Answer:
The domain is all real numbers
The y-intercept is 3.
Step-by-step explanation:
Let's analyze each statement separately. The function is
[tex]f(x)=(x+1)^2+2[/tex]
We have the following statements:
The domain is all real numbers, --> TRUE. The domain of a function is the set of values that the variable x can take. For this function, there are no restriction on the values that x can take, so the domain is all real numbers.
The range is all real numbers greater than or equal to 1 --> FALSE. The range of a function is the set of values that the variable y can take. For this function, we see that the factor [tex](x+1)^2[/tex] is always equal or greater than zero; this means that the minimum of the function is [tex]f(x)=2[/tex], so the range is all real numbers greater than or equal to 2.
The y-intercept is 3. --> TRUE. The y-intercept is the value of the function when x = 0. For this function, if we substitute x = 0, we find:
[tex]f(0)=(0+1)^2+2=1^2+2=3[/tex]
The graph of the function is 1 unit up and 2 units to the left from the graph of [tex]y=x^2[/tex] --> FALSE. The graph of a function is scaled n units up when [tex]g(x)=f(x)+n[/tex]; in this case, we see that the factor n in our fuction is n = 2, so the function is actually scaled 2 units up, not 1.
The graph has two x-intercepts --> FALSE. The x-intercept of a graph is the value of x when [tex]f(x)=0[/tex]. If we require [tex]f(x)=0[/tex] for our function, we get:
[tex]0=(x+1)^2+2\\\rightarrow (x+1)^2=-2[/tex]
However, this equation has no solutions: so, the graph has no x-intercepts.
The graph of the function [tex]f(x) = (x + 1)^2 + 2[/tex] has a domain of all real numbers, a range of all real numbers greater than or equal to 2, a y-intercept of 3, and is 1 unit left and 2 units upwards shifted from the base graph [tex]y = x^2[/tex]. It has one x-intercept, not two.
Explanation:The function in question is f(x) = (x + 1)2 + 2. To analyze its characteristics, we first need to look at its general shape, domain, and range. Since it is based on the parent function f(x) = x2, which is a parabola, the transformations will affect the position but not the overall shape or domain.
The domain is all real numbers because for any x-value, there is a corresponding y-value. This applies to all quadratic functions.The range is all real numbers greater than or equal to 2, not 1. The minimum point of the graph occurs when the squared term is zero, which in this case is at f(-1) = 2.The y-intercept is the value of the function when x=0. Substituting into the function gives f(0) = (0 + 1)2 + 2 = 3.The graph is a standard parabola that opens upward. It is shifted 1 unit to the left (not Daft) and 2 units upwards from the graph of y = x2.The graph has only one x-intercept (not two), which can be found by setting the function equal to zero and solving for x.
evaluate 3/2 y - 3 + 5/3 z
when y = 6 and z= 3
Answer:
Step-by-step explanation:
Substitute the numbers in for y and z.
3/2(6)+5/3(3)-3
9+5-3
14-3=11
answer: 11
Find the value of 4x^2– 2y when x = 3 and y = 2.
Answer:
The answer is 32.
Step-by-step explanation:
Remember that order of operation is very important in this problem.
Substitute x for 3 and y for 2 in the equation.
When solving the first term, we must note that we have to square the 3 first before we multiply it by 4. So, 4(3)^2 is basically 36. To simplify the second term you just have to do 2*2, which is 4. 36-4=32, which is the answer.
Final answer:
The value of the expression 4x² - 2y when x = 3 and y = 2 is 32, found by substituting the values of x and y into the expression and simplifying.
Explanation:
To find the value of 4x² - 2y when x = 3 and y = 2, we need to substitute these values into the expression.
Start by substituting x with 3: 4(3)² = 4(9) = 36.Next, substitute y with 2: -2(2) = -4.Now, combine these results: 36 - 4 = 32.So, the value of the expression 4x² - 2y when x = 3 and y = 2 is 32.
What is the volume of the die?
Answer:
3375
Step-by-step explanation:
Because you need to do length x width x height
3/15 divided by 4/9
please help me my dudes
Answer:
9/20
(9 over 20)
Step-by-step explanation:
Answer:
9/20 or 0.45
Step-by-step explanation:
Find the reciprocal of the divisor
Reciprocal of 4/9: 9/4
Now, multiply it with the dividend
So, 3/15 ÷ 4/9 = 3/15 × 4/9= 3 × 9/15 × 4
3 × 9
15 × 4
=
27 /60
After reducing the fraction, the answer is
9 /20 or 0.45
Round answer to the nearest hundredth if necessary. If YV= 28in, find the length of VYX
Answer:
282°
Step-by-step explanation:
VYX = 360° - (YW + 15°)YW = 180° - 117° = 63°VYX = 360° - (63° + 15°) = 360° - 78° = 282°To find the length of VYX, use the Pythagorean theorem and set up an equation to solve for the length by squaring the lengths of the other sides and adding them together. Then, take the square root of the sum to find the length of VYX.
Explanation:To find the length of VYX, we can use the Pythagorean theorem. In a right triangle, the square of the hypotenuse (VYX) is equal to the sum of the squares of the other two sides (VY and YX). Since we know VY (28 inches), we can solve for the length of VYX
Using the Pythagorean theorem: (VYX)2 = (VY)2 + (YX)2
Plugging in the values: (VYX)2 = (28)2 + (YX)2
Since the question asks for the length of VYX, we can take the square root of both sides to find the length of VYX: VYX = √[(28)2 + (YX)2]
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A small town in kansas with a population of 2300 people 80 years ago. Now, the town has experienced significant growth and has a population of about 3234956 people. Approximately how many times larger is the current population in the Kansas town than it was 80 year's ago?
Answer:
It has grown by 1406.50%
Step-by-step explanation:
Take 3234956 and divide it by 2300 and you get your percentage from population then to now
Please make me the Brainliest Answer
Nasim is making hot sauce. She puts in chile peppers and tomatoes in a ratio of 1 to 3. If she puts in 9 tomatoes, how many chile peppers should she put in?
Answer: 3
Step-by-step explanation:
Nasim is making hot sauce. Nasim puts in chile peppers and tomatoes in a ratio of 1 to 3.
Assuming Nasim puts in 9 tomatoes, the number of chile peppers should she put will be:
Ratio of chile peepers to tomato= 1;3
Since she put 9 tomatoes, chile peppers= (1×9)/3 = 9/3 = 3.
For 1 chile peeper, there'll be 3 tomatoes.
For 3 chile pepper, thee will be 9 tomatoes.
Answer: She needs to add 3 chile peppers.
Step-by-step explanation:
The ratio of chile peppers to tomatoes is 1:3
this means that for each 3 tomatoes, she puts one chile pepper.
Then if she puts 9 tomatoes, this means that she puts 3 tomatoes 3 times.
And we know that for each 3 tomatoes she needs to add 1 chile pepper, then she needs to add 1 chile pepper 3 times:
3*1 = 3 chile peppers.
She needs to add 3 chile peppers.
The combined average weight of an okapi and llama is 450 kg average weight of three llamas is 190 more than average weight of an oak park on average how much does an UGG Poway and how much does a llama way
Answer:
The average weight of okapi is 290 kg
The average weight of llama is 160 kg
Step-by-step explanation:
To solve the question, we are to resolve the word problem as follows;
Let the average weight of Okapi be X
The average weight of llamas be Y
X + Y = 450 and
3 Y = X + 190
Solving the above simultaneous equation, we have
X = 450 - Y
∴ 3·Y = 450-Y+190
4·Y =640
Y = 160 and X = 450 - 160 = 290
Therefore, the average weight of okapi = 290 kg while the average weight of llama = 160 kg.
9a=81 a=? Please help
Si un cono lo obtienes haciendo girar un triángulo rectángulo cuya base es de 10cm y su altura es de 16cm ¿cuánto mide el radio de la base del cono?
Answer:
10 cm.
Step-by-step explanation:
In order to better understand this question, I will attach an allusive image to the question.
Keep in mind that in this case the base of the triangle is equal to the radius of the base of the cone since the triangle rotates on its own axis, therefore the measurement of the base corresponds to 10 cm, therefore the radius measures 10 cm.
You invest $2,800 in an account that pays an interest rate of 6.5% compounded continuously calculate the balance of your account after 19 years. Round your answer to the nearest hundredth
Answer:
$9627.46
Step-by-step explanation:
-The amount after 19 years for a 6.5% compounded continuously is given by the formula:
[tex]A=Pe^{rt}[/tex]
Where:
A is the final amount after investment
P is the initial amount invested
r is the stated annual interest rate.
t is period of investment
#We then substitute our values in the equation to solve for A:
[tex]A=Pe^{rt}\\\\=2800e^{19\times 0.065}\\\\=9627.46[/tex]
Hence, the amount after 19 years is $9,627.46
Maya decided to paint some of the rooms in her hotel. She found out that a room required 3/2 cans of paint. If Maya buys 9 cans of paint, how many rooms can she paint?
Answer:
She can paint 6 rooms.
Step-by-step explanation:
Given:
Maya decided to paint some of the rooms in her hotel. She found out that a room required 3/2 cans of paint.
If Maya buys 9 cans of paint.
Now, to find the rooms she can paint.
So, we use unitary method to get the number of rooms:
If, [tex]\frac{3}{2}[/tex] cans of paint is needed to paint 1 room.
Then, 1 can of paint is needed to paint = [tex]\frac{1}{\frac{3}{2}} =\frac{2}{3}[/tex] room.
Thus, 9 cans of paint is needed to paint = [tex]\frac{2}{3} \times 9[/tex]
[tex]=\frac{18}{3} \\\\=6\ rooms.[/tex]
Therefore, she can paint 6 rooms.
20 POINTS HELP ASAP
Indicate the formula for the following conditions P^c(n,r)=
Answer:
The answer is C(n,r) = n!/[(n-r)!r!]
The formula for the following conditions is [tex]C(n,r) = \dfrac{n!}{[(n-r)!r!]}[/tex]
How many ways k things out of m different things (m ≥ k) can be chosen if order of the chosen things doesn't matter?We can use combinations for this case,
A total number of distinguishable things is m.
Out of those m things, k things are to be chosen such that their order doesn't matter.
This can be done in a total of
[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!} ways.[/tex]
If the order matters, then each of those choice of k distinct items would be permuted k! times.
So, a total number of choices, in that case, would be:
[tex]^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}[/tex]
This is called the permutation of k items chosen out of m items (all distinct).
The formula for the following conditions is [tex]C(n,r) = \dfrac{n!}{[(n-r)!r!]}[/tex]
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A 10 foot ladder is leaning against the wall. The bottom of the ladder is 4 feet from the base of the wall. Which is closest to the distance from the top of the ladder to the base of the wall
Answer: 9.16 feet
Step-by-step explanation:
Hi, to answer this question, since we have formed a right triangle (see attachment) we have to apply the Pythagorean theorem:
a2 +b2 = c2
Where c is the hypotenuse of a right rectangle (the longest side) and a and b are the lengths of the other 2 sides.
In this case the hypotenuse us the ladder.
So, replacing with the values:
4^2 + b ^2 = 10^2
16 + b^2 = 100
b^2 = 100-16
b^2 = 84
b = √84
b= 9.16 feet
Suppose that $6500 is placed in an account that pays 3% interest compound each year. Assume that no withdrawals are made from the account
Find the amount in the account at the end of 1 year
Find the amount in the account at the end of 2 years
Answer:
1 year:
The amount is $6695 and the interest is $195
2 years:
The amount is $6895.85 and the interest is $395.85.
The balance in the account at the end of 1 year would be approximately $6695 and at the end of 2 years would be approximately $6899.85 with an initial investment of $6500 with a 3% interest rate compounded annually.
Explanation:The subject of this question is compound interest. When an amount of money is placed in an account with a certain interest rate, the amount grows over time. In this case, the initial investment is $6500 and the interest is compounded annually at a rate of 3%.
To calculate the total amount in the account after a certain period, you can use the following formula:
A = P(1 + r/n)^(nt)
A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount), r is the annual interest rate (in decimal), n is the number of times that interest is compounded per year, and t is the time in years.
Applying this formula to the problem: for the end of first year, t=1, we will have:
A=6500(1 + 0.03/1)^(1*1) ≈ $6695
For the end of 2 years, t=2, we will get:
A=6500(1 + 0.03/1)^(1*2) ≈ $6899.85
Therefore, the balance in the account at the end of 1 year would be approximately $6695 and at the end of 2 years would be approximately $6899.85. Assume there are no withdrawals from the account during this period.
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Identify the zeros if the quadratic function.
A) x=2 and x=5
B) y=2 and y=5
C) x=-2 and x=-5
D) y=-2 and y=-5
Answer:
C) x=-2 x=-5
Step-by-step explanation:
When you look at the X-axis you can see that is crosses at the points (-5,0) and (-2,0)
Answer:
The zeros are x=-2 and x=-5.
As of a certain date, 94,696 of the four-character sequences using either letters or digits had not yet been claimed. If a four-character name is randomly selected on that date, what is the probability that it is already owned? (Round your answer to four decimal places.)
Answer:
Hence the probability that are already owned are 0.943620
Step-by-step explanation:
Given:
No fo character sequences using either letter or digits had not been claimed=94696
To find :
What is probability that letter are already claimed ?
Solution:
We know that there are 26 alphabets and digits are 0,1,2.. 9
Hence total will be of 36.
Now we are going to Arrange the sequence for all possible values
as there 4 characters we get ,each of them with 36 possible values
=36*36*36*36
=36^4
=1679616.
Now we have a sequence with 94696 character and digits are not claimed .
Its probability
=94696/1679616
=0.05637.
So the required probability will be ,
P(claimed)=1- P(Not claimed)
= 1-0.056379
=0.943620
Hence the probability that are already owned are 0.943620
I deliver truck is transporting box of two sizes large and small large box weigh 50 pounds each and a small box weighs 35 pounds each they’re 150 bucks an hour if the truck is you’re a total of 4775 pounds in boxes how many of each type of boxes of carrion
Answer:
95 and 136 respectively
Step-by-step explanation:
4775/50=95R25
4775/35=136R15
Callie evaluated the expression (8-2*2)3 to find 448. However, Callie’s calculations below are incorrect. Find the correct value of the expression (8-2*2)3 and explain where Callie made a mistake.
Answer:
64
Step-by-step explanation:
Callie is incorrect because of the way she distributes the exponent inside the brackets. This is what she did:
[tex](8 - 2*2)^3 = 8^3 - (2*2)^3 = 512 - 4^3 = 512 - 64 = 448[/tex]
The correct calculation should be done inside the bracket first, then the exponent outside
[tex](8 - 2*2)^3 = (8 - 4)^3 = 4^3 = 64[/tex]
Answer:
In step 1, when Callie distributed the One-half to the 8, she multiplied incorrectly.
Step-by-step explanation:
allie solved this one-variable equation. When she was done, she tried to verify her answer, but found that it was wrong. Can you find her mistake?
1
2
(4k + 8) = 10
1. 2k + 16 = 10
2. 2k = −6
3. k = −3
What was Callie’s mistake?
Callie should have added 10 to both sides in step 2.
In step 1, when Callie distributed the One-half to the 8, she multiplied incorrectly.
Callie divided by 2 instead of multiplying by 2 in step 3.
Callie should have added 16 to both sides in step 2.
Use the quadratic formula to solve 2x^2 + 2x - 12?
Answer:
If you plug it all in you will get x=2 x=-3
Step-by-step explanation:
The quadratic formula is
-b+/-[tex]\sqrt[/tex]-b^2-4ac all over 2(a)
your equation 2x^2+2x-12
you can label it
a=1 b=2 c=-12
If you plug it all in and solve you will get x=2 x=-3
The values of x would be 2 and 3 which are determined by using the quadratic formula to solve the given quadratic function.
What is a quadratic function?The quadratic function is defined as a function containing the highest power of a variable is two.
We have been given that quadratic function as
2x² + 2x - 12
Compare the given function to the standard quadratic function f(x) = ax² + b x + c.
We get a = 2, b = 2 and c = -12
Using the quadratic formula to solve the above quadratic function
[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Substitute the values of a = 2, b = 2 and c = -12 in the quadratic formula,
[tex]x = \dfrac{-2\pm\sqrt{2^2-4\times2\times-12}}{2\times2}[/tex]
[tex]x = \dfrac{-2\pm\sqrt{4+96}}{4}[/tex]
[tex]x = \dfrac{-2\pm\sqrt{100}}{4}[/tex]
[tex]x = \dfrac{-2\pm10}{4}[/tex]
x = (-2+10)/4 and x = (-2-10)/4
x = (8)/4 and x = (12)/4
x = 2 and x = 3
Therefore, the values of x would be 2 and 3 which are determined by using the quadratic formula to solve the given quadratic function.
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The following are the ages (years) of 5 people in a room:
20, 21, 13, 22, 18
A person enters the room.
The mean age of the 6 people is now 18.
What is the age of the person who entered the room?
Answer:
The person is 14 years old
Step-by-step explanation:
1. Multiply 6 times 18 which is 108
2. Add all numbers together in list which is 94
3. Subtract 94 from 108 which is 14
4. To check answer add 94 plus 14 and divide by 6 and you will get the median which is 18, now you know this answer is correct.
A washer and a dryer cost $713 combined. The washer costs $37 less than the dryer. What is the cost of the dryer
Answer:
375
Step-by-step explanation:
713 - 37 = 676
676 divided by 2 = 338
That would be the washer but we need to add the 37 again for the dryer
338 + 37 = 375
Mitchell received a stipend at the beginning of the semester to buy textbooks. During the semester, he spent $429.17 on textbooks. He had $77.85 of the stipend left at the end of the semester How much was Mitchell's stipend? A. $584.87 B. $351.32 C. $390.25 D. $507.02
Final answer:
(Option D)Mitchell's stipend was $506.02.
Explanation:
To find out how much Mitchell's stipend was, we can subtract the amount he spent on textbooks from the amount he had left at the end of the semester.
Let's assume Mitchell's stipend was X dollars.
He spent $429.17 on textbooks, so the remaining amount would be X - $429.17.
We know that he had $77.85 left, so we can set up the equation:
X - $429.17 = $77.85
Now, we can solve for X:
X = $77.85 + $429.17 = $506.02
So, Mitchell's stipend was $506.02. This corresponds to answer (Option D).
Tim and Cynthia leave Cynthia's house at the same time. Tim drives north and Cynthia drives west. Tim's average speed is 10 mph slower than Cynthia's. At the end of one hour, they are 70 miles apart. Find Cynthia's average speed. (Round your answer to the nearest tenth.)
Answer:
54.2 mph
Step-by-step explanation:
Since the drivers leave at the same time and travel in directions 90° from each other, their separation speed can be found using the Pythagorean theorem. Let c represent Cynthia's average speed. Then (c-10) will represent Tim's average speed. Their combined separation speed is 70 miles per hour, so we can write ...
70² = c² +(c -10)²
4900 = 2c² -20c +100 . . . . eliminate parentheses
c² -10c -2400 = 0 . . . . . . . . divide by 2; put in standard form
(c -5)² -2425 = 0 . . . . . . . . . rearrange to vertex form
c = 5 ±5√97 . . . . . . . . . . . . solve for c, simplify radical
c ≈ 54.244 ≈ 54.2 . . . . . . . use the positive solution
Cynthia's average speed was 54.2 miles per hour.
Which of the following probabilities is the greatest for a standard normal distribution?
Answer:
The Correct choice is: p(-0.5≤z≤0.5) .
Answer:
It's B on Edg
Step-by-step explanation:
I just took the test
3h=15 solve the equation
Answer:5
Step-by-step explanation:PLS GIVE ME BRAINLIEST
Value of h is 5 for 3h=15.
An equation is a mathematical statement that shows that two mathematical expressions are equal. It is used to calculte the values of the variable such they satisfy the expression on both the side of the equal symbol. The equation may involve one variable, two variables, three variable,s and so on.
Given equation:
3h=15
This is an equation in one variable, which can be solved by transposition.
To calculate the value of h
On dividing 3 both sides,
3h/3=15/3
h=5
Thus , for equation 3h=15, value of h is 5
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On Monday, 343 students went on a trip to the zoo. All 8
buses were filled and 7 students had to travel in cars. How many students were
in each bus ?
Answer:
42
Step-by-step explanation:
343-7 equals to 336
divide it by 8, for 8 buses, there would be 42 in each bus
Chase halls health insurance cost $373.50 per month he must pay 25% of the amount and his employer pay 75% of the amount how much does mr hall pay for health insurance each month
Answer:
$93.38
Step-by-step explanation:
To solve this, we simply multiple $373.50 by 25% to figure out how much Mr.Hall pays for health insurance each month. Don't forget that we need to change 25% to its decimal form (25% -> 0.25).
$373.50 x 0.25 = $93.38
Mr.Hall must pay $93.38 dollars a month for his health insurance.
I am unable to solve this problem. Tap for examples... if prices increase at a monthly rate of 2.4%, by what percentage do they increase in a year?
Answer:
[tex]28.8\%[/tex].
Step-by-step explanation:
We have been given that prices increase at a monthly rate of 2.4%. We are asked to find the percentage at which prices will increase in a year.
We know that 1 year equals 12 months.
To find the increase in one year, we will multiply monthly increase rate by 12 as:
[tex]\text{Yearly increase rate}=12\times 2.4\%[/tex]
[tex]\text{Yearly increase rate}=28.8\%[/tex]
Therefore, the prices will increase at a rate of [tex]28.8\%[/tex] in a year.
how many solutions does the system have
4x−2y=8
2x+y=2
Under the elimination method, we normalized the systems of equations, resulting in the equation: 0=1. Since this is not possible, the system has no solutions.
Explanation:To determine the number of solutions for the system of equations, we can use the method of substitution or elimination. Let's use elimination:
First, we normalize the equations by dividing the first equation by 4 and the second equation by 2. This gives us:Because 0 does not equal 1, we can conclude that the system of equations has no solutions.
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