a...cause she's having trouble concentrating,for her to work she needs to tell her realtor she can only receive text messages it enables her to know the process of the house hunt
f (x) = 3r + 6. Find the inverse of f(x).
Answer:
The inverse is 1/3x -2
Step-by-step explanation:
f (x) = 3x + 6
y = 3x+6
Exchange x and y
x = 3y+6
Subtract 6 from each side
x-6 = 3y+6-6
x-6 = 3y
Divide by 3
1/3x - 6/3 = y
1/3x -2 = y
The inverse is 1/3x -2
If p-1/p=4,find the value of P2+1/p2
Answer:
18
Step-by-step explanation:
(p-1/p)² = 4²
p² + 1/p² - 2(p)(1/p) = 16
p²+1/p² -2 =16
so, p²+1/p² = 16+2
= 18
A bag contains 8 red balls and 3 white balls. Two balls are drawn without replacement. (Enter your probabilities as fractions.) (a) What is the probability that the second ball is white, given that the first ball is red
Answer:
12/55
Step-by-step explanation:
Probability is the ratio of the number of possible outcomes to the number of total outcomes.
Given that the bag contains 8 red balls and 3 white balls, the probability of picking a red ball
p(r) = 8/(8+3) = 8/11
Probability of picking a white ball
= 3/11
when a red ball is picked first, the total number of balls reduces to 10 hence the probability that the second ball is white, given that the first ball is red
=8/11 * 3/10
= 24/110
= 12/55
2.
The reflector of a satellite dish is in the shape of a parabola with a diameter of 4 feet and a depth of 2 feet. To get the maximum reception we need to place the antenna at the focus.
a. Write the equation of the parabola of the cross section of the dish, placing the vertex of the parabola at the origin. Convert the equation into standard form, if necessary. What is the defining feature of the equation that tells us it is a parabola?
b. Describe the graph of the parabola. Find the vertex, directrix, and focus.
c. Use the endpoints of the latus rectum to find the focal width.
d. How far above the vertex should the receiving antenna be placed?
Answer:
Step-by-step explanation:
Assume the dish opens upwards. The cross-section through the vertex is a parabola. You know three points on the parabola: (0,0), (2,2), and (-2,2). Plug the points into y = ax² + bx + c to get a system of three equations where a=0.5, b=c=0.
Equation of parabola: y = 0.5x²
:::::
Vertex (0,0)
Focal length = 1/(4×0.5) = 0.5
Focus (0,0+0.5) = (0, 0.5)
Directrix y = 0-0.5 = -0.5
:::::
At endpoints of latus rectum, y = 0.5
x = ±√0.5 = ±√2/2
Focal width = 2×√2/2 = √2
:::::
Place antenna at focus, (9,2)
One month Kaitlin rented 2 movies and 5 video games for total of $34. The next month she rented 8 movies and 3 video games for total of $51. Find the rental cost of each movie and each video game.
Answer:
A movie is $4.50 and a video game is $5
Step-by-step explanation:
Create a system of equations where m is the cost of each movie and v is the cost of each video game:
2m + 5v = 34
8m + 3v = 51
Solve by elimination by multiplying the top equation by -4:
-8m - 20v = -136
8m + 3v = 51
Add these together and solve for v:
-17v = -85
v = 5
So, a video game is $5. Plug in 5 as v into one of the equations, and solve for m:
2m + 5v = 34
2m + 5(5) = 34
2m + 25 = 34
2m = 9
m = 4.5
A movie is $4.50 and a video game is $5
A cyclist rides his bike at a speed of 15 miles per hour. What is this speed in kilometers per hour? How many kilometers will the cyclist travel in 4 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
Answer:
Step-by-step explanation:
Speed = (15 mi)/hr × (1.6 km)/mi = (24 km)/hr
:::::
(4 hr) × (24 km)/hr = 96 km
What is the slope of a relation with ordered pairs of (-5, 3) and (4.1).
9/2
2/9
-9/2
-2/9
2
-2
Graph the function g(x) = 3^x + 3 and give its domain and range using interval notation
The question is an illustration of a function using graphs. When a function is plotted on a graph, the x-axis represents the domain, while the y-axis represents the range of the function.
The domain and the range of the given function are:
Domain: [tex](-\infty,\infty)[/tex]
Range: [tex](3,\infty)[/tex]
From the question, we have the function to be:
[tex]g(x) = 3^x + 3[/tex]
First, we plot the graph of g(x)
To do this, we first generate values for x and g(x). The table is generated as follows:
[tex]x = 0 \to g(0) = 3^0 + 3 = 4[/tex]
[tex]x = 1 \to g(1) = 3^1 + 3 = 6[/tex]
[tex]x = 2 \to g(2) = 3^2 + 3 = 12[/tex]
[tex]x = 3 \to g(3) = 3^3 + 3 = 30[/tex]
[tex]x = 4 \to g(4) = 3^4 + 3 = 84[/tex]
In a tabular form, we have the following pair of values
[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ g(x) & {4} & {6} & {12} & {30} & {84} \ \end{array}[/tex]
See attachment for graph
From the attached graph of g(x), we can observe that the curve stretches through the x-axis and there are no visible endpoints.
This means that the curve starts from - infinity to +infinity
Hence, the domain is: [tex](-\infty,\infty)[/tex]
Also, from the same graph, we can observe that the curve of g(x) starts at y = 3 on the y-axis and the curve faces upward direction.
This means that the curve of g(x) is greater than 3 on the y-axis.
Hence, the range is: [tex](3,\infty)[/tex]
Read more at:
https://brainly.com/question/20207421
What is the length of AC?
a. 3ft
b. 4ft
c. 18ft
d. 12ft
plz hurry
d. 12ft
Answer:
Solution given:
∆ABC is similar to∆MBN
since their corresponding side are proportional.
so
AB/MB=AC/MN
[since AM=BM=4ft
AB=AM+BM=4+4=8ft]
8/4=AC/6
doing crisscrossed multiplication
2*6=AC
AC=12ft
Suppose (-13,2) is a point on the graph of y=f(x). What is a point that will be on the graph of y=9f(x)-5
9514 1404 393
Answer:
(x, y') = (-13, 13)
Step-by-step explanation:
At the given value of x, f(x) = 2. Then 9f(x)-5 = 9(2) -5 = 13.
The point on the scaled, translated graph will be ...
(x, y') = (-13, 13)
_____
The graph shows a function f(x) with a distinct feature (vertex) at (-13, 2). It also shows where that distinct feature moves to when the function is scaled and translated.
A rectangle has a length of 27 inches less than 4 times it’s width. If the area of the rectangle is 2790 square inches, find the length of the rectangle
Let the width = x
The length would be 4x-27
Area = length x width
2790 = (4x-27) * x
Expand:
2790 = 4x^2 - 27x
Subtract 2790 from both sides:
4x^2 - 27x - 2790 = 0
Use the quadratic formula to solve for the positive value of x:
X = -(-27) + sqrt(-27^2 -4*4(-2790)) /(2*4)
X = 30
Now replace x with 30 in the lengths:
Width = x = 30 inches
Length = 4x -27 = 4(30) -27 = 120-27 = 93 inches
According to Fidelity Investment Vision Magazine, the average weekly allowance of children varies directly as their grade level. In a recent year, the average allowance of a 9th-grade student was 9.66 dollars per week. What was the average weekly allowance of a 5 th-grade student?
The average weekly allowance of a 5th grade student as calculated using direct variation with the information provided by Fidelity Investment Vision Magazine is 5.367 dollars per week.
The question given is a direct variation problem:
Let:
• Average weekly allowance = [tex]a[/tex]
• Grade level = [tex]g[/tex]
If Average weekly allowance varies directly as grade level , then , then the direct variation between the variables can be expressed as :
[tex]a = k * g[/tex]
Where , [tex]k[/tex] = constant of proportionality
We can obtain the value of k from the given values of a and g
[tex]9.66 = k * 9\\9.66 = 9k\\k = 9.66/9[/tex]
Our equation becomes:
[tex]a = (9.66/9) * g[/tex]
[tex]a = (9.66/9) * 5\\a = 5.367[/tex] (rounded to 3 decimal places)
Hence, using proportional relationship, the average weekly allowance for a 5th grade student is [tex]5.367[/tex] per week
Learn more about direct variation here:
https://brainly.com/question/17257139
(7/8*9)*3/4*(9/3*5)=
Answer:
2835/32 or 88 19/32Step-by-step explanation:
(7/8 × 9) × 3/4 × (9/3 × 5)= 63/8 × 3/4 × (3 × 5)= 63/8 × 3/4 × 15= 2835/32 or 88 19/32[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
Answer:
[tex]88 \frac{19}{32} [/tex]
Slope - 9; through (6,-9)
Answer:
Y= -9x+45
y = -9 X + b
-9 = -9(6) + b
-9 = -54 + b
b=45
Step-by-step explanation:
if x=2 and y=3. What is x*y/xy+x*y
Answer
its uhhhhh i dont know
Step-by-step explanation:
Change to cylindrical coordinates. 3∫−3 9-x^2∫0 9−x^2-y^2∫x^2+y^2 dz dy dx
I think the given integral reads
[tex]\displaystyle \int_{-3}^3 \int_0^{9-x^2} \int_{x^2+y^2}^{9-x^2-y^2} \mathrm dz\,\mathrm dy\,\mathrm dx[/tex]
In cylindrical coordinates, we take
x ² + y ² = r ²
x = r cos(θ)
y = r sin(θ)
and leave z alone. The volume element becomes
dV = dx dy dz = r dr dθ dz
Then the integral in cylindrical coordinates is
[tex]\displaystyle \boxed{\int_0^\pi \int_0^{(\sqrt{35\cos^2(\theta)+1}-\sin(\theta))/(2\cos^2(\theta))} \int_{r^2}^{9-r^2} r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta}[/tex]
To arrive at this integral, first look at the "shadow" of the integration region in the x-y plane. It's the set
{(x, y) : -3 ≤ x ≤ 3 and 0 ≤ y ≤ 9 - x ²}
which is the area between a paraboloid and the x-axis in the upper half of the plane. So right away, you know θ will fall in the first two quadrants, so that 0 ≤ θ ≤ π.
Next, r describes the distance from the origin to the parabola y = 9 - x ². In cylindrical coordinates, this equation changes to
r sin(θ) = 9 - (r cos(θ))²
You can solve this explicitly for r as a function of θ :
r sin(θ) = 9 - r ² cos²(θ)
r ² cos²(θ) + r sin(θ) = 9
r ² + r sin(θ)/cos²(θ) = 9/cos²(θ)
(r + sin(θ)/(2 cos²(θ)))² = 9/cos²(θ) + sin²(θ)/(4 cos⁴(θ))
(r + sin(θ)/(2 cos²(θ)))² = (36 cos²(θ) + sin²(θ))/(4 cos⁴(θ))
(r + sin(θ)/(2 cos²(θ)))² = (35 cos²(θ) + 1)/(4 cos⁴(θ))
r + sin(θ)/(2 cos²(θ)) = √[(35 cos²(θ) + 1)/(4 cos⁴(θ))]
r = √[(35 cos²(θ) + 1)/(4 cos⁴(θ))] - sin(θ)/(2 cos²(θ))
Then r ranges from 0 to this upper limit.
Lastly, the limits for z can be converted immediately since there's no underlying dependence on r or θ.
The expression above is a bit complicated, so I wonder if you are missing some square roots in the given integral... Perhaps you meant
[tex]\displaystyle \int_{-3}^3 \int_0^{\sqrt{9-x^2}} \int_{x^2+y^2}^{9-x^2-y^2} \mathrm dz\,\mathrm dy\,\mathrm dx[/tex]
or
[tex]\displaystyle \int_{-3}^3 \int_0^{\sqrt{9-x^2}} \int_{x^2+y^2}^{\sqrt{9-x^2-y^2}} \mathrm dz\,\mathrm dy\,\mathrm dx[/tex]
For either of these, the "shadow" in the x-y plane is a semicircle of radius 3, so the only difference is that the upper limit on r in either integral would be r = 3. The limits for z would essentially stay the same. So you'd have either
[tex]\displaystyle \int_0^\pi \int_0^3 \int_{r^2}^{9-r^2} r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]
or
[tex]\displaystyle \int_0^\pi \int_0^3 \int_{r^2}^{\sqrt{9-r^2}} r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]
The Richter scale measures the magnitude, M, of an earthquake as a function of its intensity, I, and the intensity of a reference earthquake, .
Which equation calculates the magnitude of an earthquake with an intensity 10,000 times that of the reference earthquake?
Answer:
Option B. M = Log 10000
Step-by-step explanation:
From the question given above, we were told that the intensity (I) is 10000 times that of the reference earthquake (I₀).
Thus, we can obtain the magnitude (M) of the earthquake as follow:
Let the reference earthquake (I₀) = A
Then, the intensity (I) = 10000 × A
M = Log(I/I₀)
M = Log(10000A / A)
M = Log 10000
Thus, option B gives the right answer to the question.
I need to solve for x and z if you could explain as well. Thank you
Answer:
x = 6
z = 60
Step-by-step explanation:
Solve for x
(6x + 84) = 120
- 84 -84
6x = 36
6x/6 = 36/6
x = 6
Then solve for z
120 + z = 180
-120 -120
z = 60
Please help!!! what is x: |6n+7|=8
Answer:
-5/2, 1/6
Step-by-step explanation:
|6n+7|=8
6n+7=8
n=1/6
6n+7=-8
n=-5/2
Answer:
[tex]n=-\frac{5}{2}[/tex] and [tex]n=\frac{1}{6}[/tex]
Step-by-step explanation:
There is no x variable present in the question, but if you are asking for the value of n, I can help with that.
The absolute value function always results in a positive number, so that means 6n+7 can equal 8 or negative 8, and the absolute value function takes care of the rest. First, we will solve for 6n + 7 equaling 8.
[tex]6n+7=8[/tex]
Subtracting 7 from both sides gets us
[tex]6n=1[/tex]
Dividing by 6 from both sides is equal to
[tex]n=\frac{1}{6}[/tex]
Now we will solve for 6n + 7 equaling negative 8.
[tex]6n+7=-8[/tex]
Subtracting 7 from both sides is equal to
[tex]6n=-15[/tex]
Dividing by 6 from both sides gets us
[tex]n=-\frac{15}{6}[/tex]
Simplifying, we have
[tex]n=-\frac{5}{2}[/tex]
6. Find the missing side. Round to the nearest tenth.
Answer:
31.9617 rounded to 32
Step-by-step explanation:
set up is sin24=13/x
Suppose a young sedentary woman wanted to lose 30 pounds of body fat in a period of 20 weeks. She now weighs 160 pounds and her activity level is such so she needs 15 Calories per pound of body weight to maintain her weight. Calculate the number of Calories she may consume daily in order to lose the 30 pounds by diet only. 1,000 1,250 1,400 1,650 1,900
Answer:
The answer is "1900"
Step-by-step explanation:
It takes 500 fewer calories per day for her to lose 1 lb of weight every week.
[tex]\to (15 \times 160)-500 =(2400)-500 =2400-500=1900[/tex]
QUESTION 2
A board is 86 cm. in lenght and must be cut so that one piece is 20 cm. longer than the other piece
Find the lenght of each piece.
A26 cm and 60 cm
b. 33 cm and 53 cm
C 30 cm and 56 cm
d. 70 cm and 16 cm
One piece will be length x and the other piece will be 20 cm longer, so it will be x + 20 cm long.
Added together the length of these two boards will equal 86 cm. So you can write an equation:
x + (x + 20) = 86
Remove the parentheses and add the two x's together to get:
2x + 20 = 86
Subtract 20 from both sides:
2x = 66
Divide both sides by 2 and you have:
x = 33
The short piece is 33 cm and the other piece is 20 cm longer or 33 + 20 = 53 cm.
Simplify the given expression.
Answer:
8x-21
----------------------
(2x-7)(2x+7)
Step-by-step explanation:
7 4
----------- + ------------
4x^2 -49 2x+7
Factor ( notice that it is the difference of squares)
7 4
----------- + ------------
(2x)^2 - 7^2 2x+7
7 4
----------- + ------------
(2x-7)(2x+7) 2x+7
Get a common denominator
7 4(2x-7)
----------- + ------------
(2x-7)(2x+7) (2x-7)(2x+7)
Combine
7 +4(2x-7)
----------------------
(2x-7)(2x+7)
7 +8x-28
----------------------
(2x-7)(2x+7)
8x-21
----------------------
(2x-7)(2x+7)
Answer:
(8x - 21) / (2x + 7)(2x - 7)
Step-by-step explanation:
7 / (4x^2 - 49)+ 4 / (2x + 7)
= 7 / (2x + 7)(2x - 7) + 4 / (2x + 7)
LCM = (2x + 7)(2x - 7) so we have
(7 + 4(2x - 7) / (2x + 7)(2x - 7)
= (8x - 21) / (2x + 7)(2x - 7).
In the equation 11 - 4(x +4) = 6x, the first step is to simplify 11 - 4.
True
False
Answer:
False
Step-by-step explanation:
You first need to distribute the -4 to (x+4).
One of the non-right angles of a right triangle has a
measure 20º more than twice the measure of the other
non-right angle. Find the measures of the angles of the
right triangle.
Answer:
Step-by-step explanation:
one angle is 50
i need help on this PLS
I REALLY HOPE THIS HELPS! I’m sorry if this was wrong but I really believe it’s true.
Answer:
The value of P is $6.75.
Step-by-step explanation:
In the diagram to the left, we see 6 apples, and are labeled that the price is $4.50.
If the prices are proportional, that may mean that each apple has the same price. To find the price of apples in the diagram to the right, divide the total price by 6:
4.50/6 = 0.75
So the price per apple is 0.75.
As seen on the diagram, P represents the total price of 9 apples.
Multiply the price per apple by 9:
0.75 x 9 = 6.75
So the value of P is $6.75
Solve the System of Inequalities
Elimination method
3x +4y ≥ 0
2x +3y ≥ 1
Multiply by 2, -3
6x +8y ≥ 0
-6x +-9y ≥ -3
Add
-1y ≥ -3
y = 3
3x + 12≥ 0
3x + ≥ -12
x = -4
answer: y = 3 x = -4
what is the answer I need help?
Answer:
8 1/8 units^3
Step-by-step explanation:
This figure is a rectangular prism, and the volume of a rectangular prism is given by the formula:
lwh
But since we have the area of the base snd the height of the figure, there is also one formula that we can use to find the volume:
bh
Which means area of base times the height.
USE THE FORMULA bh:
16 1/4 x 1/2
= 65/4 x 1/2
= 65/8
SIMPLIFIED: 8 1/8
Volume is measured in cubic units
SO YOUR ANSWER IS 8 1/8 units^3
An F test for the two coefficients of promotional expenditures and district potential is performed. The hypotheses are H0: 1 = 4 = 0 versus Ha: at least one of the j is not 0. The F statistic for this test is 1.482 with 2 and 21 degrees of freedom. What can we say about the P-value for this test?
Answer:
Pvalue > 0.10
Step-by-step explanation:
Given the hypothesis :
H0 : β1 = β4 = 0
H1 : Atleast one of βj is not 0
F statistic = 1.482 ;
Degree of freedom = 2 and 21 ;
DFnumerator = 2
DFdenominator = 21
Using the Pvalue calculator from Fstatistic ;
Pvalue(1.482, 2, 21) = 0.24999 = 0.25
Hence, Pvalue for the test is 0.25
Pvalue > 0.10
Express 80 inches in standard notation using feet and inches.
80 inches in standard notation using feet and inches would be expressed as 6 ft 8 inches by converting inches into feet and inches.
The solution to the given problem is to use some standard conversion units that are:
1 foot = 12 inches1 inch = 0.8333 feetSolution:
As mentioned above that one inch is equal to 0.8333 foot therefore
1 foot = 12 inches
then,
80 inches would be equal to
= [tex]\frac{80}{12}[/tex] ft
= [tex]\frac{20}{3}[/tex] ft
= 6ft 8 inches
= 6' 8"
Thus, 80 inches in standard notation using feet and inches would be expressed as 6 ft 8 inches by converting inches into feet and inches.
Learn more:
https://brainly.com/question/884268
