The values of the composite function are (f o g)(x) = √2x² - 8 and (f o g)(x) = 2x - 8, while their domains are x > 2 and 0 < x < oo, respectively
Lastly, the value of (g o f)(3) is -2
How to evaluate the function?Composite function 1
The functions are given as
f(x) = √x
g(x) = 2x² - 8
The composite function definition is given as
(f o g)(x)
This composite function is calculated using the following composite function formula
(f o g)(x) = f(g(x))
Substitute the known values in the above equation
(f o g)(x) = √g(x)
This gives
(f o g)(x) = √2x² - 8
For the domain, we have
2x² - 8 > 0
This gives
x > 2
Composite function 2
The functions are given as
f(x) = √x
g(x) = 2x² - 8
The composite function definition is given as
(g o f)(x)
This composite function is calculated using the following composite function formula
(g o f)(x) = g(f(x))
Substitute the known values in the above equation
(g o f)(x) = 2f(x)² - 8
This gives
(g o f)(x) = 2(√x)² - 8
Evaluate
(g o f)(x) = 2x - 8
The function is a linear function
So the domain is the set of all real values
Substitute 3 for x in (g o f)(x) = 2x - 8
(g o f)(3) = 2(3) - 8
Evaluate
(g o f)(3) = -2
Read more about composite function at
brainly.com/question/10687170
#SPJ1
Why is triangle DFC congruent to triangle AEB?
By Side - Angle - Side congruency (SAS) rule, ΔDFC is congruent to ΔAEB as shown below.
What are Congruent triangles?Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
Given is a geometrical diagram as shown in the image.
We can prove ΔDFC ≅ ΔAEB as follows -
AE = CF [Given]
Add length EF on both sides of the equation, we get
AE = CF ...[1]
∠ 1 = ∠ 2 [Given] ...[2]
Given is ∠ 1 = ∠ 2. Than the tangent of both angles will be same. On solving the tangent ratio, we get -
BE = FD ...[3]
From equation 1, 2 and 3, we can say that
ΔDFC ≅ ΔAEB
Therefore, by Side - Angle - Side congruency (SAS) rule, ΔDFC is congruent to ΔAEB.
To solve more questions on Congruent triangles, visit the link below-
https://brainly.com/question/21360865
#SPJ1
six tickets to a movie cost $76.50. What constant of proportionality relates the number of tickets and total cost?
The constant of proportionality is 12.75
The constant of proportionality is the ratio of the constant values of two proportional quantities.
Two changing values are said to be in proportion when either their ratio or product results in a constant. The proportionality constant's value is determined by the Direct Variation and Inverse Variation types of proportions between the two supplied values.The direct proportionality equation, y = kx, shows that when x increases, y increases at the same rate. As an illustration, y x stands for the cost per item(y), which is inversely related to the quantity of items(x) bought.The indirect proportionality equation, y = k/x, shows that when y increases, x decreases, and vice versa.The direct variation is given by y = k x where k is the constant of proportionality.
Now the cost of 6 tickets is $76.50
76.50 = k × 6
or, k = 12.75
Therefore the constant of proportionality is 12.75
To learn more about constant of proportionality visit:
https://brainly.com/question/8598338
#SPJ1
In the given triangle, prove that
[tex] \frac{1}{ {ab}^{2} } + \frac{1}{ {ac}^{2} } = \frac{1}{ {ad}^{2} } [/tex]
Answer:
. .........................
What are precise definitions of perpendicular and parallel lines
Answer:
Perpendicular lines: When a line intersects another line at exact 90 degrees the lines are said to be perpendicular to each other.
Parallel lines: When two lines are formed such that the two lines are never intersecting and no angle is formed is known as parallel lines.
–2.29(d + 1) = –6.87
Isolate the variable by dividing each side by factors that don't contain the variable.
[tex]-2.29(d+1)=-6.87[/tex]
[tex]d=2[/tex]
^Hence, our solution
________________________________________________
Hope this helps!
What is the solution to |2x - 8| ≤ 6?
[5*(54-:6-3)]+6*2-60
i need help?
Answer:
177
Step-by-step explanation:
5(54 − 6 − 3) + (6)(2) − 60
= 177
is 5 square root-2 square root rational?
5 square root - 2 square root is 0.821854415 and it is rational.
Given,
5 square root - 2 square root
That is,
√5 - √2
We have to find this is rational or not.
First we have to solve the equation:
√5 - √2 = 0.821854415
Irrational numbers cannot be stated as a fraction, although rational numbers can be expressed as ratios (such as P/Q and Q0). However, both of the numbers are genuine and can be shown on a number line.
So, here 0.821854415 is a rational number.
That is, 5 square root - 2 square root is rational.
Learn more about rational and irrational numbers here:
https://brainly.com/question/3120622
#SPJ1
Solve the exponential equation
4^x = 7(3^x)
The solution to the given exponential equation is; x = 6.48
What is the solution to the exponential equation?
We want to solve the exponential equation;
4^(x) = 7 - (3^x)
We can use logarithm or inverse of logarithm to solve this but in this case we will use the logarithm to get;
x log 4 = 7 - (x log 3)
x log 4 + x log 3 = 7
x(log 4 + log 3) = 7
1.08x = 7
x = 7/1.08
x = 6.48
Read more about Exponential Equation at; https://brainly.com/question/2456547
#SPJ1
wHAT IS THE ANSWER OF THIS? the correct answer will be marked brainliest
a function is graphed below. on which interval of c is the average rate of change of the function the greatest?
1. x=0 to x=2
2. x=12 to x=18
3. x=2 to x=12
4. x=18 to x=24
Find a point-slope form for the line with slope = 1/5 and passing through the point
(- 6, -7).
The equation of the line in point-slope form is…
Answer:
y+5 = 1/5 (x+6)
Step-by-step explanation:
The point slope form looks like this.
y - y1 = m (x - x1)
the m represent slope and (x1, y1) are the coordinates of the point that the line passes through.
7 231/500 As a decimal
Answer:
7.462
Step-by-step explanation:
Answer:
7 231/500 As a decimal
Step-by-step explanation:
To write 231/500 as a decimal you have to divide numerator by the denominator of the fraction.
We divide now 231 by 500 what we write down as 231/500 and we get 0.462
Hope this helps!
3. What is the next term in the sequence?
243, 81, 27,9,...
O
O
-3
O
-9
O`
3
The next term would be 3 then 1 in the sequence 243, 81, 27, 9,... by the term of sequence and series through mathematical sequencing.
What are a series and a sequence?A grouping of numbers in a kind of a specific order is known as a sequence. On the other hand, a series can also be described as the accumulation of a kind of a sequence’s constituent parts.
Basically, the sequence proceeds with a dividing term of 3. The sequence will go on with the square root of the previous number. Basically, from backward, the sequence is an exponential multiple of 3.
What do the terms sequence and series mean?Mathematical sequence and series formulas pertain to several kinds of sequences and series. A series is the accumulation of elements in a sequence, which is a group of arranged elements that follow a pattern.
The formulas for the nth term and the sum are typically included in the sequence and series formulas.
What distinguishes serial from sequential data?A series is made up of all the elements in a sequence, while a sequence is a certain arrangement of elements in a specific order.
To know more about sequence and series visit:
https://brainly.com/question/12429779
#SPJ13
Mary lives between points (3,-1) and (7,5) on Duval street. Val lives between points (2,15) and (-6,3) on Braxton lane. Are duval st and Braxton lane parallel or perpendicular
Duval Street between latitudes (3,1) and (7,5). Val resides between coordinates (2, 15) and (-6, 3). Braxton Lane and Duval Street are not parallel or perpendicular.
Given that,
Mary resides on Duval Street between latitudes (3,1) and (7,5). On Braxton Lane, Val resides between coordinates (2, 15) and (-6, 3).
We have to find is Braxton Lane and Duval Street parallel or perpendicular.
To find the lines are parallel or perpendicular we have to find the slope of those points.
If slopes are equal then the lines are parallel.
If slopes are negative reciprocal then the lines are perpendicular.
We find the slope of Mary resides on Duval Street between latitudes (3,1) and (7,5).
m₁=[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
m₁=[tex]\frac{5 -1 }{7-3 }[/tex]
m₁=4/4
m₁=1
The slope of the Mary resides on Duval Street between latitudes (3,1) and (7,5) is 1.
We find the slope of Braxton Lane, Val resides between coordinates (2, 15) and (-6, 3).
m₂=[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
m₂=[tex]\frac{3 -15 }{-6-2 }[/tex]
m₂=-12/-8
m₂=3/2
The slope of the Braxton Lane, Val resides between coordinates (2, 15) and (-6, 3) is 3/2.
m₁≠m₂
Therefore, Braxton Lane and Duval Street are not parallel or perpendicular.
To learn more about parallel visit: https://brainly.com/question/16701300
#SPJ1
PLEASE help! 20 points!
There is a 6% sales tax on your clothing purchase.
You pay $1.80 in tax.
What is the total amount you pay?
well, the amount paid was "x", which oddly enough is 100%, but we also know that 6% of that is $1.80, so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 1.80& 6 \end{array} \implies \cfrac{x}{1.80}~~=~~\cfrac{100}{6} \implies 6x=180\implies x=\cfrac{180}{6}\implies x=30[/tex]
The necklace is priced $85. You have a 15% discount and tax is 6%. What
will your final price be?
Why is diffusion considered a form of passive transport?
Responses
It requires no energy from the cell.
It requires no energy from the cell.
It's a process that occurs automatically.
It's a process that occurs automatically.
It has no effect on the health of the cell.
It has no effect on the health of the cell.
It's carried out while the cell does other things.
Answer:
It requires no energy from the cell.
Step-by-step explanation:
Algebraic Identity help
In the picture, the polynomial equation is (3x-k)². The values of k=4 and p=-24.
Given that,
In the picture, the polynomial equation is (3x-k)²
We have to find the k value and p value if (3x-k)²=9x²+px+16
Polynomial means polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable). The expression is divided into three categories: monomial, binomial, and trinomial depending on how many terms are included in it.
We get,
(3x-k)²=9x²+px+16
9x²-6xk+k²=9x²+px+16
We get,
p=-6k and k²=16
k²=16
k=4
Substitute in p=-6k
p=-6×4
p=-24
Therefore, the values of k=4 and p=-24.
To learn more about polynomial visit: https://brainly.com/question/11536910
#SPJ9
can anybody help me the process on how to convert fractions into decimals and decimals
into fractions.
Fractions into Decimals-
15/5 = 3
Decimals into Fractions-
0.5 = 5/10
How to convert fractions into decimals and decimals into fractions ?Place the decimal number above its place value to convert it to a fraction.
For instance, since the number six is in the tenths place in the fraction 0.6, we multiply it by 10 and get the comparable fraction 6/10.
Simplify the fraction if necessary.
The division is shown by the fractional bar between the "part" and the "whole."
By dividing the numerator by the denominator, any fractions can be transformed into decimals.
For instance, the fraction 45 denotes the ratio of 4 to 5, or 4/5.
By dividing 4 by 5, this fraction can be changed into a decimal.
Fractions into Decimals-
15/5 = 3
Decimals into Fractions-
0.5 = 5/10
To know more about fraction and decimal visit-
https://brainly.com/question/548650
#SPJ10
Round 0.699 to the nearest hundredth.
Answer: 0.700
0.699 is the closest to 0.700, the hundredth would go up by one creating 0.700 hope this helps
A recipe calls for 3/4 of a pound of flour to make 1 batch of cookies. how many batches of cookies can be made with 5 pounds of flour? include parts of the batch in the answer.
Answer:
20/3 batches of cookies can be made with 5 pounds of flour.
Step-by-step explanation:
given-
A recipe calls for 3/4 of a pound of flour to make 1 batch of cookies
asking-how many batches of cookies can be made with 5 pounds of flour
3/4 pound of flour=> 1 batch of cookies
then,
1 pound of flour=> 4/3 batch of cookies
so, required answer---
5 pound of flour=>5*( 4/3) batch of cookies
=>20/3=6.66 batch of cookies
link-https://brainly.com/question/2228115
#SPJ4
5x4 6/11 give your answer in simplest form
The answer in simplest form is [tex]20\frac{30}{11}[/tex] .
What is fraction in simplest form?When the numerator (top) and denominator (bottom) of the fraction do not have any common factors, the fraction is said to be in its simplest form. When the top and bottom of a fraction are whole numbers that are coprime to one another, the fraction is said to be in its simplest form.Any fraction can be easily found in its simplest form. By dividing both the numerator and denominator by the greatest common factor that entirely divides them, we need to simplify the fraction's numerator and denominator. Both the numerator and the denominator should still be whole numbers after division. Reducing fractions is another name for this process of simplifying fractions.Given fraction is [tex]5*4\frac{6}{11}[/tex].
So we convert the mixed fraction into an improper fraction to calculate further.
[tex]4\frac{6}{11} =\frac{50}{11}[/tex]
Next, we calculate the above fraction given in the question
[tex]5*\frac{50}{11}[/tex] = [tex]\frac{250}{11}[/tex]
So now we convert obtained improper fraction to mixed fraction which is its simplest form,
[tex]\frac{250}{11} = 20\frac{30}{11}[/tex]
To learn more about fractions visit:
https://brainly.com/question/17172929
#SPJ9
The graph of y = 2x^2 - 8x + 7 is identical to the graph of y = a(x-h)^2 + k$ for some real numbers $a, h, k$.
What is the value of $k$?
The form:
y = a(x-h)^2 + k
Is the vertex form of the quadratic equation, by finding the vertex, we conclude that k = -1.
How to get the value of k?For any quadratic equation of the form:
y = a*x^2 + b*x + c
With a vertex (h, k), we can rewrite the equation as:
y = a*(x - h)^2 + k
And the value h of the vertex is given by:
h = -b/(2a)
In this case, the quadratic equation is:
y = 2x^2 - 8x + 7
Then the value h of the vertex is:
h = -(-8)/(2*2) = 2
Evaluating the quadratic equation in x = 2 we will get the value of k, so we have.
y = 2*(2)^2 - 8*2 + 7 = -1
Then the vertex is (2, -1), which means that the value of K is -1.
Learn more about quadratic equations:
https://brainly.com/question/1214333
#SPJ1
Round 387.869911589 to 3 decimal places.
\Big(\frac{1}{6}-0.5\Big) \div\frac{5}{11}
(
6
1
−0.5)÷
11
5
387.869911589 to 3 decimal places is 387.870.
What is the number rounded to 3 decimal placesA decimal is a number that is made up of integers and non-integers. The integers are separated from the non-integers by a decimal point.
In order to round off a number to 3 decimal places, there must be 2 numbers to the right of the decimal point.
In order to round off a number to 3 decimal places, if the ten thousandth figure is equal to five or greater than 5, one is added to the thousandth figure. If the ten thousandth figure is less than 5, there is no change in the thousandth digit.
The ten thousandth is greater than 9, so one is added to the thousandth digit. The number becomes 387. 870
To learn more about decimals, please check: https://brainly.com/question/15287678
#SPJ1
What is the zero of the function represented by this graph?
Answer:
Correct answer should be x= -6
Step-by-step explanation:
prove me wrong
x+1 2/3 =2 3/8 what is x
Answer:
X=17/24
Step-by-step explanation:
first you need to find common denominators. To find it, you would multiply the denominator of the 1 2/3 and the 2 3/8.8*3=24, which means the denominator is 24. For 1 2/3, we multiplied 3*8 so we also have to do it for 2. The new equation is x+1 16/24=2 3/8. But remember, we still have to multiply 8*3, which means we have to multiply 3*3 too.
New equation:x+1 16/24=2 9/24
Now we can subtract 1 16/24 from each side
X=17/24
a foot ball team lost 4 yards, lost 3 yards and then gained 10 yards in three subsequent plays. what was their net change in yards after those three plays
PLISS HELP
Evaluate a/b if a=-48 and b = 6
Answer:
-8
Step-by-step explanation:
A= - 48
B= 6
-48/6
= 8
Negative x Negative = Positive
Negative x Positive = Negative
Positive + Positive = Positive
I dont know what im doing Help Meeee
Answer:
the x = 0 and y = 1
so start off at the zero on the x-axis, and move up to the 1 on the y- axis