The following expressions are equivalent to 36x + 24y is 6(6x+4y).
6x(6+4y)
6(6x+4y)
12(3x+2y)
4(9x+6y)
We have,
What is the expression?The expression consists of numbers and arithmetic operators. It does not contain equality or inequality symbols. The expression consists of unknown variables
36x + 24y
=6(6x)+6(4y)
=6(6x+4y)
Therefore, The following expressions are equivalent to 36x + 24y is 6(6x+4y).
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What is the slope of the line in the graph?
Answer:
The slope of this line is 1 and the equation for the line is y=x+1
Step-by-step explanation:
So take 2 points passing through the the line (0,1), (-1,0)
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
First, let's find what m is, the slope of the line...
So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (0,1), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=0 and y1=1.
Also, let's call the second point you gave, (-1,0), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-1 and y2=0.
Now, just plug the numbers into the formula for m above, like this:
m=
0 - 1
-1 - 0
So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:
y=1x+b
Now, what about b, the y-intercept?
To find b, think about what your (x,y) points mean:
(0,1). When x of the line is 0, y of the line must be 1.
(-1,0). When x of the line is -1, y of the line must be 0.
Because you said the line passes through each one of these two points, right?
Now, look at our line's equation so far: y=x+b. b is what we want, the 1 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (0,1) and (-1,0).
So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.
You can use either (x,y) point you want..the answer will be the same:
(0,1). y=mx+b or 1=1 × 0+b, or solving for b: b=1-(1)(0). b=1.
(-1,0). y=mx+b or 0=1 × -1+b, or solving for b: b=0-(1)(-1). b=1.
In both cases we got the same value for b. And this completes our problem.
The equation of the line that passes through the points
(0,1) and (-1,0)
is
y=x+1
Given f(x) = 3sqrt(2x-1).
6(2x-1)^2-3
What is lim f(x)?
Answer:
[tex]\displaystyle 51[/tex]
General Formulas and Concepts:
Algebra I
Terms/CoefficientsFactoringFunctionsFunction NotationAlgebra II
Piecewise functionsCalculus
Limits
Right-Side Limit: [tex]\displaystyle \lim_{x \to c^+} f(x)[/tex]Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]
Limit Property [Addition/Subtraction]: [tex]\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)[/tex]
Limit Property [Multiplied Constant]: [tex]\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f(x) = \left \{ {{3\sqrt{2x - 1}, \ x \leq 2} \atop {6(2x - 1)^2 - 3, \ x > 2}} \right.[/tex]
Step 2: Solve
Substitute in function [Limit]: [tex]\displaystyle \lim_{x \to 2^+} 6(2x - 1)^2 - 3[/tex]Factor: [tex]\displaystyle \lim_{x \to 2^+} 3[2(2x - 1)^2 - 1][/tex]Rewrite [Limit Property - Multiplied Constant]: [tex]\displaystyle 3\lim_{x \to 2^+} 2(2x - 1)^2 - 1[/tex]Evaluate [Limit Property - Variable Direct Substitution]: [tex]\displaystyle 3[2(2 \cdot 2 - 1)^2 - 1][/tex]Simplify: [tex]\displaystyle 51[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Book: College Calculus 10e
The radius of a sphere is increasing at a rate of 3 mm/s. How fast is the volume increasing when the diameter is 60 mm
Answer:
The volume is increasing at a rate of 33929.3 cubic millimeters per second.
Step-by-step explanation:
Volume of a sphere:
The volume of a sphere of radius r is given by:
[tex]V = \frac{4\pi r^3}{3}[/tex]
In this question:
We have to derivate V and r implicitly in function of time, so:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
The radius of a sphere is increasing at a rate of 3 mm/s.
This means that [tex]\frac{dr}{dt} = 3[/tex]
How fast is the volume increasing when the diameter is 60 mm?
Radius is half the diameter, so [tex]r = 30[/tex]. We have to find [tex]\frac{dV}{dt}[/tex]. So
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
[tex]\frac{dV}{dt} = 4\pi (30)^2(3) = 33929.3[/tex]
The volume is increasing at a rate of 33929.3 cubic millimeters per second.
Evaluate −3w − 6p for w=2 and p = −7
-3w-6p when w=2 and p=-7
-3(2)-6(-7)
= -6 + 42
= 36
Answer:
48
Step-by-step explanation:
-3w-6p when w=2 and p--7
you want to plug in the numbers to their letters
-3(2)-6(-7)
then you want to times the numbers.
-6-42
=48
bisects ∠EDG. Find the value of x
Answer:
where is the question? please attatch the angle
What the distance between -6,2 -6,-15
Answer:
The answer is 17
Step-by-step explanation:
-15-2= -17
Please help due tomorrow
Answer:
10x8=80 that would be the area for the picture 14x11=154 for the boards area
PLEASE HELP please I need this done now
The total cost of a truck rental, y, for x days, can be modeled by y = 35x + 25.
What is the rate of change for this function?
Answers
A- 35$
B-25$
C-60$
D-10$
Answer:
35
Step-by-step explanation:
y = 35x+23 is in the form
y = mx+b where m is the slope and b is the y intercept
The slope can also be called the rate of change
35 is the slope
Rita earns scores of 70, 76, 86, 87, and 85 on her five chapter tests for a certain class and a grade of 85 on the dass project.
The overall average for the course is computed as follows: the average of the five chapter tests makes up 60% of the course
grade; the project accounts for 10% of the grade; and the final exam accounts for 30%. What scores can Rita earn on the final
exam to earn a "B" in the course if the cut-off for a "B" is an overall score greater than or equal to 80, but less than 90? Assume
that 100 is the highest score that can be earned on the final exam and that only whole-number scores are given.
To obtain a "B", Rita needs to score between and inclusive.
Answer:
To obtain a "B", Rita needs to score between 76.7 and 100.
Step-by-step explanation:
Chapter tests mean:
[tex]M = \frac{70 + 76 + 86 + 87 + 85}{5} = 80.8[/tex]
Grades:
80.8 worth 60% = 0.6
85 worth 10% = 0.1
x worth 0.3.
So her grade is:
[tex]G = 80.8*0.6 + 85*0.1 + 0.3x = 56.98 + 0.3x[/tex]
What scores can Rita earn on the final exam to earn a "B" in the course if the cut-off for a "B" is an overall score greater than or equal to 80, but less than 90?
G has to be greater than or equal to 80 and less than 90, so:
[tex]80 \leq G < 90[/tex]
Lower bound:
[tex]G \geq 80[/tex]
[tex]56.98 + 0.3x \geq 80[/tex]
[tex]0.3x \geq 80 - 56.98[/tex]
[tex]x \geq \frac{80 - 56.98}{0.3}[/tex]
[tex]x \geq 76.7[/tex]
Upper bound:
[tex]G < 90[/tex]
[tex]56.98 + 0.3x < 80[/tex]
[tex]0.3x < 90 - 56.98[/tex]
[tex]x < \frac{90 - 56.98}{0.3}[/tex]
[tex]x < 110[/tex]
Highest grade is 100, so:
To obtain a "B", Rita needs to score between 76.7 and 100.
A cable that weighs 6 lb/ft is used to lift 600 lb of coal up a mine shaft 500 ft deep. Find the work done. Show how to approximate the required work by a Riemann sum. (Let x be the distance in feet below the top of the shaft. Enter xi* as xi.)
Answer:
A cable that weighs 6 lb/ft is used to lift 600 lb of coal up a mine shaft 500 ft deep. Find the work done. Show how to approximate the required work by a Riemann sum.
Step-by-step explanation:
Translate the triangle. Then enter the new coordinates. A(-3, 4) A'([?], [?]) B'([ ], [ ] C([],[]) B(0, 1) C(-4,1)
or
Answer:
The new coordinates are [tex]A'(x,y) = (3, 0)[/tex], [tex]B'(x,y) = (6, -3)[/tex] and [tex]C'(x,y) = (2, -3)[/tex].
Step-by-step explanation:
Vectorially speaking, the translation of a point can be defined by the following expression:
[tex]V'(x,y) = V(x,y) + T(x,y)[/tex] (1)
Where:
[tex]V(x,y)[/tex] - Original point.
[tex]V'(x,y)[/tex] - Translated point.
[tex]T(x,y)[/tex] - Translation vector.
If we know that [tex]A(x,y) = (-3,4)[/tex], [tex]B(x,y) = (0,1)[/tex], [tex]C(x,y) = (-4,1)[/tex] and [tex]T(x,y) = (6, -4)[/tex], then the resulting points are:
[tex]A'(x,y) = (-3, 4) + (6, -4)[/tex]
[tex]A'(x,y) = (3, 0)[/tex]
[tex]B'(x,y) = (0,1) + (6, -4)[/tex]
[tex]B'(x,y) = (6, -3)[/tex]
[tex]C'(x,y) = (-4, 1) + (6, -4)[/tex]
[tex]C'(x,y) = (2, -3)[/tex]
The new coordinates are [tex]A'(x,y) = (3, 0)[/tex], [tex]B'(x,y) = (6, -3)[/tex] and [tex]C'(x,y) = (2, -3)[/tex].
A street light is mounted at the top of a 15-ft-tall pole. A man 6 feet tall walks away from the pole with a speed of 5 ft/s along a straight path. How fast (in ft/s) is the tip of his shadow moving when he is 45 feet from the pole
Answer:
25/3 ft/s
Step-by-step explanation:
Height of pole , h=15 ft
Height of man, h'=6 ft
Let BD=x
BE=y
DE=BE-BD=y-x
All right triangles are similar
When two triangles are similar then the ratio of their corresponding sides are equal.
Therefore,
[tex]\frac{AB}{CD}=\frac{BE}{DE}[/tex]
[tex]\frac{15}{6}=\frac{y}{y-x}[/tex]
[tex]\frac{5}{2}=\frac{y}{y-x}[/tex]
[tex]5y-5x=2y[/tex]
[tex]5y-2y=5x[/tex]
[tex]3y=5x[/tex]
[tex]y=\frac{5}{3}x[/tex]
Differentiate w.r.t t
[tex]\frac{dy}{dt}=\frac{5}{3}\frac{dx}{dt}[/tex]
We have dx/dt=5ft/s
Using the value
[tex]\frac{dy}{dt}=\frac{5}{3}(5)=\frac{25}{3}ft/s[/tex]
Hence, the tip of his shadow moving with a speed 25/3 ft/s when he is 45 feet from the pole.
Answer:
The tip pf the shadow is moving with speed 25/3 ft/s.
Step-by-step explanation:
height of pole = 15 ft
height of man = 6 ft
x = 45 ft
According to the diagram, dx/dt = 5 ft/s.
Now
[tex]\frac{y-x}{y}=\frac{6}{15}\\\\15 y - 15 x = 6 y \\\\y = \frac{5}{3} x\\\\\frac{dy}{dt} = \frac{5}{3}\frac{dx}{dt}\\\\\frac{dy}{dt}=\frac{5}{3}\times 5 =\frac{25}{3} ft/s[/tex]
The combined value of the ages of Mary, Kate and Tom is 26 years. What will be their age in total after 2 years?
Answer:
32
Step-by-step explanation:
they will each age two years, 3x2 is 6, add 6 to 26
Answer:
32
Step-by-step explanation:
they will each age two years, 3x2 is 6, add 6 to 26
Simplify the expression. 8x^-10 y^'6 -2x^2y^-8 Write your answer without negative exponents.
Answer:
[tex]8x^{-10}y^6 - 2x^2y^{-8} = \frac{8y^{14} - 2x^{12}}{x^{10}y^8}[/tex]
Step-by-step explanation:
Given
[tex]8x^{-10}y^6 - 2x^2y^{-8}[/tex]
Required
Simplify
Rewrite as:
[tex]8x^{-10}y^6 - 2x^2y^{-8} = \frac{8y^6}{x^{10}} - \frac{2x^2}{y^8}[/tex]
Take LCM
[tex]8x^{-10}y^6 - 2x^2y^{-8} = \frac{8y^6*y^8 - 2x^2 * x^{10}}{x^{10}y^8}[/tex]
Apply law of indices
[tex]8x^{-10}y^6 - 2x^2y^{-8} = \frac{8y^{14} - 2x^{12}}{x^{10}y^8}[/tex]
Given: F = {(0, 1), (2, 4), (4, 6), (6, 8)} and G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}
(F + G) (2) =
4
5
9
9514 1404 393
Answer:
9
Step-by-step explanation:
The ordered pair (2, 4) in the relation for function F tells you F(2) = 4.
The ordered pair (2, 5) in the relation for function G tells you G(2) = 5.
Then the sum is ...
(F+G)(2) = F(2) +G(2) = 4 +5
(F+G)(2) = 9
HELP ME WITH THIS MATHS QUESTION
PICTURE IS ATTACHED
Answer:
In picture.
Step-by-step explanation:
To do this answer, you need to count the boxes up to the mirror line. This will give us the exact place to draw the triangle.
The picture below is the answer.
Identify the domain of the function shown in the graph.
A. -5
B. x> 0
C. 0
D. x is all real numbers.
Determine la razón de la siguiente progresión geométrica: 81,27,9,3,1,....
Answer:
BẠN BỊ ĐIÊN À
Step-by-step explanation:
CÚT
14. Which property is shown by 3 + 2 = 2 + 3? (1 point)
O Commutative Property of Addition
O Identity Property of Addition
O Distributive Property
O Associative Property of Addition
Answer: Commutative Property of Addition
Explanation: The problem 3 + 2 = 2 + 3 demonstrates the commutative property of addition. In other words, the commutative property of addition says that changing the order of the addends does not change the sum.
For example here, we can easily see that the sum of 3 + 2,
which is 5, is equal to the sum of 2 + 3, which is also 5.
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]
3 + 2 = 2 + 3It is commutative property of additionaccording to the fundemental theorem of algebra, how many roots exist for the polynomial function? f(x) = (x^3-3x+1)^2
Answer:
6
Step-by-step explanation:
First, we can expand the function to get its expanded form and to figure out what degree it is. For a polynomial function with one variable, the degree is the largest exponent value (once fully expanded/simplified) of the entire function that is connected to a variable. For example, x²+1 has a degree of 2, as 2 is the largest exponent value connected to a variable. Similarly, x³+2^5 has a degree of 2 as 5 is not an exponent value connected to a variable.
Expanding, we get
(x³-3x+1)² = (x³-3x+1)(x³-3x+1)
= x^6 - 3x^4 +x³ - 3x^4 +9x²-3x + x³-3x+1
= x^6 - 6x^4 + 2x³ +9x²-6x + 1
In this function, the largest exponential value connected to the variable, x, is 6. Therefore, this is to the 6th degree. The fundamental theorem of algebra states that a polynomial of degree n has n roots, and as this is of degree 6, this has 6 roots
Matthew actually drew the 10 of hearts and the 3 of clubs. If he keeps those to one side and selects two more from the pack, what is the chance that he'll get a pair of 10s this time? As before, give your answer in its simplest form. 2nd Attempt: Probability of getting a pair of 10s
If the rate of inflation is 2.6% per year, the future price p(t) (in dollars) of a certain item can be modeled by the following exponential function, where t is the number of years from today.
p(t)=600(1.026)t
Find the current price of the item and the price 9 years from today.
Round your answers to the nearest dollar as necessary.
Answer:
The current price of the item is $600.
The price of the item 9 years from today will be of $756.
Step-by-step explanation:
Price of the item:
The price of the item, in dollars, after t years, is given by:
[tex]p(t) = 600(1.026)^t[/tex]
Current price of the item
This is p(0). So
[tex]p(0) = 600(1.026)^0 = 600[/tex]
The current price of the item is $600.
9 years from today.
This is p(9). So
[tex]p(9) = 600(1.026)^9 = 756[/tex]
The price of the item 9 years from today will be of $756.
Which of the following statements are correct? Select ALL that apply!
Select one or more:
O a. -1.430 = -1.43
O b. 2.36 < 2.362
O c.-1.142 < -1.241
O d.-2.33 > -2.29
O e. 2.575 < 2.59
O f. -2.25 -2.46
Log6^(4x-5)=Log6^(2x+1)
Answer:
[tex]x = 3[/tex]
Step-by-step explanation:
Given
[tex]\log6^{(4x-5)} =\log6^{(2x+1)}[/tex]
Required
Solve for x
We have:
[tex]\log6^{(4x-5)} =\log6^{(2x+1)}[/tex]
Remove log6 from both sides
[tex](4x-5) = (2x+1)[/tex]
Collect like terms
[tex]4x - 2x = 5 + 1[/tex]
[tex]2x = 6[/tex]
Divide by 2
[tex]x = 3[/tex]
What is the percent increase from 250 to 900?
1. Write the percent change formula for an increase.
Percent Increase =
Amount of Increase
Original Amount
2. Substitute the known quantities for the amount of the increase and the original amount.
Percent Increase =
900 − 250
250
3. Subtract.
Percent Increase =
650
250
Answer:
260% is the correct answer
Step-by-step explanation:
i hope i helped
The owner of a greenhouse wants to test the effectiveness of a new fertilizer on African violets. She has 60 violet seedlings that were grown for 8 weeks. She wants to test the new fertilizer on 10 of the plants, and decides to use a random number table to select a simple random sample. She labels the violets 01–60. Refer to the given line from a random number table. Which numbers represent the first 5 plants selected?
60633 78034 99602 83440 55120 61551
33, 03, 49, 02, 40
06, 33, 03, 49, 02
60, 63, 37, 80, 34
60, 37, 34, 28, 40
Answer:
60, 37, 34, 28, 40
(D)
ED2021
Please help me out really need it
Answer:
[tex]{ \tt{hypotenuse = { \boxed{5}}}} \\ { \tt{opposite = { \boxed{3}}}} \\ { \tt{adjacent = { \boxed{4}}}} \\ \\ { \tt{ \sin \angle R = \frac{{ \boxed{3}}}{{ \boxed{5}}} }} \\ \\ { \tt{ \cos \angle R = \frac{{ \boxed{4}}}{{ \boxed{5}}} }} \\ \\ { \tt{ \tan \angle R = \frac{ \boxed{3}}{{ \boxed{4}}} }}[/tex]
X = The set of months in a year?
there are 12 set of months in a year
Determine if the triangle is Right, Acute or Obtuse.
Answer:
I think the right answer is: Acute
Blair & Rosen (B&R) plc is a U.K. based brokerage firm that specializes In building investment portfolios designed to meet the specific needs of its clients who are mostly private investors willing to invest their r savings in stocks and shares. One client who contacted B&R recently has a maximum of $500,000 to invest. The company`s investment advisor has decided to recommend the portfolio consisting of two investment funds: An internet fund where the companies are all active in internet businesses of one kind or another and the blue-chip fund which is more conservative and traditional. The internet fund has a projected annual return over the next few years of 12 %, while the blue-chip fund has a projected annual return of 9%. The investment advisor has decided that at most, $350,000 of the client`s funds should be invested in the internet fund. B&R services include risk rating for each investment alternative. The internet fund which is more risky of the two alternatives has a risk rating of 6 for every thousand dollar invested while the blue-chip fund has a risk rating of 4 per thousand dollar invested. So, for example, if $10000 is invested in each of the two investments funds, B&R risk rating for the portfolio would be 6(10) + 4(10)= 100. Finally B&R has developed a questionnaire to measure each client`s risk tolerance. Based on the responses, each client is classified as conservative, moderate or aggressive investor. The questionnaire results have classified the current client as a moderate investor. B&R recommends that a client who`s a moderate investor limit his or her portfolio to a maximum risk rating of 240. You have been asked to help the B&R investment advisor. What is the recommended investment portfolio for this client? What is the annual return for the portfolio? A second client , also with $500,000 has been classified as aggressive. B&R recommends that the maximum portfolio risk rating for an aggressive investor is 320. What is the recommended investment portfolio for this aggressive investor
Answer:
Blair & Rosen (B&R) Plc.
Recommendation for moderate investor:
Internet fund = 96/240 * $500,000 = $200,000
Blue-chip fund = 144/240 * $500,000 = $300,000
Annual return for the portfolio:
Internet fund = $200,000 * 12% = $24,000
Blue-chip fund = $300,000 * 9% = $27,000
Total portfolio returns = $51,000
Annual returns of portfolio = $51,000/$500,000 * 100 = 10.2%
Recommendation for aggressive investor:
Internet fund = 192/320 * $500,000 = $300,000
Blue-chip fund = 128/320 * $500,000 = $200,000
Step-by-step explanation:
a) Data and Calculations:
Maximum investible savings = $500,000
Projected annual return of the internet fund = 12%
Projected annual return of the blue-chip fund = 9%
Maximum determined amount to invest in the internet fund = $350,000
Risk rating for the internet fund = 6/1,000
Risk rating for the blue-chip fund = 4/1,000
Maximum risk rating for a moderate investor = 240
Maximum risk rating for an aggressive investor = 320
Recommendation for moderate investor:
Internet fund = 96/240 * $500,000 = $200,000
Blue-chip fund = 144/240 * $500,000 = $300,000
Annual return for the portfolio:
Internet fund = $200,000 * 12% = $24,000
Blue-chip fund = $300,000 * 9% = $27,000
Total returns = $51,000
Annual returns of portfolio = $51,000/$500,000 * 100 = 10.2%
Recommendation for aggressive investor:
Internet fund = 192/320 * $500,000 = $300,000
Blue-chip fund = 128/320 * $500,000 = $200,000
