(2, 11) is the vertex of f(x) = 4(x - 2)² +11.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .
The given equation is f(x) = 4(x - 2)² +11.
The vertex form is y=a(x-h)²+k
y=a(x-h)²+k of a parabola is said to be in vertex form because the vertex can be determined by examining the equation: (h, k) is the vertex.
(h, k) are the vertices of the given equation.
a=4,
h=2 and
k=11
so the (2,11) is the vertex of the function.
Hence, the vertex of f(x) = 4(x - 2)² +11 is (2, 11).
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Find each probability and then order from least probable to most probable.
AnSwErS:
Target:
1. The probability of rolling a 7 on a 6-sided die.
2. The probability of rolling a 4 on a 6-sided die.
3. The probability of flipping a head on a coin.
4. The probability of drawing a green or red marble from a bag with 6 red, 5 blue, and 3 green marbles.
5. The probability of rolling a number less than 7 on a 6-sided die.
Step-by-step explanation:
HOPE THIS HELPS!!!!
Enter the number that belongs in the green box
Two bells P and Q ring at intervals of 3hours and 4hours respectively. After how many hours will the two bells first ring simultaneously (at the same time)
Answer:
12 hours
Step-by-step explanation:
4 / 2
2/2
1
4 = 2²
2² x 3 = 4 x 3 = 12
Given 2x + 3 is the hypotenuse, use the Pythagorean
Theorem to find the length of the side labeled x.
Answer:
24
Step-by-step explanation:
Given right triangle sides x, 2x-3, and 2x+3, you want to know the length of the side labeled x.
Pythagorean theoremThe Pythagorean theorem tells you the square of the hypotenuse is equal to the sum of the squares of the other two sides.
(2x +3)² = (2x -3)² +x²
4x² +12x +9 = 4x² -12x +9 +x²
x² -24x = 0 . . . . . subtract 4x² +12x +9
x(x -24) = 0 ⇒ x = 0 or 24
The length of the side labeled x is 24 units.
__
Additional comment
The triangle is an 8-15-17 triangle scaled up by a factor of 3.
2. Mike Williams, an electrician, is single, claims 1 allowance, and earns $425 per week. Find the federal tax withheld each week
The federal tax withheld each week for Mike Williams is given as follows:
$37.
How to obtain the amount he pays in taxes?Mike Williams salary is given as follows:
$425 a week.
The range that contains the salary, from the table given at the end of the answer, is given as follows:
Between $420 and $430.
The number of allowances that he claims is given as follows:
One allowance.
Hence the federal tax withheld each week is given by the 4th column of the interval between 420 and 430, as he claims one allowance, and the numeric value of this tax is given as follows:
$37.
(which is the weekly amount that he pays in taxes).
Missing InformationThe table with the tax information is given by the image shown at the end of the answer.
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What is the slope of the line that passes through the points (2, 3) and (0,11)?
What are the possible rational zeros of f(x) = x^4+2x^3-3x^2-4x-12
The solution of the function f(x) = (x - 2)(x + 6)(x² + x + 2) will be 2, -3, - 1/2 + (√7/2)i, and - 1/2 - (√7/2)i.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The function is given below.
f(x) = (x⁴ + 2x³ - 3x² - 4x - 12)
Factorize the expression, then we have
f(x) = (x⁴ + 2x³ - 3x² - 4x - 12)
f(x) = x⁴ - 2x³ + 4x³ - 8x² + 5x² - 10x + 6x - 12
f(x) = x³(x - 2) + 4x²(x - 2) + 5x(x - 2) + 6(x - 2)
f(x) = (x - 2)(x³ + 4x² + 5x + 6)
f(x) = (x - 2) (x³ + 3x² + x² + 3x + 2x + 6)
f(x) = (x - 2)[x²(x + 3) + x(x + 3) + 2(x + 3)]
f(x) = (x - 2)(x + 6)(x² + x + 2)
The zeroes of the function are given as,
f(x) = 0
(x - 2)(x + 3)(x² + x + 2) = 0
x = 2, -3, - 1/2 + (√7/2)i, - 1/2 - (√7/2)i
The solution of the function f(x) = (x - 2)(x + 6)(x² + x + 2) will be 2, -3, - 1/2 + (√7/2)i, and - 1/2 - (√7/2)i.
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The width of a rectangular table top is 2 1/2 feet shorter than 3 times it’s length. If the perimeter of the table is 43 feet, what is the length, L, of the table
Answer: length=6 feet
Step-by-step explanation:
For this you need to create one equation from the question and use the equation for perimeter.
equation 1 is 2W+2L=P where perimeter is 43.
equation 2 is w=3L-2.5
-Now you want to take equation two and plug it into equation 1 for w to find L
It will be 2(3L-2.5)+2L=43 and you want to solve for L
distribute the 2 2(3L-2.5)+2L=43
add up the Ls 6L-5+2L=43
add 5 to each side 8L-5=43
divide each side by 8L=48
Then you get L=6
Now use L=6 to plug into equation two to get W(width)
w=3(6)-2.5=18-2.5=15.5
Now plug in both W and L into equation 1 to make sure you get 43
P=2(15.5)+2(6)=32+12=43 this means that w and l are correct and you get the perimeter given. So length (L) is 6.
compute the integral
integral 2x+11/x^2-x-2 dx
The Integral value of (2x+11)/(x²-x-2) is[tex]2(\frac{1}{3} log|x+1|+\frac{2}{3} log|x-2|)-\frac{11}{3} (log|\frac{2}{3} x+\frac{2}{3}|-log|\frac{2}{3} x-\frac{4}{3}|)+c[/tex]
What is Integration?An integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data.
The given integral is [tex]\int\dx \frac{2x+11}{x^{2} -x-2} dx[/tex]
By partial fractions we divide the integral
Apply the sum rule:
∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx
[tex]=\int\dx \frac{2x}{x^{2} -x-2} dx+\int\dx \frac{11}{x^{2} -x-2} dx[/tex]
Let us calculate the first integral part
[tex]=\int\dx \frac{2x}{x^{2} -x-2} dx[/tex]
Let us use the partial fraction of [tex]\frac{x}{x^{2} -x-2} dx:\frac{1}{3(x+1)} +\frac{2}{3(x-2)}[/tex]
[tex]\int\dx \frac{2x}{x^{2} -x-2} dx=2\int\dx \frac{1}{3(x+1)} dx+ \frac{2}{3(x-2)} dx[/tex]
[tex]\int\dx \frac{2x}{x^{2} -x-2} dx=2(\frac{1}{3} log|x+1|+\frac{2}{3} log|x-2|)[/tex]
Now let us integrate second term.
[tex]\int\dx \frac{11}{x^{2} -x-2} dx=11\int\dx \frac{1}{x^{2} -x-2} dx[/tex]
We can write denominator as x²-x-2= (x-1/2)²-9/4
[tex]=11\int\dx \frac{1}{(x-\frac{1}{2}) ^{2} -\frac{9}{4}} dx[/tex]
We apply u substitution method
[tex]\int\dx \frac{11}{x^{2} -x-2} dx=-\frac{11}{3} (log|\frac{2}{3} x+\frac{2}{3}|-log|\frac{2}{3} x-\frac{4}{3}|)[/tex]
[tex]=2(\frac{1}{3} log|x+1|+\frac{2}{3} log|x-2|)-\frac{11}{3} (log|\frac{2}{3} x+\frac{2}{3}|-log|\frac{2}{3} x-\frac{4}{3}|)+c[/tex]
Hence, [tex]2(\frac{1}{3} log|x+1|+\frac{2}{3} log|x-2|)-\frac{11}{3} (log|\frac{2}{3} x+\frac{2}{3}|-log|\frac{2}{3} x-\frac{4}{3}|)+c[/tex] is the integral value of of (2x+11)/(x²-x-2).
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Is this a false or true statement? Extrapolation is the use of the regression line to estimate a mean of y-values for an x-value that is far outside the x-range of data.
This is False in light of the stated statement. due to the employment of a regression line to calculate the mean of y for x that are outside the x-range of the data.
How is regression calculated?Y = mX + b, where X is the predictive (independent) factor, m is really the approx slope, and b is the expected intercept, is the methodology for simple linear regression.
What makes regression math so special?Regress, from whence the word "regression" is derived, means "to go back" in Latin (to something). Regression is the method that enables "going back" from muddled, challenging data to a clearer and more significant model in this manner.
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Complete the square to re-write the quadratic function in vertex form:
y =
-8x²+32x - 28
Answer:
y = -8(x - 2)² + 4
50 POINTSSSSSS ASAP!!!! 50 POINTSSSSSS ASAP!!!! 50 POINTSSSSSS ASAP!!!!
Quadrilateral RUST has a vertex at T (5, 2).
An image displaying a quadrilateral RUST.The vertex of R is R of 1 comma 5.
What are the coordinates of T' after the translation (x, y) → (x – 1, y + 2), followed by a dilation by a scale factor of 2, centered at the origin?
A.
(8, 8)
B.
(6, 2)
C.
(4, 4)
D.
(10, 4)
Answer:
A) (8, 8)-------------------------------
Apply the rules to point T.
Translation:
T(5, 2) → T'(5 - 1, 2 + 2) = T'(4, 4)Dilation:
T'(4, 4) → T''(4*2, 4*2) = T''(8, 8)The matching choice is A.
A line passes through the point (3,2) and has a slope of 4
The equation of the line that passes through the point (3,2) and has a slope of 4 is; y = 4x - 10
What is the Point-slope form?The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
Which is the required equation of a line in a point-slope form.
Point (3,2)
Then Slope m = 4
Now Write the equation as;
y - 2 = 4(x - 3)
y = 4x - 10
Hence, The equation of the line is; y = 4x - 10
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Can you please help me
Answer:
The Answer is B/2/middle option
Step-by-step explanation: im great at math
94.36 rounded tenths
Answer:
94.4
Step-by-step explanation:
1/2 times 4/5 what’s the answer
Answer:
2/5.
Step-by-step explanation:
1/2 times 4/5 is equal to (1/2) * (4/5), which simplifies to 4/10. Since 4/10 can be simplified to 2/5, the answer is 2/5.
Answer:
the answer is 2/5 or as a decimal 0.4
What is the value of the expression
4(2+y)
______
2y-x
when x = 2 and y = 47
Answer:
Step-by-step explanation:
I got 196/90
I got this by plugging in 47 for y so I got 4(2+47) and got 196 when I solved it. The bottom one I did 2(47-2) and got 90...( I don't know if it's right though, if wrong I'm sorry)
Solve the inequality and graph the solution.
k/2 – 20 ≥ –18
To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.
The graph of the inequality is attached below.
What is inequality?
In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.
Consider, the given inequality
K/2 - 20 ≥ -18
Add 20 on both sides,
K/2 - 20 + 20 ≥ -18 + 20
K/2 ≥ 2
Multiply both sides by 2,
K/2 x 2 ≥ 2 x 2
K ≥ 4
Now to graph the inequality.
The graph of the inequality is attached below.
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How to write the unit form for 1/3
Answer:
To write the unit form for 1/3, you can simply write "1/3" or use the fraction symbol, which looks like a horizontal line with the numerator above the denominator. For example, you can write the unit form for 1/3 as follows:
1/3
Alternatively, you can use the fraction symbol, like this:
1/3
In both cases, the numerator (the number on top of the fraction) is 1 and the denominator (the number on the bottom of the fraction) is 3. This indicates that the value of the fraction is one-third.
Find the product of -1.5x and -0.25x.
O 0.375x²
O-1.75x²
O 0.375x
O -1.75x
Step-by-step explanation:
(-1.5)x × -0.25x = 0.375x²
remember, -×- = +
For 50 points if someones solves this for me
Answer:
It will take 48 seconds before the planes are at the same altitude.
When there are at the same altitude, they will be at 3864 feet.
Step-by-step explanation:
Because its right :)
please give brainliest
Alex came home after school one day and found that his mother had left a plate of cookies. Alex ate 1/4 of the cookies. When his sister Bernice came home, she ate 1/3 of the remaining cookies, and when Carla came home, she ate 1/2 of the cookies on the plate. When their mother came home, there were 5 cookies on the plate. How many did each child eat?
Answer: Children ate 15 cookies and 5 each because Alex ate 1/4 and bernice ate 1/3 and carla ate 1/2
and 5 were left
5 into 3 is 20
and 5 are left so
20-5 is 15
15 divide by 3 is 5
Frame calculation process in your words but the final answer is each child ate 5 cookies.
Ben lost half of his candies while walking home. His mom gave him 8 more candies. Now he has
22 candies. How many candies did he have to begin with?
NO LINKS!! Help me with these 2 column proofs 7aa
Here is the two column proof:
Statement Reason
Diagram GivenOS ≅ OS Reflexive property of congruence Proved===================================================
Statement Reason
Diagram Given∠C ≅ ∠C Reflexive property of congruence ProvedAccording to a weather report, there is a 53% chance it will
rain tomorrow. What is the probability that it will not rain
tomorrow?
Answer:
47% or .47
Step-by-step explanation:
:)):))):)/):)::!:&’s
The congruent reason for 5 is (c) ASA
How to determine the congruent reason for 5?From the question, we have the following parameters that can be used in our computation:
Triangles = VWX and ZYX
The ASA similarity theorem implies that the corresponding angles of the triangles in question are similar and the sides between these angles are congruent
From the question, we can see that the following corresponding angles on the triangles:
Angles W and Y
Angles X and X
This implies that these angles are congruent angles
For the triangle to be congruent by ASA, the following sides must also be congruent
WX must be congruent to YX
This is indicated in the table of values at (3)
Hence, the additional information on the similarity of the triangles is (d) ASA
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Please help me on this.
Determine whether the relation is a function. Explain.
{(6,-1), (-4, 2), (5, 2), (4, 6), (6,5)}
Answer:
It's not a function
Step-by-step explanation:
Answer:
[tex]\huge\boxed{\sf No}[/tex]
Step-by-step explanation:
Given relation:{(6,-1), (-4, 2), (5, 2), (4, 6), (6,5)}
For a relation to be a function, the domain (x-values) should NOT repeat values.
Here,
Domain = {6, -4, 5, 4, 6}
The number 6 in domain is repeated. Hence, this relation is not a function.
[tex]\rule[225]{225}{2}[/tex]
Solve for the variable
m/9-1=-2
Answer:
m = -9
Step-by-step explanation:
m/9 - 1 = -2
m/9 = -1
m = -1 × 9
m = -9
------------------------------
check
-9/9 -1 = -2
-2 = -2
the answer is good
A store pays $70 for a bicycle. The percent of markdown is 20%. What is the selling price?
Answer: $56
Step-by-step explanation:
20% of 70=14
70-14=56