Answer:
The function is [tex]\left(f \circ g \right) \left( x \right) = - 30 x - 21[/tex] and the domain is all real numbers.
Step-by-step explanation:
Composition of functions is when one function is inside of another function.
The notation used for the composition of functions looks like this, [tex]\left(f \circ g \right) \left( x \right) = f(g(x))[/tex].
We have the following functions
[tex]f(x)= -6x + 3\\\\g(x) = 5x + 4[/tex]
The composite function is
[tex]\left(f \circ g \right) \left( x \right) = f \left( g \left( x \right) \right)=f \left(5 x + 4 \right) = 3 - 6 {\left(5 x + 4\right)} = - 30 x - 21[/tex].
The domain is the set of all possible x-values which will make the function "work", and will output real y-values.
The function [tex]\left(f \circ g \right) \left( x \right) = - 30 x - 21[/tex] has no undefined points nor domain constraints. Therefore, the domain is [tex]-\infty \:<x<\infty \:[/tex] or all real numbers.
The first two terms in a sequence are 8 and 11. What is the next value if this sequence is arithmetic?
Answer:
14
Step-by-step explanation:
From the question we are given the first term 8,second term 11 and we are to find the third term.
Using the formula:Tn=a+(n-1)d
Where a=first term=8
n=number of terms =3
d= difference between terms( second term -first term)=11-8=3
T3=8+(3-1)3
=8+2(3)
=8+6
The next term =14
In need everyone's help!!!! 6-y+3 Answers: A -1 B 0 C 3 D 6
Answer: y=3
Step-by-step explanation:
6-y+3
-3 -3
6-3=3 and 3-3 is 0
so the answey is y=3
hope this Helps :)
find the circumference use 3.14 for pie r=2 m
Answer:
= 12.56 m
Step-by-step explanation:
The circumference is found by
C = 2* pi *r
C = 2 * 3.14 * (2)
= 12.56 m
Answer:
12.56 meters
Step-by-step explanation:
The circumference of a circle can be found using the following formula.
c= d* pi
We are given the radius. First, we must find the diameter. The diameter is twice the radius.
d=2*r
We know the radius is 2 meters. Therefore, we can substitute 2 in for r.
d=2*2
Multiply 2 and 2
d=4
The diameter is 4 meters.
Now we know the diameter, and can substitute 4 in for d in the circumference formula.
c= d* pi
d= 4 m
c= 4 m* pi
We also know we are using 3.14 for pi, so we can plug 3.14 in for pi.
c= 4 m * 3.14
c=12.56 m
The circumference of the circle is 12.56 meters.
The triangle is: scalene and obtuse. isosceles and acute. equilateral and acute. None of these choices are correct.
Answer:
Isosceles and acute
Step-by-step explanation:
=> This triangle have two sides congruent so it's isosceles.
=> This triangle has all of it's angles less than 90 so it is an acute triangle.
Which expression can be used to determine the average rate of change in f(x) over the interval 2, 9? On a coordinate plane, a curve opens down and to the right. The curve starts at (0, 0) and goes through (1, 3), (4, 6), and (7, 8). f(9 – 2) f(9) – f(2) StartFraction f (9 minus 2) Over 9 minus 2 EndFraction StartFraction f (9) minus f (2) Over 9 minus 2 EndFraction
Answer:
(D) [tex]\dfrac{f(9)-f(2)}{9-2}[/tex]
Step-by-step explanation:
To determine the average rate of change in f(x) over the interval [a,b], we use the formula:
[tex]\text{Average rate of change}=\dfrac{f(b)-f(a)}{b-a}[/tex]
Therefore, given a function f(x), the average rate of change in f(x) over the interval [2,9] is given as:
[tex]\text{Average rate of change}=\dfrac{f(9)-f(2)}{9-2}[/tex]
The correct option is D,
Answer:
D
Step-by-step explanation:
please help me for brainliest
Answer:
Step-by-step explanation:
A) These are the squares of another number or we can say the prime numbers
B) THE NEXT NUMBER IN THE SEQUENCE IS 9 BECAUSE ALL THESE ARE SQUARES OF 8 7 6 5 4 AND THE LAST ONE WILL BE 9
Which statement is true?
Answer:B
Step-by-step explanation:
Answer:
The real correct answer is C
Step-by-step explanation:
Which two values of x are roots of the polynomial below?
x²-11x+17
Answer:
It is E and F
Step-by-step explanation:
A quadratic equation is written in the form of ax²+bx+c. The two values of x that are the roots of the polynomial are E and F.
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
The roots of the quadratic equation are found as shown below,
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
If the given equation x²-11x+17 is compared with the general quadratic equation ax²+bx+c, then the value of a, b, and c is 1, -11, and 17, respectively.
The roots of the given polynomial x²-11x+17=0 can be found as shown below. Therefore, The roots of the polynomial are,
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\x = \dfrac{-(-11) \pm \sqrt{(-11)^2 - 4(1)(17)}}{2(1)}\\\\x = \dfrac{11 \pm \sqrt{121 - 68}}{2}\\\\x = \dfrac{11 \pm \sqrt{53}}{2}[/tex]
x= (11 + √53)/2 , (11 - √53)/2
Hence, the two values of x that are the roots of the polynomial are E and F.
Learn more about Quadratic Equations:
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Plz HELP!!!!!!!!!!!!!!!!!!!!!
They are Parallel, Intersecting, and perpendicular, if it's helpful let me know
Can someone please help me I really need help
Answer:
3 3/4
Step-by-step explanation:
1 5/12 2 1/3
First, we must convert the fractions to have the same denominator.
We can turn 2 1/3 is equal to 2 4/12.
1 5/12 + 2 4/12 = 3 9/12
Now we simplify.
3 9/12 = 3 3/4
Can someone help me please
Answer:
SSS similarity postulate
Step-by-step explanation:
Since all sides are similar and proportional, so the SSS similarity postulate !
Determine whether the geometric series 36 + 39.6 + 43.56 + ... converges or diverges, and identify the sum if it exists.
Answer:
Diverges
There is no sum.
Step-by-step explanation:
A geometric series has a general formula of:
[tex]\sum ar^n[/tex]
Where 'a' is the initial term, 'n' is the number of terms, and 'r' is the constant ratio. If |r| < 1 than the series converges, but if |r| > 1, than the series diverges.
In this problem, the initial term is a = 36, the ratio can be found by:
[tex]r = \frac{39.6}{36}=\frac{43.56}{39.6}\\ r=1.1[/tex]
Since the ratio is r =1.1 and 1.1 > 1.0, the series diverges.
In a diverging series, it is not possible to determine the sum of infinite terms, since it would be infinite.
The geometric series diverges and the sum does not exists.
What is a Geometric Series ?A geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms .
A geometric series has a general formula of:
∑arⁿ
Where 'a' is the initial term, 'n' is the number of terms, and 'r' is the constant ratio. If |r| < 1 than the series converges.
In this particular case, the initial term is a=36 and each term is multiplied by 1.1 to get the next term
Therefore r = 1.1 and as it is >1 therefore the series diverges.
The sum of a divergent series is not finite so the sum does not exists.
To know more about Geometric Series
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Instructions: Find the angle measures given the figure is a rhombus.
Answer:
m∠1 = 90°
m∠2 = 55°
Step-by-step explanation:
1. m∠1 = 90° because by definition, the diagonals of a rhombus are perpendicular, or intersect at 90°.
2. Because of vertical angles, the angle opposite of ∠1 is also 90°. A triangle has a total of 180°.
m∠2 + 90 + 35 = 180
90 + 35 = 125
m∠2 + 125 = 180
subtract 125 from both sides to solve for m∠2
m∠2 = 55°
If the point (x, y) is on the y-axis, which of the following must be true? A). x=0 B). y=0
Answer:
X = 0
Step-by-step explanation:
Convert the decimal to a percent.
3.06 = a number here %
U 3 4
Lucy buys 7 kg of nuts to sell.
She pays £10 for the nuts.
Lucy puts all the nuts into bags.
She puts 350 g of nuts into each bag.
She then sells each bag of nuts for 75p.
Lucy sells all the bags of nuts.
Work out her percentage profit.
Answer: 50%
Step-by-step explanation:
I'm converting 7kg to grams to make it easier. So £10 = 7000g
£1 = 7000÷10 = 700g
700g÷2 = 350g and if you follow the ratios on top, she payed 50p per 350g
She sells a bag of 350g for 75p.
Percentage profit=[tex]\frac{Change in cost}{original cost}[/tex] × 100
75p - 50p = 25p = change in cost
Percentage profit= [tex]\frac{25}{50}[/tex] × 100
= 50%
The function of fx has been transformed to give go. Witch of the following functions represent gx?
Answer:
Sorry your mouse is blocking the fx equation. Is it x squared? I can't help you if I can't see what the equation is I'm sorry
Step-by-step explanation:
if x4x2/3=x^awhat is the value of a?
(Number 7)
Answer:
4 2/3
Step-by-step explanation:
[tex]x^4x^{2/3}= \\\\x^{4+2/3}= \\\\x^{4 \ 2/3}[/tex]
Therefore, a= 4 2/3.
Hope this helps!
What friction is equivalent to 2/-6
Answer:
-1/3
Step-by-step explanation:
The negative sign can be moved: 2/-6 => -2/6 => -1/3
I need help! -4y-4+(-3)
Answer:
-4y-7
Step-by-step explanation:
-4y-4-3
-4y-7
Select 222 strategies that we can use to subtract 563-192563−192563, minus, 192. Choose 2 answers: Choose 2 answers: (Choice A) A Add 100+90+2100+90+2100, plus, 90, plus, 2. (Choice B) B Evaluate (563-200)+8(563−200)+8left parenthesis, 563, minus, 200, right parenthesis, plus, 8. (Choice C) C Subtract 571-200571−200571, minus, 200.
When something is parallel to each other there what
Answer:
they are 2 lines that look ;like this =
Step-by-step explanation: the 2 lines of the equal sign are parallel
Help please :) much appreciated
Answer:
x^2 +2x -5
Step-by-step explanation:
f(x) = 2x+3
g(x) = x^2 -8
f(x)+g(x) = 2x+3+ x^2 -8
Combine like terms
= x^2 +2x -5
evaluate 0.53n + 5 when n= 3 and when n= -3
Answer:
6.59 and 3.41
Step-by-step explanation:
To evaluate, substitute n for each of the given values.
So when n= 3:
0.53n + 5 = 1.59 + 5 = 6.59
And when n = -3
0.53 n + 5 = -1.59+5=3.41
Hope this helps
Use synthetic division to divide x^3+5x^2−9x−7 by x−2 1 5 -9 -7 The quotient is: _____ The remainder is: ______
Answer:
The quotient is x² + 6x +3
Remainder = -1
Step-by-step explanation:
Explanation:-
Given Polynomial equation
f(x) = x³+5x²−9x−7
By using synthetic division
x = 2 1 5 -9 -7
0 1 12 6
1 6 3 -1
The quotient is x² + 6x +3
Remainder = -1
3×-y=5,2×+y=5 pleaseplease
Answer:
x = 2
y = 1
Step-by-step explanation:
3x - y = 5..............(1)× 1
2x + y = 5...….......(2)× 1
3x - y = 5..............(3)
2x + y = 5.............(4)
Cancel y
3x + 2x = 5 + 5
5x = 10
Divide both sides by 5
x = 2
Substitute for the value of y
3x - y = 5
3(2) - y = 5
6 - y = 5
6 - 5 = y
1 = y
y = 1
i’m not sure how to solve “system of equations”
Hey there! :)
Answer:
(2, -2)
Step-by-step explanation:
-2x + y = -6
4x + 3y = 2
We can begin by setting the first equation equal to y:
-2x + y = -6
Add 2x to both sides:
y = 2x - 6
Plug this equation for y into the second equation:
4x + 3(2x - 6) = 2
Distribute:
4x + 6x - 18 = 2
Combine like terms:
10x = 20
x = 2
Plug the value of 'x' into an equation to solve for 'y':
-2(2) + y = -6
-4 + y = -6
y = -2
Therefore, the solution is (2, -2)
May you please Simplify this for me
|7−10|
Answer:
Step-by-step explanation:
|7-10|=3
absolute value of any number is always positive
Answer:
-3
Step-by-step explanation:
As the equation is written, you will be subtracting 10 from 7.
Subtract 10 from 7 and you will go past 0.
Your answer will be negative.
please help to solve this problem 1) a^2-b^2+4b-4
Answer: (a-b+2)x(a+b-2)
Step-by-step explanation:
1) factor out the negative sign from the expression: a^2(b^2-4b+4)
2) Using a^2-2ab+b^2=(a-b)^2, factor the expression: a^2-(b-2)^2
3) Using a^2-b^2=(a-b)(a+b), factor the expression: (a-(b-2))x(a+(b-2))
4) When there is a - in front of an expression in parentheses, change the. Sign of each term in the expression: (a-b+2)x(a+(b-2))
5) When there is a + in front of an expression in parentheses, the expression stays the same: (a-b+2)x(a+b-2)
5^x+3=300
solve for X
Answer: x=3.537715
Step-by-step explanation:
5x+3=300
5x+3+−3= 300+ −3
5x=297
Step 2: Solve Exponent.
5x=297
x=3.537715
Hope this helps :)