Given:
[tex](x+y)^4[/tex]To Determine: The binomial expansion of the given
Solution
Using binomial expansion formula below
[tex](x+y)^n=\sum_{k\mathop{=}0}^n(^n_k)x^{n-k}y^k[/tex]Find the slope and y intercept of the line shown below question number 4
The image of the line provided seems to go through the following points:
(0, 4) , (-4, 5), and (4, 3)
Knowing at least two points is essential to calculate the slope via the formula:
[tex]\text{slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]so, for example if we use the points (0, 4) and (-4, 5) to calculate the slope, we get:
[tex]\text{slope}=\frac{5-4}{-4-0}=-\frac{1}{4}[/tex]Therefore, the slope is -1/4 (negative one fourth)
Notice as well that one of the points we chose is (0, 4) which in fact is the y-intercept of the line (the point at which the line crosses the y-axis ).
so we have al the elements to built the equation of this line:
slope = -1/4
y intercept = 4 for the (0, 4) on the plane
Then the equation could be built using:
y = (-1/4) x + 4
Construct an obtuse angle called ABC. Bisect ABC and call the new angles ABP and PBC. Now bisect the ABP so that there are 3 angles. The measure of angle PBC is 66 degrees. Fe measures of the two smaller angles are equal to 11y and 3x respectively. What are the values of x and y in degrees?
Now,
3x + 11y + 66 = 66x2
3x + 11y + 66 = 132
3x + 11y = 132 - 66
3x + 11y = 66 ...............................(equ 1)
find the standard deviation of 3, 7, 4, 6, 5 if necessary, round your answer to the nearest tenth
3, 7, 4, 6, 5
First, find the mean.
Mean = Sum of the values / number of values
Mean = (3+7+4+6+5) /5 = 25/5 = 5
Then, find the variance:
Calculate each value difference from the mean
5-3 = 2
7-5 = 2
5-4= 1
6-5=1
5-5= 0
Square each difference, add them, and divide by the number of values.
Variance : (2^2+2^2+1^2+1^2+0^2 )/ 5 = (4+4+1+1) /5 = 10 /5 = 2
Standard deviation= square root of the variance:
√2 = 1.4
A rare manuscript increased in value 400% over the past 4 years. This was an increase of $1,000. What was the value of the manuscript 4 years ago? What is the value of the manuscript now?The value of the manuscript 4 years ago was $.The manuscript is now worth $
Given
A rare manuscript increased in value 400% over the past 4 years.
This was an increase of $1,000.
To find:
a) What was the value of the manuscript 4 years ago?
b) What is the value of the manuscript now?
Explanation:
It is given that,
A rare manuscript increased in value 400% over the past 4 years.
This was an increase of $1,000.
Then, let x be the value of manuscript 4 years ago.
That implies,
[tex]\begin{gathered} 400\%\times4x=1000+x \\ \frac{400}{100}\times4x=1000+x \\ 16x=1000+x \\ 16x-x=1000 \\ 15x=1000 \\ x=\frac{1000}{15} \\ x=\text{ \$}66.67 \end{gathered}[/tex]And, the value of the manuscript now is,
[tex]\begin{gathered} 4x=4(66.67) \\ =\text{ \$}266.67 \end{gathered}[/tex]Hence, the value of the manuscript is $66.67, and the value off the manuscript now is $266.67.
Fill in the missing number to complete the pattern.18, 12, ,0
using Ap formula,
[tex]\begin{gathered} a+(n-1)d \\ a=18 \\ d=12-18=-6 \\ 18+(3-1)-6 \\ 18-12=6 \end{gathered}[/tex]The missing term = 6
a debt company wants to build a uniquely shaped decks how many square feet of wood will the company need to cover the deck designer below shaped like a regular pentagon a trapezoid the height of the trapezoid is 4.5 ft round your answer to one decimal place to find the area of the Pentagon divided into 5 similar triangles you see if I could the radius at the Pentagon the distance from each vertex Center is 4.25 ft
72.2 square feet of wood will the company need to cover the deck designer shaped like a regular pentagon and a trapezoid.
To find the total wood required we need to add the area of pentagon and area of trapezoid.
Firstly we will draw the 5 similar triangle in the pentagon as shown below:
Lets name one triangle as ABC.
Given, radius of pentagon = 4.25 ft. (Let x)
Now, in triangle ABC,
BD=DC=2.5 ft. (half of the BC)
By applying Pythagoras theorem,
[tex]AB^{2} =AD^{2} +BD^{2} \\AD=\sqrt{AB^{2} -BD^{2} } \\AD=\sqrt{11.81} \\AD=3.44 ft.[/tex]
We know that AD is the height of triangle ABC.
So, Height = AD = 3.44 ft.
Area of triangle ABC = [tex]\frac{1}{2}[/tex] * base * height
=[tex]\frac{1}{2}[/tex] * 5 ft. 3.44 ft. = 8.59 square feet.
Area of pentagon = area of 5 similar triangle
= 5 * area of triangle ABC
= 5 * 8.59 = 42.96 square feet
Area of trapezoid = [tex]\frac{1}{2}[/tex] * (sum of the parallel side) * height
= [tex]\frac{1}{2}[/tex] * (5+8) * 4.5
= [tex]\frac{1}{2}[/tex] * 13 * 4.5 = 29.25 square feet.
Total square feet of wood required = area of pentagon + area of trapezoid
= 42.96 + 29.25 = 72.21 square feet
Rounding to one decimal place 72.21 square feet ≈ 72.2 square feet.
Thus, 72.2 square feet of wood will the company need to cover the deck designer shaped like a regular pentagon and a trapezoid.
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7th grade math I'm stuckhelp me fill in the blanks!
ok
item price before tax sales tax price including tax
pillow 8 8 x 0.0725 = 0.58 8 + 0.58 = $8.58
blanket 22 22 x0.0725 = 1.595 22 + 1.595 = $23.595
trash can 14.5 14.5 x 0.0725 = 1.051 14.5 + 0.0725 =$15.55
Which expression represents the area of the remainingpaper shape in square centimeters?O (x-7)(x-9)O (3x-2)(3x-8)O (3r-4)(3x +4)O (9x - 1)(x+16)
A square corner of 16 cm² is removed from a square paper with an area of 9X squared, square centimeters. which expression represents the area of the remaining paper shape in the square centimeters?
we have taht
Find out the difference
9x^2-16
apply difference of squares
9x^2-16=(3x-4)(3x+4)
answer is
(3x-4)(3x+4)
(08.01 LC)Find the area of a circle with a diameter of 20 inches. Use 3.14 for pi.(1 point)
The area of a circle can be calculated using the following formula:
[tex]A=\pi r^2[/tex]Where
A represents the area
r represents the radius of the circle
π is the number pi, you have to use 3.14 for the calculatins
You have to calculate the area of a circle that has a diameter of 20 inches. The radius of a circle is half the diameter:
[tex]\begin{gathered} r=\frac{d}{2} \\ r=\frac{20}{2} \\ r=10in \end{gathered}[/tex]The area of the circle can be determined as follows:
[tex]\begin{gathered} A=3.14\cdot10^2 \\ A=314in^2 \end{gathered}[/tex]The area of the circle is 314in²
If Angle A is acute and Angle B is obtuse and Angle A is 2X+5 and Angle B is 6X+55, then how many degrees would Angle A be?
Angle A is 35° and Angle B is 145°
Supplementary angles are angles that give 180° when added together
Angle A and Angle B are supplementary angles such that
∠A + ∠B = 180°
Given that ∠A is acute angle and ∠B is obtuse angle
also , ∠A = 2x+5 and ∠B = 6x+55
using supplementary angle property ,
2x+5 + 6x+55 = 180
solving for x ,
8x + 60 = 180
x = 15
8x = 180 - 60
8x = 120
∠A = 2x+5
substituting value of x
∠A = 2(15)+ 5 = 30+5
∠A = 35°
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Let f(x)=8x+5 and g(x)=6x^2+2x after simplifying (f+g)(x)=
We have to find (f+g)(x), where:
[tex]\begin{gathered} f(x)=8x+5 \\ g(x)=6x^2+2x \end{gathered}[/tex]We can write:
[tex](f+g)(x)=f(x)+g(x)=(8x+5)+(6x^2+2x)=6x^2+10x+5[/tex]Answer: (f+g)(x) = 6x^2+10x+5
Mobile Cookies delivers packs of cookies which cost $2.60 per package to deliver. The fixed cost to run the delivery truck is $252 per day. If the company charges $5.60 per pack, how many packages must be delivered daily to make a profit of $33?
95 packages must be delivered daily to make a profit of $33.
What is the meaning of profit?
Profit is the term used to describe the financial gain experienced when the revenue from a commercial activity exceeds the costs, costs, and taxes associated with maintaining that activity.
Given that the delivers cost per packets is $2.60 and the cost to run a truck is $252.
Assume that they need deliver x packs of cookies to make a profit of $33.
The total cost to deliver x packs of cookies is $(2.60x + 252).
Given that company charges $5.60 per pack.
The revenue is $5.60x.
The total profit is $(5.60x - (2.60x + 252)) = $(5.60x - 2.60x - 252) = $(3x - 252).
Given that the profit is $33.
Thus 3x - 252 = 33
Add 252 on both sides:
3x = 285
Divide both sides by 3:
x = 95.
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The number of McDonald's restaurants worldwide in 2014 was 36.258. In 2009, there were 32,737 McDonald's restau- rants worldwide. Let y be the number of McDonald's res- taurants in the year, where r = O represents the year 2009 (Source: McDonald's Corporation) a. Write a linear equation that models the growth in the number of McDonald's restaurants worldwide in terms of the year x. [Hinr. The line must pass through the points (0.32.737) and (5.30,258).]b. use this equation to predict the number of McDonald's restaurants worldwide in 2016.
a) y = 704.2x + 32737
b) There are 37,666 McDonald's restaurants in 2016
Explanations:The equation of a line passing through the points (x₁, y₁) and (x₂, y₂) is given as:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{where m is the slope, and is given by the formula: } \\ \text{m = }\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]For the line passing through the points (0, 32737) and (5, 36258)
x₁ = 0, y₁ = 32737, x₂ = 5, y₂ = 36258
Substituting the values into the equations above:
[tex]\begin{gathered} \text{m = }\frac{36258-32737}{5-0} \\ \text{m = }\frac{3521}{5} \\ m\text{ = }704.2 \\ y\text{ - 32737 = 704.2}(x\text{ - 0)} \\ y\text{ - 32737 = 7}04.2x \\ y\text{ = 7}04.2x\text{ + 32737} \\ \end{gathered}[/tex]b) In 2016, x = 7
substitute x = 7 into the equation
[tex]\begin{gathered} y\text{ = 704.2(7) + 32737} \\ y\text{ = }4929.4+32737 \\ y\text{ = }37666.4 \end{gathered}[/tex]There are 37,666 McDonald's restaurants in 2016
Travis was walking to school when hesaw some friends walking a block aheadof him. After running to catch up with hisfriends, his heart was beating 24 beatsevery 10 seconds. At this rate, how manytimes would his heart beat in 3 minutes?
his heart would beat 432 times in 3 minutes
Explanation
we can easily solve this by using a rule of three,
then
Step 1
to do that we need the same measure unit for the time, let's use seconds
so, we need to convert 3 minutes into seconds,
the equivalence is
[tex]1\text{ minute = 60 seconds}[/tex]hence, to convert from minutes into seconds just mutlply by 60
then
[tex]3\text{ minutes}\Rightarrow3\cdot60\text{ seconds=180 seconds}[/tex]Step 2
now, let's make the proportion
let x represents the number of times his heart would be in 180 seconds( 3 minutes)
so
[tex]\begin{gathered} \text{if} \\ 24\text{ beats}\Rightarrow10\text{ s} \\ \text{then} \\ x\text{ beats}\Rightarrow180\text{ s} \end{gathered}[/tex]so, the proportion is
[tex]\begin{gathered} \frac{24\text{ beats}}{10\text{ s}}=\frac{x}{180\text{ s}} \\ \frac{24}{10}=\frac{x}{180} \\ \end{gathered}[/tex]finally, to solve for x multiply both sides by of the equation by 180 and reduce
[tex]\begin{gathered} \frac{24}{10}=\frac{x}{180} \\ \frac{24}{10}\cdot180=\frac{x}{180}\cdot180 \\ \frac{4320}{10}=x \\ 432=x \end{gathered}[/tex]therefore, his heart would beat 432 times in 3 minutes
I hope this helps you
Elisa designed a flower garden in the shape of a square with a side length of 10 feet. She plans to build a walkway along the diagonal. What is the closest measure of the length of the walkway?
A square has all equal sides, then each side has a measure of feet
The diagonal can be found using the following formula:
[tex]d=\sqrt[]{2a}[/tex]Where a represents a side.
Replacing:
[tex]\begin{gathered} d=\sqrt[]{2(10)} \\ d=\sqrt[]{20} \\ d=14.1421 \end{gathered}[/tex]Hence, the closest measure of the walkway length is 14.1421 feet.
Simplify the following trig expressions to an expression involving at most one trig function
we know that:
• cot x = adjacent /opposite
,• secx = hypotaneus / adjacent
,• cscx = hypotaneus / opposite
Therefore , our expression can be re-rewritten as follows :
(cot x * secx) /(cosec x)
→{adj /opp * hyp /adj }/( hyp/opp)... [note that adj cancels each other ]
→(hyp /opp)/ hyp/opp
→(hyp /opp) * (opp /hyp) .......( each variable cancels each other)
→1*1
= 1
On a certain day the probability of rain is 80% probability of thunder is 3/5 and the probability of both is 2/5. What is the probability that it will rain or thunder?
The probability it will rain or thunder = 100%
Explanation:Probability it will rain = 80%
P(rain) = 4/5 (simplest term in fraction)
Probability of thunder = 3/5
P(thunder) = 3/5
Probability of both rain and thunder = 2/5
P(rain and thunder) = 2/5
We need to find the probability of rain or thinder = P(rain or thunder)
To find the probability of P(rain or thunder), we will apply the formula for the addition rule on any two events:
[tex]P(A\text{ or B\rparen = P\lparen A\rparen +}P(B)\text{ - P\lparen A and B\rparen}[/tex]Applying the formula in our question:
[tex]P(rain\text{ or thunder\rparen = P\lparen rain\rparen + P\lparen thunder\rparen - P\lparen rain and thunder\rparen}[/tex]substitute the values in order to find the probability:
[tex]\begin{gathered} P(rain\text{ or thunder\rparen = }\frac{4}{5}\text{ + }\frac{3}{5}-\text{ }\frac{2}{5} \\ \\ P(rain\text{ or thunder\rparen = }\frac{4\text{ + 3 - 2}}{5} \\ P(rain\text{ or thunder\rparen = }\frac{5}{5} \\ \\ P(rain\text{ or thunder\rparen = 1} \end{gathered}[/tex]In percentage, the probability it will rain or thunder = 100%
Find the volume of a pyramid with a square base, where the side length of the base is10 m and the height of the pyramid is 7.2 m. Round your answer to the nearesttenth of a cubic meter.
hello
to find the volume of the figure, we need to know the formula of a pyramid with a square base
once we know that, we can proceed to simply substitute the values into the equation
[tex]\begin{gathered} \text{volume}=\frac{1}{3}\times l^2\times h \\ l=\text{side length} \\ h=\text{height} \end{gathered}[/tex][tex]\begin{gathered} l=10m \\ h=7.2m \end{gathered}[/tex][tex]\begin{gathered} \text{volume}=\frac{1}{3}\times10^2\times7.2 \\ \text{volume}=\frac{100\times7.2}{3} \\ \text{volume}=240m^3 \end{gathered}[/tex]the volume of the figure is 240m^3
the number of girls is 75% of the number of boys.There are 28 students altogether. how many are girls and how many are boys?use a tape diagram
Let x be the number of boys
Let the number of girls be 75% of x = 75x/100
Boys + girls = 28
75x/100 + x = 28
0.75x + x = 28
1.75x = 28
Divide both-side of the equation by 1.75
x = 16
There a
how do you do how do you point plot on a graph
To point plots on a graph, take the following steps:
1. Identify the x-coordinates and y-coordinates from the variable/data you have. It should be written in this form: (x, y)
2. Label both axes on the graph(x-axis and y-axis). The x-axis is usually on the horizontal line while the y axis is the horizontal line.
3. Start plotting your first 2 points on both axes (usually the numbers on first row). Plot the x value and also plot the y value at the appropriate points
4. Finally, Continue plotting the numbers by pointing each point on the graph (take them in rows)
the 4000N boat picks up 5 passengers who each weigh 500N. what is the total mass of the boat and passengers
The weight of the boat is 4000 N
and each passenger weigh 500 N,
then the total weigh of boat and passengers is:
4000 N + 5 * 500 N = 4000 + 2500 = 6500 N
the figure below has a point marked with a large dot.first rotate the figure 90 degrees counterclockwise about the origin.then give the coordinates of the Mark point in the original figure in the final figure.
When we do a 90 degree counterclockwise rotation about the origin, a point moves from ( x,y) to ( -y,x)
Using the point with the blue dot
It is originally at (2,-3)
It will move to (3,2)
i need help with math
The following basic properties and characteristics can be used to easily identify parallel lines:
They always are straight lines with equal spacing between them.They are parallel lines.They never cross, no matter how much farther you stretch them in just about any given direction.A transversal line intersecting two parallel lines at two separate positions will form four angles at each point.The statement are given as;
The measurement for the angles for the transversal are-
∠2 = 91° and ∠5 = 89°
Thus,
∠2 = ∠3 = 91° (vertically opposite angles)
The sum ∠3 + ∠5 = 180 (for the parallel lines)
91° + 89° = 180° (supplementary angles).
Thus, two lines are parallel.
The two lines are parallel; True.The measure of ∠7 = 89°; False,Correct; ∠7 = ∠3 = 91°(corresponding angles)
∠3 = ∠6 are same side of interior angles; FalseCorrect; They are opposite side of interior angles.
∠1 is congruent to angle ∠4 because they are vertical angles; True,Thus, the results for the given transversal lines are found.
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suppose the odds against winning the lottery are 59,000,000 to 1. What is the probability of the event of winning the lottery given those odds? P(E) = __________
The odds against winning the lottery is 59,000,000 : 1
Thus,
Not winning bets = 59,000,000
Winning bets = 1
Total bets = 59,000,000 + 1 = 59,000,001
Thus,
The probability of winning = 1/59,000,001
Answer[tex]P(E)=\frac{1}{59,000,001}[/tex]27,9,3,1,1/3,1/9....Write the sigma notation for the infinite series. ________________
Given
Series,
[tex]27,9,3,1,\frac{1}{3},\frac{1}{9},...[/tex]Find
Write the sigma notation for the infinite series.
Explanation
as we see the given series is a geometric series .
here , a = 27
common ratio , r = 9/27 = 1/3
so ,
[tex]\begin{gathered} \sum_{n\mathop{=}1}^{\infty}ar^{n-1} \\ \\ \sum_{n\mathop{=}1}^{\infty}(27)(\frac{1}{3})^{n-1} \\ \\ \sum_{n\mathop{=}1}^{\infty}(\frac{1}{3})^{-3}(\frac{1}{3})^{n-1} \\ \\ \sum_{n\mathop{=}1}^{\infty}(\frac{1}{3})^{n-4} \end{gathered}[/tex]Final Answer
Hence , the sigma notation for the infinite series is
[tex]\sum_{n\mathop{=}1}^{\infty}(\frac{1}{3})^{n-4}[/tex]Which of the following is an equation of a line parallel to the equaticy = 4x+12O A. y=-x-2y4O B. y = -4x – 2O c. y = 4x-2O O D. y=-x-2
Given
The equation of the line is,
[tex]y=4x+1[/tex]To find the equation of the line parallel to y=4x+1.
Explanation:
It is given that,
The equation of the line is,
[tex]y=4x+1[/tex]Since two parallel lines have same slope.
Then,
The slope of the line parallel to y=4x+1 is, 4.
Therefore, the equation of the line parallel to y=4x+1 is of the form,
[tex]y=4x+k[/tex]Hence, the equation of the line parallel to y=4x+1 is c) y=4x-2.
A student has 42 coins worth a total of $5.90. Each coin is either a nickel (five cents) or a quarter (twenty-five cents). If x is the number of nickels, then x can be determined from the equation---
Given
no. of coins = 42
worth of coins = $5.90
Find
number of nickels
Explanation
The number of quaters is 42 - x
0.05x + 0.25(42 - x) = 5.9
-0.2x + 10.5 = 5.9
-0.2x = -4.6
x = 23
Final Answer
Number of Nickels, x = 23
I need to make my birthday into a polynomial my birthday is 11/01/2005
EXPLANATION:
To express a number or value as a polynomial we must take into account some steps:
-The polynomial may or may not have grouping signs.
-The polynomial can have more than one variable, constants and exponents.
-A polynomial must be ordered, the monomials that form it must be written from highest to lowest degree.
Since a polynomial is an algebraic expression that shows the sum of monomials and we have 3 separate monomials, so we must do the following:
[tex]\begin{gathered} (11)\rightarrow a\text{ monomial} \\ (01)\rightarrow a\text{ monomial} \\ (2005)\rightarrow a\text{ monomial} \\ \text{Now }we\text{ add }the\text{ t}hree\text{ }monomials\colon \\ (2005+11+01);\text{ there }the\text{ poly}nomial\text{ }must\text{ be organized }from \\ highest\text{ }to\text{ lowe}st\text{ }coefficient; \\ \text{ANSWER: (2005+11+01)} \end{gathered}[/tex]If a different number in domain of a function have different outputs the function is called?
A function is a rule that assigns each input exactly one output. We call the output the image of the input. The set of all inputs for a function is called the domain.
A function is one-to-one if no two elements in the domain correspond to the same element in the range.
Thus, if a different number in the domain of a function has different outputs the function is called a one-to-one function
Which of the following is a quadratic equation that has the roots x = 5 and x = 6?
Answer:
the quadratic equation that has the roots x=5 and x=6 is;
[tex]x^2-11x=-30[/tex]Explanatio
We want to derive the quadratic equation that has the roots x=5 and x=6;
To derive the equation, we have;
[tex](x-5)(x-6)=0[/tex]Expanding;
[tex]\begin{gathered} x^2-5x-6x+30=0 \\ x^2-11x+30=0 \\ x^2-11x=-30 \end{gathered}[/tex]Therefore, the quadratic equation that has the roots x=5 and x=6 is;
[tex]x^2-11x=-30[/tex]