Answers
Given:
The quadratic function is:
[tex]f(x)=(x+2)^2+1[/tex]
To find:
The graph of the given quadratic function.
Solution:
The vertex form of a quadratic function is:
[tex]f(x)=a(x-h)^2+k[/tex] ...(i)
Where, a is a constant and (h,k) is the vertex of the graph of the quadratic function.
We have,
[tex]f(x)=(x+2)^2+1[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]a=1[/tex]
[tex]h=-2[/tex]
[tex]k=1[/tex]
Now,
[tex](h,k)=(-2,1)[/tex]
It means the vertex of the graph of the given function is at point (-2,1).
Only in graph C, the vertex of the parabola is at (-2,1).
Therefore, the correct option is C.
Related Questions
PLEASE HELPPPPPP..........
Answers
Answer:
D.
Step-by-step explanation:
Polyhedron
Answer:
Polyhedron
Step-by-step explanation:
A solid that is bounded by polygons, called faces, that enclose a single region of space.
•18 POINTS• (don’t answer icebrain)
a.)
b.)
c.)
Answers
Answer: C
Step-by-step explanation:
The HL Theorem states that if the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.
In this case, 16 is the hypotenuse (the longest side of a right triangle) and 13 is the leg.
PLZZ HELP RN ASAP I NEED THIS RN TYSM
Answers
Answer:
34
Step-by-step explanation:
a + 90 + 56 = 180
a + 146 = 180
a = 180 - 146
a = 34
Gracie has made 2 gallons o punch that contains 50% juice. After Gracie pours out some of her mixture and replaced with an equal amount of pure 100% juice, she has 2 gallons of punch that contains 65% juice. How many gallons of the original mixture did Gracie pour out? Express your answer as a common fraction.
Answers
Gracie poured out 3/10 gallons of the original mixture.
What is percentage?In mathematics →
a percentage is a number or ratio expressed as a fraction of 100.it is often denoted using the percent sign "%".Given is that Gracie has made 2 gallons o punch that contains 50% juice. After Gracie pours out some of her mixture and replaced with an equal amount of pure 100% juice, she has 2 gallons of punch that contains 65% juice.
Assume that she pour out {x} gallons of original mixture. We can write -
{50% of 2} - {x} = {(100 - 65)% of 2}
{50/100 x 2} - {x} = {35/100 x 2}
{1/2 x 2} - {x} = {35/100 x 2}
1 - x = 7/10
1 - 0.7 = x
x = 0.3
x = 3/10
Therefore, Gracie poured out 3/10 gallons of the original mixture.
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Two angles of a quadrilateral measure 210° and 20°. The other two angles are in a ratio of 6:7. What are the measures of those two angles?
Answers
Answer:The sum of first angle second angle =150
⇒ The ratio of third and fourth angle is 2:3
⇒ Let third angle fourth angle be 2x and 3x.
Step-by-step explanation:
150 +2x+3x=360
⇒ 5x=210
⇒ x=42
⇒ Now, 2x=2×42
=84
⇒ 3x=3×42
=126
⇒ The measure of two angles are 84
and 126
PLEASE GIVE BRAINLIEST
Step-by-step explanation:
Sum of angles of quadrilateral = 360 degree
so 210+20+6x+7x = 360
230+13x= 360
13x= 360-230=130
x= 130/13=10
so third angle =6x= 6*10=60 degree
and 4th angle= 7x= 7*10=70 degree
PLEASE HELP DUE IN 1 HOUR, AND PLEASE DON'T PUT THOSE LINKS OR ELSE I WILL REPORT YOU.
Answers
Answer:
i think c < 7
Step-by-step explanation:
let me know if this incorrect
Answer:
c < 7
Step-by-step explanation:
If she plans to buy fewer then 7 the inequality would be c is less than 7.
Picture is how you graph that. Since c is less than 7 you would go left. The circle is open because c is not equal to 7.
What is line segment Theorem?
Answers
Line segment theorem states that if a line segment is bisected by another line, then the two parts of the line segment are equal.
This theorem is also known as the Midpoint Theorem. The formula for the Line Segment Theorem is A/B = C/D, where A and C are the two halves of the line segment, and B and D are the distances from the midpoint to the two endpoints of the line segment.
For example, consider a line segment AB with endpoints at A(-3, 2) and B(3, 2). The midpoint of the line segment is at (0,2). To calculate the length of each half of the line segment, we would use the distance formula and plug in the coordinates of the two endpoints and the midpoint.
For half A, the distance is d(A, M) = sqrt[(-3 - 0)^2 + (2 -2)^2] = 3.
For half C, the distance is d(M, B) = sqrt[(3 - 0)^2 + (2 -2)^2] = 3.
Therefore, A/B = 3/3 = 1 and C/D = 3/3 = 1. This confirms that the two halves of the line segment are equal in length.
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find the total surface area of this cuboid.
Answers
The total surface area of the cuboid is 2 (lh + lw+ hw) square units.
What is surface?A surface is the part of solid matter that can be touched by hand or seen with eyes. In other words, it is the place where the solid matter encounters the outside world through contact, light, etc. Solid matter not only effects humans with its surface, but also air, water, and other solid matter. Therefore, things around us work cooperatively with the outside world and with other things through surfaces, without a surface, solid matter would not be able to interact with anything.By changing the characteristics of solid matter, interactions such as the impact on the solid matter from other things (such as environmental conditions and people) as well as the effect that solid matter has on other things can be changed. In other words, certain features of the solid matter can be controlled as needed.To learn more about surface refer to:
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The diagram shows a cuboid with a volume of 42 cm³. K ? cm Work out the missing length of the cuboid. 2 cm 3 cm
Answers
Using the formula for the volume of cuboid that is the product of length, breadth and height, The answer is 7cm.
What is a cuboid?A cuboid is a three-dimensional shape with six rectangular faces, three of which are pairs of congruent squares and the other three are rectangles. It is also known as a rectangular prism. The opposite sides of a cuboid are parallel and equal in area. The length, width, and height of a cuboid are three of its measures of size.
What do you mean by volume and formula for volume of cuboid?The volume of a three-dimensional object is a measure of the amount of space it occupies. It is typically measured in units of cubic units, such as cubic centimeters (cm^3) or cubic meters (m^3). The formula for the volume of a cuboid is length x width x height. For example, if a cuboid has a length of 5 cm, a width of 3 cm, and a height of 2 cm, its volume would be 5 x 3 x 2 = 30 cubic centimeters. In general, the volume of a three-dimensional object can be found by multiplying the area of its base by its height.
length = 2cm
breadth =3cm
volume = 42 cm³
volume = l*b*h
42 = 2*3*h
h= 42/6 =7cm
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сm
What is the area of
circle
with circumference of 10cm ? 3
Answers
It is 10
I REALLY HOPE THIS HELPS :D
Answer:
7.96 centimeters squared
Step-by-step explanation:
In the photo.
Can a polynomial have no zero?
Answers
A quadratic polynomial does not cross the x axis at any point since it has no zeros.
An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
x^2 - 2x + 5 when compared with the standard form of the quadratic equation, a = 1, b=- 2, c=5
Value of the discriminant =b^2 - 4 ac
= (-2)2 - 4(1) (5)= 4 - 20
= - 15
The value of the discriminant is negative i.e less than zero.
Hence, the quadratic equation x^2 - 2x + 5 has no real zeroes.
Since a quadratic polynomial may only have two real roots, the number of times the graph will cross the x-axis at most is two, and at least zero when there are no roots in the equation.
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What is the 3 variable?
Answers
A three-variable system is a system of equations or inequalities involving three variables.
The three variables could refer to any three related quantities, such as a person's age, height, and weight. In a three-variable system, the number of equations is equal to the number of variables, so three equations are needed to solve the system. Each equation in the system will involve all three variables and will be solved through a combination of algebraic manipulation, substitution, and elimination techniques. Once all three equations have been solved, the values of the variables can be found.
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Dean Wormer wants to compare the grade point average of athletes at Faber College with the overall grade point average at Faber College. She randomly selects three students from each team and determines that their combined grade point average, 2. 3, is the same as that of all students at Faber. In this example, what is the population
Answers
yes it is the same as that of all students at Faber GPAs as 2.32 and lower will mean that a track team athlete will be recommended for extra tutoring and population is 2.3* student number
What is the definition of a population?
In ordinary usage, a population is a distinct group of individuals with shared citizenship, identity, or characteristics. In statistics, a population is a representative sample of a larger group of people (or even things) with one or more characteristics in common.
When the distribution is normal, we use the z-score formula.
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
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find the measurement of angle 7
Answers
Answer:
76 degrees
Step-by-step explanation:
find angle 5 by subtracting 76 from 180 to get 104 degrees
the find angle 7 by subtracting 104 from 180 to get 76
180-76 =104
180-104=76
what is the slope of the line
Answers
Based on the records for the past several seasons, a sports fan believes the probability the red team wins is . The fan also believes the probability the blue team wins is . In a season with games, how many games should the fan expect the red team to win?
Answers
See comment for complete question
Answer:
81 games
Step-by-step explanation:
Given
[tex]P(Red) = 0.45[/tex]
[tex]P(Blue) = 0.40[/tex]
[tex]n = 180[/tex]
Required
Expected game the red team will win
Expected number is calculated as:
[tex]E(x) = n * P(x)[/tex]
In this case, the number of winnings for the red team is:
[tex]Expected = 180 * P(Red)[/tex]
[tex]Expected = 180 * 0.45[/tex]
[tex]Expected = 81[/tex]
Water leaking onto a floor forms a circular pool. The circumference of the pool increases at a rate 24 cm/min. How fast is the area of the pool increasing when the radius is 5 cm
Answers
The area of the pool increasing at the rate of 753.98 cm²/min when the radius is 5 cm
How quickly does the pool's area grow when the radius is 5 cm?Given:
radius of the pool increases at a rate of 24 cm/min
To Find:
How quickly does the pool's area grow when the radius is 5 cm?
Solution:
we are given with the circular pool
hence the area of the circular pool =
A = πr²-----------------------------(1)
The area of the pool os increasing at the rate of 24 cm/min, meaning that the area of the pool is changing with respect to time t
so differentiating eq (1) with respect to t , we have
dA/dt =π 2r dr/dt
we have to find dA/dt with dr/dt = 24 cm/min and r = 5cm
substituting the values
dA/dt = π 2(5)24
dA/dt = π 26*8
dA/dt = π 240
dA/dt =240π
dA/dt = 753.98
The area of the pool increasing at the rate of 753.98 cm²/min when the radius is 5 cm
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John makes 44,000 a year. if he gets a 3% raise how much will he make the next year?
A. $44,200
B. $42,680
C. $57,200
D. $45,320
Answers
Answer: D. $45,320
Step-by-step explanation:
Simply multiply 44,000 by 0.003 and add that to 44,000!
HELP ME PLEASE AND QUICK IT'S DUE 12:00PM
c) The height of each cylinder in a set of food-storage containers is 30 cm.
The radius of the largest container is 10 cm.
The volume of the smallest container is one-third the volume of the largest container.
The volume of the middle-sized container is two-thirds the volume of the largest
container. What is the volume of each container?
Answers
Answer:
The volume of the largest cylinder is 3.14(10)^2(30) = 9424.78cm^3
The volume of the smallest cylinder is 3141.59cm^3
The volume of the medium cylinder is 6282.67 cm^3
Step-by-step explanation:
the equation for a cylinder's volume is pi(r)^2(height)
The volume of the largest cylinder is 3.14(10)^2(30) = 9424.78cm^3 (remember the units!)
The volume of t he smallest cylinder is 1/3 the largest or: 9424.78/3 = 3141.59cm^3 (remember the units!)
The volume of the medium cylinder is 2/3 the largest or 9424.78(2/3) = 6282.67 cm^3
Quadrilateral ABCD is given with ∡A=35°, ∡B=40°, ∡C=(5x+5)°, and ∡D=(5x)°. What is the value of x?
A. x = 6
B. x = 10
C. x = 28
D. x = 7
Answers
Answer:
C) x = 28
Step-by-step explanation:
35 + 40 + 5x+5 + 5x = 360
10x + 80 = 360
10x = 280
x = 28
Solve the systems algebraically please help :(
Answers
Answer:
I don't really know but I will help you if I can
Cafe A offers 2 free bottled waters or juices for every 20 purchased. If you purchased 80 drinks at the café, how many free drinks would you get?
Answers
Answer:
8 free drinks
Step-by-step explanation:
80 ÷ 20 = 4
4 × 2 = 8
solve by completing the square
-x^2=5x-14
Answers
Answer:
Roots: -7, 2
Step-by-step explanation:
-x² = 5x - 14
-x² -5x +14 = 0
x² + 5x - 14 = 0
(x + 7)(x -2) = 0
x = -7 or x = 2
The number y of duckweed fronds in a pond after t days is y=a(1230. 25)t/16, where a is the initial number of fronds. By what percent does the duckweed increase each day? Round your answer to the nearest whole number
Answers
The duckweed increases by a percentage each day which is calculated by the equation
(1230.25t/16)/a - 1.
This equation can be further simplified to 1230.25t/16a - 1 and then multiplied by 100 to get a percentage.
So the percentage increase of duckweed each day is calculated by multiplying 1230.25t/16a - 1 by 100.
1230.25t/16a×100
This will give us the percentage of increase each day, rounded to the nearest whole number.
For example, if the initial number of fronds is 1000 and the number of days is 2, the percentage increase of duckweed will be (1230.25(2)/16(1000)) - 1 = 24.6%, rounded to the nearest whole number which is 25%.
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Jane is making lunch for 12 people. she is serving hotdogs and plans on each person get eating two hotdogs. hotdog buns are sold in packages of eight. which expression can be used to find the number of packages she needs to buy?
Answers
He must purchase 3 packages of hot dogs and 2 packages of hot dog buns for a total of 24 hot dogs with buns if he doesn't want to have any leftover hot dogs or buns. You should be aware that students might respond with 24, which is the least common multiple of 8 and 12.
What are hot dog buns known as?The hot dog buns most frequently used in the American region of New England and its cuisine are New England-style hot dog buns, also referred to as New England hot dog buns or top-loading hot dog buns.
What does the slang term "hot dogs" mean?As you can see, "hot dog" is a versatile word that can be used as a noun, verb, adjective, or even as an exclamation.
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What is the Contrapositive of P → Q?
Answers
"If p then q" is a conditional statement, and its contrapositive is If ~q then ~p.
Knowing about the inverse statement makes it simple to comprehend how to build a contrapositive statement. Take the negation of the hypothesis and the conclusion to produce the conditional statement's opposite.
Create the inverted statement first, then swap the hypothesis and conclusion to create the contrapositive of the conditional statement. Adding "not" to both component statements and switching the order of the provided conditional statements will result in contrapositive assertions, in other words.
If a number n is even, then n2 is even, and vice versa, is the contrapositive statement to "If a number n is even, then n2 is even."
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Jamie's sister loaned her $15. She now has at least $50 to purchase new boots. What is m, the amount of money Jamie had before her sister loaned her the money? Write an inequality to represent this situation.
15m ≥ 50
15m > 50
m + 15 ≥ 50
m + 15 > 50
Answers
Answer:
m + 15 ≥ 50
Step-by-step explanation:
Jamie's sister gave her 15 dollars on top of what she already had. This means that it was added to her own money, m. Also, the statement says that she has at least 50; this means that she has an amount equal to or greater than 50. Therefore, the third option, m + 15 ≥ 50, is correct.
Find the measure of the indicated angle. Need help please.
I need explanation too,
THANK YOU
Answers
Answer:
AC=28
Step-by-step explanation:
Angle C=180-91-59=30
Sin30=14/AC
AC=14/sin30
AC=28
Select the correct answer. what is the height, x, of the equilateral triangle? an equilateral triangle with the angles labeled as 60 degrees and a side length of 8 inches, the height labeled as x
a. in.
b. in.
c. in.
d. in.
Answers
The height of the equilateral triangle when its side length is given as 8 inches is calculated to be 6.93 inches.
The equilateral triangle has all sides and angles equal. The angles are always equal to 60 degrees.
Given that,
Side length of the equilateral triangle = 8 inches
Angles = 60 degrees
Height = ?
Therefore, let us find the height of the triangle using the Pythagoras theorem,
c² = a² + b²
8² - 4² = b²
b² = 64 - 16
b² = 48
b = 6.93 inches
Thus, the height of the equilateral triangle is calculated to be 6.93 inches.
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How many solutions does this equation have?
9d − 8 = –8 + 9d
Answers
Answer:
Infinite many solutions
Step-by-step explanation:
9d − 8 = –8 + 9d
* add 8 to each side *
-8 + 8 cancels out
-8 + 8 cancels out
we're left with 9d = 9d
When the same number/variable is on each side of the equal sign there is an infinite amount of solutions