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).
Learn more about the vertex of a quadratic function:
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Answer:
a
Step-by-step explanation:
a
Please help me ASAP I’ll mark brainly
Answer: 7
Step-by-step explanation:
can you help me solve this?
Answer:
456*567=4890998
46766-6755=566888
Answer:
FGM and reproductive health
A set of data is normally distributed with a mean of 327 and a standard deviation of 27.
What percentage of the data is below 357?
Enter your answer as a number rounded to the nearest tenth, like this: 42.5
Answer:
86.7%
Step-by-step explanation:
For questions regarding values related to a normal distribution, a suitable calculator is required. Numerous calculators, apps, web sites, and spreadsheets are capable of answering this question.
__
One standard deviation above the mean is 327 +27 = 354, so the value is expected to be slightly more than 50% +34% = 84%. It is no surprise, then, that a calculator tells you 86.7% of the data is below 857.
_____
Additional comment
The "empirical rule" tells you 68% of the area is within 1 standard deviation of the mean. The distribution is symmetrical, so half that, 34%, is between the mean and 1 standard deviation above the mean. Of course, 50% of the data is below the mean.
Only 16 tho!!!!!please
Answer:
(5*2) + (1/2)(2+2+2)*4)
Step-by-step explanation:
Area of Triangle = (1/2)(2 + 2 + 2 )* 4)
Area of Rectangle = 5 * 2
Total Area = (5*2) + (1/2)(2+2+2)*4)
What is the area of this combined shape?
Answer:
the amount of space inside a shape composed of basic shapes put together.
Step-by-step explanation:
hope this helps.
5. What is the surface area of the figure below?
6
3
3
The surface area of the given figure is 90 feet².
What is Surface Area?The area of a three dimensional object on it's outer surface is called the surface area of the object.
The given figure is a rectangular prism.
A rectangular prism consists of 4 rectangular lateral faces and 2 rectangular bases.
Surface area of the rectangular prism is the area of each of the faces.
Combining all these area, area of a rectangular prism can be found by the formula,
Area = 2 (lw + wh + lh)
where l is the length, w is the width and h is the height.
Given, l = 3 feet, w = 3 feet and h = 6 feet
Area = 2 [ (3 × 3) + (3 × 6) + (3 × 6)]
= 2 (9 + 18 + 18)
= 90 feet²
Hence the surface area is 90 feet².
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What is the solution to 9|x – 8| < 36?
Answer:
4 < x < 12
Step-by-step explanation:
Given:
[tex]\displaystyle \large{9|x-8| < 36}[/tex]
Divide both sides by 9:
[tex]\displaystyle \large{|x-8| < 4}[/tex]
Theorem:
For [tex]\displaystyle \large{|x-a| < b}[/tex], since absolute is less than a constant, the interval or solution is:
[tex]\displaystyle \large{-b < x-a < b}\\\displaystyle \large{-b+a < x < b+a}[/tex]
Therefore:
[tex]\displaystyle \large{|x-8| < 4 \to -4 < x-8 < 4}\\\displaystyle \large{-4+8 < x < 4+8}\\\displaystyle \large{4 < x < 12}[/tex]
Therefore, the solution is 4 < x < 12
Answer:
4 < x < 12
Step-by-step explanation:
9|x - 8| < 36
Divide both sides by 9:
|x - 8| < 4
Solution 1
(x - 8) < 4
Add 8 to both sides:
x < 12
Solution 2
-(x - 8) < 4
-x + 8 < 4
Subtract 8 from both sides:
-x < -4
Divide both sides by -1 (remembering to change the direction of the sign):
x > 4
Therefore, the solution to the inequality is 4 < x < 12
Blank × 0.1 = 47.2 find the missing number
Answer:
472 :)
Step-by-step explanation:
47.2/0.1 = 472
Have an amazing day!
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what are the sin(0) and tan(0) of the picture below? i might have the answers but i want to double check if i did it right :) brainliest for help!
Step-by-step explanation:
sin(0) is opposite over hypotenuse which in this case is 12/15
tan (0) is opposite over adjacent 12/9
you can simplify if you like to 4/5 and 4/3 if you want to.
sinØ
Perpendicular/Hypotenuse12/15tanØ
Perpendicular/Base12/94/3236 megabytes and 12.6% is downloaded how many megabytes have been downloaded
236 x 0.126
29.736 MB have been downloaded
Johnson has 19 bowls of ice cream he gives away d ice cream bowls write the expression that shows the number of ice cream bowls are left?
Answer:
19 -d
Step-by-step explanation:
The number Johnson has left is found by subtracting the number he gave away from the number he started with.
19 -d . . . . . . . number of ice cream bowls left
What’s the slope of the line that passes through (10,2) and (5,9)
Answer:
y = -1.4x + 16
Step-by-step explanation:
the slope is -1.4x
Use the slope formula:-
[tex]\displaystyle\frac{y2-y1}{x2-x1}[/tex]
Plug in the values:-
[tex]\displaystyle\frac{9-2}{5-10}[/tex]
Simplify:-
[tex]\displaystyle\frac{7}{-5}= -\frac{7}{5}[/tex]
[tex].~~~~~~~\uparrow\sf{Slope}[/tex]
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)
Which of the following may fall outside a triangle?
A. incenter and circumcenter
B. orthocenter and circumcenter
C. circumcenter and centroid
0 D. centroid and incenter
Answer: B
Step-by-step explanation:
use a sum or difference formula to simplify the expression Sin (x+π)
Answer:
- sin (x)
Step-by-step explanation:
Please help. I need to get to 70%
Scale factor is 5
So
J'=5(1,-2)=(5,-10)K'=5(2,-1)=(10,-5)M'=5(0,-1)=(0,-5)L'=5(1,2)=(5,10)Answer:
Points of kite JKLM:
J = (1, -2)
K = (2, -1)
L = (1, 2)
M = (0, -1)
To dilate a figure about a point, draw a line from the point to each point of the figure, then extend (or reduce) the line so that it is the length of the original line multiplied by the scale factor.
So to dialate JKLM about the origin by scale factor of 5, draw a line from (0, 0) to each point of the kite. Extend the lines so that they are each 5 times the original lengths. These are the dilated points
Points of kite dilated by sf 5 (shown in blue on the attached diagram):
J' = (5, -10)
K' = (10, -5)
L' = (5, 10)
M' = (0, -5)
Observe the sequences below. I. 3, 6, 9, 12, ... II. 3, 9, 27, 81, III. 2, 4, 8, 16, ... IV. 3, 5, 7, 9, Which of these are geometric sequences? III only O Il and me II and IV O I and IV
Find the area of the figure.
Which net represents this solid figure?
Answer: TThere is no picture
Step-by-step explanation:
Arderi Air Conditioning sells one primary model of air conditioner. Each unit of this model costs them $61.25 to produce, but it sells for $142.50 apiece. Arderi Air Conditioning employs three salespeople, each of whom earns a different commission per unit sold, as shown on the following table. Salesperson Commission/Sale Mary $36.25 Jay $28.50 Abby $25.75 Last month, Arderi Air Conditioning had a total fixed overhead cost of $7,622.25. It is known that one salesperson sold 51 units, one salesperson sold 43 units, and one salesperson sold 54 units. Which arrangement of sales would cause Arderi Air Conditioning to break even? a. Mary sells 54 units; Jay sells 51 units; Abby sells 43 units b. Mary sells 54 units; Jay sells 43 units; Abby sells 51 units c. Mary sells 43 units; Jay sells 51 units; Abby sells 54 units d. Mary sells 43 units; Jay sells 54 units; Abby sells 51 units Please select the best answer from the choices provided
The arrangement of sales which would cause Arderi Air Conditioning to break even is Mary sells 54 units; Jay sells 51 units; Abby sells 43 units.
What is a break even point?The break even point is the point at which the cost of production of an item to produce is equal to the revenue generated after selling it.
Arderi Air Conditioning sells one primary model of air conditioner. Each unit of this model costs them $61.25 to produce, but it sells for $142.50 apiece. Thus,
Cost price C=$61.25Sells price S=$142.50Arderi Air Conditioning employs three salespeople, each of whom earns a different commission per unit sold, as shown in the following table.
Salesperson Commission/Sale Mary $36.25 Jay $28.50 Abby $25.75It is known that one salesperson sold 51 units, one salesperson sold 43 units, and one salesperson sold 54 units. Thus, the total AC sold is,
[tex]n=51+43+54\\n=148[/tex]
Now, the selling price is $142.50. Thus, the revenue after selling 148 units is,
[tex]R=148\times142.50\\R=21090[/tex]
The cost price is $61.25. Thus, the cost of production of 148 units is,
[tex]R=148\times61.25\\R=9065[/tex]
Last month, Arderi Air Conditioning had a total fixed overhead cost of $7,622.25. Suppose, Mary sells 43 units; Jay sells units; Abby sells 54 units. Thus, the total cost,
[tex]C_t=7622.25++9065+43\times36.25 +51\times28.50 +54\times25.75\\ C_t=21090[/tex]
The total cost is equal to the total revenue. This point is break even point.
Thus, the arrangement of sales which would cause Arderi Air Conditioning to break even is Mary sells 54 units; Jay sells 51 units; Abby sells 43 units.
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Answer:
c.
Mary sells 43 units; Jay sells 51 units; Abby sells 54 units
Rewrite each of the following expressions without using absolute value bars. |x-4| if x>4
we're given that x is greater than 4 (the symbol ">" indicates "greater than)
5 is greater than 4. Let's plug it in :
|5-4|
|1|
1 (remember, absolute value is always positive).
Now let's try 6 :
|6-4|
|2|
2
hope helpful ~
divide 5/8 ÷ 3/4 please please please please please
Answer:
this answer is 0.83
Step-by-step explanation:
5/8 is 0.625, 3/4 is 0.75 and 0.625 divided by 0.75 is 0.83
Answer: 5/6
All you have to do is combine the two equations, like so [tex]\frac{5*4}{8*3}[/tex]
Multiply [tex]\frac{20}{24}[/tex]
Then simplify [tex]\frac{5}{6}[/tex]
PLEASE HELP ASAP W EXPLANATION !!!
Based on the net shown below, what is the type of solid this represents and find the surface area of the solid to the nearest hundredth.
Answer:
326.6 cm²Step-by-step explanation:
The figure has 2 triangular and 3 rectangular faces.
This is a right triangular prism.
Find the area of each face and add up to get the total surface area.
Each triangle has base of 10 and height of:
[tex]h = \sqrt{10^2-5^2} =\sqrt{75} =8.66[/tex] cmTotal surface area is
[tex]A = 2(1/2*10*8.66) + 3(10*8) = 326.6[/tex]find the second derivative of the parametric equation x(t)=sin t and y(t)=cos t
Presumably you mean the second derivative of y with respect to x, d²y/dx².
Compute the first derivative. By the chain rule,
[tex]\dfrac{dy}{dx} = \dfrac{dy}{dt} \times \dfrac{dt}{dx} = \dfrac{\frac{dy}{dt}}{\frac{dx}{dt}}[/tex]
Differentiate the two parametric equations with respect to t :
[tex]x = \sin(t) \implies \dfrac{dx}{dt} = \cos(t)[/tex]
[tex]y = \cos(t) \implies \dfrac{dy}{dt} = -\sin(t)[/tex]
Then the first derivative is
[tex]\dfrac{dy}{dx} = \dfrac{-\sin(t)}{\cos(t)} = -\tan(t)[/tex]
Now, dy/dx is a function of t, so we can denote it by, say, dy/dx = f(t). Then by the chain rule, the second derivative will be
[tex]\dfrac{d^2y}{dx^2} = \dfrac{df}{dx} = \dfrac{df}{dt} \times \dfrac{dt}{dx} = \dfrac{\frac{df}{dt}}{\frac{dx}{dt}}[/tex]
Differentiating f(t) :
[tex]f(t) = -\tan(t) \implies \dfrac{df}{dt} = -\sec^2(t)[/tex]
Then the second derivative is
[tex]\dfrac{d^2y}{dx^2} = \dfrac{-\sec^2(t)}{\cos(t)} = \boxed{-\sec^3(t)}[/tex]
and since y = cos(t), we can go on to say
[tex]\dfrac{d^2y}{dx^2} = -\dfrac1{y^3}[/tex]
100 points
See attachment below
Answer:1)x =-30
2)x=-30
Step-by-step explanation: 1: 2(3x+5)=5(x-4) ( remove the parenthesis)
then 6x+-5x=-20x-10 (collect the like trems calulate) so (-20 and -20 on each side) the x=-20-10.
2: 6x+10=5x-20 (move the like trems) so move the variable to the left hand side and change its sign like this 6x+10-5x=-20
6x-5x=-20-10
x=-20-10 which it ='s x=-30
follow my TT at yvngxmiia
Solving Stepwise:
2(3x+5) = 5(x-4) [ Given ]2(3x)+2(5) = 5(x) -5(4) ---------------6x + 10 = 5x - 20 [ Distributive property ]6x + 10 - 5x = 5x -20 -5x ---------------x + 10 = -20 [ subtraction property of equality ]x + 10 -10 = -20 -10 -------------x = -30 [ subtraction property of equality ]Additional Explanation
Distributive property:
a(b+c) = a(b) + a(c)symmetric property of equality:
both sides can be interchanged, x = y, then y = xsubtraction property of equality:
when same number subtracted from both sides, a - c = b - cclosure property:
addition, subtraction and multiplication of integers, a + b = cdivision property of equality:
when both sides divided by same number, a/c = b/cWhat is the missing length?
10 yd
=
Area of shaded region
50 yd?
Answer:
Hope the picture will help you. Make sure to mark my answer brilliant
Find the area of the figure.
A: 24.5 ft²
B: 44 ft²
C: 49 ft²
D: 14.8 ft²
Answer:
49ft²
Step-by-step explanation:
A=bh
A=bh=9.8·5=49
A middle school principal wants to change the lunch menu. The principal surveys the students to determine how the students would feel about the change. What served method will produce the best repersentative sample
A)survey every 5th student who rides in a car to school
B)survey 3 randomly selected students from every homeroom
C) survey every 10 7th grade student during lunch
D) survey 5 randomly selected students
Answer:
B
Step-by-step explanation:
B is the best answer because it's a lot of students and unbiased
rewrite 4+2/3x=3/4 so it does not have fractions.
Answer:
48 + 8x = 9
Step-by-step explanation:
4 + [tex]\frac{2}{3}[/tex] x = [tex]\frac{3}{4}[/tex]
multiply through by 12 ( the LCM of 3 and 4 ) to clear the fractions
48 + 8x = 9
!!!!!!!!!!!!!!!!!!!!!
Answer:
I believe it would be 9.
Step-by-step explanation:
Finding Dialation: 16/12 = 1.3
Height: 16/1.3 = 12
Width: 12/1.3 = 9
Brianna has $620 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $261.04.
She buys 3 bicycle reflectors for $13.07 each and a pair of bike gloves for $13.57.
She plans to spend some or all of the money she has left to buy new biking outfits for $51.03 each.
Write and solve an inequality which can be used to determine xx, the number of outfits Brianna can purchase while staying within her budget.
Answer: 6 outfits
Step-by-step explanation:
$620 should be greater than the price of the new bicycle + 3 * bicycle reflectors + a pair of bike gloves + unknown number of biking outfits
Therefore, the inequality will be:
620 ≥ 261.04 + 3 × 13.07 + 13.57 + 51.03x
620 ≥ 313.82 + 51.03x
[tex]\text{Solving \ for \ x}[/tex]
[tex]620\ge \:313.82+51.03x[/tex]
[tex]\mathrm{Switch\:sides}[/tex]
[tex]313.82+51.03x\le \:620[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}100[/tex]
[tex]313.82\cdot \:100+51.03x\cdot \:100\le \:620\cdot \:100[/tex]
[tex]\mathrm{Refine}[/tex]
[tex]31382+5103x\le \:62000[/tex]
[tex]\mathrm{Subtract\:}31382\mathrm{\:from\:both\:sides}[/tex]
[tex]31382+5103x-31382\le \:62000-31382[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]5103x\le \:30618[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}5103[/tex]
[tex]\frac{5103x}{5103}\le \frac{30618}{5103}[/tex]
[tex]\text{Simplify}[/tex]
[tex]{x\le \:6}[/tex]
Therefore, Brianna can buy 6 or fewer outfits while staying within her budget
