Answer:
D. The axis of symmetry is x = 1.5 and the vertex is (1.5, 0).
Step-by-step explanation:
y=4x^2-12x+9:\quad \mathrm{Parabola\:with\:vertex\:at}\:\left(h,\:k\right)=\left(\frac{3}{2},\:0\right),\:\mathrm{and\:focal\:length}\:|p|=\frac{1}{16}
To find the vertex of this parabola, "complete the square:" Rewrite y = 4x2 - 12x + 9 in the form y = 4(x - h)^2 + k:
y = 4x^2 - 12x + 9 => y = 4(x^2 - 3x) + 9.
Now complete the square of x^2 - 3x: Take half of -3 and square the result, obtaining (-3/2)^2, or 9/4. Add 9/4 to x^2 - 3x and then subtract 9/4 from the result: We get x^2 - 3x + 9/4 - 9/4. Substitute this result back into
y = 4(x^2 - 3x) + 9: y = 4(x^2 - 3x + 9/4 - 9/4) + 9
and then rewrite the perfect square x^2 - 3 + 9/4 as the square of a binomial:
y = 4(x - 3/2)^2 - 9/4) + 9. This simplifies to:
y = 4(x - 3/2)^2 + 0.
Thus, the vertex is at (3/2, 0) and the axis of symmetry is x = 3/2. This agrees with Answer B.
Given : equation y = 4x^2 − 12x + 9
To Find :
A) The axis of symmetry is x = 0 and the vertex is (0,9).
B)The axis of symmetry is x= 1.5 and the vertex is (1.5, 0).
C)The axis of symmetry is x = 4 and the vertex is (4, -12).
D)The axis of symmetry is x = -1.5 and the vertex is (-1.5, 36).
Solution:
y = 4x² - 12x + 9
=> y = (2x)² - 2(2x)3 + 3²
=> y = (2x - 3)²
=> y = 4(x - 3/2)²
=> y = 4(x - 1.5)²
Axis of symmetry is x= 1.5
Vertex = (1.5 , 0)
The axis of symmetry is x= 1.5 and the vertex is (1.5, 0).
At the basketball game, Leo scored points in 30% of his attempts. Which of the following statements is true?
A- Leo scored points in more than 1/3 of his attempts.
B- Leo scored points in 1/4 of his attempts.
C- Leo scored points in 3/10 of his attempts,
D- Leo scored points in less than 1/6 of his attempts.
THIS IS FOR A TEST, PLEASE HELP
Answer:
2/3
Step-by-step explanation:
irdk
Richard has 650 kilograms of candy bag then Ming has 137 kilograms. What is the total mass is the candy bag?
Answer:
787 kg
Step-by-step explanation:
Help please and thank you
Answer:
a
Step-by-step explanation:
a triangle has 180 degrees in total
so adding the angles altogether we get 180
set the equation up like this
6x + 3 + 75 + 60 = 180
and then combine like terms
6x + 138 = 180
then subtract
6x = 42
and then finally divide
x = 7
Answer:
A) 7
Step-by-step explanation:
180-60=120
120-75= 45
45-3=42
42/6= 7
A) 7
The table shows information about all students doing GCSE's at a school.
Year 10 Year 11 Total
Girls 60 110 170
Boys 140 80 220
Total 200 190 390
What fraction of the boys are in Year 11?
Give your answer in its simplest form
The functions f(x) and g(x) are shown on the graph. fx) = x² What is g(x)? 10- y (f(x) 5 X >> 10 10 5 5 -5-+ g(x) -10 O A. g(x) = (-x)2 - 2 O B. g(x) = -x2 - 2 --- O c. g(x) = -x2 + 2 O D. g(x) = (- x)2 + 2
Answer:
C
Step-by-step explanation:
i hoped i did something
The value of g(x) will be -x² + 2 so option (C) will be correct.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
A function can be regarded as a computer, which is helpful.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.
Given,
f(x) = x²
g(x) = shifts graph downward by 2 units and reflected down.
Now,
The value of f(x) for positive x will be positive
But the value of g(x) for positive x is negative and 2 units shifted downward.
So it should be -x² - 2.
Hence"The value of g(x) will be -x² + 2 so option (C) will be correct".
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I am Stuck and I need help
So there is a question I am stuck on and I would appreciate it alot of I got elp
Its a triangle squeezed in between 2 parrelel lines and im trying to find angles for
A / B / C
I have added a picture for you guys to see
Thank you and have a great day
Answer:
A=35° B=65° C=80°
Step-by-step explanation:
The sum of all three inner angles needs to be 180.
alternate interior angles are congruent.
5/3n-17=3n-25solve the equation
Answer:
n= 6
Step-by-step explanation:
Solve for n by simplifying both sides of the equation, then isolating the variable.
Can somebody help ??
Step-by-step explanation:
the correct answer is 1/7
Which equations represent linear functions?
•8x – 3y = 2
•y = |x – 41-7
•y + 8 = 5(x-4)
• y=-7
•y = 6
•y=-4x* - 6
Answer:
1,3,4,5 (2 and four I can't make out what the notations are)
Step-by-step explanation:
Any equation that has a constant slope is a linear equation.
1 has a slope of 8/3
3 has a slope of 5
4 and 5 have a slope of 0
2 looks to be some form of absolute value equation and therefore is in the shape of a V and not a straight line.
6 looks to be an equation with an exponent as part of a term and will have a gradually decreasing slope (decreasing because of the negative 4)
If lines l and m are parallel find the value of X
Which expression is equivalent to 2 x + 4 ?
Answer:
Step-by-step explanation:
GCF of 2x and 4 is 2
2x+ 4 = 2*x + 2*2
= 2*(x + 2)
what is the importance of derivative classification?
Answer:
Classifying information helps to protect our national security
#Brainly lovers
The importance of derivative classification lies in its role in safeguarding sensitive information and ensuring national security. Derivative classification involves the process of determining the level of classification of information that is derived from a primary source.
what is the importance of derivative classification?Derivative classification is an essential aspect of information security and classification systems. It involves assigning the appropriate level of classification to information that is derived from a primary classified source. This process ensures that the derived information is protected and handled with the same level of care as its source material.
The importance of derivative classification lies in several key factors. Firstly, it helps prevent unauthorized disclosure of sensitive information. By classifying derived information, access to it can be controlled, limiting its availability to individuals with appropriate security clearances. This restriction ensures that only authorized personnel can access and handle the information, reducing the risk of it falling into the wrong hands.
Derivative classification promotes information sharing within authorized channels. When information is properly classified, it can be shared securely among individuals or organizations that have the necessary clearances. This controlled sharing allows for effective collaboration and coordination among different entities while maintaining the confidentiality of the information.
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somebody
help me!!!
god will bless you
Answer:
2
Step-by-step explanation:
Which is the net for this triangular prism?
1
Answer:
The first one
Step-by-step explanation:
I think, because if you fold it, it will form the shape.
What is the mean of a set of data?
The mean set of the data is the average, you find it by adding all the numbers up then dividing it by the amount of numbers added.
Conan borrows $3,000 at a yearly simple interest rate of 1.6% for 2 years. He owes in interest. He needs to pay back in all.
Answer:
Interest: $96
He needs to pay back: $3,096
Step-by-step explanation:
1.6% = 0.016
(3000)(0.016) = $48
48 x 2 = $96
3,000 + 96 = $3096
If Conan borrows $3,000 at a yearly simple interest rate of 1.6% for 2 years. Then he has to pay 3009.6 back.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
Conan borrows $3,000 at a yearly simple interest rate of 1.6% for 2 years.
A=P(1+rt)
A is final amount
P is principal amount
r is rate of interest
t is time period.
P=3000, r=0.16%=0.16/100=0.0016, t=2
A=3000(1+(0.0016)2)
=3000(1+0.0032)
=3000(1.0032)
=3009.6
Hence Canon needs to pay back 3009.6
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A parallelogram is___a rhombus.
1. always
2.sometimes
3.never
A parallelogram is SOMETIMES a rhombus.
(It can also sometimes be a rectangle, and sometimes a square.)
(But rhombuses, rectangles, and squares are ALWAYS parallelograms. Also, squares are always rhombuses and rectangles.)
Cann someone please help??
option 1 is correct [5root2]
Answer:
It can be simplified to 5√2
Step-by-step explanation:
ASAP I WILL GIVE BRANILYIST ✨✨✨
Answer:
c,d
Step-by-step explanation:
for the first question
-3×5+5×-1/2 = -10 , so the answer is C
for the last question
3(x+2)-9
3x+6-9
3x-3 , so the answer is D
pls hurry!! i need this asap
Answer:
Look at image
Step-by-step explanation:
Look at image
Look at image
Which expressions are equivalent to this expression?
4x + 4
Select each correct answer.
2(2x+2)
4(x+4)
x + 3x + 4
2x + 1 + 2x + 3
Answer:
4(x+4)
Step-by-step explanation:
Answer:
2 ( 2x + 2 )
Step-by-step explanation:
4x = 2x * 2
4 = 2 * 2
4x + 4
= 2x * 2 + 2 * 2
= 2 ( 2x + 2 )
express the question below as function of angle less than 45°
[tex]cot330 [/tex]
step by step plzzz
Giving brainliest to correct answer
1/4 + 1/3 + 11/12 6/15 + 3/10 + 3/5
4/5 + 3/15 - 2/3 4 2/5 + 5 2/6
Step-by-step explanation:
0 = 0 = 0 = 0 = 0 = 0 = 0 < 3/
15
< 1/
4
< 3/
10
< 1/
3
< 6/
15
< 3/
5
< 4/
5
< 11/
12
< 4 2/
5
< 5 2/
6
0 is equal to 0 is equal to 0 is equal to 0 is equal to 0 is equal to 0 is equal to 0 is less than 3/
15
is less than 1/
4
is less than 3/
10
is less than 1/
3
is less than 6/
15
is less than 3/
5
is less than 4/
5
is less than 11/
12
is less than 4 2/
5
is less than 5 2/
6
0/
60
= 0/
60
= 0/
60
= 0/
60
= 0/
60
= 0/
60
= 0/
60
< 12/
60
< 15/
60
< 18/
60
< 20/
60
< 24/
60
< 36/
60
< 48/
60
< 55/
60
< 264/
60
< 320/
60
Step-by-step explanation:
[tex]6 \frac{2}{5} [/tex]
Identify an equation in point-slope form for the line parallel to y = 1x-7 that
passes through (-3,-2).
Answer:
y +2 = 1 (x +3)
Step-by-step explanation:
y = 1x - 7
Slope: 1
Point: (-3, -2)
15.7 x 102 = ___
1.57
15.7
157
1,570
[tex]15.7 \times 102 = 157[/tex]
What is a formula for the nth term of the given sequence? 2, 4, 8...
Answer:
[tex]2^{n}[/tex]
Step-by-step explanation:
2=[tex]2^{1}[/tex]
4=[tex]2^{2}[/tex]
8=[tex]2^{3}[/tex]
Sequence is based on 2 to the power of n where n is greater than or equal to 1.
Engineers are draining a water reservoir until its depth is only 10 feet. The depth decreases exponentially as
shown in the graph below. The engineers measure the depth after 1 hour to be 64 feet and after 4 hours to be
28 feet. Develop an exponential equation in y=a(6)" to predict the depth as a function of hours draining.
Round a to the nearest integer and b to the nearest hundredth. Then, graph the horizontal line y = 10 and
find its intersection to determine the time, to the nearest tenth of an hour, when the reservoir will reach a
depth of 10 feet.
The draining of the reservoir follows an exponential function
The reservoir will reach a depth of 10 feet at 7.6 hour
The given parameters are:
[tex]\mathbf{(x,y) = (1,64)(4,28)}[/tex]
An exponential equation is represented as:
[tex]\mathbf{y = ab^x}[/tex]
Substitute [tex]\mathbf{(x,y) = (1,64)(4,28)}[/tex] in [tex]\mathbf{y = ab^x}[/tex]
[tex]\mathbf{64 = ab^1}[/tex]
[tex]\mathbf{64 = ab}[/tex]
[tex]\mathbf{28 = ab^4}[/tex]
Divide [tex]\mathbf{64 = ab}[/tex] and [tex]\mathbf{28 = ab^4}[/tex]
[tex]\mathbf{\frac{ab^4}{ab} = \frac{28}{64}}[/tex]
[tex]\mathbf{b^3 = 0.4375}[/tex]
Take cube roots
[tex]\mathbf{b= 0.76}[/tex]
Substitute [tex]\mathbf{b= 0.76}[/tex] in [tex]\mathbf{64 = ab}[/tex]
[tex]\mathbf{64 = 0.76a}[/tex]
Solve for a
[tex]\mathbf{a = 84}[/tex]
So, the equation is:
[tex]\mathbf{y = 84(0.76)^x}[/tex]
See attachment for the graphs of [tex]\mathbf{y = 84(0.76)^x}[/tex] and y = 10
The point of intersection is: x = 7.6
Hence, the reservoir will reach a depth of 10 feet at 7.6 hour
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Solve the math problem
Answer:
negative
Step-by-step explanation
the slope is negative and/or its going lower as you go from left to right meaning its negative
brainliest for answers
Answer:
B
Step-by-step explanation:
if this is correct can i get brainliest and i hope this helps (:
2+3×5(-4)÷5
how does it work
