ANSWER
[tex]y = - \frac{3}{x + 2} [/tex]
EXPLANATION
The given parent function is:
[tex]y = \frac{1}{x} [/tex]
When this function is vertically stretched by a factor of 3, then we have
[tex]y = \frac{3}{x} [/tex]
A reflection across the y-axis transforms the function to;
[tex]y = - \frac{3}{x} [/tex]
When the resulting function is shifted to the left, the transformed function becomes;
[tex]y = - \frac{3}{x + 2} [/tex]
Nicole has $250 in ten-dollar bills. How many ten-dollar bills does Nicole have?#10
Nicole has 25 ten-dollar bills.
To find out how many ten-dollar bills Nicole has, we can divide the total amount of money she has by the value of each bill.
$250 / $10 = 25
Therefore, Nicole has 25 ten-dollar bills.
Answer in detail:
Nicole has $250 in ten-dollar bills. This means that she has 25 groups of $10.
We can divide $250 by $10 to find out how many groups of $10 she has.
$250 / $10 = 25
Therefore, Nicole has 25 ten-dollar bills.
Another way to look at it is this way:
If Nicole has 1 ten-dollar bill, then she has $10.
If Nicole has 2 ten-dollar bills, then she has $20.
If Nicole has 3 ten-dollar bills, then she has $30.
And so on.
So, to find out how many ten-dollar bills Nicole has, we can simply divide the total amount of money she has by the value of each bill.
A direct variation function includes the ordered
pair (4,5). Which statement is true?
Answer:
Step-by-step explanation:
A direct variation suggest that the value of x in the equation would greatly affect the value of y such that when x is increasing, y also increases and the other way around. The equation for a direct variation is that,
y = kx
Substituting the given values in the ordered pair,
5 = k(4) ; k = 5/4
answer: y = kx hope this helps
The distance from around the Earth along a given latitude can be found using the formula C=2∏r cos L , where r is the radius of the Earth and L is the latitude. The radius of Earth is approximately 3960 miles. Describe the distances along the latitudes as you go from 0° at the equator to 90° at the poles.
Answer:
The distance reduces to 0 as you go from 0° to 90°
Step-by-step explanation:
The question requires you to find the distance using different values of L and check the trend of the values.
Given C=2×pi×r×cos L where L is the latitude in ° and r is the radius in miles then;
Taking r=3960 and L=0° ,
C=2×[tex]\pi[/tex]×3960×cos 0°
C=2×[tex]\pi[/tex]×3960×1
C=7380[tex]\pi[/tex]
Taking L=45° and r=3960 then;
C= 2×[tex]\pi[/tex]×3960×cos 45°
C=5600.28[tex]\pi[/tex]
Taking L=60° and r=3960 then;
C=2×[tex]\pi[/tex]×3960×cos 60°
C=3960[tex]\pi[/tex]
Taking L=90° and r=3960 then;
C=2×[tex]\pi[/tex]×3960×cos 90°
C=2×[tex]\pi[/tex]×3960×0
C=0
Conclusion
The values of the distance from around the Earth along a given latitude decreases with increase in the value of L when r is constant
This is my worse subject please help me
Hello There!
So we know Some number added to 27 gets a sum of -12
We can figure this out by subtracting 27 from -12 so we would go back.
Once we subtract, -39 will be x and that is our answer.
The correct answer is -39
A bag contains different colored candies. There are 50 candies in the bag, 28 are red, 10 are blue, 8 are green and 4 are yellow.
What is the probability of choosing five pieces of candy and getting 2 red and 3 green?
Answer:
[tex]\displaystyle \frac{54}{5405}[/tex].
Step-by-step explanation:
How many unique combinations are possible in total?
This question takes 5 objects randomly out of a bag of 50 objects. The order in which these objects come out doesn't matter. Therefore, the number of unique choices possible will the sames as the combination
[tex]\displaystyle \left(50\atop 5\right) = 2,118,760[/tex].
How many out of that 2,118,760 combinations will satisfy the request?
Number of ways to choose 2 red candies out a batch of 28:
[tex]\displaystyle \left( 28\atop 2\right) = 378[/tex].
Number of ways to choose 3 green candies out of a batch of 8:
[tex]\displaystyle \left(8\atop 3\right)=56[/tex].
However, choosing two red candies out of a batch of 28 red candies does not influence the number of ways of choosing three green candies out of a batch of 8 green candies. The number of ways of choosing 2 red candies and 3 green candies will be the product of the two numbers of ways of choosing
[tex]\displaystyle \left( 28\atop 2\right) \cdot \left(8\atop 3\right) = 378\times 56 = 21,168[/tex].
The probability that the 5 candies chosen out of the 50 contain 2 red and 3 green will be:
[tex]\displaystyle \frac{21,168}{2,118,760} = \frac{54}{5405}[/tex].
Q4 please help thanks
Answer:
[tex]\large\boxed{A==\dfrac{3-\sqrt6}{12}\ cm^2}[/tex]
Step-by-step explanation:
The shaded region is the triangle with base b and height h.
[tex]b=BD-CD\to b=\dfrac{\sqrt2}{2}-\dfrac{\sqrt3}{3}=\dfrac{3\sqrt2}{(2)(3)}-\dfrac{2\sqrt3}{(2)(3)}=\dfrac{3\sqrt2-2\sqrt3}{6}\\\\h=AD\to h=\dfrac{\sqrt2}{2}[/tex]
The formula of an area of a triangle:
[tex]A=\dfrac{bh}{2}[/tex]
Substitute:
[tex]A=\dfrac{\frac{3\sqrt2-2\sqrt3}{6}\cdot\frac{\sqrt2}{2}}{2}=\left(\dfrac{3\sqrt2-2\sqrt3}{6}\right)\left(\dfrac{\sqrt2}{2}\right)\left(\dfrac{1}{2}\right)\\\\\text{use the distributive property}\ a(b+c)=ab+ac\\\\=\dfrac{(3\sqrt2-2\sqrt3)(\sqrt2)}{(6)(2)(2)}=\dfrac{(3\sqrt2)(\sqrt2)-(2\sqrt3)(\sqrt2)}{24}\\\\\text{use}\ \sqrt{a}\cdot\sqrt{a}=a\ \text{and}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\dfrac{(3)(2)-2\sqrt6}{24}=\dfrac{2(3-\sqrt6)}{24}=\dfrac{3-\sqrt6}{12}[/tex]
Answer:
see explanation
Step-by-step explanation:
The area of the shaded triangle = area of ΔABD - area of ΔADC
A of ΔABD = [tex]\frac{1}{2}[/tex] × AD × BD
A = [tex]\frac{1}{2}[/tex] × [tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{\sqrt{2} }{2}[/tex]
= [tex]\frac{2}{8}[/tex] = [tex]\frac{1}{4}[/tex]
--------------------------------------------------------------------------
A of ΔACD = [tex]\frac{1}{2}[/tex] × AD × DC
A = [tex]\frac{1}{2}[/tex] × [tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{\sqrt{3} }{3}[/tex]
A = [tex]\frac{\sqrt{6} }{12}[/tex]
-------------------------------------------------------------------------
shaded area = [tex]\frac{1}{4}[/tex] - [tex]\frac{\sqrt{6} }{12}[/tex]
= [tex]\frac{3}{12}[/tex] - [tex]\frac{\sqrt{6} }{12}[/tex] = [tex]\frac{3-\sqrt{6} }{12}[/tex]
3. Complete the square for 3x2 - 6x = 21.
Help
Answer:
x=1+2√2 or x=1−2√2
Step-by-step explanation:
Let's solve your equation step-by-step.
3x2−6x=21
Step 1: Since the coefficient of 3x^2 is 3, divide both sides by 3.
3x2−6x
3
=
21
3
x2−2x=7
Step 2: The coefficient of -2x is -2. Let b=-2.
Then we need to add (b/2)^2=1 to both sides to complete the square.
Add 1 to both sides.
x2−2x+1=7+1
x2−2x+1=8
Step 3: Factor left side.
(x−1)2=8
Step 4: Take square root.
x−1=±√8
Step 5: Add 1 to both sides.
x−1+1=1±√8
x=1±√8
x=1+2√2 or x=1−2√2
A gumball machine contains six yellow gumballs, and five orange gumballs. Whats is the probability of obtaining, at a random with out replacement , two yellow gumballs?
A. 36/110
B.36/121
C.36/110
D.30/121
The probability of obtaining at random without replacement two gum balls is 3/11.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
Given, A gumball machine contains six yellow gumballs and five orange gumballs.
So, N(Y) = 6 and N(O) = 5 and the number of sample space N(S) = 11.
Therefore, The probability of obtaining at random without replacement two gum balls is,
P(YY) = (6/11)×(6 - 1)/(11 - 1).
P(YY) = (6/11)×(5/10).
P(YY) = 30/110.
P(YY) = 3/11.
learn more about probability here :
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What is the simplest form of the expression 6x(x - 4) – 16x2 - (9x - 1)?
A. -10x2 – 33x + 1
B. 10x2 – 33x + 1
C. -10x – 33x + 1
D. -10x2 + 33x + 1
Answer
b
Step-by-step explanation:
Answer:
− -10x^2-33x+1
Step-by-step explanation:
Evaluate the cosine if the angle of rotation which contains the point (9, -3) on its terminal side
so we know the terminal point is at (9, -3), now, let's notice that's the IV Quadrant
[tex]\bf (\stackrel{x}{9}~~,~~\stackrel{y}{-3})\impliedby \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{9^2+(-3)^2}\implies c=\sqrt{81+9}\implies c=\sqrt{90} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf cos(\theta )=\cfrac{\stackrel{adjacent}{9}}{\stackrel{hypotenuse}{\sqrt{90}}}\implies \stackrel{\textit{rationalizing the denominator}}{\cfrac{9}{\sqrt{90}}\cdot \cfrac{\sqrt{90}}{\sqrt{90}}\implies \cfrac{9\sqrt{90}}{90}}\implies \cfrac{\sqrt{90}}{10}\implies \cfrac{3\sqrt{10}}{10}[/tex]
Help on number 7 please?
Answer:
The average rate of change is 3
Step-by-step explanation:
0 to 5 is 5 in difference then the change on the next one: 1 to 9 the difference is 8 so the change is 3 and it increases by three on the rest of them.
(\) QueTooOfficial (/)officially out of brainly retirementI'm pretty sure the average rate of change would be 3
HELP!!!!!
Graphing a Piecewise-Defined Function
Which graph represents the piecewise-defined function f(x) =
Answer: Last option
Step-by-step explanation:
Note that when the point is not included in the function is marked with an empty circle, and when the point is included in the function is marked with a filled circle.
From the interval [tex]0\leq x <3[/tex] f(x) is represented by the slanted line [tex]-x +4[/tex] that cuts the y-axis at [tex]y = 4[/tex]
The starting point of the line must be filled and the end point must be empty.
Then, from the interval [tex]x \geq 3[/tex] f(x) is defined by the horizontal line [tex]y = 6[/tex]. The starting point of this line is marked with a filled circle because it includes the point [tex]x = 3[/tex]
Therefore the correct option is option D or the last graph (from left to right)
Answer:
last one
Step-by-step explanation:
simplify (a + b - c )(a + b + c )
Answer:
The simplest form of (a + b - c )(a + b + c ) is a² + 2ab + b² - c²
Step-by-step explanation:
* Lets revise how to multiply two brackets with three terms
∵ (a + b - c)(a + b + c)
- Multiply the first term of the first bracket by the three terms of the
second bracket
∵ a × a = a²
∵ a × b = ab
∵ a × c = ac
- Then multiply the second term in the first bracket by the three terms
of the second bracket
∵ b × a = ba
∵ b × b = b²
∴ b × c = bc
- Then multiply the third term term in the first bracket by the three terms
of the second bracket
∵ -c × a = -ca
∵ -c × b = -cb
∵ -c × c = -c²
- Now add all these terms together
∴ a² + ab + ac + ba + b² + bc + -ca + -cb + -c²
- We have like terms lets add them
∵ ab = ba , ac = ca , bc = cb
∴ a² + (ab + ba) + (ac + -ca) + (bc + -cb) + b² + -c²
∴ a² + 2ab + 0 + 0 + b² - c²
∴ a² + 2ab + b² - c²
∴ The simplest form of (a + b - c )(a + b + c ) is a² + 2ab + b² - c²
The answer is:
[tex]a^{2} +b^{2} -c^{2} +2ab[/tex]
Why?To solve the problem, we need to remember the distributive property.
The distributive property is defined by the following way:
[tex](a+b)(c+d)=ab+ad+bc+bd[/tex]
Also, we need to remember how to add like terms. The like terms are the terms that share the same variable and the same exponent, for example:
[tex]x+x^{2}+x=x^{2} +2x[/tex]
We were able to add the first and the third term because they share the same variable and the same exponent.
Now, we are given the following expression to simplify:
[tex](a+b-c)(a+b+c)[/tex]
So, applying the distributive property and adding like terms, we have:
[tex](a+b-c)(a+b+c)=(a*a)+(a*b)+(a*c)+(b*a)+(b*b)+(b*c)-(c*a)-(c*b)-(c*c)\\\\(a+b-c)(a+b+c)=a^{2}+ab+ac+ba+b^{2} +bc-ac-bc-c^{2}\\\\(a+b-c)(a+b+c)=a^{2} +b^{2} -c^{2} +2ab[/tex]
Hence, we have that the given expression is equal to:
[tex]a^{2} +b^{2} -c^{2} +2ab[/tex]
Have a nice day!
find the complex cube roots of 8(cos(4pi/5)+isin(4pi/5))
Answer:
-6.47+4.70i.
Brainliest
Step-by-step explanation:
100% sure
Answer:-6.47+4.70i
Step-by-step explanation:
Took test ,, good luck !!!
What is the value of median for the following:68,69,71,71,72,72,72,74,74,76
Answer:
The median is 72.
Answer:
72
Step-by-step explanation:
68 69 71 71 72 72 74 74 76
68 76 69 74 71 74 71 72 72
72 is the median
What is the solution to the system of equations?
y=-3x + 6
y= 9
(-21,9) (9, -21)
(-1,9)
(9,-1)
Answer:
y=9
Step-by-step explanation:
(9,-1) is the answer.
Find the value of the expression.
[(38 * ¼) + (33% *18)] ÷ 100
Answer:
The value of the expression is [tex]0.1544[/tex]
Step-by-step explanation:
we have
[tex][(38*\frac{1}{4})+(33\%*18)]/100[/tex]
we know that
[tex](38*\frac{1}{4})=\frac{38}{4}=9.5[/tex]
[tex](33\%*18)=(33/100)*18=0.33*18=5.94[/tex]
substitute
[tex][9.5+5.94]/100[/tex]
[tex][15.44]/100[/tex]
[tex]0.1544[/tex]
a line includes the points (10,-5) and (-10,-1). What is the equation in slope intercept form?
[tex]\bf (\stackrel{x_1}{10}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{-10}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-(-5)}{-10-10}\implies \cfrac{-1+5}{-20}\implies \cfrac{4}{-20}\implies -\cfrac{1}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-5)=-\cfrac{1}{5}(x-10) \\\\\\ y+5=-\cfrac{1}{5}x+2\implies y=-\cfrac{1}{5}x-3[/tex]
ANSWER ASAP I NEED TO GRADUATE THIS WEEK
the coordinates (4, -1). What
17. A line has a point with the coordinates (-3,-2) and a point with the coord
is the slope of the line?
a. 1
-os
la mala
18. A line has a point with the coordinates (0,6) and a point with the coordi
the slope of this line?
with the coordinates (2,9). What is
Glow
Answer:
17.C
18.A
Step-by-step explanation:
17. Slope=(y2-y1)/(x2-x1)
=(-1-(-2))/(4-(-3))
=1/7
18.Slope=(y2-y1)/(x2-x1)
=(9-6)/(2-0)
=3/2
Do you want 19 and 20 too?
Question 1:
For this case we have that by definition, the slope of a line is given by:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
Where:
[tex](x_ {1}, y_{1}) and (x_ {2}, y_{2})[/tex]are two points through which the line passes.
[tex](x_ {1}, y_{1}) = (- 3, -2)\\(x_ {2}, y_{2}) = (4, -1)[/tex]
Substituting in the equation:
[tex]m = \frac {-1 - (- 2)} {4 - (- 3)} = \frac {-1 + 2} {4 + 3} = \frac {1} {7}[/tex]
ANswer:
Option C
Question 2:
For this case we have that by definition, the slope of a line is given by:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
Where:
[tex](x_ {1}, y_{1}) and (x_ {2}, y_{2})[/tex] are two points through which the line passes.
[tex](x_ {1}, y_{1}) = (0,6)\\(x_ {2}, y_{2}) = (2,9)[/tex]
Substituting in the equation:[tex]m = \frac {9-6} {2-0} = \frac {3} {2}[/tex]
ANswer:
Option A
Question 3:
For this case we have that by definition, the slope of a line is given by the following formula:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
Where:
[tex](x_ {1}, y_{1}) and (x_ {2}, y_{2})[/tex]are two points through which the line passes.
We have as data:
[tex]m = \frac {7} {8}\\(x_ {1}, y_{1}) = (- 2,1)[/tex]
Substituting in the formula:
[tex]\frac {7} {8} = \frac {y_ {2} -1} {x_ {2} - (- 2)}\\\frac {7} {8} = \frac {y_ {2} -1} {x_ {2} +2}[/tex]
We substitute each of the points and see if the equality is met:
Point A: (6,8)
[tex]\frac {7} {8} = \frac {8-1} {6 + 2}\\\frac {7} {8} = \frac {7} {8}[/tex]
Equality is met.
Answer:
Option A
Question 4:
For this case we have that by definition, the slope of a line is given by the following formula:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
Where:
[tex](x_ {1}, y_{1}) and (x_ {2}, y_{2})[/tex]are two points through which the line passes.
We have as data:
[tex]m = \frac {1} {6}\\(x_ {1}, y_{1}) = (0, -3)[/tex]
Substituting in the formula:
[tex]\frac {1} {6} = \frac {y_ {2} - (- 3)} {x_ {2} -0}\\\frac {1} {6} = \frac {y_ {2} +3} {x_ {2} -0}[/tex]
We substitute each of the points and see if the equality is met:
Point A: (-3,0)
[tex]\frac {1} {6} = \frac {0 + 3} {- 3-0}\\\frac {1} {6} = \frac {3} {- 3}[/tex]
It is not fulfilled!
Point B: (6, -2)
[tex]\frac {1} {6} = \frac {-2 + 3} {6-0}\\\frac {1} {6} = \frac {1} {6}[/tex]
Equality is met!
ANswer:
Option B
if f(x)=(x+1)^-1 and g(x)=x-2, what is the domain of f(x)/g(x)?
Answer:
Step-by-step explanation:
Function g(x) = x - 2 is in the denominator. We cannot divide by zero, so the domain of (f/g)(x) is x ≠ 2.
To find the domain of f(x)/g(x), consider where g(x) is not zero as division by zero is undefined. The domain is all real numbers except x = 2.
The domain of f(x)/g(x) is determined by the values of x that make the expression defined while avoiding division by zero. To find the domain, we need to consider where g(x) is not equal to zero, as division by zero is undefined.
Given: f(x) = (x+1)⁻¹ and g(x) = x-2. As g(x) is not zero at x = 2, the domain of f(x)/g(x) is all real numbers except x = 2.
Draw a shape to match the clues. Yin draw a shape with 4 sides. She labels it as a rectangle
Answer:
The diagram is shown in the attached image
Explanation:
We are given that Yin labelled her diagram a rectangle
This means that the shape she drew:
1- Is a four sided closed polygon
2- Has equal opposite sides (each two opposite sides are equal)
3- Has parallel opposite sides (each two opposite sides are parallel)
4- Has 4 right angles (all its interior angles are 90°)
This is shown in the attached image
Hope this helps :)
how do I solve this
[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\displaystyle\sum \limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf S_{20}=\displaystyle\sum \limits_{n=1}^{\stackrel{\stackrel{n}{\downarrow }}{20}}~\stackrel{\stackrel{a_1}{\downarrow }}{3}(\stackrel{\stackrel{r}{\downarrow }}{1.5})^{n-1}\implies S_{20}=3\left(\cfrac{1-1.5^{20}}{1-1.5} \right)\implies S_{20}=3\left(\cfrac{1-\stackrel{\approx}{3325.3}}{-0.5} \right) \\\\\\ S_{20}=3\left(\cfrac{-3324.3}{-0.5} \right)\implies S_{20}=3(6648.6)\implies S_{20}=19945.8[/tex]
19945.8 to simplify, the answer is
given that the ratio of boys to girls in a choir group is 17:23, what is the relative frequency of the number of boys?
Answer:
50 Students
You can find the number of boys and girls by dividing the total, so there are a total of 20 boys and 30 girls in the choir of 50. The ratio 2 boys : 3 girls means we can divide the chorus into groups.
Find the slope of a line perpendicular to 3x + 5y = 15.
A. -5/3
B. 5/3
C. -3/5
D. 3/5
Answer:
B)5/3
Step-by-step explanation:
"3x + 5y = 15."
Rewrite in slope-intercept form.
The slope-intercept form is
y=mx+b
where m is the slope and b is the y-intercept.
y=mx+b
Subtract 3x from both sides of the equation.
5y=15−3x
Divide each term by "5" and simplify.
5y/5=15/5−3x/5
"5" and "5" cancel each other out
Divide 15 by 5
y=3-3x/5
Reorder 3 and −3x/5
y=-3x/5+3
Rewrite in slope-intercept form.
y=−3/5x+3
Slope:-3/5
The equation of a perpendicular line to y=−3x/5+3 must have a slope that is the negative reciprocal of the original slope.
mperpendicular=−1/(−3/5)
Simplify the result.
mperpendicular=5/3
hope this helps!
To find the slope of a line perpendicular to the line 3x + 5y = 15, you first find the slope of the given line, which is -3/5 after rearranging to slope-intercept form. The slope of the perpendicular line is then the negative reciprocal of -3/5, which is 5/3.
Explanation:To find the slope of a line perpendicular to the given line 3x + 5y = 15, we first need to find the slope of this given line. For this we rearrange the equation into y=mx+b (slope-intercept) form. The given equation can be rewritten as y = -3/5x + 3. Therefore, the slope of this line (m) is -3/5.
The slope of a line perpendicular to the original line is the negative reciprocal of the slope of the original line. Therefore the slope of a line perpendicular to 3x + 5y = 15 is the negative reciprocal of -3/5, which is 5/3. So, the correct answer is B. 5/3.
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f(x) = x 2+ 6 and g(x) = 2x - 1
g[f(x)] =
Answer:
Given,
f(x)=x^2+6
g(x)=2x-1
Now,
g[f(x)]=g(x^2+6) since f(x)=x^2+6
=2(x^2+6)-1 since x > x^2+6
=2x^2+12-1
=2x^2+11
In order to find g[f(x)], we substitute the equation for f(x) into the equation for g(x). We replace every 'x' in g(x) with f(x) to get g(f(x)) = 2*(x^2 + 6) - 1. After simplification, we get g[f(x)] = 2x^2 + 11.
Explanation:In the world of mathematics, g[f(x)] represents the composition of two functions, f(x) and g(x). In this case, f(x) = x^2 + 6, and g(x) = 2x - 1. The composition of these two functions, expressed as g[f(x)], involves plugging the equation for f(x) into the equation for g(x).
Here's how we do it:
First, we take the f(x) = x^2 + 6. Then we put this into g(x), replacing every 'x' in g(x) with our function f(x). So, g(f(x)) = 2*(x^2 + 6) - 1. Simplifying, we find:
g(f(x)) = 2x^2 + 12 - 1 = 2x^2 + 11.
Therefore, the content loaded f(x) = x^2 + 6, g(x) = 2x - 1, g[f(x)] = 2x^2 + 11.
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What is the median of the data set?
3,10,1, 6, 10,3,11,14
The median is 8. You have to arrange it and then since it’s an even number add the two middle numbers and divide by 2.
ANSWER
The median is 8
EXPLANATION
The given date set is 3,10,1, 6, 10,3,11,14
We rearrange the data set in ascending order of magnitude to get:
1,3,3,6,10,10,11,14
There are two numbers {6,10} in the middle of the data set after arranging in ascending order.
The median is the mean of thesecond two numbers.
The median is
[tex] \frac{6 + 10}{2} = \frac{16}{2} = 8[/tex]
Therefore the median is 8
Solve for the roots in the equation below. x^4+3x^2-4=0
Answer:
[tex]\large\boxed{x=-1\ or\ x=1}[/tex]
Step-by-step explanation:
[tex]x^4+3x^2-4=0\\\\x^{(2)(2)}+3x^2-4=0\qquad\text{use}\ (a^n)^m=a^{nm}\\\\(x^2)^2+3x^2-4=0\qquad\text{substitute}\ x^2=t\geq0x=\\\\t^2+3t-4=0\\\\t^2+4t-t-4=0\\\\t(t+4)-1(t+4)=0\\\\(t+4)(t-1)=0\iff t+4=0\ \vee\ t-1=0\\\\t+4=0\qquad\text{subtract 4 from both sides}\\t=-4<0\\\\t-1=0\qquad\text{add 1 to both sides}\\t=1>0\to x^2=1\\\\x^2=1\to x=\pm\sqrt1\to x=-1\ \vee\ x=1[/tex]
which is the graph of
[tex]y = \sqrt[3]{x + 1} - 2[/tex]
ANSWER
See attachment.
EXPLANATION
The given function is
[tex]y = \sqrt[3]{x + 1} - 2[/tex]
The parent function is
[tex]y = \sqrt[3]{x} [/tex]
When we shift the parent graph to the left one unit, and down 2 units, we obtain the graph of the given function.
The graph of this function is shown in the attachment.
Find the greatest common factor of the terms in the following expression: 10x + 12xy.
x
2
2x
2xy
The greatest common factor is 2x
2 can go into both 10 and 12
and so can x
Which of the following correctly names one of the vertices of the triangle
below?
i think it is m because it simply the vertex
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