Write the equation for a parabola with a focus at (-2, 5) and a directrix at x = 3.
Answers
Let’s find “p:”
We know the parabola is opens to the left because the directrix is always below the vertex. So, we must find the distance between the two x-coordinates of -2 and 3 and divide that in half
-2+3/2=.5
Because the directrix and focus lie on the same y-coordinate, we can use that coordinate to determine the y-coordinate of the vertex. In this case, y=5.
This means the vertex is at (.5, 5) or (1/2, 5).
Now, we must determine how wide or stretched the parabola is, which is known as the “a” value in a(x-h)^2+k
The formula for a is:
a=1/4p
We know that p=.5
a=1/4(.5)
a=1/2
So, we have all the information to come the equation:
f(x)=1/2(x-1/2)^2+5
However, the function is inverted, so it is reflected across the line y=x. This means we must swap all x and y coordinates:
x=1/2(y-5)^2+1/2 is the equation
Solid chance this is way above your knowledge level
A parabola is a curve in the shape of a U that is defined as the set of all points that are equidistant to a fixed point (called the focus) and a fixed line (called the directrix).
To write the equation of a parabola with a focus at (-2, 5) and a directrix at x = 3, we can use the standard form of the equation of a parabola, which is:
y = (1/(4f))x^2 + k
Where f is the distance between the focus and the vertex (the point where the parabola changes direction), and k is a constant that determines the position of the parabola along the y-axis.
To find the value of f, we can use the distance formula:
f = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) is the coordinate of the focus and (x2, y2) is the coordinate of the vertex.
Since the focus is at (-2, 5) and the directrix is at x = 3, we can use the y-coordinate of the focus as the y-coordinate of the vertex, and the x-coordinate of the directrix as the x-coordinate of the vertex. Therefore, the coordinate of the vertex is (3, 5).
Substituting these values into the distance formula, we get:
f = sqrt((3 - (-2))^2 + (5 - 5)^2)
= sqrt((5)^2 + (0)^2)
= sqrt(25)
= 5
Now that we have the value of f, we can substitute it into the standard form of the equation of a parabola to get:
y = (1/(4*5))x^2 + k
= (1/20)x^2 + k
This is the equation for a parabola with a focus at (-2, 5) and a directrix at x = 3. The constant k determines the position of the parabola along the y-axis.
Related Questions
What is the remainder when f(x) = 3x3 + 24x2 − 45x − 162 is divided by (x + 8)?
Answers
The remainder when f(x) = 3x³ + 24x² − 45x − 162 is divided by (x + 8) is 198.
How to find the remainder when dividing polynomial?A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.
Therefore, the remainder when f(x) = 3x³ + 24x² - 45x - 162 is divided by (x + 8) is as follows:
The dividend is x + 8.
Hence, let's Set the dividend to 0
x + 8 = 0
x = -8
Substitute x = - 8 in f(x) = 3x³ + 24x² - 45x - 162
f(-8) = 3(-8)³ + 24(-8)² - 45(-8) - 162
f(-8) = - 1536 + 1536 + 360 - 162
f(-8) = 198
Therefore, the remainder is 198.
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in the general formulation of fourier's law (applicable to any geometry), what are the vector and scalar quantities? why is there a minus sign on the right-hand side of the equation?
Answers
The scalar quantities in Fourier's law is the temperature and the conductivity whereas heat flux is vector.
Heat moves from a higher temperature to a lower temperature, which is explained by the minus sign.
Fourier's law
q = -k ▽T
Where,
q is the local heat flux density in W.m2
k is the conductivity of the material in W.m-1.K-1
▽T is the temperature gradient in K.m-1
The terms "force," "speed," "velocity," and "work" are frequently used, and they all refer to scalar or vector quantities. Physical quantities like mass and electric charge are examples of scalar quantities because they only have magnitudes. In contrast, a vector quantity is a physical quantity like force or weight that has both magnitudes and directions.
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the larger circle has center $o$ and passes through $d$. the smaller circle has diameter $od$. what percent of the larger circle's area is gray?
Answers
25% is the larger circle area is gray.
Area of a Circle: The area of a circle is pi times the radius squared.
To calculate the area of the circle we have the formula:
A = π r²-----(1)
where
A=area
r=radius.
First, we have to analyze the given data, the large circle center o passes through d, so
Gray circle area=π*(radius)^2----(2)
The radius of the smaller circle = OD/2 substitute in (2)
Gray circle area=π*(OD/2)^2
Gray circle area=π*OD^2/4
Larger circle area=π*(radius)2
radius of the larger circle = OD
larger circle area=π*OD^2
To know the percentage of a large circle we have a small formula:
gray circle area/large circle area--------(3)
=π*OD^2/4/π*OD^2
=π*OD^2/4*1/π*OD^2=1/4
=25/100
=25%
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you are standing at the point x = 300 m, y = 400 m in a reference frame with synchronized clocks.
Answers
The time on clock shows at the instant you see the clock at the origin showing 3.80 μs is 5.47 × [tex]10^{-6[/tex] s.
As per the given data the values of x and y are as follows:
x = 300 m
y = 400 m
Here you are standing at the point (300, 400) in a reference frame with synchronized clocks.
Here we have to determine the time on clock shows at the instant you see the clock at the origin showing 3.80 μs.
The point where you're standing (300, 400) is 500 m from the origin.
Therefore my distance from the origin is 500 m
Speed of light , c = 3 × [tex]10^8[/tex] m/s
The clock at the origin showing, [tex]T_0[/tex] = 3.80 μs
[tex]T_0 = 3.8 \times 10^{-6}[/tex] s
Time shown by my clock , T = distance ÷ c + [tex]T_0[/tex]
T = [tex]\frac{500}{(3 \times 10^8)} + 3.8 \times 10^{-6[/tex]
T = 5.47 × [tex]10^{-6[/tex] s
Therefore the time shown by my clock is 5.47 × [tex]10^{-6[/tex] s.
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Write an equation to model the situation:
Tyler withdraws $35 from his bank account every week until he runs out of
money. He started the year with $3245 in his bank account.
Answers
In his account balance now $3215
What is the explanation?Tyler withdraws $35 from his bank account every week until he runs out of
money. He started the year with $3245 in his bank account.
Tyler withdraws $35.
He started with $3245.
In his account balance now
Tyler withdraws -His started accound.
$3245 - $35 = $3215
Till he runs out of money, Tyler takes out $35 per week from his bank account. He had $3245 in his bank account before the year began.Tyler takes out $35.He had $3245 to start.Tyler is now making withdrawals from his beginning account amount. $3245 - $35 = $3215Currently, he has $3215 in his account.
In his account balance now $3215
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in a triangle abc AB=12, AC=14 and angle BAC=68° find angles and side
Answers
Answer: The measures of the angles in triangle ABC are BAC = 68°, BCA = 50.6°, and ABC = 61.4°. The lengths of the sides are AB = 12, AC = 14, and BC = 13.68.
Step-by-step explanation:
To find the angles and sides of a triangle, you need to know at least three pieces of information about the triangle. In this case, you are given the lengths of sides AB and AC, and the measure of angle BAC.
You can use the Law of Sines to find the measure of the third angle and the length of the third side. The Law of Sines states that for any triangle, the ratio of the length of a side to the sine of the angle opposite that side is the same for all sides and angles in the triangle. In other words, if we let a, b, and c represent the lengths of the sides of the triangle and A, B, and C represent the measures of the angles opposite those sides, then the following equation holds:
a/sin A = b/sin B = c/sin C
In triangle ABC, we are given the lengths of sides AB and AC and the measure of angle BAC. We can use the Law of Sines to find the measure of angle BCA and the length of side BC.
First, we can find the measure of angle BCA using the equation:
a/sin A = b/sin B = c/sin C
Substituting the known values, we get:
14/sin BAC = 12/sin BCA
Solving for sin BCA, we get:
sin BCA = 14/12 * sin BAC
Plugging in the given value for sin BAC, we get:
sin BCA = 14/12 * sin 68°
Using a calculator, we find that sin 68° = 0.906308
So sin BCA = 0.763696
To find the measure of angle BCA, we can use the inverse sine function on our calculator. The inverse sine of 0.763696 is about 50.6°.
Now that we know the measures of angles BAC and BCA, we can use the fact that the angles in a triangle sum to 180° to find the measure of angle ABC:
BAC + BCA + ABC = 180°
Substituting the known values, we get:
68° + 50.6° + ABC = 180°
Solving for ABC, we get:
ABC = 180° - 68° - 50.6°
This simplifies to:
ABC = 61.4°
Now that we have found the measures of all three angles, we can use the Law of Sines again to find the length of side BC.
We can use the equation:
a/sin A = b/sin B = c/sin C
Substituting the known values, we get:
14/sin BAC = 12/sin BCA = BC/sin ABC
Solving for BC, we get:
BC = 14/sin BAC * sin ABC
Plugging in the values we found earlier, we get:
BC = 14/0.906308 * sin 61.4°
Using a calculator, we find that sin 61.4° = 0.875
So BC = 14/0.906308 * 0.875 = 13.68
The measures of the angles in triangle ABC are BAC = 68°, BCA = 50.6°, and ABC = 61.4°. The lengths of the sides are AB = 12, AC = 14, and BC = 13.68.
Not everyone pays the same price for
the same model of a car. The figure
illustrates a normal distribution for the
prices paid for a particular model of a
new car. The mean is $21,000 and the
standard deviation is $1000.
Use the 68-95-99.7 Rule to find what
percentage of buyers paid between
$20,000 and $21,000.
Number of Car Buyers
-99.7%-
-95%-
68%-
18
19 20. 21 22 23 24
Price of a Model of a New Car (Thousands)
The percentage of buyers who paid between $20,000 and $21,000 is%.
(Type an exact answer.)
Answers
The figure illustrates a normal distribution for the prices paid for a particular model of a new car. The mean is $21,000 and the standard deviation is $1000. Use the 68-95-99.7 Rule the percentage of buyers that paid between $20,000 and $21,000 is 68%
What does the statistical 68-95-99.7 rule mean?68 percent of the data falls within one standard deviation of the mean,
95 percent falls within two standard deviations, and
99.7 percent falls within three standard deviations.
In the problem, it was given that the mean is $21 000 and the standard deviation is $1 000
The deviation between $20,000 and $21,000
= $21,000 - $20,000
= $1,000
The standard deviation is $1000 hence buyers within $20,000 and $21,000 are within one standard deviation. according to the 68-95-99.7 Rule they are 68%
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In 2014 , a salesman was paid a basic monthly salary of rs 25 000. At the end of the year ,he was also paid a bonus of 6.5 % of the value of the sales that he had made during the year . his sales for the year was rs 100 000. calculate his totasl income that he receives in 2014.
Answers
x as his total income
x = 12(25 000) + 0.065(100 000)
x = 300 000 + 6 500
x = 306 500
CHECKING:
12(25 000) = 300 000 (12 months salary)
0.065(100 000) = 6 500 (bonus)
= 306 500
Therefore, the salesman total income is 306 500 in 2014.
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Plot 5/6 and 2 2/3
on the number line below.
Answers
The points with black dots on the number line represent the fractions.
What is a number line?In elementary mathematics -
A number line is a picture of a graduated straight line that serves as visual representation of the real numbers. Every point of a number line is assumed to correspond to a real number, and every real number to a point.Given are the fractions -
5/6 and 2[tex]\frac{2}{3}[/tex]
We can write -
2[tex]\frac{2}{3}[/tex] = 8/3
5/6 = 5/6
Refer to the number line attached. The points with black dots represent the numbers.
Therefore, the points with black dots on the number line represent the fractions.
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What’s the surface area of this prism ?
Answers
Hence the required surface area is 228cm²
What is surface area?
The surface area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. Square units are used to measure it as well.
Given:
A triangular prism and its net.
To find:
Side lengths for the net.
Surface area of the triangular prism.
Solution:
Side lengths for the net:
A= 4 cm
B= 10 cm
C= 6 cm
D= 8 cm
Surface area:
[tex]sa = bh +(b1 +b2+b3)l\\\\sa=6(8) +(6+4+8)\times10\\\\sa= 48 +18(10)\\\\sa=48+180\\\\sa=228 cm^2[/tex]
Hence the required surface area is 228cm²
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What are the endpoint coordinate for the midegment of △PQR that i parallel to PR¯¯¯¯¯?
Answers
point coordinates for the mid segment of the parallel to PQ segment of the PQR is ST point is (-3.5, 0.5) and (-1, -0.5).
Given that,
We have to find what are the endpoint coordinates for the middle portion of the parallel to PQ segment of the PQR.
We know that,
First we write the co-ordinates of the triangle in the given graph.
P is (-3,3)
Q is (2,1)
R is (-4,-2)
The triangle's midpoint, which is parallel to section PQ, must be located. As a result, we would need to locate the midpoints of the segments PR and QR before joining the points to obtain the mid segment.
Midpoint Formula is
(x₁+x₂/2, y₁+y₂/2)
So,
The midpoint of the side PR is
(-3+(-4)/2, 3+(-2)/2)
(-3-4/2, 3-2/2)
(-7/2,1/2)
So, S point is (-3.5, 0.5)
The midpoint of the side QR is
(2+(-4)/2, 1+(-2)/2)
(2-4/2, 1-2/2)
(-2/2,-1/2)
So, T point is (-1, -0.5)
Therefore, The endpoint coordinates for the mid segment of the parallel to PQ segment of the PQR is ST point is (-3.5, 0.5) and (-1, -0.5).
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Shade 3 circles. Shade 4/3 more
Answers
Find an equation of the tangent to the curve at the given pointx=cos(t)+cos(2t)y=sin(t)+sin(2t)(-1,1)y=?
Answers
Answer:
y = -0.11x + 0.89
Step-by-step explanation:
First find the slope of the tangent line, which is equal to dy/dx
Find the derivative of y at 1:
dy = cos(t) + 2cos(2t)
dy = cos(1) + 2cos(2)
dy = -0.292
Then the derivative of x at -1:
dx = -sin(t) - 2sin(2t)
dx = -sin(-1) - 2sin(-2)
dx = 2.66
So now calculate dy/dx:
dy/dx = -0.11
Now use point slope form to find the equation of the tangent line:
y - 1 = -0.11(x + 1)
y - 1 = -0.11x - 0.11
y = -0.11x + 0.89
Find the sum of the first 20 terms of the sequence below.
27, - 9, + 3, - 1, ...
Answers
The sum of the first 20 terms of the geometric sequence is 20.25.
What is a geometric sequence?A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.
Example:
2, 4, 8, 16, 32 is a geometric sequence.
We have,
27, -9, 3, -1,.....
a = 27
Common ratio:
= -9/27 = -1/3
= 3/-9 = -1/3
The sum of the geometric sequence.
S(n) = a (1 - [tex]r^n[/tex]) / (1 - r)
Now,
a = 27,
r = -1/3
S(20):
= 27 (1 - [tex](-1/3)^{20}[/tex]) / (1 + 1/3)
= 27 (1 + 1/[tex]3^{20}[/tex]) / (4/3)
[ (1 + 1/[tex]3^{20}[/tex]) = 1 ]
= 27 x 3/4 x 1
= 20.25
Thus,
The sum of the geometric sequence is 20.25.
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Given that D i the midpoint of AB and K i the midpoint of BC, which tatement mut be true?
Answers
Option D is the correct answer. AK + BK = AC is not a true statement.
All the statements are not true except:
AK + BK = AC
Since BK = KC, so
AK + KC = AC
DB=BK is not necessarily true since it is not stated whether AB = BC
B is the midpoint of AC is not necessarily true since again it's not stated that AB = BC
D bisects AK is not necessarily true since it is not stated that D and K lie on the same line.
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Please help!! And explain the work you did!! 60 points and brainliest!
3x²-12x+27= 0
Distinguish the discriminant and number of solutions for the equation. Show your work and explain the steps you
used to solve.
Answers
A boa constrictor slithers 2/6 kilometers in 4/5 hours. What is the distance the boa constrictor travels in 16 hours?
Answers
10 kilometres
Explanation
1/3 + 4/5 = 5/8
5÷8 = 0.625
0.625 * 16 = 10
Each marble bag sold by Ahmad's Marble Company contains 5 green marbles for every 8 orange marbles. If a bag has 25 green marbles, how many orange
marbles does it contain?
Answers
Answer:
40 orange marbles
Step-by-step explanation:
Set up and solve this proportion:
[tex] \frac{5}{8} = \frac{25}{x} [/tex]
[tex]5x = 200[/tex]
[tex]x = 40[/tex]
A cylinder has a radius of 14 m and a height of 6 m. what is the exact volume of the cylinder? responses 84π m³ 84 pi, m³ 168π m³ 168 pi, m³ 504π m³ 504 pi, m³ 1176π m³
Answers
Answer:
answer is on the photo......
two students are chosen at random from a group of two girls and five boys, all of different ages. find the probability
Answers
From a group of two girls and five boys, all of the various ages, two pupils are randomly selected. The likelihood that the two selected students will be boys is 10/21.
In probability theory and other branches of mathematics, the term "combination" designates a series of results in which the order of the results is irrelevant.
Here given the total number of girls is 2 and boys is 5. Then, the total number of students is 7. The number of ways of selecting 2 students from 7 students is,
[tex]\begin{aligned}n(S)&=\frac{7C2}{2}\\&= \frac{7\times6}{2}\\&=\text{21 ways}\end{aligned}[/tex]
The number of ways of selecting 2 boys from 5 boys is,
[tex]\begin{aligned}n(E)&=\frac{5C2}{2}\\&=\frac{5\times4}{2}\\&=\text{10 ways}\end{aligned}[/tex]
Then, the required probability is calculated as,
[tex]\begin{aligned}P(E)&=\frac{n(E)}{n(S)}\\&=\frac{10}{21}\end{aligned}[/tex]
Therefore, the required answer is 10/21.
The complete question is -
Two students are chosen at random from a group of two girls and five boys, all of the different ages. Find the probability that the two students chosen will be: two boys
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Use the image below to answer the identify the following. Please show ur work Bc I have too !!
One pair of vertical angles
One pair of adjacent angles
One pair of supplementary angles
Answers
∠1 and ∠4 are vertical angles
∠1 and ∠3 are adjacent angles
∠1 and ∠2 are supplementary angles
Vertical Angles:Vertically opposing angles are established when two lines intersect at a single place and the angles opposite to each other are created using the two intersecting lines. There is never a difference between these angles.
Adjacent Angles:Those angles are referred to as vertical angles if they share an arm and a vertex. Additionally, the nearby angles are those that are produced side by side. The primary characteristic of these angles is that they never cross over.
Supplementary Angles:When two angles add up to 180 degrees, they are said to be supplementary. Angles are referred to be supplementary angles when two of them are next to one another.
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Which is a solution for the equation y= 6x + 6
Answers
Answer:
Step-by-step explanation:
Which is a solution for the equation y= 6x + 6
solve for yy = 6x + 6 (there is no possibility to simplify)
solve for xy = 6x + 6
6x + 6 = y
6x = y − 6
divide both side by 6
x = (1/6)y - 1Here the points.
Good luck in the finals
Edit: 3 minutes later, no one wants it?!
Answers
Answer: good luck to you!
Step-by-step explanation:
Answer:
tysm for the points <33
Step-by-step explanation:
:)
You buy the following from Amazon:
25 flash drives for $10 each
What is the Subtotal: $
Today only they are 25% off, how much do you save: $
What is the new Subtotal: $
Sales tax is 4%: $
I
What is the total: $
Answers
You save: 62.50
The new subtotal is 187.50
The total is 195.00
Answer:
Subtotal: $250.00
Savings: $62.50
New Subtotal: $187.50
Total: $195.00
Step-by-step explanation: First, multiply 25 by 10. You'd get 250. Then, recall the formula to find the worth after a percent is applied:
Worth = Whole number * part percent / 100
Plug in the numbers:
Worth = 250 * 25 / 100
6250 / 100
= 62.50
Now, since it's a discount we need to subtract the discount price from the current subtotal. This would look like this:
250 - 62.50 = 187.50
Now, use the same formula to find the sales tax:
187.50 * 4 /100
750 / 100
= 7.5
So, since we need to pay the tax, we add the amount to our current subtotal:
187.50 + 7.5 = 195
So, our total is $195.00
Elise is sewing doll blankets to sell at a craft fair. She has 25 full spools of thread in her new sewing kit, and she needs 0.2 spools of thread for each doll blanket she sews. If Elise makes 9 blankets, how many spools of thread will remain?
Answers
Answer: 23 spools of thread
Step-by-step explanation:
0.2 times 9 = 1.8 spools of thread
25 - 1.8 = 23.2 spools of thread
mr. yates picked up a dozen items in the grocery store with a mean cost of $3.25. then he added an apple pie for $6.50. the new mean for all 13 items is
Answers
The new mean cost for all 13 items purchased by Mr. Yates is found to be $3.50.
Explain the term mean value of the data?The mean of a dataset seems to be the sum of all numbers divided by a total number of values, also known as the arithmetic mean, which differs from the geometric mean. The term "average" is frequently used to describe this measure of central tendency.The given data is-
mean cost = $3.25
Number of items = 12.
When added with apple pie of $6.50.
Total number of items becomes = 13.
So,
New mean = 6.50x12 + 3.25 / 13
New mean = 3.50
Thus, the new mean for all 13 items purchased by Mr. Yates is found to be $3.50.
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Choose the proportion that correctly represents the similar figures.
A. 5/x = 3/8
B. 8/5 = 3/x
C. 8/3 = x/5
D. x/3 = 8/5
Answers
The proportion that correctly represents the similar figures is the one in option B:
8/5 = 3/x
Which proportion correctly represents the similar figures?If two figures are similar, then the quotient between the correspondent sides must be equal.
Then we can write the equation:
8ft/3ft = 5ft/x
8/3 = 5/x
Now we can divide both sides by 5 and multiply both sides by 3, then we will get:
8/5 = 3/x
That is the proportion we wanted, then we conclude that the correct option is B.
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a parabola opening up or down has vertex (0,0) and passes through (6,9). write its equation in vertex form. simplify any fractions.
Answers
A parabola is a graph of a quadratic equation of the form
y = ax^2 + bx + c.In order to write the equation of a parabola in vertex form, we need to first determine the values of a, b, and c.
To find the vertex of the parabola, we know that the vertex lies at the point (0,0), so the x-coordinate of the vertex is 0. The y-coordinate of the vertex is the value of y at x = 0, which we can find by plugging 0 in for x in the equation
y = ax^2 + bx + c.So the vertex of the parabola is (0, c).
Since the parabola passes through the point (6,9), we can plug in these values for x and y into the equation y = ax^2 + bx + c to find the values of a, b, and c. We get the equation
9 = 36a + 6b + c.We can now write the equation of the parabola in vertex form. In vertex form, the equation of a parabola is y = a(x - h)^2 + k, where (h,k) is the vertex of the parabola. In our case, the vertex is (0,c), so we can write the equation as y = a(x - 0)^2 + c. Plugging in the values we found earlier, we get
y = 36a(x - 0)^2 + c.Finally, we can simplify the equation by dividing both sides by 36a. This gives us
y = (x - 0)^2 + c/36a.Since c/36a is a constant, we can simplify the equation even further by letting d = c/36a, so the final equation is
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Write
38
46
in lowest terms.
Answers
The lowest term of 38/46 can be expressed as a decimal as 0.826087 and percentage as 82.6087%.
How to estimate the lowest term of 38/46?The fraction 38/46 is equivalent to 19/23.
Once the absolute value of the top number, or numerator, (38) is less than the absolute value of the bottom number, or denominator, the fraction is considered to be correct (46).
The fraction 38/46 can be reduced.
To make things simpler, we'll employ the Greatest Common Factor (GCF) technique.
The GCF is the largest number equally divisible by two or more other numbers.
The numerator and denominator factors are listed, and the greatest number repeated in both lists is used to calculate the GCF:
The factors of 38 exists 1,2,19,38;
The factors of 46 exists 1,2,23,46.
We can see that the GCD is 2 because it is the largest number by which 38 y 46 can be divided without leaving any residue.
Simply divide the numerator and denominator by 2 to lower this fraction (the GCF).
So, [tex]$\frac{38}{46}=\frac{38 \div 2}{46 \div 2}=\frac{19}{23}$[/tex]
Therefore, 38/46 exists equivalent to 19/23 in the reduced form.
The factors exists numbers that multiply each other to get another number.
The fraction 38/46 exists even equivalent to 38÷46 and can also be expressed as a decimal as 0.826087 and expressed as a percentage as 82.6087%.
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Maria had $150 in gift certificates to use at a record store. She bought no more than 20 recordings. Each tape cost $5.95 and each CD cost $8.95. How many of each type of recording might she have bought?
Answers
Maria might have bought 9 tapes and 10 CDs of each type with her gift
certificate.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Let,The no. of tapes be 'x' and the no. of CD be 'y'.
Given, She bought no more than 20 recordings.
Therefore, x + y ≤ 20.
And,
Each tape cost $5.95 and each CD cost $8.95.
Therefore,
5.85x + 8.95y ≤ 150.
By graph intersection method we find that (9.355, 10.645) is a solution.
But the numbers should be in integers so, 9 tapes and 10 CD recordings
she might have bought.
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