Answer:
Vertex: (4, -2)
Vertex form: [tex]y = 2(x-4)^2 - 2[/tex]
Inverse function: [tex]y = (16 \pm\sqrt{16+8x})/4[/tex]
Step-by-step explanation:
The x-coordinate of the vertex can be calculated using the formula:
[tex]x_{vertex} = -b/2a[/tex]
Where a and b are coefficients of the quadratic equation in the form:
[tex]y = ax^2 + bx + c[/tex]
So, using a = 2 and b = -16, we have:
[tex]x_{vertex} = 16/4 = 4[/tex]
To find the y-coordinate of the vertex, we calculate y using the x-coordinate of the vertex:
[tex]y=2*4^2-16*4+30[/tex]
[tex]y = -2[/tex]
So the vertex is (4, -2)
The vertex form is given by:
[tex]y = a(x-h)^2 + k[/tex]
Where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex. Therefore, we have that:
[tex]y = 2(x-4)^2 - 2[/tex]
To create an inverse function, we switch x by y and vice-versa:
[tex]x=2y^2-16y+30[/tex]
[tex]2y^2-16y+30 - x = 0[/tex]
Then, using Bhaskara's formula, we have:
[tex]\Delta = b^2 -4ac = (-16)^2 - 4*2*(30-x) = 16 + 8x[/tex]
[tex]y = (-b \pm\sqrt{\Delta})/2a[/tex]
[tex]y = (16 \pm\sqrt{16+8x})/4[/tex]
It's important to say that this inverse function is not really a function, because one value of x gives two values of y.
find the value of x A. does not exist B. -7 C. 26 D. 35
Answer:
A-does not exist
Step-by-step explanation:
The pythagorian theorem :
12²+x²= (x-2)²144+x²= x²-4x+4144-4+x²-x²= -4x 140 = -4x x = 140/-4x= -35That's absurd . A side cannot be negative since it's a distance
It was obvious from the beginning since one of the sides is greater than the hypotenus wich is impossible x≥x-2
Answer:
A. does not exist
Step-by-step explanation:
Since this is a right triangle we can find the value of x using Phytagorian Theorem
(x-2)^2 = 12^2 + x^2
x^2 -4x + 4 = 144 + x^2 (x^2 will be eliminated)
-4x = 144
x = -36 since the side lengths cannot be negative we select the option A which says it doesn't exist.
HELPPPPP NOWWWWWWWWWWWWW PLEASE
Answer:
B. SAS
Step-by-step explanation:
the line that joins the 2 triangles is considered a side, if you put an angle in between 2 sides its SAS.
Helppp!!!! please!!!
Answer:
D
Step-by-step explanation:
The arc AB is calculated as
AB = circumference of circle × fraction of circle
= 2πr × [tex]\frac{120}{360}[/tex]
= 2π × 24 × [tex]\frac{1}{3}[/tex] = [tex]\frac{48\pi }{3}[/tex] = 16π → D
The radius of a circle is given as 10cm subject to an error of 0.2cm. the error in the area of the circle is?
Answer:
12.56 [tex]cm^2[/tex] is the error in area of circle.
Step-by-step explanation:
Given that:
Radius of the circle, r = 10 cm
Error in measurement of radius, [tex]\triangle r[/tex] = 0.2 cm
To find:
The error in area of circle = ?
Solution:
First of all, let us have a look at the percentage error in measurement of radius:
[tex]\dfrac{\triangle r}{r}\times 100 = \dfrac{0.2}{10}\times 100 = 2\%[/tex]
Now, we know that Area of a circle is given as:
[tex]A = \pi r^2[/tex]
[tex]\Rightarrow \dfrac{\triangle A}{A} \times 100 = 2 \times \dfrac{\triangle r}{r} \times 100\\\Rightarrow \dfrac{\triangle A}{A} = 4\%[/tex]
Area according to r = 10
[tex]A = 3.14\times 10^2 = 314 cm^2[/tex]
Now, error in area = 4% of 314 [tex]cm^2[/tex]
[tex]\Rightarrow \dfrac{4}{100} \times 314 = 12.56 cm^2[/tex]
So, the answer is:
12.56 [tex]cm^2[/tex] is the error in area of circle.
Sean is trying to decide between four Roth IRAs. The month after the required initial contribution (RIC), he wants to start contributing the minimum subsequent investment (MSI) each month. Compare the cost of the minimum initial investment and Sean's monthly contribution for each IRA over the next 10 years. Which Roth IRA would Sean put the most money in over those 10 years?
Answer:
Option C.
Step-by-step explanation:
So, in the question above we are given that the value or parameters for the required initial contribution (RIC) and
the minimum subsequent investment (MSI) for each options and we are going to calculate the amount that will be gotten after investing in each options and the one that gives the highest values will be the correct option, which in this case is OPTION C.
So, we will be starting from the OPTION C, in white have that the
required initial contribution (RIC) = $5,000 and the minimum subsequent investment (MSI) = $100 for option C.
One year = 12 months
10 years = x months.
x = 10 × 12 = 120 months in ten years.
Thus, the formula for the Calculation is given below;
= 120 months × minimum subsequent investment (MSI) + required initial contribution (RIC).
= (120 months × $100) + $5,000 = $17,000.
If we Calculate for the other options with this format, we will have values for option A = $13, 000 and option B= $2,900 and the value for the investment in option D = $12,050.
$17,000 is the highest which is for option option C. Therefore, Sean should put his money in option c for better investment.
please I need answers
Answer:
9, 11, 1, 0, 11
There's a patern
Answer:
Ans: 9,11,1,0,11. Do u need the workings
Consider the following pair of equations: y = −2x + 8 y = x − 1 Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.
Answer:
(3,2)
Step-by-step explanation:
y = −2x + 8
y = x − 1
Substitute the second equation into the first equation for y
y = -2x+8
x-1 = -2x+8
Add 2x to each side
x-1+2x = -2x+8+2x
3x -1 = 8
Add 1 to each side
3x-1+1 = 8+1
3x =9
Divide by 3
3x/3 = 9/3
x=3
Now find y
y = x-1
y =3-1
y=2
(3,2)
Find the probability of drawing a 6 and then a 6
(without replacement) from a standard deck of carNs.
A deck of cards has 52 total cards and four 6’s
Picking a 6 first would be 4/52 = 1/13
Without replacing there are 51 cards left and three 6’s
Picking a 6 would be 3/51 = 1/17
Probability of doing both is:
1/13 x 1/17 = 1/221
A group of students plotted the number of hours they worked weekly during the holidays and the number of hours they spent cycling. Graph shows 0 to 60 on x and y axes at increments of 10. The label on the x axis is Weekly Hours Worked, and the label on the y axis is Weekly Hours Cycling. Dots are made at the ordered pairs 10, 45 and 13, 35 and 16, 42 and 24, 32 and 26, 43 and 32, 29 and 37, 23 and 39, 27 and 42, 19 and 45, 21 and 49, 19 and 50, 12. Which statement best describes the relationship between the number of hours spent working and the number of hours spent cycling? Greater hours worked, fewer hours spent cycling. Fewer hours worked, fewer hours spent cycling. Greater hours worked, greater hours spent cycling. There is no relationship between hours spent working and hours spent cycling.
Answer:
Greater hours worked, fewer hours spent cycling.
Step-by-step explanation:
Answer:
Greater hours worked, fewer hours spent cycling.
Step-by-step explanation:
:)
Find the coordinates of the points of intersection o the parabola y= x^2 and y= x+3
Answer:
Easiest and fastest way to do this is to input both equations into a graphing calc and tracing to where the 2 graphs intersect.
Alternatively, you can use substitution to solve for your answer.
Step-by-step explanation:
Which is the solution to the system of equations? y=1/3x+2 y=4/3x-5
Answer:
x = 7 . y = 13/3
Step-by-step explanation:
Solve the following system:
{y = x/3 + 2
y = (4 x)/3 - 5
Express the system in standard form:
{-x/3 + y = 2
-(4 x)/3 + y = -5
Express the system in matrix form:
(-1/3 | 1
-4/3 | 1)(x
y) = (2
-5)
Write the system in augmented matrix form and use Gaussian elimination:
(-1/3 | 1 | 2
-4/3 | 1 | -5)
Swap row 1 with row 2:
(-4/3 | 1 | -5
-1/3 | 1 | 2)
Subtract 1/4 × (row 1) from row 2:
(-4/3 | 1 | -5
0 | 3/4 | 13/4)
Multiply row 1 by 3:
(-4 | 3 | -15
0 | 3/4 | 13/4)
Multiply row 2 by 4:
(-4 | 3 | -15
0 | 3 | 13)
Divide row 2 by 3:
(-4 | 3 | -15
0 | 1 | 13/3)
Subtract 3 × (row 2) from row 1:
(-4 | 0 | -28
0 | 1 | 13/3)
Divide row 1 by -4:
(1 | 0 | 7
0 | 1 | 13/3)
Collect results:
Answer: {x = 7 . y = 13/3
The mean age of 8 women in an office is 20 years old. The mean age of 12 men in an office is 32 years old. What is the mean age (nearest year) of all the people in the office? Answer it please because it would be helpfull alot
Answer:
27.2
Step-by-step explanation:
The mean age of 8 women in the office is 20 years old
The mean age of 12 men in an office is 32 years old
The first step is to calculate the mean of the both the men and women in the office, that way we will be able to know the sum.
The mean of the women can be calculated by taking the sum of the value and dividing by the number
= 20+20+20+20+20+20+20+20/8
= 160/8
= 20
The mean of the men can be calculated by taking the sum of the values and dividing by the number
=32+32+32+32+32+32+32+32+32+32+32+32/12
= 384/12
= 32
Therefore, to find the mean age of people in the office we add the sum of both the men and women and divide by the total number of people in the office
= 384+160/20
= 544/20
= 27.2
Hence the mean age of people in the office is 27.2
What value of x is in the solution set of –2(3x + 2) > –8x + 6
Answer:
5 <x
Step-by-step explanation:
–2(3x + 2) > –8x + 6
Divide each side by -2, remembering to flip the inequality
–2/-2(3x + 2) < –8x/-2 + 6/-2
3x+2 < 4x-3
Subtract 3x from each side
3x-3x+2 < 4x-3x-3
2 < x-3
Add 3 to each side
2+3 < x-3+3
5 <x
Answer:
Step-by-step explanation:
-2( 3x + 2) > -8x + 6
-2*3x + (-2)*2 > -8x + 6
-6x - 4 > -8x + 6
Add 4 to both sides
-6x - 4 + 4 > -8x + 6 + 4 { add like terms}
-6x > -8x + 10
Add 8x to both sides
-6x + 8x > - 8x + 10 + 8x
2x > 10
Divide both sides by 2
2x/2 > 10/2
x > 5
Which of the following is the graph of a linear function?
Answer:
The first one.
Step-by-step explanation:
A linear function is a straight line, regardless of direction.
The first graph is of a linear function.
The phrase linear function denotes to function which is linear, specifically of this form:
[tex]f(x) = mx + c[/tex]
This is also written as:
[tex]y = mx + c[/tex]
It is written so that we can take the outputs of the function f(x) in a separate variable for further mathematical treatments with ease.
Now when that second equation is plotted on XY plane, you get a straight line graph since this is the equation form of any straight line, in geometry.
All the straight lines are covered under y = mx + c linear function form.
Since the first graph contains a plot of straight line, thus the first graph is of linear function.
The second graph is of downwardly opened vertical parabola which is of degree 2, thus not linear.
Thus first graph is the graph of a linear function.
Learn more here:
https://brainly.com/question/959487
I WILL NAME THEE BRAINLIEST!! (: PLZZZZZ HELP ASAPPPPP Solve for the unknown. Check your answer by substituting it in the original equation.
-A - 22 = -2A - 30 solve and check
Y - 12 = 2Y - 4 solve and check
Solve. Convert improper fractions to mixed numbers. Simplify your answers if possible. 1/4 x 4/5=
7/10 x 1/2=
3/4 x 9/10=
Step-by-step explanation:
1. -A-22=-2A-30
= -A+2A=-30+22
=A= -8
2. Y-12=2Y-4
=Y-2y=-4+12
-Y= +8
or Y = -8
1/4×4/5
4 cancels 4 which gives=1/5
7/10×1/2
= 7/20
3/4×9/10= 27/40
Gabriel note sur une frise chronologique les événements familiaux importants. Il utilise des entiers positifs ou négatifs. Pour écrire une date avant sa naissance, il utilise des nombres négatifs et pour une date après sa naissance, des nombres positifs. Par exemple, la mère de Gabriel a reçu une médaille en l'an -20−20minus, 20 et la sœur de Gabriel est née en l'an +5+5plus, 5. Que représente l'année 0~?0 ?0, space, question mark Réponse : Réponse : L'année où la sœur de Gabriel est née L'année de la naissance de Gabriel L'année où la mère de Gabriel a reçu une médaille
Answer:
L'option B est correcte. Le chiffre 0 représente l'année de naissance de Gabriel.
Option B is correct.
The number 0 represents the year when Gabriel was born.
Step-by-step explanation:
Il a été déclaré dans la question que Gabriel a enregistré des événements tge dans leur vie par rapport à quand il est entré en scène. Avec des exemples notables donnés pour illustrer que les nombres négatifs indiquent les temps avant la naissance de Gabriel et les nombres positifs indiquent les années après la naissance de Gabriel.
Par conséquent, il est simple de voir que l'année 0 en termes relatifs à la naissance de Gabriel représentera l'année de naissance de Gabriel.
J'espère que cela t'aides!!!
English Translation
Gabriel notes on a timeline important family events. It uses positive or negative integers. To write a date before his birth, he uses negative numbers and for a date after his birth, positive numbers. For example, Gabriel's mother received a medal in the year -20 and Gabriel's sister was born in the year + 5. What does the year 0 represent? Answer:
A) The year when Gabriel's sister was born
B) The year when Gabriel was born
C) The year when Gabriel's mother received a medal
Solution
It was stated in the question that Gabriel recorded tge events in their lives relative to when he came into the picture. With noticeable examples given to illustrate that the negative numbers indicate times before Gabriel's birth and positive numbers indicate years after Gabriel's birth.
Hence, it is straighforward to see that the year 0 in relative terms to Gabriel's birth will represent the year in which Gabriel was born.
Hope this Helps!!!
The first two steps in determining the solution set of the system of equations, y = x2 - 6x + 12 and y = 2x - 4
algebraically are shown in the table.
Step
Step 1
Step 2
Equation
x2 - 6x + 12 = 2x4
x2–8x+16=0
Which represents the solution(s) of this system of equations?
O (4,4)
O 64,-12)
0 (4, 4) and (44, 12)
O (-4, 4) and (4, 12)
Save and Exit
Neart
Submit
Mark this and return
Answer:
(4, 4 )
Step-by-step explanation:
Given the 2 equations
y = x² - 6x + 12 → (1)
y = 2x - 4 → (2)
Substitute y = x² - 6x + 12 into (2)
x² - 6x + 12 = 2x - 4 ( subtract 2x - 4 from both sides )
x² - 8x + 16 = 0 ← in standard form
(x - 4)² = 0 ← in factored form
x - 4 = 0 ⇒ x = 4
Substitute x = 4 into (2) for corresponding value of y
y = 2(4) - 4 = 8 - 4 = 4
Solution is (4, 4 )
What is the factored form of n2 – 25?
Answer: (n + 5)(n - 5)
Explanation: In this problem, we have a binomial that's the difference of two squares because n² and 25 are both perfect squares and we are subtracting or taking the difference of these two squares.
Since the difference of two squares factors as the product of two binomials, we can setup our parenthses and in the first position, we use the factors of n² that are the same which are n · n.
In the second position, we use +5 and -5 as our factors of -25.
So our answer is (n + 5)(n - 5).
What is the domain of y = sec(x)?
Answer:
Step-by-step explanation:
answer is c
Answer:
The answer is B, the second one on your screen. I hope I wasn't too late! :)
evaluate √ 9.6230 * 2.340 / 5.3 10 * 3.721
Answer:
[tex]\sqrt{15.76}[/tex]
Step-by-step explanation:
[tex]\sqrt{9.6230 \frac{2.340}{5.310}3.721 }[/tex]
Lets solve the fraction first
[tex]\frac{2.340}{5.310} =0.44[/tex]
9.6230 x 0.44 = 4.23
4.23 x 3.721 = 15.76
[tex]\sqrt{15.76}[/tex]
F(x)=1/3x+2????????????
14. A wheel turns through 90 revolutions per minute.
How many degrees does it turn through in 1 second?
1 revolution = 360 degrees
360 degrees x 90 revolutions per minute = 32,400 degrees per minute.
1 minute = 60 seconds.
32,400 degrees per minute / 60 seconds = 540 degrees per second.
please help Yuto has a bag containing 3 red marbles, 5 blue marbles, 2 green marbles, and 8 yellow marbles. Rin reaches into the bag, pulls out a blue marble, and puts it in her pocket. Then Misaki reaches in and pulls out a marble. What is the total number of possible outcomes for Misaki’s marble?
Answer: 47.1%
Step-by-step explanation:
Answer:
The answer is C.17
Step-by-step explanation:
Drink your daily water!! Have a nice day everyone :)
HELPPP WITH THIS PLEASEEEEEE
Answer:
Width=8
Length=11
It's an 8m x11m rectangle.
Step-by-step explanation:
2L+2W= 38
2(w+3)+2w=38
2W+6+2w=38
4W=32
W=8
L=W+3=8+3=11
CHECK: 8+8+11+11=38
which of the following rational functions is graphed below?
Answer:
D
Step-by-step explanation:
1/x+1
PLEASEEE HELP ASAP! *grade 9 work* and show your work!!
Answer:
at 0 the amount is 5
1 is 7.5
2 is 10
3 is 12.5
the initial value is the y intercept when the value ox x=0
the initial value is 5
the rate of change is the total change of a function of the out put (y) divided by the change of the input (x)
f(x2)-f(x1)/x2-x1
10-7.5/2-1
2.5/1=2.5
or m=y2-y1/x2/x1=10-7.5/2-1=2.5
y=2.5x+5
Triangle D E F is shown. The length of E F is 10, the length of D F is 7, and the length of D E is 12. What information relevant to calculating area do we have available for this triangle? Which method should we use to calculate the area for this triangle? What is the area of this triangle calculated to the nearest hundredth of a square unit?
Answer:
34.98 square units.
Step-by-step explanation:
It is given that DEF is a triangle, EF=10, DF=7 and DE=12.
Information of sides of triangle is relevant to calculating area.
We should use Heron's formula.
According to Heron's formula, the area of triangle is
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
where,
[tex]s=\dfrac{a+b+c}{2}[/tex]
For triangle DEF, let a=10, b=7 and c=12.
Now,
[tex]s=\dfrac{10+7+12}{2}=\dfrac{29}{2}=14.5[/tex]
Area of triangle is
[tex]A=\sqrt{14.5(14.5-10)(14.5-7)(14.5-12)}[/tex]
[tex]A=\sqrt{14.5(4.5)(7.5)(2.5)}[/tex]
[tex]A=\sqrt{1223.4375}[/tex]
[tex]A=34.977671[/tex]
[tex]A\approx 34.98[/tex]
Therefore, the area of triangle DEF is 34.98 square units.
Answer:
SSS, Heron's formula, and 34.98 square units
Step-by-step explanation:
Question 10(Multiple Choice Worth 1 points)
(02.05 MC)
Graph g(x), where f(x) = 2X - 5 and g(x) = f(x + 1).
(g(x)
0
g(x)
0
0
Answer:
Please refer to the attached image for the graph of g(x).
Step-by-step explanation:
First of all, let us find the value of g(x).
Given that:
[tex]f(x) =2x-5[/tex] and
[tex]g(x) = f(x+1)[/tex]
To find: The graph of g(x) = ?
Solution:
[tex]f(x+1)[/tex] means we replace 'x' with 'x+1' and we get g(x).
Let us replace x with x+1 in f(x):
[tex]f(x+1) = 2(x+1)-5\\\Rightarrow f(x+1) = 2x+2-5\\\Rightarrow f(x+1) = 2x-3\\\therefore g(x) = 2x-3[/tex]
Now let [tex]y=g(x) =2x-3[/tex]
Let us put x = 0 and then y = 0 to find two points on coordinate axis to easily plot the graph of g(x).
Putting x = 0,
[tex]y=2\times0-3\\\Rightarrow y =-3[/tex]
So, one point is A(0,-3)
Now, let us put y = 0 and find out x.
[tex]0=2x-3\\\Rightarrow x=\dfrac{3}{2}[/tex]
So, second point is [tex]B(\frac{3}{2},0)[/tex].
Now, let us plot A and B then extend the line joining AB.
Please refer to the attached image for the graph of function:
g(x) = 2x - 3
Matt bought some boards to build a wooden deck. Some of the boards were 4 ft long and some of the boards were 5 ft long. He bought 35 ft of boards altogether. How many boards altogether did Matt buy?
Answer:
8 boards.
Step-by-step explanation:
Since he bought a few of each length. The only combination that works is when he bought 5 of the 4 ft long board so 4×5=20. Than he bought 3 of the 5ft boards 3×5=15. 20+15=35 ft worth of boards.
Matt brought total 8 boards out of which the 5 boards are of 4ft and 3 boards are of 5ft.
We have a guy named Matt who bought some boards to build a wooden deck. Some of the boards were 4 ft long and some of the boards were 5 ft long. He bought 35 ft of boards altogether.
We have to find out how many boards he bought all together.
What do you mean by the solution of a equation ?The solution of an equation is the value at which the left hand side and right hand side of the equation equals to each other.
In the question, it is given that there are 4ft long and 5ft long boards and matt brought 35 ft of board all together.
Let us assume that the number of 4 ft boards he bought are = x and the number of 5ft boards be y, then according to question -
4x + 5y = 35
[tex]y = \frac{-4x + 35}{5} \\y=\frac{-4x}{5} + 7[/tex]
Now, all the points that lie on this line are the possible answers but the number of boards cannot be in decimal. Hence, the solution x = 5 and y=3, which will give us 4 x 5 + 5 x 3 which is equal to 35.
Hence, Matt brought 5 boards of 4ft and 3 boards of 5ft.
To solve more questions on linear equations in two variables, visit the link below -
https://brainly.com/question/22557080?referrer=searchResults
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Use the right triangle provided to find the missing side length. Use the Pythagorean Theorem c^2 = a^2 + b^2.
Answer:
11. C=5
12. SQRT (43)
Step-by-step explanation:
11. 3^2+4^2=9+16=25
12. 8^2-4^2=64−16=48