Answers
Answer:
The point (11, 5) is NOT on the parabola.
Step-by-step explanation:
Let [tex](x_0,y_0)[/tex] be any point on the parabola
Let [tex](a, b)[/tex] be the focus
Let [tex]y=c[/tex] be the the directrix
Distance between [tex](x_0,y_0)[/tex] and the focus: [tex]\sqrt{(x_0-a)^2+(y_0-b)^2}[/tex]
Distance between [tex](x_0,y_0)[/tex] and the directrix is [tex]|y_0-c|[/tex]
Given:
focus (6, 4)directrix y = 0Therefore:
Distance between [tex](x_0,y_0)[/tex] and the focus: [tex]\sqrt{(x_0-6)^2+(y_0-4)^2}[/tex]
Distance between [tex](x_0,y_0)[/tex] and the directrix is [tex]|y_0-0|[/tex]
Equate the two expressions and solve for [tex]y_0[/tex]:
[tex]\sqrt{(x_0-6)^2+(y_0-4)^2}=|y_0-0|[/tex]
[tex]\implies (x_0-6)^2+(y_0-4)^}=(y_0-0)^2[/tex]
[tex]\implies {x_0}^2-12x_0+36+{y_0}^2-8y_0+16={y_0}^2[/tex]
[tex]\implies {x_0}^2-12x_0-8y_0+52=0[/tex]
[tex]\implies 8y_0={x_0}^2-12x_0+52[/tex]
[tex]\implies y_0=\dfrac18{x_0}^2-\dfrac{12}{8}x_0+\dfrac{52}{8}[/tex]
[tex]\implies y_0=\dfrac18{x_0}^2-\dfrac32x_0+\dfrac{13}{2}[/tex]
Now rewrite with (x, y):
[tex]\implies y=\dfrac18x^2-\dfrac32x+\dfrac{13}{2}[/tex]
Therefore, this is the equation of the parabola
To determine if the point (11, 5) is on the parabola, input x = 11 into the equation:
[tex]\implies y=\dfrac18(11)^2-\dfrac32(11)+\dfrac{13}{2}[/tex]
[tex]\implies y=\dfrac{41}{8}[/tex]
So the point (11, 5) is NOT on the parabola.
Related Questions
Find the distance between these 2 points: (-4, 5) and (4, 0)
Answers
Answer: Length = 9.434
Step-by-step explanation: Input Data :
Point 1
(
x
A
,
y
A
)
= (-4, 5)
Point 2
(
x
B
,
y
B
)
= (4, 0)
Objective :
Find the distance between two given points on a line?
Formula :
Distance between two points =
√
(
x
B
−
x
A
)
2
+
(
y
B
−
y
A
)
2
Solution :
Distance between two points =
√
(
4
−
−
4
)
2
+
(
0
−
5
)
2
=
√
8
2
+
(
−
5
)
2
=
√
64
+
25
=
√
89
= 9.434
Distance between points (-4, 5) and (4, 0) is 9.434
Jenna runs 6km per hour, how long would it take her to run 3km
Answers
It would take Jenna half an hour, or 30 minutes, to run 3 km.
Hope this helps!
Ahhh I’m stuck on this one please help
Answers
Answer:
1.20 ÷ 4 = 0.30 per unit
Please mark as brainliest;)
Solve for x. 4x - 8 = 2x - 6
Answers
Answer:
x=7
Step-by-step explanation:
4x-8=2x-6
4x-2x=-6+8
2x=-14(divide both the sides by 2)
x=7
If y=tanx-cotx, then dy/dx =
Answers
Answer:
dy/dx=sec^2^(x)-(-csc^2(x)
=sec^2(x)+ csc^2(x)
so solution is E
Answer:
e) sec^2x+csc^2x
need help with thiss
Answers
Hello!
2( 8u² + uv²w -1) + 2( 5u²-v^6) -2( 2v)
= 16u² + 2uv²w -2 + 10u² - 2v^6 -4v
= 2uv²w - 2v^6 + 26u² -4v -2
What is the equation of the line that passes through the point (5,8) and has a slope
of 3/5?
Answers
Answer:
[tex]y=\frac{3}{5}x+5[/tex]
Step-by-step explanation:
The equation for a line in slope-intercept form is:
[tex]y=mx+b[/tex]
Let's go through what each variable represents:
"y": y-coordinate for any point on the line
"m": slope of the line
"x": x-coordinate for any point on the line
"b": y-intercept (where the line intercepts the y-axis; represented by only the y-coordinate since the x-coordinate is 0)
Given:
Slope = 3/5
Passes through point (5, 8) --> x = 5, y = 8
Find:
y-intercept
We have determined what the question has given us, and what we need to find. Now, we can substitute the given values into the equation:
[tex]y=mx+b\\8=\frac{3}{5}(5)+b\\8=\frac{15}{5}+b\\8=3+b\\$Subtract 3 from both sides\\$b=5[/tex]
Therefore the equation of the line is:
[tex]y=\frac{3}{5}x+5[/tex]
Which of the following points would be a solution to this system of linear inequalities?
Answers
Let's plug in both x and y values in the equation and check if the inequality is true...
[tex]\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}[/tex]
[tex](4,1) \\ y \leqslant x + 1 \\ y < - \frac{x}{2} - 1[/tex]
Substitute x as 4 and y as 1
[tex]1 \leqslant 4 + 1 \\ 1 < - \frac{4}{2} - 1[/tex]
[tex]0 \leqslant 4 + 1 \\ 1 < - 2 - 1[/tex]
[tex]0 \leqslant 5 \\ 1 < - 3[/tex]
This is not a solution because both are not true, Only one equation is giving true as answer which is not correct!~[tex]\purple{ \rule{300pt}{3pt}}[/tex]
[tex](0, - 3) \\ y \leqslant x + 1 \\ y < - \frac{x}{2} - 1[/tex]
Substitute x as 0 and y as -3
[tex] - 3 \leqslant 0 + 1 \\ - 3 < - \frac{0}{2} - 1[/tex]
[tex] - 3 \leqslant 1 \\ - 3 < - 0 - 1[/tex]
[tex] - 3 \leqslant 1 \\ - 3 < - 1[/tex]
This is a solution because both are true, Both the equations are true which means the ordered pair is a solution!~Thus, Option B (0,-3) is the correct choice....
In triangle dat, m < d = 27, m < a = 105, and t=21. find d to the nearest integer.
Answers
Answer:
d = 13
Step-by-step explanation:
Given:
m ∠ d = 27°
m ∠ a = 105°
t = 21°
Look at the picture I posted
Use sine law:
[tex]\mathrm{\dfrac{ sin\:a }{ A } = \dfrac{ sin\:B }{ b }}[/tex]
∠T = 180° - 27° - 105°
∠T = 48°
[tex]\mathrm{\dfrac{ sin\:48\° }{ 21 } = \dfrac{ sin\:D }{ d }}[/tex]
[tex]\mathrm{\dfrac{ sin\:48\° }{ 21 } = \dfrac{ sin\:27 }{ d }}[/tex]
Cross multiply
[tex]\mathrm{{d\:sin\:48\°} = { 21\:sin\:27\°}}[/tex]
Solve for d
[tex]\mathrm{d = \dfrac{ 21\:sin\:27\° }{ sin\:48\° }}[/tex]
Evaluate trigonometric functions in the problem
[tex]\mathrm{d = \dfrac{ 21 \times 0.453990499739547 }{ 0.743144825477394 }}[/tex]
Multiply 21 and 0.453990499739547 to get 9.533800494530487
[tex]\mathrm{d = \dfrac{ 9.533800494530487 }{ 0.74314482547394 }}[/tex]
Divide 9.533800494530487 by 0.743144825477394
[tex]\mathrm{d = 12.828993983}[/tex]
d = 13
Rounded to the nearest integer: 13
The Art and History Museum offers a family discount card for a donation of $57. I The table shows the price per person with and without the discount card. Child's Ticket (12 & Under) Price without Discount Card Price with Discount Card 58 $15 $12 Adult's Ticket For what number of visits will the total cost of the visits (including the price of the discount card) be less expensive for a family of 2 adults and 1 child if they have purchased the discount card?
Answers
Answer:
8 number of visits will be the total cost of the visits (including the price of the discount card) be less expensive for a family of 2 adults and 1 child if they have purchased the discount card
Step-by-step explanation:
Price without Discount Card Price with Discount Card
Ticket (12 & Under) $10 $8
Adult's Ticket $15 $12
Let x be the number of visits
Price without discount card for 2 adults and 1 child ticket
Price without discount for x visits = [tex]x(15 \times 2+ 10)=40x[/tex]
Price with discount for x visits =[tex]57+ x(12 \times 2+ 8)=57+32x[/tex]
Now to find For what number of visits will the total cost of the visits (including the price of the discount card) be less expensive for a family of 2 adults and 1 child if they have purchased the discount card
57+32x< 40x
57<8x
7.1<x
So, 8 number of visits will be the total cost of the visits (including the price of the discount card) be less expensive for a family of 2 adults and 1 child if they have purchased the discount card
At what rate percent per annum will the simple interest on Rs 15000 be Rs 3000 in ? 2 1/2 years
Answers
Answer:
Rate=8%
Step-by-step explanation:
Step 1: Write the given terms
Principal (p)=Rs15000
Rate(r)=?
Time(t)=2 1/2=5/2=2.5
Interest(i)=Rs3000
Step 2: Write the formula for calculating Simple interest
[tex]i = \frac{p \times r \times t}{100} [/tex]
Step 3: Make Rate(r) the subject of the equation in Step 2
[tex]by \: cross \: multiplcation \\ 100i = prt \\ divide \: both \: sides \: by \: pt \: to \: have \\ \frac{100i}{pt} = r[/tex]
Step 4: Use the new equation for r to get the rate by substitution
[tex]r = \frac{100i}{pt} \\ r = \frac{100 \times 3000}{15000 \times 2.5} \\ r = \frac{300000}{37500} \\ r = 8[/tex]
Hence, the rate of the simple interest is 8%
What is the equation of the line that passes through the point (-6,4) and has a
slope of o?
Answers
Answer:
[tex]y=0x+4[/tex]
Step-by-step explanation:
Given the following question:
Point A = (-6, 4) = (x, y)
Slope = 0
To find the equation of the line we are going to use the slope intercept form y = mx + b, substitute the values in for the variables and then solve for b to have our answer.
[tex]y=mx+b[/tex]
[tex]y=4[/tex]
[tex]m=0[/tex]
[tex]x=-6[/tex]
[tex]4=0(-6)+b[/tex]
[tex]0\times-6=0[/tex]
[tex]4=0+b[/tex]
[tex]4+0=4[/tex]
[tex]4=b[/tex]
[tex]b=4[/tex]
[tex]y=0x+4[/tex]
The equation of the line is "y = 0x + 4."
Hope this helps.
Answer:
y = 4
Step-by-step explanation:
Given :-
passes through the point (-6, 4)slope = 0To Find :-
equation of lineSlope :-
We know coordinates of y-intercept are : (0, b)Using point-slope form,b - 4 = 0(0 + 6)b - 4 = 0b = 4Substitution
Using the slope-intercept form,y = mx + by = 0x + 4y = 4Graph a line with a slope of -3/4
that contains the point (2,3) ?
Answers
Answer:
First place a mark at your point. (x=2, y=3)
Step-by-step explanation:
Now when you look at the -3/4 that is called your rise over run so you will go down 3 and over 4 so your next point will be at (x=0, y=6) and then you connect your dots to make a line.
If 8 superscript y baseline = 16 superscript y 2, what is the value of y?
Answers
The value of unknown number y for the equation 8 superscript y baseline = 16 superscript (y+2) is -8.
How to simplify power raised by another number?When the power of a number is raised by another number, then multiply both the powers and the result of this product keep as the power of the number.
Let suppose there is a number a. For this number the above rule can be given as,
[tex](a^m)^n=a^{m\times n}\\(a^m)^n=a^{mn}[/tex]
The expression which consist unknown variable y is given as,
[tex]8^y=16^{y+2}[/tex]
The above equation can be written as,
[tex](2\times2\times2)^y=(2\times2\times2\times2)^{y+2}\\(2^3)^y=(2^4)^{y+2}\\(2)^{3y}=(2^)^{4y+8}[/tex]
As the base of both side of the equation is same. Thus, the value of their exponent can be compared.
[tex]3y=4y+8\\4y-3y=-8\\y=-8[/tex]
Thus, the value of unknown number y for the equation 8 superscript y baseline = 16 superscript (y+2) is -8.
Learn more about the power raised by another number here;
https://brainly.com/question/960886
Ms. Sutton recorded the word counts and scores of the top ten essays in a timed writing contest. The table shows her data. A 3-row table with 10 columns. The first row is labeled essay rank with entries 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. The second row is labeled essay score with entries 9.7, 9.5, 9.5, 9.0, 8.9, 8.9, 8.5, 8.4, 8.2, 7.0. The third row is labeled word count with entries 324, 352, 337, 318, 299, 304, 290, 291, 278, 250. How does the word count of an essay relate to its score in the contest? Word count tends to decrease as the score decreases. Word count tends to increase as the score decreases. Word count tends to remain constant as the score decreases. Word count has no apparent relationship to the score of the essay.
Answers
Analyzing the table, it is found that:
Word count tends to decrease as the score decreases.
------------------------------------
To solve this question, we need to look at the table, where the essays are ranked.
The first four ranked essays have all above 300 words.Of the last four ranked essays, none have above 300 words.From this, it can be said that yes, there is a relation, as the word count tends to decrease as the score decreases.
A similar question is given at https://brainly.com/question/24258409
Answer:
A. Word count tends to decrease as the score decreases.
Step-by-step explanation:
edge2021
3. If each interior angle of a regular polygon has a measure
of 168.75°, find the sum of the interior angles.
Answers
Answer:
2.13333
Step-by-step explanation:
2x180 over 168.75
I AM NOT SURE OF THE ANSWER THO
Part A: Solve for A
Answers
See picture for math work and answer.
PLEASE HELP! I WILL GIVE BRAINLIEST AND NO LINKS PLEASE
Answers
Answer: 10
Step-by-step explanation:
4(2x-5)
distribute
8x-10
8x-10=8x-10
There were 6 boys for every 9 girls at Winnsboro High School last year. If there were 480 students at the school, how many were girls and how many were boys?
Answers
Answer:
288 girls and 192 boys
Step-by-step explanation:
Ratio of boys to girls is 6:9
So, first find the total parts they are dividied into. 6+9= 15
480/15= 32. So one part has 32 students.
The boys are of 6 parts of 15 (as in the ratio). So 32 x 6= 192 boys.
girls are 32 x 9= 288 girls
they add to 480.
50 POINTS FOR CORRECT AWNSER!
Answers
Answer:
[tex]y < -3x[/tex]
Step-by-step explanation:
Choose 2 points on the line: (0, 0) and (1, -3)
Let [tex]\sf (x_1,y_1)=(0,0)[/tex]Let [tex]\sf (x_2,y_2)=(1,-3)[/tex][tex]\sf slope=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-3-0}{1-0}=-3[/tex]
point-slope form of linear equation: [tex]\sf y-y_1=m(x-x_1)[/tex]
[tex]\implies \sf y-0=-3(x-0)[/tex]
[tex]\implies \sf y=-3x[/tex]
Solid line : ≤ or ≥
Dashed line: < or >
Therefore as the line is dashed, and the shading is below the line,
[tex]\implies \sf y < -3x[/tex]
Slope:-
[tex]\\ \tt\Rrightarrow m=\dfrac{6-3}{-2+1}=\dfrac{-3}[/tex]
Equation of line in point slope form
[tex]\\ \tt\Rrightarrow y-3=-3(x+1)[/tex]
[tex]\\ \tt\Rrightarrow y=-3x[/tex]
Equation of the shaded region
[tex]\\ \tt\Rrightarrow y<-3x[/tex]
Let's look at this system of equations"
2x - 4y = 20
X = 4
Solve the system using substitution or elimination. Show your work and/or explain your reasoning.
PLEASE HELP ME GUYS IM BEGGING YOU AND PLEASE SHOW ME HOW U DID IT!!!
Answers
Step-by-step explanation:
Given,
x = 4
2x - 4y = 20
Now,
2x - 4y = 20
or, 2×4 - 4y = 20
or, 8 - 4y = 20
or, -4y = 20 - 8
or, y = 12/-4
or, y = -3
therefore, y = -3
Answer:
(x,y)=(4,-3)
Step-by-step explanation:
2x-4y=20
x=4
substitute the given value of x into the equation
2×4-4y=20
solve the equation for y
y=-3
A possible solution of the system is the ordered pair
(x,y)=(4,-3)
CHECK SOLUTION!
2×4-4×(-3)=20
4=4
simplyfy the quality
20=20
4=4
since all of the qualities are true, the ordered pair is the solution of the system
(x,y)=(4,-3)
hey hi I hope this helps
1. Below are four sequences. Which of them represent an arithmetic sequence?
1.8, 12, 14, 15, ...
11. 2, 4, 8, 16 ...
III. 5, 5, 5, 5...
IV. -101,-99, -97, -95, ---
A. II only
B. IV only
C. I and III
D. II and IV
Answers
5\6 of 45kg plz can u tell me ans
Answers
You are very welcome
If a prime number is greater than 2, it is odd.
TRUE OR FALSE
Answers
Answer:
True
Step-by-step explanation:
Answer:
true
Step-by-step explanation:
Which three temperature readings all mean the same thing?
C
273 Kelvin, 100 degrees Celsius, 212 degrees Fahrenheit
O
273 Kelvin, 0 degrees Celsius, 32 degrees Fahrenheit
O
100 Kelvin, 0 degrees Celsius, 32 degrees Fahrenheit
O
373 Kelvin, 100 degrees Celsius, 273 degrees Fahrenheit
Answers
Answer:
273 K, 0 C, 32 F
This is freezing temperature for all 3 systems.
Jane bought a poster that had a length of 2 1/3 feet and a width of 3/4 feet. What is the perimeter of her poster?3 1/15 feet1 3/4 feet6 1/8 feet6 1/8 square feet
Answers
Answer:
1 1/6
Step-by-step explanation:
We are given the length and width of the poster board. The perimeter of an object is the sum of all four sides.If it helps, picture a rectangle. The length, or the long side, is 2 1/3 feet long. Since both of the rectangle's long sides would be identical, we can assume both sides are 2 1/3 feet long.This also applies to the short side, or the width. Both ends of the poster board would be 3/4 feet long.To find the perimeter, you need to add all four sides together. I assume this is the tricky part for you, as you are not sure how to add fractions yet.First, let's add the two long sides together. 2 1/3 + 2 1/3 would equal 4 2/3. How did I get this? Well, 2 + 2 = 4 (you add the number outside of the fraction first). To add fractions, you look to see if the bottom of the fraction, or the denominator, is the same. As 1/3 and 1/3 have the same denominator, you can leave the 3 alone and only add the top, giving us 2/3.Duplicate this process with the width. 3/4 + 3/4 would give us 6/4. How do we reduce this? We turn it into what is called a mixed number. This means that there will be a big number on the outside, then a fraction attached to it. How do we turn this improper fraction, or a fraction where the top is greater than the bottom, into a mixed number?A fraction can also be interpreted as a division problem. You can look at 6/4 as 6 ÷ 4. Four goes into 6 one time, with 2 left over (6 - 4 = 2). We take how many times four goes into 6 (once) and use that as our big number. All we have to do now is take our leftover number (2) and turn it into a fraction. How? We use 4 as our bottom, or denominator, because it is left over from how many times 4 goes into 6. In conclusion, our mixed number is 1 2/4. Reduced, this is 1 1/2, because 2/4 cut in half is 1/2.So now we have two numbers. 4 2/3 and 1 1/2. How do we add these together if their denominators are different? 2/3 and 1/2 are not compatible by themselves. Well, we need to find a number that both 3 and 2 go into. This number would be 6. But we can't just turn 2/3 into 2/6, we need to multiply the bottom by a number that would make it six, and multiply the top by the same number. 2 • 3 = 6 (from 2/3) so we multiply the top by 2 also. This gets us 4/6. Don't forget the big 4 on the outside to get us 4 4/6!We do the same to the other mixed number, 1 1/2. Half of 6 is 3, so we can turn 1/2 into 3/6, then we make sure our big 1 is on the outside. Now we can add 1 3/6 to 4 4/6!First, add 1 and 4 by itself to get us 5. Then, you can add the fractions 3/6 and 4/6 (don't add the bottom, just the top!) to get 7/6. To reduce this, we divide 7 by 6 to get us 1 1/6!If I am incorrect in my reasoning, please let me know so that I can plan better for my future answers. Have an amazing day.
Pls help me on this problem I’m confused
Answers
Answer:
30 × 24 = 720 inches
since there are 12 inches in a foot
720 ÷ 12 = 60
60 feet converted to yards is 20 yards
50 - 20 = 30
they should have 30 yards of string left over
1) someone answer this please
Answers
Answer:
x = 15
y = 1
Step-by-step explanation:
Bonnie deposits $180 in a savings account that earns simple interest at an annual rate of 3%. How much interest does her account earn after 10 years?
Answers
Answer: $54.00
Explanation: Three percent of $180.00 is $5.40. So Bonnie receives $5.40 annually. In ten years, she will have $54 (multiply 5.40 by 10).
How to simplify 3²y×3⁴y?
Answers
Step-by-step explanation:
please mark me as brainlest