Question: write an equation for each parabola with vertex at the origin
Problem: through (3,2); symmetric with respect to the x axis
Answers
Step-by-step explanation:
Since the axis of symmetry is the x axis, we have a sideways parabola,
[tex] {y}^{2} = x[/tex]
Since the vertex is at the orgin, our answer will be
[tex]a(y - k) {}^{2} + h = 0[/tex]
[tex]a {y}^{2} = x[/tex]
It passes through (3,2).
[tex]a(2) {}^{2} = 3[/tex]
[tex]a(4) = 3[/tex]
[tex]a = \frac{3}{4} [/tex]
So our function is
[tex] \frac{3}{4} {y}^{2} = x[/tex]
Answer:
[tex]x=\dfrac34y^2[/tex]
Step-by-step explanation:
A graph with x-axis symmetry means that for every (x, y) point there is also a (x, -y) point on the graph, i.e. the x-axis acts like a mirror. Therefore, it is a sideways parabola.
The general form of this type of equation is [tex]x=ay^2+by+c[/tex]
Since we know that the curve has a vertex of (0, 0) then [tex]c=0[/tex]
Therefore, [tex]x=ay^2+by[/tex]
Given that (3, 2) is on the curve, then (3, -2) is also on the curve.
Substituting the given point (3, 2):
[tex]3=a(2)^2+b(2)[/tex]
[tex]3=4a+2b[/tex]
Substituting the given point (3, -2)
[tex]3=a(-2)^2+b(-2)[/tex]
[tex]3=4a-2b[/tex]
Adding the equations together to eliminate [tex]b[/tex]:
[tex]\implies 6=8a[/tex]
[tex]\implies 3=4a[/tex]
[tex]\implies a=\dfrac34[/tex]
Therefore,
[tex]x=\dfrac34y^2+by[/tex]
Again, substituting point (3, 2) means that b = 0
Therefore, the final equation is:
[tex]x=\dfrac34y^2[/tex]
Related Questions
20% of a is 11, what is a
Answers
Answer:
2.2
Step-by-step explanation:
11÷5 because 20 goes into 100 5 tines hope this helps!:)
Answer:
a = 55
Step-by-step explanation:
1. Set up the equation: 0.2a = 11 (20% is equal to 0.2 because to convert a percentage to a decimal you divide it by 100. In math, "of" means "times" and "is" means "equals" so the equation is 0.2 x a = 11, which can be shortened to 0.2a = 11).
2. Divide both sides by 0.2. You will be left with a = 55.
A fundraiser is being held to raise money for a new school playground. Of every $20 raised, $16 will be spent on playground equipment. If the goal of the fundraiser is $320.00 for olayground eauipment, how much money will it need to raise?
Answers
To meet the goal of $320.00 for the playground, they need to raise a total of $400.00
How much they need to raise?
We know that for each $20 raised, they get $16 for the playground. They need to get $320.00 for the playground.
Taking the quotient:
N = $320.00/$16 = 20
This means that they need to raise $20 20 times, so they get $16 20 times which is equal to $320.
Then, we can conclude that they need to raise a total of:
$20*20 = $4,000
If you want to learn more about quotients, you can read:
https://brainly.com/question/7068223
solve for y in terms of x.
3x^2 + 2x + 4 = y
Answers
Answer:
y=-1+squareroot 47l /6, -1- squaroot 47l/6
Step-by-step explanation:
3x^2 +2x+4−x=0
3x^2 +x+4=0
y=-1+squareroot 47l /6, -1- squaroot 47l/6
The median weight of 15 dogs in a pet store is 12 pounds.
Which action could change the median?
Answers
The addition of the new dog will change the median. The correct answers may be A and D.
What is the median?The Median is the middlemost value of the numbers arranged in ascending order. If the number of the data is an odd number so the median will be a middle number if the number of the data is even then the median is the mean of the middle two numbers.
In light of the fact that the average weight of 15 dogs in a pet shop is 12 pounds. The median will shift as a result of the new dog. The right responses could be A and D.
To know more about the median follow
https://brainly.com/question/26151333
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Find the y-intercept and the slope of the line.
y=2/3
Answers
Answer:
y-intercept = 2/3
Slope = 0
Step-by-step explanation:
Equation of Line is y=mx+c
where m is the Slope
and c is the y-intercept
so for our Problem
y=2/3
which can be rewritten as y=0x+2/3 (y=mx+c)
so Slope =m=0
and y-intercept = c = 2/3
What matches with the number line?
Answers
The larger the negative number gets, the farther from zero it becomes. -9.8 is closer to zero- therefore "larger" than -11.3.
Have a nice day/night :)
~pinetree
Which expression has a value greater than 1/2?
A. 1/2 x 4/5
B. 1/2 x 4/4
C. 1/2 x 5/5
D. 1/2 x 5/4
Answers
Answer:
D. 1/2 x 5/4
Step-by-step explanation:
A.
1/2 x 4/5 = 2/5
0.5 x 0.8 = 0.4
B.
1/2 x 4/4 = 1/2
0.5 x 1 = 0.5
C.
1/2 x 5/5 = 1/2
0.5 x 1 = 0.5
D.
1/2 x 5/4 = 5/8
0.5 x 1.25 = 0.625
I hope this helps!
$miamoney2420 Anything would help
Answers
Answer:
24"?
Step-by-step explanation:
Answer:
why?..
Step-by-step explanation:
mark me brainliest!!
30 POINTSSS IS MY ANSWER 2 CORRECT???
Answers
Answer:
2286
Step-by-step explanation:
If you take 14 percent of a number and get 320, then what is that number? In other words, you know that 14 percent of a number is 320 and you want to know what that initial number is.
To solve this problem you multiply 320 by 100 and then divide the total by 14 as follows: (320 x 100) / 14
When we put that into our calculator, we get the following answer:
2285.71
can't have a portion of someone to you round it to the nearest whole number.
Answer:
The town’s population is 2286 (approximately)
Step-by-step explanation:
Let x be the number of the town’s residents :
We can translate the statement “14% of the town’s population is over the age of 65 and there are 320 residents over the age of 65” mathematically like this :
[tex]\frac{14}{100} x=320[/tex]
[tex]\Longrightarrow 14x=320\times 100\\\\\Longrightarrow 14x=32000[/tex]
[tex]\Longrightarrow x=\frac{32000}{14}[/tex]
[tex]\Longrightarrow x=2285.71428571429[/tex]
You fill a 10 1/2 gallon tub 1/3 full of water. How many gallons of water are in the tub?
Answers
Answer:
3.5
Step-by-step explanation:
10.5 divided by 3= 3.5
There are 7 times as many males as females on the maths course at university. What fraction of the course are female?
Give your answer in its simplest form.
Answers
Answer:
1/8
Step-by-step explanation:
Suppose there are 7 males so there will be 1 female according to the question.
So there is 1 female out of a total of 8 students. So the answer is 1/8.
Because the female is 1 out of the 8 people.
Which one is the smallest decimal .5 .53 .053 .503
Answers
Answer:
.053
Step-by-step explanation:
The decimal places go all the way out to the thousandths place. In order to properly compare all of the decimals, it's best to add zeroes in place of any empty decimal places in any of the numbers.
.5 would now be .500
.53 would now be .530
And the other two numbers are already in the thousandths place, so those don't need to be changed.
Now, we can put all the numbers next to each other and compare. You compare decimals the same way you compare normal numbers- just act as if the decimal points aren't there.
If the numbers were 500, 530, 053, and 503, we know that 053 would be the smallest number. Therefore, the decimal .053 is the smallest.
I hope this helps! :) have a lovely day!!
Robert plans to make a box-and-whisker plot of the following set of data.
27, 14, 46, 38, 32, 18, 21
Which of the following should Robert's box-and-whisker plot look like?
10
15
20
25
30
35
40
45
50
o
10
15
20
25
30
35
40
45
50
O
10
15
20
25
30
35
40
45
50
5
10
15
20
25
30
35
40
Answers
Answer:
To make a box and whisker plot, you need to draw a number line that would be able to represent all the values in the data (look at your lowest and highest numbers).
You will need to graph the following 5 points on your number line (median, lower quartile, lower extreme, upper quartile, and upper extreme).
Create a box around the quartiles and extend the lines to the extremes.
See the picture I have attached for the box and whisker box for this data set.
Step-by-step explanation:
27. Evaluate (x - 2y)2 if x = 2 and y=-3
Answers
Answer:
[tex](2 + 6)2 = 16[/tex]
.....
....
.....
....
Answer:
2 - 2 * 3 2 - 6 equal to -4
Find the range for the measure of the third side of a triangle given the measures of two sides. 5 m, 11 m, ?
a. 16 < x < 6
b. 3 < x < 7
c. 5 < x < 11
d. 6 < x < 16
Answers
Answer:
d
Step-by-step explanation:
the length of the third side should be less than the sum of other two sides, that is 5+ 11 = 16 and it should be greater than the 5
6 < x < 16
Suppose you are going on a vacation and leaving your dog in a kennel. While you are away,
you want your dog to be groomed. The Poochpad charges $20 per day and $30 for the
grooming. Happytrail Boarding charges $25 per day, which includes a free grooming
treatment.
Answers
Per day compared to then20 plus 30
What new ideas about mathematics did you learn?
Answers
Answer:
I learned how to multiply
Step-by-step explanation:
8×8=64
8 times the number you are multiplying
like this look
IIIIIIII there are Eight sticks each one has a value of 8
so you go 8,16,24,32,40,48,56,64. more
today at basketball practice the team worked on three skills. they ran for 22 minutes, they did passing drills for 35 minutes. they practiced shooting free throws for 27 minutes. tomorrow the coach wants the team to spend an equal amount of time on each drill. if the team spends the same total number of minutes on these 3 drills as today, how many minutes will the team spend on each drill
Answers
Answer:
28
Step-by-step explanation:
So first you need to add up the time they played yesterday which means add up the times for each drill(22+35+27) which equals 84. Now you need to divide 84 by 3 because there are 3 drills(84÷3) which equals 28 and you will get your answer
22 + 35 + 27 = 84 ÷ 3 = 28
Hope this helps
Please mark brainliest.
Can you help me solve the volume of triangular prisms.
Answers
Triangular prisms
Remember the formula for calculating volume is: Volume = Area by height. V = A X h.
For a triangle the area is calculated using the formula: Area = half of base by altitude. A = 0.5 X b X a.
So to calculate the volume of a triangular prism, the formula is: V = 0.5 X b X a X h.
Which term describes this material. A) caption, B) header, C) glossary, D) objective Will Mark Brainliest if answered correctly.
Answers
Answer:
C) glossary
Step-by-step explanation:
It is the one given in the picture.
NEED HELP ASAP, WILL MARK BRAINLIEST
Connor needs 60 mL of a 19% acid solution for a science experiment. He has available a 21% solution and a 15% solution.
How many milliliters of the 21% solution and how many milliliters of the 15% solution should he mix to make the 19%
solution?
Answers
Let x = ml of 21% solution
Let y = ml of 15% solution
ATQ,
x + y = 60.....(1)
or
0.21x + 0.15y = 0.6....(2)
Multiplying equation 1st by 0.21, we get,
0.21y+0.21y =12.6....(3)
subtracting equation 3
0.21y+0.21y =12.6
-0.21x +0.15y = 0.6
_________________
ㅤㅤㅤ 0.6y = 12
_________________
6y = 12y = 20mlx= 60-20 = 40 mlHence , Conner needs 20ml of 21% solution & 40ml of 15% solution
NO LINKS!!! Part 2: Complete the sequence
Answers
Answer:
40, 80t(n) = 5×2^(n-1)see attachedStep-by-step explanation:
The sort of sequence it is can be determined by looking at the differences of n-values and the differences of t(n)-values. When the n-value differences are constant, the nature of the relation between the t(n)-values can tell you the kind of sequence.
a)Here, the n-values all differ by 1. The t(n)-value differences double with each increase in n. That is, they are 5 and 10. We notice also that the t(n) values double with each increase in n. We can fill the rest of the table using that relationship:
t(n) = t(n-1) × 2 . . . . . each term is double the previous term
t(4) = t(3) × 2 = 20 × 2 = 40
t(5) = t(4) × 2 = 40 × 2 = 80
When the terms of the sequence have a common ratio, the sequence is geometric, and the function describing the sequence is an exponential function.
__
b)The general term of a geometric sequence is ...
t(n) = t(1) × r^(n-1)
The table tells us the first term is ...
t(1) = 5
And our observation above tells us the common ratio is r = 10/5 = 2. Then the equation of the sequence is ...
t(n) = 5 × 2^(n-1)
__
c)See the attachment for a graph.
Answer:
a) (4, 40) and (5, 80)
b) [tex]t(n)=2.5 \cdot2^n[/tex]
c) see attached
Step-by-step explanation:
As the value of t(n) doubles each time, we can conclude that this is an exponential function.
Therefore, the missing ordered pairs are (4, 40) and (5, 80)
General form of an exponential function: [tex]y=ab^x[/tex]
where:
[tex]a[/tex] is the y-intercept (or initial value)[tex]b[/tex] is the base (or growth factor)[tex]x[/tex] is the independent variableIf [tex]b > 1[/tex] then it is an increasing function
If [tex]0 < b < 1[/tex] then it is a decreasing function
Given:
(2, 10)(3, 20)Substitute these ordered pairs into the general form of the exponential function:
Equation 1: [tex]ab^2=10[/tex]
Equation 2: [tex]ab^3=20[/tex]
Divide Equation 2 by Equation 1 to find [tex]b[/tex]:
[tex]\implies \dfrac{ab^3}{ab^2}=\dfrac{20}{10}[/tex]
[tex]\implies b=2[/tex]
Now substitute the found value of [tex]b[/tex] into one of the equations and solve for [tex]a[/tex]:
[tex]\implies ab^2=10[/tex]
[tex]\implies a\cdot 2^2=10[/tex]
[tex]\implies a=\dfrac{10}{4}[/tex]
[tex]\implies a=2.5[/tex]
So the final exponential equation is: [tex]t(n)=2.5 \cdot2^n[/tex]
Graphing
Plot the points from the table
To find the y-intercept:
Substitute [tex]n = 0[/tex] into the equation:
[tex]\implies t(0)=2.5 \cdot2^0[/tex]
[tex]\implies t(0)=2.5[/tex]
Therefore, the y-intercept is at (0, 2.5)
Asymptote: [tex]t(n) = 0[/tex]
plss answer for my friend
Th
Answers
This is the Answer really
PLEASE ANSWER I'LL GIVE BRAINLIEST
Answers
Answer:
I believe it is sometimes
Step-by-step explanation:
Answer:
WRONG!!!!!!
the answer is; Is never
brainist please
Determine if true:
3^5x2=64
Answers
Answer:
False
Step-by-step explanation:
3^5=234
234x2=486
486=64
The numbers dont match.
Hence, the equation is false
Answer:
Not true
Step-by-step explanation:
= 3⁵ x 2
= 3 x 3 x 3 x 3 x 3 x 2
= 9 x 9 x 6
= 81 x 6
= 486
486 ≠ 64
Not true
The size of a typical city park is about 5 acres, or 217,800 square feet. If a developer plans to
build two basketball courts in a new city park that are 5,000 square feet each, what percent of
the park will be used for other activities?
Answers
Using the percentage concept, it is found that 95.4% of the park will be used for other activities.
What is a percentage?The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
[tex]P = \frac{a}{b} \times 100\%[/tex]
In this problem, there will be two courts of 5,000 square feet each, totaling 10,000 square feet. The remainder 207,800 square feet will be used for other activities, hence the percentage is given by:
[tex]P = \frac{207,800}{217,800} \times 100\% = 95.4\%[/tex]
95.4% of the park will be used for other activities.
More can be learned about the percentage concept at https://brainly.com/question/10491646
A cellular phone tower services a 20-mile radius. A rest stop on the highway is 5 miles east and 12 miles north of the tower. If you continue driving due east, for how many more miles will you be in range of the tower?
Answer: 11
I just need a explanation, thank you!
Answers
The tower will work within next 11 miles inasmuch the drives moves through the road.
How to determine a distance inside a cellular phone towerThe maximum distance corresponds to the radius of the tower ([tex]r[/tex]), in kilometers, the east direction corresponds to the +x semiaxis and the north direction corresponds to the +y semiaxis. The angle and magnitude of the rest stop are found below:
[tex]l = \sqrt{5^{2}+12^{2}}[/tex]
[tex]l = 13[/tex]
[tex]\theta = \tan^{-1}\left(\frac{12}{5} \right)[/tex]
[tex]\theta \approx 67.380^{\circ}[/tex]
To determine distance within the cellular phone tower works we need to solve the following system of linear equations representing vector components:
[tex]5 + x = 20\cdot \cos \theta[/tex] (1)
[tex]12 = 20\cdot \sin \theta[/tex] (2)
By (2):
[tex]\theta = 36.869^{\circ}[/tex]
By (1):
[tex]x = 11[/tex]
The tower will work within next 11 miles inasmuch the drives moves through the road. [tex]\blacksquare[/tex]
To learn more triangles, we kindly invite to check this verified question: https://brainly.com/question/25813512
what is the perimeter
Answers
Solution:
Perimeter is the sum of the figure's sides.
Note that:
10 + 10 + 4 + 10 + 4 + 10 + 10 + 30 = Perimeter of figureSimplify the expression:
5(10) + 2(4) + 30 = Perimeter of figure=> 50 + 8 + 30 = Perimeter of figure=> 88 cm = Perimeter of figureI have attached the labelled diagram, Let's find the perimeter now..
Perimeter = Sum of all sidesLength of all sides:
10 cm10 cm10 cm10 cm10 cm4 cm4 cm30 cmNow, Let's add these values
[tex] \sf: \implies \: 10 + 10 + 10 + 10 + 10 + 4 + 4 + 30[/tex]
[tex] \sf: \implies \: 50+ 4 + 4 + 30[/tex]
[tex] \sf: \implies \: 50+ 8+ 30[/tex]
[tex] \sf: \implies \: 58+ 30[/tex]
[tex] \boxed{ \tt: \multimap \: 88}[/tex]
Thus, The perimeter of the given figure is 88 cm...~
Evaluate geometric series
Answers
Answer:
7.5
Step-by-step explanation:
Sum of a geometric series,
[tex] \frac{a _{1}(1 - r {}^{n} ) }{1 - r} [/tex]
Where a1 is the first term, R is the common ratio, n is the number of terms.
a1 is 5
r is 1/3
n is 10.
[tex] \frac{5(1 - ( \frac{1}{3} ){}^{10} ) }{ \frac{2}{3} } [/tex]
Which is about
7.50
IM BEGGING YOU PLEASE HELP PLEASE HELP I NEED HELP PLEASE
Answers
Answer:
area of shaded region: 21.07 ft²
Given for semi circle:
radius of semi-circle: 7 ftGiven for rectangle:
width: 7 ftlength: 14 ftFind area of rectangle:
Length * Width
14 * 7
98 ft²
Find the area of semi circle:
1/2 * π * r²
1/2 * 3.14 * (7)²
76.93 ft²
Area of shaded region:
area of rectangle - area of semi-circle
98 ft² - 76.93 ft²
21.07 ft²