Write g(x) = –16x + x2 in vertex form. Write the function in standard form. Form a perfect square trinomial by adding and subtracting . Write the trinomial as a binomial squared. Write the function is in vertex form, if needed. g(x) = x2 – 16x b = –16, so = 64 g(x) = (x2 – 16x + 64) – 64 g(x) = (x – )2 –
Answer:
g(x) = (x - 8)² - 64 will be the answer.
Step-by-step explanation:
The given function in the standard form is g(x) = -16x + x²
We have to write this function in the vertex form.
Since vertex form of a quadratic function is in the form of
f(x) = (x - h)² + k
Therefore, g(x) = x² - 16x may be written as
g(x) = x² - 16x + 64 - 64
= x² - 2(8x) + 64 - 64
= (x - 8)² - 64
Therefore, g(x) = (x - 8)² - 64 will be the answer.
Steve drew a floorplan of his living room. The floorplan is represented by rectangle ABCD. He drew a dilation of his represented by rectangle A’B’C’D’ on the coordinate plane below. Each square unit on the coordinate plane represents a square with 1-foot sides. I WILL GIVE THE FIRST ANSWER BRAIN!
dolores is selling cucumbers from her backyard garden her garden is 48 square feet in total and she can grow 1 cucumber every 72 square inches if she can successfully grow cucumbers in every square foot of the garden and sell them for $2.50 each how much will she make?
Final answer:
Dolores will make $240 by growing and selling all the cucumbers possible in her 48 square feet garden, with each cucumber selling for $2.50.
Explanation:
To calculate the amount of money Dolores will make from selling cucumbers, we need to determine how many cucumbers she can grow in her 48 square feet garden, and then multiply that number by the selling price of $2.50 per cucumber. First, we'll convert the area of her garden into square inches since we know a cucumber takes up 72 square inches of space:
48 square feet × 144 square inches per square foot = 6,912 square inches.
Next, we divide this by the amount of space needed for one cucumber to find the total number of cucumbers she can grow:
6,912 square inches ÷ 72 square inches per cucumber = 96 cucumbers.
Finally, we'll multiply the number of cucumbers by the selling price:
96 cucumbers × $2.50 per cucumber = $240.
Therefore, Dolores will make $240 by selling all the cucumbers she can grow in her garden.
HELP FAST PLEASE!!
Martin simplified the composed function f(x)=sin(arctan x). His work is shown below.
Step 1: f(x)=sinA, where A=arctan x and x = tanA
Step 2: tanA= opp/adj=x/1
Step 3: hypotenuse= square root of 1^2-x^2= square root of 1-x^2
Step 4: sinA=opp/hyp=x/squareroot 1-x^2
In which step did Martin make is first error?
Answer:
1. B f(x)=4sinx/2-3
2. B, F, G (c=-1. a=2, b=2)
3. c. H(t)=-2.4cos(0.017t)+12
4. A, B, E, F (y=cos^-1x, y=cot^-1x, y=sin^-1x, y=tan^-1x)
5. C y=sin^-1x
6. C 48.7
7. C f(g(x))=sec(sinx) domain: all real #
8. C step 3
Step-by-step explanation:
help help quickly!!!!!
What is the measure of EG?
Consider this system of linear equations:
y = –3x + 5
y = mx + b
Which values of m and b will create a system of linear equations with no solution?
m = –3 and b = –3
m = 5 and b = –3
m = 3 and b = 5
m = 5 and b = –3
Engenuity answer is m= -3 and B= -3
m = –3 and b = –3 or A
Identify the cross section shown.
a. rectangle
b. circle
c. trapezoid
d. pentagon
Option : a is the correct answer.
a. rectangle.
Step-by-step explanation:From the figure that is provided to us we see that the cross-section is in the shape of a quadrilateral such that it has two pair of parallel sides.
b)
circle
A circle does not have any edge or sides.
Hence, option: b is incorrect.
c)
Trapezoid
A trapezoid is a quadrilateral with one pair of parallel sides and one pair of unparallel sides.
Hence, option: c is incorrect.
d)
Pentagon
A pentagon is a polygon with 5 sides.
Hence, option: d is incorrect.
Hence, the best possible answer is:
Rectangle
What is the probability that mattias picks an outfit at random that includes red shoes?
The probability that mattias picks an outfit at random that includes red shoes is 0.5
Calculating the probability that mattias picks an outfit at random that includes red shoes?
From the question, we have the following parameters that can be used in our computation:
The tree diagram
On the tree diagram, we have
Total Outfits = 12
Outfits with red = 6
So, we have the probability to be
P = Outfits with red /Total Outfits
This gives
P = 6/12
Evaluate
P = 0.5
Hence, the probability is 0.5
Question
Mattias gets dressed in the dark one morning and chooses his clothes at random. He chooses a shirt (green, red or yellow), a pair of pants (black or blue), and a pair of shoes (checkered or red).
What is the probability that mattias picks an outfit at random that includes red shoes?
Explain how the exponent of 10 changes when you multiply a number written in scientific notation by 100. Show an example.
Final answer:
When a number in scientific notation is multiplied by 100, its exponent of 10 increases by 2 since 100 is equivalent to 10 squared (10²). For example, 3.14 x 10⁴ multiplied by 100 becomes 3.14 x 10⁶.
Explanation:
When you multiply a number in scientific notation by 100, the exponent of 10 increases by 2.
This is because 100 can be written as 10² or 10 squared.
So, if we have a number like 3.14 × 10⁴ and we multiply by 100, we are essentially multiplying by 10².
We keep the coefficient the same (3.14) and add the exponents of 10:
3.14 × 10⁴ × 102 = 3.14 × 10⁴+23.14 × 10⁴ × 100 = 3.14 × 10⁶The resulting scientific notation is 3.14 × 10⁶, which means the exponent of 10 increased by 2 as we multiplied by 100.
Quadrilateral RJFT is similar to quadrilateral SYPA . JF=60 mm , AP=40 mm , and YP=25 mm . What is TF ?
Final answer:
To find the length of FT in the similar quadrilaterals RJFT and SYPA given specific side lengths, apply the scale factor method to determine FT = 37.5 mm.
Explanation:
Quadrilateral RJFT is similar to quadrilateral SYPA. Given that JF=60 mm, AP=40 mm, and YP=25 mm, we can solve for FT.
Calculate the scale factor between the two similar quadrilaterals using side lengths: JF/AP = FT/YP.
Substitute the given values to find the length of FT.
Calculate FT = (60 mm * 25 mm) / 40 mm = 37.5 mm.
WILL GIVE BRAINLIEST TO PERSON WHO ANSWERS CORRECTLY!!!!!! PLEASE HELP ASAP!!!!!
A roller coaster car follows a parabolic path over the first hill on its track. The height of the car, in feet, t seconds after the ride starts can be shown by the function given below.
h ( t ) = -3t^2 + 15t + 18
Which of the statements is true?
* The domain of the function is [0, 6], and it represents the car's time to reach maximum height.
* The domain of the function is [-1, 6], and it represents the car's time to reach maximum height.
* The domain of the function is [0, 6], and it represents the car's time to complete the hill.
* The domain of the function is [-1, 6], and it represents the car's time to complete the hill.
None of the options are entirely correct. The domain of the function is [tex]\( t \geq 0 \)[/tex] , and it does not directly represent the time to complete the hill or reach maximum height.The domain is representing all real numbers. The function doesn't directly indicate completion time or maximum height.
Let's analyze the given function [tex]\( h(t) = -3t^2 + 15t + 18 \)[/tex] to determine the domain and its meaning:
1. **Domain of the function**:
The domain of a quadratic function is all real numbers unless there are restrictions. In this case, there are no restrictions mentioned in the problem, so the domain is all real numbers. However, in the context of the roller coaster ride, the time ( t ) cannot be negative because it doesn't make sense for time to be negative in this scenario. Therefore, the practical domain is [tex]\( t \geq 0 \).[/tex]
2. **Time to reach maximum height**:
The time to reach the maximum height of the roller coaster can be found using the vertex formula: [tex]\( t = -\frac{b}{2a} \)[/tex] , where [tex]\( a = -3 \) and \( b = 15 \)[/tex] (coefficients from the quadratic function). Substituting these values into the formula:
[tex]\[ t = -\frac{15}{2(-3)} = -\frac{15}{-6} = \frac{15}{6} = \frac{5}{2} \][/tex]
Since time cannot be negative in this context, the time to reach the maximum height is [tex]\( t = \frac{5}{2} = 2.5 \)[/tex] seconds.
Now, let's analyze the given options:
- **Option 1: The domain of the function is [0, 6], and it represents the car's time to reach maximum height.**
- The domain given is correct [tex](\( t \geq 0 \)),[/tex] but it incorrectly states that it represents the time to reach maximum height. The correct time to reach maximum height is [tex]\( t = 2.5 \)[/tex] seconds, not 6 seconds.
[tex]\( t \geq 0 \),[/tex]
- **Option 2: The domain of the function is [-1, 6], and it represents the car's time to reach maximum height.**
- This option gives an incorrect domain. The domain is [tex]\( t \geq 0 \), not \( t \geq -1 \).[/tex]
- **Option 3: The domain of the function is [0, 6], and it represents the car's time to complete the hill.**
- This option correctly identifies the domain as [tex]\( t \geq 0 \).[/tex] However, it incorrectly states that it represents the time to complete the hill. The function does not directly represent the time to complete the hill; it represents the height of the car at any given time.
- **Option 4: The domain of the function is [-1, 6], and it represents the car's time to complete the hill.**
- This option gives an incorrect domain. The domain is [tex]\( t \geq 0 \),[/tex] not [tex]\( t \geq -1 \).[/tex]
Therefore, none of the options are entirely correct. The domain of the function is [tex]\( t \geq 0 \)[/tex] , and it does not directly represent the time to complete the hill or reach maximum height.
One column of numbers consists of 33, 58, and 17. When the digits of the numbers are added together, the result is 3 + 3 + 5 + 8 + 1 + 7 = 27, and when the digits of 27 are then added together, the end result is 2 + 7 = 9. If the same process is performed on the numbers in a second column, what can be concluded? a.If the end result from the second column is also 9, then the sum of the numbers in the first column is equal to the sum of the numbers in the second column. b.If the end result from the second column is also 9, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column. c.If the end result from the second column is not 9, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column. d.If the end result from the second column is not 9, then the sum of the numbers in the first column is equal to the sum of the numbers in the second column.excel sum values based on another columnsum if greater than
Zack deposited $1,200 in a savings account that paid 7.75% simple
interest. What was the balance in his account at the beginning of the
third year?
a. $180
b. $270
c. $1,393.21
d. $1,470
HELPPPPP ASAP AND GET BRAINEST
Answer:
$1386.
Step-by-step explanation:
We have been given that Zack deposited $1,200 in a savings account that paid 7.75% simple interest. We are asked to find the balance in his account at the beginning of the third year.
The balance in the account at the beginning of the third year will be equal to balance in the account at the end of 2nd year.
We will use simple interest formula to solve our given problem.
[tex]A=P(1+rt)[/tex], where,
A = Amount after t years,
P = Principal amount,
r = Annual interest rate in decimal form,
t = Time in years.
Upon converting our given interest rate in decimal form we will get,
[tex]7.75\%=\frac{7.75}{100}=0.0775[/tex]
Upon substituting our given values in simple interest formula we will get,
[tex]A=\$1200(1+0.0775\cdot 2)[/tex]
[tex]A=\$1200(1+0.155)[/tex]
[tex]A=\$1200(1.155)[/tex]
[tex]A=\$1386[/tex]
Therefore, an amount of $1386 will be in Jack's account at the beginning of third year.
Bax invested a total of $2000 in two simple interest accounts. Account A earns 3% interest and Account B earns 5% interest. Bax earned a total of $75 interest after one year. How much did Bax invest in each account?
Bax invested a total of $2000 in two simple interest accounts. Account A earns 3% interest and Account B earns 5% interest. Bax earned a total of $75 interest after one year. How much did Bax invest in each account?
Let, The amount invested in Account A=x
Then, the amount invested in Account B=2000-x
The formula of Simple Interest =[tex] \frac{Principle*Rate*Time}{100} [/tex]
Interest earned in Account A in 1 year=[tex] \frac{x*3*1}{100} [/tex]
Interest earned by Account A=[tex] \frac{3x}{100} [/tex]
Interest earned in Account B in 1 year=[tex] \frac{(2000-x)*5*1}{100} [/tex]
Interest earned by Account B=[tex] \frac{5(2000-x)}{100} [/tex]
Total Interest Earned= Interest earned by Account A+ Interest earned by Account B
Total Interest Earned=[tex] \frac{3x}{100} [/tex]+[tex] \frac{5(2000-x)}{100} [/tex]
75=[tex] \frac{3x}{100} [/tex]+[tex] \frac{10000-5x)}{100} [/tex]
75=[tex] \frac{3x+10000-5x)}{100} [/tex]
Multiply by 100 on both sides
75*100=[tex] \frac{100(10000-2x))}{100} [/tex]
7500=10000-2x
Let us subtract 7500 from both sides
7500-7500=10000-7500-2x
0=2500-2x
Adding 2x on both sides, we get
0+2x=2500-2x+2x
2x=2500
To solve for x, divide by 2 on both sides
2x/2=2500/2
x=1250
So, The Amount invested in Account A= $1250
The Amount invested in Account B= $2000-1250=$750
Noelle stands at the edge of a cliff and drops a rock. The height of the rock, in meters, is given by the function f(x)=−4.9x^2+17 , where x is the number of seconds after Noelle releases her rock. Cesar, who is standing nearby on the ground, throws a rock straight up in the air. The height of Cesar’s rock, in meters, is given by the function g(x)=−4.9x^2+13x , where x is the number of seconds after he releases his rock. There is a moment when the rocks are at the same height.
The rocks are at the same height approximately 1.31 seconds after Noelle drops her rock and Cesar throws his, and at this time, they are both at a height of approximately 8.57 meters.
To determine the moment when Noelle's and Cesar's rocks are at the same height, we need to set the two functions equal to each other and solve for x. Noelle's rock has the height function f(x) = -4.9x² + 17 and Cesar's rock has the height function g(x) = -4.9x² + 13x.
We solve for x when f(x) = g(x):
-4.9x² + 17 = -4.9x² + 13x
This simplifies to:
17 = 13x
Solving for x gives us:
x = 17/13
x ≈ 1.31 seconds
At approximately 1.31 seconds after Noelle drops her rock and Cesar throws his, both rocks are at the same height. To find this height, we substitute x back into either f(x) or g(x). Using Noelle's function, we get:
f(1.31) = -4.9(1.31)² + 17 ≈ 8.57 meters
Therefore, both rocks are at a height of approximately 8.57 meters 1.31 seconds after their respective releases.
Answer:
8.6
Step-by-step explanation:
I took the test
Which of the following is false?
the number of hours a person studies and the numerical score on the exam is a positive correlation
the speed of a vehicle and the time it takes the vehicle to travel 60 miles is a positive correlation
none, since all of the other answer choices are true
a child’s age and the height of a child is a positive correlation
Answer:
the speed of a vehicle and the time it takes the vehicle to travel 60 miles is a positive correlation
question 1.) simplify 6(2 + 0.3)5
A.) about 0.03
B.) about 12.01
C.) about 85.19
D.) about 386.18
question 2.) solve 32x = 7
A.) x = 0.22
B.) x = 4.57
C.) x = 25
D.) x = 39
Answer: Q1) 386.18
Step-by-step explanation:
Q1): You do the parenthesis first.
6(2+0.3)^5
2+0.3 = 2.3^5 = 64.36343
then do 6(64.36343) = 386.18
For Q2 I believe the answer is 0.22 if you do 7 divided by 32 you get 0.21875 and you round that to get 0.22
Graph the following inequality. Then click to show the correct graph.
3x - 2y ≥ 6
What is the Greatest Common Factor of 12 and 36? (1 point)
2
4
6
12
The greatest Common factor of 12 and 36 is 12.
A number that divide another number is called factor.
Factors of 12 is 2, 3, 4, 6, 12
Factors of 36 are 2, 3, 4, 6, 9, 12, 18, 36.
Therefore, the greatest common factor of 12 and 36 is 12.
Learn more about factor here:
https://brainly.com/question/29167102
#SPJ2
What is the length of a leg of an isosceles right triangle whose hypotenuse measures 6 inches? Let c represent the value of the hypotenuse. If the hypotenuse is c = a, then 6 = a. In inches, what is the value of a? 3 6
In iscosceles right triangle the value of the unknown sides is equal to [tex]3\sqrt{2}[/tex] and it can be deteremine by using pythagorean theorem.
Given :
Iscosceles right triangle.Hypotenuse = 6.Both remaining sides are equal.Let the length of unknown sides be 'a'. Than to deteremine the value of a, pythagorean theorem can be used.
[tex]\rm (Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2[/tex]
[tex]6^2 = a^2+a^2[/tex]
[tex]2a^2 = 36[/tex]
[tex]a^2 =\dfrac{36}{2}[/tex]
[tex]a = \sqrt{18} =3\sqrt{2}[/tex]
Therefore, by applying pythagorean theorem the value of a which is [tex]3\sqrt{2}[/tex] can be determine.
For more information, refer the link given below
https://brainly.com/question/10652623
Use the table provided to determine the total amount paid on a 30 year fixed loan, at 6.0%, of $75,000.
$162,000
c.
$143,820
b.
$153,750
d.
$133,250
Answer:
162000
Step-by-step explanation:
For 75000 paying in 30 years at 6% we have
Mortgage Summary
Monthly Payment $449.66
Total Interest Paid $86,879
9
Total of 360 Payments $161,879
Pay-off Date Feb, 2049
We find out of 4 options given 162000 is nearer to this 161879
Hence option of 162000 is the right answer.
Look at the isosceles trapezoid below.
Answer:
Not enough information to decideStep-by-step explanation:
If m were the midline, its length would be 32/2 = 16 cm. However, there is nothing in the figure to indicate that is the case. There is not enough information to decide.
An element with mass 430 grams decays by 27.4% per minute. How much of the element is remaining after 19 minutes, to the nearest 10th of a gram?
A doctor's office mails a survey to each of its patients. The results of the survey are based off of the total number of patients.
Which of the following could affect the outcome of their surveys?
A.The results could be flawed because the sample population was too large.
B.The results could be flawed due to a wide range of topics in the questions.
C.The survey is biased because they are only asking patients.
D.The results could be flawed due to non-response of patients.
Answer:
The results could be flawed due to non-response of patients.
Step-by-step explanation:
A doctor's office mails a survey to each of its patients. The results of the survey are based off of the total number of patients. The office is mailing the patients. It is very likely that patients do not read out the survey mail. So, they cannot respond to the survey or a very few patients will respond back. So, option 4th is the correct. The results could be flawed due to non-response of patients.
If f(x)=3x^2-1 and g(x)=x+2, find (f+g)(x)
Answer:
Step-by-step explanation:
X^2+3x-1 apex
If b is the midpoint of \frac{ }{ac} a c , d is the midpoint of \frac{ }{ce} c e , and bd = 19 , find ae .
The swimming relay race is 1/4mile long. Each of 3 swimmers in the relay swim the same distance. How far does each swimmer swim
An equilateral triangle has an altitude length of 36 feet. Determine the length of a side of the triangle.
Identify a possible first step using the elimination method to solve the system and then find the solution to the system.
12x – 3y = 6
2x – y = 2
A) multiply second equation by 6, solution (2,0)
B) multiply second equation by 6, solution (-2,0)
C) multiply second equation by -6, solution (0,2)
D) multiply second equation by -6, solution (0,-2)
Answer:
D) multiply second equation by -6, solution (0,-2)
Step-by-step explanation:
This pair of linear equations may be solved simultaneously by using the elimination method. This will involve ensuring that the coefficient of one of the unknown variables is the same in both equations.
As such, in the given set of equations
12x – 3y = 6
2x – y = 2
We may make the coefficients of x the same by multiplying the second by 6 or the coefficient of y by multiplying the second by 3. Using the first
12x – 3y = 6
12x – 6y = 12
equation 1 - equation 2
3y = -6
y = -2
2x + 2 = 2
x = 0