what is the turning point of the quadratic function y=1/2(x+10)^2)-6
Answers
Answer:
The coordinates of the turning point will be:
(x, y) = (-10, -6)The graph is also attached.
Step-by-step explanation:
Given the expression
\(y=\frac{1}{2}\left(x+10\right)^2-6\)
simplifying
\(y=\frac{x^2}{2}+10x+44\)
We know that the quadratic equation generally represents Parabola. We know that a turning point of the parabola of the quadratic equation depends upon the direction of the Parabola and the value of the leading coefficient.
The point, where the parabola tends to change the direction, is called the 'vertex'.
In other words, the vertex of the quadratic Parabola represents the turning point of the quadratic function.
Given the expression
\(y=\frac{x^2}{2}+10x+44\)
Parabola params are:
a = 1/2, b = 10, c = 44
As the leading coefficient = 1/2 which is less than 1, thus it represents the up-down facing Parabola.
Thus, the x-coordinate of the vertex:
x = -b/2a
\(x\:=\:-\frac{10}{2\left(\frac{1}{2}\right)}\)
\(x=-\frac{10}{1}\)
\(x=-10\)
putting x = -10 in the original equation
\(y=\frac{1}{2}\left(x+10\right)^2-6\)
\(y=\frac{1}{2}\left(-10+10\right)^2-6\)
\(y=0-6\)
\(y=-6\)
Therefore, the coordinates of the turning point will be:
(x, y) = (-10, -6)The graph is also attached.
Related Questions
9) The 50 cars used by a firm were inspected. 10 had faulty brakes and 15 had faulty tyres. There were 2 cars with faulty brakes but good tyres. How many cars had good brakes and good tyres? The answer is 33
Answers
Based on the information, there are 25 cars with good brakes and good tires.
How to calculate the valueTotal cars = 50
Cars with faulty brakes = 10
Cars with faulty tires = 15
Cars with faulty brakes and good tires = 2
Let's calculate the number of cars with good brakes and good tires:
Cars with faulty brakes or faulty tires = Cars with faulty brakes + Cars with faulty tires - Cars with faulty brakes and good tires
= 10 + 15 - 2
= 25
Cars with good brakes and good tires = Total cars - Cars with faulty brakes or faulty tires
= 50 - 25
= 25
Therefore, there are 25 cars with good brakes and good tires.
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Eliana loves music, especially 80's punk rock. Eliana looked at the number of songs in her itunes account and she has 6 less than 4 times her best friend. Eliana's classmate David has 3 more than double her best friend. When talking to her Social Studies teacher, Eliana found out social study teacher has 7 more than two times the number of songs in his library than Eliana. Define a variable, then write and solve an equation. If the total number of songs is 382, how many songs does Eliana, her best friend, David and her social study teacher have?
Answers
Answer
Step by step explantion:
bsf= 26
Eliana:98
SS teacher=203
David=55
Step-by-step explanation:
m= music
bsf: m
eliana:4m-6
David:2m+3
SS teacher: 2(4m-6)+7
m+4m-6+2m+3+8m-12+7
382=15m-7
7+ +7
389=15m
/15m /15m
m=26
multiply 26 to each one of them
Find the area of the trapezoid.
14 mm
15 mm
36 mm
1. 270 mm²
2. 375 mm²
3. 750 mm²
5. 3780 mm²
Answers
Answer: no one cares
Step-by-step explanation:
because it's to hard\(\pi \pi \pi \pi \pi \pi \pi \pi \pi \pi \pi \pi \pi \left \{ {{y=2} \atop {x=2}} \right. x_{123} \left \{ {{y=2} \atop {x=2}} \right. \lim_{n \to \infty} a_n \int\limits^a_b {x} \, dx \left \{ {{y=2} \atop {x=2}} \right. \sqrt{x} \sqrt{x} \sqrt{x} \alpha \pi x^{2} x^{2} x^{2} \\ \\ \neq \pi \pi 5069967.94389438.494898 that's the answer\)PLEASE I NEED HELP
Use composition to prove that f(x) and g(x) are inverses. Check your work
Answers
F and G are inverse if both of them satisfy the condition h(x)=x. f(g(x))=g(f(x))=x, as we discovered. The argument f(x) and g(x) are inverse functions is thus established.
How do you verify that f x and G x are inverses?If f (x) and g (x) are inverse functions, it can be determined using one of two ways. For more information, see the explanation.
Explanation:
Instance 1
Inverse functions of both functions can be found using the first method.
Example.
Inverse of f (x) = x + 7 is what we're looking for.
We attempt to determine x using the equation y = x + 7.
y = x + 7
Inferring that g (x) is the inverse of f (x) from the fact that x = y 7
Finding g (x inverse )'s is now necessary.
g( x ) = x − 7
y = x − 7
x = y + 7
As a result, we discovered that f (x) is the inverse function of g (x).
f and g are equal if g is inverse of f and vice versa.
The second approach entails locating the compound functions f ( g ( x ) ) and g ( f ( x ) ). In this case, f and g are inverse if they are both h (x ) = x.
Example:
f ( g ( x ) = [ x − 7 ] + 7
G ( x ) placed as x is the expression in brackets.
f ( g ( x ) ) = x − 7 + 7 = x
g (f ( x ) = [ x + 7 ] − 7
f ( x ) inserted as x is the expression in brackets.
g ( f ( x ) ) = x + 7 − 7 = x
The equation f ( g ( x ) ) = g ( f ( x ) ) = x was what we discovered. The argument f (x) and g (x) are inverse functions is thus established.
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The points A, B, C and D lie in order on a straight line
such that
AB:BD = 1:2
AC:CD= 7:2
Find AB:BC:CD
Answers
Answer:
7 + 2 = 9, so AC = 7/9 and CD = 2/9
1 + 2 = 3, so AB = 1/3 = 3/9 and
BD = 2/3 = 6/9
AB + BC = AC
3/9 + BC = 7/9, so BC = 4/9
AB:BC:CD = (3/9):(4/9):(2/9) = 3:4:2
PLEASEEEEEEE HELPPPPPPPP!!!!!!!!!
Answers
Answer: 2
Step-by-step explanation: The value x in f(x) is a value on the x-axis that we input into the function. F(x) is a value on the y-axis. F(2) means we are inputting the value of 2 on the x-axis and looking for the corresponding point on the y-axis. If we look at the graph at x=2, we can see that the graph is above when y=2. This means that (2,2) is a point that satisfies f(x).
Solve for x 3x+wx=20
Answers
Answer:
X=\(\frac{20}{3+w}\)
Step-by-step explanation:
We are to solve for x by factorizing the given expression
The value of x is \( \frac{20}{ 3 + w} \)
Given:
3x + wx = 20
factorize
3x + wx = 20
x(3 + w) = 20
Divide both sides by 3+w
x = \( \frac{20}{ 3 + w} \)
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What were early village leaders responsible for? Choose four answers.
Ο Making laws
Ο Making punishments
Ο Trading with other villages
Ο Building permanent houses
Ο Maintaining order
Ο Settling disputes
Answers
Answer: is A,B,E,F
Step-by-step explanation:
If this is right pls like and give me 5 star, it would really help. Thank You
will give 33 poits and will be marked brainliest please solve this and post answer is it and explain how you got it.
Answers
Answer:
9.85
Step-by-step explanation:
With all the data we get:
0.4+1+0.6+0.85+0.85+0.95+2+1.05+1.05+1.1
Add them all up and you get:
9.85
I did not do this on paper, but on a calculator, to make sure my answers were correct.
happy learning!
--Applepi101
Answer:
9.85 inches
Step-by-step explanation:
Total amount rain that fell in desert :
Amount of rain in inches * number of times recorded in the year
Amount of rain is on the horizontal axis
Number of times is given by the number of dots on each Rainfall amount.
Therefore ;
(1*0.4) + (2*0.5) + (1*0.6) + (2*0.85) + (1*0.95) + (2*1) + (2*1.05) + (1*1.1)
= 9.85 inches
10 points. please answer
Answers
The measure of the angles for the similar triangles are ∠G = 105°; ∠H = 55° and ∠I = 20°
What are similar triangles?Two triangles are said to be similar if the ration of their corresponding sides are in the same proportion. Also, all their corresponding angles are congruent with each other.
From the diagram shown:
∠X + ∠Y + ∠Z = 180° (sum of angles in a triangle)
20 + 105 + ∠Z = 180
∠Z = 55°
Since triangle XYZ and triangle GHI are similar, hence:
∠X = ∠G = 105°; ∠Z = ∠H = 55° and ∠Y = ∠I = 20°
The measure of the angles are ∠G = 105°; ∠H = 55° and ∠I = 20°
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I NEED URGENT HELP BY 9:20 AM today!
Answer choices;
A. A line reflection over y=x
B. A rotation of 180 centered at 1,0
C. A line reflection over the x axis followed by a translation of 6 units right,
D. A line reflection over the x axis followed by a line reflection over y=1
Answers
Answer:
Choice D
Step-by-step explanation:
Reflection over the x axis and then a line reflection over y=1 will give you the second desired triangle.
Xx
Which equation models the rational function shown in
the graph?
2(x+2)
X-2
O f(x) =
O f(x) = x-2
x+2
2(x-2)
x+2
Of(x)=.
O f(x) = x+2
X-2
Answers
At x=2, the function in the graph is approaches to infinity. This is satisfied by equation 1 that models the rational function, hence option 1 is the correct answer.
What is equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.
Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.
From given graph we can see that
At x=2, the function in the graph is approaches to infinity.
It means function is not defined at x=2
We know that a rational function is undefined when denominator is equal to zero.
For equation 1:
f(x)= 2(x+2)/(x-2)
Equating the denominator:
x-2=0
x=2
It means function is not defined at x=2
The y-intercept is: y= -2
The function is passing through the point (1,-6).
When we substitute x=1
Hence, option 1 is true.
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What's the area of a rectangle with side lengths of 6/8 metter and 4/10 metter?
Answers
Answer:
3/10 meters^2
Step-by-step explanation:
we multiply length by width to get are
6/8x4/10
6*4/8*10
24/80
3/10
Hopes this helps please mark brainliest
Answer: Hi the answer to that would be 3/10.
Step-by-step explanation: The first one explains the formula and the second one shows my work. I hope this helps!!!
Graph the point on the graph.
Answers
Answer:
see below
Step-by-step explanation:
To graph this equation, start at the origin (0,0) since there is not y-intercept.
Because slope is characterized by rise/run ( i.e. how many units up or down depending on whether it is positive or negative and then however many units to the right.
Because the rise (up and down, numerator) is 1, we know that we will go up one unit.
The run (side to side, denominator) is 4, so we will go to the right 4 units.
This makes the first point (4, 1).
Continue doing this until you get an idea of the line and connect the points to get the graph
Answer:
Info down in Explaination
Step-by-step explanation:
To graph this equation, start at the origin (0,0) since there is not y-intercept.
Because slope is characterized by rise/run ( i.e. how many units up or down depending on whether it is positive or negative and then however many units to the right.
Because the rise (up and down, numerator) is 1, we know that we will go up one unit.
The run (side to side, denominator) is 4, so we will go to the right 4 units.
This makes the first point (4, 1).
Continue doing this until you get an idea of the line and connect the points to get the graph
3/5 - 1/3 simplified
Answers
Answer:
4/15
Step-by-step explanation:
\(\frac{3}{5}=\frac{9}{15} \\ \\ \frac{1}{3}=\frac{5}{15} \\ \\ \frac{3}{5}-\frac{1}{3}=\frac{9}{15}-\frac{5}{15}=\frac{4}{15}\)
worms are used to break down food waste and create a soil conditioning compost. Some worm populations double every 3 months. Suppose the formula y=2(2^x/3) represent the pounds of worms in a population after x months. If there are initially 2 pounds of worms, how many pounds of worms will there be in 1 year? If 2 pounds is approximately 2,000 worms, how many worms will there be after 1 yesr?
Answers
8,000 each three months the population is doubled so i figured that each three months there are 2000 more worms i multiplied 3 by 4 Because 3 x 4 is 12 and a year is 12 months, and got 8,000 by multiplying 2,000 by 4. Hope this helps
A troupe of 8 dancers is going to line up on stage. Of these dancers, 4 are wearing black and 4 are wearing red. A dancer wearing black must be in the first position and they must alternate between colors. In how many ways can the dancers line up?
Answers
Using the Fundamental Counting Theorem, it is found that there are 576 ways for the dancers to line up.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with \(n_1, n_2, \cdots, n_n\) ways to be done, each thing independent of the other, the number of ways they can be done is:
\(N = n_1 \times n_2 \times \cdots \times n_n\)
In this problem, considering the order:
Black - Red - Black - Red - Black - Red - Black - Red
The number of ways for each is given by:
4 - 4 - 3 - 3 - 2 - 2 - 1 - 2
Hence:
\(N = 4^2 \times 3^2 \times 2^2 = 576\)
There are 576 ways for the dancers to line up.
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Please helps
……………………
Answers
Answer:
V= 21.7
Step-by-step explanation:
180-90=90
2v+v+25=90
3v+25=90
3v=65
V=21.7
Find the length of the hypotenuse. Round your answer to the nearest tenth if necessary.
Answers
Answer:
a^2 + b^2 = c^2
8^2 + 15^2 = c^2
64 + 225 = c^2
289 = c^2
17 = c
The hypotenuse is 17.
Brainliest? ;)
three blocks are placed together as shown below. 3.8cm 8.7cm 9.4cm
Answers
1. If 4r – 10 = 18, what is the value of 2r + 9?
Answers
Answer:
23
Step-by-step explanation:
4r-10=18
4r=28
4r/4=28/4
r=7
2(7)+9=23
How would you explain the way to solve #18 for the value of the variable?
Answers
Answer:
x = 75°Step-by-step explanation:
We know that:
2x - 30 = 45 + x (Reason in picture)Solution:
2x - 30 = 45 + x=> 2x - x = 45 + 30=> x = 75°Hence, the value of x is 75°
Graph the line with the slope -3/4 passing through the point (4,-1)
Answers
Answer:
Step-by-step explanation:
Plot the point (4, -1) in the 4th Quadrant.
The slope (-3/4) tells us what to do next:
With your pencil point initially on (4, -1), move it 4 units to the right, to (8, -1).
With your point initially on (8, -10, move it down 3 units, to (8, -4). Plot (darken) (8, -4).
Draw a line through (4, -1) AND (8, -4)
The equation of a line for the given slope and the coordinate point is 4y=-3x+8.
Given that, the line with the slope -3/4 passes through the point (4,-1).
We need to find the line of equations.
What is slope intercept form?The slope-intercept form of a straight line is used to find the equation of a line. For the slope-intercept formula, we have to know the slope of the line and the intercept cut by the line with the y-axis. Let us consider a straight line of slope 'm' and y-intercept 'b'. The slope intercept form equation for a straight line with a slope, 'm', and 'b' as the y-intercept can be given as y = mx + b.
Now, substitute m=-3/4 and the point (4,-1) in y = mx + b and find the value of b.
That is, -1 = -3/4 (4)+b
⇒b=2
Then the equation becomes y=-3/4 x+2
⇒4y=-3x+8
Therefore, the equation of a line for the given slope and the coordinate point is 4y=-3x+8.
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Find m
A)36
B)80
C)56
D)44
E)124
Answers
Answer:
44
Step-by-step explanation:
vertical angles
Which of the following is never a quadrilateral with four right angles?
rectangle
square
trapezoid
parallelogram
Answers
their angles never have 4 right angles like rectangles and squares do. And parallelograms can have 4 right angles too. So the answer is 100% trapezoid! Yw
Answer: C.Trapezoid
Step-by-step explanation: I got it correct on pearson
If the probability that a vaccine you took will protect you from getting the flu is 0.977, what is the probability that you will get the flu?
Probability that you will get the flu =
Answers
Answer:
Step-by-step explanation:
0.033
a bacteria population is 10,000. it triples each day. The bacteria population. p, is a function of the number of days, d.
A. p(d) = 10000(3)d
B. d(p) = 10000(3)p
C. p(d) = 3(10000)d
D. p(d) = 3(10000)p
Answers
Answer: D. p(d) = 3(10000)p
Step-by-step explanation:
The function is p(d) = 3(10000)p, where p is the bacteria population and the number of days, d. The correct answer would be option (D).
What are the functions?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
As per the given situation, we can write the function would be as:
⇒ p(d) = 3(10000)p
It states that the population of the bacteria, p, is equal to the starting population of 10,000 multiplied by 3 number of days, d. This function correctly represents the idea that the population triples each day.
Hence, the correct answer would be an option (D).
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jake went on a road trip with his family this summer. On Monday, they drove 629 miles. Tuesday, they drove 215 miles. On Wednesday, they drove 111 miles. And, on Thursday, they drove 588 miles. what is the total number of miles that Jake's family traveled
Answers
Body temperature (in degrees Fahrenheit) of randomly selected normal and healthy adults are shown below. Compute the mean, median, and mode of the data set.
98.1
98.6
98.7
98.5
98.0
98.2
98.0
99.0
98.0
98.8
The mean is °F.
(Round to the nearest hundredth as needed.)
Answers
Answer:
Mean: 98.49
Median: 98.35
Mode: 98
The mean is the average median is the middle value of the data set while the mode is the highest frequency number thus mean median and mode are 98.39,98.35 and 98 respectively.
What are the mode and median?Mode is the highest frequency number while the median is the middle value of a data set after writing in either an increasing or decreasing manner.
The increasing order of the given data set,
98.0,98.0,98.0,98.1,98.2,98.5,98.6,98.7,98.8,99.0
Mean →
(98.0+98.0+98.0+98.1+98.2+98.5+98.6+98.7+98.8+99.0 )/10
⇒ 98.39
Median →
(98.2+98.5)/2 = 98.35
Mode →
The highest frequency of 98.
Hence "The mean is the average median is the middle value of the data set while the mode is the highest frequency number thus mean median and mode are 98.39,98.35 and 98 respectively".
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K
For each of the functions y = f(x) described below, find f(0).
(a) x
-1
1 2
f(x)
1
2
(b) y = 12 - 2x2
(c)
-10 -
0
7
조
8
10
IN 2 1
-
3
3
-6
6 8 10
(a) f(0) = ㅁ
Answers
The values of f(0) that can be read from (a similar question in part (a) and (c)) the table, functions, and graph in the question are;
(a) f(0) = 1
(b) f(0) = 12
(c) f(0) = -2
How can the table, function, and graph be evaluated to find f(0)?Part of the question appears missing. From a similar question online, we have;
(a) A table of values;
x: -1, 0, 1, 2, 3
y: 7, 1, 6, -3, -4
Taking the function, f(x) = y, we have;
From the above values in the table, when x = 0, y = f(0) = 1
Therefore;
f(0) = 1(b) y = 12 - 2•x²
Taking the function, f(x) = y, we have;
At x = 0, y = f(0) = 12 - 2 × 0² = 12
Therefore;
f(0) = 12(c) A graph of a parabola passing through the points (-1, 3), (2, -6), (5, 3)
Let f(x) = a•x² + b•x + c, represent the function, we have;
f(-1) = 3 = a•(-1)² + b•(-1) + c = a - b + c
3 = a - b + c...(1)f(2) = -6 = a•(2)² + b•(2) + c = 4•a + 2•b + c
-6 = 4•a + 2•b + c...(2)f(5) = 3 = a•(5)² + b•(5) + c = 25•a + 5•b + c
3 = 25•a + 5•b + c...(3)Solving the system of linear equations, (1), (2), (3) using a graphing calculator gives;
a = 1, b = -4, c = -2
Which gives;
f(x) = x² - 4•x - 2
Therefore;
f(0) = 0² + 4×0 - 2 = -2
Which gives;
f(0) = -2Learn more about evaluation of functions here:
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