Given:
The equation of the parabola is
[tex]y=2x^2+8x+3[/tex]
To find:
The vertex and check whether it opens up or down.
Solution:
We have,
[tex]y=2x^2+8x+3[/tex]
Here, leading coefficient is 2 which is a positive number. So, the parabola opens up.
The vertex of parabola [tex]f(x)=ax^2+bx+c[/tex] is
[tex]\left(\dfrac{-b}{2a},f(\dfrac{-b}{2a})\right)[/tex]
Here, a=2, b=8 and c=3.
[tex]\dfrac{-b}{2a}=\dfrac{-8}{2(2)}[/tex]
[tex]\dfrac{-b}{2a}=\dfrac{-8}{4}[/tex]
[tex]\dfrac{-b}{2a}=-2[/tex]
Putting x=-2 in the given equation.
[tex]y=2(-2)^2+8(-2)+3[/tex]
[tex]y=2(4)+(-16)+3[/tex]
[tex]y=8-16+3[/tex]
[tex]y=-5[/tex]
So, the vertex of the parabola is at (-2,-5) and parabola opens up.
Therefore, the correct option is D.
Fido's leash is tied to a stake at the center of his yard, which is in the shape of a regular hexagon. His leash is exactly long enough to reach the midpoint of each side of his yard. If the fraction of the area of Fido's yard that he is able to reach while on his leash is expressed in simplest radical form as [(sqrt{a})/b] * pi, what is the value of the product ab?
Answer:
a = 3
b = 6
The product ab = 3 x 6 = 18
Step-by-step explanation:
Data Given:
Fraction of the area of Fido's yard = [tex]\pi x \frac{\sqrt{a} }{b}[/tex]
Let X be the side of the hexagon.
So, the area of the Hexagon is:
Area of the Hexagon = [tex]\frac{3\sqrt{3} }{2} X^{2}[/tex]
Now, we have to calculate the length of Fido's Leash by using Lw of Sine
Law of Sine = [tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]
[tex]\frac{0.5S}{sin30}[/tex] = [tex]\frac{Length}{sin60}[/tex]
Solving for Length, where sin30 = 1/2 and sin60 = [tex]\frac{\sqrt{3} }{2}[/tex]
Suppose Length = Y
Y = [tex]\frac{\sqrt{3} }{2}[/tex]X
Now, as we have got the length we can calculate the area that Fido can cover,
So, the area covered by Fido = [tex]\pi[/tex] x [tex]Y^{2}[/tex]
Area = [tex]\pi[/tex] x [tex](\frac{\sqrt{3} }{2}X) ^{2}[/tex]
Area = [tex]\pi[/tex] x [tex]\frac{3}{4}[/tex] x [tex]X^{2}[/tex]
So, now, we can get the fraction of the area of Fido's Yard by dividing the area of hexagon by area that fido can cover.
Fraction of the area of Fido's yard = [tex]\pi x \frac{\sqrt{a} }{b}[/tex]
[tex]\pi[/tex] x [tex]\frac{3}{4}[/tex] x [tex]X^{2}[/tex] / [tex]\frac{3\sqrt{3} }{2} X^{2}[/tex]
[tex]\pi[/tex] x [tex]\frac{3}{4}[/tex] / [tex]\frac{3\sqrt{3} }{2}[/tex]
6 [tex]\pi[/tex] / [tex]12\sqrt{3}[/tex]
[tex]\pi[/tex] / [tex]2\sqrt{3}[/tex]
Which can be rewritten as by multiplying and dividing by [tex]\sqrt{3}[/tex]
[tex]\sqrt{3} \pi[/tex]/ 6
By comparing the above equation and the given equation we can find a and b :
So,
a = 3
b = 6
And the product ab = 3 x 6 = 18
6x+12 factorizar mediante a factor comun
You want to obtain a sample to estimate how much parents spend on their kids birthday parties. Based on previous study, you believe the population standard deviation is approximately
σ
=
62.5
dollars. You would like to be 95% confident that your estimate is within 3 dollar(s) of average spending on the birthday parties. How many parents do you have to sample?
Answer:
The number of parents spend their kids birthday parties
'n' = 1667
Step-by-step explanation:
Explanation:-
Given standard deviation of the Population = 62.5
Given the estimate error = 3 dollars
Level of significance =0.05
Z₀.₀₅ = 1.96
The margin of error defined by
[tex]M.E = \frac{Z_{0.05} S.D}{\sqrt{n} } \\3 = \frac{1.96 X 62.5}{\sqrt{n} }[/tex]
cross multiplication , we get
3√n = 1.96 X 62.5
√n = 40.833
Squaring on both sides, we get
n = 1667.34
The number of samples are 'n' = 1667
Isaac is deciding between two truck rental companies. Company A charges an initial fee of $75 for the rental plus $1.50 per mile driven. Company B charges an initial fee of $45 for the rental plus $2.50 per mile driven. Let A represent the amount Company A would charge if Isaac drives x miles, and let B represent the amount Company B would charge if Isaac drives x miles. Write an equation for each situation, in terms of x, and determine the interval of miles driven, x, for which Company A is cheaper than Company B.
Answer:
A= 1.50x+75 B= 2.50x+45
Company A is cheaper than Company B when x > 30 miles.
Step-by-step explanation:
Company A charges$75 for the rental even when driving x=0 miles, and will charge and additional $1.50 per mile driven. Therefore the amount Company A would charge for xx miles is:
A=1.50x+75
Company B charges $45 for the rental even when driving x=0 miles, and will charge and additional $2.50 per mile driven. Therefore the amount Company B would charge for x miles is:
B=2.50x+45
When x takes less than 30 miles, Company A is cheaper than Company B. This is the equation of price that companies i.e. A = 1.50x+75 and B= 2.50x + 45.
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
When driving x = 0 miles, Company A charges $75 for the rental and an additional $1.50 for each mile driven. Thus, the price that Company A would charge for x miles is as follows:
⇒ A = 1.50x + 75
When driving x = 0 miles, Company B charges $45 for the rental and an additional $2.50 for each mile driven. Thus, the price that Company B would charge for x miles is as follows:
⇒ B = 2.50x + 45
Hence, when x takes less than 30 miles, Company A is less expensive than Company B. This is the equation of price that companies i.e. A = 1.50x+75 and B= 2.50x + 45.
Learn more about the Linear equations here:
https://brainly.com/question/13738061
#SPJ5
PLEASE HELP THANK YOU :)
Answer:
the first option
A detective determines that the number of robberies on a given day and the number of days since the start of the month can be modeled by a square root function. On the fourth day of the month, there were 4 robberies. On the ninth day of the month, there were 6 robberies. On the sixteenth day of the month, there were 8 robberies. Which points should be plotted to graph this function?
A. (2, 2) , (3, 3) , (4, 4)
B. (4, 4) , (9, 6) , (16, 8)
C. (4, 2) , (9, 3) , (16, 4)
D. (2, 4) , (3, 6) , (4, 8)
Answer:
B. (4, 4) , (9, 6) , (16, 8)Step-by-step explanation:
Describes pairs are:
(4, 4), (9, 6) and (16, 8)This is matching the option B
Answer:
B. (4,4), (9,6), (4,4)
Step-by-step explanation:
:)
The measures of the angles of a triangle are shown in the figure below. Solve for x. (3x+12) 54°
Answer:
14
Step-by-step explanation:
Write the equation of the line.
Jamie wants to run 2 3/4 miles today. He has already run 1 1/4 miles. How much farther must he run to reach his goal?
Answer:
0 miles
Step-by-step explanation:
Just subtract 11/4 from 2 3/4
2 3/4 - 11/4 = 0
So, he doesn't need to run any more
This recipe makes 6 portions of chocolate mousse.
Cali has 600 g chocolate, 36 eggs, 100 ml of lemon juice and 200 g of sugar.
Cali makes 18 portions of mousse by following this recipe.
How much of each ingredient will she have left?
Recipe: Serves 6
180 g chocolate
9 eggs
15 ml lemon juice
60 g sugar
Answer:
Chocolate - 420g
Eggs - 27
Lemon juice - 85ml
Sugar - 140g
Step-by-step explanation:
Given that:
Initial amount of ingredients:
Chocolate - 600g
Eggs - 36
Lemon juice - 100ml
Sugar - 200g
Amount of ingredients used :
Chocolate - 180g
Eggs - 9
Lemon juice - 15ml
Sugar - 60g
Amount of ingredient left :
Initial amount - Amount used :
Chocolate : 600g - 180g = 420g
Eggs : 36 - 9 = 27
Lemon juice : 100ml - 15ml = 85ml
Sugar : 200g - 60g = 140g
What is 80% of 92? you will get 23 points if you answer. lol
Answer:
368/5
Step-by-step explanation:
hope it helps
.........
Answer:
73.6
Step-by-step explanation:
80% = 0.8
0.8 * 92 = 80% of 92
0.8 * 92 = 73.6
80% = 73.6
:3))
An airline estimates that each passenger with baggage weighs 205 pounds.
A gallon of fuel weighs 5 pounds
An airplane can carry 495 passengers and 49,500 gallons of fuel.
Estimate how much an airplane can carry
Options:
A: 300,000 pounds
B: 400,00 pounds
C: 350,000 pounds
Answer:
The estimated weight that the airplane can carry is: Option C: 350,000 pounds
Step-by-step explanation:
Given that each individual weighs 205 pounds with baggage and one gallon of fuel weighs 5 pounds.
We will work out the passengers weight first.
For Passengers:
Let w be the total weight of all passengers
[tex]w = weight\ of\ one\ passenger * number\ of\ passengers\\w =205 * 495\\w =101475\ pounds[/tex]
For Fuel:
Let f be the total weight of fuel
Then
[tex]f = Weight\ of\ one\ gallon * Number\ of\ gallons\\f = 5 * 49500\\f =247500[/tex]
Total weight = 101475 + 247500 = 348975 pounds
As 350000 is nearest to the calculated answer, it will be the right answer.
Hence,
The estimated weight that the airplane can carry is: Option C: 350,000 pounds
Dexter runs around a track at 10 laps in 20 minutes. How many minutes per lap is that?
Answer:
10 minutes
Step-by-step explanation:
Answer: that would be 83 seconds a lap i believe
Ps: this dexter kid is really fast
Step-by-step explanation:
I hope this helps if not sorry :(
(-2/3)3 = (-2/3) (-2/3) (-2/3) =
Answer:
-0.296296296296...
Answer:
TRUE/ −0.296296
Step-by-step explanation:
(-2/3)^3 = (-2/3) (-2/3) (-2/3) =
−0.296296=−0.296296
True
Find the unit vector of -2i - j.
Answer:
maybe a
Step-by-step explanation:
4x+3y=32
4x+y=16
work out x and y pleaseeeeeee
Answer:
The answer is xy=16-4 and xy=12
What is the slope of the following line: y=3x−7
Answer:
The slope is 3
Step-by-step explanation:
A cylindrical water tank near the town library is 20 meters high and has a circumference of 39 meters. What is the approximate volume, to the nearest whole number, of the water tank? Use 3.14 as an approximation for π and round to the nearest whole number.
Step-by-step explanation:
height of the cylindrical tank = 20m
circumference of the tank = 39m
volumn of tank =
perimetre formula = 2πrh
= 2 x 3.14 x r x 20 = 39
= 188.4r = 39
r = 188.4/39
r = 4.83
volumn = πr^/2
h
= 3.14 x 4.83^2 x 2 x 20
= 1465.05
volumn of tank = 1465.05
renting company Charge 35 per day to rent
a boat allong with a 50$ one-time cleaning fee.
Enter the equation in y=Mx+b form
Answer:
y=35x+50
Step-by-step explanation:
The 50 is a one-time fee, therefore it is shown as addition
35 per day means that for 3 days, you would pay 105
X represents the number of days
3/4n=-1 3/4n-18
Step by step please
Answer:
Solving the expression [tex]\frac{3}{4}n=-1\frac{3}{4}n-18[/tex] we get [tex]\mathbf{n=-\frac{36}{5} }[/tex]
Step-by-step explanation:
We need to solve the expression: [tex]\frac{3}{4}n=-1\frac{3}{4}n-18[/tex]
Solving:
[tex]\frac{3}{4}n=-1\frac{3}{4}n-18[/tex]
First we convert mixed fraction into improper fraction
[tex]\frac{3}{4}n=-\frac{7}{4}n-18[/tex]
Now adding 7/4 n on both sides
[tex]\frac{3}{4}n+\frac{7}{4}n=-\frac{7}{4}n-18+\frac{7}{4}n\\\frac{3}{4}n+\frac{7}{4}n=-18[/tex]
Now, taking LCM on left side
LCM of 4 and 4 is 4
[tex]\frac{3}{4}n+\frac{7}{4}n=-18\\\frac{3*1n+7*1n}{4}=-18\\\frac{3n+7n}{4}=-18\\\frac{10n}{4}=-18[/tex]
Now, multiply both sides by 4/10
[tex]\frac{10n}{4}\times \frac{4}{10} =-18\times \frac{4}{10}\\n=-\frac{36}{5}[/tex]
So, solving the expression [tex]\frac{3}{4}n=-1\frac{3}{4}n-18[/tex] we get [tex]\mathbf{n=-\frac{36}{5} }[/tex]
Identify the pair of angles shown in the picture
Answer:
Adjacent
Step-by-step explanation:
Angles WYX and XYZ are next to eachother.
Please help ASAP !!!!!
Answer:
(goh) (0) = 4
Step-by-step explanation:
Given that,
g(x) = 2x
h(x) = x² + 4
We need to find the value of (goh) (0).
Firstly we find (goh),
(goh) = g(h(x))
=g(x²+4)
(goh) (0) = 0²+4
=4
Hence, the required answer is 4.
Do you see the figures inside these boxes? They form a pattern. Choose the figure in the answer row below that continues the pattern.
Answer:
1
Step-by-step explanation:
The blocks are rotating counterclockwise.
if M is the midpoint of AB, find the co-ordinator of a/ A if the co-ordinator of M and B are M(2,8) and B(-4,19)
Answer:
M (2,8)= (x1y1)
B(-4,19)= (x2y2)
here,
midpoint = (x1+x2/2) (y1+y2/2)
= ( 2+ (-4)/2) (8 +19/2)
= (-2/2) (27/2)
= -1, 13.5
Step-by-step explanation:
by using midpoint formula
The table and graph both represent the same relationship. Which
equation also represents that relationship?
Х
у
-2
4
3
-1
1
2
0
0
1
NA
4
х
-2
-1
o
1
2
y = x
y = x2
y = -2x + 8
y = 2x2 + 2
Answer:
We conclude that all the points of the table satisfy the equation y = x²
Hence, the option containing the equation y = x² is true.
The graph of y = x² is also attached below.
Step-by-step explanation:
Given the table
x y
-2 4
-1 1
0 0
1 1
2 4
Let us substitute the x-values of the table in the equation
y = x²
plun in x = -2
y = (-2)² = 4
so the point (2, 4) lies on the graph of y = x²
y = x²
plun in x = -1
y = (-1)² = 1
so the point (-1, 1) lies on the graph of y = x²
y = x²
plun in x = 0
y = (0)² = 0
so the point (0, 0) lies on the graph of y = x²
y = x²
plun in x = 1
y = (1)² = 1
so the point (1, 1) lies on the graph of y = x²
y = x²
plun in x = 2
y = (2)² = 4
so the point (2, 4) lies on the graph of y = x²
Therefore, we conclude from the above calculations that all the points of the table satisfy the equation y = x²
Hence, the option containing the equation y = x² is true.
The graph of y = x² is also attached below.
petra claims that he can use the associative property of multiplaction to rewrite(9.5 x 9) + 1 as 9.5 x 10. is petra correct explain
Answer:
No Petra is wrong
Step-by-step explanation:
The associative property of multiplication goes thus :
(x * y) * z = x * (y * z)
The equation give in the question :
(9.5 x 9) + 1 = 9.5 * 10
The associative property cannot be used to rewrite the equation as claimed above.
Because, the equation includes both multiplication and addition functions. Hence, it has to be solved separately following tbe rule of BODMAS., THE sign preceeding 9 in the equation is multiplication and as such not mathematically correct to add such number to +1
To ascertain :
(9.5 x 9) + 1 = 86.5
9.5 * 10) = 95
Hence,
(9.5 x 9) + 1 ≠ 9.5 * 10
Use the following rules to graph and label the ordered pairs on a coordinate grid with at least 4 points on the coordinate
plane:
Maddy and Ted worked together to graph points on a coordinate plane.
1. Maddy wrote a pattern for all the x coordinates starting at 3 and followed the rule "add 2.".
2. Ted wrote a pattern for all the y coordinates starting at O and followed the rule "add 4."
Answer:
3
Step-by-step explanation:
1,A ladder with nine rungs is to be built, with the bottom rung 24cm. wide and the top rung
18cm. wide. If the length of the rungs decreases uniformly from bottom to top, how long
should each of the seven intermediate rungs be?
3,Find the first term of the sequence 10, 5, 2.5, 1.25, . . . which is less than 0.0001.
3,In an arithmetic sequence, if the p
th term is q and the q
th term is p, find the (p + q)
th term.
Answer:
bottom rung 24cm. wide and the top rung
18cm. wide. If the length of the rungs decreases uniformly from bottom to top, how long
should each of the seven intermediate rungs be?
3,Find the first term of the sequence 10, 5, 2.5, 1.25, . . . which is less than 0.0001.
3,In an arithmetic sequence, if the p
th term is q and the q
th term is p, find the (p + q)
th term.
An athlete runs 8 miles in 50 minutes on a treadmill. At this rate how far can the athlete run in 1 hour?
Answer:
9.6
Step-by-step explanation:
8/50=x/60
cross multiply
50x=480
x=9.6
PLSSSS HELP ME I HAVE TRIED SOLVING THIS SOOO MANY TIMES
MY ANSWER:
-32 (Wrong)
Find the value of the polynomial: 7x^2y−2xy^2−6x^2y+3xy^2−xy+8 for x=−2, y=4
Step-by-step explanation:
7x^(2y) - 2xy² - 6x^(2y) + 3xy² - xy + 8
= x^(2y) + xy² - xy + 8.
When x = -2 and y = 4, we have:
(-2)^(8) + (-2)(4²) - (-2)(4) + 8
= 256 - 32 + 8 + 8
= 240.
There is ambiguity between x^(2y) and x²y written in your question.
Answer:
The answer is 0.
Step-by-step explanation:
x = -2 , y = 4
7(-2)²(4) - 2(-2)(4)² - 6(-2)²(4) + 3(-2)(4)² - (-2)(4) + 8
112 + 64 - 96 - 96 + 8 + 8
176 - 192 + 16 = 0