The Equation of parabola with focus (3,1) and directrix y = 3 is [tex]10x^2 + 9y^2-60x -14y+91 =0[/tex]
What is Parabola?A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.
Here, focus (3,1) and directrix y=3
Let the locus of parabola be (x, y)
We know that, in Parabola
Distance between locus to focus = Distance between locus to directrix line
[tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex] = [tex]\frac{Ax_{1}+By_{1}+C }{\sqrt{A^2 + B^2 + C^2} }[/tex]
[tex]\sqrt{(x-3)^2+(y-1)^2} = \frac{0.x+1.y-3}{\sqrt{0^2+1^2+(-3)^2} }[/tex]
On squaring both sides, we get
[tex](x-3)^2 + (y-1)^2 = (\frac{y-3}{\sqrt{10} } )^2[/tex]
[tex]x^2 -6x + 9 + y^2 -2y + 1 = \frac{y^2 -6y +9}{10}[/tex]
[tex]10x^2 + 9y^2-60x -14y+91 =0[/tex]
Thus, The Equation of parabola with focus (3,1) and directrix y = 3 is [tex]10x^2 + 9y^2-60x -14y+91 =0[/tex]
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17. Evaluate and Synthesize
Tobacco smoking is extremely expensive to our society in economic and health costs as well as in human suffering. How would you solve the tobacco smoking problem? How would you specifically target young people?
Answer:
I would ban smoking in your county or ild advertise and ill make jobs to get people to help smokers so than they stop smoking and quit.
a package of buttery round crackers contains 4 sleeves of crackers each package of crackers cost $2.49 A function, f(x) is written to represent the cost of purchasing x packages of crackers
What is the practical domain for the function f(x)?
.All positive integers
.All whole numbers
.All whole numbers that are multiples of 4
.All real numbers
The practical domain of function f(x) has all positive integers and all whole numbers that are multiples of 4 that is option A or D is correct
What is domain?The domain is "set of all possible inputs value for the function".
According to the question,
A package of buttery round crackers contains 4 sleeves of crackers each
package of crackers cost $2.49. A function f(x) written to represent the cost of purchasing x packages of crackers.
In order to find the practical domain for the function f(x) only if analysis the value of domain function 'x' must positive number so contain 'all positive integers' and since a package of buttery round crackers contains 4 sleeves then domain must contain 'all whole numbers that are multiples of 4'.
Hence, the practical domain of function f(x) has all positive integers and all whole numbers that are multiples of 4.
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Find the value of x 63° (2x + 3)°
Answer:
x = 20
Step-by-step explanation:
63−3x=3
−3x=−60
x=20
You need to spend at least $50 in one day to receive a store discount. You have already spent $30. Let s be the amount of money (in dollars) you can now spend to qualify
for the discount. Which inequality and solution represent this situation?
s+30<50; 8 < 20
s+30 ≤ 50; s ≤ 20
s+30> 50; 8 > 20
s+ 30 ≥ 50; 8 ≥ 20
Answer: s + 30 ≥ 50; s ≥ 20
Step-by-step explanation:
let s be the amount you have yet to spend in order to reach $50 or more
you already have $30.
This means you need to spend at least $20 more ($50 - $30 = $20)
S can be greater than or equal to $20 because your total will be 50 or more, therefore qualifying for the discount.
Help me, please.. +50 points (and brainliest if someone else answers)
Given phrase - 66 less than twice Greg's age
In the given phrase, "twice" means "double", which means "2 times".
⇒ 66 less than 2(Greg's age)In the given phrase, "less than" means "subtraction in reverse form".
⇒ 66 - 2(Greg's age)Reversing the expression, we get:
⇒ 2(Greg's age) - 66The question has stated that "Greg's age" will be represented as "g". Let's substitute "Greg's age" as "g". Then,
⇒ 2(Greg's age) - 66⇒ 2(g) - 66 = 2g - 66Therefore, the expression that represents the phrase is 2g - 66.
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URGENT! please answer. i'll give 5 stars + brainilest if correct
To estimate the height of a mountain, two students find the angle of elevation from a point (at ground level)
b
=
560
meters from the base of the mountain to the top of the mountain is
β
=
51
∘
. The students then walk
a
=
1850
meters straight back and measure the angle of elevation to now be
α
=
34
∘
. If we assume that the ground is level, use this information to estimate the height of the mountain.
The height of the mountain is
_____ meters.
Answer:
times the nimbers
Step-by-step explanation:
240
Which of the following graphs is not a function ?
Answer:
I believe it should be the first one
Step-by-step explanation:
in the first one if you put a line straight it would cross it twice making it not function.
Answer:
The first one is not a function.
Step-by-step explanation:
When you perform the vertical line test on the graphs, the first graph is the only one that passes through a X value multiply times.
solve quadratic 2x^2 -7 +6 =0
Answer:
Assuming you meant 2x^2-7x+6=0,
the answer is x=2, x=1.5
Use the quadratic formula. (-b (+ or -) sqrt(b^2 - 4ac) )/ (2a)
A ladder 20 m long rests against a vertical wall so that the foot of the ladder is 9 m from the wall. a Find, correct to the nearest degree, the angle that the ladder makes with the wall. b Find, correct to 1 d.p., the height above the ground at which the upper end of the ladder touches the wall.
Answer:
(a) 27°
(b) 17.9m
Step-by-step explanation:
According to the attachment
⠀
let AB be the ladder
BC be the distance between the ladder and wall
⠀
(a) We have to find ∠A by trigonometry formula
[tex] \sf \sin A = \frac{perpendicular}{hypotenuse} [/tex]
Here angle A is facing BC so it is perpendicular
and AB is the longest side so it is hypotenuse
[tex] \sf \implies \sin A = \frac{BC}{AB} \\ \\ \\ \sf \implies \sin A = \frac{9}{20} \\ \\ \\ \sf \implies \sin A = 0.45 \\ \\ \\ \sf \implies \sin A = \sin27{ \degree} \\ \\ \\ \sf \purple {A = 27{ \degree}}[/tex]
(b)
AC is the distance from the upper end of the ladder to ground
we will find it by Pythagoras theorem
[tex] \sf {hypotenuse}^{2} = {perpendicular}^{2} + {base}^{2} \\ \\ \\ \sf \implies {AB}^{2} = {BC}^{2} + {AC}^{2} \\ \\ \\ \sf \implies {20}^{2} = {9}^{2} + {AC}^{2} \\ \\ \\ \sf \implies 400 = 81 + {AC}^{2} \\ \\ \\ \sf \implies 400 - 81 = {AC}^{2} \\ \\ \\ \sf \implies 319 = {AC}^{2} \\ \\ \\ \sf \implies \sqrt{319} = AC \\ \\ \\ \sf \blue{\implies 17.86 = AC}[/tex]
Look at the image below.
3
2.2
2
What is the area of the parallelogram?
square units
Which inequality represents the graph shown below?
Answer:
x>-2
since the arrow goes to the right from -2 it is definitely greater than -2. now see that the line does not include the value -2 itself.. thus, we say it is greater than -2
Answer:
x > -2
Step-by-step explanation:
Details understood from the graph :
Open dot from starting pointIncreases from -2Hence,
Open dot means > or <Greater means ⇒ >The inequality is : x > -2Lisa is on a trip of 1,579 miles. She has already traveled 220 miles. She has 3 days left in her trip. How many miles does she need to travel each day to complete the trip?
A. 673
B. 906
C. 1,359
D. 453
Answer: D. 453
Step-by-step explanation:
First, we will find out how many miles she has left.
-> We will subtract miles travled from total trip.
1,579 miles - 220 miles = 1,359 miles
Now, we will find the answer to your question.
-> If she has three days left in her trip, we will divide the rest of the miles to travel by 3.
1,359 miles / 3 days = 453 miles
The answer to your question is;
D. 453
> Next question
Find the last term to make the trinomial into perfect square
x2 – 2x
Answer:
+ 1.
Step-by-step explanation:
That would be (-2/2)^2
= + 1.
x2 - 2x + 1 = (x - 1)(x - 1)
[tex]\text{If a quadratic expression is a perfect square, then}\\\\~~~~~~~\text{Discriminant = 0}\\\\\implies b^2 -4ac = 0\\\\\implies (-2)^2 -4 c = 0\\\\\implies 4-4c = 0\\\\\implies 4c = 4\\\\\implies c = 1 \\\\\text{Hence, the last term should be 1.}\\\\x^2 -2x +1 = (x-1)^2[/tex]
Help me plsssssssssssssss
A 5-pound bag of candy costs $13.05. What is the unit price?
Answer:
1.85 because: 9.25 divided by 5 equals 1.85
I hope I have helped you and if you like go to my profile that I also need a hand, thanks.
please help me with this question !!
Answer:
x is (0,15), because when you place x as zero you'll the coordinate D when you plot these coordinates on your graph.
Find the area of each. Round your answer to the nearest tenth. 28) 2.6 cm
Answer:
Here is the answer...hope it helps
find the prime factorization of the following number 252?
Answer:
2,3,7 are the prime factorization of number of 252
Hi Student!
Prime factorization is the process of stripping down a number to it's basic elements. We take a number and bring it down the most we can. For example we take 4 and make it 2 x 2. In this case we are given a number of 252 so we can began by dividing by 2.
[tex]252 / 2[/tex]
[tex]126[/tex]
Looking at the numbers that we have now, 126 x 2, we can see that 126 can still be divisible by another 2 so lets do that again.
[tex]126 / 2[/tex]
[tex]63[/tex]
Now, looking at the numbers that we have, 63 x 2 x 2, we see that we can no longer divide it by a 2 because 63 is not divisible by 2. However, we can divide 3 away from the number so lets do that.
[tex]63 / 3[/tex]
[tex]21[/tex]
Once again, looking at the numbers that we have, 21 x 3 x 2 x 2, we see that we can once again divide a 3 away from our first number so lets do that again.
[tex]21 / 3[/tex]
[tex]7[/tex]
Finally, we have come down to the last line where our final elements are 7 x 3 x 3 x 2 x 2. This is our prime factorization of the number 252 and this is where we can conclude our solution seeking.
Find the time that that the projectile will reach a height of 96 ft and return to the ground when v0 = 112 feet per second
The time that the projectile will reach a height of 96 ft and return to the ground will be 6 seconds.
What is kinematics?It is the study of the motion of a body without considering mass. And the reason behind them is neglected.
The projectile will reach a height of 96 ft and return to the ground when v₀ = 112 feet per second
The time it takes to reach feet and return to the ground will be
T = 2v₀ / g
Where g = 32.2 feet per square second.
Then we have
T = 2 x 112 / 32.2
T = 5.956
T ≅ 6 seconds
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Please help plsass….
Step-by-step explanation:
the area of a circle is
pi×r²
that is for the whole circle, which is the same as 360 degree arc.
now that we have only 254 out of the total of 360 degrees, the sector area is
pi×r² × 254/360
pi×9² × 254/360 = pi×9 × 254/40 = pi×57.15 =
= 179.5420202... cm²
rounding to 1/10 is 180.0 cm².
so, it is actually D - none of the above.
Answer:
D. none of the above
Step-by-step explanation:
the area of a circle is
pi×r²
that is for the whole circle, which is the same as 360 degree arc.
now that we have only 254 out of the total of 360 degrees, the sector area is
pi×r² × 254/360
pi×9² × 254/360 = pi×9 × 254/40 = pi×57.15 =
= 179.5420202... cm²
rounding to 1/10 is 180.0 cm².
so, it is actually D - none of the above.
Find the area.
14 in
6.8 in
Answer:
95.2Step-by-step explanation:
It nearly confused me, but I got the entire thing in my brain.
Given equation:
14 * 6.8Solve:
Transfer:6.8 ⇒ 68Solve:14 * 68= 952Transfer a decimal point to the right 1 space:952 → 95.2.Answer is 95.2.
Match the trigonometric ratios with their values based on the triangle shown in the diagram.
The trigonometric ratios with their values are based on the triangle will be sin D = 4 / 5, sin C = 3 / 5, sin D x cos D = 12 / 25, tan C x tan D = 1, and cos C x tan D = 16 / 15.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
The triangle is given below.
Then the trigonometric ratios with their values are based on the triangle shown in the diagram and will be
sin D = 4 / 5
sin C = 3 / 5
sin D x cos D = 4 / 5 x 3 / 5
sin D x cos D = 12 / 25
tan C x tan D = 3 / 4 x 4 / 3
tan C x tan D = 1
cos C x tan D = 4 / 5 x 4 / 3
cos C x tan D = 16 / 15
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These questions kinda hard help
Answer:
Step-by-step explanation:
Remark
All of the given listed figures have the property of 4 sides and 4 angles. There is also some relationship between the angles or pairs of angles. Only the square follows the same path. The others cannot be chosen because the sides differ and the angle properties are quite different.
Answer: Square
Y=3x+2
X
-2
-1
0
1
2
Answer:
x y ordered pair
-2 3(-2) + 2 = -4 (-2, -4)
-1 3(-1) + 2 = -1 (-1, -1)
0 3(0) + 2 = 2 (0, 2)
1 3(1) + 2 = 5 (1, 5)
2 3(2) + 2 = 8 (2, 8)
PLSS HELPPP: A water cooler holds 18 liters of sports drink. Approximately how many gallons is this? (1 gallon = 3.785 liters
Answer:
4.75561426684
Step-by-step explanation:
Use websites that are calculators
The owner of a smart watch would like to estimate the mean number of steps they take per day. To do so, they select a random sample of 30 days from the previous year's data and record the number of steps they took on each of those days. The mean number of steps taken per day was 8,575 with a standard deviation of 2,125 steps. What is the value of the standard error of the mean?
O 70.833 O 387.970 O 394.603 O 2,125
The standard error is an estimate of the standard deviation of the sampling distribution. The value of the standard error of the mean is 387.970.
What is the standard error?It is an estimate of the standard deviation of the sampling distribution. It measures the variability of a considered sample statistic.
Suppose that we're given that:
Population standard deviation = σ
Size of the sample we're working on = n
Then, the standard error can be calculated as:
[tex]SE = \dfrac{\sigma}{\sqrt{n}}[/tex]
where SE denotes the standard error.
The standard error of the mean can be written as,
SE = σ/√n
SE = 2,125/√30
SE = 387.970
Hence, the value of the standard error of the mean is 387.970.
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What is the area of the triangle Base is 6 ft height is 5 ft.
Answer:
Area of a triangle = 0.5 * base * height = 0.5 * 6 * 5 = 15 sq. ft
Answer:
Area = 0.5 * base * height
0.5 * 6 * 5 = 15
Area = 15 sq ft
Please help I am struggling really bad thank you so much
Answer:
1) A
2) A
3) C
Step-by-step explanation:
Answer: B, A, A
Step-by-step explanation:
I'm not 100% sure this is the answer sorry if I'm wrong
help will mark Brainliest!!
Answer:
Jonah should shade 6 parts of 10 equal parts to show 3/5
Step-by-step explanation:
Jonah should shade 6 parts of 10 equal parts to show 3/5
3/5 * 2 = 6/10
7/10 + 6/10
if your 14 and you have a kid at 21 how old will your kid be when your 30
Answer:
Your kid will be 9 years old.
Step-by-step explanation:
It's not relevant, that you are 14 now.
Answer: 9
Step-by-step explanation: Regardless of if you are 14 or not, 30-21=9
