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The term used to describe the equidistance from a given directrix and focus is: C. a locus of points called a parabola.
What is a Parabola?A parabola can be defined as a curve on a plane where any given point is at equal distance from the focus (fixed point), and from a directrix (fixed straight line).
Thus, we can conclude that what is a locus of points called a parabola is equidistant from a given directrix and focus.
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Related Questions
I really had some trouble with this problem:( & I need some help
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Express 5 1/2 and 2 1/2 as a ratio of whole numbers
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Answer:
your answers are 5.5 and 2.5 as they both have a half extra
Suppose there is a simple index of three stocks, stock ABC, stock XYZ, and stock QRS. Stock ABC opens on day 1 with 8000 shares at $4.25 per share. Stock XYZ opens on day 1 with 5000 shares at $2.90 per share. Stock QRS opens on day 1 with 2000 shares at $6.40 per share. The price of stock ABC on day 8 begins at $3.90. The price of stock XYZ on day 8 begins at $2.50. Stock QRS opens on day 8 with a price of $6.10 per share. Assume that each stock has the same number of shares that it opened with on day 1. What is the rate of change of this simple index over 1 week?
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The rate of change of this simple index over 1 week is - 8.81%
What is the rate of change ?The rate of change is the ratio of the difference in the value of the simple index to the original value of simple index.
Total value of the simple index at day 1 = (8000 x $4.25) + (5000 x $2.90) + (2000 x $6.40) = $61,300
Total value of the simple index at day 8 = (8000 x $3.90) + (5000 x $2.50)+(2000*6.10) = 55900
the rate of change of this simple index over 1 week
= (55900-61300)/ 61300 * 100 %
= -8.81 %
the rate of change of this simple index over 1 week is - 8.81%
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What division problem does this area model represent?
Answers
Answer:
2,160 ÷ 36 = 60
Step-by-step explanation:
The division problem that this area model represents is,
2,160 ÷ 36 = 60
In the given triangles, PR ≅ AC and ∠P ≅ ∠A.
Which additional fact is needed in order to use the ASA criterion to prove that the two triangles are congruent?
Answers
Answer:
option c and d are correct
Step-by-step explanation:
if there is only one choosing option you can choose option c
Need your help now please; the assignment is due tonight and this is the last problem I am having trouble with. The red box is the value I keep getting wrong
The region R is bounded by the x-axis, the straight line in the graph and the vertical line x=2.
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The volume of the region R bounded by the x-axis is: [tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}[/tex]
What is the volume of the solid (R) on the X-axis?If the axis of revolution is the boundary of the plane region and the cross-sections are parallel to the line of revolution, we may use the polar coordinate approach to calculate the volume of the solid.
From the given graph:
The given straight line passes through two points (0,0) and (2,8). Thus, the equation of the straight line becomes:
[tex]\mathbf{y-y_1 = \dfrac{y_2-y_1}{x_2-x_1}(x-x_1)}[/tex]
here:
(x₁, y₁) and (x₂, y₂) are two points on the straight lineSuppose we assign (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 8) from the graph, we have:
[tex]\mathbf{y-0 = \dfrac{8-0}{2-0}(x-0)}[/tex]
y = 4x
Now, our region bounded by the three lines are:
y = 0 x = 2y = 4xSimilarly, the change in polar coordinates is:
x = rcosθ, y = rsinθwhere;
x² + y² = r² and dA = rdrdθTherefore;
rsinθ = 0 i.e. r = 0 or θ = 0rcosθ = 2 i.e. r = 2/cosθrsinθ = 4(rcosθ) ⇒ tan θ = 4; θ = tan⁻¹ (4)⇒ r = 0 to r = 2/cosθ θ = 0 to θ = tan⁻¹ (4)Then:
[tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^2 (rdr d\theta )}[/tex]
[tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}[/tex]
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calculate time if distance is 53km and speed is 60km/hour?
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53km / 53min
=53 minutes
The graph of the absolute value parent function, f(x) = |x, is stretched
orizontally by a factor of 3 to create the graph of g(x). What function is g(X)
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Answer:
g(x) = 1/3 • |x|
Step-by-step explanation:
To stretch a parent function, you multiply by whatever you want to stretch it with. If you multiplied by 3, it would be a vertical stretch... if you multiplied by 1/3, it makes it horizontal.
Hope this helps!
I need some help please
Answers
Answer:
HexagonHeptagonStep-by-step explanation:
The first shape has 6 sides. Hence, it is called a hexagon.
The second shape has 7 sides. Hence, it is called a heptagon.
The mathematical name for the given 2 polygons.
Solution:The first polygon has 6 sides with an angle sum of 720°, which means the mathematical name given for this polygon is,
[tex]\large\boxed {Hexagon}[/tex]
The second polygon has 7 sides with an angle sum of 900°, which means the mathematical name given for this polygon is,
[tex]\large\boxed {Heptagon}[/tex]
Hence, the first polygon is a hexagon and the second polygon is a heptagon.
help me with this please
Answers
Answer:
A- 17/24 sugar all together
B- yes the bowl would be big enough because when you add all the ingredients together it equals 3 5/24 and it's less than 3 1/2.
A motion sensor has a range of 65 meters as shown. The ultrasonic waves sweeping out from the sensor span an angle of 135°.
A figure shows the appendix cone has a range of 65 meters in which waves with an angle of 135 degrees.
What is the approximate area that is within range of the motion sensor? Use the value = 3.14.
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The approximate area that is within range of the motion sensor is 4975 square meters
How to determine the area of the range?The figure is not given, however the area of the range can be calculated without the figure.
The given parameters are:
Angle, ⊕ = 135°
Radius, r = 65 meters
The area of the range is calculated using the following sector area
[tex]A = \frac{\theta}{360} * \pi r^2[/tex]
This gives
[tex]A = \frac{135}{360} * 3.14 * 65^2[/tex]
Evaluate
A = 4974.9375
Approximate
A = 4975
Hence, the approximate area that is within range of the motion sensor is 4975 square meters
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Zahid started the construction of an equilateral triangle inscribed in a circle. Which segments need to be drawn to create the triangle?
To finish his construction, Zahid needs to draw segments df ,
, and
.
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The rule for construction of Inscribed equilateral triangle
Draw 6 marks as per the picture.Then join one with next alternative leaving second .Means if marks are from 1 to 6 then
133551Or
244662Now
Here the rest two segments are
DFBFBDAnswer:
FB and DB
Step-by-step explanation:
got it right on the test
Evaluate the expression below when x = 6 and y = 2. 6x2y3
Answers
Answer:
I think that the answer is 432.
Step-by-step explanation:
6x2y3.We have x as 6 and y as 2.So we replace them with their numbers.
We'll have 6*6*2*2*3 which will give us 432. I HOPE THIS HELPS.
Select whether the pair of lines is parallel, perpendicular, or neither. x=−2, y=10
Answers
Answer:
perpendicular
Step-by-step explanation:
x = -2 is a vertical line at x = -2
y is a horizontal line the two lines are perpindicular
the lines x=−2, y=10 are perpendicular to each other.
What is a linear equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Here, The given equations are :
x=−2 and y=10
First, consider x = -2 equation :
equation x = -2 is a vertical line, parallel to x = 0 line and perpendicular to line y = 0.
Consider second line y = 10 :
line y = 10 is horizontal line and is parallel to line y = 0 and is perpendicular to line x = 0.
Therefore, the lines x=−2, y=10 are perpendicular to each other.
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Cynthia beach wants to buy a rug for a room that is 22 ft wide and 31 ft long.she wants to leave a uniform strip of floor around the rug.she can afford to buy 580 square feet of carpeting.what dimensions should the rug have?
Answers
The dimensions the rug should have is 20 by 29
How to determine the dimension?The dimension of the rug is given as:
22 ft by 31 ft
The area of the carpet is given as:
Area = 580
Represent the length of the empty space with x.
So, the dimension of the carpet is:
22 - 2x by 31 - 2x
The area is calculated as:
Area = (22 - 2x) * (31 - 2x)
Expand
Area = 682 - 62x - 44x + 4x^2
Evaluate the difference
Area = 682 -106x + 4x^2
Substitute Area = 580
682 -106x + 4x^2 = 580
Subtract 580 from both sides
102 -106x + 4x^2 = 0
Rewrite as:
4x^2 - 106x +102 = 0
Using a graphing calculator, we have:
x = 1 and x = 22.5
Substitute these values in 22 - 2x by 31 - 2x
So, we have:
Length = 22 - 2(1) = 20 or Length = 22 - 2(22.5) = -23
Width = 31 - 2(1) = 29 or Length = 31 - 2(22.5) = -14
The dimensions cannot be negative.
So, we have:
Length = 20 and Width = 29
Hence, the dimensions the rug should have is 20 by 29
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Suppose that 50% of all babies born in a particular hospital are boys. If 6 babies born in the hospital are randomly selected, what is the probability that fewer than 3 of them are boys?
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Using the binomial distribution, it is found that there is a 0.3438 = 34.38% probability that fewer than 3 of them are boys.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem, the values of the parameters are given as follows:
n = 6, p = 0.5.
The probability that fewer than 3 of them are boys is given by:
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{6,0}.(0.5)^{0}.(0.5)^{6} = 0.0156[/tex]
[tex]P(X = 1) = C_{6,1}.(0.5)^{1}.(0.5)^{5} = 0.0938[/tex]
[tex]P(X = 2) = C_{6,2}.(0.5)^{2}.(0.5)^{4} = 0.2344[/tex]
Then:
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0156 + 0.0938 + 0.2344 = 0.3438[/tex]
0.3438 = 34.38% probability that fewer than 3 of them are boys.
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y-intercept: 4
-: x-intercepts: -2, 5, 7
-: Relative maximum at (0,4)
-: Relative maximum at (6, -3)
-: As → −∞, → −∞
-: As → ∞, →
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The attached figure represents the sketch of the graph
The missing part of the questionThe complete question requires that we sketch the graph that follows the given parameters
How to sketch the graph?The given parameters are:
y-intercept: 4x-intercepts: -2, 5, 7Relative maximum at (0,4)Relative maximum at (6, -3)As x → −∞, y → −∞As x → ∞, y → ∞To start with, we plot the points on an empty coordinate plane.
Next, we connect the points using a rough curve
Lastly, the points are labelled
See attachment for the sketch of the graph
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Which equation could generate the curve in the graph below?
y=3x² - 2x + 1
y=3x² - 6x +3
y=3x² - 7x + 1
y=3x² - 4x-2
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using the figure below identify 1 pair of the following angle relationships
Answers
Answer:
\begin{gathered}\\1) \: \: \underline{ \sf{ Alternate \: interior \: angles \: \: : }}\\\end{gathered}
1)
Alternateinteriorangles:
\begin{gathered} \sf \implies \: 2\: \: and \: \: 7\\\end{gathered}
⟹2and7
\begin{gathered} \sf \implies \: 6\: \: and \: \: 3\\\\\end{gathered}
⟹6and3
\begin{gathered}\\2) \: \: \underline{ \sf{ Alternate \: interior \: angles \: \: : }}\\\\\end{gathered}
2)
Alternateinteriorangles:
\begin{gathered} \sf \implies \: 1\: \: and \: \: 8\\\end{gathered}
⟹1and8
\begin{gathered} \sf \implies \: 5\: \: and \: \: 4\\\\\end{gathered}
⟹5and4
\begin{gathered}\\3) \: \: \underline{ \sf{ Corresponding \: angles \: \: : }}\\\end{gathered}
3)
Correspondingangles:
\begin{gathered} \sf \implies \: 3\: \: and \: \: 1\\\end{gathered}
⟹3and1
\begin{gathered} \sf \implies \: 5\: \: and \: \: 7\\\end{gathered}
⟹5and7
\begin{gathered} \sf \implies \: 4\: \: and \: \: 2\\\end{gathered}
⟹4and2
\begin{gathered} \sf \implies \: 6\: \: and \: \: 8\\\\\end{gathered}
⟹6and8
\begin{gathered}\\4) \: \: \underline{ \sf{ Consecutive\: Interior \: angles \: \: : }}\\\end{gathered}
4)
ConsecutiveInteriorangles:
\begin{gathered} \sf \implies \: 2\: \: and \: \: 3\\\end{gathered}
⟹2and3
\begin{gathered} \sf \implies \: 6\: \: and \: \: 7\\\\\end{gathered}
⟹6and7
\begin{gathered}\\5) \: \: \underline{ \sf{ Consecutive\: Exterior \: angles \: \: : }}\\\end{gathered}
5)
ConsecutiveExteriorangles:
\begin{gathered} \sf \implies \: 1\: \: and \: \: 4\\\end{gathered}
⟹1and4
\begin{gathered} \sf \implies \: 5\: \: and \: \: 8\\\\\end{gathered}
⟹5and8
Which graph represents the function f(x) = |x + 3|?
On a coordinate plane, an absolute value graph has a vertex at (0, 3).
On a coordinate plane, an absolute value graph has a vertex at (negative 3, 0).
On a coordinate plane, an absolute value graph has a vertex at (0, negative 3).
On a coordinate plane, an absolute value graph has a vertex at (3, 0).
Answers
Answer:
Graph of Modulus
The graph of a modulus or absolute value function is in a form of a 'V' shape whose vertex depends upon the coordinates. The equation for the graph is given as,
where,
(a, b) are the coordinates of the vertex of 'v' in the form of (x, y),
And h shows how wider or lean will be the function, for h=0, it is a straight line, while for a negative value the graph will face downwards and opposite for a positive value.
Given to us
y = |x-3|
On the coordinate plane
The graph will be in the shape of a 'V' whose vertex will lay at the coordinates (3, 0). As the value of a is 1 the graph will face upwards. As shown below on the graph.
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Step-by-step explanation:
Answer:
C
Step-by-step explanation:
edge 23
heIp??
everyone??
Brainliest = Good Answer/Solution
Answers
To Find = Diameter, Area
Solution :
Diameter = 2 × Radius
Diameter = 2 × 6cm
Diameter = 12 cm
Area = 2πr
[tex]area \: = 2 \times \frac{22}{7} \times 6cm[/tex]
[tex]area \: = \frac{264}{7} [/tex]
[tex]area \: = 37.7 \: cm[/tex]
____________________________________2. Given : Diameter = 8 DM
( 1dm = 10 cm
8dm = 8 × 10 = 80cm )
To find : Radius , area
Solution :
[tex]raduis \: = \frac{1}{2} \times diameter[/tex]
[tex]radius \: = \frac{1}{2} \times 80cm[/tex]
[tex]radius \: = 40 \: cm \: or \: 4dm[/tex]
Area = 2πr
[tex]area \: = 2 \times \frac{22}{7} \times 40[/tex]
[tex]area \: = \frac{1760}{7} [/tex]
[tex]area \: = 251.4cm \: \: \: or \: 25.14dm[/tex]
____________________________________3. Given : Radius = 2.5m
To find : Diameter , Area
Solution :
Diameter = 2 × radius
Diameter = 2 × 2.5m
Diameter = 5m
Area = 2πr
Area = 2 × 22/7 × 5m
Area = 220/7
Area = 31.4m
can someone help me on part B please? I've done the answer to the rest please thanks!
Answers
Answer:
84 circular tiles are needed to make pattern number 20
4(20+1)
Step-by-step explanation:The number of circular tiles is 1 more than the pattern number on each side of the square.
circular tiles = 4(n +1)
A bottle of coke cost 3/4 as much as a $5 milkshake. How much would 3 bottles of coke and 2 milkshakes cost?
Answers
Answer:
Total, 2 milkshakes, and 3 cokes would cost $12.50
Step-by-step explanation:
The cokes cost $11.50 and the milkshakes $10.00
70 POINTS !!! Measure each angle and write the measure on the line.
Answers
Answer:
See below
Step-by-step explanation:
You will just need to use your protractor to measure the given angles..
Here is some gross guesses starting with top row
45 120 100 25 90 80 135 120 °
5. Solve for x.
21
4
Answers
Answer: 10
Step-by-step explanation:
By the geometric mean theorem, if we let the length of the altitude to the hypotenuse be [tex]y[/tex], this means that [tex]y^{2}=84 \longrightarrow y=\sqrt{84}[/tex].
So, by the Pythagorean theorem, [tex]x=\sqrt{(\sqrt{84})^{2}+4^{2}}=\boxed{10}[/tex]
Otto used 5.5 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can be used to find the value of y, the total amount of flour that Otto used in the recipe, and what are the constraints on the values of x and y?
Answers
The equation that can be used to represent the situation is y = 5.5 + x
How to write and solve equation?Whole wheat flour = 5.5 cupsWhite flour = x cupsTotal flour = yThe equation:
Total flour = Whole wheat flour + White flour
y = 5.5 + x
Therefore, the equation that can be used to represent the situation is y = 5.5 + x
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Answer:
C
Step-by-step explanation:
The graph of y= (x + 2)(x-2)(x + 1) is shown.
4
3
2-
D
-6-5-4-3-2-1₁
23 456x
D
76
B
C
Which point is a relative minimum?
OA
OD
Answers
Answer:
Point C
Step-by-step explanation:
At point C, the graph is changing from decreasing to increasing.
Given f(x) = x² + 4x - 3, find f(-3)
O -3
O -6
O 0
O 18
Answers
Answer:
f(-3) = -6
Step-by-step explanation:
f(x) = x^2 + 4x - 3
f(-3) means to put -3 in place of x and then do the calculation.
f(-3)
= (-3)^2 + 4(-3) - 3
= 9 - 12 - 3
= -3 - 3
= -6
First square -3, its 9. Then multiply -3 and 4, that's -12. Then add everything.
f(-3) = -6
what is the area of the figure?
Answers
Answer:
area = 62ft
Step-by-step explanation
so you section the polygon into a big rectangle and 2 small rectangles
the area of the small rectangle will be 2ft x 3ft which will be 6 ft, and as there are 2 of them the area of it will be 12ft
the area of the big rectangle will be 10ft x 5ft, as 8ft - 3ft is 5ft so 5x10=50ft
now add the areas you got, 50+12 which is 62ft
hope this helps:)
factoring / gcf ??? (in picture)
got really sick and missed a bunch of school, would really appreciate the help !
Answers
Step-by-step explanation:
hope this will help you....