Think about all of the ways in which a circle and a parabola can intersect.
Select all of the number of ways in which a circle and a parabola can intersect.
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DONE
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There will be four ways a circle and a parabola can intersect because the solution of the quartic equation will be 4.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have a circle and a parabola:
As we know the standard form of a circle:
[tex]\rm (x-h)^2 +(y-k)^2=r^2[/tex]
The standard form of the parabola:
[tex]\rm y = a(x-h)^2+k[/tex]
If we plug the value of y from the parabola equation in the circle equation, we get a quartic equation(4th order equation)
The solution of the quartic equation will be 4.
Thus, there will be four ways a circle and a parabola can intersect because the solution of the quartic equation will be 4.
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Related Questions
Simplify: √64(6z-7)² (square root over entire equation)
Answers
[tex]\sqrt{64(6z-7)^2}=\sqrt{64}\cdot\sqrt{(6z-7)^2}=8\cdot |6z-7|=8|6z-7|[/tex]
The scatter plot shows a correlation between the cost of a helmet and the consumer rating.
The line of regression models that correlation.
Enter a number to complete each statement.
Answers
Answer:
1. 65
2. 52
3. 13
Step-by-step explanation:
For these answers, we can look at the graph:
Question 1:
For the helmet that costs 35 dollars, we look at the x-axis until we find the helmet that aligns with 35.
Then, we look at the y-axis and find the blue dot. The blue dot is the actual consumer rating that was recorded, NOT the red line. The red line is the predicted consumer rating in correlation to the price.
Hence, the consumer rating is 65.
Question 2:
For this, we can look back at the graph and apply the same concept as above. Notice how the 65 plot is 13 points away from the point predicted by the red line.
Therefore, 65 - 13 = 52
Question 3:
Just like the last two questions, we can look at the graph for this. The green line gives us this answer flat out, displaying the distance from the actual rating to the predicted rating.
Hence, the actual consumer rating was 13 above the predicted rating.
Solve x2 + 4x + 12 = 0 by completing the square.
x = –2 + 2i, x = –2 –2i
x = –2 + i, x = –2 – i
x = –2 + 2i, x = –2 – 2i
x = 0, –4
Answers
Answer:
See below
Step-by-step explanation:
x2 + 4x + 12 = 0 Complete the square ( take 1/2 of the 'x' coefficient, then square it and add it to both sides of the equation
x^2 + 4x + 2^2 + 12 = 2^2 Subtract 12 from both sides
x^2 + 4x + 4 = -8
(x+2)^2 = - 8 sqrt both sides
(x+2) =± sqrt (-8) simplify just a bit
x+2 = ±(2i sqrt2) subtract 2 from both sides
x = -2 ± 2i sqrt 2 <===== I do not see that answer listed
-2y = x + 6 Graph A On a coordinate plane, a line goes through (negative 6, 0) and (1, negative 3). Graph B On a coordinate plane, a line goes through (0, 3) and (2, 4). Graph C On a coordinate plane, a line goes through (0, 3) and (2, 2). Graph D On a coordinate plane, a line goes through (0, negative 3) and (6, 0). a. Graph A c. Graph C b. Graph B d. Graph D Please select the best answer from the choices provided
Answers
On a coordinate plane, a line goes through (negative 3, 0) and (0, negative 6).
The graph for the first equation of a system is shown in orange. The second equation is: 3y+30=6x
What is the solution to the system?
A. (2, –10)
B. (1, –8)
C. (–2, –14)
D. (2, –6)
Answer: 4.9/5
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Answer:
B. (1,-8)
Step-by-step explanation:
Slope of the first one:
(-6-0)/(0--3) = -6/3 = -2
y = -2x - 6
3y + 30 = 6x
y + 10 = 2x
-2x - 6 + 10 = 2x
4 = 4x
x = 1
y = -2(1) - 6
y = -8
Difference between y and 23 is 12
Answers
Answer:
[tex]y=11[/tex]
Step-by-step explanation:
⇒ [tex]23 - y[/tex] (Difference means subtraction)
⇒ [tex]23 - y = 12[/tex] (Subtract 12 from 23)
⇒ [tex]y = 11[/tex] (The difference from 23 - 12)
Hii!
___________________________________________________________
Answer:
y=11
Step-by-step explanation:
Let's set up an equation.
"difference between y and 23" tells us to subtract y from 23, so we'll do just that.
23-y=12
Now subtract 23 from both sides
-y=-11
Divide both sides by -1
y=11 "We solved for the variable"
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Hope that this helped! Best wishes.
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In which expression would you complete the operation first and then find the absolute value of the sum?
a |11/8+2/3|
b|-17.3| - |9.05|
c|-35| - |22|
d|-18.531| + |19.2894|
Answers
Tacoma's population in 2000 was about 200 thousand, and has been growing by about 9% each year. If this continues, what will Tacoma's population be in 2019?
Answers
The population of Tacoma in 2019 would be 1,028,332.
What will be the population in 2019?The population can be represented with an exponential equation that has the form:
FV = P (1 + r)^n
FV = Future populationP = Present population R = rate of growth N = number of years200,000 (1.09)^19 = 1,028,332.
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Please help me answer this mathematics question
Answers
Answer:
[tex]x = 172.75[/tex]
Hope this help!!!
Have a good day♡
6. Divide:
6x²+7x-2/3x-1
using Long Division.
Answers
Step-by-step explanation:
3x-1) 6x^2 + 7x -2 ( 2x+3
-6x^2 -2x
+
0 + 9x -2
- 9x -3
+
1
2 divided by what times what equals 7
Answers
Answer:
2/7Step-by-step explanation:
I answer for what I understand, the question is not clear.
2 divided by what times what equals 7
2 : x = 7
x = -2/-7
x = 2/7
-------------
check
2 : 2/7 = 7
2 * 7/2 = 7
7 = 7
the answer is good
Jade bought a home for $129,500. She sold it fifteen years later for $9000 less than twice the amount she originally purchased for. Find the percent change in the purchase price of her home
Answers
Answer:
See below
Step-by-step explanation:
129 500 original price
selling price = 2 ( 129 500) - 9000 = 250 000
% change Questions worded like this are often up for debate as to exactly answer the question
250 000 / 129 500 = 193 % Selling price was 193% of original price
(250 000 - 129500)/ 129500 = 93 % INCREASE
You started this year with $413 saved and you continue to save $21 per month.
Write an equation to model this situation (use m for months and s for savings)
Answers
Answer:
y = 21x + 413
Step-by-step explanation:
Use y = mx + b
m represents the slope which in this case is 21.
b represents the y - intercept which in this case is 413.
Now, just fill in the variables.
y = 21x + 413
Hope this helps!
Someone explain the equation
Answers
Answer:
An equation connects two expressions with an equal sign. It shows that the two expressions are equal to each other, like 5 = 5, or for variables, 5x = 2x, which means that x = 0.
Brainliest, please :)
Answer:
An equation is a problem consist sting of many numbers mostly division or mulitiplication
Step-by-step explanation:
Which pair of expressions are equivalent using the Associative Property of Multiplication?
4(2a ⋅ 5) = (4 ⋅ 2a) ⋅ 5
4(2a ⋅ 5) = 8a ⋅ 20
4(2a ⋅ 5) = (2a ⋅ 5) ⋅ 4
4(2a ⋅ 5) = 4 ⋅ 2a ⋅ 5
Answers
Answer:
4 (2a ⋅ 5) = (4 ⋅ 2a) ⋅ 5
Step-by-step explanation:
3 more than half a number
Answers
1/2n + 3
Or
1/2x + 3
Answer:
3 + a/2
Step-by-step explanation:
3 + a/2
Which expression
is equivalent to 4(x+2)?
Answers
Answer:
[tex]\huge\boxed{\sf 4x + 8}[/tex]
Step-by-step explanation:
Given expression:= 4(x + 2)
Distribute
= 4x + 8
[tex]\rule[225]{225}{2}[/tex]
= 4(x + 2)
= 4 * x + 4 * 2
=> 4x + 8
If 4x + 8 is an Option, then that is the Correct Answer. Since options are not given, I don’t know which option corresponds to this Answer.
write in slope intercept form
2y+x=1
Answers
Answer:
y = -x/2 + 1/2 or
y = -1/2 x + 1/2
(these are equivalent)
Step-by-step explanation:
Slope-intercept form is:
y = mx + b
So we have to get the y all by itself on the left.
2y + x = 1
Subtract x from both sides.
2y = 1 - x
Divide both sides by 2. Divide all the terms by 2.
2y/2 = 1/2 - x/2
Simplify.
y = 1/2 - x/2
Rearrange the terms on the right side so that the x term is first and the constant is last.
y = -x/2 + 1/2
I think this is a good, reasonable and correct answer. But maybe you really want to see that m number (the slope) out in front of the x. Then you can write is as:
y = -1/2 x + 1/2
Step-by-Step Solution:
Slope Intercept Form :-
• y = mx + b
Therefore,
2y + x = 1
2y = 1 - x
y = 1/2 - x/2 (We know, a - b = -b + a)
y = -x/2 + 1/2
=> y = -1/2x + 1/2
The graph shows a relationship between x and y.
What are the zeros of the function?
Answers
Answer:
x = -3
x = -1
x = 2
Step-by-step explanation:
The zeros of a function are the x-values of the points at which the curve crosses the x-axis.
From inspection of the given graph, the curve crosses the x-axis at:
x = -3x = -1x = 2Therefore, these are the zeros of the function.
A manufacturer makes two type if products X and z at each if two different locations A and B. the materials used to make each if the products are steel, glass and plastic. suppose it takes three units of steel, one unit of glass and two units of plastic to make one unit of product X and four units of steel and one half units of glass and three units of plastic to make one unit of product Z. suppose further that steel, glass and plastic cost birr 10, 2, and 3 per unit respectively at location A. at location B steel, glass abd plastic cost 9,3 and 4 per unit respectively. using matrix algebra. find the material cost of making one of each product at each of the two locations.
Answers
Using matrix algebra, the material cost of making one of each product at each location is as follows:
Product X Product Z
Location A birr 38 birr 50
Location B birr 38 birr 49.5
What is matrix algebra?Matrix algebra involves the arrangement of numbers in a rectangular array.
Matrices are arranged in columns and rows to express some mathematical values.
Data and Calculations:Matrix O: Materials Requirement Per UnitSteel Glass Plastic
Product X 3 1 2
Product Z 4 0.5 3
Matrix P: Materials Cost Per UnitSteel Glass Plastic
Location A 10 2 3
Location B 9 3 4
Matrix R: (O x P) Material Cost of Product XSteel Glass Plastic Total
Location A 30 2 6 38
Location B 27 3 8 38
Matrix R: (O x P) Material Cost of Product ZSteel Glass Plastic Total
Location A 40 1 9 50
Location B 36 1.5 12 49.5
Thus, Product X costs birr 38 at locations A and B, respectively, while Product Z costs birr 50 and birr 49.5 at locations A and B, respectively.
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how do i solve this??
Answers
-6 ≤ x < -2
Step-by-step explanation:
[ => this shows ≤ sign
) => this shows < sign
Need help with this geometry question
Answers
2) [tex]\overline{EK} \cong \overline{KG}, \overline{HK} \cong \overline{KF}[/tex]
3) Opposite sides of a parallelogram are congruent.
4) [tex]\triangle EF \text{ }K \cong \triangle GHK[/tex]
A house’s was valued at 269,00. After several years, the value increased by 18%. By how much did it increase in dollars? What is the current house value
Answers
Answer:
31742
Step-by-step explanation:
[tex]26900 \times \frac{100 + 18}{100 } = 31742 [/tex]
How do I simplify the following expression by writing it as a term with only one trigonometric function?
(4-2sec^2(x))/(sec^2(x))
Answers
Answer:
2 cos (2x)
Step-by-step explanation:
[tex]\frac{4 -2 sec^2x}{sec^2x} \\=\frac{4-\frac{2}{cos^2x} }{\frac{1}{cos^2 x} } \\=\frac{\frac{4 cos^2x-2}{cos^2 x} }{\frac{1}{cos^2x} } \\=\frac{2(2 cos^2x-1)}{cos^2x} \times \frac{cos^2x}{1} \\=2(2cos^2x-1)\\=2cos(2x)[/tex]
3(2x - 3) = 4(2x + 4)
Answers
Answer:
Step-by-step explanation:
Open the brackets
3 x 2x = 6x
3x -3 = -9
4 x 2x= 8x
4 x 4= 16
6x - 9 = 8x + 16
Move same to same side
-16 -9 = 8x - 6x
-25 = 2x
x -25/2
x = -12.5
Answer:
x = -25/2 or -12.5Step-by-step explanation:
3*(2x - 3) = 4*(2x + 4)
6x - 9 = 8x + 16
6x - 8x = 16 + 9
-2x = 25
x = -25/2 or -12.5
------------------------
check
3 * (2 * (-12.5) - 3) = 4 * (2 * (-12.5) + 4)
3 * (25 - 3) = 4 * (12.5 + 4)
3 * 22 = 4 * 16.5
66 = 66
the answer is good
Use the drawing tool(s) to form the correct answer on the provided graph.
Consider the function given below.
Plot this piecewise function on the provided graph.
Drawing Tools
Select
Point
Open Point
Line Segment
Ray
●
O
y = -2;
-10
--5;
Click on a tool to begin drawing.
-8
7;
-6
-8 <
-2 < <5
≤ 9
5 < 1
10
8-
6-
4-
2
< -2
Delete
Undo
8
Reset
10
Answers
The attached graph represents the piecewise function.
How to plot the graph?The complete question is in the image
The function is given as:
[tex]f(x) = \left[\begin{array}{cc}3&x \le -3\\2x + 1&-3 < x < 4 \\-2&x \ge 4\end{array}\right[/tex]
Next, we plot the functions by their domain
See attachment for the piecewise function.
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Jaira is completing construction of a regular hexagon inscribed in a circle, as shown below: What should be the next step in her construction?
Answers
Jaira is completing the construction of a regular hexagon inscribed in a circle, as shown below: The next step in her construction should be:
construct another pont E by placing her compass at the locus DRepeat the process to get 6 more points on the given circle then join all of them together.What is a regular hexagon?
A closed polygon with six equal sides and six equal angles is called a regular hexagon.
Thus, the steps highlighted above will help Jaira complete her construction.
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Similar Polygons
Not quite sure how to get this question.
Answers
Answer:
No
Step-by-step explanation:
We know that the 3-4-5 and 9-12-15 right triangles are similar. If you add 6 units to the length of each side of both of these triangles, you obtain 9-10-11 and 15-18-21 triangles, which are not similar since 9/15 is not equal to 10/18.
What is the domain of the function represented by the list of ordered pairs?
(0, 2), (-3, 6), (4, 8), (2, 5), (-2, 4)
Answers
Answer:
D: (-3,4).
Step-by-step explanation:
There is really no need to solve it. Plot those points onto a graph and draw lines. I have done it on desmos. Looking at the x-axis to find the domain. From the left to right x-axis we can see that the domain should be D: (-3,4).
A treasure map says that a treasure is buried so that it partitions the distance between a rock and a tree in a 5:9 ratio. Marina traced the map onto a coordinate plane to find the exact location of the treasure.
x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1
y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1
What are the coordinates of the treasure? If necessary, round the coordinates to the nearest tenth.
(11.4, 14.2)
(7.6, 8.8)
(5.7, 7.5)
(10.2, 12.6)
Answers
The correct answer is option B i.e. (7.6, 8.8)
What is Distance?The length along a line or line segment between two points on the line or line segment.
Let the coordinates of the treasure be (x, y).
Let d₁ = distance from the rock to the treasure.
Let d₂ = distance from the tree to the treasure.
d₁ = [tex]\sqrt{x^2 + (y-2)^2}[/tex]
d₂ = [tex]\sqrt{(16-x)^2 + (21-y)^2}[/tex]
We want d₁/d₂ = 5/9 in order to locate the treasure.
Note that 5/9 = 0.556 (approx)
Test (11.4, 14.2)
d₁ = 14.8, d₂ = 8.2, d₁/d₂ = 1.8 Incorrect
Test (7.6, 8.8)
d₁ = 8.2, d₂ = 14.8, d₁/d₂ = 0.554 Correct
Test (5.7, 7.5)
d₁ = 6.13, d₂ = 16.98, d₁/d₂ = 0.36 Incorrect
Test (10.2, 12.6)
d₁ = 12.8, d₂ = 10.2, d₁/d₂ = 1.255 Incorrect
Thus, The correct answer is option B i.e. (7.6, 8.8).
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Review the graph. Given z = , which letter represents z3?
A
B
C
D
Answers
By writing Z in polar form, we will see that:
[tex]z^3 = C[/tex]
How to get the value of Z³?
First, we can see that:
z = (-1 - i)
If we write it in polar form, we get:
[tex]z = \sqrt{2} *e^{i(\pi + \pi/4)[/tex]
If we apply the power 3, we get:
[tex]z^3 = (\sqrt{2} *e^{i(\pi + \pi/4)})^3\\\\z^3 = 2^{3/2}*e^{i*(3\pi + 3\pi/4)}\\\\z^3 = 2^{3/2}*e^{i*15\pi/4}[/tex]
Notice that:
[tex]\frac{15\pi}{4}[/tex]
Is an angle equivalent to:
[tex]\frac{15\pi}{4} - 2\pi = \frac{15\pi}{4} - \frac{8\pi}{4} = \frac{7\pi}{4} = 1.75\pi[/tex]
Because the angle is measured from the positive x-axis, this means that we will have:
[tex]z^3 = C[/tex]
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