Answer:
C.
Step-by-step explanation:
i took the test
The standard form of the equation of the parabola that has a vertex of (-4,-3) and a directrix of x = 2 is (x+3)² = -24(y+4), the correct option is D.
What is vertex form of a quadratic equation?If a quadratic equation is written in the form
y=a(x-h)^2 + k
then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)
First of all, i used this vertex formula thing since it is visible that there are quadratic functions. Otherwise, you had to use calculus to get critical points, then second derivative of functions to find the character of critical points as minima or maxima or saddle etc to get the location of vertex point.
This point (h,k) is called the vertex of the parabola that quadratic equation represents.
We are given that;
The vertex of parabola=(-4,-3)
Directrix of x is 2
Now,
The distance from a point (x,y) to the directrix x = 2 is the horizontal distance between the point and the line, which is |x - 2|. The distance from a point (x,y) to the focus (-4,f) is the distance between the point and the vertex plus the distance between the vertex and the focus, which is |y - (-3)| + |-4 - 2| = |y + 3| + 6.
|y + 3| + 6 = |x - 2|
To eliminate the absolute value, we can square both sides of the equation:
(y + 3)² + 12(y + 3) + 36 = (x - 2)²
(x - 2)² = (y + 3)² + 12(y + 3) + 36
x² - 4x + 4 = y² + 6y + 9 + 12y + 36
x² - 4x = y² + 18y + 45
x² - 4x + 4 = y² + 18y + 49
(x - 2)² = (y + 9)²
This is the standard form of the equation of the parabola, which has a vertex of (-4,-3) and a directrix of x = 2. Comparing this equation with the standard form of the equation of a parabola, we can see that the parabola opens horizontally to the left, and its focus is the point (-6,-3).
(x-2)² = -24(y+9)
Therefore, the equation will be (x+3)² = -24(y+4).
Learn more about vertex form of a quadratic equation here:
https://brainly.com/question/9912128
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MCR3U1 Culminating 2021.pdf
#7.
A colony of bacteria is introduced into a growth medium. Its initial population
size is 350 thousand. 12 hours later, the colony has grown to a size of
800 thousand. If its population size increases exponentially, determine:
(a)
the exponential growth model for the size of the population Alt), after
t hours.
(b)
the population size after (i) 8 hours and (ii) 24 hours.
(c)
the rate of increase in the population size as a %/hour
(d)
the doubling time of the bacteria population.
Answer:
(a) [tex]y = 350,000 \times (1 + 0.07132)^t[/tex]
(b) (i) The population after 8 hours is 607,325
(ii) The population after 24 hours is 1,828,643
(c) The rate of increase of the population as a percentage per hour is 7.132%
(d) The doubling time of the population is approximately, 10.06 hours
Step-by-step explanation:
(a) The initial population of the bacteria, y₁ = a = 350,000
The time the colony grows, t = 12 hours
The final population of bacteria in the colony, y₂ = 800,000
The exponential growth model, can be written as follows;
[tex]y = a \cdot (1 + r)^t[/tex]
Plugging in the values, we get;
[tex]800,000 = 350,000 \times (1 + r)^{12}[/tex]
Therefore;
(1 + r)¹² = 800,000/350,000 = 16/7
12·㏑(1 + r) = ㏑(16/7)
㏑(1 + r) = (㏑(16/7))/12
r = e^((㏑(16/7))/12) - 1 ≈ 0.07132
The model is therefore;
[tex]y = 350,000 \times (1 + 0.07132)^t[/tex]
(b) (i) The population after 8 hours is given as follows;
y = 350,000 × (1 + 0.07132)⁸ ≈ 607,325.82
By rounding down, we have;
The population after 8 hours, y = 607,325
(ii) The population after 24 hours is given as follows;
y = 350,000 × (1 + 0.07132)²⁴ ≈ 1,828,643.92571
By rounding down, we have;
The population after 24 hours, y = 1,828,643
(c) The rate of increase of the population as a percentage per hour = r × 100
∴ The rate of increase of the population as a percentage = 0.07132 × 100 = 7.132%
(d) The doubling time of the population is the time it takes the population to double, which is given as follows;
Initial population = y
Final population = 2·y
The doubling time of the population is therefore;
[tex]2 \cdot y = y \times (1 + 0.07132)^t[/tex]
Therefore, we have;
2·y/y =2 = [tex](1 + 0.07132)^t[/tex]
t = ln2/(ln(1 + 0.07132)) ≈ 10.06
The doubling time of the population is approximately, 10.06 hours.
Kendra is saving to buy a new computer write an expression to represent them out of money she will have if she has a dollar saved and adds D dollar per week for the next 12 weeks
PLEASE I HAVE BRAINLY PLUS AND IT NOT WORKING SEND HELLP
Step-by-step explanation:
the answer is in the above image
but I do not get the meaning of Dy
PLEASE HELP ASAP, THIS IS A TIMED MATH QUESTION!!!
I'LL MARK BRAINLIEST FOR CORRECT ANSWERS!
the value of each square root
Answer:
root 324=18
root 441=21
root 529=23
Step-by-step explanation:
root 324 = 18
root 441 = 21
root 524 = 23
Help out please !!!!
Answer:
B maybe
Step-by-step explanation:
HELlLlLlPllLl is it
10
2
1
9
Answer:
2
Step-by-step explanation:
the volume of a cuboid is 480cm cube,it's breadth and height are 8cm are 6cm respectively find its length
The area of the base is 15cm. The height is 6 cm. What is the volume of the rectangular prism?
Step-by-step explanation:
P O R N G I R L S O N L Y
xni-jwtm-twb
Solve for x Log2 x=-5
g(x) = 3x -1. Find x such that g(x)= 20.
g(x)= 3x+1. Find x such that g(x)= 22.
g(x)= 2x-5. Find g(1/2) and g(a)=99.
g(x)=x+5/2. Find g(3), g(0), g(-3) and g(x)=0
Please solve this quickly. I need it right now. No silly answer will not be allowed.
Step-by-step explanation:
i. 3x-1=20
or, 3x= 21
x= 7
ii. 3x+1= 22
3x= 21
x= 7
iii. 2x-5=99
2x= 104
x=52
iv. g(3)= 3+5/2= 11/2
g(0)= 0+ 5/2=5/2
g(-3)= -3+5/2 = -1/2
x+5/2= 0
so, x= -5/2
2 to the power of 4 - 3+2x5
Answer:
121
Step-by-step explanation:
(4 - 3+2·5)²
Multiply
(4-3+10)²
Now add and subtract
(1+10)²
11²
121
Is each statement true for OA? Drag “true” or “false” below each statement
Answer:
true. true. false.
Step-by-step explanation: i’m in love with the shape of u. we push and pull like magnet whatever
Can somebody pls help
Answer:
A, c, d
Step-by-step explanation:
Answer:
C & D
Step-by-step explanation:
In order to find the perimeter, we would need to add all the sides. w+L+w+L would be adding the lengths and the widths. Simplifying this, we would get 2w, because there are 2 sides that are the same width, and 2 sides that are 2 lengths.
w+L+w+L or w+w+L+L or 2w+2L
Hope this helps!
--Applepi101
Factor the common factor out of each expression: 30+6k+18k^5
how do you do this?
Step-by-step explanation: 6 22 22 51
one orange box is 10 the other box looks like 15
the scale factor is 15/10 or 1.5
the smaller triangle blue box is a 4
multiply 4 by the scale factor 1.5
4 × 1.5 = 6
Assume that a cell is a sphere with a radius of 10-³ or 0.001 centimeters and that a cell’s density is 1.1 grams per cubic centimeter.
Koalas weigh 6 kilograms on average. How many cells are in the average koala?
Answer:
[tex]n=1.3\times 10^{12}[/tex]
Step-by-step explanation:
Given that,
The radius of a cell, r = 10⁻³ cm
The density of the cell, d = 1.1 g/cm³
The weight of the Koala, m = 6 kg = 6000 grams
The density of an object is given by:
[tex]d=\dfrac{m}{V}[/tex]
For n cells,
[tex]nd=\dfrac{m}{V}\\\\n=\dfrac{m}{dV}[/tex]
Put all the values,
[tex]n=\frac{6000}{\frac{4}{3}\cdot\pi\cdot\left(10^{-3}\right)^{3}\cdot1.1}\\\\n=1.3\times 10^{12}[/tex]
So, there are [tex]1.3\times 10^{12}[/tex]cells in the average koala.
expand and simplify
2(3x - 5) + 3(x + 3)
can someone do this ASAP pls with no links :)
Answer:
9x-7
Step-by-step explanation:
2(3x-5) = 6x - 10
3(x+3) = 3x + 3
= 9x-7
Answer:
Step-by-step explanation:
2*(3x-5)+3(x+3)=2*3x - 5*2 + x*3 + 3*3
= 6x - 10 + 3x + 9
= 6x + 3x - 10 + 9 {Combine like terms}
= 9x - 1
Which quadrilateral makes this statement true? Quadrilateral ABCD ≅ _____  A.   B.   C.   D. 
Which of the following correctly maps figure ABCD onto figure EFGH? Select two that apply.
Answer:
Option A
Step-by-step explanation:
From the graph attached,
Distance of point A of rectangle ABCD = 5 units
Distance of point E of rectangle EFGH = 5 units
Similarly, all the vertices of the rectangles ABCD and EFGH are equidistant from the y-axis.
Therefore, rectangle ABCD and rectangle EFGH may overlap each other by reflecting each other across y-axis.
Let's check by the rule of reflection,
Rule for the reflection of a point (x, y) across y-axis is given by,
(x, y) → (-x, y)
Following this rule,
A(-5, 5) → E(5, 5)
B(-3, 4) → F(3, 4)
C(-4, 1) → G(4, 1)
D(-6, 2) → H(6, 2)
Therefore, rule for the reflection is applicable in this question.
Option A will be the answer.
Simo scored 65 points in a game. Ella scored e points in the same game. If they scored a total of t points for the game, write an equation that expresses t in terms of e. You will not solve this equation, just write it.
Answer:
Step-by-step explanation:
Lucy=65
Eva= X points
Total:
Points = 65 + 65 = 130
Suppose the population of a small town is 567 in 2011. The population DECREASES at a
rate of 5% every year. What will be the population of the town in 2021? Round your answer
to the nearest whole number.
Answer:
2011: 567 2012: 567*(1-.015) 2013: 567*(1-.015)*(1-.015) 2014: 567*(1-.015)567*(1-.015)*(1-.015) you see the pattern; and, if so, you can build an little equation giving you the answer
Answer:
339
Step-by-step explanation:
a = 567 (.95)¹⁰
a = 339.4838445482
Rounded
339
Name the set(s) of numbers to which –5 belongs. a. whole numbers, natural numbers, integers b. rational numbers whole numbers, integers, rational numbers d. integers, rational numbers c.
5 belong to whole number. b I don't know
Someone PLEASE HELP!!!!! it’s urgent please help ASAP
The line the puck traveled is the hypotenuse of a right triangle.
Using the Pythagorean theorem:
Travel = sqrt( 4^2 + 30^2)
Travel = sqrt( 16 + 900)
Travel = sqrt(916)
Travel = 30.265 feet ( round the answer as needed)
Can some help me solve this.
Answer:
The fourth (last) function is the correct one.
Step-by-step explanation:
Look at the parent function y = √x, Its graph goes through (0, 0). On the other hand, if y = √(x - h), the graph goes through (h, 0) if h is positive, and the graph is translated h units to the right from the graph of y = √x. If h is negative, the graph is translated h units to the left.
In the four possible answers given, the values of h are {-4, 9, 5, -9}, in that order. h = -9 results in the graph that is positioned 9 units to the left of the graph of y = √x. This graph is furthest to the left. Thus the fourth choice is the correct one.
If 3x - 4y = 15 and -2x + 3y = 10, then x - y = ?
Answer:
x - y = 25
Step-by-step explanation:
3x - 4y = 15
-2x + 3y = 10
Add the two equations together
3x - 4y = 15
-2x + 3y = 10
----------------------
x - y = 25
Answer:
[tex]{\Huge{\underline{\underline{\textbf{\textsf{Answer}}}}}}[/tex]
>> 3x - 4y = 15
>> -2x + 3y = 10
Add the two equations together
>> 3x - 4y = 15
>> -2x + 3y = 10
----------------------
Hence, x - y = 25
Please help i'm struggling with this!
Answer:
second option is correct (for question no 20)
Step-by-step explanation:
coordinate points are:
(3,1) = (x1,y1)
(5,9) = (x2,y2)
slope (m) = y2-y1/x2-x1
=9-1/5-3
=8/2
=4
Now using slope intercept form
y=mx + b
y=4x + b
since the line passes through the point (3,1) it satisfies the equation
y=4x + b
1=4*3 + b
1-12 = b
-11 = b
substituting the value of b in equation
y=4x + b
y=4x +(-11)
y=4x - 11
I just want to make sure or is it b?
how many tons is 9,000 lbs?
Answer:
9000 Pounds (lbs) = 4.017859 Tons (t)
1 lbs = 0.000446 t
1 t = 2,240 lbs
Step-by-step explanation:
Determine the vertex of the quadratic relation y= 4x2 + 32x – 11
Answer:
vertex = (- 4, - 75 )
Step-by-step explanation:
Given a quadratic in standard form
y = ax² + bx + c ( a ≠ 0 )
Then the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
y = 4x² + 32x - 11 ← is in standard form
with a = 4, b = 32 , then
x = - [tex]\frac{32}{8}[/tex] = - 4
Substitute x = - 4 into the equation for corresponding y- coordinate
y = 4(- 4)² + 32(- 4) - 11
= 4(16) - 128 - 11
= 64 - 139
= - 75
vertex = (- 4, - 75 )
