Answer:
(f o g)(4) = - 49Step-by-step explanation:
F(x) = 3x - 7
g(x) = -2x - 6
To find (f o g)(4) we must first find (f o g)(x)
To find (f o g)(x) substitute g(x) into f(x) that's for every x in f (x) replace it with
g (x).
We have
(f o g)(x) = 3( - 2x - 6) - 7
= - 6x - 18 - 7
We have
(f o g)(x) = - 6x - 25
To find (f o g)(4), substitute the value of x that's 4 into (f o g)(x)
We have
(f o g)(4) = - 6(4) - 25
= - 24 - 25
We have the final answer as
(f o g)(4) = - 49Hope this helps you
Bepotastine besilate (BEPREVE) ophthalmic solution contains 1.5% w/v of the therapeutic agent. Express this concentration in mg/mL.
Answer:
15mg/ml
Step-by-step explanation:
Percent mass per volume ( % m/v) is unit expression that tells us how many grams of a solute that we can find 100 ml of a particular solution.
In the above question, we are asked to express 1.5%w/v Bepotastine besilate (BEPREVE) ophthalmic solution as mg/mL
Step 1
1.5% w/v = 1.5 g of Bepotastine besilate (BEPREVE) in 100ml ophthalmic solution
Hence, if
100ml = 1.5g
1 ml = y g
We Cross Multiply
100ml × yg = 1 ml × 1.5g
yg = 1 ml × 1.5g/100ml
= 0.015g
Therefore, in 1 ml we have 0.15 g.
Step 2
Since we are asked to express as mg/ml
We convert 0.015g to mg
1 gram = 1000 milligrams
0.015 grams =
Cross Multiply
0.015grams × 1000 milligrams/ 1 gram
= 15 mg
Therefore, the concentration in mg/ml of 15% m/v of Bepotastine besilate (BEPREVE) ophthalmic solution is 15mg/ml
How is mulhplying intergers
Similar to multiplying whole
numbers?
Answer: Multiplying integers is very similar to multiplying whole numbers. A positive number times a negative number equals a negative number. A negative number times a negative number equals a positive number. A negative number times a positive number equals a negative number.
Solve for y: 3x - 4y = 12
Answer:
y = 3/4x -3
Step-by-step explanation:
[tex]3x-4y=12\\[/tex]
Move 3x to the right and change its sign
[tex]-4y = -3x+12[/tex]
Divide both sides of the equation by -4
[tex]\frac{-4y}{-4} =\frac{-3x}{-4} + \frac{12}{-4} \\\\y = \frac{3}{4} x -3[/tex]
Find the 10th term of the geometric sequence a9=-5 r=-1/2
Answer:
2.5
Step-by-step explanation:
multiply -5 by -1/2
Write 20% as a decimal.
Answer ?
Answer:
0.2
Step-by-step explanation:
Step 1:
20 divided by 100 = 0.2
Answer:
0.2
If you want to get a decimal from a percent you need to divide the percent by 100.
Hope This Helps :)
Remember all decimal are basicaly,
x% = (x)/(100)
so
20%=(20)/(100)=0.20
The expression 3A + 2.5S gives the cost in dollars of A adult tickets and S student tickets. What is the cost of 2 adult tickets and 4 student
Answer:
16
Step-by-step explanation:
A = 2; S = 4
3A + 2.5S =
= 3(2) + 2.5(4)
= 6 + 10
= 16
Please help!
Add [-6-2 2] + [-3 2 1].
Answer:
Step-by-step explanation:
[-6 + -3 -2 + 2 2 + 1} = [-9 0 3}
You bought a magazine for $2 and three candy bars. You spent a total of $11. How much did each candy bar cost?
Answer:
$3 each
Step-by-step explanation:
Minus the $2 from $11 gives you $9. So $9÷3=$3 per candy bar.
Given f(x) = 52x, evaluate f-1), f(o), and K2).
01/25, 1, 625
Answer:
[tex]f(-1) = \frac{5}{2}[/tex]
[tex]f(0) = 5[/tex]
[tex]f(2) = 20[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 5(2^x)[/tex]
Required
Determine f(-1); f(0) and f(2)
Solving f(-1)
In this case, we simply take x as;
[tex]x = -1[/tex]
Substitute -1 for x in [tex]f(x) = 5(2^x)[/tex]
[tex]f(-1) = 5(2^{-1})[/tex]
Apply law of indices
[tex]f(-1) = 5 * \frac{1}{2}[/tex]
[tex]f(-1) = \frac{5}{2}[/tex]
Solving f(0)
In this case, we simply take x as;
[tex]x = 0[/tex]
Substitute 0 for x in [tex]f(x) = 5(2^x)[/tex]
[tex]f(0) = 5(2^0)[/tex]
[tex]f(0) = 5(1)[/tex]
[tex]f(0) = 5[/tex]
Solving f(2)
In this case, we simply take x as;
[tex]x = 2[/tex]
Substitute 2 for x in [tex]f(x) = 5(2^x)[/tex]
[tex]f(2) = 5(2^2)[/tex]
[tex]f(2) = 5(4)[/tex]
[tex]f(2) = 20[/tex]
10 times as many as 5 tens is 5thousand
Answer:
This question does not make sense for very specific reasons
Step-by-step explanation:
1. 5,000 does not look like 5thousand
2. 10 times as many as 5 tens is not really a question at all
3. the question itself already contains the answer 5,000
If you borrow $450.00 at a 5% interest, how much will you pay in one month?
Answer: Between about 31 and 33 dollars per month
Step-by-step explanation:
Factor this trinomial 4x^2-6x-10 If you can please try to show me how to do it.
Answer:
[tex]=2(2x-5)(x+1)[/tex]
Step-by-step explanation:
So we have the trinomial:
[tex]4x^2-6x-10[/tex]
First, factor out a 2:
[tex]=2(2x^2-3x-5)[/tex]
Now, factor within the parentheses.
To do so, we want to find two numbers. When multiplied, these two numbers must equal (a)(c) and when added, they must equal b
(a)(c) is 2(-5) or -10 and b is -3. So, we want two numbers that when multiplied together gives -10 and when added gives -3.
-5 and 2 works. Therefore:
[tex]=2(2x^2-3x-5)[/tex]
Replace -3x with 2x and -5x:
[tex]=2(2x^2+2x-5x-5)[/tex]
Factor out a 2x for the first two terms. And factor out a negative 5 for the remaining two:
[tex]=2(2x(x+1)-5(x+1))[/tex]
Grouping:
[tex]=2(2x-5)(x+1)[/tex]
And we're done!
If a =5, 0, −1,find a vector b such that compab = 2.b = _______.
Answer:
[tex]b = (q,r , 5q-2\sqrt{26} )[/tex]
Step-by-step explanation:
From the question we are told that
The vector given is
[tex]a = (5,0,-1)[/tex]
Also [tex]comp_a b = 2[/tex]
Generally
[tex]comp_a b = \frac{a \cdot b}{|a|}[/tex]
Here [tex]|a|[/tex] is the magnitude of a which is mathematically represented as
[tex]|a| = \sqrt{5^2 + 0^2 +(-1)^2 }[/tex]
=> [tex]|a| = \sqrt{26}[/tex]
b is vector which we will assume to have the following parameters
[tex]b = (q , r , x)[/tex]
So
[tex]comp_a b = \frac{(5,0,-1) \cdot (q,r,x)}{\sqrt{26} } = 2[/tex]
=> [tex]\frac{5q + 0 -x}{\sqrt{26} } = 2[/tex]
=> [tex]x = 5q-2\sqrt{26}[/tex]
Hence the vector be can be mathematically represented as
[tex]b = (q,r , 5q-2\sqrt{26} )[/tex]
This means that the vector b is more than one value since it is made up of variable
This means that if
[tex]q = 1\\r=1\\x =1[/tex]
Then
[tex]b = (1,1,5-2\sqrt{26} )[/tex]
A quantity has magnitude but not position, that's why in this the vector [tex]b =(0,0, -2\sqrt{26}).[/tex]
Vector:If[tex]a =(5,0,-1)[/tex] Our goal is to determine a vector b that will allow comp to work properly [tex]_{a}b = 2.[/tex]
Allow the vector to flow naturally [tex]b =(x, y,z)[/tex]
Recalling
comp[tex]_{a}b =\frac{a.b}{|a|}[/tex]
Therefore,
comp [tex]_{a}b= 2 \\\\[/tex]
[tex]\to \frac{a.b}{|a|}= 2\\\\[/tex]
[tex]\to \frac{(5,0,-1)\cdot (x,y,z)}{ |(5,0,-1)|} =2\\\\\to \frac{5x+0-z}{5^2+0+(-1)^2}=2\\\\ \to \frac{5x-z}{\sqrt{26}}= 2 \\\\\to 5x-z = 2\sqrt{26}\\\\ \to z=5x-2\sqrt{26}\\\\[/tex]
As a result, the vector b can be expressed as,
[tex]\to b =(x,y,z) =(x, y, 5x-2\sqrt{26}) \\\\[/tex]
As a result, this aforementioned form can be found in an endless number of vectors.
One of them is [tex]b =(0,0, -2\sqrt{26}).[/tex]
Find out more about the vector here:
brainly.com/question/13322477
Solve the following proportion for
5/11=y/6
Round your answer to the nearest tenth
Answer:
Step-by-step explanation:
5 y
_ = _
11 6
Cross multiply to get:
11y = 30
y = 2.7272
y = 2.7
If i am in texas then I am in the south
━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━
Of the United States, true, you are in the south.
Texas is a southern state of the USA.
Of the world, false, you are more north than south, and also you are around the middle north of the world.
The pictures I attached are maps of the USA and the world.
As you can see in the USA map, Texas is one of the states are are the lowest.
But if you look at the world map, Texas is not very south.
━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━
Find the slope of the curve below at the given points. Sketch the curve along with its tangents at these points. R = sin 2 theta: theta = plusminus pi/4, plusminus 3 pi/4 The slope of the curve at theta = pi/4 is:__________
Answer:
-1
Step-by-step explanation:
Given that:
r = sin 2θ , θ = ± π/4 , ± 3π/4
Recall that:
x = r cosθ
y = r sinθ
The differential of y with respect to x
[tex]\dfrac{dy}{dx} = \dfrac{\dfrac{dy}{d \theta}}{\dfrac{dx}{d \theta}}[/tex]
[tex]\dfrac{dy}{dx} =\dfrac{\dfrac{dy}{d \theta}}{\dfrac{dx}{d \theta}} = \dfrac{ r cos \theta + sin \theta* \dfrac{dr}{d \theta} } {\dfrac{dr}{d \theta} *cos \theta- sin \theta \ r}[/tex]
at θ = π/4 , r = sin π/2
r = 1
[tex]\dfrac{dy}{dx} = \dfrac{ r cos \theta + 2 cos (2 \theta)*sin \ \theta } {2 \ cos (2 \theta) *cos \theta- sin 2 \theta * sin \theta}[/tex]
where;
θ = π/4
[tex]\dfrac{dy}{dx} = \dfrac{ 1 \times cos (\dfrac{\pi}{4}) + 2 cos (\dfrac{\pi}{2})*sin (\dfrac{\pi}{4}) } {2 \ cos (\dfrac{\pi}{2})*cos (\dfrac{\pi}{4})- sin (\dfrac{\pi}{2}) * sin (\dfrac{\pi}{4})}[/tex]
[tex]\dfrac{dy}{dx} = \dfrac{\dfrac{1}{\sqrt{2}}+0 }{0-1 * \dfrac{1}{\sqrt{2}}}[/tex]
[tex]\dfrac{dy}{dx} = \dfrac{\dfrac{1}{\sqrt{2}} }{- \dfrac{1}{\sqrt{2}}}[/tex]
[tex]\mathbf{\dfrac{dy}{dx} =-1}[/tex]
slope of the curve (dy/dx) at theta(θ) = pi/4 is -1
Find z such that the proportion of observations that are less than z in a standard normal distribution is 0.23. (Enter your answer rounded to two decimal places.)Z=______
Answer:
-0.74
Step-by-step explanation:
The computation of Z is shown below:
According to the question, data provided in the question is as follows
P(Z > Z) = 0.23
Based on the above information, the calculation for Z is
Use the table of the standard normal distribution for z
By using this the Z value comes is -0.74
hence, in case of the standard normal distribution, the value of z is -0.74 and the same is to be considered
Which of the following is the solution of the equation 3x + 4=19 use substitution to identify the correct answer
Answer:
5
Step-by-step explanation:
Step 1:
3x + 4 = 19
Step 2:
3x = 19 - 4
Step 3:
3x = 15
Answer:
x = 5
Hope This Helps :)
the sum of m and 188 is 232
write the sentence as an equation
Answer:
m + 188 = 232
Step-by-step explanation:
sum → +
m + 188 = 232
Answer:
m + 188 = 232
Thats is an equation for your problem
How many hours are there in 360 mins
Answer: 6 hours
Step-by-step explanation:
You have to divide 360 by 60 minutes.
Answer:
There are 360 minutes in 6 hours.
Hope this helps :)
what is -1/3 + (-5/6) step by step
Answer:
[tex]-\frac{7}{6}[/tex]
Step-by-step explanation:
Change -1/3 to match denominators with -5/6: 3 × 2 = 6, -1 × 2 = -2Re-write the expression: -2/6 + (-5/6)Simplify: -2/6 - 5/6[tex]-\frac{2}{6} - \frac{5}{6} = -\frac{7}{6}[/tex]I hope this helps!
Answer:
-7/6
Step-by-step explanation:
-1/3=-2/6
-2/6-5/6=-7/6
Find the slope of the line containing the pair of points. (5,-7) and (-4,-4)
Answer:
1/-3
Step-by-step explanation:
What can you conclude about the slope of the values in
the table? Check all that apply.
lope
The slope is 0.
The slope is undefined.
The graph will be a horizontal line.
The graph will be a vertical line.
The graph will have a line with a positive slope.
Answer:
The slope is undefined.
The graph will be a vertical line.
Step-by-step explanation:
just did it
The graph will be a vertical line. Option C is correct.
Given that,
The slope of the line is zero we have to determine what are the conditions.
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
What is simplification?
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The slope of the line is zero,
m = 0
tanФ = 0
y / x = 0
for the above condition, Δy must be zero or Δx must be infinite and the line will be a verticle.
Thus, the graph will be a vertical line. Option C is correct.
Learn more about slopes here:
https://brainly.com/question/3605446
#SPJ2
30 POINTS Type the correct answer in the box. Use numerals instead of words.
Answer:
15 rubber bands per day
Step-by-step explanation:
Write 0.0000002711 in scientific notation. (Use 2 numbers after the decimal point.)
Answer:
[tex]Number = 2.71 * 10^{-7}[/tex]
Step-by-step explanation:
Given
[tex]Number = 0.0000002711[/tex]
Required
Write, using scientific notation
The scientific notation is written in the form:
[tex]Form = a * 10^n[/tex] Where n is an integer and [tex]1 \leq a \leq 10[/tex]
To start with; Represent the given number as fraction
[tex]Number = \frac{2711}{10000000000}[/tex]
Represent the denominator as an exponent
[tex]Number = \frac{2711}{10^{10}}[/tex]
This can be rewritten in form of:
[tex]Number = 2711 * 10^{-10}[/tex]
Remember that: [tex]Form = a * 10^n[/tex] Where n is an integer and [tex]1 \leq a \leq 10[/tex]
This implies that; we need to adjust 2711 to a number between 1 and 10;
This gives:
[tex]Number = 2.711 * 1000 * 10^{-10}[/tex]
Write 1000 as an exponent
[tex]Number = 2.711 * 10^3 * 10^{-10}[/tex]
Apply law of indices
[tex]Number = 2.711 * 10^{3-10}[/tex]
[tex]Number = 2.711 * 10^{-7}[/tex]
The question requires 2 numbers after the decimal point;
So, 2.711 will be approximated to 2.71
[tex]Number = 2.71 * 10^{-7}[/tex]
Hence;
[tex]0.0000002711[/tex] is equivalent to [tex]2.71 * 10^{-7}[/tex]
Which number is the same distance from 0 on a number line as 3/2 answers -3 -3/2 -2/3 2/3 3
Answer: -3/2
Step-by-step explanation:
To find its distance away from 0, then just find its opposite.
On the number line if you graph 3/2, its opposite will be -3/2
find simple interest on #1200 for 3 years at 4.25% per anum
Answer:
$153.00
Step-by-step explanation:
A = $1,353.00
(I = A - P = $153.00)
Equation:
A = P(1 + rt)
Calculation:
First, converting R percent to r a decimal
r = R/100 = 4.25%/100 = 0.0425 per year.
Solving our equation:
A = 1200(1 + (0.0425 × 3)) = 1353
A = $1,353.00
The total amount accrued, principal plus interest, from simple interest on a principal of $1,200.00 at a rate of 4.25% per year for 3 years is $1,353.00.
Answer:
$153
Step-by-step explanation:
Simple Intrest = P ( money invested ) * R ( percentage ) * T ( year )
I = P * R * T / 100
I = 1200 * 4.25 * 3 = 15300 / 100 = $153
This is the easiest method for me and I hope it helps :)
Using calculus, it can be shown that if a ball is thrown upward with an initial velocity of 16 ft/s from the top of a building 704 ft high, then its height h above the ground t seconds later will be h = 704 + 16t − 16t2. During what time interval (in seconds) will the ball be at least 32 ft above the ground? (Enter your answer using interval notation.)
Answer:
[0, 7]
Step-by-step explanation:
We want the height to be greater than or equal to 32 ft, so ...
704 +16t -16t^2 ≥ 32
t^2 -t -42 ≤ 0 . . . . . . . . . . . subtract 32, divide by -16
(t -7)(t +6) ≤ 0
This inequality will be true for values of t between -6 and +7. Since we're only concerned with times t ≥ 0, the appropriate solution interval is ...
0 ≤ t ≤ 7 . . . . [0, 7] in interval notation
range of 2.45 3.50 2.89 2.99
Answer:
[tex]\huge\boxed{\mathrm{Range = 1.05}}[/tex]
Step-by-step explanation:
Given Data:
2.45 , 3.50 , 2.89 , 2.99
Arrange it in ascending order.
2.45 , 2.89 , 2.99 , 3.50
Range = Highest No - Lowest No.
Range = 3.50 - 2.45
Range = 1.05
Answer:
Range=largest value-smallest value
Range=2.99-2.45
Range=0.54
Step-by-step explanation:
hope it is helpful for you
if it is please follow
Find the domain and range. {(-2,0), (1,-2), (3,4)}
Answer:
[tex] \boxed{ \bold{ \boxed{ \sf{domain = { (- 2 \: , \: 1 \: , \: 3)}}}}}[/tex]
[tex] \boxed{ \bold{ \boxed{ \sf{range = ( \: - 2 \: , \: 0 \: , \: 4)}}}}[/tex]
Step-by-step explanation:
Domain is the set of all x values.
Range is the set of all y - values.
{ ( - 2 , 0 ) , ( 1 , -2 ) , ( 3 , 4 )}
Domain = { -2 , 1 , 3 }
{ ( -2 , 0 ) , ( 1 , -2 ) , ( 3 , 4 )}
Range = { - 2 , 0 , 4 }
Hope I helped!
Best regards! :D