Select the equation for a graph that is the set of all points in the plane that are equidistant from the point F(0, −8) and line y = 8.
Answers
Answer:
-1/32 × x
Step-by-step explanation:
let's define and identify the correct markers of the correct parabola.
so, we have the focus point F (0, -8).
we have the directrix y = 8.
that means the the vertex point (the middle between the focus and the directrix) is (0, 0).
a parabola is turning away from the directrix. the vertex here is below the directrix, so the parabola is opening downwards and has therefore a negative factor of x.
so, we can rule out the 2 positive answer options.
to decide between the other 2, let's use a value of x and see, if the point is equidistant to the focus and the directrix.
e.g. x = 1
so,
y = -1/8 × x²
gives us y = -1/8 for x = 1
that means the point is (1, -1/8).
the distance to the focus (0, -8) is
(1 - 0)² + (-1/8 - - 8)² = 1 + (7 7/8)² = 1 + (63/8)² =
= 64/64 + 3969/64 = 4033/64
the distance to the directrix is the distance to the point (1, 8) as the point on the directrix must have the same x value.
so, the distance (1, -1/8) to (1, 8) is
(1 - 1)² + (-1/8 - 8)² = 0 + (-65/8)² = 4225/64
that is not equal to the distance to the focus.
so, let's try
y = -1/32 × x
the point for x = 1 is (1, -1/32)
distance to focus
(1, -1/32) to (0, -8) = (1-0)² + (-1/32 - -8)² = 1 + (255/32)² =
= 1024/1024 + 65025/1024 = 66049/1024
distance to directrix
(1, -1/32) to (1, 8) = (1-1)² + (-257/32)² = 66049/1024
which is the same distance as to the focus.
so, y = -1/32 × x is the right answer.
FYI - for an actual distance I would have to create the square roots of the numbers used here.
but since we only needed to see, if distances are equal or not, it was sufficient to check if the squares of the distances are equal or not.
Related Questions
A Cyclist rides her bike of a rate of 18 Kilometers per hour. What is this rate in Kilometers per minute? How many Kilometers will the cyclist travel in 20 minutes? Do not Round your answers.
Answers
Step-by-step explanation:
18 ÷ 60 = 0.3
so 0.3 km per min.
0.3 × 20 = 6
so 6 km per hour
Find the value of each variable in the parallelogram.
Answers
Answer:
h=9
g=61
Step-by-step explanation:
16-h=7
g+4=65
&
Opposite angles and sides are equal in a paralleogram
g+4=65g=65-4g=61Amd
16-h=7h=16-7h=9Please help solve by elimination I hope its not blurry Have a nice day and Goodnight
Answers
Answer:
[tex]\displaystyle \textcolor{black}{4.}\:[-3, -5][/tex]
[tex]\displaystyle \textcolor{black}{3.}\:[8, -1][/tex]
[tex]\displaystyle \textcolor{black}{2.}\:[4, -7][/tex]
[tex]\displaystyle \textcolor{black}{1.}\:[3, -2][/tex]
Step-by-step explanation:
When using the Elimination method, you eradicate one pair of variables so they are set to zero. It does not matter which pair is selected:
[tex]\displaystyle \left \{ {{2x - 3y = 9} \atop {-5x - 3y = 30}} \right.[/tex]
{2x - 3y = 9
{⅖[−5x - 3y = 30]
[tex]\displaystyle \left \{ {{2x - 3y = 9} \atop {-2x - 1\frac{1}{5}y = 12}} \right. \\ \\ \frac{-4\frac{1}{5}y}{-4\frac{1}{5}} = \frac{21}{-4\frac{1}{5}} \\ \\ \boxed{y = -5, x = -3}[/tex]
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[tex]\displaystyle \left \{ {{x - 2y = 10} \atop {x + 3y = 5}} \right.[/tex]
{x - 2y = 10
{⅔[x + 3y = 5]
[tex]\displaystyle \left \{ {{x - 2y = 10} \atop {\frac{2}{3}x + 2y = 3\frac{1}{3}}} \right. \\ \\ \frac{1\frac{2}{3}x}{1\frac{2}{3}} = \frac{13\frac{1}{3}}{1\frac{2}{3}} \\ \\ \boxed{x = 8, y = -1}[/tex]
_______________________________________________
[tex]\displaystyle \left \{ {{y = -3x + 5} \atop {y = -8x + 25}} \right.[/tex]
{y = −3x + 5
{−⅜[y = −8x + 25]
[tex]\displaystyle \left \{ {{y = -3x + 5} \atop {-\frac{3}{8}y = 3x - 9\frac{3}{8}}} \right. \\ \\ \frac{\frac{5}{8}y}{\frac{5}{8}} = \frac{-4\frac{3}{8}}{\frac{5}{8}} \\ \\ \boxed{y = -7, x = 4}[/tex]
------------------------------------------------------------------------------------------
[tex]\displaystyle \left \{ {{y = -x + 1} \atop {y = 4x - 14}} \right.[/tex]
{y = −x + 1
{¼[y = 4x - 14]
[tex]\displaystyle \left \{ {{y = -x + 1} \atop {\frac{1}{4}y = x - 3\frac{1}{2}}} \right. \\ \\ \frac{1\frac{1}{4}y}{1\frac{1}{4}} = \frac{-2\frac{1}{2}}{1\frac{1}{4}} \\ \\ \boxed{y = -2, x = 3}[/tex]
_______________________________________________
I am joyous to assist you at any time.
PLEASE HELP WILL GIVE BRANLIEST
Answers
A square pyramid has a base with a side length of 7.5 feet and lateral faces with heights of 16 feet. Write an expression that can be used to find the surface area, in square feet, of the square pyramid.
Please provide an expression, not just the surface area please :)
Answers
Check the picture below.
so the surface area of the pyramid will be the sum of the areas of the base and the four triangular faces.
[tex]\stackrel{\textit{\Large Areas}}{\stackrel{\textit{4 triangular faces}}{4\left[ \cfrac{1}{2}(7.5)(16) \right]}~~ + ~~\stackrel{\textit{rectangular base}}{(7.5)(7.5)}}\implies 240~~ + ~~56.25\implies 296.25~ft^2[/tex]
Factor completely 4a^2-b^2-2a+b GUYS HELP THERE ARENT ANY CORRECT ANSWERS ON BRAINLY URGENT
Answers
Answer:
(2a-b)(2a+b-1)
Step-by-step explanation:
Find the measures of the interior angles that maximize the area of an isosceles trapezoid
where the length of the non-parallel sides are each 4 inches and the length the shorter of
the two bases is 6 inches.
Answers
The measure of the angle that would maximize the area of this isosceles trapezoid is equal to 0.4395 rad.
Given the following data:
Base length = 6 inches.Sides length = 4 inches.How to calculate the area of a trapezium.Mathematically, the area of a trapezium is given by this formula:
A = ½ × (a + b) × h
A = ½ × (12 + 2l) × h
A = h(6 + l)
Next, we would derive a mathematical expression for A in terms of h as follows;
Let l = 4sinθ Let h = 4cosθA = (6 + 4sin(θ)) × 4cosθ
In order to determine the value of θ for which the area of this isosceles trapezoid is maximized, we would differentiate the area (A) with respect to angle (θ):
Note: sin²θ + cos²θ = 1 ⇒ cos²θ = 1 - sin²θ.
[tex]\frac{dA}{d\theta} =16 cos^{2} \theta - 4sin \theta(6+4sin \theta)\\\\\frac{dA}{d\theta} = 16 cos^{2} \theta - 16 sin^{2} \theta - 24sin\theta\\\\\frac{dA}{d\theta} =16(1-sin^{2} \theta)- 16 sin^{2} \theta - 24sin\theta\\\\\frac{dA}{d\theta} = - 32 sin^{2} \theta - 24sin\theta+16\\\\32 sin^{2} \theta + 24sin\theta-16=0[/tex]
Next, we would use the quadratic formula to solve for the value of sinθ.
Mathematically, the quadratic formula is given by this equation:
[tex]sin\theta = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
Where:
a = 32.b = 24.c = -16.Substituting the parameters into the formula, we have;
[tex]sin\theta = \frac{-24\; \pm\; \sqrt{24^2 - 4(32)(-16)}}{2(32)}\\\\sin\theta = \frac{-24\; \pm\; \sqrt{2624}}{64}\\\\sin\theta = \frac{-24\; \pm\; 51.23}{64}\\\\sin\theta = \frac{-24\;+\; 51.23}{64}\\\\sin\theta = \frac{27.23}{64}\\\\sin\theta = 0.4255\\\\\theta = sin^{-1}(0.4255)[/tex]
θ = 0.4395 rad.
Note: We would only consider the positive value of the quadratic root.
For the obtuse interior angles of the trapezoid, we have [tex](\frac{\pi}{2} +0.4395)[/tex]
Similarly, the measure of the acute interior angles of the trapezoid is [tex](\frac{\pi}{2} -0.4395)[/tex]
Read more on isosceles trapezoid here: https://brainly.com/question/4758162
I will give the brainiest if you get it right.
Answers
Answer:
1 ≤ x < 7/4
Step-by-step explanation:
The function f(x) is defined as increasing on the domain (-8, 4), so the ordering of the arguments is not changed by the function. We can solve the inequality as though f(x) = x, which is increasing everywhere.
Inequality solutionsf(4x -3) ≥ f(2 -x²)
4x -3 ≥ 2 -x² . . . . . . using our assumed definition of f(x)
x² +4x -5 ≥ 0 . . . . . subtract 2-x²
(x -1)(x +4) ≥ 0 . . . . factored form; zeros at -4, +1
The values of x that make this true are ones that make the factors have the same signs: x ≤ -4 or x ≥ 1.
Domain restrictionsThe domain of f(x) is -8 < x < 4, so we require the arguments of f be restricted to those values
Left side
-8 < 4x -3 < 4
-5 < 4x < 7
-5/4 < x < 7/4
Right side
-8 < 2 -x² < 4 . . . . . right side is always true
x² < 10 . . . . . . . . . . . add x² +8
|x| < √10 . . . . . . . . . . less restrictive than the the left-side restriction
SolutionWith the given domain restrictions on f(x), the inequality will be true on the interval ...
1 ≤ x < 7/4
__
Additional comment
The attached graph shows the left-side function argument (dashed blue) and the right-side function argument (dashed green) with the given domain restrictions. The red curve is the difference in function values for the function defined as above. It is only non-negative between 1 and 1.75 as we found above.
This general behavior is applicable for any f(x) that can be described as in the problem statement. For example, f(x) = √(x+8) also gives an increasing curve for the difference f(4x-3)-f(2-x²) on the interval (-5/4, 7/4) with an x-intercept of +1.
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What is the least common multiple of 324 and 245?
Answers
the lcm would be 79380
Step-by-step explanation:
5×7×7
2×2
×3×3×3×3
muliply all the 3 numbers and then you get 79380
Pam’s monthly food budget is equal to 40% of her monthly rent payment. If her food budget is $200 a month, how much is her rent payment each month?
Answers
so we know that 40% for the rent payment is for food, and we also know that those 40% are really 200 bucks, so what would it be for the 100%?
[tex]\begin{array}{ccll} \%&amount\\ \cline{1-2} 40 & 200\\ 100& x \end{array} \implies \cfrac{40}{100}=\cfrac{200}{x}\implies \cfrac{2}{5}=\cfrac{200}{x} \\\\\\ 2x=1000\implies x=\cfrac{1000}{2}\implies x=500[/tex]
Carly needs $149 to buy a skateboard. She already has $52. She earns money washing cars for $20 a car.
Carly says that if she washes 5 cars she will have enough money to buy the skateboard.
Use the drop-down menus to explain how to solve this problem.
First multiply
Choose...
× $20 to find how much money Carly will earn washing cars. Then add this amount to
Choose...
to find how much money Carly has in all. Finally,
Choose...
the total to the cost of the skateboard.
Answers
Answer:
$149 - skateboard price
$52 - carly's money
$20 × 5 cars = $100
$100 + $52 = $152
$152 - $149 = $3 left
Robin got home from school
at 3:45. She spent 2 hours
working on her homework, a
half an hour walking the dog,
and forty-five minutes eating
dinner with her family. Then
she began reading her book.
At what time was she finished
eating dinner?
Answers
Answer:
She was finished with dinner at 6:50
Step-by-step explanation:
3:45 + 2 = 5:45
5:45 + 30 = 6:05
6:05 + 45 = 6:50
5:45+ 30= 6:15
6:15 + 45 = 7:00
Hope this helped
A student was asked to simplify the expression 2(x+3)+(4x−8)−7x.
Identify the line which contains the initial error.
1: 2(x+3)+(4x−8)−7x
2: 2x+6+4x+8−7x
3: (2x+4x−7x)+(6+8)
4: −x+14
Answers
Answer:
Line 2
Step-by-step explanation:
When factoring the second bracket, 1 x -8 is -8.
Answer:
4
Step-by-step explanation:
2{x+3}+{4x_8}_7x is same2x+6+4x+8_7x the first bracket was multiply by 2 {2x+4x_7x}+{6+8} the like term was collected and grouped with bracketsSolve | x + 6| - 7 = 8
A: x= -9 and x = -21
B: x = 9 and x = -9
C: x = -9 and x = 21
D: x = 9 and x = -21
Answers
Answer:
x = 9,-21
Step-by-step explanation:
Given:
[tex]\displaystyle \large{|x+6|-7=8}[/tex]
Transport -7 to add 8:
[tex]\displaystyle \large{|x+6|=8+7}\\\displaystyle \large{|x+6|=15}[/tex]
Cancel absolute sign and add plus-minus to 15:
[tex]\displaystyle \large{x+6=\pm 15}[/tex]
Transport 6 to subtract ±15:
[tex]\displaystyle \large{x=\pm 15-6}[/tex]
Consider:
[tex]\displaystyle \large{x= 15-6}[/tex] or [tex]\displaystyle \large{x = -15-6}[/tex]
[tex]\displaystyle \large{x=9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]
Solution:
[tex]\displaystyle \large{x = 9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]
__________________________________________________________
Second Method
Given:
[tex]\displaystyle \large{|x+6|-7=8}[/tex]
Transport -7 to add 8:
[tex]\displaystyle \large{|x+6|=8+7}\\\displaystyle \large{|x+6|=15}[/tex]
Absolute Function Property:
[tex]\displaystyle \large{|x-a| = \begin{cases} x-a \ \ (x \geq a) \\ -x+a \ \ (x < a) \end{cases}}[/tex]
Consider both intervals:
When x ≥ a then:
[tex]\displaystyle \large{|x+6|=15}\\\displaystyle \large{x+6=15}[/tex]
Transport 6 to subtract 15:
[tex]\displaystyle \large{x=15-6}\\\displaystyle \large{x=9}[/tex]
When x < a then:
[tex]\displaystyle \large{|x+6|=15}\\\displaystyle \large{-(x+6)=15}\\\displaystyle \large{-x-6=15}[/tex]
Transport -6 to add 15:
[tex]\displaystyle \large{-x=15+6}\\\displaystyle \large{-x=21}[/tex]
Transport negative sign to 21:
[tex]\displaystyle \large{x=-21}[/tex]
Solution:
[tex]\displaystyle \large{x=9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]
__________________________________________________________
Let me know if you have any questions regarding this question, my answer or explanation. Hope this answer and explanation helps you and good luck with your assignment!
Palil used 6 pieces of ribbon that were each 9 inches long on a project.
How many inches of ribbon did he use?
Use the bar diagram to show how many inches of ribbon Palil used.
Drag the numbers to the bar diagram. Numbers may be used once, more than once, or not at all.
Answers
Answer:
54
Step-by-step explanation:
9x6=54
can someone please help me with this
Answers
Answer:
"4 or less, let it rest. 5 or more, raise the score."
Step-by-step explanation:
1) 5.57, 5.62, 5.59
2) 2.349, 2.352, 2.346, 2.354
3)
0.7
0.3
1.5
3.4
4)
3.74
0.93
0.33
1.56
I hope this helps! Have a lovely day!! :)
(I would appreciate brainliest!!)
How many subsets does the following set (4,5,6,7,8) have?
Answers
Answer:Number of subsets will be given by 2^n, where n is the number of elements in the set.
Step-by-step explanation:
Number of elements is 5. Therefore, the number of subsets that can be formed from the given set is 2^5 = 32.
Determine the type of symmetry of r=-7+ 2cos3ø from the equation, if any. Make sure to confirm graphically. Symmetric with respect to the:
A) pole
B) none of these
C)line /2
D) polar axis
Answers
well, hmmm to check for polar symmetry, hmmm say we simply replace the value for either "r" or "θ" or both in the original equation, if the equation rendered is the same as the original, there you have it, symmetry, so let's do that.
[tex]\underline{\textit{testing for symmetry to the }\frac{\pi }{2}~line\qquad \qquad r=-r~~,~~\theta =-\theta } \\\\\\ r=-7+2cos(3\theta )\implies (-r)=-7+2cos[3(-\theta )]\implies -r=-7+2cos(-3\theta ) \\\\\\ \stackrel{symmetry~identity}{-r=-7+2\stackrel{\downarrow }{cos(3\theta )}}\implies r=7-2cos(3\theta )\impliedby \textit{woopsie, no dice} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\underline{\textit{testing for symmetry to the polar axis}\qquad \qquad \theta =-\theta} \\\\\\ r=-7+2cos(3\theta )\implies r=-7+2cos[3(-\theta )]\implies r=-7+2cos(-3\theta ) \\\\\\ \stackrel{symmetry~identity}{r=-7+2\stackrel{\downarrow }{cos(3\theta )}}\impliedby \textit{low and behold\qquad \Large \checkmark}[/tex]
now, we could run a test for "the pole" or namely the origin by simply changin r = -r, however we already know where the symmetry is, so no need.
Check the picture below.
solve please. find volume
Answers
The figure given in the image is a cuboid which have 3 sides, with Length, breadth and height, it's basically a 3-D shape, so here for volume of the cuboid, we can just multiply all the sides and we will be just done then after writing the SI unit of volume against it
[tex]{:\implies \quad \sf So,\:\: Volume=4\dfrac{2}{5}\times 10\times 3}[/tex]
[tex]{:\implies \quad \sf Volume=\bigg(\dfrac{20+2}{5}\bigg)\times 10\times 3}[/tex]
[tex]{:\implies \quad \sf Volume=\dfrac{22}{5}\times 10\times 3}[/tex]
[tex]{:\implies \quad \sf Volume=22\times 2\times 3}[/tex]
[tex]{:\implies \quad \sf Volume=44\times 3=\boxed{\bf{132\:\: m^{3}}}}[/tex]
PLEASE ANSWER THIS ASAP IT'S DUE IN 5 MINUTES!!!!
1. The rule for an arithmetic sequence is: __________?
2. The rule for a geometric sequence is: __________?
Answers
Answer:
an = a1 + d (n - 1)
aⁿ = a₁ˣ⁻1
NO LINKS!!!
Part 3: Figure A is a dilated image of Figure B. Find the scale factor. #5 and 6
Answers
Answer:
Step-by-step explanation:
Scale:- 1box=1units
So
Take one side of each
B=6unitsA=10unitsScale factor(A to B)
[tex]\\ \rm\rightarrowtail \dfrac{6}{10}=\dfrac{3}{5}[/tex]
Scale factor (B to A) is 5/3#6
B=12A=6Scale factor (A to B)
[tex]\\ \rm\rightarrowtail \dfrac{12}{6}=2[/tex]
Scale factor (B to A)
[tex]\\ \rm\rightarrowtail \dfrac{6}{12}=0.5[/tex]
What is the area in polynomial form
Answers
Answer:
[tex] \orange{ \boxed{ \sf{ ( \: {x}^{2} + 11x + 18 \: ) \: sq. \: units}}}[/tex]
Solution :
Area = lenght x widthLenght = x + 9
Width = x + 2
[tex] \sf \green{area \: = \: (x + 9)(x + 2)} \\ \sf \green{ = \: { {x}^{2} + 11x + 18}} [/tex]
Answer:
[tex]x^2+11x+18\: \sf(square\:units)[/tex]
Step-by-step explanation:
To use the area model of solving multiplication and division problems, calculate the area of each of the colored rectangles and add them together.
Area of a rectangle = Length × Width
Area of blue rectangle: [tex]x \times x = x^2[/tex]
Area of pink rectangle: [tex]x \times 9 = 9x[/tex]
Area of green rectangle: [tex]2 \times x=2x[/tex]
Area of orange rectangle: [tex]2 \times 9=18[/tex]
Area of entire rectangle = blue + pink + green + orange
= [tex]x^2+9x+2x+18[/tex]
= [tex]x^2+11x+18\: \sf(square\:units)[/tex]
Work out the length of x.
Give your answer rounded to 3 significant figures.
х
16.5 mm
6.6 mm
Answers
Answer:
x=17.771mm
Step-by-step explanation:
given a right triangle
to find vslue of x
solution (perpendicular) ² + (base) ² =(hypotenus) ²
using pythagorus theorem
(16.5)²+(6.6)²=(x)²
272.25+43.56=(x)²
315.81=(x)²
√315.81=x
x=17.771mm
Answer:
By Pythagoras theorem
H^2=P^2+B^2
x^2=(6.6)^2+(16.5)^2
x^2=43.56+272.25
x^2=315.81
x=√315.81
x=17.771mm
What is the answer for this question?
Answers
Answer:
is this from flvs?
Step-by-step explanation:
Pls help pls pls help me pls pls help pls
Answers
Answer:
D should be the answer because the rate of Mason and Evan is 3 pages per a minute because three goes into both like so 30÷10=3 and 12÷4=3. Which is why D is your answer.
please help I'm so stuck on this
Answers
Answer:
divide the anser in the pasage
Step-by-step explanation:
divide the two numbers
In two or more complete sentences, compare the number of x-intercepts in the graph of f(x)=x2 to the number of x-intercepts in the graph of g(x)= (x+2)2 -7
Answers
I hope this is the answer you were looking for!
the length of a rectagle is 5 in longer than its width. if the perimeter of the rectangle is 56 in, find its length and width
Answers
Answer:
Step-by-step explanation:
Let the width of the rectangle = x
As length is 5 inches longer than width, we have to add 5 to width
Length = x + 5
Perimeter of ractangle = 56 in
2* (length + width) = 56
2*( x + 5 + x) = 56
2* (2x + 5) = 56
Use distributive property: a*(b +c) =(a*b) + (a * c)
2*2x + 2*5 = 56
4x + 10 = 56
Subtract 10 from both sides
4x = 56- 10
4x = 46
Divide both sides by 4
x = 46/4
x = 11.5
Width = 11.5 in
length = 11.5 + 5
= 16.5 in
Can i have help on #3 and #2? Thanks<3
Answers
Answer:
I don't know if these are right
2.756
3. 1,426.42
how many positive integers are between 28/3 and 83/5
Answers
Answer: ur dad
Step-by-step explanation:
lol
There are 7 positive integers in between 28/3 and 83/5.
What is an integer?
An integer is a whole number (not a fractional number) that can be positive, negative or zero.
Given that;
Two fractions are;
28/3 and 83/5.
Now, Write fraction into decimal form as;
28/3 = 9.33
83/5 = 16.6
So, All Integers in between 9.33 and 16.6 are;
⇒ 10, 11, 12, 13, 14, 15, 16
Thus, There are 7 positive integers in between 28/3 and 83/5.
Learn more about the integers visit:
https://brainly.com/question/24653557
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