The answer can't be determined by the amount of data given in the question for ellipse.
What is ellipse?
In addition to being drawn outside the ellipse, the directrix of the ellipse is parallel to its latus rectum. There are two directions on the ellipse that are parallel to its principal axis. The ratio of distances between any point on an ellipse and its foci, as well as the directrix of the ellipse, is used to define an ellipse's eccentricity, and it is less than 1.
The standard equation for an ellipse is (x-h)²/a²+(y-k)²/b² = 1
a, b = semi-major and semi-minor axes respectively.
The center of the ellipse is at (0,0).
here, h=0, k=0.
One focus is at (12, 0)
Therefore
c = 12,
We can't find out the directrix with the given data.
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f(x) = 2x ^2 - 3x + 1; k+2
Use the remainder theorem to find the remainder when f(x) is divided by x-k.
The remainder will be (k - 1) or (2k - 1) after using the remainder theorem.
What is a polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
The remainder theorem:
f(x) = 2x² - 3x + 1
f(x) is divided by (x - k)
The remainder = f(k)
The remainder = 2k² - 3k + 1
After factoring:
(k - 1)(2k - 1)
The remainder will be (k - 1) or (2k - 1)
Thus, the remainder will be (k - 1) or (2k - 1) after using the remainder theorem.
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A first number plus twice a second number is 8. Twice the first number plus the second totals 28. Find the numbers.
Answer:
x = 16, y = -4
Step-by-step explanation:
First, we can say that "x = the first number" and "y = the second number"
The first number plus twice the second number is 8:
x + 2y = 8
Twice the first number plus the second number totals 28:
2x + y = 28
Next, we solve the system of equations.
x + 2y = 8 ---> 2x + 4y = 16 ---> 2x = 16 - 4y
2x + y = 28 ---> 2x = 28 - y
16 - 4y = 28 - y
-4y + y = 28 - 16
-3y = 12
y = -4
Now, we plug "y = -4" into either one of the equations to find x:
x + 2(-4) = 8
x + -8 = 8
x = 8 + 8
x = 16
asap
Calculate the value of x.
Answer:7.07 m
Step-by-step explanation:
ab=5
ab=bc
bc=5
(ab)^2+(bc)^2=(ac)^2
25+25=50
ac^2=50
ac=7.07
Jeremy has $120 in his savings account and katie has $180 in her account. Each week jeremy adds $14 to his account, and katie adds $10 to hers. How many weeks will it be before jeremy and katie have the same amount of money saved up?.
It will takes 15 weeks before Jeremy and Katie have the same amount of money saved up.
Define Expression
An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given,
Jeremy has balance in his savings account = $120
Each week Jeremy adds amount to his account = $14
Katie has balance in her savings account = $180
Each week Katie adds amount to her account = $10
Let, x = number of weeks
At the end of each week Jeremy has = 120 + 14x
At the end of each week Katie has = 180 + 10x
As we want to have same amount in both the account for that just equate the values of each week of Jeremy and Katie.
120 + 14x = 180 + 10x
14x - 10x = 180 - 120
4x = 60
x = 15
Hence, it will takes 15 weeks before Jeremy and Katie have the same amount of money saved up.
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What is an equation that represents the line if the points are (0,2) (3,-2).
Answer: y=-4/3x+2
Step-by-step explanation:
First, find the slope: -2-2/3-0 = -4/3
Next, choose one pair of points and insert them into the y=mx+b equation:
2=-4/3(0)+b
Simplify the equation: 2=0+b —> 2=b
Final equation: y=-4/3x+2
Madelyn was out at a restaurant for dinner when the bill came. Her dinner came to $30. After adding in a tip, before tax, she paid $38. 40. Find the percent tip.
Answer:
28%
Step-by-step explanation:
38.40 - 30 = 8.40
x : 100 = 8.40 : 30
x = 8.40 * 100 / 30
x = 840/30
x = 84/3 = 28%
Help, The distance between point (2, 2) and point (8, 2) is 6 units on a coordinate plane. Which other pairs of points are also 6 units apart? Select all that apply.
art 1 of 2 Question content area top Part 1 Swimming Pool, On a certain hot summer's day, people used the public swimming pool. The daily prices are $1.25 for children and $2.25 for adults. The receipts for admission totaled $294.75. How many children and how many adults swam at the public pool that day?
Step-by-step explanation:
x = number of children
y = number of adults
1.25x + 2.25y = 294.75
this has many different solutions.
we would need a total number of persons in the pool in order to solve that to a single solution.
so, it could be 131 adults and 0 children.
for every reduction of 5 adults we can add 9 children and keep the same total
so, it could be 126 adults and 9 children
121 adults and 18 children
116 adults and 27 children
...
1 adult and 234 children
how did I get to the 5 to 9 ratio ?
1.25 is 5/4.
2.25 is 9/4
so, I was looking for the smallest common multiple of 5 and 9. which is 45 or 5×9. there is no simpler ratio between them.
so, the ticket price of 9 children is the same as the ticket price of 5 adults.
in order to keep the total of $294.75, when I reduce the number of adults, I have to compensate by adding children with the same amount of ticket prices.
this does not charge the fact that your teacher gave you an incomplete problem to solve.
but maybe your teacher wanted you to discover this problem.
A local recreation center offers a yearly membership and charges
an additional fee for aerobics classes as shown in the table.
Number of classes (x)
1
5
10
15
Total cost (y)
270
290
315
340
a. Write an equation in slope-intercept form that represents the total cost of the membership.
b. Carly spent $500 one year. How many aerobics classes did she take?
An equation in slope-intercept form that represents the total cost of the membership is y = 5x + 265.
The number of aerobics classes that Carly took at $500 one year is 47 aerobics classes.
How to write an equation in slope-intercept form?In order to write the equation in slope-intercept form, we would have to determine the slope of the line representing the total cost of the membership.
Mathematically, the slope of any straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Substituting the given parameters into the formula, we have;
Slope, m = (290 - 270)/(5 - 1)
Slope, m = 20/4
Slope, m = 4
At point (1, 270), an equation of this line in slope-intercept form can be calculated by using this standard formula:
y = mx + c
Where:
m represents the slope.x and y are the points.c represents the intercept.Substituting the given points into the formula, we have;
y = mx + c
270 = 5(1) + c
Intercept, c = 270 - 5
Intercept, c = 265.
Therefore, the required equation is given by:
y = 5x + 265
For the number of aerobics classes at $500 one year, we have:
500 = 5x + 265
5x = 500 - 265
5x = 235
x = 235/5
x = 47 aerobics classes.
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what percent is 1/3 of a circle
Answer:
120
Step-by-step explanation:
360
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3
mark me on brainliest please follow me to
find the value of u
8^2 + u^2 = 17^2
Answer:
u = 15
Step-by-step explanation:
It appears that you have already created an equation to solve for u and just need help solving it
So we have 8² + u² = 17²
==> simplify exponents
64 + u² = 289
==> subtract 64 from both sides
u² = 225
==> take the square root of both sides
u = 15
a tire manufacturer has a 60,000 mile warranty for tread life. the manufacturer considers the overall tire quality to be acceptable if less than 5% are worn out at 60,000 miles. the manufacturer tests 250 tires that have been used for 60,000 miles. they find that 3.6% of them are worn out. with this data, we test the following hypotheses. h0: the proportion of tires that are worn out after 60,000 miles is equal to 0.05. ha: the proportion of tires that are worn out after 60,000 miles is less than 0.05. what assumption about the sample underlies the hypothesis test?
Assumption about the sample underlies the hypothesis test is; the samples comes from a population of tires with 60,000 miles where 5% of tires are worn out.
From the information given, the null and alternative hypothesis are:
Null hypothesis;
The proportion of tire that are worn out after 60,000 miles is equal to 5% or 0.05
[tex]H_{0} :p=0.05[/tex]
Alternative hypothesis;
The proportion of tire that are worn out after 60,000 miles is less than 5% or 0.05
[tex]H_{a} :p < 0.05[/tex]
Hence the assumption about the sample underlies the hypothesis test is; the samples comes from a population of tires with 60,000 miles where 5% of tires are worn out.
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equation like that passes through (4,1) and perpendicular to y=1/2x-1
The equation of the line passing through (4,1) and perpendicular to y=1/2x-1 is y = -2x+9.
According to the question,
We have the following information:
A line passes through (4,1) and perpendicular to y=1/2x-1.
Now, the slope of the given line is 1/2.
We know that the slope of the perpendicular line is given by -1/m.
Slope of perpendicular line = -1/(1/2)
Slope of perpendicular line = -2
Equation of the required line:
(y-y') = m(x-x')
(y-1) = -2(x-4)
y-1 = -2x+8
y = -2x+8+1
y = -2x+9
Hence, the equation of the line passing through (4,1) and perpendicular to y=1/2x-1 is y = -2x+9.
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a neonate order is 0.03 mg/kg of a 1:10,000 solution. the patient weighs 4.4 lb. how many milliliters of the solution will be needed?
600 milliliters of the solution will be needed.
Given:
Let x be the solution needed.
A neonate order is 0.03 mg/kg of a 1:10,000 solution. the patient weighs 4.4 lb.
4.4 lb = 1.99581 kg
4.4 lb ≈ 2 kg
neonate order = 2*0.03
= 2*3/100
= 6/100
= 0.06 mg
1 : 10000 = 0.06 : x
1/10000 = 0.06/x
x = 0.06 * 10000 / 1
= 0.6*1000
= 6*100
= 600 milliliters.
Therefore 600 milliliters of the solution will be needed.
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Given r(x) =x' - 4x2 + 4x - 6, find the value of r(2). What does your answer tell you about x - 2 as a factor of r(x)? Explain.
We can conclude that the value of r(2) which is -6 and x - 2 is not the factor for r(x).
What is Factor?A function that accepts a real number as input, typically represented by the variable x and outputs another real number, typically the value of the function denoted by f is known as a real-valued function of a real variable (x).Any polynomial that is divisible by the polynomial P(x) is a factor of that polynomial (x).So, we know that the equation is:
r(x)=x^3-4x^2+4x-6:Now, calculate the equation when x = 2.
r(2)=2^3-4(2)^2+4(2)-6r(2)=8-16+8-6r(2)=-6Now, we can conclude that:
As we see that x=2 is not equal to zero.Implies x-2 does not divide r(x) evenly.Thus x-2 is not a factor of given r(x).Therefore, we can conclude that the value of r(2) which is -6 and x - 2 is not the factor for r(x).
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The After School Program has soccer from 2:45 P.M. to 3:32 P.M.How many minutes are there for soccer?
Determine if the statements are true or false
The standard form of 4.4 x 10-4 is 0.00044.
The standard form of 6.39 x 105 is 63,900,000.
The standard form of 3.02 x 10° is 3,020,000,000.
The statements are true or false.
The standard form of 4.4 x 10-4 is 0.00044.
= 4.4 * 10^-4
= 4.4/10^4
= 4.4/10000
0.00044 = 0.00044
This statement is true.
The standard form of 6.39 x 10^5
= 6.39 * 100000
= 639*1000
639000 ≠ 63,900,000
This statement is false
The standard form of 3.02 x 10^10 is 3,020,000,000.
= 3.02 * 10^10
= 3.02 *10000000000
= 3,020,000,0000
This statement is false.
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z/m - z/n = 1 if m≠n
solve for z
pls do this fast
The solution for z is [tex]z=\frac{nm}{(n-m)}[/tex]
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
The equation is [tex]\frac{z}{m} -\frac{z}{n}=1[/tex]
On simplifying , we get
[tex]\frac{(zn-zm)}{nm} =1[/tex]
Multiply both sides by 'nm' , we get
[tex]zn-zm=nm[/tex]
Taking z as the common term in LHS , we get
[tex]z(n-m)=nm[/tex]
Divide by ( n - m ) on both sides ,we get
[tex]z=\frac{nm}{(n-m)}[/tex]
Since , n ≠ m
n - m ≠ 0
So , the solution is [tex]z=\frac{nm}{(n-m)}[/tex]
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3x - y = 17
4x + y = -3
Answer:
x = 7, y = 4
Step-by-step explanation:
simultaneous equation:
3x-y=17
4x+y=-3
Solving for x: add the two equations together to cancel out y (-y + y = 0)7x = 14divide both sides by 7 to get the value of 1 xx = 7solving for y: substitue the value of x (7) into any equation (we'll use the top one for ease)3(7) - y = 17so in other words; 21 - y = 17subtract 21 from both sides to get the value of -y-y = -4therefore, y = 4Determine if the triangles below are similar. If so, state the reason and write the similarity statement.
QRS is similar to _______.
A. Similar due to AA . Triangle QRS is similar to triangle VUT.
B. Similar due to SSS and a scale factor of 0.29. Triangle QRS is similar to triangle VUT.
C. Not similar
D. Similar due to SSS and a scale factor of 3.5. Triangle QRS is similar to triangle TUV.
E. Similar to due SAS and a scale factor of 0.29. Triangle QRS is similar to triangle TUV.
The correct statement is "Similar, due to SSS and a scale factor of 0.29. Triangle QRS is similar to triangle VUT".
What is similarity in triangles?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.
Given that, two triangles Δ QRS and Δ VUT
We have,
QR/VU = RS/UT = QS/VT = 2/7 = 0.29
Hence, the two triangles are similar by SSS property with a scale factor of 0.29
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Janice currently has 26 marbles and is collecting 3 per week. Oliver currently has 10 marbles and is collecting 5 per week. how many weeks will it take so that janice and oliver have the same amount of marbles?
It will take 8 weeks so that janice and oliver have the same amount of marbles.
What do you mean by linear expression?
An algebraic expression known as a linear expression has terms that are either constants or variables raised to the first power. Alternatively put, none of the exponents can be greater than 1.
Coefficients in linear equations can be either positive or negative values. The exponent is important. The entire equation becomes non-linear when a single variable is raised to a power greater than 1.
Let number of weeks be x
According to question, Janice currently has 26 marbles and is collecting 3 per week and Oliver currently has 10 marbles and is collecting 5 per week.
This means ,
26 + 3x = 10 + 5x
26 - 10 = 5x - 3x
16 = 2x
x = 16/2 = 8
Therefore, it will take 8 weeks so that janice and oliver have the same amount of marbles.
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Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
The given problem can be solved by using the properties of the parabola.
The following statements are true about the function and its graph are as follows;
The value of a is 1 which is positive then the parabola opens upward.
What is a parabola?
A parabola is a plane curve that is mirror-symmetrical and roughly U-shaped in mathematics. It fits several seemingly disparate mathematical descriptions, all of which can be shown to define the same curves. A point and a line are two ways to describe
According to the question,
1. The value of the function when f(-10) is,
[tex]f(x)=x^2-5x+12\\\\f(-10) =(-10)^2-5(-10)+12\\\\f(-10)=100+50+12\\\\f(-10)=162[/tex]
So the first option is false.
2. The graph of the function is a parabola.
The value of a is 1 which is positive then the parabola opens upward.
3. The graph contains the point f(x) = 20,
[tex]f(x)=x^2-5x+12\\\\f(20) =(20)^2-5(20)+12\\\\f(20)=400-100+12\\\\f(20)=312\\[/tex]
The graph contains the point (20, 312).
4. The graph contains the point f(x) = 0,
[tex]f(x)=x^2-5x+12\\\\f(0) =(0)^2-5(0)+12\\\\f(0)=0-0+12\\\\f(0)=12\\[/tex]
The graph contains the point (0, 12).
Hence, the given problem can be solved by using the properties of the parabola. The following statements are true about the function and its graph are as follows;
The value of a is 1 which is positive then the parabola opens upward.
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PLEASE help me math 50 points
Given:
h(x) = 3x - 5
Find:
h(-2)
________
h(-2) = 3·(-2) - 5 = - 6 - 5 = - 11
Answer:
- 11
What is the % of $62= $31?
Answer:
50%
Step-by-step explanation:
62-31=31
31/62x100%
=50
A glitter glue recipe takes a mixture of
1
5
cup of glitter to
2
5
cup of glue.
For A, how many cups of glitter are used for 1 cup of glue?
For B, how many cups of glitter glue is made with 1 cup of glue?
A. cups of glitter
B cups of glitter glue
0.6 cup of gliter is used for 1 cup of glue and 1.6 cup of gliter glue is made with 1 cup of glue.
Part A
Given that,
15 cup of gliter is for 25 cup of glue ,
Therefore, "X" cup of gliter is for 1 cup of glue
X = (1*15)/25
X= 0.6 cup of gliter
Part B,
Given that,
From part A 0.6 cup of gliter is for 1 cup of glue
Thus, 1 cup of glue and 0.6 cup of gliter when mixed will form "Y" cup of gliter glue
Now, Y= 0.6 cup of gliter + 1 cup of glue
Y= 1.6 cup of gliter glue
which approximates to 2 cup of gliter glue.
Which graph represents the equation y=2x+5
Answer:
The one where the line passes 5 on the y-axis. Last pic
Answer:
your fourth option is your answer
2. A theater has 36 rows. Each row has 24 seats. About how many seats does the theater have?
Answer:
864 seats
Step-by-step explanation:
A theater has 36 rows. Each row has 24 seats. About how many seats does the theater have?
36 * 24 = 864 seats
Max buys a car for £8500 after one year it's value has decreased to £7225 what's the percentage decease in the value?
Answer:
15%
Step-by-step explanation:
[tex]\frac{7225-8500}{7225}=-15\%[/tex]
Find the equation of the line. Show all steps.
LOOK AT PICTURE
THANK YOU!!
ITS NUMBER 5
y=7.5x+52.5
y2-y1/x2-x1
100-85/6-4 = 7.5
60=7.5+b
b=52.5
if WX=22 and WY=26 what is WZ
Answer:
30
Step-by-step explanation:
WX = 22
WY = 26
WZ = 30
22 + 4 = 26
26 + 4 = 30
