Answers
The vertex form of the quadratic function f(x) = x² + 2x + 3 is given as follows:
f(x) = (x + 1)² + 2
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.
In this problem, the function is:
f(x) = x² + 2x + 3
Completing the squares, we find the equation in vertex form, as follows:
f(x) = (x + 1)² + 2
As (x + 1)² = x² + 2x + 1, hence 2 has to be added to find the equivalent function.
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Related Questions
The number of wrecks at a certain intersection varies directly as the number of cars that travel through the intersection. If there are 31 wrecks when 1,085 cars have traveled through the intersection, how many cars have passed through the intersection after 7 wrecks?
Answers
Answer:
Step-by-step explanation:
Comment
This can be done as a proportion. A proportion is 2 equal ratios. If you know three parts of the proportion then you can solve for the 4th.
Proportion
31 wrecks/1085 cars = 7 wrecks / x cars
Solution
31 wrecks/1085 cars = 7 wrecks / x cars Cross Multiply
31 * x = 1085 * 7 Simplify the right
31 * x = 7595 Divide both sides by 31
31 * x/31 = 7595/31
x = 245
Answer 7 wrecks means 245 cars have passed the intersection
Simplify: √64(6z-7)² (square root over entire equation)
Answers
[tex]\sqrt{64(6z-7)^2}=\sqrt{64}\cdot\sqrt{(6z-7)^2}=8\cdot |6z-7|=8|6z-7|[/tex]
The difference between two numbers is -1 and their sum is 1. Find the two numbers.
Answers
Answer:
Let the no. be X and Y
X - Y = (-1)
X + Y = 1
X = (-1)+ Y
X = 1 - y
- 1.+ y = 1 - y
Y + Y = 1 + 1
2y = 2
Y = 1
X = 0
Answer:
x = 0 (first number), y = 1 (second number)
Step-by-step explanation:
x will represent the first number, and y will represent the second.
x - y = -1
x + y = 1
Now, it's time to get y by itself in one equation so that we can substitute.
x - y = -1 (subtract x from both sides)
-y = -1 - x (multiply both sides by -1)
y = x + 1
Plug in x + 1 for y in the second equation.
x + x + 1 = 1 (combine the x with the x)
2x + 1 = 1 (subtract 1 from both sides)
2x = 0 (divide both sides by 2)
x = 0
Since x = 0, we can plug 0 in for x into any equation to solve for y.
0 + y = 1
y = 1
Brainliest, please :)
Help me PLEASEEE!!! ASAP
Answers
Please help! Will give the brainliest :)
Answers
Answer: J. A translation of △XYZ to the right.
Step-by-step explanation:
I'll explain each bullet point one by one. A good hint is to pay attention to where the letters are.
-J is correct because the figure was shifted to the right.
-K is incorrect because if it was a reflection across the x-axis, the figure would be in Quadrant 3, or the bottom left.
-L is incorrect because if you pay attention to the letters, they are in the exact same place. If it was a reflection across the y-axis, the X' and Y' would switch places if you know what I mean.
-M is incorrect because if the figure was rotated 90°, point Z' would be furthest from the x-axis. In other words, the triangle would have been pointing up and not down.
-N is incorrect because if the figure was rotated 180° clockwise, the figure would have been in Quadrant 4, or the bottom right.
Given this information, the most appropriate answer is J.
I hope this helps! Pls give brainliest!! :)
he table shows the height of water in a pool as it is being filled. A table showing Height of Water in a Pool with two columns and six rows. The first column, Time in minutes, has the entries, 2, 4, 6, 8, 10. The second column, Height in inches, has the entries, 8, 12, 16, 20, 24. The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water in the pool? The height of the water increases 2 inches per minute. The height of the water decreases 2 inches per minute. The height of the water was 2 inches before any water was added. The height of the water will be 2 inches when the pool is filled.
Answers
The height of water increases by 2 inches per minute option first "The height of the water increases 2 inches per minute" is correct.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have given a table:
Time height
2 8
4 12
6 16
8 20
10 24
The slope of the line = (12-8)/(4-2) = 4/2 = 2
The value of the slope is positive we can say, the height of water increases as time passes.
Thus, the height of water increases by 2 inches per minute option first "The height of the water increases 2 inches per minute" is correct.
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the answer is A: The height of the water increases 2 inches per minute.
hope this helped :)
If BC is 1
CD is 2
DA is 3
AB is 4,
what is EF?
Answers
The length of the side EF will be 1 unit, approximately.
The complete figure is attached below.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
The figure is given below.
The length of EF will be
EF = CF – CE
Then the value of CF will be
CF = BC × cos 30
CF = 2 × 0.866
CF = 1.732
Then the value of CE will be
CE = BC × cos 42
CE = 1 × 0.743
CE = 0.743
Then we have
EF = 1.732 – 0.743
EF = 0.989 ≈ 1
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a straight line passes through points A(-2,6) and B(4,2). M is the midpoint of line AB.Find the coordinates of M
Answers
Answer:
(1,4)
Step-by-step explanation:
Jared made sixty dollars mowing lawns over the summer. If he spent thirty-nine dollars buying new mower blades, how many seven-dollar games could he buy with the money he had left?
Answers
Answer:
three
Step-by-step explanation:
60 - 39 = 21
21/7 = 3
60-39
21 divided by 7
3
If f(x) = 3x-2 and g(x) = x+²,
find f(g(x)).
f(g(x)) = [?]
Simplify your answer as much as possible.
Answers
Answer:
x
Step-by-step explanation:
[tex]f(g(x)) = 3(\frac{x+2}{3} )-2\\= x + 2 - 2\\= x[/tex]
Each point has been reflected over the x-axis or y-axis.
Select the axis over which each point has been reflected.
Answers
The reflection is
x-axisx-axisy-axisWhat is reflection over axis?A reflection of a point, a line, or a figure in the X axis involved reflecting the image over the x axis to create a mirror image. In this case, the x axis would be called the axis of reflection.
For reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same.
and, for reflecting over the Y axis is to negate the value of the x-coordinate of each point, but leave the y value the same.
So, by considering the above value rules the reflection of the given points as follows over respective axis.
E(7, 1) ⇒ (7, -1)
Here, the reflection is over x-axis because the y value is changing
F(-3, 5) ⇒ (-3, -5)
Here, the reflection is over x-axis because the y value is changing
G(6, -2) ⇒ (-6, -2)
Here, the reflection is over y-axis because the x value is changing.
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Giraffe Jack is 19 feet tall, and Ostrich Jim is 9 feet tall. A) What percent of Jack's height is Jim's height? B)What percent of Jim's height is Jack's height?
Answers
A percentage is a way to describe a part of a whole. Jim's Height is 47.37% of Jack's height.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Giraffe Jack is 19 feet tall, and Ostrich Jim is 9 feet tall.
A.) The percent of Jack's height is Jim's height,
Percentage = (Height of Jack/Height of Jim) × 100%
= 19/9 × 100%
= 211.11%
Hence, Jack's Height is 211.11% of Jim's height.
B.) The percent of Jim's height is Jack's height,
Percentage = (Height of Jim/Height of Jack) × 100%
= 9/19 × 100%
= 47.37%
Hence, Jim's Height is 47.37% of Jack's height.
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Answer:
211.11%
Step-by-step explanation:
What is the point of intersection of the lines represented by these equations
Jy = -2x + 2
y = x - 4
A. (-2, 2)
B. (1, -3)
c. (2,-2)
D. (3,-4)
Answers
To find the point of intersection of two lines, we can use substitution to find the x and y coordinates.
Solving the QuestionWe're given:
[tex]y = -2x + 2[/tex][tex]y = x - 4[/tex]Use substitution to find x:
[tex]-2x + 2=x-4\\-2x=x-6\\-3x=-6\\x=2[/tex]
Use substitution to find y:
[tex]y=x-4\\y=2-4\\y=-2[/tex]
AnswerThe point of intersection is (2,-2).
supposed an individual has a body fat percentage of 17.5% and weighs 164 lbs. how many pounds of his weight is made up of fat? round your answer to the nearest tenth.
Answers
The amount of pounds of his weight is made up of fat is 28.7lbs
Percentages and valuesGiven the following parameters
Total weight of body = 164lbs
Percentage fat = 17.5%
Determine the amount made up of fat
Fat amount = 17.5% of 164
Fat amount = 0.175 * 164
Fat amount = 28.7lbs
Hence the amount of pounds of his weight is made up of fat is 28.7lbs
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There are 10 USB drives in a box and 3 are defective. Two drives are to be selected, one after the other. What is the probability of selecting a defective USB followed by another defective USB?
Answers
[tex]|\Omega|=10\cdot9=90\\|A|=3\cdot2=6\\\\P(A)=\dfrac{6}{90}=\dfrac{1}{15}\approx6.7\%[/tex]
Jessie bought a vacuum cleaner priced at $79 with a 6% sales tax rate. What is the total cost of the vacuum cleaner after-
tax?
Answers
Answer:
83.74
Step-by-step explanation:
First find the amount of the tax
79 * .06
4.74
Add this to the original price
79+4.74
83.74
Based on the graph of g (x), on which intervals
are the function's values positive? Select all that
apply.
Answers
Answer:
[tex]\text{A}) \text{ } -\infty < x < 3\\\\\text{C}) \text{ } -1 < x < 2\\\\[/tex]
Step-by-step explanation:
The graph lies above the x-axis for these intervals.
Quick please!
Will give brainliest
100 points
3(4j + 7 + 2j) or 3(6j +7) b. Use the distributive property to create an equivalent expression.
Answers
Answer:
3(4j + 7 + 2j)
12j + 21 + 6j
12j + 6j + 21
18j + 21 ----- (1)
3(6j +7)
18j + 21 --------(2)
eq 1 = eq. 2
both are equal
There are two colored marbles and one white marble in a box. Julie mixes the marbles and then Sam draws two marbles at random without replacement. If the two marbles match, Sam wins; otherwise, Julie wins. Does each player have an equal chance of winning? Will adding another white marble give each player an equal chance of winning? What if a game with the same rules was played using three colored marbles and one white marble?
Answers
adding a white marble would change the possibilities to 1/2 and 1/3 consequently, meaning Sam wins in 1/2 * 1/3 = 1/6 = 16.7% cases, which is even less fair.
adding a colored marble would change the possibilities to 3/4 and 2/3 consequently, meaning Sam wins in 3/4 * 2/3 = 6/12 = 50% cases, which finally makes the game fair.
The graph below shows the solution to which system of inequalities?
Answers
Inequalities help us to compare two unequal expressions. The inequalities that represent this graph are y<8/10x and y>-x. The correct option is C.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
To find the inequality, we need to find the equation of the dashed line and then substitute the inequality as per the requirement. The dashed line is used instead of a solid line to show greater than or less than.
The inequality for the first graph can be written as,
[tex]y < \dfrac{8}{10}x[/tex]
The inequality for the second graph will be,
y>-x
Hence, the inequalities that represent this graph are y<8/10x and y>-x. Thus, the correct option is C.
The complete question is:
The graph below shows the solution to which system of inequalities?
A.) y>x , y ≥ (8/10)x
B.) y>-x, y ≤ (8/10)x
C.) y>-x, y < (8/10)x
D.) y>x, y > (8/10)x
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Analia is a school district manager. Here are some details about two schools in her district for the last school year:
School A School B
Number of students 300030003000 400040004000
Number of teachers 190190190 380380380
Graduation rate 86\%86%86, percent 90\%90%90, percent
Budget per student \$10{,}500$10,500dollar sign, 10, comma, 500 \$10{,}000$10,000dollar sign, 10, comma, 000
% of students in sports club 62\%62%62, percent 68\%68%68, percent
Number of sports medals won 999 777
SAT average 120012001200 105010501050
SAT range (max-min) 900900900 700700700
Analia wants to know which school has higher athletic achievements relative to the SAT average.
1) Analia thought of two different ways to define this quantity. Identify these two definitions among the following options.
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
% of students in sports club divided by SAT average
(Choice B)
B
Graduation rate divided by SAT average
(Choice C)
C
Number of sports medals won
(Choice D)
D
Number of sports medals won divided by SAT average
2) Determine which school has higher athletic achievements relative to the SAT average, according to the two definitions. Did you get the same result for both definitions?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Yes. According to both definitions, School A has higher athletic achievements relative to the SAT average.
(Choice B)
B
Yes. According to both definitions, School B has higher athletic achievements relative to the SAT average.
(Choice C)
C
No. The definitions have opposite results.
Answers
Answer is in this link:
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Complete this shape so that it is symmetrical about the reflection line
Answers
A balanced and proportionate likeness observed in two sides of an item is characterized as symmetry. The shape can be completed as shown below.
What is symmetry?A balanced and proportionate likeness observed in two sides of an item is characterized as symmetry. It signifies that one side is a mirror image of the other. The line of symmetry is the imaginary line or axis along which you can fold a figure to produce the symmetrical halves.
The shape can be completed as shown below, so that the complete shape is symmetrical about the given axis.
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What is the equation of the line perpendicular to 2x - 3y = 13 that passes through the point (-6, 5)?
y=x+9
y=-3x-4
y=-x-13
y-x-1
Answers
Rewriting the equation of the given line in slope-intercept form,
[tex]2x-3y=13\\\\2x-13=3y\\\\y=\frac{2}{3}x-\frac{13}{3}[/tex]
Thus, the slope of the given line is 2/3. Since perpendicular lines have slopes that are negative reciprocals of each other, we want to find the line with a slope of -3/2.
Substituting into point-slope form,
[tex]y-5=-\frac{3}{2}(x+6)\\\\y-5=-\frac{3}{2}x-9\\\\\boxed{y=-\frac{3}{2}x-4}[/tex]
The present value of $100 to be received 10 years from today, assuming an opportunity cost of 9 percent, is
Answers
An opportunity cost of 9 percent, is $42.
We have given that,
The present value of $100 is to be received 10 years from today,
assuming an opportunity cost of 9 percent,
present value =$100
N=10 years
I/y=9
What is the formula for the present value?PV= FV/(1+r)^n
Where FV is the future value.
Use the given values in the formula we get,
Therefore the correct answer is 42.
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yo
24
yx
SECTION B
(a) Identity element;
(b) Inverse of 3 and -5 under *
Range y
[30 marks]
Answer all the questions in this section. All questions carry equal marks.
1. A binary operation is defined on the set of real numbers, R, by x + y = x + y + 10.
Find the:
X
x
Inverse
Answers
Answer:
Sike
Step-by-step explanation:
That's the wrong number only 123
What are m and b in the linear equation y=2x+8
Answers
Answer:
m=2 and b=8
Step-by-step explanation:
this is a linear equation, which takes on the formula of y=mx+b
therefore in the equation y=2x+8, 2 is the m, and 8 is the b
Max is going to order a breakfast platter at The Breakfast Club. He can choose one style of eggs, one type of meat, and one kind of toast. The following table shows the options available to him.
Breakfast platter
Egg options Fried, Scrambled, Poached, Hard boiled
Meat options Bacon, Sausage, Ham, Steak
Toast options White, Wheat, Rye
How many different breakfast platters could Max create?
Answers
the answer is 48
Step-by-step explanation:
since there are 4 egg options 4 meat options and 3 bread options. so u multiply this.
4×3×4=48
In 2009, there were 12,078 Burger King restaurants; in 2017, there were 16,717 Burger King restaurants. Calculate the average rate of change (slope) for the number of Burger King restaurants over this time period.
Answers
The average rate of change (slope) is 579.875 if, in 2009, there were 12,078 Burger King restaurants; in 2017, there were 16,717 Burger King restaurants.
What is the slope?
The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have:
In 2009, there were 12,078 Burger King restaurants; in 2017, there were 16,717 Burger King restaurants.
The slope:
[tex]\rm m =\dfrac{16717-12078}{2017-2009}[/tex]
m = 4639/8
m = 579.875
Thus, the average rate of change (slope) is 579.875 if, in 2009, there were 12,078 Burger King restaurants; in 2017, there were 16,717 Burger King restaurants.
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What is 43.808 in written form
Answers
Answer:
fourty-three.(point) eight zero eight
Step-by-step explanation:
hope it helps...
Hope this helps!
Is 7/7 a proper fraction, an improper fraction, a mixed number, or decimal fraction?
None of these choices are correct.
O a decimal number
an improper fraction
O a mixed number
O a proper fraction
