2x^2 -4 and q(x)=x-3, what is (p*q)(x)
Answer:
2x^3 - 6x^2 - 4x + 12.
Step-by-step explanation:
(p*q) (x) = (2x^2 - 4)(x - 3)
= 2x^3 - 6x^2 - 4x + 12.
For this case we have the following functions:
[tex]p (x) = 2x ^ 2-4\\q (x) = x-3[/tex]
We must find [tex](p * q) (x).[/tex] For definition, we have to:
[tex](p * q) (x) = p (x) * q (x)[/tex]
So:
[tex](p * q) (x) = (2x ^ 2-4) (x-3)[/tex]
We apply distributive property:
[tex](p * q) (x) = 2x ^ 3-6x ^ 2-4x + 12[/tex]
Answer:
[tex](p * q) (x) = 2x ^ 3-6x ^ 2-4x + 12[/tex]
A school district needs 3 teachers for every 70 students. They expect to have 14,700 in the district next year. At this time they have 612 teachers. How many more teachers are needed.
Answer:
18
Step-by-step explanation:
We can use a proportion to find out the number of teachers that are needed.
3/70 = x/14,700
70x = 3 * 14,700
70x = 44,100
x = 630
630 teachers are needed altogether. Since there are already 612 teachers, the number of more teachers who are needed is the difference between 630 and 612.
630 - 612 = 18
Answer: 18
Mr. Jones asks his students to generate the next two numbers in the sequence beginning –5.5, 11, ....
Taquan suggests that the sequence is geometric and the next two numbers are –22 and 44. Julia suggests that the sequence is arithmetic and the next two numbers are 27.5 and 44.
Which best explains which student is correct?
Taquan is correct. When the signs change in a sequence, the sequence is geometric. Each successive term is generated by multiplying by –22 .
Julia is correct. When the numbers alternate between decimals and whole numbers, the sequence is arithmetic. Each successive term is generated by adding 16.5.
Both students could be correct about the types of possible sequences. However, one student made a computational error because it is not possible to arrive at a fourth term of 44 in two different ways.
Both students could be correct. Because two numbers are given in the original sequence, it is possible to find a common difference and common ratio between the successive terms.
Answer:
D
Step-by-step explanation:
Both students could be correct. Because two numbers are given in the original sequence, it is possible to find a common difference and common ratio between the successive terms.
A sequence could either be arithmetic or geometric. The truth statement about the correct student is:
Both students could be correct. Because two numbers are given in the original sequence, it is possible to find a common difference and common ratio between the successive terms.
Given that:
[tex]-5.5, 11, .....[/tex]
If the sequence is arithmetic, then the common difference is
[tex]d = 11 --5.5[/tex]
[tex]d = 16.5[/tex]
So, the next two elements are:
[tex]T_3 = 11 + 16.5 =27.5[/tex]
[tex]T_4 = 27.5 + 16.5 =44[/tex]
If the sequence is geometric, then the common ratio is
[tex]r =\frac{11}{-5.5}[/tex]
[tex]r= -2[/tex]
So, the next two elements are:
[tex]T_3 = 11 \times -2 = -22[/tex]
[tex]T_4 = -22 \times -2 = 44[/tex]
Based on the above computations, both students are correct.
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A coffee distributor needs to mix a(n) Organic Free Trade coffee blend that normally sells for $8.30 per pound with a Rift Valley coffee blend that normally sells for $13.90 per pound to create 80 pounds of a coffee that can sell for $10.82 per pound. How many pounds of each kind of coffee should they mix?
Answer: They must mix
_____ pounds of the Organic Free Trade Blend
______ pounds of the Rift Valley Blend.
Round your answers to the nearest whole number of pounds.
Answer:
They must mix
_44_ pounds of the Organic Free Trade Blend
_36__ pounds of the Rift Valley Blend.
Round your answers to the nearest whole number of pounds.
Step-by-step explanation:
The formula you are using is:
Total price * total amount= Organic price * amount organic + Rift price * amount rift
First we will simplify it by calculating it for each pound of final mix.
So this is 10.82 * 1 = 8.30 * x + 13.90 * y.
Since the total amount should be 1 pound, you could say that x+y = 1, or that y = 1-x.
If you fill this in you get
10.82 * 1 = 8.30 * x + 13.90 * (1-x)
Which you can solve as follows.
10.82 * 1 = 8.30 * x + 13.90 - 13.90x
10.82 = 13.90 - 5.6x
-5.6x = -3.08
x = -3.08/-5.6 = 0.55
So you will need 0.55 of Organic coffee for each pound of the final mix.
So in total you will need 0.55 * 80 = 44 pounds of Organic coffee.
So you need 80 - 44 = 36 pounds of Rift Valley Coffee.
To produce the desired coffee blend, the coffee distributor needs to mix approximately 51 pounds of Organic Free Trade Blend with 29 pounds of Rift Valley Blend.
Explanation:This problem falls under a category of Mathematics known as Algebra. We'll start by defining two variables: x, representing the weight of the Organic Free Trade Blend, and y, representing the weight of the Rift Valley Blend.
From the total weight of the mix, we get our first equation: x + y = 80
Then, by weighing the cost of each part against the total, we get our second equation: 8.3x + 13.9y = 10.82 * 80.
Solving these two equations simultaneously, we find that approximately 51 pounds of Organic Free Trade and 29 pounds of Rift Valley blend are needed to create the desired mixture.
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what will be the circumference of a circle if the area is 64cm
Given that area of circle is 64cm we can assume we will need to first find radius and then calculate circumference.
First we know that area of a circle is [tex]A=\pi r^2[/tex] hence [tex]r=\sqrt{\dfrac{A}{\pi}}[/tex]
We can now put in our area,
[tex]r=\sqrt{\dfrac{64}{\pi}}\approx20.37[/tex]
Then we use the formula for circumference,
[tex]C=2\pi r\Longrightarrow C=2\pi\cdot20.37\approx\boxed{128\mathbf{cm}}[/tex]
Hope this helps.
r3t40
What is the slope of the line?
y+5=2(x+1)
A. 1/5
B. 2/5
C. 2
D. 1/2
Rewrite the equation in slope-intercept form:
y+5=2(x+1)
Use the distributive property:
y+5 = 2x +2
Subtract 5 from each side:
y = 2x -3
The slope is the value with the X
The slope = 2
Answer:
2.5
Step-by-step explanation:
2(x+1)=y+5
2x+1=y+5
y+5=6
in addtion y can be add
so we have now...
2x+1=6
minus 1 from 6 and get 5
2x=5
5 divide by 2 = 2/5
Hope it helps
A bag has 4 yellow, 6 red, 2 green, and 8 purple marbles. What is the probability of picking a purple marble, not replacing it, and then picking another purple marble?
A.12/95
B.1/190
C.14/95
D.2/25
Answer:
Step-by-step explanation:
Add all 8/20 marbles multiply Times 5 40/100 = 40%
Answer =40%
The area of a rectangular back yard is 55 square meters. The length of the yard is one meter greater than twice the width.
What is the width of the yard in meters?
Provide your answer below:
Step-by-step explanation:
Area of a rectangular backyard is given as 55 m²
the length is 1 m greater than the twice the width
=>l=2w+1---(say A)
we know that
Area of a rectangle is always length * width=A=l*w
Divide both sides by w
A/w=l
put this value of l in (A)
A/w=2w+1
multiply both sides by w
A=w(2w+1)
55=2w²+w
subtract 55 from both sides
2w²+w-55=0
2w²-10w+11w-55=0
2w(w-5)+11(w-5)=0
(2w+11)(w-5)=0
(2w+11=0 , w-5=0
2w=-11. , w=5
w=-11/2 m
width can never be a negative integer so we omit -11/2
we will consider w=5m
put this in (A)
l= 2(5)+1
l=10+1
l=11m
checking ,
A=lw
A=(11m)(5m)
A=55m²
Answer:
5
Step-by-step explanation:
Area= 55
width=y(unknown)
length=1+2y(given)
formula for finding A.=l*b
(1+2y)(y)= y+2y^2
y+2y^2=55
2y^2= 55-y
y=5
verification
2*5^2=55-5
2*25=55-5
How do you do 6 divided by 11 bus stop method, please explain the steps?
What is the area of the sector having ....
Answer:
D) 160π/3 units²
Step-by-step explanation:
Step 1: Write the formula for area of sector
Area of sector = 1/2 x r² x angle in radians
Step 2: Substitute values in the formula
Area of sector = 1/2 x 8² x 5π/3
Step 3: Solve to find the value of area of sector
Area of sector = 160π/3 units²
Therefore, the correct option is D
!!
30m = 6000 Find m
I don't have any answers to choose from, I have to figure this out myself, but i can't, evidently
Answer:
m = 200
Step-by-step explanation:
30 m = 6000 Divide both sides by 30
30 m / 30 = 6000 / 30
m = 200
Simplify (1 − cos x)(1 + cos x). (2 points)
Answer:
sin²x
Step-by-step explanation:
we have
(1 − cos x)(1 + cos x)=1-cos²x
Remember that
sin²x+cos²x=1 ------> i-cos²x=sin²x
therefore
(1 − cos x)(1 + cos x)=sin²x
Answer:
[tex]sin^2x[/tex]
Step-by-step explanation:
Given expression,
[tex](1 - cos x)(1 + cos x)[/tex]
By using [tex]a^2-b^2=(a+b)(a-b)[/tex]
[tex](1 - cos x)(1 + cos x)=1^2 - cos^2x = 1 - cos^2x[/tex]
[tex]\because sin^2x+cos^2x=1[/tex]
[tex]\implies (1 - cos x)(1 + cos x)=sin^2x+cos^2x - cos^2x=sin^2x[/tex]
Since, further simplification is not possible,
Hence, the simplified form of the given expression is [tex]sin^2x[/tex]
Find the measure of C in the picture please
Answer:
Option A. The measure of angle C is 140°
Step-by-step explanation:
see the attached figure with letters to better understand the problem
we know that
The triangle OAB is an isosceles triangle
Because
OA=OB=radius
m∠BAO=m∠ABO=20°
Find the measure of angle C
Remember that the sum of the interior angles of a triangle must be equal to 180 degrees
so
m∠BAO+m∠ABO+m∠C=180°
substitute the given values
20°+20°+m∠C=180°
m∠C=180°-40°=140°
Point C is reflected across the y-axis.
Point C is reflected across the y-axis.
Which point represents the reflection?
A. Point D
B. Point E
C. Point G
D. Point M
Identify the parent function of the equation below.
Answer:
y = x² ⇒ answer C
Step-by-step explanation:
* Lets explain the problem
∵ The function is y = 1/2 x² + 3 , that means the parent function is
transformed by some transformation
- If the parent function is y = x²
- y = x² is a quadratic function represented graphically by upward
parabola with vertex (0 , 0)
∵ y = x² changed to y = 1/2 x² that means we multiply each
y-coordinates of the points on the graph of the function by 1/2
∴ The graph of the function is compressed vertically by scale
factor 1/2
- That means the graph is squeezing toward the x-axis
∵ y = 1/2 x² changed to y = 1/2 x² + 3 that means we add each
y-coordinates of the points on the graph of the function by 3
∴ The function translated 3 units up
- That means the vertex of the parabola changed to (0 , 3)
∴ The new function is y = 1/2 x² + 3
* The parent function of y = 1/2 x² + 3 is y = x²
# Look to the attached graph for more understand
- y = x² ⇒ the red graph (parent function)
- y = 1/2 x² + 3 ⇒ the blue graph
To describe a specific arith-
metic sequence, Elijah wrote
the recursive formula:
[ f(0) = 30
f(n+1)=f(n)+7
Write a linear equation that
models this sequence
Answer:
[tex]f(x) = 7x + 30[/tex]
Step-by-step explanation:
We need at least two points to write the equation of a straight line.
The recursive formula that Elijah wrote is:
[tex]f(0) = 30[/tex]
[tex]f(n + 1) = f(n) + 7[/tex]
When we substitute n=0, we get:
[tex]f(0 + 1) = f(0) + 7[/tex]
[tex]f(1) = 30 + 7[/tex]
[tex]f(1) = 37[/tex]
The points (0,30) and (1,37) lies on this line.
The equation of this line is of the form:
[tex]f(x) = mx + b[/tex]
where b =30 is the y-intercept and m=7 is the slope.
We plug in these values to get:
[tex]f(x) = 7x + 30[/tex]
Note that the slope of the line is equal to the common difference of the Arithmetic Sequence.
You could also use the two points to find the slope:
[tex]m = \frac{37 - 30}{1 - 0} = 7[/tex]
Use synthetic division to solve (x4- 1) = (x - 1). What is the quotient?
x3 -x2+x-1
O x3
x+x2+x+1
x3-2
Answer:
The quotient is x³+x²+x+1
Step-by-step explanation:
=(x^4-1) ÷ (x-1)
=(x^4-1)/ (x-1)
Solve the numerator by using perfect square formula:
⇒x^4-1 = (x²-1)(x²+1)
=(x²-1)(x²+1)/(x-1)
Further solve the numerator by using perfect square formula:
=(x+1)(x-1)(x²+1)/(x-1)
Cancel the like terms of numerator and denominator
We get;
=(x+1)(x²+1)
Multiply the terms:
=x³+x+x²+1
Re-arrange the terms:
=x³+x²+x+1
Hence the quotient is x³+x²+x+1....
Answer:
C
Step-by-step explanation:
Help asap
Congruent Angle pairs
Answer:
Option A ∠RWQ, ∠WPS and ∠PWU
Step-by-step explanation:
we know that
Two angles are supplementary if their sum is equal to 180 degrees
Part 1)
∠OPW+∠WPS=180° ------> by supplementary angles
we have
∠OPW=110°
substitute
110°+∠WPS=180°
∠WPS=180°-110°=70°
Part 2) we know that
∠RWQ+(50°+60°)=180° ------> form a linear pair
∠RWQ=180°-(50°+60°)=70°
so
∠OPW+∠RWQ=180° -----> by supplementary angles
Part 3) we know that
∠PWU=∠RWQ -------> by vertical angles
so
∠OPW+∠PWU=180° -----> by supplementary angles
therefore
The angles that are supplements to angle ∠OPW are
∠WPS, ∠RWQ and ∠PWU
Which of the following are solutions to the equation below. Check all that apply
Answer:
B. -2√2 - 5
C. 2√2 - 5
Step-by-step explanation:
The left side of the equation is already a perfect square.
Let us factorize it first.
x²+10x+25=8
x(x+5)+x(x+5)=8
(x+5)²=8
Let us take the square roots of both sides.
x+5=±√8
But √8=±2√2
Therefore in surd form, the two solutions become:
x+5=2√2 or x+5=-2√2
Therefore x= 2√2-5 and -2√2+-5
3 radical 12 times 5 radical 2
Answer:
Step-by-step explanation:
3*√12 * 5*√2
15 √24
15 √(2*2*2*3)
15*2 √6
30√6
What is the solution set for x-4>2?
Answer:
(6,∞)
x > 6
Step-by-step explanation:
Solve by adding 4 to both sides.
[tex]x-4>2\\x>6[/tex]
To put this in interval notation for your solution set, consider your sign.
You have a greater than sign, which means that 6 is not a solution. In interval notation, that means that you should use parentheses " ( " instead of brackets " [ ".
Your solution set goes on infinitely, and infinity also uses parentheses rather than brackets.
You can write your solution set in interval notation as follows:
(6, ∞)
Find the distance between -18 and 8 using the ruler postulate
[tex]\bf \underset{\textit{\Large 18 + 8 = 26 units}}{\stackrel{\textit{18 units}}{\boxed{-18}\rule[0.35em]{10em}{0.25pt}}0\stackrel{\textit{8 units}}{\rule[0.35em]{5em}{0.25pt}\boxed{8}}}[/tex]
Answer:
26Step-by-step explanation:
The ruler Postulate:
the distance between number A and number B
AB = |B - A|
We have A = -18 and B = 8. Substitute:
|8 - (-18)| = |8 + 18| = |26| = 26
PLEASE HUREY IXL QUESTION
Answer:
5 12/24 -> -0.5 -> -5 6/20
Step-by-step explanation:
Negatives are lasts and positive goes first! Since the order is greatest to least.
-5 6/20 is less than -0.5 because *think of a number line -5 6/20 will be all the way to the left because it large in negative value
HELPP MEEEEEEEE pleaasssssssseeeeee
Answer: Not sure if I’m correct but I’m pretty sure
x = 90
Step-by-step explanation:
Total figure = 360 degrees
107+72+91=270
360-270=90
Answer:
x=90 degrees
Step-by-step explanation:
The sum of the 4 angles of a quadrilateral add to 360 degrees
Add the 4 angles
72+107+x+91 = 360
Combining like terms
270 +x = 360
Subtract 270 from each side
270+x-270 = 360-270
x = 90
The unknown angle is 90