Answers
Answer:
(a) [tex]y=x^2-2x-8[/tex]
(b) [tex]y= -\dfrac12x^2+4x-6[/tex]
Step-by-step explanation:
(a) From inspection of the graph, the x-intercepts (where [tex]y = 0[/tex]) are at
[tex]x = -2[/tex] and [tex]x =4[/tex].
Therefore [tex]y = a(x + 2)(x - 4)[/tex] where [tex]a[/tex] is some constant
The y-intercept is at (0, -8)
Expanding the equation:
[tex]y = a(x + 2)(x - 4)[/tex]
[tex]\implies y = a(x^2-4x+2x-8)[/tex]
[tex]\implies y= ax^2-2ax-8a[/tex]
Therefore, -8a is the y-intercept
Comparing y-intercepts: -8 = -8a ⇒ a = 1
Substituting a = 1, the final equation in standard form is:
[tex]y=x^2-2x-8[/tex]
--------------------------------------------------------------------------------------------------
(b) From inspection of the graph, the x-intercepts (where [tex]y = 0[/tex]) are at
[tex]x = 2[/tex] and [tex]x =6[/tex].
Therefore [tex]y = a(x -2)(x - 6)[/tex] where [tex]a[/tex] is some constant
The y-intercept is at (0, -6)
Expanding the equation:
[tex]y = a(x -2)(x - 6)[/tex]
[tex]\implies y = a(x^2-6x-2x+12)[/tex]
[tex]\implies y= ax^2-8ax+12a[/tex]
Therefore, 12a is the y-intercept
Comparing y-intercepts:
[tex]-6 = 12a \implies a = -\dfrac12[/tex]
Substituting found value of a into the equation:
[tex]\implies y= (-\dfrac12)x^2-8(-\dfrac12)x+12(-\dfrac12)[/tex]
[tex]\implies y= -\dfrac12x^2+4x-6[/tex]
y = a(x-h)²+k where (h,k) denotes the vertex
Q.1)
vertex: (1, -9) where h=1, k = -9
coordinates: (0, -8) where x = 0, y = -8
find for a:
y = a(x-h)²+k
-8 = a(0-1)²-9
-8 = a -9
a = 1
============
equation: y = (x-1)²-9
Q.2)
vertex: (4, 2) where h=4, k = 2
coordinates: (2, 0) where x = 2, y = 0
find for a:
y = a(x-h)²+k
0 = a(2-4)²+2
-2 = 4(a)
a = -1/2
============
equation: y = -1/2(x-4)²+2
Related Questions
AA culture started with 4000 bacteria. after 5 hours it grew to 4800 bacteria. Predict how many bacteria will be present after 15 hours. Round your answer to the nearest whole number. p=ae^kt
Answers
Answer:
p = 6912 after 15 hoursp = 4000·e^(0.036463t)Step-by-step explanation:
We want to model the growth of a population of bacteria using an exponential function. We find it convenient to use an "exact" exponential function that relies directly on the numbers given in the problem statement. That function has the form ...
p(t) = (initial population) × (growth factor)^(t/(growth period))
where the "growth factor" is the multiplying factor of the population in period "growth period."
__
Exponential Function (1)Here, the "growth factor" is 4800/4000 = 1.2, and the corresponding "growth period" is 5 hours. Then the population function can be ...
p(t) = 4000×1.2^(t/5)
__
PopulationThe population after 15 hours is ...
p(15) = 4000×1.2^(15/3) = 4000×1.728
p(15) = 6912
__
Exponential Function (2)To change this to the form ae^(kt), we find the value of k to be ...
k = ln(1.2^(1/5)) = ln(1.2)/5 ≈ 0.036463
Then the desired form of the function for p is ...
p(t) = 4000·e^(0.036463t)
_____
Additional comment
In the form p=ae^(kt) the value of k is often rounded to 3 or 4 decimal places. We believe that best accuracy is obtained if k has at least the number of significant digits expected in the answer. Here, the population of almost 7000 has 4 significant digits, so we choose to express k to 5 significant figures. That still gives a small error relative to the first formula that is only "corrected" by rounding the result to an integer.
Choose an appropriate metric unit for the mass of bowling ball
A)
kilogram
B)
milligram
C)
meter
D)
gram
Answers
Answer:
i think that the correct answer would A
Step-by-step explanation:
hope this helps
Find the volume of the
following triangular prism.
height: 2cm
length: 5cm
width: 3.5cm
A. 17.5cm3
B. 35cm3
C. 42.5cm3
D. 45cm3
Answers
9. If triangle GFE - triangle GHJ, find the value of x.
Answers
Answer:
2
Step-by-step explanation:
→ Find the scale factor
12 ÷ 7.5 = 1.6
→ Form an equation
x + 6 = 1.6 ( 2x+ 1 )
→ Solve
x = 2
Pharmaceutical scientists tested the effectiveness of a new drug designed to cure malaria. They randomly
assigned 400 infected lab rats to receive either the new drug or an existing drug and recorded how many
rats were cured at the end of the study. Here are their results:
Cured
Not
Total
New drug
176
24
200
Existing drug
168
32
200
They want to use these results to construct a 99% confidence interval to estimate the difference in the
proportion of these rats that would be cured under each drug (new - existing). Assume that all of the
conditions for inference have been met.
Which of the following is a correct 99% confidence interval based on their data?
Choose 1 answer:
8 +0.068
Answers
Using the z-distribution, as we are working with a proportion, it is found that the 99% confidence interval is (-0.049, 0.129).
What is the mean and the standard error for the distribution of differences?For each sample, we have that:
[tex]p_N = \frac{176}{200} = 0.88, s_N = \sqrt{\frac{0.88(0.12)}{200}} = 0.023[/tex]
[tex]p_E = \frac{168}{200} = 0.84, s_E = \sqrt{\frac{0.84(0.16)}{200}} = 0.0259[/tex]
Hence, for the distribution of differences, the mean and the standard error are given as follows:
[tex]p = p_N - p_E = 0.88 - 0.84 = 0.04[/tex]
[tex]s = \sqrt{s_N^2 + s_E^2} = \sqrt{0.023^2 + 0.0259^2} = 0.0346[/tex]
What is the confidence interval?It is given by:
[tex]p \pm zs[/tex]
99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
Then:
[tex]p - zs = 0.04 - 2.575(0.0346) = -0.049[/tex]
[tex]p + zs = 0.04 + 2.575(0.0346) = 0.129[/tex]
The 99% confidence interval is (-0.049, 0.129).
To learn more about the z-distribution, you can check https://brainly.com/question/25890103
Answer: 0.04, 0.089
Step-by-step explanation:
The Pythagorean theorem states that a² + b² = c² for a right triangle with leg lengths, a and b, and hypotenuse length, c.
The hypotenuse of a right triangle is 5 units long and has the points (3, 0) and (0, 4) as end points. One of the legs has length 3.
Use the Point and Segment tools to draw a right triangle at demonstrates the other leg length is 4.
Answers
Answer:
Step-by-step explanation:
Draw the third point at (0, 0). This would make the distance from (3,0) to (0,0) equal to 3, and the distance from (0,4) to (0,0) be 4.
what is equivalent to 2
x
2
−
7
x
−
3
=
0
Answers
Answer:
I'm confused with this, I dont understand what you are asking.
Step-by-step explanation:
2 is equivalent with a lot of things,
1+1
3-1
92-90
7×7-47
4÷2
the list goes on...
In the past year, Jose watched 32 movies that he thought were very good. He watched 80 movies over the whole year. Of the movies he watched, what percentage did he rate as very good?
Answers
Answer:
40%
Step-by-step explanation:
Givens and Formula
% Good = (number good / total number) * 100
% Good = ?
Number Good = 32
Total Number = 80
Solution
% Good = (32 / 80) * 100
% Good = 2/5 * 100
% Good = 40%
Irwin rode his bicycle from one end of a trail to another and back at a speed of 20 miles per hour. If the trail is 4 miles long, for how many hours was Irwin riding?
Answers
Answer:
it’s C. 2.5
Step-by-step explanation:
Sonya took out a mortgage of $65,000 at 7% for 25 years. What is the cost of the mortgage?
Answers
The cost of the mortgage is $81250
What are interests?
Interests are percentages of a principal
Given the following parameters
Principal = $65000
Rate = 7% = 0.07
Time = 5 years
I = PRT/100
I = 65000*0.07*25
I = 16,250
Cost of mortgage = Principal + Interest
Cost of mortgage = 65000 + 16250
Cost of mortgage = 81,250
Hence the cost of the mortgage is $81250
Learn more on mortgage here: https://brainly.com/question/22846480
Answer:
$72,823
Step-by-step explanation:
just took test
According to the labor statistics document, which educational level has the highest median
income?
Answers
The doctoral degree educational level has the highest median income
What are educational level?Education level refers to the years of formal instruction received and successfully completed.
From research in 2017 for those with the highest levels of educational level (doctoral and professional degrees) income is more than triple those with the lowest level (high school diploma)
Find out more on educational level at: https://brainly.com/question/2987151
Answer: Bachelor's Degree, and Male
Step-by-step explanation:
Jerry poured water to a height of 1 feet into a
new aquarium with dimensions shown below.
2 ft.
1 ft.
Water
2
3 ft.
One cubic foot of water weighs approximately
62 pounds. What is the weight of the water that
Jerry put in the aquarium?
B. 465 pounds
A. 403 pounds
C. 558 pounds
D. 744 pounds
Answers
Since 1 cubic feet = 62 pounds, the weight of the water that Jerry put in the aquarium is 558 pounds
How to calculate the volume/weight of waterWe have to find the volume of water in the aquarium.
Recall the shape of the aquarium is a rectangular prism. Therefore,
volume = lwh
where
l = lengthw = widthh = heightTherefore,
l = 3 ft
w = 2 ft
h = 1.5 ft
volume = 3 × 2 × 1.5
volume of water = 9 ft³
Therefore,
1 ft³= 62 pounds
9 ft³ = ?
cross multiply
weight of water = 9 × 62
weight of water = 558 pounds
learn more on volume here:https://brainly.com/question/24357711
Drag each expression to its equivalent.
Answers
Answer:
5x+4=2x+3-x+1+4x
7x=3+2x+4+5x-7
2x+3=8+10x-8x-5
2x+3-x+1+4x = 5x+4 and 7x-5-2x+9 = 5x +4
3+2x+4+5x-7 = 7x and x-1+2x+2+4x-1 = 7x
3+2x+4+5x-7 = 7x and x+6-2x-3=2x+3
These are the equivalent expressions.
What is an expression?
It is a sentence with a minimum of two numbers or variables and at least one math operation.
Given expression can be solved like:
1. 2x+3-x+1+4x = 5x+4
Which is same as the first option.
2. 7x-5-2x+9 = 5x +4
Which is same as the first option.
3. 8+10x-8x-5 = 2x+3
Which is same as the third option.
4. 3+2x+4+5x-7 = 7x
Which is same as the second option.
5. x-1+2x+2+4x-1 = 7x
Which is same as the second option.
6. 4x+6-2x-3=2x+3
Which is same as the third option.
Hence, the equivalent options are :
2x+3-x+1+4x = 5x+4 and 7x-5-2x+9 = 5x +4
3+2x+4+5x-7 = 7x and x-1+2x+2+4x-1 = 7x
3+2x+4+5x-7 = 7x and x+6-2x-3=2x+3
To learn more about expression, use the link given below:
https://brainly.com/question/14083225
#SPJ2
find the equation (in the terms of x) of the line through the points (-2,-5) and (5,0)
Answers
Answer:
-5x+7y+25=0
Step-by-step explanation:
vecto AB= (7;5)
vecto n = (-5;7)
line through the points (-2;5) and (5;0) :
-5*(x+2)+7*(y+5)=0
-5x+7y+25=0
Q. 1. Solve for x using determinants, x + y = 9, x - y + 3z = 2 and 4y - 32 - 5 = 0.
Answers
Hello!
x + y = 9,
x= 9-y
x - y + 3z = 2
x= 2+y -3z
4y - 32 - 5 = 0.
4y = 32+5
4y = 37
y = 37/4
A rectangular prism has a length of 20 meters, a height of 12 meters,
and a width of 12 meters. What is its volume, in cubic meters?
Answers
Answer:
2880 cubic meters.
Step-by-step explanation:
To find the area of a rectangular prism, multiply the length width and height.
20*12*12=144*20=2880
The volume of the Rectangular Prism is 2880 cubic meters.
What is Rectangular Prism?Rectangular prism can be defined as a" 3-dimensional solid shape which has six faces that are rectangles. A rectangular prism is also a cuboid".
According to the question,
Length of the rectangular prism = 20 meters
Height of the rectangular prism = 12 meters
Width of the rectangular prism = 12 meters
Formula for Rectangular Prism = length × breadth × height
= 20 × 12 × 12
= 2880 cubic meters.
Hence, the volume of the Rectangular Prism is 2880 cubic meters.
Learn more about Rectangular Prism here
https://brainly.com/question/22539378
#SPJ2
Which of the following expressions does NOT represent
91 +91 + 91?
O 91(3)
O 91.3
O (91)(3)
0913
Answers
Answer:
91.3 and 0913
Step-by-step explanation:
91 + 91 + 91 is an expression that can be simplified into a multiplication problem, because there is a number being added by itself a certain amount of times. So we have to look for a multiplication problems within our answers.
Leading us up to 91(3) and (91)(3), these are both examples of multiplcation.
91.3 would happen if you were adding .3 to 91
And 0913 would happen if you added 91 and 822
Choose the number (X) that should come next in this series (1 4 9 16 X).
20
23
25
27
Answers
Answer:
25
Step-by-step explanation:
[tex]1^2=1\\\\2^2=4\\\\3^2 = 9\\\\4^2=16\\\\\text{So the next number should be}~ 5^2=25[/tex]
A group of people are fundraising, and each person raises a certain amount of money for every mile they walk. Each person's fundraising is represented below using d for the dollars that person raises and w for the miles that person walks. Select all the representations that can be described by the equation d = 2w.
Answers
Answer:
B, C, EStep-by-step explanation:
According to coordinates on the graphs and numbers in the tables we have the following relationship:
A) d = 1/2wB) d = 2wC) d = 2wD) d is not proportional with w since 12/6 ≠ 18/10 ≠ 20/12E) d = 2wAs we see B, C and E have same relationship, matching the target.
Step-by-step explanation:
hope it's help you this answer
i am confused please help
Answers
Answer:
volume = lenght x width x height
v= 12x20x14
v=3,360 in³
Determine whether the following statement is true or false. If false, provide a counterexample. If two events are independent, then the probability of both events is less than 1
Answers
Answer:
TRue
Step-by-step explanation:
5th root of 0.06
please I need fast only answer
Answers
Steps:
Raise 0.06 to the power of 1/5
0.56967905
7*8/10 product lies between what numbers
Answers
Answer:
5 and 6.
Step-by-step explanation:
7*8 is 56. 56 divided by 10 is 5 6/10
Help help help ASAP help
Answers
Answer:
(8, -2)
Step-by-step explanation:
While reflection over x-axis, the x-coordinate remains the same and the y-coordinate changes to it's opposite.
So,
Rx-axis => = (8, -2)
linear exponential function
y=5.3×
Answers
Answer:
y=5x
which means 3 will be dedicated to 5
so 5=3y
Question 3 of 5
The cylindrical part of an architectural column has a height of 295 cm and a
diameter of 30 cm. Find the volume of the cylindrical part of the column. Use
3.14 for it and round your answer to the nearest cubic centimeter if needed.
30 cm
-I
295 cm
O A. 833,670 cm3
OB. 208,418 cm
O C. 27,789 cm3
O D. 29,217 cm
Answers
Solve each of the following equations. Show its solution set on a number line. Check your answers. 7m+4=1
PLS HELP WILL GIVE BRAINLIEST
Answers
Subtract 4 from both sides 7m+4-4=1-4
7m=-3
Divide both sides by 7
7/7m =-3/7
M=-3/7
Answer:
x=-3/7;x=-5/7
Step-by-step explanation:
Consider the rectangle with width 4 ft and length 18 ft, write a ratio of the length to the width.
Answers
Answer: 18:4
Step-by-step explanation:
Ez
Answer:
9 : 2
Step-by-step explanation:
length : Width = 18 : 4
[tex]\sf = \dfrac{18 \ \div \ 2}{4 \ \div \ 2}\\\\=\dfrac{9}{2}[/tex]
= 9 : 2
Z
77°
P
W
X
What is the measure of arc XWZ?
OA
257°
O B. 1039
O C. 206°
O D. 1543
Answers
Under a dilation, the point (2, 6) is moved to (6, 18).
What is the scale factor of the dilation?
Enter your answer in the box.
Answer quick please !!!
Answers
Answer:
3
Step-by-step explanation:
Answer: The correct answer is 3
Step-by-step explanation:
:) it should be correct have a good day!