Given:
The equation is
[tex]y=x^2+2x+3[/tex]
To find:
The vertex form of the given equation, i.e., [tex]y=x^2+2x+3[/tex].
Solution:
We have,
[tex]y=x^2+2x+3[/tex]
It can be written as
[tex]y=(x^2+2x)+3[/tex]
Add and subtract square of half of coefficient of x, i.e., [tex]\left(\dfrac{2}{2}\right)^2=1[/tex].
[tex]y=(x^2+2x+1)-1+3[/tex]
[tex]y=(x^2+2(x)(1)+1^2)+2[/tex]
[tex]y=(x+1)^2+2[/tex] [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]
Therefore, the required form of given function is [tex]y=(x+1)^2+2[/tex].
PLEASE help me. This is due today
Answer:
negative linear
Step-by-step explanation:
Answer:
A. A negative linear association
Step-by-step explanation:
The points are close enough for a line of best fit, therefore they are linearly associated and they are going down so it is negative association.
Please help me with this i will give brainliest
Answer:
i think it's 10%
Step-by-step explanation:
hi im confused with this one question its about properties and exponents on math i really need help:(
In Eduardo's collection, the number of butterflies is 12 more than twice the number of moths. If there are x moths, choose the expression that represent the number of butterflies he has.
Answer:
y = 12 + 2x
Step-by-step explanation:
Given that :
Let number of butterflies = y
Number of moths = x
y = 12 more than twice the number of moths
y = 12 + 2x
Hence, the expression which relates the number of butterflies he has is :
y = 12 + 2x
NEED HELP ASAP Wayne bought some toy cars, c, and some baseball cards, b. Each toy car cost $3 and each baseball card cost $2. Which expression represents the total cost of Wayne's purchase?
A.
3 + b + 2 + c
B.
3b + 2c
C.
3 × 2 + b × c
D.
3c + 2b
Answer:
Hey mate.....
Step-by-step explanation:
This is ur answer.....
D. 3c + 2bHope it helps!
Mark me brainliest pls.....
Follow me!!! :)
1,2,2,3,4,6,8,9,10 what is the median HELP
The elements of the dataset are integers, and the median of the dataset 1,2,2,3,4,6,8,9,10 is 4
How to determine the median?The data elements are given as:
1,2,2,3,4,6,8,9,10
The median element is the middle element, and the middle element is: 4
Hence, the median of the dataset 1,2,2,3,4,6,8,9,10 is 4
Read more about median at:
https://brainly.com/question/8892632
#SPJ2
Find the angle measure. Round to the nearest tenth
Answer:
45.6
Step-by-step explanation:
IF x is theta
arccos(7/10)
*make sure your calculator is in degree mode
x= 45.57
PLXXXXXXXXXXZZZZZZZZZZZZZZZZZZZZZZZ
Answer:2
\left(-3\times \:3\right)+15-2^2
=-9+15-2^2
-9+15-4
=6-4
6-4=2
the answer is 2
The St. Petersburg paradox goes as follows. A fair coin is tossed repeatedly until it comes up heads. If the first heads appears on the nth toss, you win $2 n . First, show that the expected monetary value of this game is infinite (the paradox is that no one would actually pay a huge amount to play this game). Second, consider a possible resolution of the paradox: suppose your utility for money is given by a log 2 x b where x is the number of dollars you have. Suppose you start with 0 dollars, what is the expected utility of this game
Answer:
a) attached below
b) 2a + b
Step-by-step explanation:
a) show that the expected monetary value of this game is infinite
Given that the probability of getting first head on nth toss = $2^n
attached below is the prove
b) what is the expected utility of this game
using the Logarithm ; [tex]U(x) = a log_{2} n + b[/tex]
x = number of dollars you have
attached below is a detailed solution to the given problem
Solve the equation. You may find using algebra tiles to be helpful.
2x + 7 = 13
x =
Answer:
x= 3
Step-by-step explanation:
Move all the terms that do not contain x to the right side and solve.
Hope this helped!
⭐ Please consider giving Brainliest if this answer helped you ⭐
YOU WILL GET BRAINLIEST. A cone is circumscribed by a hemisphere radius of which is equal to the height of the cone. Find the ratio of the volume of the cone to the volume of the hemisphere
Answer: 1:2
Step-by-step explanation: plz mark me brainliest
which graph represents the solution to 7x < 21 or 6x -9 > 21
Answer:
There is no solution, though the lines are confirmed as dashed with the shaded area being on the outer sides.
Step-by-step explanation:
above
A trampoline park costs $12 for the first hour and $6 for each additional hour. Flynn pays $30 at the trampoline park. Select the equation that represents the given situation and find the number of additional hours Flynn stays at the trampoline park after the first hour.
A. 12x + 6 = 30; 3 hours
B. 6x + 12 = 30; 3 hours
C. 6x + 12 = 30; 2 hours
D. 12x + 6 = 30; 2 hours
The equation that represents the given situation is 12 + 6x = 30.
The number of additional hours is 3.
Option B is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 9 is an equation.
We have,
A trampoline park costs $12 for the first hour and $6 for each additional hour.
Amount paid at the park = $30
Now,
12 + 6x = 30
x is the number of hours.
Solve for x.
12 + 6x = 30
6x = 30 - 12
6x = 18
x = 3
Thus,
The equation is 12 + 6x = 30.
The number of hours is 3.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ2
Help ASAP Need This Answered RN
If the speed of sound is 1230 km/h, calculate the speed of sound in metres per second.
Write down your answer correct to the nearest metre.
Answer:
342 m/s
Step-by-step explanation:
1230x 1000 = 1230000
1230000 / 60 = 20500
20500 / 60 = 341.666 = 342
Answer: 3.4 * 10^(5)
Step-by-step explanation:
Find the value of each variable.
Answer:
a. a×3= -30
a= -30-3
a= 33
What is the greatest common factor of 45x^3, 24x^2, and 16x?
Answer:
[tex]\huge\boxed{\sf GCF = x}[/tex]
Step-by-step explanation:
Firstly we'll factorize the terms:
45x³ = 3 * 3 * 5 * x * x * x
24x² = 2 * 2 * 2 * 3 * x * x
16x = 2 * 2 * 2 * 2 * x
The factor which is common in all three terms is:
= x
Hence GCF = x
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807find the slope of the line through each pair of points
(3,-2),(-13,-8)
can someone help me! The person who gets it right gets brainliest
Answer:
The answer is 17.6
Step-by-step explanation:
Multiply 8 x 2.2, and act as if you are cutting off the left "triangle" and simply moving it to the other side, making it act like a rectangle.
4cos(x) = 3
solve this
Answer:
41.4 degrees
Step-by-step explanation:
Find cos x by dividing both sides of this equation by 4:
cos x = 3/4 = 0.75
Using a calculator's inverse cosine function, find x:
arccos 0.75 = 0.723 radian, or
0.723 rad 180 deg
--------------- * ------------- = 41.4 degrees
1 pi rad
Mike discovered that the pool in his backyard is leaking slowly. The pool holds 17,085 gallons of water, and is leaking at a rate of 20
gallons per day.
If Mike does not replace the water that has leaked from the pool, how many gallons of water will remain in the pool
after 103 days?
A. 15,025 gallons
B. 16,055 gallons
C. 17,188 gallons
D. 19,145 gallons
What is the distance between the points (5, 13) and (-8, -9) on a coordinate plane rounded to the nearest tenth unit?
Answer:
25.6
Step-by-step explanation:
Use the distance formula.
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}\\d = \sqrt{(-8 - 5)^2 + (-9-13)^2}\\d = \sqrt{(-13)^2 + (-22)^2}\\d = \sqrt{169 + 484}\\d = \sqrt{653}[/tex]
The distance between the points (5, 13) and (-8, -9) is 25.6 units after using the distance formula.
What is a distance formula?It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.
The distance formula can be given as:
[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have two points (5, 13) and (-8, -9)
[tex]\rm d=\sqrt{(-8-5)^2+(-9-13)^2}[/tex]
d = √(169+484)
d = 25.55 units ≈ 25.6 units
Thus, the distance between the points (5, 13) and (-8, -9) is 25.6 units after using the distance formula.
Learn more about the distance formula here:
brainly.com/question/18296211
#SPJ2
Giovanni is visiting his grandmother who lives in an apartment building on the 25th floor. Giovanni enters the elevator in the lobby, which is the first floor of the building. The elevator stops on the 16th floor. What percentage of 25 floors does Giovanni have left to reach his grandmothers floor?
Answer:
the percentage is 36%
Step-by-step explanation:
The computation of the percentage of 25 floors does Giovanni have left to reach his grandmothers floor is shown below:
= (25 floor - 16 floor) ÷ (25 floor)
= 9 floor ÷ 25 floor
= 36%
Hence, the percentage is 36%
The graph of which equation is shown below?
y = −2x + 3
A.) y = -2x + 3
B.) y = 2x + 1.5
C.) y = 2x + 3
D.) y = −2x + 1.5
Answer: The answer is y=-2x+3
2. Mr. Hoffman has a circular chicken coup with a radius of 2.5 feet. He wants to put a chain link fence around the coup to protect the chickens. Which measurement is closest to the length of fence he will need?
A: 19.63ft
B: 31.42ft
C: 15.7ft
D:7.85ft
Answer:
C
Step-by-step explanation:
using the formula for circumference of a circle.
2πr is the formula.
closest answer is 15.7 ft
Pls answer correctly brainliest and 29pts
Answer:
A
Step-by-step explanation:
Distance covered by Amy in one hour = 1/3 x 15 miles = 5 miles
Distance covered by John in one hour = 1/5 x 30 miles = 6miles
As a result, John would jog 1 mile (6-5) farther than Amy, the answer is A
Answer: John goes 1 mile further than Amy
Step-by-step explanation:
Figure out how far each person can go in an hour
Amy can go 1/3 of a mile in 1/15 of an hour- Multiple by 15 to see how far she can go in 1 hour
[tex]\frac{1}{3} *15= \frac{15}{3} = 5[/tex] so in 1 hour Amy can go 5 miles
John goes 1/5 of a mile in 1/30 of an hour- so multiple by 30 to see how far he goes in 1 hour
[tex]\frac{1}{5} * 30 = \frac{30}{5} = 6[/tex]
John goes 6 miles in an hour
So John goes 1 mile further than Amy (6-5)=1
HELP ME PLZZ, ASAP!!
Suppose one of your friends was absent from school on the day your math class learned about graphing rational numbers on the number line. Using complete sentences, explain to your friend how to graph the opposite of 6.2 on the number line.
if x = 5, find the value of (x+3)²
Step-by-step explanation:
Given
if x = 5 Then
(x+ 3)²
= ( 5 + 3) ²
= 8²
= 64
Hope it will help :)❤
20% of _____ is 11
_____% of 60 is 21
(fill the blank)
(they're both seperate questions)