Answer:
The value of [tex]$(f \circ g)(x)$[/tex] is 17-18x and [tex]$(g \circ f)(x)$[/tex] is -7-18x.
Step-by-step explanation:
It is given in the question functions f(x) as 3x+2 and g(x)=5-6x.
It is required to find [tex]$(f \circ g)(x)$[/tex] and [tex]$(g \circ f)(x)$[/tex].
To find [tex]$(f \circ g)(x)$[/tex], substitute g(x) for x in f(x) and simplify the expression.
To find [tex]$(g \circ f)(x)$[/tex], substitute f(x) for x in g(x) and simplify the expression.
Step 1 of 2
Substitute g(x) for x in f(x) and simplify the expression.
[tex]$$\begin{aligned}&(f \circ g)(x)=f(5-6 x) \\&(f \circ g)(x)=3(5-6 x)+2 \\&(f \circ g)(x)=15-18 x+2 \\&(f \circ g)(x)=17-18 x\end{aligned}$$[/tex]
Step 2 of 2
Substitute f(x) for x in g(x) and simplify the expression.
[tex]$$\begin{aligned}&(g \circ f)(x)=g(3 x+2) \\&(g \circ f)(x)=5-6(3 x+2) \\&(g \circ f)(x)=5-18 x-12 \\&(g \circ f)(x)=-7-18 x\end{aligned}$$[/tex]
If the r-value, or correlation coefficient, of a data set is negative , the coefficient of determination is negative
true or false
On a coordinate plane, a quadrilateral has points E (negative 2, 0), D (0, 4), G (4, 2), and F (0, 0).
Which are true if figure DEFG is reflected across the x-axis? Check all that apply.
D(0, 4) → D'(0, –4)
E(–2, 0) → E'(–2, 0)
The perpendicular distance from G' to the x-axis will equal 2 units.
The perpendicular distance from D' to the x-axis will equal 8 units.
The orientation will be preserved.
By applying the reflection rule across the x-axis to quadrilateral DEFG, we obtain the following true statements:
D(0, 4) → D'(0, -4)E(-2, 0) → E'(-2, 0)The perpendicular distance from G' to the x-axis will be equal to 2 units.The reflection of a quadrilateral.In Geometry, the x-axis would remain the same if a quadrilateral is reflected across the x-axis and the sign on the y-axis would change either from positive to negative and vice-versa.
By applying the reflection rule across the x-axis (x, y) → (x, -y), we obtain the following true statements:
D(0, 4) → D'(0, -4)E(-2, 0) → E'(-2, 0)The perpendicular distance from G' to the x-axis will be equal to 2 units.Read more on reflection here: https://brainly.com/question/10929277
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Answer:
A
B
C
Are the right answer
Step-by-step explanation:
A and b are monomials where a = 125 and b = 27p12. what is the factored form of a – b? (5 – 3p4)(25 15p4 9p8) (25 – 3p4)(5 15p3 9p3) (25 – 3p4)(5 15p4 3p8) (5 – 3p4)(25 15p3 3p4)
The correct option is (A). The factored form of a-b is (5-3p⁴)(25+15p⁴+9p⁸).
Given that A and B are monomials where a = 125 and b = 27p¹².
Monomial expressions include only one non-zero term. Numbers, variables, or multiples of numbers and variables are all examples of monomials.
Firstly, substitute a=125 and b = 27p¹² into a-b, we get
a-b=125-27p¹² ......(1)
As we know, 125=(5)³, 27p¹²=(3p⁴)
So, equation (1) can be rewritten as
a-b=(5)³-(3p⁴)
Now, apply a³-b³=(a-b)(a²+ab+b²).
a³-b³=(5-3p⁴)(5²+5(3p⁴)+(3p⁴)²)
Further, Simplify using exponent rule with the same exponent (ab)ⁿ=aⁿbⁿ.
a³-b³=(5-3p⁴)(5²+5×3p⁴+3²×(p⁴)²)
Furthermore, calculate the power, we get
a³-b³=(5-3p⁴)(5²+5×3p⁴+9(p⁴)²)
Then, Simplify using exponent power rule (aˣ)ⁿ=aˣⁿ, we get
a³-b³=(5-3p⁴)(5²+5×3p⁴+9p⁸)
Now, multiply the monomials, we get
a³-b³=(5-3p⁴)(5²+15p⁴+9p⁸)
Further, calculate the power, we get
a³-b³=(5-3p⁴)(25+15p⁴+9p⁸)
Finally, reorder the expressions, we get
a³-b³=(5-3p⁴)(9p⁸+15p⁴+25)
Hence, the factored form of a-b where a and b monomials and a = 125 and b = 27p¹² is (5-3p⁴)(9p⁸+15p⁴+25).
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Answer:a
Step-by-step explanation:
i just did it
find the product (2y - 2nb) (y+4nb)
Answer: 2y^2+6bny-8n^2b^2
Step-by-step explanation: I hope this helps!
if t is 25% of u, then what percent of 4t is 2u?
Step-by-step explanation:
t = .25u (given)
4 t = 4 (.25u) = u
then u = 50% of 2 u
1. One group (A) contains 180 people.
One-fourth of the people in group A will be
selected to win free tickets to a concert.
There is another group (B) in a nearby town
that will receive the same number of tickets,
but there are 292 people in that group.
What will be the ratio of non-winners in
2
group A to non-winners in group B after the
selections are made?
Answer:
135:147
Step-by-step explanation:
180/4=45
180-45=135
292-45=247
135:247
can you help me im stuck here
Answer:
its dependent varaible
Answer:
Step-by-step explanation:
NOW WATSH ME WIP WAHS E NYA NAY
6) A basket contains 5 yellow, 3 blue and 2 white balls. If a ball is drawn randomly from the basket, find the probability of not getting a blue ball.
Answer: 70%
Step-by-step explanation:
A basket contains:
5 yellow balls
3 blue balls
2 white balls
What would be the probability of randomly picking a ball and the ball not being blue?
So, we can find the probability of picking up a blue ball. Let's do that first.
To calculate the probability of getting a blue ball, we need to divide the number of blue balls by the number of possible balls.
The number of blue balls = 3
The total number of balls = 2 + 3 + 5 = 10 balls
3 blue balls divided by 10 balls = 0.3.
If you multiply 0.3 by 100%, it will give you a probability of finding a blue ball equal to 30%
Now, we just need to find the probability of NOT finding a blue ball. Because we have 30% of finding a blue ball, we just need to subtract 30% from 100%.
100 - 30$ = 70%
The probability of not getting a blue ball is equal to 70%.
Hope I Helped!
[tex]|\Omega|=5+3+2=10\\|A|=5+2=7\\\\P(A)=\dfrac{7}{10}=70\%[/tex]
una fracción de reducción a su mínima expresión en igual a 1/8. si la suma de sus terminos es 72. hallar la diferencia entre ellos
Por lo tanto el número es p/q = 8/64.
¿Qué es una fracción?Fracción es un número que se puede representar en forma de p/q, donde q no es igual a cero.
It is given that :
En su forma más simple, el número es 1/8
Sea el número p/q
p + q = 72 (dado)
p/q = 1/8
q = 8p
p+8p = 72
9p = 72
p = 8
q = 8p
q = 8 * 8 = 64
Por lo tanto el número es p/q = 8/64.
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Convert from Decimal Notation to Scientific Notation
In the following exercises, write each number in scientific notation.
554. 0.026
Answer:
Hence, 0.026 can be expressed as [tex]$2.6 \times 10^{-2}$[/tex].
Step-by-step explanation:
- Given 0.026
- Use given, move the decimal point so that first factor is greater than or equal to 1 but less than 10 .
- Then count n and write in scientific notation.
Step 1 of 1
Consider 0.026
[tex]$$\Rightarrow 2.6$$[/tex]
Decimal has moved 2 places to right.
The power will be negative as original no. is less than 1 .
[tex]$$\begin{aligned}&2.6 \times 10^{-2} \\&0.026=2.6 \times 10^{-2} .\end{aligned}$$[/tex]
Which equation is represented by the model? 3x2 – 4x – 1 = (3x 1)(x – 1) 3x2 – 2x – 1 = (3x – 1)(x 1) 3x2 – 4x 1 = (3x – 1)(x – 1) 3x2 – 2x 1 = (3x – 1)(x – 1)
The equation represented by the model is 3x²-4x+1=(3x-1)(x-1).
Given model represents a polynomial of the form ax²+bx and model is in figure.
Consider the given table.
The first row in the table represents first term of the polynomial.
In first row first three terms are variables and last term are constant.
Write all the terms of the first row in the form of sum.
+x+x+x-1=3x-1
The first column in the table represents second term of the polynomial.
In first column first term are variable and last term are constant.
Write all the terms of the first column in the form of sum.
+x-1=x-1
The product of first term of polynomial (3x-1) and second term of polynomial (x-1) is equal to the sum of all remaining terms in this table.
+x²+x²+x²-x-x-x-x+1=3x²-4x+1.
We can also check this by multiplying (3x-1) and (x-1) as
(3x-1)(x-1)=3x(x-1)-1(x-1)
(3x-1)(x-1)=3x(x)-3x(1)-1(x)+1(1)
(3x-1)(x-1)=3x²-3x-x+1
(3x-1)(x-1)=3x²-4x+1
Hence, the equation represented by the given model in the form of polynomial ax²+bx is (3x-1)(x-1)=3x²-4x+1.
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Using the following image, if E is the midpoint of FD find ED.
What is ED?
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: ED = 5 \:\: units[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \:FE + ED = FD[/tex]
[tex]\qquad \tt \rightarrow \:5 + x = 10[/tex]
[tex]\qquad \tt \rightarrow \:x = 10 - 5[/tex]
[tex]\qquad \tt \rightarrow \:x = 5[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
The value of ED is 5 units, which is determined by using the concept of midpoint.
The figure given below shows a line segment FD, where the length of line segment FD refers to the distance between its endpoints, F and D.
Given that E is the midpoint of FD.
FE = 5 units
FD = 10 units
Since M is the midpoint of FD, So FE = ED
⇒ FD = FE + ED
Substitute the values of FE = 5 and FD = 10, in the above equation,
⇒10 = 5 +ED
⇒ ED = 10 - 5
⇒ ED = 5
Therefore, the value of ED is 5 units.
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The seismic activity density of a region is the ratio of the number of earthquakes during a given time span to the land area affected. The table shows the land area and seismic activity density.
The correct statement about the earthquake in the state is option c. State A had approximately 3,362 more earthquakes than State B.
How to solve for the earthquake in the state Awe have x/y = 0.00299
y = 163696
To solve for x we have
163696 * 0.00299
= 4895 earthquakes
Next we have to solve for earth quakes in state Bx = 0.1402 x 10931
= 1533
Next we have to find the difference
4895 - 1533 = 3362 earthquakes.
We have to conclude that state A has 3362 earthquakes more than B. Hence the answer is c.
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Complete question
The seismic activity density of a region is the ratio of the number of earthquakes during a given time span to the land area affected. The table shows the land area and seismic activity density.
Which statement about the number of earthquakes the states had for the given time span is true?
State A had approximately 1,533 more earthquakes than State B.
State B had approximately 1,533 more earthquakes than State A.
State A had approximately 3,362 more earthquakes than State B.
State B had approximately 3,362 more earthquakes than State A.
Help me help me help me help me help me please
Answer:
x = 1, 4
Step-by-step explanation:
We assume the graph is of the relation y = f(x). The desired values of x are those that correspond to points where the y-value is -2.
Reading the graphWe are only interested in the x-coordinates of points that lie on the horizontal line where y = -2. Those points are (1, -2) and (4, -2).
The values of x such that f(x) = -2 are x=1 and x=4.
Find the image of G when A IMG is rotated 180 around the origin.
O (2,4)
O (-2,-4)
O (-1.3)
O (2.-4)
The image of G when A IMG is rotated 180 around the origin is (-2,-4).
To rotate a figure 180 degrees around the origin, we reverse the signs of both the x-coordinate and the y-coordinate. In the image, the point G has coordinates (2,4). Reversing the signs of these coordinates gives us (-2,-4).
Rotate the figure 180 degrees around the origin. This means that we imagine the figure being flipped over the origin.
Reverse the signs of both the x-coordinate and the y-coordinate of the point G. This is because when we rotate a figure 180 degrees around the origin, the signs of both the x-coordinate and the y-coordinate are reversed.
The new coordinates of G are the coordinates of the point that is the result of rotating the figure 180 degrees around the origin and reversing the signs of the coordinates of point G. In this case, the new coordinates of G are (-2,-4).
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Geometry Question with Circles: If GP=PH, GA=17, mED=37, and mAB =87c find each measure.
The geometry illustrates that the value of DB is 34°
How to calculate the angles?AB = 87°
ED = 37°
BCD will be:
= (360° - 87° - 32°)/2
= 118°
FA will be:
= 118°/2
= 59°
DC = 118/2 = 59°
HB = GA = 17°
DB = 2 × 17° = 34°
EG = GA = 17°
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Please help me its due soon! :(
Select all the correct answers.
Consider the graph of the function : f(x)=logx
Which are features of function g if g(x)= 4log(x)+4
The features of the function g(x) = 4log(x) + 4 are
(b) range (-∞, ∞)(d) x-intercept (0.1, 0)(e) Vertical asymptote, x = 0How to determine the features of g(x)?The function is given as;
g(x) = 4log(x) + 4
The intercept
A logarithmic function has no y-intercept.
Set g(x) to 0, to determine the x-intercept
4log(x) + 4 = 0
Divide through by 4
log(x) + 1 = 0
This gives
log(x) = -1
Take the inverse of both sides
x = 10^-1
Evaluate
x = 0.1
The x-intercept is (0.1, 0)
The vertical asymptote
Recall that:
A logarithmic function has no y-intercept.
This is so because it is undefined at x = 0
So, the vertical asymptote is x = 0
The domain and the range
A logarithmic function cannot take a negative input or 0 input
So, the domain is x > 0
However, the range is all set of real numbers i.e (-∞, ∞)
Hence, the features of g(x) are (b), (d) and (e)
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Write root of fourth 81x³y4z8 with rational exponents
The fourth root of ⁴√(81x³y⁴z⁸)with rational exponents is [tex]3x^{\frac{3}{4} }yz^{2}[/tex]
How to find the fourth root of ⁴√(81x³y⁴z⁸)To find the fourth root of ⁴√(81x³y⁴z⁸) with rational exponents, we use the root rule of indices which states that [tex]\sqrt[n]{a} = a^{\frac{1}{n} }[/tex]
So, ⁴√(81x³y⁴z⁸) = ⁴√(81 × ⁴√x³ × ⁴√y⁴ × ⁴√z⁸)
We now apply the
So, ⁴√(81x³y⁴z⁸) = ⁴√81 × ⁴√x³ × ⁴√y⁴ × ⁴√z⁸
[tex]= 3 X x^{\frac{3}{4} } X y^{\frac{4}{4} } X z^{\frac{8}{4} } \\= 3 X x^{\frac{3}{4} } X y^{1} X z^{2} \\= 3x^{\frac{3}{4} }yz^{2}[/tex]
So, the fourth root of ⁴√(81x³y⁴z⁸)with rational exponents is [tex]3x^{\frac{3}{4} }yz^{2}[/tex]
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Kara wants to make a histogram of the number of students who wear blue shirts in her class throughout the week. She gathered the following information:
Day 1 4 students
Day 2 9 students
Day 3 5 students
Day 4 7 students
Day 5 6 students
What data would be on the horizontal axis?
names of the students wearing the blue shirts
the exact color of the blue shirt
school day
number of students wearing blue shirts
Answer:
school day
Step-by-step explanation:
When drawing a chart or a graph:
x-axis: Independent variabley-axis: Dependent variableThe two given variables are:
number of students who wear blue shirtsdays of the weekTherefore, in this scenario the independent variable is the school day and the dependent variable is the number of students since the former effects the latter.
So the data on the horizontal axis (x-axis) is: school day
Find the slope of the line A. -1/4 B. 4 C. -4 D. 1/4
Answer:
4!
Step-by-step explanation:
using the slope formula and the points (-1, 0) and (-2, -4) on the line:
-4 - 0 / -2 - -1 = -4 - 0 / -2 + 1 = -4 / -1, and since both the top and bottom are negative, they make a positive, giving you a positive 4
the slope formula is rise/run, or y2 - y1 / x2 - x1!
Which value is in the domain of f(x)?
f(x) = StartLayout Enlarged left-brace 1st row 1st column 2 x + 5, 2nd column negative 6 less-than x less-than-or-equal-to 0 2nd row 1st column negative 2 x + 3, 2nd column 0 less-than x less-than-or-equal to 4
The domain of the function f(x) is: -6 < x ≤ 4, and the value that is in the domain of the function f(x) is 4
How to determine the value in the domain?The function is given as:
f(x) = 2x + 5, -6 < x ≤ 0
f(x) = 2x + 3, 0 < x ≤ 4
The above means that the domain of the function f(x) is:
-6 < x ≤ 0 and 0 < x ≤ 4
When combined, we have:
-6 < x ≤ 4
This means that x is greater than -6 but does not exceed 4
Hence, the value that is in the domain of the function f(x) is 4
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Answer:
4
Step-by-step explanation:
got it right on edge
John swims 2.5 miles and sees a total of 12 fishes if he swims 8 miles how many fish will he see
Answer:
Step-by-step explanation:
2.5 miles = 12 fishes
Therefore,
8 miles = 12*8/2.5=96/2.5= 960/25=38.4 fishes
Given that the triangles shown below are similar, what is the value of x?
A. 5
B. 1.8
OC. 10
D. 15
M
31
25
15
A
S
31
L3 E
D
Using proportions, it is found that the value of x is of x = 5, hence option A is correct.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Since the triangles are similar, the lengths are proportional. Researching the problem on the internet, we have that the proportions are given as follows:
A side with a length of x is proportional to a side with length 25.A side with a length of 3 is proportional to a side with length 15.Hence:
[tex]\frac{x}{25} = \frac{5}{25}[/tex]
Simplifying the denominators:
x = 5.
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In the following exercises, multiply the binomials. Use any method.
258. (5x − y)(x − 4)
Answer:
Hence the expression [tex]$$(5x-y)(x-4)=5x^2-xy-20x+4y$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (5 x-y)(x-4).We have to multiply the given expression.Multiply the (5 x-y) by -4, multiply the (5 x-y) by x then add like terms.[tex]$$\begin{matrix}{} & {} & {} & {} & 5x & - & y \\ \times & {} & {} & {} & x & - & 4 \\ \end{matrix}$$[/tex]
_________________
[tex]$$\begin{matrix}{} & {} & {} & - & 20x & + & 4y \\ 5{{x}^2} & - & xy & {} & {} & {} & {} \\ \end{matrix}$$[/tex]
_________________
[tex]$$\begin{matrix}5{{x}^2} & - & xy & - & 20x & + & 4y \\ \end{matrix}$$[/tex]
Find a₁0 given that a7 = 6 and d = 3 in the arithmetic sequence.
A. 15
B. 12
C. 18
D. 21
The tenth term of the arithmetic sequence will be 15. Then the correct option is A.
What is the arithmetic sequence?Let a₁ be the first term and d is the common difference between the terms. Then the nth term will be given as
[tex]\rm a_n = a_1 + (n - 1)d[/tex]
We have
a₇ = 6
d = 3
n = 7
Then the first term will be
a₇ = a₁ + (7 – 1)3
6 = a₁ + 18
a₁ = 6 – 18
a₁ = -12
Then the 10th term will be
a₁ = -12
d = 3
n =10
Then we have
a₁₀ = -12 + (10 – 1)3
a₁₀ = -12 + 27
a₁₀ = 15
Then the tenth term of the arithmetic sequence will be 15.
Then the correct option is A.
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Question
(01.02 MC)
For which of the following distributions is the mean most likely to be less than the median?
The distribution where the mean is most likely to be less than the median is the third histogram.
How to illustrate the information?It should be noted that when the histogram shows the day is left skewed, it means the mean is less than the median.
If it right skewed, the mean is greater than the median.
When they're equal, the data is symmetric.
In this case, based on the information, the distribution where the mean is most likely to be less than the median is the third histogram.
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Write a function to represent the point (x, y) being translated of 3 units to the right and 2 units down.
Type the correct answer in the box.
(101 0°
Vo 4
T(x,y) =
√0
Question 2
+ -
A X
<
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VI
IV
र
a B
X
=
11
E
p
%8
9
sin cos tan sin costan
csc sec cot log
log
in
10
F E
I
ΕΔ Π
0 U
7
The translation function is T(x,y) = (x + 3, y - 2) and the reflection function is (-x, y)
The translation functionThe point is given as:
(x, y)
The translation is given as:
3 units to the right and 2 units down.
This is represented as:
(x + 3, y - 2)
Hence, the translation function is T(x,y) = (x + 3, y - 2)
The reflection functionThe point is given as:
(x, y)
The reflection is given as:
Reflection across the y-axis
This is represented as:
(-x, y)
Hence, the reflection function is (-x, y)
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on the first day the apple iphone 5 was released, the local store had 200 in stock. by 8:00 pm, the store had sold 3/5 of their stock. how many phone were left in the store’s stock?
Answer:
120 Phones
Step-by-step explanation:
3/5 of 200
Step 1: Divide 200 by 5
200 ÷ 5 = 40
Step 2: Multiply 40 by 3
40 · 3 = 120
Answer: 3/5 of 200 = 120
Tip: When finding a fraction of a whole, divided the whole by the denominator, then multiply the quotient you got by dividing the whole by the denominator by the numerator
Example: 1/2 of 80
80 ÷ 2 = 40
40 · 1 =40
1/2 of 80 = 40
Geometry question Need help with #10
Answer:
x = 6
Step-by-step explanation:
Line segment SU is a bisector of angle <TSV which means it divided the angle into two equal parts:
The measure of <TSV = 62 in this case the measure of <VSU = 62/2 = 31
we can write the following equation to find the value of x
5x + 1 = 31 subtract 1 from both sides
5x = 30 divide both sides by 5
x = 6
How do you represent a table with linear functions
A table can be represented with a linear function equation as y = mx + b, where m is the slope and b is the y-intercept.
How to Represent a Table with Linear Function?Assuming we have a table of values as shown in the image attached below, to write an equation of linear function for the table, do the following:
Pick two pairs of values, say, (1, 5) and (2, 25) and find the slope (m):
Slope (m) = change in y / change in x = (25 - 5)/(2 - 1)
Slope (m) = 20
Find the y-intercept (b) by substituting (x, y) = (1, 5) and m = 20 into y = mx + b:
5 = 20(1) + b
5 = 20 + b
5 - 20 = b
-15 = b
b = -15
Write the equation of the linear function by substituting m = 20 and b = -15 into y = mx + b:
y = 20x - 15
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