Considering the definition of axis of symmetry and vertex of a quadratic function, the correct answer is the first option: the coordinates of the vertex of the graph is (-5,41).
Quadratic function
The general form of a quadratic function is f(x = ax²+ bx+ c, whose graph is a parabola.
Axis of symmetry and vertex of a quadratic function
Quadratic functions have a maximum (if a<0) or a minimum (if a>0). This point is the vertex of the parabola.
That is, the vertex of a quadratic equation or parabola is the highest or lowest point on the graph corresponding to that function. The vertex is in the plane of symmetry of the parabola; anything that happens to the left of this point will be an exact reflection of what happens to the right.
In other words, the vertex divides the graph into two halves that are mirror images of each other, so that the axis of symmetry always passes through the vertex.
Vertex of f(x) = −x² − 10x + 16
In this case, you know that the axis of symmetry for the function is x = −5.
So the vertex on the x-axis has a value of -5. To calculate the value of the vertex on the y-axis, you must substitute the value of the vertex on the x-axis in the function:
f(-5) = −(-5)² − 10×(-5) + 16
Solving:
f(-5)= 41
In summary, the correct answer is the first option: the coordinates of the vertex of the graph is (-5,41).
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Answer:
a
Step-by-step explanation:
a
a rectangular field is 50 M long and 30 M broad . find a perimeter b) the length of wire required to fence it thrice c)calculate area of a rectangular field
Answer: b) 160 c) 1500
Step-by-step explanation: b) 50 + 50 + 30 + 30 = 160 c) 50 x 30 = 1500
Step-by-step explanation:
[tex]length \: of \: a \: field \: = 50m[/tex]
[tex]breadth \: of \: a \: field \: = 30m[/tex]
[tex]Perimeter \: of \: a \: field \: = ? [/tex]
We know,
Perimeter ( p ) = 2 ( l + b )
= 2 ( 50m + 30m )
= 2 × 80 m
= 160 m
The length of a wire required to fence it thrice
= 3 × 160 m
= 480 m
Area ( A ) = l × b
= 50 × 30 m
[tex] = {1500m}^{2} [/tex]
Adam deposited $50,000 in a savings account with simple interest. Three years later, he had earned $6,000 in interest. What was the interest rate
John was at the store and he saw his favorite video game
Answer:
That's cool
Step-by-step explanation:
Answer:
Thats cool and all but whats the wuestion
Step-by-step explanation:
What is the next number in the sequence? 9….16….24….33…
Answer:
43
Step-by-step explanation:
The first increase from 9 to 16 is 7
The second increase from 16 to 24 is 8
The third from 24 to 33 is 9
Following the pattern the next increase must be by 10. 33+10=43
Give the equation of the line in point-
slope form that goes through the point
(-3,7) and is parallel to the line 4x-3y=7
Answer:
[tex]y-7=\frac{4}{3} (x+3)[/tex]
Step-by-step explanation:
Hi there!
We are given the point (-3, 7)
We want to write the equation of the line containing that point, in point slope-form, and that is also parallel to 4x-3y=7
Parallel lines contain the same slope
So first, let's find the slope of 4x-3y=7
To do that, we can convert the line from standard form (ax+by=c) to slope-intercept form (y=mx+b, where m is the slope, and b is the y intercept)
To do that, we need to isolate y on one side
So start by subtracting 4x from both sides
4x-3y=7
-4x -4x
________________
-3y=-4x+7
Divide both sides by -3
y=[tex]\frac{4}{3}x[/tex]- [tex]\frac{7}{3}[/tex]
Since 4/3 is in the place of where m should be, the slope of the line is 4/3
It is also the slope of our new line, which we are trying to find
As stated earlier, we want to write this line in point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point
This is where the point we were given earlier comes in. We simply need to substitute our values (of the point and the slope) into the formula to find the equation.
First, with the slope; substitute 4/3 as m in the equation
[tex]y-y_1=\frac{4}{3} (x-x_1)[/tex]
Now substitute -3 as [tex]x_1[/tex] in the equation
[tex]y-y_1=\frac{4}{3} (x--3)[/tex]
We can simplify this to:
[tex]y-y_1=\frac{4}{3} (x+3)[/tex]
Now substitute 7 as [tex]y_1[/tex] into the equation
[tex]y-7=\frac{4}{3} (x+3)[/tex]
Hope this helps!
what is the mean of these number 8 40 50 85 1 5 46 65 41 13 34 67 53 71 44
Answer:
41.53
Step-by-step explanation:
add all the numbers and divide by how much there is
623 /15
41.53
hope this helps!!
Find the missing side of the right triangle. Leave answer in
simplest radical form.
If the legs of a right triangle are 6 and 8, then the hypotenuse
is
a 40
b 30
C 20
d 10
Altitude (AB) = 6cm
Base (BC) = 8cm
To FindHypotenuse (AC) = ?
[tex] \fbox \text{According To Pythagoras Theorem = }[/tex]
[tex] \text{(Hypotenuse)² = (Altitude)² + (Base)²}[/tex]
Inserting The Values
[tex] \text{(Hypotenuse)²} =( {6})^{2} + (8) {}^{2} [/tex]
[tex] (\text{AC}) {}^{2} = (6) {}^{2} + (8) {}^{2} \\ \implies \text{(AC)} {}^{2} = 36 + 64 \\ \implies\text{AC} = \sqrt{100} \\ \implies\text{AC} = 10 \\ \\ \therefore \text{Hypotenuse (AC)} = 10 \text{cm}[/tex]
Correct Option D= 10cm
Hope this helpsPLEASE HELP ME FIND THE SURFACE AREA OF THIS PRISM
Answer: i don't know
Step-by-step explanation: i don't know sorry
Simplify using the order of operations.
9−4 ·5+6
we know that the multiplication comes first in the family then we start from left to right
4 x 5= 20
9-20 = -11
-11 + 6 = -5
there you go!
[tex]9 - 4 \times 5 + 6[/tex]
[tex]9 - 20 + 6[/tex]
[tex] - 11 + 6[/tex]
[tex] - 5[/tex]
hii i need help, helppp thank you
Answer:
i think c
Step-by-step explanation:
i hope this helped
Answer:
c
Step-by-step explanation:
Find the area of the shape.
Pls help! ASAP [tex] [/tex]
Answer:
BC
Seg AC
Ray KM
equivalent (x+ 4)(2r - 1)
Answer:
Step-by-step explanation:
r (2 x + 8) - x - 4
(2 r - 1) x + 8 r - 4
Hi! I'm giving 35 points for this question! No scams or anything unrelated or you will get reported, thanks!
How could the relationship of the data be classified?
A fairly strong positive correlation
A fairly weak positive correlation
A fairly strong negative correlation
A fairly weak negative correlation
Answer:
A fairly weak positive correlation
Step-by-step explanation:
Answer:
B; A fairly weak positive correlation.
Step-by-step explanation:
Tip: You will know it's a negative if the line in the graph can be part of an N.
What is the area of the trapezoid?
7 cm
10 cm
6 cm
7 cm
1
13 cm
O A. 43 cm?
O B. 60 cm?
O C. 70 cm?
Answer:
B. 60 cm²
Step-by-step explanation:
The formula for the area of a trapezoid is: [tex]\frac{1}{2}(b_{1} + b_{2} )h[/tex]
Plugging in the given values, we can solve:
[tex]\frac{1}{2} (13+7)(6)\\\\\frac{1}{2}(20)(6)\\\\10(6)\\\\= 60[/tex]
hope this helps!
27. To compare the effectiveness of two treatments, researchers conducted a well-designed experiment using a
randomized block design in which the subjects were blocked by age-group (under 40 years and 40 years or
older). Which of the following must be true about the randomized block design of the experiment?
(A) The number of subjects in each block is different.
88 Treatments are randomly assigned to subjects within each block.
(C) The design cannot have a control group because subjects are blocked by age-group.
fo) The experiment uses a matched-pairs design, where subjects from one block are paired with subjects from
the other block.
E) The subjects in one block receive one treatment, and the subjects in the other block receive the other
treatment
In a randomized block design, it is expected treatments are randomly assigned within each block.
What does a randomized block design imply?Subjects are divided into blocks based on a specific features such as age, gender, education, etc.Within each block subjects that receive treatment and does who do not are randomly assigned.The treatment in all blocks is the same. For example, if the purpose is to study the effect of medicine all treatment subjects should receive the same medicine and dose.What is the purpose of this design?The purpose is to minimize the effect of certain factors such as age.
Based on the above, it is expected in this experiment the treatment is randomly assigned to a specific number of subjects within each block.
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Using two or more complete sentences, describe how to find the general rule for the arithmetic sequence with a4=−1 and a6=−13. In your final answer, include all of your calculations
Answer:
-4 is your final answer in it
The equation x2 + 4y2 = 36 represents which conic section?
ellipse
circle
hyperbola
parabola
Answer: The answer is ellipse
What is the measure of the angle x?
Answer:
40
Step-by-step explanation:
angle AOB= 2x=80
x=80/2
x=40
Find the value of the given trigonometric function.
cos 420°
Recall that cos(x + y) = cos(x) cos(y) - sin(x) sin(y). So
cos(420°) = cos(360° + 60°)
cos(420°) = cos(360°) cos(60°) - sin(360°) sin(60°)
cos(420°) = cos(60°)
since cos(360°) = 1 and sin(360°) = 0. Then
cos(420°) = cos(60°) = 1/2
pls help me i really need help
Answer:
hey pls help me I urgently need help
Find the minimum distance from the parabola x-y^2=0
to the point (0,3).
Answer:
√5
Step-by-step explanation:
The distance from the given point to the curve can be found using the distance formula. The resulting expression can be minimized to find the minimum distance.
d = √((x2 -x1)² +(y2 -y1)²)
__
Point on the ParabolaA point on the parabola can be described by ...
x -y² = 0
x = y² . . . . . add y²
Then a point on this curve is ...
(y², y)
Distance to Given PointThe distance to it from (0, 3) is ...
d = √((0 -y²)² +(3 -y)²) = √(y⁴ +y² -6y +9)
Find the MinimumThe distance will be minimized when the derivative of the radical expression is zero:
d(y⁴ +y² -6y +9)/dy = 0 = 4y³ +2y -6
0 = 2y³ +y -3 . . . . . . . . remove a factor of 2
This will have a rational root in the set {±1, ±3}.
Trial and error shows that y=1 is the only real solution to this equation.
__
Then the minimum distance is ...
d = √(1⁴ +1² -6·1 +9) = √5
_____
Additional comment
The attached graph shows that a circle with radius √5 centered at (0, 3) will intersect the parabola at exactly one point. That confirms our solution.
please help the assignment is due today
Answer:
[tex]\tt B)\;93^o[/tex]
Step-by-step explanation:
[tex]\tt 2(19x+1)+(19x+1)+15x=360[/tex]
[tex]\tt 38x+2+19x-2+15x=360[/tex]
[tex]\tt 38x+19x+15x+2-2=360[/tex] (Add similar elements)
[tex]\tt 72x+2-2=360[/tex] (2-2=0)
[tex]\tt 72x=360[/tex]
[tex]\tt \cfrac{72x}{72}=\cfrac{360}{72}[/tex] ( Divide both sides by 72)
[tex]\tt x=5[/tex]
Now,
m∠km:-
[tex]\tt 19x-2[/tex]
[tex]\tt 19(5)-2[/tex] (Multiply 19*5= 95)
[tex]\tt =95-2[/tex] (Subtract)
[tex]\tt = 93[/tex]
Therefore, m∠km=93° is the answer.
_____
sebuah Mobil memerlukan Benson sebanyak 45 liter until menempuh jarak 480 km, jika Mobil tersebut menempuh jarak 320 km, maka banyak bensin Yang diperlukan adalah...
jelaskan ya..
Answer:
what??? I can't understand you sorry
What is 8 cm enlarged by a scale factor of 6.5
Answer:
8cm enlarged by a scale factor of 6.5 is 52cm I believe.
Step-by-step explanation:
8 times 6.5= 52cm
Ella and Amy are planning trips to
ten countries this year. There are
12 countries they would like to
visit. They are deciding which
countries to skip, how many ways
are there?
Applying the combination formula, the number of ways there are is: 66.
What is Combination?Combination is a technique in maths used in selecting objects from a group of objects in a way that the order in which they are selected does not matter.
Combination formula is given as:
[tex]nC_r = \frac{n!}{r(n - r)!}[/tex]
Given the following:
n = 12 r = 2Plug in the values:
[tex]12C_2 = \frac{12!}{2(12 - 2)!}\\\\12C_2 = \frac{12!}{2(10)!}\\\\12C_2 = \frac{12 \times 11}{2(1)}[/tex]
[tex]\mathbf{12C_2 = 66}[/tex]
Therefore, applying the combination formula, the number of ways there are is: 66.
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Find the value of xxx in the isosceles triangle shown below. Choose 1 answer: Choose 1 answer: (Choice A) A x = 20x=20x, equals, 20 (Choice B) B x = 7x=7x, equals, 7 (Choice C) C x=\sqrt{52}x= 52 x, equals, square root of, 52, end square root (Choice D) D x = \sqrt{40}x= 40 x, equals, square root of, 40, end square root
Answer:
look at pic
Step-by-step explanation:
In the given case, the value of "x" in the given isosceles triangle is 18 degrees.
The given triangle is an isosceles triangle, which means that it has two equal sides. Let's denote the length of each equal side as "x".
To find the value of "x", we need to use the properties of an isosceles triangle. In an isosceles triangle, the base angles (the angles opposite to the equal sides) are congruent (equal in measure).
Since the base angles are congruent, we can set up the following equation: 2x + 3x + 5x = 180 degrees
Combining like terms, we have: 10x = 180 degrees
To solve for "x", we divide both sides of the equation by 10: x = 18 degrees
Therefore, the value of "x" in the given isosceles triangle is 18 degrees.
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help me please
I couldn't solve it
[tex]\text{L.H.S}\\\\=\dfrac{\sin^4 A - \cos^4 A}{ \sin A + \cos A}\\\\\\=\dfrac{(\sin^2 A)^2-(\cos^2 A)^2}{\sin A + \cos A}\\\\\\=\dfrac{(\sin^2 A + \cos^2 A)(\sin^2 A-\cos^2 A)}{\sin A + \cos A}\\\\\\=\dfrac{1\cdot(\sin A+\cos A)(\sin A - \cos A)}{\sin A +\cos A}\\\\\\=\sin A - \cos A\\\\\\=\text{R.H.S}~~~ \\\\\text{Proved.}[/tex]
Answer:
heya! ^^
[tex] \\ \frac{ \sin {}^{4} (A) - \cos {}^{4} (A) }{ (\sin \: A + \cos \: A) } = ( \: sin \: A\: - \: cos \: A \: )\\[/tex]
[tex] \\LHS = \frac{ \sin {}^{4} (A) - \cos {}^{4} (A) }{ (\sin \: A + \cos \: A) } \\ \\ \frac{( \sin {}^{2} \: A + \cos {}^{2} \: A)( \sin {}^{2} A - \cos {}^{2} A) }{ (\sin \: A + \cos \: A) } \\ \\ we \: know \: that \: - \: sin {}^{2} A + cos {}^{2} A = 1 \\ \\ \therefore \: \frac{(1)(\sin {}^{2} \: A - \cos {}^{2} \: A)}{(\sin \: A + \cos \: A)} [/tex]
now , we're well aware of the algebraic identity -
[tex]a {}^{2} - b {}^{2} = (a + b)(a - b)[/tex]
using the identity in the equation above ,
[tex]\dashrightarrow \: \frac{(sin \:A - \: cos \: A)\cancel{(sin \:A + \: cos \: A )}}{\cancel{(sin \: A\: + \: cos \: A)}} \\ \\ \dashrightarrow \: (sin \: A \: - \: cos \: A) = RHS[/tex]
hence , proved ~
hope helpful :D
PLEASE HELP PLEASE PLEASE HELP
Answer:
False
Step-by-step explanation: Matter All was take up place
If f (x)=
(3 + x)/
(x-3)
what is f(a + 2)?
[tex]f(x) = \frac{3 + x}{x - 3} [/tex]
[tex]f(a + 2) = \frac{3 + a + 2}{a + 2 - 3} = \frac{a + 5}{a - 1} [/tex]