Answers
and of course as you already know the volume of the prism is just the area of the base times the length, namely A * 20.
Related Questions
The solution to 15 a2 − 1 = 5 2a − 2 is a = . The extraneous solution is a = .
Answers
15 / (a ^ 2 - 1) = 5 / (2a - 2)
Rewriting we have:
3 / (a ^ 2 - 1) = 1/2 (a - 1)
6 / (a ^ 2 - 1) = 1 / (a - 1)
6 (a - 1) = (a ^ 2 - 1)
6 (a - 1) = (a-1) (a + 1)
(a + 1) = 6
a = 6-1
a = 5
Answer:
The solution is:
a = 5
Answer:
5 and 1
1 is extraneous
Step-by-step explanation:
Q1 :Let f(x)=2x^2−8
The quadratic function g(x) is f(x) translated 2 units down
What is the equation for g(x)
Q2 Let f(x)=[tex] \frac{3}{4} [/tex]x2−1.
The function g(x) is a vertical stretch of f(x) by a factor of 8.
What is the equation of g(x)?
Q3 The graph of the function g(x) is a transformation of the parent function f(x)=x2 .
Which equation describes the function g?
(refer to picture attached)
A. g(x)=x2+2
B. g(x)=(x−2)2
C. g(x)=(x+2)2
D. g(x)=x2−2
Answers
[tex]f(x) = 2 x^{2} -8 \\[/tex]
g(x) is the translation of f(x) 2 units down.
Vertical translation can be expressed as addition or subtraction of a number from the function value. Subtraction indicates that the function is translated down. So, translation of f(x) by 2 units down can be expressed as:
g(x) = f(x) - 2
Using the value of f(x), we can write:
[tex]g(x)= 2x^{2} -8-2 \\ \\ g(x)=2 x^{2} -10[/tex]
Question # 2
[tex]f(x)= \frac{3}{4} x^{2} -1 [/tex]
A function can be vertically stretched by multiplying it with a number having magnitude greater than 1. f(x) is to be stretched by a factor of 8 to get g(x), so we can write:
g(x) = 8 * f(x)
Using the value of f(x) we can write:
[tex]g(x)=8* (\frac{3}{4} x^{2} -1) \\ \\ g(x)=6 x^{2} -8[/tex]
What is the radius of convergence of the maclaurin series (2x)/(1+x^2)?
Answers
1. You have to find the radius of convergence of the following Maclaurin series:
[tex](2x)/(1+ x^{2} ) [/tex]
2. Let's take the denominator and find the roots:
[tex]1+ x^{2} =0[/tex]
[tex] x^{2} =-1 \\ x= \sqrt{-1} \\ x1=i \\ x2=-i[/tex]
3. The roots are [tex]x1=i \\ x2=-i[/tex] and the distance from the origin is [tex]1[/tex].
Therefore, the answer is: [tex]1[/tex]
The radius of convergence of the maclaurin series is 1 unit.
It is given that maclaurin series [tex]\rm \frac{2x}{(1+x^2)}[/tex]
It is required to find the radius of the convergence of the maclaurin series.
What is maclaurin series?It is defined as the expansion of a function that provide the approximation of the given function at any point of function.
We have:
[tex]\rm \frac{2x}{(1+x^2)}[/tex]
To find the radius of convergence of the maclaurin series, we must find the roots of denominator hence:
[tex]\rm 1+x^2= 0\\\\\rm x^2 = -1\\\\[/tex]
From the complex number: the roots are imaginary:
[tex]\rm x_1 = i\\x_2 = -i[/tex]
i is the iota
and the distance from the origin (0,0) is 1.
Thus, the radius of convergence of the maclaurin series is 1 unit.
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Daniela is a stain glass artist; she created the window below for her living room. What is
the area of the window she created?
Answers
We know the diameter d = 12 ft.
The area of a (complete) circle is given by the formula:
A = π × r²
The radius can be found by halving the diameter:
r = d ÷ 2
= 12 ÷ 2
= 6 ft
Therefore the area of the circle will be:
A = π × r²
= 3.14 × 6²
= 3.14 × 36
= 113.04 ft²
And the area of the semi-circle:
A = 113.04 ÷ 2
= 56.52 ft²
Hence, the area of the window will be 56.52 ft².
Write the function associated with the graph below
Answers
Since the value of the function is decreasing exponentially as x decreases ,
The function is of the form [tex] y=ae^{bx}+c,b>0 [/tex].
Since the curve passes through (0,6),
[tex] 6=ae^{0}+c,6=a+c [/tex],
Since the curve passes through (-1,0),
[tex] 0=ae^{-b}+c [/tex].
Since [tex] y=-3 [/tex] is a horizontal asymptote,
[tex] -3=ae^{-\infty}+c,c=-3 [/tex]
From the above 3 equations,
[tex] c=-3,a=9,9e^{-b}=3,e^b=3,b=\ln 3 [/tex].
Therefore, the required function is
[tex] y=9e^{\ln 3 x}-3\\
y=9*3^{ x}-3 [/tex].
It can be verified that the curve [tex] y=9*3^{ x}-3 [/tex] passes through [tex] (-2,-2) [/tex].
22 POINTS, NEED URGENT HELP
Write the equation of each circle:
1. R with center R(-1, 8) and radius 5
2. K with center K(4,0) and that passes through (2,0)
Answers
(x+1)^2 + (y-8)^2 = 5^2 (answer)
If you add the lengths of the focal radii of an ellipse, what other value will you produce?
2a
2b
2c
The eccentricity
Answers
Equation of an ellipse
→having center (0,0) , vertex ([tex](\pm a ,0)[/tex] and covertex [tex](\pm b ,0)[/tex] and focus [tex](\pm c ,0)[/tex] is given by:
[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2}=1[/tex]
As definition of an ellipse is that locus of all the points in a plane such that it's distance from two fixed points called focii remains constant.
Consider two points (a,0) and (-a,0) on Horizontal axis of an ellipse:
Distance from (a,0) to (c,0) is = a-c = [tex]F_{1}[/tex]
Distance from (-a,0) to (c,0) is = a + c = [tex]F_{2}[/tex]
[tex]F_{1} + F_{2} =[/tex] a -c + a +c
= a + a
= 2 a →(Option A )
solve for z (attachment)
Answers
z / 4 = (16 + 4)/z
z^2 / 4 = 20
z^2 = 80
z = 4√5
Therefore the answer to this question is z = 4√5.
[tex]\Delta ABD\ and\ \Delta BCD\ are\ similar,\ therefore:\\\\\dfrac{y}{4}=\dfrac{16}{y}\ \ \ \ |cross\ multiply\\\\y\cdot y=4\cdot16\\\\y^2=64\to y=\sqrt{64}\to y=8[/tex]
Use Pythagorean theory:
[tex]z^2=4^2+8^2\\\\z^2=16+64\\\\z^2=80\to z=\sqrt{80}\\\\z=\sqrt{16\cdot5}\\\\z=\sqrt{16}\cdot\sqrt5\\\\\boxed{z=4\sqrt5}[/tex]
What is the trigonometric ratio for sin C?
Answers
A typist charges $0.90 a page and averages 45 pages per work day. If she works 3 days a week, how much does she earn in a week?
Answers
Final answer:
The typist earns $121.50 per week by multiplying the charge per page ($0.90) with the daily page average (45 pages) and the number of days worked per week (3 days).
Explanation:
The question asks us to calculate the weekly earnings of a typist who charges $0.90 per page and averages 45 pages per day, working 3 days a week. To find the total weekly earnings, we can multiply the number of pages typed per day by the charge per page, and then multiply that result by the number of days worked in a week.
Multiply the number of pages (45) by the charge per page ($0.90): 45 pages × $0.90 = $40.50 per day.
Multiply the daily earnings by the number of days worked in a week (3): $40.50 × 3 days = $121.50 per week.
Therefore, the typist earns $121.50 per week.
A rectangular plot of land that contains 1500 square meters will be fenced and divided into two equal portions by an additional fence parallel to two sides. find the dimensions of the land that require the least amount of fencing.
Answers
Let w= the width
Two sections are required, hence 2w of fence required
2x+3w=500
this can be written as:
3w=1500-2x
w=(1500-2x)/3
Area=x*w
replacing w with our expression:
A=x(1500-2x)/3
A=(500x-2x^2)/3
This is a quadratic equation, if we find the axis of symmetry we will know what value of x gives maximum area:
Axis of symmetry: x=-b/2a
From our equation we get:
a=-2/3; b=1500/3
thus
x=(1500/3)/(-(-2/3))
x=750
thus the maximum area will be given by length of 750
Which of the following gives all of the coefficients of the algebraic expression -2x^2 +17-15x+7xy
Answers
The coefficients of the algebraic expression -2x² + 17 -15x + 7xy are -2, 17, -15 and 7
How to determine the coefficient of the expression
From the question, we have the following parameters that can be used in our computation:
-2x² + 17 -15x + 7xy
Consider an expression represented as
Ax
Where A is a constant and x is the variable
The coefficient of the expression is A
Using the above as a guide, we have the following:
The coefficients of the algebraic expression are -2, 17, -15 and 7
Question
Which of the following gives all of the coefficients of the algebraic expression -2x^2 +17-15x+7xy
a. 2, 17, 15 and 7
b. -2, 17, -15 and 7
c. -2, -17, -15 and 7
d. -2, -17, 15 and 7
After a 40% discount an item costs $360. what is the original cost
Answers
So...
OP = 360 / 100 - 0.40
OP = 360 / 0.60
OP = 600
The original price is $600.
To check, do 600 - (600 * 0.40) in a calculator. You get 600 - 240 = 360, the discounted cost.
Answer:
It is $600
Step-by-step explanation:
hope it helps, murdle
how do you convert cos(x) into sin(x) and tan(x) ?
Answers
tan x
cos x = ---------- In other words, rewrite "cos x" in an expression as
tan x
-----------
sin x
Park rangers notice a negative correlation between the number of available campsites in a park and the amount of litter on the park's trails. Which variable is most likely the lurking variable that explains the correlation? Question 3 options: age of trees in the park number of eagles spotted in the park number of visitors to the park density of trees in the park
Answers
We have been given that a park rangers notice a negative correlation between the number of available campsites in a park and the amount of litter on the park's trails.
We need to figure out the lurking variable that describes the given correlation.
Out of the given options, the most appropriate variable that describes that negative correlation between number of available campsites in the part and the amount of litter on the park's trails is number of visitors to the park.
The reason, why number of visitors to the park is the lurking variable for the given negative correlation, is that more the number of visitors, more the litter they produce and consequently, lesser the number of available campsites.
What is the equation of the line that passes through the points (0, -4) and (2, 8)?
A. y = 6x - 4
B. y = 6x + 4
C. y = 4x + 6
D. y = -4x + 6
Answers
m = Y₂ - Y₁ / X₂ - X₁
m = 8 - (- 4) / 2 - 0
m = 12 / 2
m = 6
So now your equation is y = 6x + b. This eliminates options C and D. Plug in any of your ordered pairs to find b. I picked the first one.
- 4 = 6(0) + b
- 4 = 0 + b
- 4 = b
Your equation is y = 6x - 4.
The resonance frequency f in an electronic circuit containing inductance L and capacitance C in series is given by f=1/2π√LC. Determine the inductance L in an electric circuit if the resonance frequency is 6.2 and the capacitance is 0.0001. Round your answer to the nearest tenth.
10270.1
6.6
256.8
0
Answers
f = 1 / (2π√LC)
Clearing L we have:
√LC = 1 / (2πf)
LC = (1 / (2πf)) ^ 2
L = (1 / C) * (1 / (2πf)) ^ 2
Substituting values:
L = (1 / 0.0001) * (1 / (2 * 3.14 * 6.2)) ^ 2
L = 6.596253438
Round to the nearest tenth:
L = 6.6
Answer:
L = 6.6
f = 1 / (2π√LC)
To find L
√LC = 1 / (2πf)
LC = (1 / (2πf)) ^ 2
L = (1 / C) * (1 / (2πf)) ^ 2
Substitute the values:
L = (1 / 0.0001) * (1 / (2 * 3.14 * 6.2)) ^ 2
L = 6.596253438
L = 6.6
So the Answer is this:
L = 6.6
Which system of inequalities is represented by the graph
Answers
y = x
y = -x
We then have to evaluate points that belong to the shaded region:
For (0, 1) we have:
1> = 0
1> = - 0
We observe that both equalities are fulfilled, therefore, we have that the inequalities are:
y> = x
y> = - x
Answer:
y> = x
y> = - x
option D
Rico saved $30 to buy office supplies. He needed a binder that cost $9.99 , including tax,and three pens that cost $1.99 each,including tax. How much money will Rico have left after he buys the pens and the binder?
Answers
What is the solution to the linear equation ? 2/5+p=4/5+3/5p
Answers
Answer:
p=1
Step-by-step explanation:
2/5+p=4/5+3/5p
[tex]\frac{2}{5} +p= \frac{4}{5} +\frac{3}{5} p[/tex]
p or p/1 are same
LCD is 5, multiply 5 with each term. the equation becomes
[tex]\frac{2}{5} \cdot 5+p \cdot 5= \frac{4}{5} \cdot 5 +\frac{3}{5}p \cdot 5[/tex]
[tex]2+5p = 4 +3p[/tex]
Subtract 3p from both sides
[tex]2+2p = 4[/tex]
Subtract 2 on both sides
[tex]2p= 2[/tex]
Divide by 2 on both sides
p= 1
So the value of p =1 for the given equation
PLEASE ANSWER + BRAINLIEST!!!
What is the value of 3x^2 - 5xy + 5y^2 for x = -6 and y = 2?
A. -68
B. -4
C. 188
D. 208
Answers
Simplifying all the numbers, it's 3(36) + 30(2) + 5(4), and then 108+60+20. Going along, you get 188
Complete the equation of the line through (-8,8) and (1,-10). Use exact numbers.
Answers
y = mx + b
-10 = m(1) + b
m + b = -10
b = -10 - m
Now that we have a value for b, we can plug this into the other equation:
8 = m(-8) + b
8 = -8m + (-10 - m)
8 = -9m -10
18 = -9m
m = -2
Now that we know what m is equal to, we can plug this into our first equation to get an answer for b:
b = -10 - m
b = -10 -(-2)
b = -10 + 2
b = -8
Our final equation is y = -2x - 8
The equation of the line through (-8,8) and (1,-10) is y = -2x - 8
Using the slope intercept form equation.
y = mx + b
where
m = slope
b = y-intercept
Therefore,
(-8,8) (1,-10)
m = -10 - 8 / 1 + 8 = - 18 / 9 = -2
Therefore,
let's find b as follows:
(1, -10)
y = -2x + b
-10 = -2(1) + b
b = -10 + 2
b= -8
Therefore,
y = -2x - 8
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Find the amount in a continuously compiunded account for the following condition. Principal, $4000; Annual interest rate, 5.1%; time, 2 years
Answers
Using the given principal of $4000, an annual interest of 5.1%, and a time period of 2 years, the amount in a continuously compounded account will be approximately $4483.48 using the formula A = P*e^(rt).
Explanation:In this question, we are asked to find the amount in a continuously compounded account. The formula to calculate this is A = P*e^(rt), where A is the amount, P is the principal, r is the rate, t is the time, and e is the base of the natural logarithm, approximately equal to 2.71828.
In this case, P = $4000, r = 0.051 (5.1% expressed as a decimal), and t = 2.
Substituting these values into the formula, we get: A = 4000 * e^(0.051*2). Using a calculator, we can find this to be approximately $4483.48.
So, after 2 years with an annual interest rate of 5.1%, compounded continuously, the account will contain about $4483.48.
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A. (-3,-5)
B.( -2,-2)
C. (4,9)
D.(13,5)
Answers
The appropriate choice is ...
D. (13, 5)
Express answer in exact form.
Find the area of one segment formed by a square with sides of 6" inscribed in a circle.
(Hint: use the ratio of 1:1:√2 to find the radius of the circle.)
Answers
Answer:
A = { 9/2 π - 9 } in^2
Step-by-step explanation:
I just did this
Hope this helps !
To find the area of the segment, subtract the area of the triangle from the area of the sector.
Explanation:To find the area of one segment formed by a square with sides of 6 inches inscribed in a circle, we need to find the area of the sector formed by the circle and subtract the area of the triangle formed by the diagonal of the square.
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For the function f(x) = x2, what effect will multiplying f(x) by 1/2 have on the graph?
Answers
f (x) = x2
We apply the following transformation:
Vertical expansions and compressions:
To graph y = a * f (x)
If 0 <a <1, the graph of y = f (x) is compressed vertically by a factor a. (Shrinks)
We have then:
f (x) = (1/2) * x2
Answer:
is compressed vertically by a factor 1/2
20 points!
Looking at circle O, ∠BOC is a(n)
Please contact your teacher immediately if you do not see the image.
Question options:
minor angle
central angle
inscribed angle
major angle
Answers
A central angle is one that goes through the center of a circle. It's two ends are the endpoints of the chord BC which you should draw on your sheet.
If you do, we can talk about the other answers.
An inscribed angle is one that has it's vertex on the circumference. <BAC is an example. A is the vertex.
A major angle is the part above BC that goes around the circle such that the angle is larger than 180 degrees. It is described above by BAC going clockwise. It is associated with the arc of a circle.
A minor angle is the angle not included in the major angle. In this case it is the angle formed by sweeping around from B to C underneath the chord BC
The square root of 53 lies between which two numbers?
Answers
There are a couple ways to find this. You could...
A. Use a calculator and simply find the square root of 53 (7.280...) OR
B. You could square each number (1^2, 2^2, 3^2...) until you get the closest 2 numbers (one less than and one greater than) to 53 (7^2 = 49) and (8^2 = 64).
I hope this helps!
Anyone know this geometry question? Will give brainiest
Answers
This is because of the following rule:
When two lines are parallel, which is the occasion with AB and CD, then the corners in which the intecepting parallel lines (AC and BD) stand must be the same. So corner 6 is equivalent to corner 3, corner 1 and corner 5. Corner 2 and corner 4 are equivalent too.
The Candle Emporium is pouring cylindrical candles. Each candle has a radius of 5 inches and a height of 18 inches. Which formula represents the correct way to find the volume of a candle?
a. Volume= 5x18
b. Volume= pi (5) (18)
c. Volume= pi (18)squared (5)
d. Volume= pi (5)squared (18)
Answers
The formula for finding the volume of a cylinder is [tex]V = \pi r ^{2}h[/tex]. The answer choice that matches this is answer choice D. Hope I helped! :3
Answer:
Option D is correct.
Step-by-step explanation:
We are given,
Height of the candles, h = 18 inches
Radius of the candles, r = 5 inches
Candles are in shape of cylinder.
We have to find correct representation of volume of candle.
Volume of cylinder = [tex]\pi r^2h[/tex]
Volume of candle = ]tex]\pi (5)^2\times18[/tex]
Therefore, Option D is correct.