The coordinates points of intersection of the circle and the parabola are (1,6) and (-1,6).
The equation of the given circle is x²+y²=37
The equation of the given parabola is x²=y-5
To find the point of intersection of the parabola and the circle,
Putting the value of x²=y-5 in the equation of circle,
So, we get,
y-5+y²=37
y²+y-42=0
This is a quadratic equation, so using quadratic formula,
y = [-b±√(b²-4ac)]/2a
Here,
a = 1
b = 1
c = -42
y = [-1±√(1²-4(1)(-42))]/2(1)
y = [-1±√(1+168)]/2
y = [-1±13]/2
y = -14/2 and 12/2
y = -7 and 6.
Putting the values of y in x²=y-5,
We get,
x² = 6-5
x = ±1
And,
x²=-7-5
x²=-12
Not possible,
So, when y is 6, the value of x is ±1.
So the coordinate of point of intersection are (1,6) and (-1,6).
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Four students were scheduled to give book reports in 1 hour. After tue first report, 2/3 hour remained. The next two reports took 1/6 hour and 1/4 hour. What fraction of the hour remained?
The fraction of the hour that remained is 1/4 hour.
The portion or part of the complete item is represented by a fraction. It stands for the equal components of the whole. The denominator and numerator are the two components of a fraction. The top number is referred to as the numerator, and the bottom number is referred to as the denominator.
The students have to submit the book reports in 1 hour.
After the first report, 2/3 hours remained. The next two reports took 1/6 hour and 1/4 hour respectively.
After the first report, 2/3 hours remained.
The next two reports took 1/6 and 1/4 hours.
So, the total time to complete the next two reports is:
= 1/6 + 1/4
= 10/24
= 5/12 hours
Therefore, the fraction of hour remained will be:
= 2/3 - 5/12
= ( 2/3 ) × ( 4/4 ) - 5/12
= 8/12 - 5/12
= 3/12
= 1/4 hour
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Hi. could someone please help me with this question? the answers that I'm getting arent making sense to me. thanks.
The dilation of the geometric figure with a scale factor of 1/4 about the origin is: J' (-0.5, -0.25), K' (-0.25, 1), L' (0.75, 0.25), M' (0.75, -0.75).
What is dilation?Dilation simply refers to a type of transformation which changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.
Note: Each interval on this graph represents 1 unit.
For the given coordinates, the dilation with a scale factor of 1/4 about the origin or center of dilation (0, 0) should be calculated as follows:
Point J (-2, -1) → Point J' (-2 × 1/4, -1 × 1/4) = Point J' (-0.5, -0.25).
Point K (-1, 4) → Point K' (-1 × 1/4, 4 × 1/4) = Point K' (-0.25, 1).
Point L (3, 1) → Point L' (3 × 1/4, 1 × 1/4) = Point L' (0.75, 0.25).
Point M 3, -3) → Point M' (3 × 1/4, -3 × 1/4) = Point M' (0.75, -0.75).
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The formulas below are the cost and revenue functions for a company that manufactures and sells small radios.
C(x)=90,000 +42x and R(x) = 47x
a. Use the formulas shown to write the company's profit function, P, from producing and selling x radios.
b. Find the company's profit if 23,000 radios are produced and sold.
***
Answer:
(a) The profit function is P(x) = 89x - 90,000.
(b) The company's profit at x=23,000 is 1,957,000.
Step-by-step explanation:
Given,
The cost function of the company is C(x)=90,000 +42x and
The revenue function is R(x) = 47x
where x is the number of radios.
(a)
The company's profit function, P, is from producing and selling x radios is
The formula for profit:
Profit (P) = Revenue (R) - Cost (C)
P = R - C
P = 47x - 90,000 + 42x
P = (47x + 42x) - 90,000
P = 89x - 90,000
For (a), The company's profit function, P, from producing and selling x radios is P = 89x - 90,000
(b)
The radios produced and sold are 23,000
So, x = 23,000
putting x value in the profit function, P
P = 89x - 90,000
P = 89 x 23,000 - 90,000
P = 2,047,000- 90,000
P = 1,957,000
For (b), the company's profit at x = 23,000 is 1,957,000.
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Shelby prepared 9 kilograms of dough after working 3 hours. How many hours did Shelby work if she prepared 15 kilograms of dough? Assume the relationship is directly proportional.
Shelby works for 5 hours to prepare 15 kgs of dough.
Here, we are given that Shelby prepared 9 kilograms (kgs) of dough after working 3 hours.
from this information we can calculate the amount of dough she can prepare in 1 hour.
3 hours ⇒ 9 kgs
1 hour ⇒ 9/3 kgs
9/3 = 3
Thus, she will prepare 3 kgs of dough in 1 hour.
Now, we are given that Shelby prepares 15 kgs of dough in all.
we have, 3 kgs ⇒ 1 hour
Thus, 15 kgs ⇒ 15/3 hours
15/3 = 5
Thus, Shelby works for a total of 5 hours to prepare 15 kgs of dough.
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Find the measure of EG.
Thank you :)
Measure of EG is 9.5 cm.
Define triangles.A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total. A triangle's third side is always equal to the sum of any two of its sides' lengths. Having three sides, three angles, and three vertices, a triangle is a closed, two-dimensional object. A polygon also includes a triangle. As a polygon, a triangle.
Given Data
Lengths
EH = 24, GH = 24
The third side of a triangle is always equal to the sum of the lengths of any two of its sides.
24 = 9.5 + x + 24
9.5 = x
Measure of EG is 9.5 cm.
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Give me an example of a graph with 4 vertices, with at least one vertex having a degree of 1: ( This is a word problem)
An example of a graph with 4 vertices, with at least one vertex having a degree of 1 is a square graph.
2K₂= C₄C4 = K2,2There are 11 simple graphs on 4 vertices.
A graph is a set of points, known as vertices, and lines between those points are referred to as edges. there are many exclusive styles of graphs, along with linked and disconnected graphs, bipartite graphs, weighted graphs, directed and undirected graphs, and simple graphs.
This sort of graph with an even wide variety of vertices of diploma 4 has an even length, so our graphs must have 1, three, or 5 vertices of degree four. as much as isomorphism, there is precisely one graph of each type. A related graph G is known as a Hamiltonian graph if there's a cycle that includes each vertex of G and the cycle is referred to as a Hamiltonian cycle. Hamiltonian stroll in graph G is a walk that passes via every vertex precisely as soon as.
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Select all that apply.
Which of the following are equal to 450?
300 increased by 50%
240 increased by 25%
250 increased by 50%
225 increased by 100%
Answer:
300
Step-by-step explanation:
if you were to translate and then dilate a figure,
would the image and preimage be congruent? Why or why not?
For dilation, a figure's size and shape only change during transformation, but during translation, the size of the figure's image and preimage are congruent.
Congruent in geometry refers to being the same size and shape. Congruence can be used with figures, angles, and line segments. If any two line segments are equal in length, they are said to be congruent. If two angles have the same measure, they are said to be congruent.
Techniques for transformation: In a xy-plane, transformation involves changing the size and shape of an item.
Translation and dilation are a couple of the transformation methods used.
For dilation, a figure's size and shape only change during transformation, but during translation, the size of the figure's image and preimage are consistent.
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Given f(x) = 4-x² and (f - g)(x)=-x²+x+2, find the function g.
Answer:
g(x) = 2 - xStep-by-step explanation:
Givenf(x) = 4 - x²,(f - g)(x) = - x² + x + 2.Find g(x)SolutionWe know that:
(f - g)(x) = f(x) - g(x)Use the given to find the missing function:
g(x) = f(x) - (f - g)(x) g(x) = 4 - x² - (- x² + x + 2) =4 - x² + x² - x - 2 =2 - xAnswer:
[tex]{ \rm{f(x) = 4 - {x}^{2} }}[/tex]
[tex]{ \rm{(f - g)(x) = - {x}^{2} + x + 2}}[/tex]
- From functions;
[tex]{ \boxed{ \tt{(f - g)(x) = f(x) - g(x)}}} \\ \\ { \rm{ - {x}^{2} + x + 2 = (4 - {x}^{2} ) - g(x) }} \\ \\ { \rm{g(x) = (4 - {x}^{2}) + {x}^{2} - x - 2 }} \\ \\ { \boxed{ \rm{g(x) = 2 - x}}}[/tex]
this system is flawed
The system is sadly flawed ._.
a jar contains 40 marbles and 24 of those marbles are red. If a marble is drawn from the jar at random, what is the probability that the marble picked is red?
Answer: 60% chance or 3:5
Step-by-step explanation: well, 40/24 is 0.6, which is 60%, or you can see 4 is 10%, and 20 is 50%, and add them together to get 60%. 60% is also 6:10, which can be simplified to 3:5
an extrasolar is observed at a distance of 4.2x10 9power kilometers away.A group of scientist has designed a spaceship that can travel at speed of 7x10 8power.how many years will the spaceship take to reach the extrasolar planet
The time taken by the ship to reach that distance will be 6 years.
What is time in kinematics?
Time is defined as the total duration of motion of an object in order to achieve some specific distance.
Given is an extrasolar which is observed at a distance of 4.2 x 10⁹ kilometers away. A group of scientist has designed a spaceship that can travel at speed of 7 x 10⁸ Kilometers/year.
Now, in order to calculate the time, we can use the simple formula as -
Time = distance / speed
Substituting the values -
Time [t] = (4.2 x 10⁹) / (7 x 10⁸)
Time [t] = 0.6 x 10
Time [t] = 6 years
Therefore, the time taken by the ship to reach that distance will be 6 years.
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The midpoint of CD is M(6, 9). One endpoint is D(2, 10). Find the coordinates of the other
endpoint C.
endpoint: (14, 28) coordinates of the other endpoint c.
What do the coordinates for midway mean?The x-value at the midpoint lies halfway between the values at the two positions. The y-value midway between the two positions is known as the midpoint.
I start by placing the endpoint coordinate at the top and the halfway coordinate at the bottom.
(2, 10)
(6, 9)
I then calculate the difference between endpoint 1 and the midpoint.
+8 and+19
Applying that to the second coordinate's midpoint
(6 ,9)
8 +19
endpoint: (14, 28)
you can check using the midpoint formula ( x + x / 2, y + y / 2)
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A bookshop owner sells educational books to the school students and earns 500 BD .He paid 300 dinars to install new shelves. How much profit did this entrepreneur make?
500 BD
200 BD
Didn't make a profit.
The entrepreneur make a profit of 200 BD .
In the question ,
it is given that ,
Amount for which the bookshop owner sells educational books to school students = 500 BD .
Amount of money paid to install new shelves = 300 BD .
So, the profit can be calculated using the formula
profit = (Amount for which the bookshop owner sells educational books to school students) - (Amount of money paid to install new shelves) .
Substituting the values from above , we get
profit = 500BD - 300 BD
= 200BD
hence , profit is 200 BD .
Therefore , the entrepreneur make a profit of 200 BD .
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Can you help me please it’s. 4 part question but I can only post a picture of one part at a time
Part a
we have the function
R=-0.1x^3+11x62-100x
using a graphing tool
The answer Part a is 2 turning pointsPart b
we have that
The value of x cannot be a negative number
The value of R can be a negative number
therefore
The answer part b is option Bpart c
the answer part c is the option A and C
Norman has a coin collection. There are 3 dimes for every 5 quarters in his collection. If Norman has a total of 72 dimes, how many quarters does he have?
43
74
102
120
There are 120 quarters if Norman has a total of 72 dimes option (D) 120 if there are 3 dimes for every 5 quarters.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
Norman has a coin collection. There are 3 dimes for every 5 quarters in his collection.
3 dimes → 5 quarters
72 dimes → x quarters
x = (5x72)/3
x = 120 quarters
Thus, there are 120 quarters if Norman has a total of 72 dimes option (D) 120 if there are 3 dimes for every 5 quarters.
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Answer:
120
Step-by-step explanation:
Math pls answer and show work
Answer:6 trays
Step-by-step explanation:
36 people two cupcakes each means 36x2=72
on tray holds 12 cupcakes 72/12=6 trays
An article claimed that the typical price for a textbook is $84.95. The prices of six textbooks found in a bookstore were $76.95, $84.95, $108.95, $63.95, $75.95, and $84.95.
According to this data, what is wrong with the article's statement?
help please
rewrite y=1/4x+3 solving for x. what feature of the line can easily be found using the rearranged equation?
x intercept is x = -12
What is linear equation ?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
x = 4y - 12
y = 0
x intercept is
x = -12
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Determine the y-intercept of the linear equation 5x + 4y = -40
5x + 4y = -40
4y = -40 -5x
4y/4 = -40/4 -5x/4
y = -10 -5x/4
hence the y-intercept is -10
Answer:
dog
Step-by-step explanation:
i have 2 mins pleaseeeee
Answer: 179.07 this is ur answer
Step-by-step explanation:
Decrease 58 by 41%.
Give your answer to 2 decimal places.
Answer: 34.22
Find 41% of 58 first.
[tex]58*0.41=23.78[/tex]
The problem asks to decrease it, meaning you would subtract the percentage from 58.
[tex]58-23.78=34.22[/tex]
34.22
MA.912.AR.2.5
23. A hot air balloon company charges for evening sunset flights are based on the function y = 25x + 100, where x is
the number of people traveling in the basket (note the basket capacity limit is 8) and y is the cost of the trip in dollars.
What is the base fee for the balloon ride before passengers are figured in? What does the 25 represent?
100$ before passengers. 25 is the price per person. 225 for 5 people to fly.
What are linear equation?One variable can be used to solve a linear equation by moving the variables to one side of the problem and the numerical component to the other. As an example, the equation x - 1 = 5 - 2x can be solved by moving the numerical components to the equation's right side while leaving the variables on the left. Consequently, we get x + 2x = 5 + 1. 3x = 6 as a result. Consequently, x = 2. A linear equation with two variables has the formula Ax + By + C = 0, where A and B are the coefficients, C is a constant term, and the two variables, x and y, each have a degree of one. 7x + 9y + 4 = 0, for instance, is a two-variable linear equation.
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what is 2 1/2 - 1 5/6 as an fraction
The value of [tex]2\frac{1}{2} -1\frac{5}{6}[/tex] as an fraction is 2/3 .
In the question ,
the expression is given as
[tex]2\frac{1}{2} -1\frac{5}{6}[/tex]
To convert a mixed fraction [tex]a\frac{b}{c}[/tex] into a improper fraction , we use the formula
[tex]a\frac{b}{c}[/tex] = (a*c+b)/c
let us first convert the given mixed fraction into improper fraction ,
using the formula of conversion , we get
[tex]2\frac{1}{2}[/tex] = (2*2+1)/2 = 5/2
and
[tex]1\frac{5}{6}[/tex] = (1*6+5)/6 = 11/6
Substituting the values , the expression becomes
= 5/2-11/6
taking the LCM as 6 and solving further , we get
= 15/6 - 11/6
= (15-11)/6
= 4/6
= 2/3
Therefore , The value of [tex]2\frac{1}{2} -1\frac{5}{6}[/tex] as an fraction is 2/3 .
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Given ∠2 and ∠4 are vertical
Prove ∠2 ≅ ∠4
Assemble the proof by dragging tiles to the Statements and Reasons columns.
We proved that [tex]\angle2\cong\angle4[/tex].
Given: [tex]\angle2[/tex] and [tex]\angle4[/tex] are vertical.
We have to prove [tex]\angle2\cong\angle4[/tex]
The [tex]\cong[/tex] means congruence which means [tex]\angle2[/tex] and [tex]\angle4[/tex] both have same size and angle. We have to show that they both have same size or angle to prove them congruence.
As we know that the value of straight line is [tex]180^{o}[/tex].
From the given figure we can see that
[tex]\angle1+\angle2=180^{o}[/tex]
[tex]\angle3+\angle4=180^{o}[/tex]
[tex]\angle1+\angle4=180^{o}[/tex]
[tex]\angle2+\angle3=180^{o}[/tex]
To prove the [tex]\angle2\cong\angle4[/tex] we subtract [tex]\angle1+\angle2=180^{o}[/tex] and [tex]\angle1+\angle4=180^{o}[/tex]
[tex]\angle1+\angle2-(\angle1+\angle4)=180^{o}-180^{o}[/tex]
We first simplify bracket. When we multiply with the subtraction sign then the sign under the bracket will changed.
[tex]\angle1+\angle2-\angle1-\angle4=0[/tex]
There have [tex]\angle1[/tex] in addition and subtraction then there only remains
[tex]\angle2-\angle4=0[/tex]
We can write that notation as
[tex]\angle2=\angle4[/tex]
Since [tex]\angle2=\angle4[/tex], that means they both have same angle.
So we proved that [tex]\angle2\cong\angle4[/tex].
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If A = {x|x is an even integer}, B = {x|x is an odd
integer}, and
C= {x|x<0}, list the elements of each set.
5. A n B
6. A u B
7. B n C
8. B u C
Answer:
Step-by-step explanation:
5. A n B = ∅ (the empty set)
6. A u B = {x|x is an integer, x ≠ 0}
7. B n C = {x|x<0}
8. B u C = {x|x<0 or a positive odd integer}
Identify the vertex of each parabola,and then write its corresponding equation.Use the form: y = (x – h) + k
From the graph we get that:
The vertex of the parabola 1 has coordinates (5,4), and its equation is:
[tex]y=(x-5)^2+4[/tex]
The vertex of parabola 2 has coordinates (-3,-2), and its equation is:
[tex]y=(x-(-3))^2+(-2)=(x+3)^2-2[/tex]Garrett is a member of The Mighty Manatees, an outdoor swim team. Every practice, his coach tells him to swim a target number of laps. One day, Garrett swims 31 laps before practice is canceled due to a thunderstorm. Garrett still has 29 laps left to reach his target number.
The tangent line to the graph of y=h(x) at the point (-1,4) passes through the point (3,6). Find h(-1) and h'(-1).
The value for h(-1) is 4
The value for h'(-1) is 1
Given the tangent line to the graph of y=h(x) at the point (-1,4) passes through (3,6), to get h(-1) and h'(-1), we should calculate the following:
Gradient of the tangent line:
Gradient=change in y axis/change in x axis=Δy/Δx
Using the x and y coordinates (-1,4) and (3,6)
Gradient=(6-4)/(3--1)
=2/4
=1/2
Gradient=1/2 or 0.5
Equation of the tangent line:
This should be in the form of y=mx+c, where m is the gradient of the line
We use the gradient and one of the x and y coordinates get the equation of the tangent line
Gradient=change in y axis/change in x axis=Δy/Δx, and gradient was found as 1/2
Δy/Δx=1/2
(y-4)/(x--1)=1/2
(y-4)/(x+1)=1/2
2y-8=x+1
y=(1/2)x+4.5
Equation of the tangent line is y=(1/2)x+4.5 or y=0.5x+4.5
And y=h(x)
So, h(x)=0.5x+4.5
Calculate h(-1), here x=-1:
h(x)=0.5x+4.5
h(-1)=(0.5*-1)+4.5
=4
h(-1)=4
Calculate h'(-1), x=-1:
Here we get the derivative of the equation of the tangent line h(x)=0.5x+4.5,
h'(x)=0.5x^0+0
h'(-1)=1+0
h'(-1)=1
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please help with this question!! not sure if i'm correct or not, thank you!!!
The solution is TRUE
What is union and intersection of sets?
The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B
The union of two sets is a new set that contains all of the elements that are in at least one of the two sets
The intersection of two sets is a new set that contains all of the elements that are in both sets
Given data ,
Let the equation be x
x = A ∩ ( B' ∪ C' )
Now , from Distributive law of set
A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
And , ( A ∩ B' ) = A - B
So , substituting the formulas in the equation , we get
x = A ∩ ( B' ∪ C' )
x = ( A ∩ B' ) ∪ ( A ∩ C' )
x = ( A - B ) ∪ ( A - C )
Hence , the solution is TRUE
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