Answer: (f-g)(x) = - 5^x + 3x - 2
Step-by-step explanation:
if f(x) = -5^x - 4 and g(x)= - 3x - 2,find (f-g)(x)
(f-g)(x) = -5^x - 4 - (-3x - 2)
(f-g)(x) = -5^x - 4 + 3x + 2
(f-g)(x) = - 5^x + 3x - 2
Using the applet, explore the results for simulating a group of 30 people and noting whether there is a duplicated birthday (whether at least two people have a matching birthday). Run at least 40 trials. What is the relative frequency of trials that had at least two people with the same birthday
Answer:I just need points
Step-by-step explanation:
Hey
Identify the coefficients for the following quadratic equation.
2x squared minus 9x equals negative 4
a =
b=
c=
Answer:
2
Step-by-step explanation:
the number before the x² is regarded as the identity element
PLEASE HELPPPPPPPPPPPPPP
Answer:
False
Step-by-step explanation:
To find the inverse of a function, switch the variables and solve for y.
The inverse of f(n)=-(n+1)^3:
[tex]y=-(n+1)^3[/tex]
[tex]n=-(y+1)^3[/tex]
[tex]\sqrt[3]{n} =-(y+1)[/tex]
[tex]\sqrt[3]{n} =-y-1[/tex]
[tex]\sqrt[3]{n} +1=-y[/tex][tex]-(\sqrt[3]{n} +1)=y[/tex]
[tex]-\sqrt[3]{n} -1=y[/tex]
Answer:
False
Step-by-step explanation:
square root of 12321 by prime factorization
12321-3x3x37x37
(3)^2×(37)^2
square root = 3×37=111
Hope it helps you..!!
Prove that A.M, G.M. and H.M between any two unequal positive numbers satisfy the following relations.
i. (G.M)²= (A.M)×(H.M)
ii.A.M>G.M>H.M
Answer:
See below
Step-by-step explanation:
we want to prove that A.M, G.M. and H.M between any two unequal positive numbers satisfy the following relations.
(G.M)²= (A.M)×(H.M) A.M>G.M>H.Mwell, to do so let the two unequal positive numbers be [tex]\text{$x_1$ and $x_2$}[/tex] where:
[tex] x_{1} > x_{2}[/tex]the AM,GM and HM of [tex]x_1[/tex] and[tex] x_2[/tex] is given by the following table:
[tex]\begin{array}{ |c |c|c | } \hline AM& GM& HM\\ \hline \dfrac{x_{1} + x_{2}}{2} & \sqrt{x_{1} x_{2}} & \dfrac{2}{ \frac{1}{x_{1} } + \frac{1}{x_{2}} } \\ \hline\end{array}[/tex]
Proof of I:[tex] \displaystyle \rm AM \times HM = \frac{x_{1} + x_{2}}{2} \times \frac{2}{ \frac{1}{x_{1} } + \frac{1}{x_{2}} } [/tex]
simplify addition:
[tex] \displaystyle \frac{x_{1} + x_{2}}{2} \times \frac{2}{ \dfrac{x_{1} + x_{2}}{x_{1} x_{2}} } [/tex]
reduce fraction:
[tex] \displaystyle x_{1} + x_{2} \times \frac{1}{ \dfrac{x_{1} + x_{2}}{x_{1} x_{2}} } [/tex]
simplify complex fraction:
[tex] \displaystyle x_{1} + x_{2} \times \frac{x_{1} x_{2}}{x_{1} + x_{2}} [/tex]
reduce fraction:
[tex] \displaystyle x_{1} x_{2}[/tex]
rewrite:
[tex] \displaystyle (\sqrt{x_{1} x_{2}} {)}^{2} [/tex]
[tex] \displaystyle AM \times HM = (GM{)}^{2} [/tex]
hence, PROVEN
Proof of II:[tex] \displaystyle x_{1} > x_{2}[/tex]
square root both sides:
[tex] \displaystyle \sqrt{x_{1} }> \sqrt{ x_{2}}[/tex]
isolate right hand side expression to left hand side and change its sign:
[tex]\displaystyle\sqrt{x_{1} } - \sqrt{ x_{2}} > 0[/tex]
square both sides:
[tex]\displaystyle(\sqrt{x_{1} } - \sqrt{ x_{2}} {)}^{2} > 0[/tex]
expand using (a-b)²=a²-2ab+b²:
[tex]\displaystyle x_{1} -2\sqrt{x_{1} }\sqrt{ x_{2}} + x_{2} > 0[/tex]
move -2√x_1√x_2 to right hand side and change its sign:
[tex]\displaystyle x_{1} + x_{2} > 2 \sqrt{x_{1} } \sqrt{ x_{2}}[/tex]
divide both sides by 2:
[tex]\displaystyle \frac{x_{1} + x_{2}}{2} > \sqrt{x_{1} x_{2}}[/tex]
[tex]\displaystyle \boxed{ AM>GM}[/tex]
again,
[tex]\displaystyle \bigg( \frac{1}{\sqrt{x_{1} }} - \frac{1}{\sqrt{ x_{2}}} { \bigg)}^{2} > 0[/tex]
expand:
[tex]\displaystyle \frac{1}{x_{1}} - \frac{2}{\sqrt{x_{1} x_{2}} } + \frac{1}{x_{2} }> 0[/tex]
move the middle expression to right hand side and change its sign:
[tex]\displaystyle \frac{1}{x_{1}} + \frac{1}{x_{2} }> \frac{2}{\sqrt{x_{1} x_{2}} }[/tex]
[tex]\displaystyle \frac{\frac{1}{x_{1}} + \frac{1}{x_{2} }}{2}> \frac{1}{\sqrt{x_{1} x_{2}} }[/tex]
[tex]\displaystyle \rm \frac{1}{ HM} > \frac{1}{GM} [/tex]
cross multiplication:
[tex]\displaystyle \rm \boxed{ GM >HM}[/tex]
hence,
[tex]\displaystyle \rm A.M>G.M>H.M[/tex]
PROVEN
Divide 500 in the ratio 4:5:1
Answer:
200 : 250 : 50
Step-by-step explanation:
Sum the parts of the ratio, 4 + 5 + 1 = 10 parts
Divide the amount by 10 to find the value of one part
500 ÷ 10 = 50 ← value of 1 part of ratio , then
4 parts = 4 × 50 = 200
5 parts = 5 × 50 = 250
500 = 200 : 250 : 50
Answer:
200, 250 and 50.
Step-by-step explanation:
First find the 'multiplier'.
4 + 5 + 1 = 10
500/10 = 50 = multiplier.
So the answer is
4*50 = 200
5 * 50 = 250
and 1 * 50 = 50.
Flying against the wind, an airplane travels 3360 kilometers in hours. Flying with the wind, the same plane travels 7560 kilometers in 9 hours. What is the rate of the plane in still air and what is the rate of the wind?
Answer:
606.6 and 233.3 respectively
Step-by-step explanation:
Let the speed of plane in still air be x and the speed of wind be y.
ATQ, (x+y)*9=7560 and (x-y)*9=3360. Solving it, we get x=606.6 and y=233.3
If the roots of ax² + bx + c = 0 differ by 3. Show that b² =9a² + 4ac
Answer:
Step-by-step explanation:
Diane must choose a number between 49 and 95 that is a multiple of 2, 3, and 9. Write all the numbers that she could choose. If
there is more than one number, separate them with commas?
The set of numbers that Diane can choose is:
{54, 60, 66, 72, 78, 84, 90}
Finding common multiples of 2, 3, and 6:
A number is a multiple of 2 if the number is even.
A number is a multiple of 3 if the sum of its digits is multiples of 3.
A number is a multiple of 6 if it is a multiple of 2 and 3.
Then we only need to look at the first two criteria.
First, let's see all the even numbers in the range (49, 95)
These are:
{50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94}
All of these are multiples of 2.
Now we need to see which ones are multiples of 3.
To do it, we sum its digits and see if that sum is also a multiple of 3.
50: 5 + 0 = 5 this is not multiple of 3.
52: 5 + 2 = 7 this is not multiple of 3.
54: 5 + 4 = 9 this is multiple of 3, so 54 is a possible number.
And so on, we will find that the ones that are multiples of 3 are:
54: 5 + 4 = 9.
60: 6 + 0 = 6
66: 6 + 6 = 12
72: 7 + 2 = 9
78: 7 + 8 = 15
84: 8 + 4 = 12
90:9 + 0 = 9
Then the numbers that Diane could choose are:
{54, 60, 66, 72, 78, 84, 90}
If you want to learn more about multiples, you can read:
https://brainly.com/question/1553674
write your answer as an integer or as a decimal rounded to the nearest tenth
Answer:Mark Brainliest please
Answer is 4.86 which is rounded to 5
Step-by-step explanation:
Cos 40 degree = VW/7
0.694 =VW/7
0.694 * 7 =VW
4.858 =VW
VW=4.86 is the answer
F(x)=x+8;g(x)=x+2. Find f=g
Answer:
f(x) can not be equal to g(x)
Step-by-step explanation:
If the result is possible:
f(x) = g(x)
x + 8 = x + 2
x + 8 - (x + 2) = x + 2 - (x + 2)
6 = 0
Because 6 can't be equal to 0, so do f(x) can't be equal to g(x)
15. (x - 3)
If f(x) = 2x2 – 5, find the following.
16.fly-2)
17. f(a+h)-f(a)
Answer:
16. f(y-2) = 2(y-2)²-5
= 2(y²-4y+4)-5
= 2y²-8y+8-5
= 2y²-8y+3
17. f(a+h)-f(a) = 2(a+h)²-5-(2a²-5)
= 2(a²+2ah+h²)-5-2a²+5
= 2a²+4ah+h²-2a²
= h²+4ah
Find the length of BC
Answer:
53.68
Step-by-step explanation:
tan54 = bc/39
bc = 39tan54
Step-by-step explanation:
Hey there!
From the given figure;
Angle CAB = 54°
Side AC = 39
To find: side BC
Taking Angle CAB as reference angle;
Perpendicular (p) = BC = ?
Base (b) = AC = 39
Hypotenuse (h) = AB
Taking the ratio of tan;
[tex] \tan( \alpha ) = \frac{p}{b} [/tex]
Keep value;
[tex] \tan(54) = \frac{bc}{39} [/tex]
Simplify it;
1.376381*39 = BC
Therefore, BC = 53.678.
Hope it helps!
A sample of 375 college students were asked whether they prefer chocolate or vanilla ice cream. 210 of those surveyed said that they prefer vanilla ice cream. Calculate the sample proportion of students who prefer vanilla ice cream.
Answer:
The sample proportion of students who prefer vanilla ice cream is 0.56.
Step-by-step explanation:
Sample proportion of students who prefer vanilla ice cream:
Sample of 375 students.
Of those, 210 said they prefer vanilla ice cream.
The proportion is:
[tex]p = \frac{210}{375} = 0.56[/tex]
The sample proportion of students who prefer vanilla ice cream is 0.56.
Find m∠F=....................
.................................
What would it equal??
m∠F= what is it???
Answer:
45°
Step-by-step explanation:
[tex] \sin \: m\angle F = \frac{EG}{FG} \\ \\ \sin \: m\angle F = \frac{2 \sqrt{11} }{2 \sqrt{22} } \\ \\ \sin \: m\angle F = \frac{\sqrt{11} }{ \sqrt{22} } \\ \\ \sin \: m\angle F = \frac{1}{ \sqrt{2} } \\ \\ \sin \: m\angle F = \sin \: 45 \degree \\ \\ \huge \boxed{ \purple{m\angle F = 45 \degree }}[/tex]
Geometry help I don’t know any of this stuff!!
Answer:
radius chordsecant linecenterpoints of tangency circumferenceIn 1815, Sophie Germain won a mathematical prize given by the Institut de France for her work on the theory of elasticity. The prize was a medal made of 1 kilogram of gold. How much is the medal worth today in U.S. dollars and in euros
Answer:
gold price : $58.72/gram
$58,720 per kilo(1000) grams
Step-by-step explanation:
Please answer all of these
Answer:
1a 300
b 180
c 330
d 1470
e 180
f 7344
Step-by-step explanation:
Determine the product of (46.2 × 10^-1) ⋅ (5.7 × 10^–6). Write your answer in scientific notation.
A)
2633.4 × 10^–5
B)
2.6334 × 10^–7
C)
2.6334 × 10^–1
D)
2.6334 × 10^–5
Step-by-step explanation:
here's the answer to your question
If y = ax^2 + bx + c passes through the points (-3,10), (0,1) and (2,15), what is the value of a + b + c?
Hi there!
[tex]\large\boxed{a + b + c = 6}[/tex]
We can begin by using the point (0, 1).
At the graph's y-intercept, where x = 0, y = 1, so:
1 = a(0)² + b(0) + c
c = 1
We can now utilize the first point given (-3, 10):
10 = a(-3)² + b(-3) + 1
Simplify:
9 = 9a - 3b
Divide all terms by 3:
3 = 3a - b
Rearrange to solve for a variable:
b = 3a - 3
Now, use the other point:
15 = a(2)² + 2(3a - 3) + 1
14 = 4a + 6a - 6
Solve:
20 = 10a
2 = a
Plug this in to solve for b:
b = 3a - 3
b = 3(2) - 3 = 3
Add all solved variables together:
2 + 3 + 1 = 6
Let V be the volume of the solid obtained by rotating about the y-axis the region bounded y = sqrt(25x) and y = x^2/25. Find V by slicing & find V by cylindrical shells.
Explanation:
Let [tex]f(x) = \sqrt{25x}[/tex] and [tex]g(x) = \frac{x^2}{25}[/tex]. The differential volume dV of the cylindrical shells is given by
[tex]dV = 2\pi x[f(x) - g(x)]dx[/tex]
Integrating this expression, we get
[tex]\displaystyle V = 2\pi\int{x[f(x) - g(x)]}dx[/tex]
To determine the limits of integration, we equate the two functions to find their solutions and thus the limits:
[tex]\sqrt{25x} = \dfrac{x^2}{25}[/tex]
We can clearly see that x = 0 is one of the solutions. For the other solution/limit, let's solve for x by first taking the square of the equation above:
[tex]25x = \dfrac{x^4}{(25)^2} \Rightarrow \dfrac{x^3}{(25)^3} = 1[/tex]
or
[tex]x^3 =(25)^3 \Rightarrow x = \pm25[/tex]
Since we are rotating the functions around the y-axis, we are going to use the x = 25 solution as one of the limits. So the expression for the volume of revolution around the y-axis is
[tex]\displaystyle V = 2\pi\int_0^{25}{x\left(\sqrt{25x} - \frac{x^2}{25}\right)}dx[/tex]
[tex]\displaystyle\:\:\:\:=10\pi\int_0^{25}{x^{3/2}}dx - \frac{2\pi}{25}\int_0^{25}{x^3}dx[/tex]
[tex]\:\:\:\:=\left(4\pi x^{5/2} - \dfrac{\pi}{50}x^4\right)_0^{25}[/tex]
[tex]\:\:\:\:=4\pi(3125) - \pi(7812.5) = 14726.2[/tex]
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).
Look at the image for the question
Answer:
Does the answer help you?
The distance from the green point on the parabola to the parabolas focus is 11. What is the distance from green point to the directrix?
Answer:
answer 11
Step-by-step explanation:
I think it the right answer
the ages of two students are in the ratio of 3:5,if the older is 40yrs. How old is the younger student
Answer:
24 years
Step-by-step explanation:
total ratio =8
older student=40 years
3/8*40 ÷ 5/8=24
Add .003, 265.8, 83.04
and 1972
A car travels 630 miles in 14 hours. At this rate, how far will it travel in 42 hours?
Assuming the car's speed [tex]\frac{630}{14}=45\mathrm{mph}[/tex] does not change, the car will travel [tex]45\cdot42=\boxed{1890}[/tex] miles.
Hope this helps :)
IS THSI RIGHTTTTTTTT??????????????
Answer:
No. It is EF and GH
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
The answer will be EF and GH, both are 7 units long.
Find the missing segment in the image below
Answer:
Step-by-step explanation:
i keel asking for the dang answer why wont anyone tell me it a store sells pencils pens and markers that sells two times as many markers as pencils and three times as many pens as pencils is the store sells a total of 1950 pencils and pens and markers in a week how many of each were sold
Answer:
Pencils = 325 ; Pens = 975 ; Markers = 650
Step-by-step explanation:
Let :
Number of Pencils = x
Number of pens = y
Number of markers = z
2 times as many markers as pencils
z = 2x
3 times as many pens as pencils
y = 3x
x + y + z = 1950
Write z and y in terms of x in the equation :
x + 3x + 2x = 1950
6x = 1950
Divide both sides by 6
6x / 6 = 1950 / 6
x = 325
Number of pencils = 325
Pens = 3 * 325 = 975
Markers = 2 * 325 = 650
Pencils = 325 ; Pens = 975 ; Markers = 650
