Answer:
[tex]2(3a-1)=6a-2[/tex]Step by step explanation:
To multiply the expression 2(3a-1), we need to use the distributive property of multiplication which states that:
[tex]a(b+c)=a\cdot b+a\cdot c[/tex]Then, for the expression 2(3a-1), the correct answer would be:
[tex]\begin{gathered} 2(3a-1)=2\cdot3a-2\cdot1 \\ 2(3a-1)=6a-2 \end{gathered}[/tex]Bob had three 10' lengths of conduit. If he used a total of 13.75' of conduit to install a motor, how much total conduit does he have left?
Given that Bob had three 10' lengths of conduit and he used a total of 13.75' of conduit to install a motor.
To find how much total conduit he has left we would subtract the initial from what was used.
The initial length = three 10' lengths = 30'
Length used = 13.75'
[tex]\begin{gathered} \text{Conduit left = Initial length - length used} \\ \text{Conduit left }=\text{ 30 - 13.75} \\ =16.25 \\ \end{gathered}[/tex]
The total conduit he has left is
Answer: 16.25 feet
In a canoe race, Team A is traveling 6 miles per hour and is 2 miles ahead of Team B. Team B is also traveling 6 miles per hour. The teams continue traveling at their current rates for the remainder of the race. Using d for distance (in miles) and t for time (in hours), write a system of linear equations that represent this situation.Equation for Team A:Equation for Team B:Will team B catch up to Team Ao Yeso No
First of all, we need to remember the equation of the speed and time:
distance = speed x time
Now, for the first team (team A):
[tex]\begin{gathered} x=6\frac{miles}{hour}\cdot t+2; \\ x\text{ - distance} \\ t\text{ - time} \end{gathered}[/tex]After that, for the second team (team B):
[tex]x=6\frac{miles}{hour}\cdot t[/tex]Finally, the team B never catch up to team A!
Ed spends 21 hours practicing drums over a fortnight. At that rate, how much time will he spend on practicing drums over a 7 week period?
This problem can be solve with the simple rule of three:
[tex]\begin{gathered} 1\text{ fortnight}\to21\text{hours of practice} \\ 7\text{ weeks}\to x \\ x=\frac{7weeks\cdot21\text{ hours of practice}}{1fortnight} \\ 7\text{ we}eks=7\cdot7days=49days \\ 1\text{ fortnight=15days} \\ x=\frac{49days\cdot21\text{ hours of practice}}{15\text{ days}}=68.6\text{ hours of practice} \end{gathered}[/tex]In 7 weeks Ed practice 68.6 hours.
Note we convert week and fortnight to days.
Consider the system of linear equalities:2+>26+3<12This is the graph of the solution.
Given inequality is 2x+y>2 and 6x+3y<12.
Solve 2x+y>2 for y:
[tex]undefined[/tex]Using the table, what is the average daily balance of the credit card for the December 1 - December 31 billing period? Round your answer to the nearest cent. Do not include a dollar sign or comma in your answer. For example, $5,678.00 should be entered as 5678.00.
Answer
ADB= 8145.16
Problem Statement
The question tells us to calculate the Average Daily Balance (ADB) for a period of December 1 - December 31 using the balances given in the table.
Method
To find the Average Daily Balance (ADB), we apply the formula given below:
[tex]\text{ADB}=\sum ^n_{i=1}\frac{(\text{Balance after Day}_i)}{Total\text{ number of days in Billing cycle}}[/tex]The question has given us the Balance after Day 1 - Day 10 (10 days) to be 11,000. We are also given that the Balance from Day 11 to Day 20 (10 days) is 8000, from Day 21 to 30 (10 days), the Balance is 5500 while Day 31 (1 day) with a balance of 7500.
The total number of days in the billing cycle is from Day 1 to Day 31, which is 31 days altogether.
Thus we can use the above formula to find the Average Daily Balance (ADB).
Implementation
[tex]\begin{gathered} \text{ADB}=\frac{(10\times11,000)+(10\times8,000)+(10\times5,500)+(1\times7,500)}{31} \\ \\ \text{ADB}=\frac{252,500}{31} \\ \\ \therefore ADB=8,145.16 \end{gathered}[/tex]
Final Answer
The Answer is:
ADB= 8145.16
The area of a rectangle is x^2+14x+24. What is the length when the width is x+2?
we have that:
[tex]\frac{x^2+14x+24}{x+2}=\frac{(x+2)(x+12)}{x+2}=x+12[/tex]so the length is x+12
Find the slope of the line.
Jackson has a points card for a movie theater.He receives 55 rewards points just for signing upHe earned 12.5 points for each visit to the movie theaterHe needs at least 210 points for a free movie ticketWrite and solve an inequality which can be used to determine x, the number of visits Jackson can make to earn his first free movie ticket
Given data:
The given reward is 55.
The point earned by visit is 12.5.
The number of point for the movie ticket 210.
The given expression for the inequality is,
55+12.5x ≥ 210
12.5x ≥ 155
x ≥12.4
Thus, the minimum number of visit is 13.
Find the volume of a cylinder with a height of 3 m and a diameter of 3 . Round to the nearest tenth
EXPLANATION
The volume of a cylinder will be:
Volume= π*(d/2)^2*h
Substituting:
Volume= π*(3/2)^2*3 = 21.2 m^2
The answer is 21.2 m^2
What did I do wrong? Need help with this equation
Recall that :
1) A function
[tex]f\mleft(x\mright)[/tex]translated n-units to the left is
[tex]f\mleft(x-n\mright).[/tex]2) A function
[tex]h\mleft(x\mright)[/tex]translated m-units up is:
[tex]h\mleft(x\mright)+m.[/tex]3) A function g(x) reflected over the x-axis is:
[tex]-g(x)\text{.}[/tex]The parent function is:
[tex]y=\sqrt[]{x}\text{.}[/tex]The function of the graph of the above function translated horizontally 3 units to the left is:
[tex]y=\sqrt[]{x+3}.[/tex]The function of the graph of the above function translated vertically 4 units up is:
[tex]y=\sqrt[]{x+3}+4.[/tex]The function of the graph of the above function reflected over the x-axis is:
[tex]y=-(\sqrt[]{x+3}+4)=-\sqrt[]{x+3}-4.[/tex]Finally, the function of the graph of the above function stretched vertically by a scale factor of 2 is:
[tex]y=-2\sqrt[]{x+3}-4.[/tex]Answer:
The graph of the function has a horizontal translation Left 3 and vertical translation Up 4. The graph has been reflected over the x-axis and has been Vertically stretched.
Use calculus to find the dimensions of a rectangle with area of 196 square-feet that has the smallest perimeter.
Explanation
In the question, we are given that the area of the rectangle is;
[tex]\text{Area}=196\text{ square fe}et[/tex]Recall that the area and perimeter of a rectangle are given by the formulas below.
[tex]\begin{gathered} \text{Area = Lenth x Width = L}\times W \\ \text{Perimeter = 2(L+W)} \end{gathered}[/tex]From the area of the rectangle, we can isolate the variable of the width.
[tex]\begin{gathered} \text{Area}=\text{ L x W} \\ W=\frac{\text{Area}}{L} \\ W=\frac{196}{L} \end{gathered}[/tex]Therefore, the formula for the perimeter is transformed to give;
[tex]\begin{gathered} \text{Perimeter = 2( L + }\frac{\text{196}}{L}) \\ \text{Simplifying the expression gives;} \\ P=2(\frac{L^2+196}{L}) \\ P=\frac{2L^2+392^{}}{L} \\ P=2L+392L^{-1} \end{gathered}[/tex]Recall, via the rules of differentiation
[tex]\begin{gathered} \text{for y = x}^n \\ \frac{dy}{dx}=nx^{n-1} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \frac{dP}{dL}=2-392L^{-2}^{} \\ \text{But }\frac{dP}{dL}=0 \\ 0=2-392L^{-2} \\ 392^{}L^{-2}=2 \\ \frac{1}{L^2}=\frac{2}{392}^{} \\ L^2=\frac{392}{2} \\ L^2=196 \\ L=\sqrt[]{196} \\ L=14 \end{gathered}[/tex]Since
[tex]W=\frac{196}{L}=\frac{196}{14}=14[/tex]Answer: Length = 14 and Width = 14
3.If F, G, and H are the midpoints of the sidesof AJKL, FG = 37, KL = 48, and GH = 30,find each measure.Ka) FH=Gb) JL =F>Lc) KJ =H||Jd) FJ =
3.If F, G, and H are the midpoints of the sides of AJKL, FG = 37, KL = 48, and GH = 30,
Find each measure.
a) FH = 1/2 KL; FH= 24
b) JL = 2* FG = 2* 37
c) KJ = 2* GH = 2*30 =
d) FJ = 1/2 KJ = GH = 30
__________________________________________________
I'm working on your image, please give me a few minutes
Use the graph to find the appropriate solutions to the equation
The first thing that you should notice is that you have two functions:
[tex]f(x)=\text{ -}2|x\text{ -}3|+1;\text{ and }g(x)=\text{ -}2\sqrt{x\text{ -}1}[/tex]Then their respective graphs are given by the blue and the red functions in your picture. Now, the main idea, is to know the points where they are equal and in that way, you will have the initial equation as follows:
[tex]f(x)=\text{ -}2|x\text{ - }3|+1=\text{ -}2\sqrt{x\text{ - }1}\text{ }=g(x)[/tex]The equation will be satisfied in terms of their graphs at the points where they intersect themselves, at the x-coordinate.
The intersection points A and B at the x-coordinate are the answer for the equation. Then
[tex]x\approx1.7\text{ or }x\approx5.7[/tex]Is the following pair of vectors Parallel, Perpendicular/Orthogonal or Neither?m = < 1 , 5 > n = < 3 , 15 >
1) To find out we need to calculate the dot product of those two vectors
[tex]\begin{gathered} m\cdot n=\mleft\langle1,5\mright\rangle\cdot\mleft\langle3,15\mright\rangle=1\cdot3+5\cdot15=3+75=78 \\ \end{gathered}[/tex]Since these vectors have a dot product different than zero, then they are not Orthogonal.
2) Let's now check if they are perpendicular, calculating the norm of each one and the angle between them:
[tex]\begin{gathered} \mleft\|m\mright\|=\sqrt[]{1^2+5^2}=\sqrt[]{26} \\ \|n\|=\sqrt[]{3^2+15^2}=\sqrt[]{9+225}=\sqrt[]{234} \end{gathered}[/tex]And finally the angle theta between them:
[tex]\begin{gathered} \theta=\cos ^{-1}(\frac{u\cdot v}{\|m\|\cdot\|n\|}) \\ \theta=\cos ^{-1}(\frac{78}{\sqrt[]{26}\cdot\sqrt[]{234}}) \\ \theta=0 \end{gathered}[/tex]3) Since the angle is 0, these vectors are parallel since parallel vectors for 0º or 180º
round each number to the nearest ten, hundred, and thousand5,999
SOLUTIONS
Round each number to the nearest ten, hundred, and thousand
5,999
[tex]5999=6000\text{ \lparen nearest thousand\rparen}[/tex][tex]5999=6000\text{ \lparen nearest ten\rparen}[/tex][tex]5999=6000\text{ \lparen nearest hundred\rparen}[/tex]Which equation is represented by the table of values below
Choosing two points: A(0, 3) and B(3, -9)
• Sope (m):
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1}=\frac{-9-3}{3-0}=\frac{-12}{3}=-4 \\ m=-4 \end{gathered}[/tex]• Find b: choosing point A
y = mx + b
[tex]\begin{gathered} y=mx+b \\ 3=-4\cdot(0)+b \\ b=3 \end{gathered}[/tex]• Education:
[tex]\begin{gathered} y=m\cdot x+b \\ y=-4x+3 \end{gathered}[/tex]
Answer: A. y= -4x + 3
find the slope of the line. (-3,0), (2,2), (7,4), (12,6)
find the slope of the line.
(-3,0), (2,2), (7,4), (12,6)
To find the slope we need two points
so
we take
(-3,0), (2,2)
so
m=(2-0)/(2+3)
m=2/5
Verify with the other two points
(7,4), (12,6)
m=(6-4)/(12-7)
m=2/5 ----> is ok
therefore
the slope is 2/5Suppose that the functions p and q are defined as follows.p(x) = -2x-1q(x)=x²+1Find the following.(q*p)(-2)=(p*q)(-2)=
Answer:
(a)10
(b)-11
Explanation:
Given the function p(x) and q(x) defined as follows:
[tex]\begin{gathered} p(x)=-2x-1 \\ q(x)=x^2+1 \end{gathered}[/tex]Part A
[tex]\begin{gathered} (q\circ p)(x)=q(p(x)) \\ =(-2x-1)^2+1 \\ (q\circ p)(-2)=(-2(-2)-1)^2+1 \\ =(4-1)^2+1 \\ =3^2+1 \\ (q\circ p)(-2)=10 \end{gathered}[/tex]Part B
[tex]\begin{gathered} (p\circ q)(x)=p(q(x)) \\ =-2(x^2+1)-1 \\ (p\circ q)(-2)=-2((-2)^2+1)-1 \\ =-2(4+1)-1 \\ =-2(5)-1=-10-1 \\ (p\circ q)(-2)=-11 \end{gathered}[/tex]use the circle unit to evaluate csc(-/2)
The definition of the cosecant function is
[tex]\csc \theta=\frac{1}{\sin \theta}[/tex]Therefore,
[tex]\Rightarrow\csc (-\frac{\pi}{2})=\frac{1}{\sin (-\frac{\pi}{2})}[/tex]To find sin(-pi/2), use the diagram below.
Consider that the circumference has a radius equal to 1. Then, the coordinates of the orange point are (0,-1). Furthermore, the points on the circumference are given as (cos(theta), sin(theta)); therefore,
[tex]\begin{gathered} \Rightarrow(0,-1)=(\cos (-\frac{\pi}{2}),\sin (-\frac{\pi}{2})) \\ \Rightarrow\sin (-\frac{\pi}{2})=-1 \\ \Rightarrow\csc (-\frac{\pi}{2})=\frac{1}{-1}=-1 \\ \Rightarrow\csc (-\frac{\pi}{2})=-1 \end{gathered}[/tex]Thus, the answer is csc(-pi/2)=-1
Please help me to classify each of the numbers below as an integer or not
The integers are the number that are written without a factional component.
The fraction -6/19 can be expressed with fraction. So it is not a integer.
The fraction -10/5 can be expressed as -2, so this is a integer.
The number -40 is expressed wth fraction component. So it is a integer.
The number -33 is expressed with fraction component. So it is a integer.
The decimal number 8.98 can be expressed as fraction and not expressed without fraction. So it is not a interger.
Answer:
-6/19 No
-10/5 Yes
-40 Yes
Food Express is running a special promotion in which customers can win a free gallon of milk with their food purchase if there is a star on their receipt. So far, 219 of the first 264 customers have not received a star on their receipt. What is the experimental probability of winning a free gallon of milk?options: 3/11....15/88....73/88.....1/78
Solution:
Experimental probability is a probability that is determined on the basis of a series of experiments. A random experiment is done and is repeated many times to determine their likelihood, and each repetition is known as a trial.
[tex]\begin{gathered} P(E)=\frac{n(E)}{n(T)} \\ \\ Where; \\ n(E)=\text{ number of event} \\ \\ n(T)=\text{ total outcome} \end{gathered}[/tex]If 219 of the first 264 customers have not received a star on the receipt, then a customer that would win a free gallon of milk would be among (264 - 219) customers. Thus;
The experimental probability of winning a free gallon of milk is;
[tex]\begin{gathered} =\frac{264-219}{264} \\ \\ =\frac{45}{264} \\ \\ =\frac{15}{88} \end{gathered}[/tex]CORRECT OPTION:
[tex]\frac{15}{88}[/tex]
Raina got a prepaid debit card with $30 on it .For her first purchase with the card ,she bought some bulk ribbon at a craft store. The price of the ribbon was 6 cents per yard.If after that purchase there was $27.90 left on the card ,how many yards of ribbon did Raina buy?
Data:
• Total: $30
,• Price of ribbon: 6 cents per yard
,• Left after purchase: $27.90
Procedure:
[tex]30-27.90=2.1[/tex]Raina spent a total of $2.1 on ribbons.
To know how many yards she bought, we have to homogenize the units. For that, a conversion to dollars must be made.
[tex]6\frac{cents}{\text{yard}}\cdot\frac{0.01dollar}{1cent}=0.06\frac{\text{dollars}}{\text{yard}}[/tex]The yard is $0.06 per yard.
Finally, we can get the yards bought:
[tex]2.1dollars\cdot\frac{1\text{yard}}{0.06\text{dollars}}=35[/tex]Answer: 35 yards
Find f(5) for f(x)= 2(2)*O A. 32B. 2O C. 4D. 8
Given function is
[tex]2^x[/tex]Fo
What is 1584 in terms of pi?
In ΔKLM, the measure of ∠M =90°, the measure of ∠K=,86°, and MK = 86 feet. Find the length of KL to the nearest tenth of a foot.
ΔKLM is a right triangle, the following measures are known:
∠M= 90º
∠K=86º
MK= 86 feet
The side KL is the hypotenuse of the right triangle. To determine its measure you have to apply the trigonometric ratios. In this case, we know one of the angles of the triangle and the length of the side next to the angle, the trigonometric ratio that relates the adjacent side and the hypotenuse is the cosine:
[tex]\cos \theta=\frac{adjacent}{hypotenuse}[/tex]From this expression, you can calculate the measure of the hypotenuse.
[tex]\cos 86=\frac{86}{x}[/tex]-Multiply both sides of the expression by x to take the term out of the denominators place:
[tex]\begin{gathered} x\cos 86=x\cdot\frac{86}{x} \\ x\cos 86=86 \end{gathered}[/tex]-Divide both sides of the expression by cos 86 to reach the value of x:
[tex]\begin{gathered} x\cdot\frac{\cos86}{\cos86}=\frac{86}{\cos 86} \\ x=\frac{86}{\cos 86} \\ x=1232.86 \\ x\approx1232.9ft \end{gathered}[/tex]The length of KL is equal to 1232.9ft
The perimeter of a geometric figure is the sum of the lengthsof its sides. If the perimeter of the pentagon (five-sided figure)to the right is 140 meters, find the length of each side.
Given figure is a regular pentagon, it means it will have 5 sides of equal length.
Let the length of each side of the polygon be 'x' meters.
The perimeter of the pentagon will be the sum of all its 5 sides,
[tex]\begin{gathered} P=x+x+x+x+x \\ P=5x \end{gathered}[/tex]Given that the perimeter of the pentagon is 140 meters,
[tex]P=140[/tex]Substitute the value in the equation,
[tex]\begin{gathered} 140=5x \\ x=\frac{140}{5} \\ x=28 \end{gathered}[/tex]Thus, the length of each side of the regular pentagon is 28 meters.
PLS HELP ME I BEG OF YPU PLS PLS
Answer: Y= 2x + 4
Step-by-step explanation:
The line is going up which means it is positive, giving it a positive slope of 2x. It intersects with the Y-axis at (0, 4), giving it a positive Y-int of 4. You can use rise over run to find the slope; pick two easy points and count how many units up and over it is to the next point!
The table below, from the Statistical Abstract of the United States, showsamusement park attendance at the top 15 amusement parks for given years. Findthe equation of the line that best fit the data.Year (x) | ,Amusement Park Attendance at Top 15 Amusement Parks (in thousands) (y)2009 | 107,3482010 | 109,3212011 | 112,5092012 | 116,4202013 | 119,951
Year (x) | Attendance (in thousands) (y)
2009 | 107,348
2010 | 109,321
2011 | 112,509
2012 | 116,420
2013 | 119,951
Using Excel the next equation is obtained:
[tex]y=3230.5x-6\cdot10^6[/tex]Explain why we need math? (Need three sentences)
1. Mathematics is necessary for engineering. Without them we could not have the technological advances that make our lives easy.
2. Mathematics is necessary just as art is necessary. For its beauty. They have a spiritual and aesthetic value.
3. Mathematics is necessary for our daily life. From calculating the cost of things or calculating how we can carry out our dreams.
4. Mathematics is fundamental for the intellectual development of human beings: that is, because it helps them to be logical, to reason in an orderly manner and to have a mind prepared for thought, criticism and abstraction
please help with this problem I have a test in a few minutes which be about this kind of topic but I don't Understand
We want to find f(2) for the following function
f(x) = 2x² + 3x
This means that we want to find the value of f(x) when x = 2. So, we replace all the x by 2:
f(x) = 2x² + 3x
f(2) = 2(2)² + 3 · 2
Since 2² = 4 and 3 · 2 = 6 then
f(2) = 2(2)² + 3 · 2
f(2) = 2 · 4 + 6
f(2) = 8 + 6
f(2) = 14
Answer: f(2) = 14