Find the coefficient of third term of (x + 2)³. A. 40 OB. 10 OC. 20 D. 80 Reset Selection A
Answers
Given:
The expression given is,
[tex]\left(x+2\right)^5[/tex]Required:
To find the coefficient of the third term.
Explanation:
Let us expand the expression to find the coefficient.
[tex]\begin{gathered} \left(x+2\right)^5 \\ =\frac{5!}{5!}x^52^0+\frac{5!}{4!}x^42^1+\frac{5!}{2!3!}x^32^2+\frac{5!}{3!2!}x^22^3+\frac{5!}{4!1!}x^12^4+\frac{5!}{5!0!}x^02^5 \\ =x^5+10x^4+40x^3+80x^2+80x+32 \end{gathered}[/tex]Hence, the coefficient of the third term is 40.
Final Answer:
The coefficient of the third term is 40.
Option A is correct.
Related Questions
Write an equation of the parabola that passes through the point (-9, 2) and has vertex (-3,1).
Answers
Answer:
[tex]\textsf{Vertex form}: \quad y=\dfrac{1}{36}(x+3)^2+1[/tex]
[tex]\textsf{Standard form}: \quad y=\dfrac{1}{36}x^2+\dfrac{1}{6}x+\dfrac{5}{4}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
Given:
Vertex = (-3, 1)Point = (-9, 2)Substitute the given vertex and point into the formula and solve for a:
[tex]\begin{aligned}y&=a(x-h)^2+k\\\\\implies 2&=a(-9-(-3))^2+1\\2&=a(-6)^2+1\\2&=36a+1\\36a&=1\\a&=\dfrac{1}{36}\end{aligned}[/tex]
Therefore, the equation of the parabola in vertex form is:
[tex]\boxed{y=\dfrac{1}{36}(x+3)^2+1}[/tex]
In standard form:
[tex]\implies y=\dfrac{1}{36}(x+3)(x+3)+1[/tex]
[tex]\implies y=\dfrac{1}{36}(x^2+6x+9)+1[/tex]
[tex]\implies y=\dfrac{1}{36}x^2+\dfrac{6}{36}x+\dfrac{9}{36}+1[/tex]
[tex]\implies y=\dfrac{1}{36}x^2+\dfrac{1}{6}x+\dfrac{5}{4}[/tex]
what percentage increase from 9,620,000 to 9,980,000. Round to the earedt tenth of a percent.
Answers
Answer:
3.7%
Explanation:
Given
Original value = 9,620,000
New values = 9,980,000.
Increment = New - Original
Increment = 9,980,000 - 9,620,000
Increment = 360,000
%increae = 360,000/9,620,000 * 100
%increase = 3.7%
Hence the percentage increase is 3.7%
(3m + 5) - (6 - 5m) answer this for me
Answers
Answer: If you are simplifying the expression, 8m-1 is your answer.
If you are finding the roots of this polynomial, 1/8 is your answer. (Can also be written as 0.125, 2^-3)
PLS HELP!! WILL MARK BRANLIEST What are the coordinates of the midpoint of segment whose endpoints are A(-2,7) and B(4,-2)?
Make sure to use decimals, if necessary, and write with no spaces in the format (x,y) with you solving for x and y.
Answers
When we want to determine the midpoint of two points on a line segment, we must first determine the coordinates of the two points. Then we divide the sum of the abscissa [tex](x)[/tex] by [tex]2[/tex] to find the abscissa of the midpoint and divide the sum of the ordinates [tex](y)[/tex] by [tex]2[/tex] to find the ordinate of the midpoint.
Let the coordinates of our midpoint be [tex]F(a,b)[/tex].
[tex]F(a)=\frac{4+(-2)}{2}=1[/tex][tex]F(b)=\frac{7+(-2)}{2} =\frac{5}{2}=2.5[/tex]We found our midpoint.
[tex]F(a,b)=(1,2.5)[/tex]all you need is on the photo this is homework please i really needed heeeeelp
Answers
the zeros of the graph tell us the time needed for the tank to be drain.
(2t-7)(2t-9)
For any positive numbers, a, b and d, with b = 1, logb = d•log b a
Answers
The exponent multiplies the logarithm of the base
So:
[tex]\log_ba^d=d\log_ba[/tex]The answer is option C
Week 1: saves $ 35 Week 2 : saves $ 10 Week 3: spends $ 20 Week 4: spends $ 5 Week 5 saves $15 Week 6: saves $10 Susan wants to go on a vacation to the beach with her friends . For six weeks she keeps track of how much money she spends and saves . For the next six weeks she plans on increasing the amount she saves by $10 and decreasing the amount she spends by $5. How will this affect the MEAN amount of money that Susan has ? A) The mean will not change . B) The mean will increase by approximately $5. ) The mean will increase by approximately $ 8. D) The mean will increase by approximately $15. E) The mean will increase by approximately $30.
Answers
B) The mean will increase by $5
1) The first scenario has the following mean, adding all the spendings and savings:
[tex]x=\frac{35+10+20+5+15+10}{6}=\frac{95}{6}=15.83[/tex]2) Since for the following week there's an increase of $10 for her savings and a decrease of $ 5 we can write:
[tex]\begin{gathered} x=\frac{(35+10)+(10+10)+(20-5)+(5-5)+(15+10)+(10+10)}{6}= \\ =\frac{45+20+15+0+25+20}{6}=\frac{125}{6}=20.83 \end{gathered}[/tex]3) We can see that the mean changes, and examining the options we can state that:
the answer is B, the mean will increase by $5
Question Use the Distributive Property to simplify the expression. 12(6−k) =
Answers
After simplifying and using the Distributive Property, the final solution would be [tex]72-12k[/tex].
Hope this helps!
Please help me solve question 6 on this algebra 1 worksheet
Answers
We have that one simply way to write that equation is
[tex]\frac{2}{3}(21q^2-3q+7)[/tex]Because we have that
[tex]undefined[/tex]And also state the vertex and the axis of symmetry. I need help with number 2
Answers
In order to complete the square remember that
[tex](x\pm a)^2=x^2\pm2\cdot x\cdot a+a^2[/tex]first, equal the expression divide all the expressions by 2,
[tex]\begin{gathered} f(x)=2x^2+4x+7 \\ 2x^2+4x+7=0 \\ 2x^2+4x=-7 \\ x^2+2x=-\frac{7}{2} \end{gathered}[/tex]then, we can find "a" using the second portion of the definition
[tex]\begin{gathered} 2\cdot x\cdot a=2x \\ a=\frac{2x}{2x} \\ a=1 \end{gathered}[/tex]then,
[tex]a^2=1^2=1[/tex]add 1 on both sides
[tex]\begin{gathered} x^2+2x+1=-\frac{7}{2}+1 \\ x^2+2x+1=-\frac{5}{2} \end{gathered}[/tex]rewrite as a square expression on the left,
[tex](x+1)^2=-\frac{5}{2}[/tex]multiply both sides by 2
[tex]2(x+1)^2=-5[/tex]bring all to the left side and equal to f(x)
[tex]\begin{gathered} f(x)=2(x+1)^2+5 \\ \text{The vertex is at (-1,5)} \\ \text{the axis of symmetry is x=-1} \end{gathered}[/tex]Kendall rode her bike 7 miles in 45 minutes. If she maintains this speed, how far can she ride in 2 hours? Round your answer to the nearest tenth of a mile.
Kendall can ride about ___ miles in 2 hours.
Answers
Answer:
18.7 miles
Step-by-step explanation:
You want to know how far Kendall can ride her bike in 2 hours if she rides at the speed of 7 miles in 45 minutes.
ProportionThe question assumes that distance is proportional to time, so the distance (d) of interest can be written in the proportion ...
miles/minutes = 7/45 = d/120 . . . . . . 120 minutes is 2 hours
Multiplying by 120, we have ...
d = 120(7/45) = 7(8/3) = 18 2/3 ≈ 18.7
Kendall can ride about 18.7 miles in 2 hours.
Instructions: Find the measure of the indicated angle to thenearest degree.
Answers
Given:
• Length of side adjacent the indicated angle = 48
,• Length of hypotenuse = 56
Let's find the measure of the indicated angle.
To find the measure of the indicated angle, apply the trigonometric ratio formula for cosine:
[tex]cos\theta=\frac{adjacent}{\text{ hypotenuse}}[/tex]Thus, we have:
[tex]\begin{gathered} cos\theta=\frac{48}{56} \\ \\ cos\theta=\frac{6}{7} \\ \\ \text{ Take the inverse cosine of both sides:} \\ \theta=cos^{-1}(\frac{6}{7}) \\ \\ \theta=31^o \end{gathered}[/tex]Therefore, the measure of the indicated angle is 31 degrees.
ANSWER
The product of two consecutive
odd positive integers is one hundred forty-three. Find the integers.
Answers
The integers are 71 and 72 respectively
What is an algebraic expression?An algebraic expression can be defined as an expression that is composed of terms, variables, coefficients, factors and constants.
They are also known to be composed of mathematical operations such as;
SubtractionAdditionMultiplicationDivisionBracketParentheses, etcFrom the information given , we have;
x + 1 + x + 2 = 143
collect like terms
2x = 143 - 3
Subtract like terms
2x = 140
Make 'x' the subject
x = 140/2
x = 70
The numbers are;
x + 1 = 70 + 1 = 71
x + 2 = 70 + 2 = 72
Hence, the numbers are 71 and 72
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If the point (2,-5) is reflected in the line y=x, then the image is:
Answers
Answer:
(-5, 2)
Explanation:
If a point (x,y) is reflected in the line y=x, the x-coordinate and y-coordinate change places.
That is:
[tex](x,y)\to(y,x)[/tex]Therefore, the image of (2, -5) when reflected in the line y=x is:
[tex](-5,2)[/tex]help l need to finish this
Answers
Answer:
Your answer is [tex]y = 2x - 2[/tex]
Step-by-step explanation:
Just test it out on all of them, it fits.
Three pencils are on sale for $0.45 at this rate what is the cost per pencil
Answers
1) Gathering the data
3 pencils ----------- $0.45
The heights of ten-year-old males are normally distributed with a mean of 57.4 inches and a standard deviation of 5.1 inches. If a pediatrician selects a random sample of 46 ten-year-old males from his patient population, what is the probability that the mean height of this sample will be greater than 57 inches?Round your answer to at least three decimal places
Answers
Given:
[tex]Means,\text{ }\mu=57.4[/tex][tex]Standard\text{ deviation, }\sigma=5.1[/tex][tex]The\text{ sample size, n=46.}[/tex]Required:
We need to find the probability that the mean height of this sample will be greater than 57 inches,
[tex]P(x>57).[/tex]Explanation:
Consider the formula to find the z-score.
[tex]z=\frac{\mu-x}{\frac{\sigma}{\sqrt{n}}}[/tex][tex]Subst\text{itue }\mu=57.4\text{, }\sigma=5.1,\text{ n=46 and x=57 in the formula.}[/tex][tex]z=\frac{57-57.4}{\frac{5.1}{\sqrt{46}}}[/tex][tex]z=\frac{-0.4}{\frac{5.1}{\sqrt{46}}}[/tex][tex]z=-0.4\times\frac{\sqrt{46}}{5.1}[/tex][tex]z=-0.5319[/tex]From the z table, we get
[tex]P(x<57)=0.2974[/tex][tex]\text{We know that }P(x>57)=1-P(x<57).[/tex][tex]Substitut\text{e }P(x<57)=0.2974\text{ in the equation.}[/tex][tex]P(x>57)=1-0.2974.[/tex][tex]P(x>57)=0.7026.[/tex][tex]P(x>57)=0.703.[/tex]
Final answer:
The probability that the mean height of this sample will be greater than 57 inches is 0.703.
How do you write a point slope form equation from this graph?
Answers
Answer: y-1=3(x-3)
this in the correct answer. you take one point on the line and substitues x and y of the point into the equation. M is your slope. y-y1=m(x-x1)
8 Real life /
and are blue.
Rasheed and Kamal did a survey on car colours.
Problem-solving Approximately of cars in the UK are silver
a Rasheed found 120 people had silver cars.
How many people could he have asked?
b Kamal found 120 people had blue cars.
How many people could he have asked?
Answers
Using proportions, it is found that the number of people that each asked is given as follows:
a) Rasheed: 571 people.
b) Kamal: 667 people.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations, especially multiplication and division, with the unit rates or percentages of the problem.
For Rasheed, since he was counting people with silver cars, we have that 21% of the n people is equivalent to 120 people, hence the number of people n is calculated as follows:
0.21n = 120
n = 120/0.21
n = 571 people. (rounding)
For Kamal, since he was counting people with blue cars, we have that 18% of the n people is equivalent to 120 people, hence the number of people n is calculated as follows:
0.18n = 120
n = 120/0.18
n = 667 people. (rounding)
Missing informationThe percentages of car colors in the UK are mussing and are given as follows:
Silver: 21%.Blue: 18%.More can be learned about proportions at https://brainly.com/question/24372153
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Dave's wardrobe contains 25 T-shirts, of which 13 are gray. Dave selects a T-shirt at random.
What is the probability that Dave will select a gray T-shirt?
Enter a reduced fraction
What are the odds in favor of Dave selecting a gray T-shirt?
Enter the ratio in lowest terms
Answers
The probability that Dave will select a gray T-shirt is 13 / 25.
The odds in favor of picking a gray T-shirt is 13 : 25
What is the probability?
Probability is used to calculate the odds that are in favor or against a random event happening. The odds in favor or against a random event happening has a probability value that lies between 0 and 1. The higher the odds that are in favor of the event happening, the closer the probability value would be to 1.
The probability that Dave will select a gray T-shirt = number of gray T-shirts / total number of T-shirts
13 / 25
Ratio is used to compare two or more numbers together.
The odds in favor of picking a gray T-shirt = number of gray T-shirt : total number of T-shirts = 13 : 25
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Use the distributive property to write an equivalent expression.
8(4n+ 3) =
12x-6=
5x+20=
3(x+6)=
7x-35=
20p + 16 =
Answers
The distributive property to write an equivalent expression.
8(4n+ 3) = 32n + 24
12x-6= 1/2
5x+20= 4
3(x+6)= 3x + 18
7x-35= 5
20p + 16 = 4/5
A distributive property in mathematics is defined:The distributive property states that multiplying the sum of two or more addends by a number yields the same result as multiplying each addend separately by the number and combining the resulting products.
We use distributive property for what purposes?One of the most common properties in arithmetic is the distributive property. The multiplier is applied to each integer inside the parentheses, and the results are added to obtain the answer. This technique is used to simplify and solve multiplication problems.
According to the given data:the distributive property to write an equivalent .
8(4n+ 3)
= 8 * 4n + 3* 8
= 32n + 24
for 12x-6
12x-6 = 0
x = 6/12
x = 1/2
For 5x+20
5x+20 =
x = -4
For 3(x+6)
= 3 * x + 3 * 6
= 3x + 18
For 7x-35
= 35/7
= 5
For 20p + 16
= 20/16
= 5/4
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2 is subtracted from the square of a numberWrite as an algebraic expression.
Answers
Answer:
x²-2
Explanation:
Let the number be x.
The square of the number = x²
If 2 is subtracted from the square of the number, we have:
[tex]x^2-2[/tex]Therefore, an algebraic expression for the statement "2 is subtracted from the square of a number" is x²-2.
please help me ASAP!!!
Answers
This is the correct answer, this is because it only function that the inverse is correctly represented
[tex]\begin{gathered} y\text{ = }\sqrt[3]{x+3} \\ y^3=\text{ x+3} \\ x=y^3-3 \\ f^{-1}(x)=x^3-3 \end{gathered}[/tex]Find the x-intercepts of the polynomial y = a2 + 16a + 64
Answers
Given the polynomial:
[tex]y=a^2+16a+64[/tex]The x-intercepts are the points in which the polynomial crosses the x-axis. That is, are the points (x, 0).
To find these points, use the quadratic formula according to the steps below.
Step 01: Substitute the values in the quadratic formula.
For a equation y = ax² + bx + c, the x-intercepts are:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this question,
a = 1
b = 16
c = 64
Substituting the values:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-16\pm\sqrt[]{16^2-4\cdot1\cdot64}}{2\cdot1} \end{gathered}[/tex]Step 02: Solve the equation above.
Begin by solving the square and the multiplications:
[tex]x=\frac{-16\pm\sqrt[]{256^{}-256}}{2}[/tex]Now, subtract the values inside the root.
[tex]x=\frac{-16\pm\sqrt[]{0}}{2}[/tex]Solve the root:
[tex]x=\frac{-16\pm0}{2}[/tex]And find the values of x:
[tex]\begin{gathered} x_1=\frac{-16-0}{2}=-\frac{16}{2}=-8 \\ x_2=\frac{-16+0}{2}=-\frac{16}{2}=-8 \end{gathered}[/tex]Answer: The x-intercepts are: (-8, 0), (-8, 0).
Certain pieces of antique furniture increased very rapidly in price in the 1970s and 1980s. For example, che value of a particular rocking chair is well approximated byV = 60(1.25)^twhere V is in dollars and t is the number of years since 1975. Find the rate, in dollars per year, at which the price is increasing.Rate= ____ dollars/yr
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Certain pieces of antique furniture increased very rapidly in price in the 1970s and 1980s.
For example, the value of a particular rocking chair is well approximated by:
[tex]V=60(1.25)^t[/tex]where V is in dollars and t is the number of years since 1975.
Find the rate, in dollars per year, at which the price is increasing.
Step 2:
Next,
[tex]\begin{gathered} \text{Given,} \\ V=\text{ }60(1.25)^t \\ \text{Calculating the rate, } \\ we\text{ ne}ed\text{ to differentiate V with respect to t, we have that:} \\ \frac{dV}{\differentialDt t}=(1.25)^t\ln (1.25)\text{ 60} \end{gathered}[/tex]
Now, we need to evaluate:
[tex]\begin{gathered} \ln (1.25)60\text{ = 13. 38861308 }\approx\text{ 13. 3886} \\ \end{gathered}[/tex]Hence, the rate, in dollars per year since 1975, at which the price is increasing is:
[tex]\frac{dV}{\differentialDt t}=13.3886(1.25)^t[/tex]
An item costs $430 before tax, and the sales tax is $8.60.
Find the sales tax rate. Write your answer as a percentage.
Answers
The sales tax rate of an item which cost $430 and tax of $8.60 is 2%
How to find the sales tax rate?Sales tax refers to local or state tax imposed as a percentage of the selling price of goods or services payable by the customer. The tax is not recognized as the seller's earnings as the seller only collects the tax and transmits it to local or state authorities.
Cost of item before tax = $430Sales tax = $8.60Sales tax rate = Sales tax / Cost of item before tax × 100
= $8.60 / $430 × 100
= 0.02 × 100
= 2%
In conclusion, the sales tax rate of the item is given by 2%.
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Write +/99 +/44 in the form avb where a and b are integers.
Answers
Step-by-step explanation:
[tex] \sqrt{99} = 3 \sqrt{11} \\ \sqrt{44} = 2 \sqrt{11} \\ 3 \sqrt{11} + 2 \sqrt{11} = 5 \sqrt{11} [/tex]
Answer:
[tex]3 \sqrt{11} [/tex]
[tex]4 \sqrt{11} [/tex]
because we rewrite it as integer statements
Determine the magnitude and direction of vector a = (3,8) Round to the nearest tenths. |a| =theta =
Answers
Recall the definitions of the magnitude and direction of a vector:
[tex]\begin{gathered} \parallel a\parallel=\sqrt[]{3^2+8^2}=\sqrt[]{73}=8.5 \\ \theta=\tan ^{-1}(\frac{8}{3})=69.4^{\circ} \end{gathered}[/tex]2. The graph below shows the relationship between the number of pages printed (x) at a print shop and the total price (y), in dollars. Print Shop Prices у 9 Total Price ($) Based on the graph, what is the unit price at the print shop?
Answers
Let:
[tex]\begin{gathered} (x1,y1)=(2,1) \\ (x2,y2)=(4,2) \\ so\colon \\ m=\frac{y2-y1}{x2-x1}=\frac{2-1}{4-2}=\frac{1}{2}=0.5 \end{gathered}[/tex]Which of the statements is true for the two equations below?
Answers
Explanation:
Equation A
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