The ellipse's equation is [tex]$\frac{x^2}{3^2}+\frac{y^2}{4^2}=1$[/tex] , The hyperbola's equation is [tex]$ \frac{x^2}{(-4)^2}-\frac{y^2}{(-7)^2}=1$[/tex] and [-3, 3] is the ellipse's domain.
What is the domain of ellipse ?The ellipse's equation is (Part A) [tex]$\frac{x^2}{3^2}+\frac{y^2}{4^2}=1$[/tex] , The hyperbola's equation is shown in Part B as [tex]$ \frac{x^2}{(-4)^2}-\frac{y^2}{(-7)^2}=1$[/tex]
Part C: [-3, 3] is the ellipse's domain.
The hyperbola's domain lies between [-, -4].
The ellipse and hyperbola's domains do not intersect, hence the system of equations cannot be solved. The origin is the location of the ellipse's centre;8 units make up the vertical main axis. The minor axis equals six units.
Here is a general representation of the ellipse equation:;[tex]$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$[/tex]
a= The semi-major axis, where 8/2 = 4.
The semi-minor axis, b= 6/2 = 3.
Therefore, the ellipse's equation is
[tex]${\frac{-x^2}{3^2}+\frac{y^2}{4^2}=1}$[/tex]
The negative vertex and the domain of the hyperbola are equal.
∴ The hyperbola's domain is [x -4] = [-, -4]
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solve x^2+3x+2=0
x=
OR
x=
Solve x^2+3x+2=0
[tex]x_{1} = -1\\x_{2} = -2[/tex]
The first is to use the quadratic formula
x= (-b±[tex]\sqrt[{} ]{b^{2} -4ac}[/tex]) ÷ 2a
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
[tex]x^{2} +3x+2 = 0[/tex]
Where,
a = 1
b = 3
c = 2
So,
x = (-b±[tex]\sqrt[{} ]{b^{2} -4ac}[/tex]) ÷ 2a
= (-3±[tex]\sqrt[]{3^{2}-4.1.2 }[/tex]) ÷ 2.1
The next step is to simplify numbers.
x= (-3±1) ÷ 2
The next step is separate it into two equations: one with the plus sign and the other with the minus sign.
x = (-3+1) ÷ 2
and
x = (-3-1) ÷ 2
Then,
[tex]x_{1}[/tex] = (-2)÷2 = -1
Or,
[tex]x_2}[/tex] = (-4)÷2 = -2
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1) Which of the following pairs of ratios does NOT form a proportion?
a) 2/7, 8/28
c) 27/9, 12,4
b) 36/30, 7/6
d) 52/13, 4/1
36/30, 7/6 does NOT form a proportion.
What is proportion?A proportion refers to the similarity of the two ratios.Write proportion to help you find equivalent ratios and solve for unknown quantities.A proportion is an equation that equates two ratios.For example, if you have one boy and her three girls, the ratio can be written as:1:3 (for every boy he has 3 girls) 1/4 are boys and 3/4 are girls. 0.25 boys (1 divided by 4)Direct proportionality or direct proportion is the ratio of two quantities where the ratio is equal to a constant value.It is denoted by the proportional sign ∝.In fact, the same symbol is used to represent the inverse proportion, because the difference in magnitude is reversed here.36/30 = 16/15 not equal to 7/6.
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The perimeter of AABC equals 12 in. The midpoints of the sides, M, N and K,
are connected consecutively. Find the perimeter of AMNK.
According to the Triangle midline theorem, slicing across a triangle's midline results in a section that is parallel to the base and only half as long. MNK=6 INCH
What is Triangle midline theorem?Theorem of the triangle midline: In a triangle, the midline connecting the midpoints of two sides is parallel to and half as long as the third side.
The midsegment linking the midpoints of two sides of a triangle is parallel to the third side of the triangle, and its length is half that of the third side, according to the midsegment theorem.
The midpoints of the sides AB, BC, and AC are points M, N, and K. The Triangle Midline Theorem states that
MN=1/2AC
NK=1/2AB
MK=1/2BC
The perimeter of the triangle MNK is
P(MNK)=MN+NK+MK
=1/2AC+1/2AB+1/2BC
=1/2(AC+AB+BC)
=1/2PABC
=1/2.12
=6 inch
Therefore MNK=6 INCH
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Please give me the vertical value in a pair of coordinates.
The vertical values or points lying on y-axis are - 0, 3, 6, 9, -3, -6.
The ordinate of a typical two-dimensional graph is referred to as the (y) coordinate, while the (x) coordinate is referred to as the abscissa.
The abscissa, also known as the x coordinate of the point, is the distance between a point and the y-axis, scaled with the x-axis. The term "ordinate" refers to a point's separation from the x-axis when scaled with the y-axis. The first coordinate in the plane (x) is referred to as the abscissa and the second coordinate (y) is the ordinate, for instance, if (x, y) is an ordered pair in the Cartesian plane.
The coordinates of the given graph are -
(0,3) (1,6) (2,9)
(-1,0) (-2,-3)(-3,-6)
From the above coordinates, the vertical values or points lying on y-axis are - 0, 3, 6, 9, -3, -6.
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How do you simplify radicals explain and give examples?.
Simplifying radicals is the process of reducing a radical expression to its simplest form. There are several ways to simplify radicals, but the most common method is to factor .
The number or expression inside the radical sign and extract any perfect nth root factors.For example: √36 = √(36) = √(6*6) = √(6^2) = 6
Here, 36 can be factorized into 6*6, and since 6 is a perfect square, we can simplify the radical as 6.
Another example: √100 = √(100) = √(10*10) = √(10^2) = 10
Here, 100 can be factorized into 10*10, and since 10 is a perfect square, we can simplify the radical as 10.
Another way to simplify radicals is to use the product property of radicals which states that: √(a*b) = √(a) * √(b)
For example: √(1215) = √(12) * √(15) = √(4355) = √(43) * √(55) = 2√(3) * 5 = 6√(3)
Here, 1215 can be factorized into 4355. And since 43 is a perfect square, we can simplify the radical by taking the square root of 43 and 5*5.
You can simplify radicals as much as possible by applying these methods.
It's important to note that not all radicals can be simplified completely, in some cases we can simplify the radical as much as possible but still have an irrational number inside the radical.
Simplifying radicals is a useful process in algebra and trigonometry, it helps to simplify the expressions and make calculations easier.
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What is the end behavior for f(x)=x^5?
The end behavior for f(x)=x^5 is asymptotic growth to positive infinity as x approaches positive infinity and asymptotic growth to negative infinity as x approaches negative infinity.
What is asymptotic growth?Asymptotic growth is a term used to describe the behavior of a function as it approaches a certain value, usually infinity. In mathematics, an asymptotic function is one that grows or shrinks towards a certain point without ever actually reaching it. In other words, it approaches a limit without bound. Asymptotic growth is often used to describe the rate of growth of a function as its input values approach infinity. It is also used to describe the rate at which a function expands or contracts as its argument approaches a certain point. Asymptotic growth is a useful concept in many areas of mathematics, from calculus to number theory.
This is because x^5 becomes increasingly larger as the absolute value of x increases, resulting in an ever-growing value of f(x).
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You just switched to a cell phone plan where you have to pay by the minute because you can’t afford Verizon anymore. You have to pay an activation fee of $13.00 and then you pay $0.30 per minute. This month, your bill was $40. For how many minutes did you talk?
Answer:90 minutes
Step-by-step explanation:
40 dollars a month minus the 13.00 fee. 40-13=27. 27-.30=90 so 90 minutes
What are the types of multiplication method?.
The types of multiplication method: addition method, long multiplication, grid method, drawing lines and by splitting two digit numbers into Tens and Ones
We know that the multiplication is nothing but a method of finding the product of two or more numbers.
In case of small numbers a multiplication is considered repeated addition, and we can solve simple multiplication problems by adding repeatedly.
But in case of larger numbers, we need to do long multiplication.
Multiplication methods:
1) by Repeated Addition
Consider example 4 × 5
This means, we can solve it as by adding 4 repeatedly five times 4 4 + 4 + 4 + 4 + 4 OR by adding 5 repeatedly four times 5 + 5 + 5 + 5
2) Long Multiplication
3) grid method,
4) by drawing lines
3) by splitting two-Digit Numbers into Tens and Ones
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how do u interpret the fraction 12/4
How do you solve linear systems with linear combinations?.
In mathematics, a linear combination is any expression of the form ax + by, where a and b are constants, that are created from a set of terms by multiplying each term by a constant and adding the results.
The linear equations can be solved through the given steps-
Three methods exist for resolving a linear combination: Utilize the equations as is. A different equation should be used. Both equations should be changed. Use the equations exactly as they are. The two equations can be subtracted from one another to eliminate x because the coefficient of x is 1 in both instances.For example, a linear combination of x and y would be any expression of this form.To learn more about linear equations here
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How do you solve systems of equations with 3 variables using substitution?.
We can solve systems of equations with 3 variables using substitution by finding the value of one variable from one equation then putting the value of that variable in second equation and 3 equation then solving them properly.
The algebraic approach for system can significantly systems of equations at once is called the substitution method. As the name implies, this method involves substituting a variable's value from one equation into another. In this manner, a pair of linear equations are combined into a single, simple linear equation with just one variable.
Equations linear in three variables:
1. Use all but one of your equations to find all the variables that can be expressed in terms of one of the variables.
2. Determine the variable's numerical value using the one remaining equation.
3. Using that figure, determine the answers to all of the other variables.
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hi pls help math math
The number of teams who took less than 40 minutes to complete the game is 34 teams
How many of the team took less than 40 minutes to complete the game?0 ≤ t < 20 = 6
time greater than or equal to 0 less than 20 minutes
20 ≤ t < 40 = 28
time greater than or equal to 20 minutes less than 40 minutes
40 ≤ t < 60 = 12
time greater than or equal to 40 minutes less than 60 minutes
60 ≤ t < 80 = 7
time greater or equal to 60 minutes less than 80 minutes
The number of the team who took less than 40 minutes to complete the game are;
0 ≤ t < 20 = 6
20 ≤ t < 40 = 28
So,
6 + 28 = 34 teams
Hence, 34 teams took less than 40 minutes to complete the game.
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In ΔEFG, g = 8.4 inches,
�
m∠G=79° and
�
m∠E=25°. Find the length of f, to the nearest 10th of an inch.
The image explains it all. First we find the third degree using the sum of angles in a triangle (180), then, using the rule of sines, we find the f and round it to the nearest 10th inch
If 92 people attend a concert and ticket for adult cot $3 while ticket for children cot $2. 25 and total receipt for the concert wa $246. 75, how many of each went to the concert?
The people who went to the concert will be 53 Adults and 39 Children respectively.
We will solve this problem with the help of a Binomial equation.
Let the number of adults is X and the number of children is Y.
Our first equation will be =
X + Y = 92
The total cost for adults is $3 and for Children is $2.25.
The total receipt for the concert is $246.75.
Our second equation will be =
3X + 2.25Y = 246.75
From equation 1, we get
X + Y = 92
X = 92-Y
Substitute this in equation second equation, and we get
3(92-Y) + 2.25Y = 246.75
276 - 3Y + 2.25Y = 246.75
-0.75Y = 246.75 - 276
-0.75Y = -29.25
Y = 39
So, our number of Children is 39.
Putting the value of Y in the first equation, we get:
X = 92 - 39 = 53
So, our number of adults is 53.
Therefore 53 Adults and 39 Children went to the concert respectively.
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Alyssa has a cell-phone plan that charges a fixed price for each text message, no mater how many she sends. The table below shows the number of text messages Alyssa sent and the amounts she was charged for them on her last three bills.
(Table showed in attached image)
Using x for the number of text messages sent and y for the amount charged, find the equation of the line that models this relationship and find the rate Alyssa is charged for each text message.
The equation of the line is ____ .
Alyssa is charged $____ for each text message.
Answer: Alyssa is charged $0.15 for each text message.
Step-by-step explanation: 5-star
Answerrrr....
....................
(i) The required frequency is 12 for the class interval 50-60.
(ii) The mean height of students in a class is 155.3.
(iii) The median of the given data is 33.
(i)
Class Interval Frequency f Mid-value x fx
0-10 22 5 110
10-20 24 15 360
20-30 35 25 875
30-40 30 35 1050
40-50 27 45 1215
50-60 m 55 55m
60-70 6 65 390
70-80 4 75 300
∑f = 148+m ∑fx = 4300+55m
The mean of the data set shown in the table above is 31.
mean = ∑fx/∑f
Substitute the known values in the above formula, and we get
31 = (4300+55m)/(148+m)
31(148+m) = 4300+55m
4588 +31m = 4300+55m
55m - 31m = 4588 - 4300
24m = 288
m = 288/24
m = 12
Thus, the required frequency is 12 for the class interval 50-60.
(ii)The table below summarizes the data about the heights of students in a class.
Height (in cm) (x) d = (x -A)/10 Number of students (f) fd
130-140 135 -2 8 -16
140-150 145 -1 6 -6
150-160 155 0 14 0
160-170 165 1 20 20
170-180 175 2 12 24
∑f = 60 ∑fd = 22
Mean = A + ∑fd/∑f
Mean = 155 + 22/60
Mean = 155 + 0.3
Mean = 155.3
So, the mean height of students in a class is 155.3.
(iii) Given that the mean of data is 27 and the mode is 45
Mode = 3Median - 2Mean
45 = 3Median - 2(27)
45 = 3Median - 54
3Median = 54 + 45
Median = 99/3
Median = 33
Thus, the median of the given data is 33.
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A store has a
25
%
25%25, percent off sale on coats. With this discount, the price of one coat is
$
34.50
$34.50dollar sign, 34, point, 50.
The price of one coat is $46.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number. So the percentage actually means a part per 100.
Given that,
a store has 25% off sale on coats.
Discounted price of one coat = $34.50
We have to find the original price of the coat. Let it be x.
x - (25% x) = 34.5
x - 0.25x = 34.5
0.75x = 34.5
x = 46
Hence the original price of the coat is $46.
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1+1=x
if i were trying to find x what would x be
Answer:
X = 2
Because x means our answer and the answer to 1 + 1 is 2!
Answer:
2
Step-by-step explanation:
1+1=2
x=2
PROBLEM SOLVING Plutonium-238 is a material that generates steady heat due to decay and is used in power systems for some spacecraft.The function y=a(0.5)t/x represents the amount y of a substance remaining after t years, where a is the initial amount and x is the length of the half-life (in years).
Plutonium- 238, Half-life is approximately 88 years.
a. A scientist is studying a 3-gram sample. Write a function that represents the amount y of plutonium-238 remaining after t years.
Question 2
b. Use the function to estimate the amount of plutonium-238 remaining after 8 years.
Question 3
c. Use the graph of the function to estimate the amount remaining after 12 years.
About grams
The equation is [tex]\rm y = 3 \times \left (0.5 \right)^{t/88}[/tex]. Then the amount remaining after 8 years and 12 years will be 2.8168 grams and 2.729 grams, respectively.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the factor.
The exponent is given as
y = a(b)ˣ
The function is given below.
[tex]\rm y = a \left (0.5 \right)^{t/88}[/tex]
A scientist is studying a 3-gram sample. Then the function is written as,
[tex]\rm y = 3 \times \left (0.5 \right)^{t/88}[/tex]
The amount of plutonium-238 remaining after 8 years will be given as,
[tex]\rm y = 3 \times \left (0.5 \right)^{8/88}[/tex]
y = 3 × 0.9389
y = 2.8168 grams
From the graph, the amount remaining after 12 years will be 2.729 grams.
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In exploration 4. 1. 1 problem 3, which is the strongest answer on why the equation is or is not an identity?.
The equation is an identity because it is true for all values of the variables within the equation.
The equation is an identity because it is true for all values of the variables within the equation. This means that when the equation is evaluated for any given values of the variables, the left-hand side and the right-hand side of the equation will be equal. This is different from an equation that is not an identity, which will only be true for certain values of the variables. An identity equation is also different from an equation that is not an identity, which may be true for some values of the variables but not for all values. An identity equation is one that is true for all values of the variables, no matter what values are chosen.
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What is the measure of an angle if it is five times?.
The measure of an angle if it is five times its complement: 75 degrees
Let us assume that the complement of the angle measures m degrees.
we have been given the measure of the angle is five times its complement.
So we get the measure of the angle = 5 × m
We know that two angles are complementary when their measures add to 90 degrees.
So we get an equation, m + 5m = 90
We solve above equation to find the value of m.
m + 5m = 90
6m = 90
m = 90/6
m = 15 degrees
This means, the measure of complement of the angle is 15 degrees.
And the required angle would be,
5 × 15 = 75 degrees
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The comple question is:
What is the measure of an angle if it is five times its complement?.
The entire graph of the function f is shown in the figure below.
Write the domain and range of fas Intervals or unions of intervals.
domain
range
The graph of the entire function f has a domain of (-3 < x < -2) ∪ (0 < x < 1) and the range of (-5 < y < 5).
What do a function's domain and range mean?The set containing all input values is known as a function's domain.
A function's range is the collection of all possible output values.
In a graph:
The x-values, or horizontal axis, define the domain.
The y-values, or vertical axis, define the range.
The domain of the graph is given by the coordinates of x. For the given graph the x- coordinates are:
(-3 < x < -2) ∪ (0 < x < 1)
The range of the graph is given by the y-coordinates of the graph. For the given graph the y-coordinates are:
(-5 < y < 5).
Hence, the graph of the entire function f has a domain of (-3 < x < -2) ∪ (0 < x < 1) and the range of (-5 < y < 5).
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I need help on this asap! Greatly appreciated!
We can fill in the fields as:
a) %6.50 shipping fee: x >= $0.01 and x < $20.
b) %9.00 shipping fee: x >= $20 and x < $50.
c) %11.00 shipping fee: x >= $50 and x < $75.
d) %12.25 shipping fee: x >= $75 and x < $100.
e) %13.10 shipping fee: x >= $100.
What is inequality?
An inequality is a mathematical statement that describes the relationship between two values, where one value is not equal to the other.
a) %6.50 shipping fee: x >= $0.01 and x < $20.
b) %9.00 shipping fee: x >= $20 and x < $50.
c) %11.00 shipping fee: x >= $50 and x < $75.
d) %12.25 shipping fee: x >= $75 and x < $100.
e) %13.10 shipping fee: x >= $100.
Each inequality represents a different shipping fee category at GoodSportsBuys.com, with the total cost of items purchased (x) falling within a certain range. The inequality symbol used in each statement represents the range of values that correspond to a particular shipping fee.
Hence, we can fill in the fields as:
a) %6.50 shipping fee: x >= $0.01 and x < $20.
b) %9.00 shipping fee: x >= $20 and x < $50.
c) %11.00 shipping fee: x >= $50 and x < $75.
d) %12.25 shipping fee: x >= $75 and x < $100.
e) %13.10 shipping fee: x >= $100.
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8.
(6.6) Lizzy is buying oranges and pineapples for an evemt. Oranges cost $3 per pound and
pineapples cost $4 per pound. Lizzy needs to buy at least 16lbs of fruit for her event, but she only
has $60 to spend.
a) Define the variables and write a system of inequalities to represent this situation,
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality.
Explain about the inequalities?
In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.
The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3. Finding the x numbers for which the inequality holds true is what we are most interested in.
Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.
= Orange she bought 8 kg x 3 = $24
= Pineapple she bought 9KG X 4 = $36
= $24 +36
= $60
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Use cross products to solve for x. Type your answer as a simplified fraction (Ex. 37/4).
5/x+3 = 4/x
X =
Answer:
x=1/3
Step-by-step explanation:
= 5/x - 4/×=3
= 1/x=3/1
= 1=3×
= x=1/3
At a real etate agency, an agent old a houe for $342,000. The commiion rate i 4. 5% for the real etate agency and the commiion rate for the agent i 30% of the amount the real etate agency get. How much did the agency make on the houe? How much did the agent earn in commiion?
So, the agency made $15,390 on the sale of the house and the agent earned $4,617 in commission.
First, to find out how much the agency made on the house, you need to calculate the commission they received. The commission rate for the agency is 4.5%, so to find the commission you would multiply the sale price of the house ($342,000) by the commission rate (0.045)
$342,000 x 0.045 = $15,390
The agency made $15,390 on the sale of the house.
To find out how much the agent earned in commission, you need to first find out how much the agency earned in commission ($15,390) and then multiply that by the agent's commission rate (30%).
$15,390 x 0.3 = $4,617
The agent earned $4,617 in commission.
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To calculate the commission, multiply the selling price of the home ($342,000) by the agency's commission rate, which is 4.5%. (0.045)
$342,000 x 0.045 = $15,390
The sale of the property brought in $15,390 for the organization.
To calculate the amount of commission earned by the agent, multiply the amount of commission received by the agency ($15,390) by the agent's commission rate (30%).
$15,390 x 0.3 = $4,617
The dealer received a commission of $4,617.
PLEASE HELP ME, I WILL BE REALLY GRATEFUL EMERGENCY 50 POINTS!!
I am the superintendent of Minie Couty schools. My staff is made up of an assistance superintendent, a director, and an accountant. Our names are Mr. Wilson, Mr. Jones, Ms. Bigge, and Mr. Smith. Mrs. Jones and the assistant superintendent used to share the same office. I play bridge with my accountant every Monday night. Mr. Wilson confers with me every week. Mr. Smith, who holds a degree in mathematics, may get my job when I retire. Mrs. Jones is so busy she doesn't have time to play card games. Mr. Wilson has never shared an office in his life. Who am I and what are the names of the members of my staff?
Answer:
I'm rlly bad at these so I'll try and good luck lol
they are the superintendent
assistance superintendent: Mr Wilson
director: Mr Jones
accountant: Ms bigge
assistants: Mr Smith and Mrs jones
Step-by-step explanation:
good luck yay -14 year old
if do= (6y-17.81) and ro= (3y+10.54) what is the length of hv
If do= (6y-17.81) and ro= (3y+10.54) then the measure of length of hv = 26
What about the length?A measurement that is longer than or longest than another. a dimension or distance that can be measured. Dimensions: 10 ft. Weights and Measures Table, Metric System Table being lengthy is a quality or a state.
In addition to utilising handspan, foot span, and other methods, one can measure length in many units, such as centimetres, inches, metres, and so on. The several types of units used to measure length can be divided into two categories: standard units and non-standard units.
The number of digits in the base-numerical for, as determined by the formula, determines a number's base length.
HF = 10x + 6
VH = 8 x – 14 and
FV = 4x+10
Substitute
8x - 14 + 4x + 10 = 10x +6
12x - 4 = 10x + 6
12x - 10x = 6 + 4
2x = 10
x = 5
Identify the VH's length.
VH = 8x - 14
VH = 8(5) - 14
VH = 26
Consequently, VH is 26 units long.
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Which is bigger -1/8 or -2/11
let's put both fractions using the same denominator by multiplying each top and bottom by the other's denominator.
[tex]-\cfrac{1}{8}\cdot \cfrac{11}{11}\implies \boxed{-\cfrac{11}{88}}\hspace{15em}-\cfrac{2}{11}\cdot \cfrac{8}{8}\implies \stackrel{\textit{\LARGE \checkmark}}{\boxed{-\cfrac{16}{88}}}[/tex]
well, let's take a looksie above, on the positive side of the number line, 16/88 is larger than 11/88, however, on the negative side, the closer to "0", the larger, for that matter -1 is a much larger number than -1,000,000.
So, -11/88 is closer to 0 on the negative side, and because of that, is larger than -16/88 that is farther from 0.
Please help somebody it’s due in one hour
The first, fourth and eight terms of the given sequence are the ones in the last option.
-2, -250, -156,250
How to find the terms in the given sequence?We know that the n-th term of the given sequence is given by the formula:
A(n) = -2*5ˣ⁻¹
The first term is what we get when x = 1, then the first term is:
A(1) = -2*5⁰ = -2
The fourth term is what we get when we use x = 4, we will get:
A(4) = -2*5⁴⁻¹ = -2*5³ = -250
The eight term is what we get when x = 8
A(8) = -2*5⁸⁻¹ = -2*5⁷ = -156,250
Then the correct option is the last one.
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