Step-by-step explanation:
f(x)=x^2-4x-9
g(x)=-3x-5
so when f(g(x)) that x is a number
-3x-5 equals the number in f(x) so that x is -3x-5
f(-3x-5) and if f(x)=x^2-4x-9
then inserting in -3x-5 for x in f(x) and distrubute
(-3x-5)^2-4(-3x-5)-9
9x^2+42x+36
I hope that helps :)
Answer:
9x^2 + 42x + 16
Step-by-step explanation:
f(g(x))
Plug in the expression for g(x)
f(g(x)) = f(-3x - 5)
f(x) = x^2 - 4x - 9
For every x in f(x) replace it with -3x - 5
f(-3x - 5) = (-3x - 5)^2 - 4(-3x -5) -9
Expand
f(-3x - 5) = (9x^2 + 30x + 25) + (12x + 20) - 9
Combine like terms
f(-3x - 5) = 9x^2 + 42x + 16
f(g(x)) = 9x^2 + 42x + 16
2. A number m is less than -3 or greater than or equal to 1.
The absolute value of m is equal to the positive distance between m and 0.
What is value?Value is an important concept in economics, finance, and accounting. It is the worth of a thing, such as a product, service, or currency. Value can be determined by the amount of goods or services it can exchange for, or the amount of money it can produce. Value is subjective, so it is up to the individual to decide what is valuable to them. Value is also a measure of the relative worth of a good or service, and it can have an effect on the price of a good or service. Value is an important concept to understand in economics, finance, and accounting.
The absolute value of m can be calculated by taking the distance between m and 0, regardless of whether m is negative or positive. For example, if m is -7, the absolute value of m is 7, since the distance between -7 and 0 is 7. If m is 3, then the absolute value of m is also 3, since the distance between 3 and 0 is also 3.
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The absolute value of m is equal to the positive distance between m and 0.
What is value?Value is an important concept in economics, finance, and accounting. It is the worth of a thing, such as a product, service, or currency. Value can be determined by the amount of goods or services it can exchange for, or the amount of money it can produce. Value is subjective, so it is up to the individual to decide what is valuable to them. Value is also a measure of the relative worth of a good or service, and it can have an effect on the price of a good or service. Value is an important concept to understand in economics, finance, and accounting.
The absolute value of m can be calculated by taking the distance between m and 0, regardless of whether m is negative or positive. For example, if m is -7, the absolute value of m is 7, since the distance between -7 and 0 is 7. If m is 3, then the absolute value of m is also 3, since the distance between 3 and 0 is also 3.
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Find a formula for the sequence 3, 9/4, 27/7, 81/10,... in sigma notation
9514 1404 393
Answer:
[tex]\displaystyle S_n=\sum_{k=1}^n{\frac{3^k}{3k-2}}[/tex]
Step-by-step explanation:
The sequence terms appear to have numerators that are powers of 3, and denominators that are a linear (arithmetic) sequence with a first term of 1 and a common difference of 3.
numerator: 3^x
denominator: 1 +3(n -1) = 3n-2
Then the sum of n terms of the sequence can be described by ...
[tex]\displaystyle \boxed{S_n=\sum_{k=1}^n{\frac{3^k}{3k-2}}}[/tex]
How many solutions can be found for the system of linear equations represented on the graph?
A) no solution
B) one solution
C) two solutions
D) infinitely many solutions
Answer:
B) One solution
Step-by-step explanation:
Clearly, the two linear equations graphed have one point of intersection, which means one solution.
Answer:
B
Step-by-step explanation:
the solution is the intersection of the two lines
Please help me with this question
Answer:
Step-by-step explanation:
i have no idea
in the xy-plane what is the y-intercept of the graph of the equation y=(x-2)^2?
As a result, the graph of the equation y=(x-2)2 in the xy plane has the y-intercept of y = -9.
what is equation ?The number is said to be in its simplest form when divided into its smallest equivalent fraction. What should be done to find the most basic form. Look for common factors in the numerator and denominator. Verify a fractional integer to verify if it qualifies as a prime number. A statement having two collinear and an equal marker in the middle is called an equation in mathematics. The general form of any equation contains the degrees of all the variables in descending order. The conventional form of a linear equation is an x + b = 0. The general form of a linear equation with two variables is an x + b y + c = 0. (or something similar). An identity holds true regardless of the value given to the variables.
given
Equation as given:
y = 6 (x - 1/2)(x+3)
To identify the equation's graph's y-intercept
Put x = 0 in place of it in the equation.
y = 6 (0 - 1/2)(0+3)
Apply the math operation, then find y.
y = -9
As a result, the graph of the equation y=(x-2)2 in the xy plane has the y-intercept of y = -9.
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There are 200 raffle tickets in a box. There are four 1st prize tickets, eight 2nd prize tickets, and sixteen 3rd prize tickets. When one ticket is selected, what is the probability of it being a 1st prize, 2nd prize, or 3rd prize ticket?
0.08
0.16
0.04
0.14
Answer:
0.14
Step-by-step explanation:
The answer is: 0.14
I hope this helps!
Gloria is categorizing triangles based on their properties. The side lengths of the triangles are listed below. Triangle 1: 3 cm, 4 cm, 5 cm Triangle 2: 5 cm, 5 cm, 7 cm Triangle 3: 6 cm, 7 cm, 9 cm Triangle 4: 8 cm, 8 cm, 8 cm She places the triangles into 3 different groups: scalene, isosceles, and equilateral. Which pair of triangles would Gloria put in the same group?
A. 1 and 2 B. 1 and 3 C. 2 and 3 D. 2 and 4
Is the point (4,0) on the parabola given by the equation: y=x^2-4x? Explain your answer
HELPP PLEASE ILL MARK BRAINIEST
A bag contains only red marbles and blue marbles.
• The number of red marbles in the bag can be represented by x.
• The number of blue marbles is 12 more than 3 times the number of red marbles.
• There are a total of 48 marbles in the bag.
What is x, the number of red marbles in the bag?
Answer:
12 red marbles in the bag
13. Communicate and Justify During a chemistry experiment, Julian
records how the temperature changes over time using ordered
pairs (time in minutes, temperature in °C).
(0, 15), (5, 20), (10, 50), (15, 80), (20, 100), (25, 100)
a. Which variable is the independent variable?
The dependent variable? Explain in need answerssss
Julian uses ordered pairs to record the temperature variations over time during a chemistry experiment (time in minutes, temperature in °C). (0, 15), (5, 20), (10, 50), (15, 80), (20, 100), (25, 100) (25, 100).
What do you meant by depend and independent variable ?It is the cause that is the independent variable. Its worth is unrelated to other study variables. The effect serves as the dependent variable. The independent variable's modifications determine its value. It is a thing that is dependent on other things. The amount of study you did, how much sleep you had the night before the test, or even how hungry you were when you took it.
Could all affect your test result, which makes it a dependent variable. The dependent variable is impacted by the independent variable. For instance, your exam results are influenced by how much sleep you get (an independent variable) (dependent variable). This is understandable, but Ex. How much sleep you get depends on your test results.
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on Monday the solar panels on a house produced 37.124 units of energy. On Tuesday, the solar panels produced 2,846 fewer units of energy than on Monday. What is the total number of units of energy in two days.
The total number of units of energy produced in the two days is 71,402.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Monday:
Energy = 37,124
Tuesday:
Energy = 37,124 - 2846 = 34278
The total energy produced.
= 37124 + 34278
= 71402
Thus,
The total number of energy in two days is 71,402.
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how many terms of AP - 6. - 11 by 2 .minus 5 are needed to be the sum -25
Given:
The terms of a sequence are:
[tex]-6,-\dfrac{11}{2},-5[/tex]
To find:
The number of terms whose sum is -25.
Solution:
We have, the given sequence:
[tex]-6,-\dfrac{11}{2},-5[/tex]
Here, the first term is -6.
[tex]-\dfrac{11}{2}-(-6)=-5.5+6[/tex]
[tex]-\dfrac{11}{2}-(-6)=0.5[/tex]
Similarly,
[tex]-5-(-\dfrac{11}{2})=-5+5.5[/tex]
[tex]-5-(-\dfrac{11}{2})=0.5[/tex]
The difference between consecutive terms are same. So, the given sequence is an arithmetic sequence with common difference 0.5.
The sum of n terms of an arithmetic sequence is:
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
Where, a is the first term, d is the common difference.
Putting [tex]S_n=-25,a=-6,d=0.5[/tex], we get
[tex]-25=\dfrac{n}{2}[2(-6)+(n-1)0.5][/tex]
[tex]-50=n[-12+0.5n-0.5][/tex]
[tex]-50=-12.5n+0.5n^2[/tex]
[tex]0=0.5n^2-12.5n+50[/tex]
Splitting the middle term, we get
[tex]0.5n^2-2.5n-10n+50=0[/tex]
[tex]0.5n(n-5)-10(n-5)=0[/tex]
[tex](0.5n-10)(n-5)=0[/tex]
Using zero product property, we get
[tex](0.5n-10)=0[/tex] and [tex](n-5)=0[/tex]
[tex]n=\dfrac{10}{0.5}[/tex] and [tex]n=5[/tex]
[tex]n=20[/tex] and [tex]n=5[/tex]
Therefore, the sum of either 5 or 20 terms is -25.
a) calculer: f(1,5); f(2,5); f(2)
Answer:
Step-by-step explanation:
you should give the function, if i haven't it, how can i help you.
i can give u some tips, put 1.5, 2.5, 2 in function respectively. then calculate them, u will get the answer.
The coordinates of cd are C(-7,-2) and D (-3,-5) Point E is the midpoint of cd What are the coordinates of the midpoint E?
The coordinates of the midpoint of CD with endpoint at C(-7,-2) and D(-3,-5) is E(-5, -3.5)
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let (x, y) represent the coordinate of the midpoint E. Point E is the midpoint of CD, hence:
x = [(-7) + (-3)] / 2 = -5
y = [(-2) + (-5)] / 2 = -3.5
Therefore the coordinates of the midpoint of CD with endpoint at C(-7,-2) and D(-3,-5) is E(-5, -3.5)
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some1 hurry up i need help
Answer:
9 because the opposite of -9 is 9
hope this helped gl
Step-by-step explanation:
Which algebraic expression represents the phrase "seven more than half of a number”?
Evaluate (99)3 using suitable identities
Answer:
297Step-by-step explanation:
(99)3 =
(99) x 3 =
(90 + 9) x 3 =
(90) x 3 + (9) x 3 =
90 x 3 + 9 x 3 =
270 + 27 =
297
Hope that helps! :)
-Aphrodite
Step-by-step explanation:
Correction:Evaluate (99)^3 using suitable identities.
Solution:(99)^3 = (100 - 1)^3
since, (a - b)^2 = a^3 - b^3 - 3ab (a-b)
Where,
a = 100 andb = 1Now,
(99)^3
=> (100)^3 - (1)^3 - 3(100)(1)(100 - 1)
=> 1000000 - 1 - 3(100)(100 - 1)
=> 1000000 - 1 - 300 (99)
=> 1000000 - 1 - 29700
=> 970299 Ans.
can someone pls help me w this question ??
PLEASE HURRY AND HELP!!!
Which of the following tables represents a linear relationship that is also proportional?
x y
0 3
3 6
6 9
x y
0 4
2 6
4 8
x y
0 0
6 3
12 6
x y
0 3
5 5
10 7
Table (x, y) equals (0, 0), (6, 3), and (12, 6) represents a linear relationship that is also proportional.
What are ratio and proportion?In its most basic form, a ratio is a comparison between two comparable quantities.
There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.
If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.
The first option is linear but not proportional as 3 ×2 = 6 and 6×2 = 12.
By observing the given options we conclude that the third option is linear and proportional as,
6 ÷ 2 = 3 and 12 ÷ 2 = 6.
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Please help me asap
On solving the provided question, we cans ay that By unitary method, the amount to be removed = original - shortened = 3/9 - 2/9 = 1/9
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
By unitary method,
original length of pipe = 3/9 inch
shortened length of pipe = 2/9
so, the amount to be removed = original - shortened = 3/9 - 2/9 = 1/9
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Greatest common factor
Step-by-step explanation:
To find the GCD or GCF of two numbers , you should:
List the prime factors of each one of them(the 2 numbers)choose the common number+least exponent multiply themSuppose $28,000 is deposited into an account paying 5.25% interest, which is compounded continuously. How much money will be in the account after 4 years if no withdrawals or additional deposits are made?
The formula for continuously compounded interest is:
A = P * e^(rt)
where:
A is the final amount
P is the initial amount (the principal)
r is the annual interest rate (in decimal form)
t is the number of years the interest is compounded
Substituting in the given values, we get:
A = $28,000 * e^(0.0525 * 4) = $28,000 * e^0.21 = $28,000 * 1.23 = $28000*1.23 = 34,540
Therefore, there will be $34,540 in the account after 4 years.
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Helppppppppppppppppppppppppppp
Answer:
20 inches
[tex]c = \sqrt{12 ^{2} + 16 ^{2} } \\ c = \sqrt{400} \\ c = 20[/tex]
5. A candy company used 12 gallons of syrup to make 6 batches of candy. What is the rate of syrup per batch? (Please explain!)
Answer: 2 gallons of syrup per batch
Step-by-step explanation:
12/6=2
Canvas Reproductions, Inc has RM4,500 researching a new project. The project requires RM20,000 worth of new machinery which would cost RM3,000 to install. The company would realize RM4,500 in after tax proceeds from the sale of the old machinery. If Canvas’s working capital is unaffected by this project, what is the initial investment amount for this project?
Hi. This is an informal letter .
The body of letter goes like this
Hi friend hope u are enjoying ur life and luck find u in best state of mind. My exam have been over and wanted to share my experience with my near and dear one so I was planning to come to ur place to enjoy my vacationHi. This is an informal letter .
The body of letter goes like this
Hi friend hope u are enjoying ur life and luck find u in best state of mind. My exam have been over and wanted to share my experience with my near and dear one so I was planning to come to ur place to enjoy my vacationHi. This is an informal letter .
The body of letter goes like this
Hi friend hope u are enjoying ur life and luck find u in best state of mind. My exam have been over and wanted to share my experience with my near and dear one so I was planning to come to ur place to enjoy my vacationHi. This is an informal letter .
The body of letter goes like this
Hi friend hope u are enjoying ur life and luck find u in best state of mind. My exam have been over and wanted to share my experience with my near and dear one so I was planning to come to ur place to enjoy my vacation
If these two shapes are similar, what is the measure of the missing length j?
Step-by-step explanation:
since the 2 shapes are similar then their sides are proportional
9/18= j/90
then j equals 45
PLS HELP FOR 10 POINTS PLEASE SHOW YOUR WORK
IF YOUR A BOT JUST SENDING A FILE TO CLICK ON THERE THEN YOU WILL BE REPORTED.
THANK YOU!
question: find the measure of the missing angle
Answer:
25ºStep-by-step explanation:
Answer = 180 - (100 + 55)
Answer = 180 - 155
Answer = 25º
Hope that helps! :)
-Aphrodite
Answer: The measure of the missing angle is 25 degrees
Step-by-step explanation:
A triangle equals 180 degrees so you would add the 100 degrees and 55 degrees and then subtract that from 180. Then you have your answer. :)
Which expression is equivalent to 3(6m) + m? A. 19m B. 21m C. 7m + 3 D. 18m + 6m²
Answer:
3(6m)+m=18m+m=19m so your answer would be A. 19m
Step-by-step explanation:
Use Pythagorean Theorem to find the missing
measurement. Show your work. Round to the nearest
hundredth if necessary.
a, 12 ft; b. 12 ft
Answer:
12^2+12^2=c^2
Step-by-step explanation:
12x12=144 + 12x12=144=c^2
288=c^2
find the square root of 288
19.97=c 20=c
Find the area
of this figure.
12m
15m
5m
8m
5m
Answer:
The answer is 12×15×5×8×5 =36,000m