Given:
The function is:
[tex]f(x)=2x^2-14x+10[/tex]
The function g(x), the image of f(x) after a [tex]r_{y=x}[/tex] (reflection over the line y=x).
To find:
The function g(x).
Solution:
We have,
[tex]f(x)=2x^2-14x+10[/tex]
Substitute [tex]f(x)=y[/tex] in the given function.
[tex]y=2x^2-14x+10[/tex]
The function g(x), the image of f(x) after a [tex]r_{y=x}[/tex] (reflection over the line y=x). So, interchange x and y.
[tex]x=2y^2-14y+10[/tex]
Now, we need to find the value of y.
[tex]x=2(y^2-7y+5)[/tex]
[tex]\dfrac{x}{2}=y^2-7y+5[/tex] [Divide both sides by 2]
[tex]\dfrac{x}{2}-5=y^2-7y[/tex] [Subtract 5 from both sides]
Add both sides half of square of coefficient of y, i.e. [tex](\dfrac{-7}{2})^2[/tex], to make it perfect square.
[tex]\dfrac{x}{2}-5+(\dfrac{-7}{2})^2=y^2-7y+(\dfrac{-7}{2})^2[/tex]
[tex]\dfrac{x}{2}-5+\dfrac{49}{4}=y^2-7y+(\dfrac{7}{2})^2[/tex]
[tex]\dfrac{x}{2}-5+\dfrac{49}{4}=\left(y-\dfrac{7}{2}\right)^2[/tex] [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]
[tex]\dfrac{x}{2}+\dfrac{49-20}{4}=\left(y-\dfrac{7}{2}\right)^2[/tex]
Taking square root on both sides, we get
[tex]\pm\sqrt{\dfrac{x}{2}+\dfrac{29}{4}}=y-\dfrac{7}{2}[/tex]
[tex]\dfrac{7}{2}\pm\sqrt{\dfrac{2x+29}{4}}=y[/tex]
[tex]\dfrac{7}{2}\pm\dfrac{\sqrt{2x+29}}{2}=y[/tex]
[tex]\dfrac{7\pm \sqrt{2x+29}}{2}=y[/tex]
Substituting [tex]y=g(x)[/tex], we get
[tex]\dfrac{7\pm \sqrt{2x+29}}{2}=g(x)[/tex]
Therefore, the required function is [tex]g(x)=\dfrac{7\pm \sqrt{2x+29}}{2}[/tex].
Claris invested $140. She earned a simple interest of 3% per year on the initial investment. If no money was added or removed from the investment, what was the amount of interest Claris received at the end of two years? Show all work. Calculator allowed
Answer:
$8.40
Step-by-step explanation:
The formula for calculating simple interest is
principal * interest rate * time .
Plugging 140 into the principal, or starting value, 3% as the interest rate, and 2 (years) for the time, we get 140*0.03*2 = 8.4, or $8.40 as our answer. Note that 3% turned into 0.03 as turning a percentage into a decimal requires us to divide the decimal by 100
ase helppppppppppppppppp <33
Answer:
C none of the above
Step-by-step explanation:
A negative divided by a negative is a positive
- ( l/ -m) = + l/m
A is negative
B is negative ( negative negative negative is negative)
Two parallel lines are crossed by a transversal.What is the value of a?
Answer:
No solution is possible form the given informantion
Step-by-step explanation:
There seems to be something missing.
What is |x - 9| = 0 in word form?
Answer:
x = 9
Step-by-step explanation:
|x - 9| = 0
x = 9
|9 - 9| = 0
|0| = 0
0 = 0
Which number is a rational number?
Answer:
C
Step-by-step explanation:
17.156 is the irrational number as it is terminating(means it ends)
Rest all are irrational
6th grade math help me pleaseeee
A) En un videojuego el número de pruebas que hay que superar es el doble de las del nivel anterior, si en el nivel 1 hay dos pruebas, ¿Cuántas habrá en el nivel 5? ¿y en el 9? ES PARA MAÑANAAAAA
Answer:
En el nivel 5 habrá 32 pruebas mientras que en el nivel 9 habrá 512 pruebas.
Step-by-step explanation:
En un videojuego en el nivel 1 hay 2 pruebas.
El número de pruebas que hay que superar es el doble de las del nivel anterior. Entonces en el nivel 2 se deben superar 4 (2 pruebas del nivel 1*2, el doble) pruebas, mientras que en el nivel 3 hay que superar 8 pruebas (4 pruebas del nivel 2*2, el doble).
Una sucesión es una secuencia ordenada de números. Si observamos en este caso, la sucesión que se forma para calcular el número de pruebas es 2ⁿ, donde n es el número de nivel en el videojuego.
Entonces, por ejemplo, en:
el nivel 1: 2ⁿ= 2¹= 2 pruebasel nivel 2: 2ⁿ= 2²= 4 pruebasel nivel 3: 2ⁿ= 2³= 8 pruebasEntonces, para calcular la cantidad de pruebas en el nivel 5 se realiza el cálculo:
2ⁿ= 2⁵= 32 pruebas
mientras que para calcular la cantidad de pruebas en el nivel 5 se realiza el cálculo:
2ⁿ= 2⁹= 512 pruebas
Entonces, en el nivel 5 habrá 32 pruebas mientras que en el nivel 9 habrá 512 pruebas.
Sabiendo como cambia el número de pruebas por nivel, veremos que en el nivel 5 hay 32 pruebas y en el nivel 9 hay 512 pruebas.
Sabemos que la cantidad de pruebas que hay que superar en cada nivel es el doble de las que hay en el nivel anterior.
Entonces, esto es una serie geometrica, que se puede escribir como:
[tex]A_n = A_1*2^{n - 1}[/tex]
Donde A₁ es la cantidad de pruebas en el primer nivel, que sabemos que son 2.
Entonces escribimos:
[tex]A_n = 2*2^{n-1} = 2^n[/tex]
En el nivel 5 tenemos n = 5, entonces la cantidad de pruebas que hay en e nivel 5 esta dado por:
[tex]A_5 = 2^5 = 32[/tex]
Es decir, hay 32 pruebas en el nivel 5.
Para el nivel 9 tenemos n = 9, entonces hay:
[tex]A_9 = 2^9 = 512[/tex]
Hay 512 pruebas en el nivel 9.
Sí quieres aprender más. puedes leer:
https://brainly.com/question/18790599
a mobile phone company changes its rental charge from $80 to per to $7.50per month.
work out the percentage increase
Answer:
6.6%
Step-by-step explanation:
Note: I had to correct the given data
Given data
Initial charges= $7.50
Final charges= $8.0
Percent increase
% increase= Final-initial/initia*100
% increase= 8-7.5/7.5*100
% increase= 0.5/7.5*100
% increase= 0.066*100
% increase= 6.6%
i need help as soon as possible please and thank you
Step-by-step explanation:
yes that's the answer
can you please give me brainliest
and use DESMOS app for drawing graphs
help me out please asap
Answer:
Step-by-step explanation:
There are 2 repeating digits in .64(with a line over both of those numbers). The value to multiply on to both sides will be 100. To find the fraction that represents the repeating decimal, there are steps to follow. First, make sure the decimal is just before the repeating decimals. It is, so we are good there. Next, move the decimal over how ever many places to get it right after the repeating numbers. That means moving the decimal 2 places to the right. That's the same as multiplying by 100:
100x = 64.6464
What we have now is a system with the equation above and
x = .6464
We subtract them:
100x = 64.6464
- x = .6464
to get
99x = 64. Solving for x:
x = 64/99
That's how you change a repeating decimal to a fraction.
Which expression is equivalent
Answer:
[tex]\sqrt[6]{2\\}[/tex]
Step-by-step explanation:
Rewriting
2 ^1/2 ÷ 2 ^ 1/3
We know a^ b ÷ a^c = a^ (b-c)
2 ^ (1/2 -1/3)
Getting a common denominator
2^ ( 3/6 - 2/6)
2^ 1/6
[tex]\sqrt[6]{2\\}[/tex]
Answer:
[tex]\sqrt[6]{2}[/tex]
Step-by-step explanation:
We can start by writing the expression as one power of two, and then comparing it to the options. The square root of two is the same and [tex]2^{\frac{1}{2} }[/tex] and the cube root of two is the same as [tex]2^{\frac{1}{3} }[/tex]. Therefore, we can rewrite the expression:
[tex]\frac{2^{\frac{1}{2} }}{2^{\frac{1}{3} }}[/tex]
Now, to write them as one power of two, we can use the quotient rule which states, [tex]\frac{x^m}{x^n} = x^{m-n}[/tex]:
[tex]2^{\frac{1}{2} -\frac{1}{3}}[/tex]
We just need to subtract 1/3 from 1/2 to get:
[tex]2^{\frac{1}{6} }[/tex]
This is the same as the 6th root of 2, which is the second option.
What's Is m
32
58
74
148
Answer:
x=74
Step-by-step explanation:
The angle H = x
We know angle M also is x because the sides are the same length
The sum of the angles of a triangle add to 180
x+x+32 = 180
Combine like terms
2x+32 =180
Subtract 32 from each side
2x = 180-32
2x =148
Divide by 2
2x/2 =148/2
x=74
1.5 in.
1.5 in.
8 inches tall
The tube of toothpaste shown costs $3.45. Estimate the price per cubic inch of toothpaste.
Answer:
per inch 0.90 cents hhhhhhjjkolllll
Find the value of x. PLEASE HELP ASAP!!!!!!
Answer:
I don't want to be silly here, but....
if x > 9 and < 13...
there is only one answer that is >9 and < 13
that is answer "A" (11)
Step-by-step explanation:
Answer:
A. 11
Step-by-step explanation:
Hi there!
We're given the trapezoid EBFD, with bases (the parallel sides) EB and DF, which equal 9 and 13 respectively
AC is a segment that belongs to EBFD, and has the measure of x
AC is a midsegment, which is a segment that connects the midpoints of 2 sides
the midpoint divides a segment to create create two congruent segments
In this example, point A is a midpoint, as it divides ED into the congruent segments EA and AD (you can tell they are congruent by their markings)
C is also a midpoint, as it divides BF into the congruent segments BC and CF
line segment AC connects the points A and C together
anyway, the measure of a midsegment in a trapezoid is the average of the bases
in other words, the midsegment (AC, or x) is equal to (EB+DF)/2
since we know the measures of EB and DF, we can substitute them into the expression above to find x
x=(EB+DF)/2
x=(9+13)/2
add the numbers on the numerator
x=22/2
divide
x=11
So the answer is A
Hope this helps! :)
Eliza says, “Every member of the population is equally likely to be selected for the sample”. Which type of sample is Eliza describing?
a
a random sample
b
a biased sample
c
a stratified sample
d
a quota sample
Answer: A. A random sample
Step-by-step explanation:
Since everyone is equally as likely yo be selected for this sample, is has to be random because there won't be any interference to the probability of your chances of being selected in the population
I hope this helps!
which table represents a nonlinear function?
Answer:
C
Step-by-step explanation:
Determine if the following triangles are similar. Show all work to justify your answer.
If they are similar write the correct similarity statement for the triangles.
Answer:
they are similar
Step-by-step explanation:
1.6/1.2=1.3333
2.8/2.1=1.3333
they are similar as their ratios of the legs are equal
Question is in picture
Answer:
obtion b and d
Step-by-step explanation:
4x + 5 = -4x + 5
4x + 4x = 5 - 5
8x = 0
x = 0/8
x = 0 (this has solution)
-4x + 5 = -4x - 4
-4x + 4x = -4 + 5
0 = -1 (this has no solution)
5x + 5 = -4x - 4
5x + 4x = -4 - 5
9x = -9
x = -9/9
x = -1 (this has solution)
-4x + 5 = -4x - 5
-4x + 4x = -5 -5
0 = -10 (this has no solution)
Find two numbers whose difference is 5 and sun of whose squares is 100.
(I believe this is the quadratic formula!)
I’m not sure how to go about it. If someone go go through it step by step, that’d be helpful. (Or even give me the values to put into the quadratic formula)
Answer:
I. x = 14.115 and y = 9.115
II. x = 0.885 and y = -4.115
Step-by-step explanation:
Let the two numbers be x and y respectively.Translating the word problem, we have;
x - y = 5 ......equation 1
x² + y² = 100 ...... equation 2
x = y + 5 ...... equation 3
Substituting eqn 3 into eqn 2, we have;
(y + 5)² + y² = 100
Simplifying further by opening the bracket, we have;
(y + 5)(y + 5) + y² = 100
y² + 5y + 5y + 25 + y² = 100
y² + 10y + 25 + y² = 100
2y² + 10y + 25 = 100
2y² + 10y + 25 - 100 = 0
2y² + 10y - 75 = 0
To find the roots of the quadratic equation, we would use the quadratic formula;
Note: the standard form of a quadratic equation is ax² + bx + c = 0
a = 2, b = 10 and c = -75
The quadratic equation formula is;
[tex] x = \frac {-b \; \pm \sqrt {b^{2} - 4ac}}{2a} [/tex]
Substituting into the formula, we have;
[tex] y = \frac {-10 \; \pm \sqrt {10^{2} - 4*2*(-75)}}{2*2} [/tex]
[tex] y = \frac {-10 \pm \sqrt {100 - (-600)}}{4} [/tex]
[tex] y = \frac {10 \pm \sqrt {100 + 600}}{4} [/tex]
[tex] y = \frac {10 \pm \sqrt {700}}{4} [/tex]
[tex] y = \frac {10 \pm 26.46}{4} [/tex]
[tex] y_{1} = \frac {10 + 26.46}{4} [/tex]
[tex] y_{1} = \frac {36.46}{4} [/tex]
[tex] y_{1} = 9.115 [/tex]
Or
[tex] y_{2} = \frac {10 - 26.46}{4} [/tex]
[tex] y_{2} = \frac {-16.46}{4} [/tex]
[tex] y_{2} = -4.115 [/tex]
Next, we would find the value of x;
x = y + 5
When y = 9.115
x = 9.115 + 5
x = 14.115
When y = -4.115
x = -4.115 + 5
x = 0.885
Check:
x - y = 5
14.115 - 9.115 = 5
A bag has 5 green balls, 7 blue balls, 2 red balls, and 3 yellow balls. How many elements are in the sample space?
A) 7
B) 210
C) 17
D) 5
Answer:
the answer is D
Answer:
Option C
Step-by-step explanation:
There are 17 elements in the sample space, here.
the quotient of 4 divided by 7 is a decimal number. how many digits in the quotient are overlined?
Answer:
6 digits.
Step-by-step explanation:
The repeating numbers after the decimal is 571428.
find the greatest number in which 60,90 and 120 are exactly divisible
Answer:
30
Step-by-step explanation:
To find the greatest number divisible : find the GCF
[tex]60 = 2 \times 2 \times 3 \times 5 = 2^2 \times 3^1 \times 5^1\\\\90 = 2 \times 3 \times 3 \times 5 = 2^1 \times 3^2 \times 5\\\\120 = 2 \times 2 \times 2 \times 3 \times 5 = 2^3 \times 3^1 \times 5^1[/tex]
[tex]Therefore \ , GCF = 2 \times 3 \times 5 = \ 30[/tex]
Therefore greatest number in which 60, 90 , 120 are divisible = 30
The greatest number is 30 which is divisible by 60, 90, and 120.
What is Least Common Multiple(LCM)?The least common multiple is defined as the least positive integer that is dividable by both given numbers. A group's Least Common Multiple (LCM) is the smallest number that is a multiple of all the numbers.
To find the greatest number in which 60, 90, and 120 are all exactly divisible, we can find the least common multiple (LCM) of these three numbers.
The LCM is the smallest positive integer that is exactly divisible by all of the numbers in question.
One way to find the LCM of 60, 90, and 120 is to list the prime factorization of each number and then take the highest exponent of each prime factor:
60 = 2 x 2 x 3 x 5
90 = 2 x 3 x 3 x 5
120 = 2 x 2 x 2 x 3 x 5
The LCM of 60, 90, and 120 is then 2 x 3 x 5 = 30.
Therefore, 30 is the greatest number in which 60, 90, and 120 are all exactly divisible.
To learn more about the Least Common Multiple(LCM) here :
https://brainly.com/question/17256135
#SPJ2
The quotient of 1/2 divided by 1 3/4
Answer:
2/7
Step-by-step explanation:
1
2
÷
1 3
4
=
1
2
÷
7
4
=
1
2
×
4
7
=
1 × 4
2 × 7
=
4
14
=
4 ÷ 2
14 ÷ 2
=
2
7
please help giving brainlest and points!
Answer: the last one
Step-by-step explanation:
of the 400 members in a health club, 270 use the weight room, 180 use the pool and 80 use both. Determine the number of members that do not use either the weight room
or the pool.
A 30
B) 130
C 190
D) 100
a man bought 250 electric lanterns in the united States of America for $5000. he sold them them in lagos at 1,920 naira each. at the time of his journey back to USA, the exchange rate was #96 to dollar
1. if selling at the lanterns at 1920 naira each, he made a profit of 20% cal the exchange rate the time he bought the lantern
2. how much in dollar will the sales amount to the of his journey back to USA
Answer: 4166.67$
Step-by-step explanation:
1920 x 250 = amount
Amount = 120%
Cost price = 100%
1920 x 250= 120%
Cost price = 100%
Cross multiply and divide both side by 120
1920 x 250 x 100/120 = price
Exchange rate = cost in #/cost in $
= (1920 x 250 x 5/6)/(5000)
= (96 x 5/6) = 16 x 5= 80
Exchange rate then was 80 to 1$
The sales will be 400000/96 = 4166.67$
Answer:
1. $1:#80
2.$5000
Step-by-step explanation:
ok... lots of moving parts here ....
$5000 / 250 = $20 per lantern.
~~~~~~~~~~~~~~~~~~
x (1 + .2) = 1920
x = 1600
~~~~~~~~~~~~~~
$5000 : (1600*250)
$5,000:#400,000
c
~~~~~~~~~~~
sales back to the us at $1:#96
1920*250 = 480000
#480000/#96=$5000
I need help with this can someone help me please!!! I will give brainlist, no links!!
Leo is visiting New York City to see the Empire State building. He knows that the Empire State building is 1,484 feet tall. When he spots it, he stops and has to look up at an angle of 84.7 degrees to see the top. How far away from the base of the Empire State building is he?
Answer:
Leo stop at 1339. 3 feet tall and Leo almost reach the top of the building
f(x)=1/x−4−6f(x)= x−41 −6. Find the inverse of f(x) and its domain.
Answer:
C
Step-by-step explanation:
Given f(x) then f(x + a) is a horizontal translation of f(x)
• If a > 0 then a shift left of a units
• If a < 0 then a shift right of a units
The graph of g(x) is the graph of f(x) shifted 6 units left , then
g(x) = f(x + 6) → C
I am leaning pre-cal right now and I don't understand it. I did arctan (3/-5) but got it wrong, how do you do this?
9514 1404 393
Answer:
149.04°
Step-by-step explanation:
You must consider the signs of the components of the vector. The value -5+3i will be in the 2nd quadrant of the complex plane.
When you use the single-argument arctan function, it will tell you the angle is -30.96°, a 4th-quadrant angle. (arctan( ) is only capable of giving you 1st- or 4th-quadrant angles.)
You find the 2nd-quadrant angle by adding 180° to this value:
-30.96° +180° = 149.04° = arg(-5+3i)
__
The attachments show the calculation using a suitable calculator (1st) and a spreadsheet (2nd). The spreadsheet function ATAN2(x,y) gives the 4-quadrant angle in radians, considering the signs of the two arguments. Here, we converted it to degrees. The calculator can be set to either degrees or radians.
The midpoint of AB is M(- 2, 1) . If the coordinates of (1, - 2) , what the coordinates of B?
Answer:
(-5, 4)
Step-by-step explanation:
Finding the X of B
-2 = x2+x1/2
-2 = x2+1/2 (substituted X co-ord of A into x1)
-4=x2+1 (multiplied both sides by 2)
-5=x2 (brought 1 to the other side)
Finding the Y of B
1 = y2+y1/2
1 = y2 - 2/2 (substituted Y co-ord of A into y1)
2 = y2 -2 (multiplied both sides by 2)
4 = y2 (brought 2 to the other side)