Graph the equation y = x2 + 6x + 5 on the accompanying set of axes. You must
plot 5 points including the roots and the vertex.
Answers
Answer:
Please check the graph below.
Step-by-step explanation:
Given the function
[tex]y\:=\:x^2\:+\:6x\:+\:5[/tex]
Axis interception points of the function
x-axis interception points can be computed by setting y=0
[tex]x^2+6x+5=0[/tex]
[tex]\left(x+1\right)\left(x+5\right)=0[/tex]
Using the zero factor principle
if [tex]\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)[/tex]
[tex]x+1=0\quad \mathrm{or}\quad \:x+5=0[/tex]
[tex]x=-1,\:x=-5[/tex]
Hence,
x-axis interception points are: (-1, 0), (-5, 0)
y-axis interception points can be computed by setting x=0
[tex]x^2+6x+5=0[/tex]
[tex]y\:=\:\left(0\right)^2\:+\:6\left(0\right)\:+\:5[/tex]
[tex]y=0+0+5[/tex]
[tex]y=5[/tex]
Hence,
y-axis interception points are: (0, 5)
From the graph, it is clear that at (-3, -4) the parabola changes direction, hence (-3, -4) it the "vertex".
Also at the point x=-2, then y is = -3
So, all the points are labeled and the graph is attached below.
Related Questions
2. Convert 25.2625° from decimal degrees to degrees-minutes-seconds.
Answers
Answer:15
Step-by-step explanation:
Can anyone help me with this plzz?
Answers
===========================================================
Explanation:
Check out figure 1 in the attached images below. In this figure, I've plotted the function y = 6/(2x-3) on a 2D grid system. The function curve is in blue. Then I've plotted (2,0) and (3,0) on the x axis. Point A is somewhere between those endpoints. Point A is also on the x axis. Directly above A is point B such that B is on the blue function curve.
The distance from A to B is found by subtracting the y values of each point.
The y coordinate of A is y = 0. The y coordinate of B is y = 6/(2x-3)
Therefore, the distance from A to B is 6/(2x-3) units. This will form the radius of each cylindrical slice as figure 2 shows. Note the color coding to help see how the 2D view corresponds to the 3D view. The xy plane has been laid flat on the floor. So we're viewing the function curve at a downward angle now. Each of those gray cylinders combine to form an approximate 3D volume. The more cylinders we have, and the finer the cuts, the more accurate the total volume.
So it comes down to finding the volume of each cylindrical slice and adding up the volumes. This is effectively what integral calculus is all about.
------------------------------------
Since the radius of each cylinder is y = 6/(2x-3), this means r = 6/(2x-3) is plugged into the formula
V = pi*r^2*h
which is the volume of a cylinder formula
The height of each cylinder is delta x, which we'll use dx for short. So this is where the dx comes from in integrals.
This is what the integral will look like
[tex]\displaystyle V = \int_{2}^{3} \pi*\left(\frac{6}{2x-3}\right)^2dx[/tex]
which turns into
[tex]\displaystyle V = 36\pi\int_{2}^{3}\frac{1}{(2x-3)^2}dx[/tex]
after a bit of algebra. We're able to factor the 36pi out because it's a constant
From here we use u-substitution. Let u = 2x-3
This leads to du/dx = 2 which can be solved to dx = du/2
Since u = 2x-3, the lower endpoint x = 2 leads to
u = 2x-3 = 2*2-3 = 1
and x = 3 leads to
u = 2x-3 = 2*3-3 = 3
So the interval 2 < x < 3 turns into 1 < u < 3
After using u-sub, making the proper replacements, and integrating, we get
[tex]\displaystyle V = 36\pi\int_{2}^{3}\frac{1}{(2x-3)^2}dx\\\\\\\displaystyle V = 36\pi\int_{1}^{3}\frac{1}{u^2}\frac{du}{2}\\\\\\\displaystyle V = 36\pi*\frac{1}{2}\int_{1}^{3}\frac{1}{u^2}du\\\\\\\displaystyle V = 18\pi\int_{1}^{3}u^{-2}du\\\\\\\displaystyle V = 18\pi\left[-u^{-1}+C\right]_{1}^{3}\\\\\\\displaystyle V = 18\pi\left[-\frac{1}{u}+C\right]_{1}^{3}\\\\\\[/tex]
Let's evaluate that to get the following
[tex]\displaystyle V = 18\pi\left[-\frac{1}{u}+C\right]_{1}^{3}\\\\\\\displaystyle V = 18\pi\left[\left(-\frac{1}{3}+C\right)-\left(-\frac{1}{1}+C\right)\right]\\\\\\\displaystyle V = 18\pi\left(-\frac{1}{3}+1\right)\\\\\\\displaystyle V = 18\pi\left(\frac{2}{3}\right)\\\\\\\displaystyle V = 12\pi\\\\\\[/tex]
So the 3D volume formed by rotating that region (under the curve from x = 2 to x = 3) is exactly 12pi cubic units
if the cost of 8 mobile set is rs 40,000.how many mobile sets can be purchased for Rs 100,000
Answers
Answer:
20 mobile sets.
Step-by-step explanation:
Every mobile set costs:
40000 / 8
= 5000 Rs.
Therefore, for 100,000 Rs, the number of mobile sets that can be purchased is:
100,000 / 5000
= 20 mobile sets.
Hope this helped!
A car travels 61 miles per hour. At this rate, how far will the car travel in 5 hours?
Answers
Answer:
305 miles per hour
Step-by-step explanation:
61 miles per hour
61(5)= 305 miles/ hour
There were 42 mangoes in each crate. 12 such crates of mangoes were delivere to a factory. 4 mangoes were rotten and had to be thrown away. The remaining mangoes were packed into boxes of 10 mangoes each. How many mangoes were left after the 4 rotten ones were thrown away? * Your answer
Answers
Answer: 50
Step-by-step explanation: 42x12=504. 504-4=500. 500/10=50.
Answer:
Total Mangoes = 50
Rotten = 46
Step-by-step explanation:
50 divided by 10 = 5.
50 minus 4 is 46.
Answer correctly please !!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!!
Answers
m HGJ = (2x + 36)
Find m FGH
X = 14
7x16 112
2x16 32+36 68
68+112= 180
The answer is x = 16
Give brainest pls
A cuboid with a volume of 925cm^3 has dimensions.
4cm, (x + 1) cm and (x + 11) cm.
Show clearly that x^2 + 12x - 220 = 0
Solve the equation by factorising, making sure you show the factorisation.
State both values of x on the same line.
Finally, find the dimensions of the cuboid, writing all three on one line.
Answers
Answer:
Step-by-step explanation:
Volume of the cuboid = Length * Width * Height
Given
Length = 4cm
Width = (x+1)cm
Height = (x-11)cm
Volume of the cuboid = 4(x+1)(x+11)
Volume of the cuboid = 4(x^2+11x+x+11)
Volume of the cuboid = 4(x^2+12x+11)
Volume of the cuboid = 4x*2+48x+44
925 = 4x*2+48x+44
4x*2+48x+44-925 = 0
4x*2+48x-881 = 0
Divide through by 4
x^2 + 12x - 220.25 = 0
Factorize using the general formula;
x = -12±√12²-4(-220.25)/2
x = -12±√144+881/2
x = -12±√1025/2
x = -12±32/2
x = 12+32/2
x = 20/2
x = 10
Hence the dimension of the cuboid is 4cm, (10+1)cm and (10+11)cm
Dimension is 4cm by 11cm by 21cm
Simplify.
Rewrite the expression in the form 4^x.
4^4 x 4^3 = ??
Answers
Answer:
[tex]4^{7}[/tex]
Step-by-step explanation:
To simplify the expression [tex]4^{4}\times4^{3}[/tex], we can use the first law of the law of indices which states that the exponent is added together when multiplying numbers with the same base. Eg: [tex]a^{x}\times a^{y} = a^{x+y}[/tex].
[tex]4^4 \times4^3=4^{4+3}[/tex]
[tex]=4^{7}[/tex]
Hope this helps :)
If using the method of completing the square to solve the quadratic equation x squared -20x+24=0, which number would have to be added to “complete the square”
Answers
Oksuru k diyaf ramincok ani kasilm asiyla olusan bir refle kstir.
A carpenter use 65 shelves to make 13 bookcases. She uses the same number of shelves for each bookcase. Are 32 shelves enough to build 6 more bookcases?
Answers
Answer:
Yes.
Step-by-step explanation:
First, find the unit rate for 1 bookcase.
65 ÷ by 13 = 5 (unit rate)
Then, multiply the unit rate by the bookcases the carpenter wants to make.
6 · 5 = 30
Finally, subtract the shelves the carpenter wants to use by 30.
32 - 30 = 2 shelves.
Therefore, 32 shelves is enough to build 6 more bookcases. <3
a university department administers a survey regardring student satisfaction based on the survey results the department provides a confidence interval estimate of 60% to 80% for student satisfaction if the department wishes to construct a confidence interval the more accurate represents the proportion of a student satisfaction how should the design be altered
Answers
Answer:
Change the confidence interval.
Step-by-step explanation:
The confidence interval should be altered . If a 95 % or 90% confidence interval is set then better results can be obtained for student satisfaction.
A 90 or 95 or 99 percent confidence interval will show a greater range of the data that lies within or without the given criteria.
95 % confidence interval does not mean that the probability is 95% . It means that we are 95% of the data lies or does not lie within the specific range.
This gives better results as compared to 60- 80 % confidence intervals.
If 95% of the students are satisfied as compared to 60% or 80% , this shows more accuracy.
A rock is thrown from a cliff into a ravine. The function ℎ() = −16^2 + 19 + 2560 describes the height, in feet, of the rock from the ground seconds after it is thrown. What is the height of the rock, in feet, 2 seconds after it is thrown?
Answers
Answer:
d
Step-by-step explanation:
At Cheng's Bike Rentals, it costs 31 to rent a bike for 6 hours.
How many hours of bike use does a customer get per dollar?
Answers
Answer:
0.2hrs/dollars
Step-by-step explanation:
Given parameters:
Cost of bike = $31
Time duration = 6hrs
Unknown:
Hours customers get per dollar = ?
Solution:
The number of hours customer gets per dollar is;
Number of hrs/dollar = [tex]\frac{time duration }{cost}[/tex]
Number of hrs/dollar = [tex]\frac{6hrs}{31}[/tex]
Number of hrs/dollar = 0.2hrs/dollars
A small town has two local high schools. High School A currently has 850 students and is projected to grow by 35 students each year. High School B currently has 700 students and is projected to grow by 60 students each year. Let AA represent the number of students in High School A in tt years, and let BB represent the number of students in High School B after tt years. Write an equation for each situation, in terms of t,t, and determine after how many years, t,t, the number of students in both high schools would be the same.
Answers
An equation for each situation, in terms of t, is y = 850e^35t and
y = 700e^70t
The required equation will be in the form y = Ae^kt
where:
k is the growth constantA represents the number of students in High School A in t years.B represents the number of students in High School B after t years.If High School A currently has 850 students and is projected to grow by 35 students each year, hence;
A = 850k = 35 (growth factor)Substituting into the formula, we will have:
y = 850e^35t
If High School B currently has 700 students and is projected to grow by 60 students each year, hence;
A = 700k = 60 (growth factor)Substituting into the formula, we will have:
y = 700e^70t
An equation for each situation, in terms of t, is y = 850e^35t and
y = 700e^70t
Learn more on exponential function here: https://brainly.com/question/12940982
What's 6+2x^2 in factored form?
Answers
Answer:
2 ( x^2 + 3 )
Step-by-step explanation:
The points in each table lie on a line. Find the slope of the line.
O 1/2
O 1
O 2
O None of the above
Answers
Answer:
1
Step-by-step explanation:
Given table:
x -1 1 3 5
y -2 0 2 4
Unknown:
Slope of the line = ?
Solution:
Each x and y pair on the table lies on the line. Therefore, we can use them to find the slope;
Slope = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
let us take;
x₁ = -1 x₂ = 3
y₁ = -2 y₂ = 2
Insert the parameters and solve;
Slope = [tex]\frac{2 - (-2)}{3- (-1)}[/tex] = [tex]\frac{4}{4}[/tex] = 1
The slope of the line is 1
PLEASE HELP!!!!! 2.) What is the perimeter of a polygon with vertices at (-3, 1), (5, 1), (-3, 4), (5, 4)? 30 points if you can help
Answers
Answer:
22 units
Step-by-step explanation:
Known Quantities:
AB = CD and AC = BDCalculations:
AB = 8AC = 3CD = 8BD = 3Final Calculations:
perimeter = 2 x (3+8)perimeter = 22Subtract the following using horizontal method
i.)2x from-5x
ii.)-5a from 18a
Answers
Answer:
[tex] \huge{ \boxed{ \text{ i. \: \ - 7x}}}[/tex]
[tex] \huge{ \boxed{ \text{ii. \: 23a}}}[/tex]
▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
☄ Question : Subtract the following using horizontal method :
i. 2x from -5x-5a from -18a✎ Step - by - step Explanation :
2x from -5xIn horizontal method , terms are arranged in same row and put sign for subtraction and remove the brackets and then simplify.
[tex] \longrightarrow{ \sf{ - 5x - (2x)}}[/tex]
[tex] \longrightarrow{ \sf{ - 5x - 2x}}[/tex]
Like terms can be added or subtracted. Only coefficients of like terms can be added or subtracted.
[tex] \longrightarrow{ \boxed{\sf{ - 7x}}}[/tex]
Likewise , Let's do next too:
-5a from 18 a[tex] \dashrightarrow{ \sf{ 18a - ( - 5a)}}[/tex]
Remember : [tex] \sf{( - ) \times ( - ) = ( + )}[/tex]
[tex] \dashrightarrow{ \sf{ 18a + 5a}}[/tex]
[tex] \dashrightarrow{ \boxed{ \sf{ 23a}}}[/tex]
And we're done!
Hope I helped!
Have a wonderful time ツ
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Answer:
i)-7x ii)23a
Step-by-step explanation:
i)U well get -5x-2x, after solving, u well get -7x since all is negetive. ii)U well get 18a-(-5a) which u well get 18a+5a whict is equal to 23a
D=
R=
Function?
Find the domain and range of each relation. Then, determine if the relation is a function.
Answers
Answer:
Step-by-step explanation:
D = { - 4 , 0 , 2 , 7 }
R = { - 8 , - 1 , 3 }
Yes the relation is a function.
what is the solution to this??
4x + 12x =320
then using the solution to this do _x=_
Answers
Answer:
x=20
Step-by-step explanation:
Add like terms:
4x + 12x = 16x
16x = 320
320/16 = 20
what is the value of q in the equation 4/5q = 32
Answers
Answer:
40
Step-by-step explanation:
4/5 * q = 32
First you divide 4/5 by itself so you can eliminate it from the equation and then you have to divide 32 by 4/5 n when you do that you get 40. So q = 40.
I need to know what's 1131÷29 pronto
Answers
the answer is 39 because you need to divide.
Kiran's family is having people over to watch a football game. They plan to serve sparkling water and pretzels. They are preparing 12 ounces of sparkling water and 3 ounces of pretzels per person. Including Kiran's family, there will be 10 people at the gathering.
A bottle of sparkling water contains 22 ounces and costs $1.50. A package of pretzels contains 16 ounces and costs $2.99. Let LaTeX: nn represent number of people watching the football game, LaTeX: ss represent the ounces of sparkling water, LaTeX: pp represent the ounces of pretzels, and LaTeX: bb represent Kiran's budget in dollars. Which equation best represents Kiran's budget?
Answers
write 9.68 in expanded form
Answers
Answer:
9+0.6+0.08
Step-by-step explanation:
The given decimal number in expanded form is 9+0.6+0.08.
The given decimal number is 9.68.
What is expanded from of a decimal number?Unlike whole numbers, decimal numbers can also be written in the expanded form. For writing the decimals in expanded form, we multiply each of the decimal digits with increasing exponent values of (1/10).
Now, the expanded form of 9.68 is
9×1 + 6×1/10 + 8×1/100
= 9+0.6+0.08
= 9.68
Therefore, the given decimal number in expanded form is 9+0.6+0.08.
To learn more about the expanded form of a decimal numbers visit:
https://brainly.com/question/145272.
#SPJ2
Sebastian drove for 2.2 hours at an average rate of 43.5 miles per hour. He calculates that he drove 95.7 miles. He knows the answer should be near 80, because 40 times 2 is 80. Which best explains Sebastian’s actual solution?
The actual product is reasonable because it is near 80 but greater than 80. Both factors were rounded down, making the estimate lower than the actual product.
The actual product is unreasonable. It should be near 80 but less than 80 because both factors were rounded down.
The actual product is reasonable because the estimate and actual answers both have two places to the left of the decimal.
The actual product is unreasonable because the estimate has zero places to the right of the decimal and the actual product has one decimal place to the right of the decimal.
Answers
Answer:
The actual product is reasonable because it is near 80 but greater than 80. Both factors were rounded down, making the estimate lower than the actual product.
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
How many solutions exist for the system of equations in the graph?
one
two
three
four
Answers
Answer:
2 solutions
Step-by-step explanation:
The solutions are found at the points where the 2 graphs intersect.
From the graph there are 2 points of intersection, thus 2 solutions.
Answer this question and get it right I will mark right one Brainliest
I am thinking of a number from 1-10 what is it ?
Answers
Answer:
6
Step-by-step explanation:
6 is the most common lol
Answer:
I'll say 5
Step-by-step explanation:
Hoped this helped!
Solve each system by graphing or using a table. Check your answers.
- 2x + y = 2
- x + 2y = -2
Use the graphing tool to graph the system.
Click to
enlarge
graph
What is the solution to the system of equations? Select the correct choice below and, if necessary, fill in the
answer box to complete your choice.
O A. The solution is
(Type an ordered pair.)
B. There are infinitely many solutions.
OC. There is no solution.
Answers
Answer: no solution
A health insurance policy requires that each
person covered pay the first $300 of a bill and
then 0.2 times the rest of the bill. Fran is
covered by this policy and had to pay $500.
What was her total bill?
Answers
What is the point slope form of a line that has a slope of 3 and passes through point (1, 4)?
Answers
Answer:
3x - y = -1
Step-by-step explanation:
y - y₁ = m(x - x₁)
substitute (1,4) in for (x₁, y₁) respectively and the slope of 3 in for m
y -4 = 3(x - 1)
distribute 3 to (x - 1)
y - 4 = 3x -3
isolate 3x by itself by adding 3 to both sides
y - 1 = 3x
subtract y from each side
-1 = 3x - y
and just flip around the equation to make it look nicer
3x - y = -1