Answer:
Translation 2 units to the right
Vertical stretch by a factor of 3
Translation 1 unit up
Step-by-step explanation:
Correct on plato :}
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
Determine la razón de la siguiente progresión geométrica: 81,27,9,3,1,....
Answer:
BẠN BỊ ĐIÊN À
Step-by-step explanation:
CÚT
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
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 additionWhat the distance between -6,2 -6,-15
Answer:
The answer is 17
Step-by-step explanation:
-15-2= -17
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.
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
3 st Post Office charges for an ordinary telegram are sh 4 for the first 10 words and 40 cents for each extra word. Calculate the cost of sending this telegram: MR KAMAU ARRIVING AT 0630 EAST AFRICAN TIME ON BOARD KQ 46 INFORM THE WIFE
Answer:
The cost of sending the telegram is $6.
Step-by-step explanation:
Since 3 St. Post Office charges for an ordinary telegram are $ 4 for the first 10 words and 40 cents for each extra word, to calculate the cost of sending this telegram: MR KAMAU ARRIVING AT 0630 EAST AFRICAN TIME ON BOARD KQ 46 INFORM THE WIFE must perform the following calculation:
The telegram has 15 words.
4 + ((15 - 10) x 0.40) = X
4 + (5 x 0.40) = X
4 + 2 = X
6 = X
Therefore, the cost of sending the telegram is $ 6.
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
I need help ASAP is anyone available
Answer:
C
Step-by-step explanation:
The graph has asymptotes at x = 2 and x = -1 corresponding to the denominator of option C.
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
What is the slope of a line thal is perpendicular to the line 2y - 3x = 8?
9514 1404 393
Answer:
-2/3
Step-by-step explanation:
The slope of the given line can be found by solving for y.
2y -3x = 8
2y = 3x +8 . . . . add 3x
y = 3/2x +4 . . . . divide by 2
The slope is the coefficient of x: 3/2. For the perpendicular line, the slope is the opposite reciprocal of this:
-1/(3/2) = -2/3
The slope of a perpendicular line is -2/3.
Student Engineers Council at an Indiana college has one student representative from each of the five engineering majors (civil, electrical, industrial, materials, and mechanical). Compute how many ways a president, a vice president, and a secretary can be selected.
Answer:
A president, a vice president, and a secretary can be selected in 60 ways.
Step-by-step explanation:
The order in which the people are chosen is important(first president, second vice president and third secretary), which means that the permutations formula is used to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this question:
3 students from a set of 5, so:
[tex]P_{(5,3)} = \frac{5!}{2!} = 5*4*3 = 60[/tex]
A president, a vice president, and a secretary can be selected in 60 ways.
A data set includes 103 body temperatures of healthy adult humans having a mean of 98.5°F and a standard deviation of 0.61°F. Construct a 99% confidence interval estimate of the mean body temperature of all healthy humans. What does the sample suggest about the use of 98.6°F as the mean body temperature? What is the confidence interval estimate of the population mean μ?
Answer:
The 99% confidence interval estimate of the mean body temperature of all healthy humans is between 98.3ºF and 98.7ºF. 98.6°F is part of the confidence interval, which means that the sample suggests that this is a correct measure.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.575\frac{0.61}{\sqrt{103}} = 0.2[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 98.5 - 0.2 = 98.3ºF.
The upper end of the interval is the sample mean added to M. So it is 98.5 + 0.2 = 98.7ºF.
The 99% confidence interval estimate of the mean body temperature of all healthy humans is between 98.3ºF and 98.7ºF. 98.6°F is part of the confidence interval, which means that the sample suggests that this is a correct measure.
what is the vertical change from point a to point b
what is the horizontal change from point a to point b
Answers:
Vertical change = 1Horizontal change = 2Rate of change = 0.5====================================================
Explanation:
Imagine that we have point A as a buoy in the water. So the horizontal line through 1 on the y axis is the water line. How much should the water line go up so that points A and B are on the same horizontal level? That would be 1 unit up. This is the vertical change. Another term for this is "rise".
After the water goes up, and A and B are on the same level, the question is now: how far to the right do we go from A to B? That would be 2 units. This is the horizontal change. Another term for this is "run".
Using those two values, we can compute the rate of change aka slope.
slope = rise/run = 1/2 = 0.5
So each time we go up 1 (rise) we move to the right 2 (run).
The slope is positive since we're moving uphill while moving to the right.
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
Identify the domain of the function shown in the graph.
A. -5
B. x> 0
C. 0
D. x is all real numbers.
bisects ∠EDG. Find the value of x
Answer:
where is the question? please attatch the angle
What is the solution to 3×^2-2×+4=0
Answer:
this has no real solution.
only in the realm of complex and imaginary numbers.
x = 1/3 ± sqrt(11)i/3
Step-by-step explanation:
I read as the equation to be solved :
3x² - 2x + 4 = 0
the solution to such a quadratic equation is
x =(-b ± sqrt(b² - 4ac))/(2a)
in our case
a=3
b=-2
c=4
so,
x = (2 ± sqrt(4 - 48))/6 = (2 ± sqrt(-44))/6 =
= (2 ± sqrt(4×-11))/6 = (2 ± 2×sqrt(-11))/6 =
= (1 ± sqrt(11)×i)/3 = 1/3 ± sqrt(11)i/3
Develop the estimated regression equation that can be used to predict the price given the weight. Also report the standard error of the estimate, , and . The regression equation is (to 1 decimal) (to 4 decimals) (to 4 decimals) (to 4 decimals) Test for the significance of the relationship at the .05 level of significance. -value is (to 4 decimals). We _________ that the two variables are related. Did the estimated regression equation provide a good fit
Answer:
Following are the response to the given question:
Step-by-step explanation:
For question 1:
Following are the regression equation:
[tex]price = 2044.03 - 28.35 \ \ (weight)[/tex]
[tex]\sigma = 94.353\\\\R^2 = 0.7647\\\\R^2\ (adj.) = 0.75\\\\[/tex]
For question 2:
Test of connection importance at 5 percent significance:
[tex]p-value < 0.000001\\\\p-value< 0.05[/tex]
Two variables could be said to be connected.
For question 3:
[tex]R^2 = 0.7647[/tex]
The computed equations of the regression fit well.
Please help due tomorrow
Answer:
10x8=80 that would be the area for the picture 14x11=154 for the boards area
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.
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]
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].
Marquise has 200200200 meters of fencing to build a rectangular garden.
The garden's area (in square meters) as a function of the garden's width xxx (in meters) is modeled by:
A(x)=-x^2+100xA(x)=−x
2
+100xA, left parenthesis, x, right parenthesis, equals, minus, x, squared, plus, 100, x
WHAT IS THE MAXIMUM AREA POSSIBLE SQUARE METERS
Hence the maximum possible area is 2500 square meters
Given the area of the rectangular garden expressed as;
[tex]A(x)=-x^2+100x\\[/tex]
The maximum area occurs when dA(x)/dx = 0
[tex]\frac{dA(x)}{dx} = -2x + 100\\0= -2x + 100\\ 2x = 100\\x = \frac{100}{2}\\x = 50[/tex]
Next is to get the maximum area possible. Substitute x = 50 into the original function as shown;
[tex]A(50)= -50^2 + 100(50)\\A(50) = -2500+5000\\A(50) = 2500[/tex]
Hence the maximum possible area is 2500 square meters
Learn more here: https://brainly.com/question/17134596
2500 square meters
This question was on Khan Academy and I got it correct
Solve for x and simplify answer as much as possible
Answer:
[tex]x=-1[/tex]
Step-by-step explanation:
[tex]4=6+2x[/tex]
Flip the equation:
[tex]2x+6=4[/tex]
Subtract 6 from both sides:
[tex]3x+6-6=4-6[/tex]
[tex]2x=-2[/tex]
Divide both sides by 2:
[tex]2x/2=-2/2[/tex]
[tex]x=-1[/tex]
Answer:
x= -1
Step-by-step explanation:
firstly group the like terms
4-6=2x
-2=2x
divide both sides by 2
-2/2=2x/2
-1=x
therefore x is -1
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:
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.
simplify the expression: (3x+y2)
please help me to solve
We have to,
Simplify the expression,
→ (3x + y²)
Now remove brackets in expression,
→ (3x + y²)
→ 3x + y²
Therefore, 3x + y² is simplest form.
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]