Which conic's equation has 2 squares with the same signs and different leading coefficients?
Answers
We want to see which is the conic equation that has 2 squares with the same sign and different leading coefficients.
We will see that it is the equation of the ellipse.
Now let's see why that is the correct answer.
The general conic equation is of the form:
\(A*(x - a)^2 + B*(x - b)^2 = R^2\)
Where A and B are the leading coefficients, (a, b) is the center of the figure, and R is the average radius of the figure.
For example, if A = B, this would be the equation of a circle, but we must have two different leading coefficients.
If we write:
A = 1/C
B = 1/K
(both are positive, because "it has two squares with the same signs").
Then we get the equation:
\(\frac{ (x - a)^2}{C} + \frac{(x - b)^2}{K} = R^2\)
We get the equation we wanted.
The same sign in both square parts and different leading coefficients.
The above equation is the general equation of an ellipse.
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Related Questions
Sally bought five books.Their mean price was 3.25. The total cost for four books was 11.75.what was the cost of the fifth book
Answers
Answer:
$4.50
Step-by-step explanation:
Use the mean formula: mean = sum of elements / number of elements
Let x represent the cost of the fifth book, and solve for x:
mean = sum of elements / number of elements
3.25 = (11.75 + x) / 5
16.25 = 11.75 + x
4.5 = x
So, the cost of the fifth book was $4.50
whats 3-6h if h = -1
Answers
Answer:
9 is the answer.
Step-by-step explanation:
Given:
h = -1=> 3-6h
=> 3 - 6(-1)
=> 3 + 6
=> 9
Therefore, 9 is the answer.
Hoped this helped.
Find the equation of the line that satisfies the conditions given in each of the following: 1. Through (3, 2) and (5, 7) 2. Through (-3, 4), m = 2 3. m = -3, b = 5 4. x-intercept = 3, y-intercept
Answers
The equation of each line that satisfies the given conditions are:
1. y - 2 = 5/2(x - 3)
2. y - 4 = m(x + 3)
3. y = -3x + 5
What is the Equation of a Line?If we know the slope (m) and the y-intercept (b) of a line, we can write the equation of the line as y = mx + b in slope-intercept form.If we know the point (a, b) and the slope (m) of the line, we can write the equation of the line in point-slope form as y - b = m(x - a).1. Given the points, (3, 2) and (5, 7), find the slope (m):
Slope (m) = change in y / change in x = (7 - 2)/(5 - 3)
m = 5/2
Write the equation in point-slope form by substituting m = 5/2 and (a, b) = (3, 2) into y - b = m(x - a):
y - 2 = 5/2(x - 3)
2. Given:
A point = (-3, 4)
Slope (m) = 2
Substitute (a, b) (-3, 4), and m = 2 into y - b = m(x - a):
y - 4 = m(x + 3) [equation of the line]
3. Given:
Slope (m) = -3
Y-intercept (b) = 5
Substitute m = -3 and b = 5 into the equation y = mx + b:
y = -3x + 5
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Complete the following table:
Note: Do not round net price equivalent rate and single equivalent discount rate. Round the dollar amounts to the nearest cent.
Answers
The completion of the table showing the net price equivalent rate, the single equivalent discount rate, and the net price for the chain discounts of the HP computer's listed price is as follows:
Net price equivalent rate = 0.9504Single equivalent discount rate = 0.0496Trade discount = 4.96%Net Price = $1,140.48.What are chain discounts?Chain discounts represent a series of trade discounts offered to customers who fulfill certain conditions.
To compute the single equivalent discount rate for chain discounts, the rates are computed separately based on the remaining percentages or rates following the previous discounts.
For instance, for the second chain discount, the actual rate is not just 1% but 1% of 96%, which results to 0.96%.
The list of a HP Computer = $1,200
Chain discount = 4/1 (0.04/0.01)
Single equivalent discounts = 0.0496 (0.04 + 0.0096)
The total trade discount rate = 4.96% (0.04 + 0.01 x 0.96)
Net price = 0.9504 (1 - 0.0496)
Net price in dollars = $1,140.48 ($1,200 x 0.9504)
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Convert 16 quarts to gallons. There are 4 quarts in a gallon.
OA. 32 gallons
OB. 64 gallons
OC. 4 gallons
OD. 8 gallons
Answers
16 quarts is equal to 4 gallons.
The correct option is C.
To convert quarts to gallons, we divide the number of quarts by 4 (since there are 4 quarts in a gallon).
Given that we have 16 quarts, we can calculate:
16 quarts / 4 quarts/gallon
= 4 gallons
Therefore, 16 quarts is equal to 4 gallons.
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Anybody know the answer to this one ?
Answers
The function value of g[f(-1)] when f(x) = 2x² + 4x and g(x)=-3x-1 is 5.
What is function?In mathematics, a function is a rule that assigns each element from a set (called the domain) to a unique element from another set (called the range or codomain). It is a way of describing the relationship between two sets of numbers. The input values of a function are called the independent variable or argument, and the output values are called the dependent variable. The most common way to represent a function is by using an equation.
Here,
To evaluate g[f(-1)], we need to first find f(-1), then use that value as the input to the function g.
We have:
f(x) = 2x² + 4x
So, to find f(-1), we substitute -1 for x:
f(-1) = 2(-1)² + 4(-1)
= 2 - 4
= -2
Now that we have f(-1) = -2, we can evaluate g[f(-1)] by substituting -2 for x in the function g:
g[f(-1)] = g[-2]
= -3(-2) - 1
= 5
Therefore, g[f(-1)] = 5.
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Andre read a report saying that 35% of people in his country approved of the job their current Prime Minister was doing, 35% disapproved, and 30% neither approved or disapproved. He wondered if these percentages held true in his city, so he obtained a random sample of 16 responses from people in his city, Here are the results: Opinion Approve Disapprove Neither Observed counts 5 8 3 Andre wanted to use these results to carry out a x^2 goodness-of-fit test to determine if the sample disagreed with the reported distribution. Which count(s) make this sample fail the large counts condition for this test? A. The observed count of people who approve of the Prime Minister's job. B. The observed count of people who disapprove of the Prime Minister's job. C. The observed count of people who neither approve nor disapprove of the Prime Minister's job.
D. The expected count of people who approve of the Prime Minister's job. E. The expected count of people who neither approve nor disapprove of the Prime Minister's job.
Answers
C. The observed count of people who neither approve nor disapprove of the Prime Minister's job. therefore this option is right.
To determine which count(s) make this sample fail the large counts condition for the \(χ^2\) goodness-of-fit test, we need
to first calculate the expected counts for each category (approve, disapprove, neither) and compare them with the
observed counts.
Step 1: Calculate the expected counts.
Expected count for approve = 0.35 × 16 = 5.6
Expected count for disapprove = 0.35 × 16 = 5.6
Expected count for neither = 0.3 × 16 = 4.8
Step 2: Check the large counts condition.
The large counts condition states that all expected counts should be at least 5. In this case, the expected counts for
approve and disapprove meet the condition, but the expected count for neither (4.8) does not. Therefore, the sample
fails the large counts condition due to the observed count of people who neither approve nor disapprove of the Prime
Minister's job.
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1 Write the series 3 + 6x +9x2 +12x + ... with 45 terms in sigma notation.
Answers
Answer:
Step-by-step explanation:
It looks like every time the coefficient increases by 3 while the exponent increases by 1.
\(\\45\\\sum 3(n+1)x^{n}\\n = 0\)
Notice it starts at zero so 3 is multiplied by (x+1) to make it start from 0
The exponent is simply n, because at the start is it zero \(x^0=1\), then 1, then 2, so on.
The upper limit is 45 because 45 - 0 = 45 terms
Does Kerri's dot plot match the data in the tally
table?
Use Kerri's dot plot to complete the statements.
_classmates spent 3 hours at the park.
_classmates spent 4 hours at the park.
_classmates spent 5 hours at the park.
_classmates spent 6 hours at the park.
Answers
Answer:
no 5,3,6,4
Step-by-step explanation:
i got it right
Answer:
first one is no second is 5 third is 3 forth one is 6 and last one is 4
Step-by-step explanation:
PLZ give me brainless.
2. A bag contains one red, one blue and one white marble. One marble is chosen at random
from the bag, and then replaced into the bag. A second marble is chosen.
a) Draw a probability tree and find the sample space.
(3 marks)
Answers
Answer:
Step-by-step explanation:
a bag of mixed peanuts and cashews contains pounds of peanuts that cost per pound and pound of cashews that cost per pound
Answers
The number of pounds of peanuts needed is 29.167.
Multiply the number of pounds of each type and multiply by the cost per pound to get the total cost of that part contribution to the total. Add them together and set it equal to the final total pounds (50) multiplied by its cost per pound ($2.90)
There are 5 pounds of mixed nuts.
let x = pounds of peanuts
cost of each pound of peanuts is $1.50
45 - x = pounds of cashews
Cost of each pound of cashew is $4.50
This way total pounds = 50
5 pounds($6) + x pounds ($1.50) + (45-x)pounds($4.50) = 50 pounds($2.90)
30 + 1.50x + 202.5 - 4.50x = 145
-3x = -87.5
x = 29.167
Therefore, the number of pounds of peanuts needed is 29.167.
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Disclaimer
The question given by you is incomplete, the abouve asnwer is done as per a similar question, the question is
A merchant has 5 pounds of mixed nuts that cost $30. he wants to add peanuts that cost $1.50 per pound and cashews that cost $4.50 per pound to obtain 50 pounds of a mixture that costs $2.90 per pound. how many pounds of peanuts are needed?
Refer to the given terms . A pattern defines the relationship between the first two terms . Determine the relationship and identify the missing term of the second pair , such that both the pairs are analogous . AZP : ZAR :: TXK :
Answers
The missing term in the second pair is YUL.
To determine the relationship between the first two terms, let's analyze the given pattern: AZP : ZAR.
If we look closely, we can observe that each letter in the first term is shifted one position forward in the alphabet to form the corresponding letter in the second term.
So, applying the same pattern to the second pair (TXK), we need to shift each letter one position forward in the alphabet:
T + 1 = U
X + 1 = Y
K + 1 = L
Therefore, the missing term in the second pair is YUL.
The analogy between the pairs is that each letter in the first term is shifted one position forward in the alphabet to form the corresponding letter in the second term.
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Sasha's retirement party will cost $15 if she invites 3 guests. What is the maximum number of guests there can be if Sasha can afford to spend a total of $45 on her retirement party? Solve using unit rates.
Answers
The maximum number of guests she can invite is 9.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.
Given that If Sasha invites three guests, the cost of her retirement party will be $15.
If she can afford to spend $45 the maximum number of the guest will be calculated as:-
3 guests = $15
1 guest = $5
Calculate the maximum guest,
Number of guests = $45 / $5
Number of guests = 9
Therefore, the most visitors she may invite is 9.
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Find the polynomial function f with real coefficients that has the given degree, zeros, and solution point.
Degree
Solution Point
f(0) = -8
4
Zeros
-4, 1, 1
Answers
Polynomial function f with real coefficients that has the given degree, zeros, and solution point is f(x) =2(x⁴ +3x³ -3x²+3x-4).
As given,
Polynomial function f with real coefficients for the given degree, zeros, and solution point is:
Degree 4
Solution Point f(0) = -8
Zeros -4, 1, i
f(x)=k(x +4)(x -1)(x -i)(x +i)
=k (x² + 3x -4) (x² -i²)
=k(x² + 3x -4) (x² +1) ___(1)
Solution point f(0) =-8
-8 =k(0² +3(0) -4)(0² +1)
⇒ k=2
Substitute k=2 in (1)
f(x) =2(x² + 3x -4) (x² +1)
=2(x⁴ +3x³ -3x²+3x-4)
Therefore, polynomial function f with real coefficients that has the given degree, zeros, and solution point is f(x) =2(x⁴ +3x³ -3x²+3x-4).
The complete question is:
Find the polynomial function f with real coefficients that has the given degree, zeros, and solution point.
Degree 4
Solution Point f(0) = -8
Zeros -4, 1, i
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Find all values of n for which the equation has two complex (non-real solutions)
6r² = 8r+ (n + 4)
Answers
Answer:
When n < - 6 2/3 the given equation has two complex solutions------------------------------
Given is a quadratic equation:
6r² = 8r+ (n + 4) ⇒ 6r² - 8r - (n + 4) = 0A quadratic equation has no real solutions if its discriminant is negative.
The discriminant of ax² + bx + c is:
D = b² - 4acApply to given equation:
D = (-8)² - 4*6*( - (n + 4)) = 64 + 24(n + 4) = 64 + 24n + 96 = 24n + 160Find the value of n when D < 0:
24n + 160 < 024n < - 160n < - 160/24 n < - 20/3 n < - 6 2/3If 5(x-6y) = 50y,what is the value of x in terms of y? PLS EXPLAIn
E. 16y
F. 15y
G. 11 2/5y
H.11y
EXPLAIN CORRECT ANSWER AND EXPLANATION GETS BRAINIEST
Answers
Answer:
E. 16y
Step-by-step explanation:
Given equation:
5(x - 6y) = 50y
Expand the brackets using
Distributive Property for subtraction: a(b - c) = ab - ac
⇒ 5 · x - 5 · 6y = 50y
⇒ 5x - 30y = 50y
Add 30y to both sides:
⇒ 5x - 30y + 30y = 50y + 30y
⇒ 5x = 80y
Divide both sides by 5:
⇒ 5x ÷ 5 = 80y ÷ 5
⇒ x = 16y
the graph of a quadratic function is shown on the grid. which function is the best represented by this graph?
Answers
Answer:
Step-by-step explanation:
It is H
Function for the graph of the parabola given in the picture attached will be Option (H). f(x) = x² - 6x
Equation of a parabola in vertex form: Equation of a parabola in vertex form is given by,
y = a(x - h)² + k
Here, (h, k) is the vertex of the parabola
Given in the graph,
Vertex of the parabola → (3, -9) Parabola passes through the origin (0, 0).Equation of the graph with vertex (3, -9) will be,
y = a(x - 3)² - 9
Since, the parabola passes through (0, 0),
0 = a(0 - 3)² - 9
0 = 9a - 9
a = 1
Substitute the value of 'a' in the equation of the parabola,
y = 1.(x - 3)² - 9
y = x² - 6x + 9 - 9
y = x² - 6x
Hence, the function representing the graph will be f(x) = x² - 6x
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Stained glass slope graphing linear equation Description: Identify the slope and y-intercept of the linear equation. Then, graph the linear equations on the same coordinate plane. Make sure to extend the lines to the edge of the graph paper! Darken each line when finished. Color however YOU want to create a stained glass effect
Answers
Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the y-intercept of the line in our equation, y = 7 x + 4, is 4.
What is meant by slope-intercept?When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). The y value of the y intercept point is represented by b in the equation. Given the slope of the line and the intercept it forms with the y-axis, the slope intercept form in mathematics is one of the forms used to determine the equation of a straight line. Y = mx + b is the slope intercept form, where m is the slope of the straight line and b is the y-intercept.To learn more about slope-intercept, refer to:
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Question 15 of 16
If y= 2x + 7 were changed to y = 1/2x+7, how would the graph of the new
function compare with the original?
A. It would be less steep.
B. It would be steeper.
C. It would be shifted down.
D. It would change orientation and slant down.
Answers
Answer:
If y= 2x + 7 were changed to y = 1/2x+7, It would be less steep.
Step-by-step explanation:
A. It would be less steep.
Answer:
the answer is A
Step-by-step explanation:
This is because the slope of the original function (gradient = 2) is greater than that of the other line which has a slope of 0.5
A sofa chair has a retail price of $260 and it is on sale at a 30% discount. How much less
is the sale price than the retail price?
A $54
B$72
C$78
D $182
(WILL MARK BRAINLIEST
Answers
Answer:
C. 78
Step-by-step explanation:
The answer is 78 since all your doing is finding 30% of 260. 30% of 260 equals 78. Hence, the sale price is $78 less than the retail price.
Which statements are true about dilations? Select all that apply.
Answers
Dilations produce images that have a center that is the same as the pre-image.
What is dilations?Dilations are a type of transformation that change the size, shape, and orientation of an object. Dilation is a math operation that enlarges or reduces the size of an object or figure. It is a linear transformation that stretches or contracts shapes, which preserve the shape's angles and proportions. Dilation can be used to increase or decrease the area of a shape, or to change the distance between two points.
True statements about dilations are:
• Dilations produce images that are similar to the pre-image.
• Dilations produce images that have angles that are congruent to the pre-image.
• Dilations produce images that have sides that are proportional to the pre-image.
• Dilations produce images that have a center that is the same as the pre-image.
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Complete questions as follows-
Which statements are true about dilations? Select all that apply.
Dilations produce images that are similar to the pre-image.
Dilations produce images that are always congruent to the pre-image.
Dilations produce images that have angles that are congruent to the pre-image.
Dilations produce images that have sides that are congruent to the pre-image.
Dilations produce images that have sides that are proportional to the pre-image.
A businessman bought 130 bundle of dalo for $1040.00 he made a profit of $2.00 for each bundle that he sold .How much would be the cost of each bundle bought by the businessman??
Answers
Answer: $10 each
Step-by-step explanation:
130*2
260+1040
=1300
1300/130
=10
Calculate 418 x 53 = using partial products right to left and left to right.
Answers
The product of 418 and 53 is 22,154
Partial product of expressionsGiven the expression 418 x 53. Using the partial product, this can be simplified as:
418 x 53 = (400 + 18)(50 + 3)
Expand using the distributive law:
418 x 53 = = 400(50) + 400(3) + 18(50) + 18(3)
418 x 53 = 20000 + 1200 + 900 + 54
418 x 53 = = 22,154
Hence the product of 418 and 53 is 22,154
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Given: DA≈ WG and WA≈DG. Prove that DAW≈ WGD.
Answers
Answer:
Step-by-step explanation:
Statements Reasons
DA ≅ WG Given
WA ≅ DG Given
DW ≅ WD Reflexive property
ΔDAW ≅ ΔWGD SSS
Question content area top
Part 1
The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.11°F and a standard deviation of 0.59°F. Using the empirical rule, find each approximate percentage below.
a.
What is the approximate percentage of healthy adults with body temperatures within 1 standard deviation of the mean, or between 97.52°F and 98.70°F?
b.
What is the approximate percentage of healthy adults with body temperatures between 96.34°F and 99.88°F?
Answers
Answer:
a. Using the empirical rule, approximately 68% of healthy adults have body temperatures within 1 standard deviation of the mean, or between 97.52°F and 98.70°F.
b. Using the empirical rule, approximately 99.7% of healthy adults have body temperatures between 96.34°F and 99.88°F, which is within 3 standard deviations of the mean.
Please help me with this.
Answers
Here are the correct matches to the expressions to their solutions.
The GCF of 28 and 60 is 4.
(-3/8)+(-5/8) = -4/4 = -1.
-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.
The solution of 0.5 x = -1 is x = -2.
The solution of 1/2 m = 0 is m = 0.
-4 + 5/3 = -11/3.
-2 1/3 - 4 2/3 = -10/3.
4 is not a solution of -4 < x.
1. The GCF of 28 and 60 is 4.
The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:
28 = 2 x 2 x 7
60 = 2 x 2 x 3 x 5
The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.
2. (-3/8)+(-5/8) = -1.
To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.
3. -1/6 DIVIDED BY 1/2 = -1/3.
To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.
4. The solution of 0.5 x = -1 is x = -2.
To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.
5. The solution of 1 m = 0 is m = 0.
To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.
6. -4 + 5/3 = -11/3.
To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.
7. -2 1/3 - 4 2/3 = -10/3.
To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.
8. 4 is not a solution of -4 < x.
The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.
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a)while wages have increased, spending power has mostly remained the same since 2000
b) as wages go up, so does spending power
c) the spending power of men is less than the spending power of the overall population
d) the wages of women have increased faster than the wages of men
Answers
Based on the information, the answer is A). While wages have increased, spending power has mostly remained the same since 2000.
How to explain the informationThe fact that the cost of living has also increased, eating up much of the gains from wage growth. In addition, many Americans are now working multiple jobs, which can leave them with less time and energy to spend money on discretionary items.
According to the Bureau of Labor Statistics, the average hourly wage for all workers in the United States increased by 16.3% between 2000 and 2021. However, the Consumer Price Index (CPI), which measures the cost of a basket of goods and services, increased by 26.5% over the same period. This means that the purchasing power of the average worker has actually declined by 10.2% since 2000.
The rise of the gig economy has also contributed to the decline in spending power. Many Americans are now working multiple jobs, often in low-wage industries such as food service and retail.
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While wages have increased, spending power
a)has mostly remained the same since 2000
b) as wages go up, so does spending power
c) the spending power of men is less than the spending power of the overall population
d) the wages of women have increased faster than the wages of men
9a + 8 - 20-3-50
Answer
Answers
Answer:
9a-65
Step-by-step explanation:
simply write 9a+(add the remaining numbers all together)
On a field trip, the ration of students who brought a water bottle to those who didn’t was 7 to 4. If 60 students did not bring water bottle, determine the total number of students on the field trip.
Answers
Answer:
165 students
Step-by-step explanation:
7/4 = x/60
(60*7)/4 = 105
105 + 60 = 165
There are 54 girls on the playground. There are 25 fewer boys than girls on the playground. How many kids are on the playground?
Answers
Answer:
83 kids total
Step-by-step explanation:
There are 54 girls on the playground. There are 25 fewer boys than girls on the playground. How many kids are on the playground?
girls = 54
boys = 54 - 25 = 29
54 + 29 = 83 kids total
kids that are on the playground are 83.
What is the sum?Merging objects and identifying them since one big bunch is done through addition. In arithmetic, addition is the technique of adding two or more integers together. The product can meet are the quantities that are included, and the outcome of the operation, or the final response, is referred to as the sum.
The total number of girls that are present is 54
The data given is that there are
25 fewer boys taht are4 present
The total number of boys will be
boys = 54 - 25 = 29
The number of kids that are present will be the total of boys and girls that are present.
Kids = boys + girls
54 + 29 = 83 kids total
The quantity of kids that are present in the playground is 83.
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