complete the square to rewrite y=x^2+8x+3 in vertex form and then identify the minimum y-value of the function
Answers
The vertex-form of the quadratic equation is given by y = (x + 4)² - 13, and the minimum value of y is of -13.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient. If a > 0, k is the minimum value of y, and if a < 0, it is the maximum value.
In this problem, the equation is:
y = x² + 8x + 3.
Completing the squares, the function is:
y = (x + 4)² - 13
13 is subtracted as (x + 4)² = x² + 8x + 16, hence for the equations to be equal 13 has to be subtracted. k = -13 is also the minimum value of y.
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The minimum y-value of the function for the parabolic equation is -13.
What is the vertex of a parabolic equation in quadratic form?The vertex for an up-down facing parabola of the form y = ax² + bx + c is [tex]\mathbf{x_v= -\dfrac{b}{2a}}[/tex]
From the given equation:
y = x² + 8x + 3
The parameters for the parabola are:
a = 1, b = 8, c = 3
[tex]\mathbf{x_v= -\dfrac{8}{2\times 1}}[/tex]
[tex]\mathbf{x_v= -4}[/tex]
If we replace the value of [tex]\mathbf{x_v= -4}[/tex] to find the minimum value of [tex]\mathbf{y_v}[/tex] value, we have:
[tex]\mathbf{y_v = -13}[/tex]
Thus, the parabola vertex is (-4,-13). If a< 0, the vertex is a maximum value and If a>0, the vertex is a minimum value.
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Related Questions
Identify the geometric mean of 9 and 9/4.
Answers
The geometric mean of 9 and 9/4 will be 9/2 or 4 1/2.
How to calculate the mean?It should be noted that in order to find the geometric mean of the numbers given, give to find the square root and then multiply.
This will be:
= ✓9 × ✓9/4
= 3 × 3/2
= 9/2 = 4 1/2
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Riley has 51/4 cups of chocolate chips, she needs ¾cup of chocolate chips to make one batch of cookies. how many batches of chocolate-chip cookies can Riley make
Answers
Answer:
17 batches
Step-by-step explanation:
51/4 ÷ 3/4 = 51/4 x 4/3
=17
How would i work this out?
Answers
there some visits already recorded before 12:30. These visits are visits that you want to exclude but are included in the TOTAL visits
Before 12:30 the website has 1200 visits and at 6:45 the website has 14000.
You can do 14000-1200 to find the number of visits in the time frame between 12:30 and 6:45
ANSWER 12800 visits
#5 In *triangle* ABC, AB = 9 and BC = 15. What is the range the possible lengths for CA?
Why?
Answers
For the line segments to form a triangle the length of CA cannot be less the the difference between the other sides or greater than their sum.
At either extreme the three points A, B and C will be co-linear thus forming a triangle with area of zero
In a grop of 25 student 6 study art & biology 10 study biology but not art 3 study neither subject given that a randomly selected study art what is the probability the student study art & biology
Answers
½ 0r 50% is the probability that the student studies Art and biology.
What is Probability?Probability is a branch of mathematics that deals with the occurrence of a random event . i.e. Probability means possibility.
According to the question,
Total number of students in the group;
n = 25 students
No. of students that study both art and biology;
n(P u Q) = 6
No. of students that study biology but not art;
n(Q u P') = 10
No. of students that study none of the 3 subjects;
n(P' u Q') = 3
So,
No. of students that study only arts is;
n(P n Q') = 25 - 6 - 10 - 3 = 6
Since, n(P u Q) = 6
Therefore by using formula;
n(P) = n(P u Q) + n(P n Q')
n(P) = 6 + 6
n(P) = 12
Hence,
Probability of the students who studies Art and biology is;
P(P n Q) = [tex]\frac{6}{12}[/tex]
P(P n Q) = ½ i.e. 50%
The probability the student study art & biology ½ i.e. 50%.
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what is the square root of 10,000,000
Answers
Answer:
1000√10or 3162.2776601683795
Step-by-step explanation:
what is the square root of 10,000,000?
√10000000
= √2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 x 5 x 5
= √26 x 2 x 56 x 5
= 1000√10
or 3162.2776601683795
Solve for y, Look at the picture to help.
Answers
Using two triangle concepts, it is found that the solution for y is of y = 70º.
What are the two triangle concepts used in this problem?The sum of the internal angles of a triangle is of 180º.The sum of an angle with it's external angle is also of 180º.Hence:
x + y + 70 = 180.y + 3x - 10 = 180 -> y = 190 - 3x.Then:
x + y + 70 = 180
x + 190 - 3x + 70 = 180.
2x = 80.
x = 40.
Hence:
y = 190 - 3x = 190 - 3(40) = 70º.
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Which equation represents this number sentence?
Three less than one-fifth of a number is 28.
3−15n=28
15n−3=28
(3−15)n=28
(15−3)n=28
Answers
The equation that represents this number sentence is 1/5n - 3 = 28
Translating word problemsLet the unknown number be "n". One-fifth of a number is expressed as 1/5n
Three less than one-fifth of a number is expressed as 1/5n - 3
Finally, if three less than one-fifth of a number is equal to 28, then the final expression will be 1/5n - 3 = 28
The equation that represents this number sentence is 1/5n - 3 = 28
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The amount of money that kailyn earns varies directly with the number of hours she works. if she works for 15 hours and makes 146.25, how much will she make in 40 hours.
Answers
Answer:
$390
Step-by-step explanation:
The wage rate for Kailyn is ($146.25/15 hours) = $9.75/hour
40 hours would result in:
(40 hours)*($9.75/hour) = $390
(This is an Edge question)
Question:
Which expression is equivalent to negative 3 minus 3 times a number minus 1 plus a number.
[tex] - 3 - 3x - 1 + x[/tex]
Answer Choices:
A.
[tex]2x - 4[/tex]
B.
[tex] - 2x + 4[/tex]
C.
[tex] - 2x - 4[/tex]
D.
[tex]4 - 2x[/tex]
I will verify the answer and give Brainlyest for fastest and most accurate answer and 15 pts.
Answers
Answer:
The answer is C. -2x -4
Step-by-step explanation:
Your given information.
-3 - 3x - 1 + x
Combine and simplify common numbers/variables.
(-3x + x) + (-3 - 1)
-2x - 4
Question 6 (Yes/No Worth 1 points)
(02.01 LC)
Is the following relation a function?
Answers
Complete the equations
Answers
Answer:
[tex]\boxed{\bf f(x)=4\cdot \left(\cfrac{7}{4}\right)^x}[/tex]
Step-by-step explanation:
In exponential form, a* b^x,
Where, "a" is value of the function when x=0 and "b" is the constant ratio of f(x) for consecutive for integer values of x.
Y-intercept : (0, 4) so, a = 4.
The graph also passes through (1,7), because 0 and 1 are consecutive integer x-values.
[tex]\bf b=\cfrac{7}{4}[/tex]
So therefore, the equation for f(x) is :-
[tex]\bf f(x)=4\cdot \left(\cfrac{7}{4}\right)^x[/tex]
_______________________Carol measured a straw and wrote down how long it was in inches. pete multiplied carol's straw length by and cut a straw to be that many inches long. joe multiplied carol's straw length by and cut a straw to be that many inches long. which straw belongs to whom?
Answers
Answer:
pete
Step-by-step explanation:
i think its pete???
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options.
The value of f(–10) = 82
The graph of the function is a parabola.
The graph of the function opens down.
The graph contains the point (20, –8).
The graph contains the point (0, 0).
Answers
Answer:
I will assume the equation is supposed to be f(x) = x^2 – 5x + 12 since it is said to be a quadratic equation.
Step-by-step explanation:
See attached graph.
The value of f(–10) = 82 False
f(-10) = (-10)^2 - 5*(-10) + 12
f(-10) = (100) +50 + 12
f(-10) = 162
The graph of the function is a parabola. True
The graph of the function opens down. False
The graph contains the point (20, –8). False
The graph contains the point (0, 0). False
_______________ is the value of the best alternative given up when a choice is made.
Answers
Please hit the thanks button :)
The function h(x) is a transformation of the square root parent function,
f(x)=√x. What function is h(x)?
-5
5
-5-
h(x)
f(x)
K
I
5
Answers
Answer: [tex]h(x)=\sqrt{x+4}[/tex]
Step-by-step explanation:
The graph of h(x) is the graph of f(x) shifted 4 units left.
There is a basketball court. A basketball, who never misses takes a random shot at the basket. What is the probability that the ball will go into the basket
Answers
Answer:
100% probability or 1/1
Step-by-step explanation:
This is because since the basketball NEVER misses, there is no chance the the ball will not go inside the basket, leaving room for only the ball to GO inside the basket. Hope this helps!! :D
Wesley and two of his friends are driving cross country nonstop and have agreed to take turns driving in 7 hour shifts. Each person will drive for one shift, and take two shifts off to rest. If Wesley’s first shift starts at 6:00 am, at what time will Wesley complete his third shift?
Answers
At 7:00 am Wesley complete his third shift if Wesley and two of his friends are driving cross country nonstop and have agreed to take turns driving in 7-hour shifts option (C) is correct.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have:
Wesley and two of his friends are driving cross country nonstop and have agreed to take driving in 7-hour shifts.
Wesley’s first shift starts at 6:00 am
6:00 am = 6h 0m
= 6 + 7
= 13 h = 1:00 PM (Wesley's starts to rest)
Wesley will take a rest for 14 hours (7 + 7)
First shift = 7 + 14 = 21
Second shift = 7 + 14 = 21
Third shift = 7 = 7
= 21 + 21 + 7 = 49
= 49/24 = 2 days + 1 hour
6h + 1h = 7h = 7:00 am
Thus, at 7:00 am Wesley complete his third shift if Wesley and two of his friends are driving cross country nonstop and have agreed to take turns driving in 7-hour shifts option (C) is correct.
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Select the correct answer.
One tactor of the polynomial 253 - 352 - 35 + 2 is (x - 2). Which expression represents the other factor, or factors, of the polynomial?
OA. (2:2 + 1)
OB. (252 - 5 + 1)
OC. (25 - 1 (s+1)
OD. (25 + 1) (5 - 1)
Answers
The expression which represents the other factor, or factors, of the given polynomial is option (C) (2x-1)(x+1)
A cubic equation in algebra is a one-variable equation of the form ax3+bx2+cx+d=0 where an is nonzero. The roots of the cubic function defined by the left side of this equation are the solutions to this equation.
Given expression 2x³-3x²-3x+2 whose one of factor is (x-2)
We have to find second factor of given equation
First we will be rational root theorem to given expression so will get following expression:
[tex]\left(x+1\right)\frac{2x^3-3x^2-3x+2}{x+1}[/tex]
So one factor is (x-1) and now simplifying [tex]\frac{2x^3-3x^2-3x+2}{x+1}[/tex] we get 2x² - 5x +2 and the factor of 2x² - 5x +2 will be (2x-1)(x-2)
Hence the expression which represents the other factor, or factors, of the given polynomial is option (C) (2x-1)(x+1)
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Linda purchased a birthday gift from Bed Bath and Beyond for her mother. After applying the
coupon below Linda received a $12.25 discount off her purchase. What was the price of the
gift before and after the discount?
PLS HELP SOLVE !!!
Answers
Answer:
Before discount = $61.25
After discount = $49.00
Step-by-step explanation:
Given information:
Discount = $12.25Coupon = 20%The price of the gift before the discount is 100%.
If the $12.25 discount was 20% of the purchase price, then:
⇒ original price (before discount) = (12.25 / 20) × 100 = $61.25
To find the price after the discount, simply subtract the discount from the found original price:
⇒ $61.25 - $12.25 = $49.00
Conclusion
Before discount price = $61.25After discount price = $49.00Identify the type of function represented by f(x) = 3(1.5)*.
OA. Exponential growth
B. Linear
C. Exponential decay
D. Quadratic
Answers
Answer:
A. Exponential growth function
On a map of scale 1:20000 the area of a forest is 50cm^2.On another map the area of the forest is 8cm^2.Find the scale of the second map.
Answers
Answer:
The answer is 1: 50000... If you look down here↓:
Step-by-step explanation:
With a scale of 1:20000, a unit length on the map represents a length of 20000. So 1 cm^2 = 1 cm* 1 cm which represents 20000*20000 cm^2 will be = 4*10^8 cm^2.
50 cm^2 represents that 4*50*10^8 cm^2 = 200* 10^8 cm^2.
Now, on the other hand, the map has the same. 200* 10^8 is represented by 8 cm^2. So the scale is sqrt [ 200* 10^8 / 8 ] = sqrt [ 25* 10^8 ] = 5* 10^4 = 50000.
Therefore the scale on the second map is 1: 50000.
What is the mean of the data
Answers
Answer:
hey diddle the medians the middle
you add and then divide for the mean
the mode is the one you see the most and the range is the difference between.
Hope this helps you with your question
Step-by-step explanation:
What percent of patients with type-B blood are male? Round your answer to the nearest tenth of a percent.
Answers
Answer:
54%
Step-by-step explanation:
To find the probability for a male patient to have B blood, find the number of male patients who do have B blood and divide it by the number of patients with type B.
The number of male and B blood is 99.
The number of patients with B blood is 183.
The probability is 99/183 = 0.54.
The percent is found by multiplying by 100.
0.54*100 = 54%
The price of a Year 7 mathematics textbook is $60. The store gives a discount of 20% on the textbook.
You have $50 to spend. Would you be able to buy the textbook? Explain.
Answers
Answer:
yes,you can buy the textbook
Step-by-step explanation:
determine discount
60 × 0.2(decimal form of 20%)
=12
apply discount
60-12
=48
50>48✓
share 518 in ratio 2:5
please answer fast with the steps
Answers
Answer:
148:370
Step-by-step explanation:
2+5=7 parts
518÷7=74
1 part =74
2×74=148
5×74=370
HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
write and solve a proportion to complete the statement. Round to the nearest hundredth if necessary.
1. 6km ≈ ?mi
2. 2.5 L≈ ?gal
3. 90lb ≈ ?kg
pls help
Answers
1. 6 km ≈ 3.73 mi
2. 2.5 L ≈ .66 gal
3. 90 lb ≈ 40.82 kg
Find the value of $x$ that satisfies $\frac{1}{3x-1} = \frac{2}{x+1}$. Can someone please explain this in detail?
Answers
The value of x = 3/5 or 0.6 will satisfy the equation given.
What is an Equation ?An equation is a mathematical statement which is formed when two expressions are equated by an equal sign.
It is given that
[tex]\rm \dfrac{1}{3x-1} = \dfrac{2}{x+1}\\[/tex]
It has to be solved and the value of x has to be determined
(x+1) = 2 (3x-1)
x +1 = 6x -2
5x = 3
x = 3/5
Therefore the value of x = 3/5 or 0.6 will satisfy the equation given.
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Mary has 20 flowers in 5 vases. How many flowers are there in every vase?
Answers
Distance formula: StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot
Does the point (1, StartRoot 7 EndRoot) lie on the circle shown?
Explain.
Yes, the distance from (–2, 4) to (1, ) is 4 units.
Yes, the distance from (–2, 0) to (1, StartRoot 7 EndRoot) is 4 units.
No, the distance from (–2, 0) to (1, StartRoot 7 EndRoot) is not 4 units.
No, the distance from (–2, 4) to (1, StartRoot 7 EndRoot) is not 4 units.
Answers
Yes, the distance from (-2, 0) to (1, √7) is 4 units.
How to Interpret the Equation of a Circle?
We know that the general form of equation of the circle is given by;
(x - h)² + (y - k)² = r²
where;
(h, k) is the coordinate of the center
r is the radius
From the attached image, the radius is equal to the distance between the center and the point (-2,4). Thus, r = 4 and so we have;
(x + 2)² + (y - 0)² = 4²
(x + 2)² + y² = 16
If the distance between the center and the point is equal to the radius of the circle , then the point lies on the circle and the formula to calculate the distance between two points is;
d = √[(y₂ - y₁)² + (x₂ - x₁)²]
At A(-2, 0) and B(1, √7), we have;
d = √[(√7 - 0)² + (1 - (-2))²]
d = 4 units
Therefore we can conclude that the distance from (-2, 0) to (1, √7) is 4 units.
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