The Area of the region bounded by curves = 9 sq.units.
What is Area ?Area is the space occupied by a two dimensional figure on a two dimensional space coordinate.
The two curves given are
x² + 4y - 8 = 0 and x =2y
Convert the two equation so ‘x’ is the dependent variable.
y = -(1/4) x² +2 and y = (1/2)x
Find the limit by the intersection point of both the graph
so (-4, 2) and (2, 1)
The x-values of the line are greater so subtract the parabola:
A = ∫ (1/2)x - (-(1/4) x² +2 ) in the limits of (-4 and 1)
The Area = 9 sq.units.
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Which expression represents the perimeter of the triangle?
8x + 2
18x
8x
Answer:
8x
Step-by-step explanation:
(3x+1)+(3x-1), the 1's cross out, so it is 3x+3x=6x. 6x+2x=8x.
Answer:
8x
Step-by-step explanation:
got it right!!!
Which statement about the point (-1,0) is true?
Answer:
Yes
Step-by-step explanation:
vdhdhdhdhdhshsbsbsbsjshshsjajjssjsusususu
The functions f(x) and g(x) are shown on the graph.
The image shows two graphs. The first is f of x equals log base 3 of x and it is increasing from negative infinity in quadrant four as it goes along the y-axis and passes through 0 comma 1 to turn and increase to the right to positive infinity. The second is g of x and it is increasing from negative infinity in quadrant two as it goes along x equals negative 4 and passes through 0 comma negative 3 to turn and increase to the right to positive infinity.
Using f(x), what is the equation that represents g(x)?
g(x) = log3(x) – 4
g(x) = log3(x) + 4
g(x) = log3(x – 4)
g(x) = log3(x + 4)
Answer:
[tex]g(x)=\log_3(x+4)[/tex]
Step-by-step explanation:
Translations
For [tex]a > 0[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
Parent function:
[tex]f(x)=\log_3x[/tex]
From inspection of the graph:
The x-intercept of [tex]f(x)[/tex] is (1, 0)The x-intercept of [tex]g(x)[/tex] is (-3, 0)If there was a vertical translation, the end behaviors of both g(x) and f(x) would be the same in that the both functions would be increasing from -∞ in quadrant IV.
As the x-intercepts of both functions is different, and g(x) increases from -∞ in quadrant III, this indicates that there has been a horizontal translation of 4 units to the left.
Therefore:
[tex]g(x)=f(x+4)=\log_3(x+4)[/tex]
Further Proof
Logs of zero or negative numbers are undefined.
From inspection of the graph, [tex]x=-3[/tex] is part of the domain of g(x).
Therefore, input this value of x into the answer options:
[tex]g(-3)=\log_3(-3)-4\implies[/tex] undefined
[tex]g(-3)=\log_3(-3)+4\implies[/tex] undefined
[tex]g(-3)=\log_3(-3-4)=\log_3(-7)=\implies[/tex] undefined
[tex]g(-3)=\log_3(-3+4)=\log_3(1)=0[/tex]
Hence proving that [tex]g(x)=\log_3(x+4)[/tex]
The equation that represents g(x) is: [tex]g(x) = log_3(x + 4)[/tex]
The correct answer is: the fourth option:
[tex]g(x) = log_3(x + 4)[/tex].
Here, we have to find the equation that represents g(x) using f(x), we need to consider how the graph of g(x) is related to the graph of f(x).
The graph of f(x) = log base 3 of x starts from negative infinity in quadrant four, passes through (0, 1), and increases to positive infinity.
The graph of g(x) is increasing from negative infinity in quadrant two, passes through (0, -3), and increases to positive infinity.
So, we can see that the graph of g(x) is the graph of f(x) shifted 4 units to the left along the x-axis.
Therefore, the equation that represents g(x) is:
[tex]g(x) = log_3(x + 4)[/tex]
The correct answer is: the fourth option:
[tex]g(x) = log_3(x + 4)[/tex].
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Write the equation of the line that passes through the points (4, -3) and (-5, 4).
Put your answer in fully simplified point-slope form, unless it is a vertical or
horizontal line.
Answer:
y₁ - y₂ = (-7/9)(x₁ - x₂)
Step-by-step explanation:
The general structure for an equation in point-slope form is:
y₁ - y₂ = m(x₁ - x₂)
In this form, "m" represents the slope and the "x" and "y" values come from each point. To find "m", plug the values of each point into the equation.
Point 1: (4, -3) Point 2: (-5,4)
y₁ - y₂ = m(x₁ - x₂) <---- Original equation
-3 - 4 = m(4 - (-5)) <---- Plug values in for "x" and "y"
-7 = m(4 - (-5)) <---- Simplify left side
-7 = m(9) <---- Simplify within parentheses
-7/9 = m <---- Divide both sides by 9
I don't exactly understand what "fully simplified point-slope form" means because if all of the variables are plugged in, you wouldn't be left with an equation. It may just be asking for the slope, which in this case would make the equation look like this:
y₁ - y₂ = (-7/9)(x₁ - x₂)
It may want you to find the equation in slope-intercept form (y = mx + b), and you would have to find "b". Sorry I don't quite understand what exactly you are looking for.
Can somebody help me out? Also please provide an explanation.
Answer:
38%
Step-by-step explanation:
Total: 93
Find percentage
Rain: 24
Snow: 11
24 + 11 = 35
Find what percentage of 90 35 is.
35 of 90 can be written as:
35
----
90
To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100
35 100
---- × ----
90 100
= ( 35 * 100/90) * 1/100 = 38.89/100
Therefore, the answer is 38.89%
A survey of 25 randomly selected customers found the ages shown (in years). The mean is 32.64 years and the standard deviation is 9.39 years.
a) Construct a 80% confidence interval for the mean age of all customers, assuming that the assumptions and conditions for the interval have been met.
b) How large is the margin of error?
a) What is the confidence interval?
b) What is the margin of error?
The margin of error is
Answer:
See below for answers and explanations
Step-by-step explanation:
Part A
Assuming that conditions have been met for the interval, we use the formula [tex]\displaystyle CI=\bar{x}\pm t\frac{s}{\sqrt{n}}[/tex] where [tex]\bar{x}[/tex] represents the sample mean, [tex]t[/tex] represents the critical value, [tex]s[/tex] represents the sample standard deviation, and [tex]n[/tex] is the sample size.
The critical value of [tex]t[/tex] for an 80% confidence level with degrees of freedom [tex]df=n-1=25-1=24[/tex] is equivalent to [tex]t=1.317836[/tex]
Thus, we can compute the confidence interval:
[tex]\displaystyle CI=\bar{x}\pm t\frac{s}{\sqrt{n}}\\\\CI=32.64\pm1.317836\biggr(\frac{9.39}{\sqrt{25}}\biggr)\\\\CI\approx\{30.17,35.11\}[/tex]
Therefore, we are 80% confident that the true mean age of all customers is between 30.17 and 35.11 years.
Part B
The margin of error is [tex]\displaystyle t\frac{s}{\sqrt{n}}=1.317836\biggr(\frac{9.39}{\sqrt{25}}\biggr)\approx2.47[/tex]
Which of the following statements is true of all rotations?
Answer:
21.25 m/s
Explanation:
AVERAGE SPEED=
= \frac{s1 t1+ s2t2 + s3t3}{t1 + t2 + t3}=
t1+t2+t3
s1t1+s2t2+s3t3
= \frac{20 \times 10 + 30 \times 5 + 15 \times 5}{10 + 5 + 5}=
10+5+5
20×10+30×5+15×5
= \frac{200 + 150 + 75}{20}=
20
200+150+75
= \frac{425}{20}=
20
425
= 21.25 ms=21.25ms
solve this algebra Sentence
1) A number is added to five is equal to twelve. write an algebra sentence then solve the number
Answer
Let x be that number We know x + 5 = 12 ( the number plus five equals to 12)=> x = 5-12 = 7 so, that number is 7.
explanation:
Hope this helps:)
:3
have a good day or a beautiful day:3
Keiko bought 13 pounds of sugar for $6. How many dollars did she pay per pound of sugar?
Step-by-step explanation:
13 pounds of sugar for $6.
for a single pound of sugar we need to divide everything by 13 to keep the same ratio (relationship).
1 pound cost then 6/13 = 0.461538462... ≈ $0.46
Is (2,11) a solution to the equation y = 3x - 2 ?
Answer:
No (2, 11) is not a solution.
Step-by-step explanation:
y = 3x - 2
Plug in the points:
11 = 3(2) - 2
Solve:
11 = 6 - 2
11 = 4
11 does not equal 4.
Hope this helps.
Answer:
(2,11) is not a solution
Step-by-step explanation:
Substitute the value of x and y in the equation.
y = 3x - 2
Substitute(2,11)
11= 3*2 -2
= 6 - 2
11 ≠ 4
(2,11) is not an solution of the equation
If 12 photovoltaic cells at 0.5 V each produce a total of 6 V of potential energy and carry a 1A current to your phone, what is the power output of these cells and the resistance inside your phone? P = VI and R = V/I (Show calculations and units)
Answer:
The power output is 6 W. The resistance is 6 Ω.
Step-by-step explanation:
Power output= 6V * 1 A= 6W
Resistance= 6V/1A= 6 Ω
what is its first derivative
Answer:
2ax + b + C
where C is a constant.
The radius of a semicircle is 3 kilometres. What is the semicircle's perimeter?
Answer:
In terms of Pi: [tex]3\pi + 6[/tex] km
Exact value (rounded): 15.42477 km
Approximated (3.14): 15.42 km
Step-by-step explanation:
Hello!
A semicircle's perimeter can be found using the formula: [tex]P = \pi r + 2r[/tex]
We can plug in the values to solve for the perimeter.
Solve[tex]P = \pi r + 2r[/tex][tex]P = \pi(3)+ 2(3)[/tex][tex]P = 3\pi + 6[/tex]In terms of Pi, it is [tex]3\pi + 6[/tex],
Exact value of Pi, it is 15.42477
Approximation of Pi (3.14), it is = 15.42
What ordered pair is closest to a local minimum of the function, f(x)?
A. (-1, -3)
B. (0, -2)
C. (1, 4)
D. (2, 1)
Reason:
See the screenshot below. I used GeoGebra to plot the points.
The sub group of points D, E, F form a bowl shaped region. Imagine a small parabola passing through these points. Point E is either the local min or very close to it. This is because point E is at the bottom of the bowl shape.
Seven more than a number is 15.
The equation is (Type an equation using x as the variable.)
Answer:
x + 7 = 15
Step-by-step explanation:
I hope the answer above was correct :)
Answer:
x + 7 = 15
Step-by-step explanation:
7 more is adding 7 to "a number" which is x. The sum is 15 so it shouldnt be that hard to put it all together
How many gallons of
35
% alcohol solution and
50
% alcohol solution must be mixed to get
6
gallons of
40
% alcohol solution?
Answer:
Hi,
Step-by-step explanation:
I suppose you want an integer solution.
Let's say
a the number of gallons of 35% alcohol
b the number of gallons of 50% alcohol
[tex]\dfrac{35}{100}*a+\dfrac{50}{100}*b=\dfrac{40}{100}*6\\\\35*a+50*b=240\\\\7a+10b=48\\\\b=\dfrac{48-7a}{10}\\\\a=4+10*n\\\\b=\dfrac{48-7*(4+10*n)}{10}=2-7*n\\\\As\ b\ must\ be\ a\ positive\ number \ n=0\\\\so\ b=2\ and\ a= 4[/tex]
A problem says an object's displacement is
88.8 m in a 123º direction. Which one of these
tables includes that information correctly?
The table that includes that information correctly when the problem says an object's displacement is 88.8 m is table B.
What is displacement?It should be noted that a displacement simply means the vector quantity that illustrates how far a particular place is.
In this case, the table that includes that information correctly when the problem says an object's displacement is 88.8 m is table B.
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Answer:A dude if you already know it say it to make it easier for people don't be lazy
Step-by-step explanation:
Which of the following is an example of an exponential function?
A.)f(x) = 4x3 + 2x2 – 3x + 9
B.) g(x) = log2(x)3
C.) h of x equals the quantity x squared plus 2x minus 7 end quantity divided by the quantity x plus 1
D.) p(x) = 500(1.02)x
Answer: D
Step-by-step explanation:
An example of exponential function is p(x) = 500(1.02)x Option D
Which of the following is an example of an exponential function?An exponential function is a mathematical function of the form f(x) = [tex]a * b^x[/tex], where 'a' and 'b' are constants, and 'x' is the variable. The function p(x) = [tex]500(1.02)^x[/tex] is in this form
Where 'a' is 500, 'b' is 1.02, and 'x' is the variable.
The variable 'x' is an exponent, which makes it an exponential function. Option D
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Please help me it’s for Plato on edmentum! Algebra 1 Quadratic relationships Mastery test
The equation of the function g(x) will be g(x) = (1/2) x². Then the correct option is B.
The complete question is attached below.
What is a function?Functions are found all across mathematics and are required for the creation of complex relationships.
The function f(x) is given below.
f(x) = x²
Then the function g(x) will be
g(x) = a · x²
Then the value of will be
From the graph, at x = 2, g(x) will be 2.
Then we have
2 = a · 2²
a = 1/2
Then the equation of the function g(x) will be g(x) = (1/2) x².
Then the correct option is B.
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Give a non-zero counterexample to the following statement:
Every multiple of 10 is also a multiple of 30.
Answer:
20 or 40 or 50
(there are many others)
Step-by-step explanation:
A counterexample is an example that shows the statement is not true. The statement in this question is that if a number is a multiple of 10 (10, 20, 30, 40, 50, 60...) then it is a multiple of 30. Some numbers are, like 60 and 90, but not all numbers. So for example (counterexample) 20 is a multiple of 10 but NOT a multiple of 30.
40 is a multiple of 10, but NOT a multople of 30.
50 is a multiple of 10, but NOT a multiple of 30.
can Someone helps me
Answer:
10.63
Step-by-step explanation:
To find the Hypotenuse we need to use Pythagorean Thereom. So plugging in the formula the square root of A squared plus B squared you get 10.63
Answer:
Step-by-step explanation:
To solve the triangle means to find ALL unknown elements of Δ ( sides and angles )
JH² = 8² + 7² = 113
JH = √113 ≈ 10.63 m
m∠H = β
[tex]\frac{8}{7}[/tex] = tan β ; β = arctan [tex]\frac{8}{7}[/tex] = [tex]tan^{-1}[/tex] [tex]\frac{8}{7}[/tex] ≈ 48.814°
m∠H ≈ 49 °
m∠J = 90° - 49° = 41 °
7th grade math
(Look at photo!)
Easy math
Answer:
he will buy 4 tickets
Step-by-step explanation:
firts u have to mutilpy 7.50 by a number and start at 1 and go up till u get 30
hope this helps:)!!
What is the location of the image of P(−8, 1) after a counterclockwise rotation of 90° about (−2, 6) ?
Answer:
(3, 0)
Step-by-step explanation:
Given:
Image: P = (-8, 1)Center of rotation: (-2, 6)Rotation rule for -90°: (x, y) → (y, -x)
As the center of rotation is not the origin, we cannot simply apply the above rule.
To rotate an image around a point other than the origin:
1. Subtract each point of the image from the point of rotation:
⇒ Point of rotation - point of image
⇒ (-2, 6) - P = (-2, 6) - (-8, 1)
= (6, 5)
2. Rotate this about the origin by applying the rotation rule:
⇒ (x, y) → (y, -x)
⇒ (6, 5) → (5, -6)
Add the point of rotation to each rotated point of the image:
⇒ (5, -6) + (-2, 6) = (3, 0)
Therefore, the location of the image of P (-8, 1) after a counterclockwise rotation of 90° about (-2, 6) is (3, 0).
Two exterior angles of a triangle measure 135° and 100°. What are the measures of the interior angles of the triangle?
A.
45°, 65°, 80°
B.
45°, 65°, 70°
C.
45°, 55°, 80°
D.
55°, 75°, 50°
E.
80°, 50°, 50°
Answer:
its it a
Step-by-step explanation:
Given that 24w = 14ten .Find the unknown base
Answer:
w = 5
Step-by-step explanation:
24w = (14)10
2w + 4 = 10 + 4
2w = 10
w = 5
fast!!!!!!! help me
hope you can understand
6x¹⁸ divided by 9x⁶
please answer fast thanks!
Answer:
[tex]\frac{2}{3}x^{12}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{6x^{18}}{9x^6}=\frac{6}{9}*\frac{x^{18}}{x^6}=\frac{2}{3}*x^{18-6}=\frac{2}{3}x^{12}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{6x^{18}}{9x^6}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{2}{3}x^{18-6}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{2}{3}x^{12}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{2x^{12}}{3}[/tex]
Elaina Kicks A Soccer Ball With An Initial Velocity Of 28 feet per second at an angle of 58 to the horizon
Answer:
Hi,
Answer B
Step-by-step explanation:
after 1.484 s the ball hit the ground à 22.019 feet
yes the ball will be at a height of 2.93506334 feet when time is 1.348 s and height is 20 feet
no the max height happens at 11.0 has no thing to do with hitting the grat 2.937 s the ball is at -68.2754 feet
ound
Please help
Use absolute value to find the distance between 3 and -3 on a number line.
Enter your answer in the box.
Answer:
6
Step-by-step explanation:
A bacteria population has been doubling each day for the past 5 days. It is currently
100000. What was the population 5 days ago?