The simplified expression is adbc - bc - abd√c - b√ad√c + acd√b + cd√ab.
Define distributive propertyIn mathematics, the distributive property is a property of operations that involves multiplying a factor by a sum or difference of terms. The distributive property states that the product of a factor and a sum or difference of terms is equal to the sum or difference of the products of the factor with each term individually. In other words, for any numbers a, b, and c, the distributive property can be expressed as:
a(b + c) = ab + ac
Given expression
(a√b+c√d)-b√a)×(d√c-√ab+abc)
Simplifying the expression
(a√b+c√d-b√a)×(d√c-√ab+abc)
by simplifying the given expression using the distributive property of multiplication:
(a√b+c√d-b√a)×(d√c-√ab+abc)
= adbc + acd√b - abd√c - b√ad√c + cd√ab - bc
= adbc - bc - abd√c - b√ad√c + acd√b + cd√ab
Therefore, the simplified expression is adbc - bc - abd√c - b√ad√c + acd√b + cd√ab.
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I don’t understand any of this.
With regard to the linear functions,
The point where the cost equals the revenue is (40, 48).At the point where the cost equals the revenue, the company breaks even and is not making a profit or loss.Yes, the results from Part 1 correspond with the graph.The profit equation is y = 0.8x - 32.The profit from producing 100 thousand batteries is $48,000.What is the explanation for the above response?
Part 1:
To find the point where the cost equals the revenue, we need to set the two equations equal to each other and solve for x:
Revenue: y=1.2x
Cost: y = 0.4x+32
1.2x = 0.4x + 32 (substitute y with 1.2x for revenue and y with 0.4x+32 for cost)
0.8x = 32 (subtract 0.4x from both sides)
x = 40 (divide both sides by 0.8)
Now that we have found x=40, we can find y by plugging it into either equation. Let's use the revenue equation:
y = 1.2x
y = 1.2(40)
y = 48
Therefore, the point where the cost equals the revenue is (40, 48).
Part 2:
The point (40, 48) represents the number of batteries that need to be produced in order for the cost to equal the revenue. In other words, if the company produces 40 thousand batteries, they will earn 48 thousand dollars in revenue and spend 32 thousand dollars in costs, resulting in a profit of 16 thousand dollars.
Part 3:
To check if our results from Part 1 correspond with the graph, we can plot the two equations on the same graph and look for the point of intersection.
As we can see from the graph, the two lines intersect at the point (40, 48), which confirms our result from Part 1.
Part 4:
Profit is found by subtracting cost from revenue, so the profit equation would be:
Profit: y = 1.2x - (0.4x + 32)
Simplifying the equation:
y = 1.2x - 0.4x - 32
y = 0.8x - 32
Part 5:
To find the profit from producing 100 thousand batteries, we can plug x=100 into the profit equation we found in Part 4:
y = 0.8x - 32
y = 0.8(100) - 32
y = 48
Therefore, the profit from producing 100 thousand batteries would be 48 thousand dollars.
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write as a product y^3-y^5
Answer: y^3/5
Step-by-step explanation:
Answer:
We can factor out a y^3 term from the expression y^3 - y^5:
y^3 - y^5 = y^3(1 - y^2)
So, y^3 - y^5 can be written as the product y^3(1 - y^2).
The box plot displays data collected on the shoe sizes for a group of students. A box plot uses a number line from 3.5 to 11 with tick marks every one-half unit. The box extends from 6.5 to 8 on the number line. A line in the box is at 7. The lines outside the box end at 5 and 9. The graph is titled Students' Shoe Sizes, and the line is labeled Size Of Shoe. Which of the following represents the value of the median of the data?
A 6.5
B 7
C 8
D 8.5
Answer: it’s 8.25
Step-by-step explanation: because it’s in between 8 and 8.5. Thank god
6. Two out of every five Canadians read at least 10 books a year. What percent of Canadians read at least 10 books a year?
40% of Canadians read at least 10 books a year.
Define percentageA percentage is a way of expressing a portion or a part of a whole as a fraction of 100. It is represented by the symbol "%". Percentages are often used to compare different quantities or to describe how much of a total is made up by a specific amount or group. For example, if you score 80 out of 100 on a test, your score can be expressed as 80%, meaning you got 80 out of 100 possible points.
If two out of every five Canadians read at least 10 books a year, then we can write this as a fraction:
2/5
We can multiply this fraction by 100 to turn it to a percentage:
(2/5) x 100 = 40%
Therefore, 40% of Canadians read at least 10 books a year.
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ΔABC with vertices A(-3, 0), B(-2, 3), C(-1, 1) is rotated 180° clockwise about the origin. It is then reflected across the line y = -x. What are the coordinates of the vertices of the image?
A.
A'(0, 3), B'(2, 3), C'(1, 1)
B.
A'(0, -3), B'(3, -2), C'(1, -1)
C.
A'(-3, 0), B'(-3, 2), C'(-1, 1)
D.
A'(0, -3), B'(-2, -3), C'(-1, -1)
The coordinates of the vertices of the image is A'(0, -3), B'(3, -2), C'(1, -1). The correct option is B.
What are coordinates?Triangle ABC is rotated 180 degrees clockwise about the origin and then reflected across the line y=-x.
We are to find the coordinates of the vertices of the image.
We know that
if a point (x, y) is rotated 180 degrees clockwise, then its co-ordinate changes as follows :
(a, b) ⇒ (-a, -b).
So, after getting rotated 180 degrees clockwise, the coordinates of the vertices of triangle ABC becomes
A(-3, 0) ⇒ (3, 0)
B(-2, 3) ⇒ (2, -3)
C(-1, 1) ⇒ (1, -1).
Therefore, the correct option is B. A'(0, -3), B'(3, -2), C'(1, -1).
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if f(x)= -3, then f'(x)=?
Answer:
0
Step-by-step explanation:
0
A solid glass cylinder is 31 centimeters high and has a diameter of 3 centimeters. What is the mass of the cylinder if the density of glass is 1.6 grams per cubic centimeter?
Answer:
the mass of the solid glass cylinder is approximately 350.67 grams.
Step-by-step explanation:
The diameter of the cylinder is 3 centimeters, which means that its radius is 1.5 centimeters (half the diameter). The area of the base of the cylinder is the area of a circle, calculated as pi (π) multiplied by the radius squared:
Base area = π x radius^2
Base area = π x (1.5 cm)^2
Base area = 7.07 cm^2 (approximately)
The volume of the cylinder is calculated by multiplying the area of the base by the height:
Cylinder Volume = Base Area x Height
Cylinder volume = 7.07 cm^2 x 31 cm
Cylinder volume = 219.17 cm^3 (approximately)
Now that we know the volume of the cylinder, we can calculate its mass using the density of the glass:
Mass = Density x Volume
Mass = 1.6 g/cm^3 x 219.17 cm^3
Mass = 350.67 grams (approximately)
please help me
To begin a bacteria study, a petri dish had 2300 bacteria cells. Each hour since, the number of cells has increased by 12%.
Let t be the number of hours since the start of the study. Let y be the number of bacteria cells.
Write an exponential function showing the relationship between y and t.
The exponential function showing the relationship is y = 2300(1 + 0.12)^t
The exponential function showing the relationshipThe exponential function showing the relationship between y and t can be written as:
y = 2300(1 + 0.12)^t
where 2300 is the initial number of bacteria cells, 0.12 is the growth rate (12% expressed as a decimal), and t is the time in hours since the start of the study.
This function is obtained by using the formula for exponential growth, which is y = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is the time.
In this case, a = 2300, r = 0.12, and y represents the amount of bacteria cells after t hours.
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A stack of books has a mass of 21 killagrams if each book in the stack has a mass of 3 kilograms how many books are in the stack
There are 7 books in the stack.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To find the number of books in the stack, we can divide the total mass of the stack by the mass of each book:
Number of books = Total mass of the stack / Mass of each book
In this case, the total mass of the stack is 21 kilograms, and the mass of each book is 3 kilograms.
Number of books = 21 kg / 3 kg/book
Simplifying the right side, we get:
Number of books = 7 books
Therefore,
There are 7 books in the stack.
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The can of lead below has a surface area of 18064.in^2.if the diameter of the can is 5 inches, didn’t he height if the can
The height of the cylinderical can is approximately 1147.8 inches.
What is a cylinder?
A cylinder is a three-dimensional geometric object made up of two parallel and congruent circular bases that are joined by a curving lateral surface. The lateral surface has a uniform circular cross-section and is perpendicular to the bases. A cylinder's height is the perpendicular distance between its bases. Cans, tubes, and pipes are all instances of cylinders. The volume of a cylinder may be computed by multiplying its base area by its height, and the formula for the lateral surface area is 2πrh, where r is the radius of the base and h is the cylinder's height.
Now,
We can start by finding the radius of the can using the given diameter:
radius = diameter/2 = 5/2 = 2.5 inches
The surface area of the can is given by:
Surface area = 2πrh + 2πr²
where h is the height of the can, r is the radius, and π is the mathematical constant pi.
Substituting the given values, we get:
18064 = 2π(2.5)(h) + 2π(2.5)²
Simplifying and solving for h, we get:
18064 = 15.707h + 39.269
18064 - 39.269 = 15.707h
18024.731 = 15.707h
h = 18024.731/15.707
h ≈ 1147.8 inches
Therefore, the height of the can is approximately 1147.8 inches.
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Suppose a supermarket ordered 13 cases of organic vegetable soup with a list price of $18.90 per case and 4 cases of organic baked beans with a list price of $33.50 per case. The wholesaler offered the supermarket a 39% trade discount. (Round your answers to the nearest cent.)
What is the total net amount (in $) the supermarket owes the wholesaler for the order?
The total net amount the supermarket owes the wholesaler for the order is $231.31.
What does discount mean?A discount is a reduction in the price of a product or service. It is often offered by businesses to encourage customers to buy more or to make a purchase they might not otherwise make. A discount can be expressed as a percentage or a specific dollar amount, and it is usually subtracted from the original price of the item or service.
According to the given informationTo find the total net amount the supermarket owes the wholesaler for the order, we need to first calculate the cost of each case of soup and baked beans after the 39% trade discount is applied, and then multiply those costs by the number of cases ordered.
The trade discount rate is 39%, which means the supermarket will receive a discount of 39% off the list price of each case of soup and baked beans. To calculate the cost of each case after the discount is applied, we can use the following formula:
Discounted cost = List price - (Discount rate x List price)
For the soup, the discounted cost per case is:
$18.90 - (0.39 x $18.90) = $11.51
For the baked beans, the discounted cost per case is:
$33.50 - (0.39 x $33.50) = $20.42
Now we can calculate the total net amount owed by the supermarket to the wholesaler:
Total net amount = (Number of cases of soup x Cost per case) + (Number of cases of baked beans x Cost per case)
Total net amount = (13 x $11.51) + (4 x $20.42)
Total net amount = $149.63 + $81.68
Total net amount = $231.31
Therefore, the total net amount the supermarket owes the wholesaler for the order is $231.31.
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At a real estate agency, an agent sold a house for $377,000. The commission rate is 7.5% for the real estate agency and the commission rate for the agent is 20% of the amount the real estate agency gets. How much did the agency make on the house? How much did the agent earn in commission?
The agency made $28,275 in commission on the house.
The agent earned $5,655 in commission on the sale of the house.
To calculate how much the agency made on the houseWe first need to calculate the amount of commission that the agency received.
The commission rate for the agency is 7.5%, so we can find the commission amount by multiplying the sale price of the house by 7.5% in decimal form:
Commission for the agency = $377,000 x 0.075 = $28,275
Therefore, the agency made $28,275 in commission on the house.
To calculate how much the agent earned in commission, we need to find 20% of the commission amount that the agency received:
Commission for the agent = $28,275 x 0.20 = $5,655
Therefore, the agent earned $5,655 in commission on the sale of the house.
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13. What is the surface area of a dome (a half sphere) with a radius of 12 meters?
288 meters squared
48 meters squared
967 meters squared
576 meters squared
Answer: The formula for the surface area of a sphere is given by 4πr^2, and since we have half of a sphere, the surface area of a dome (a half sphere) is 2πr^2.
Plugging in the radius r = 12 meters, we get:
Surface area = 2π(12)^2
Surface area = 2π(144)
Surface area ≈ 904.78
Rounding to the nearest whole number, we get the surface area of the dome as 905 meters squared. Therefore, the closest answer choice is 967 meters squared.
So the answer is: 967 meters squared.
Step-by-step explanation:
Please Help ( Due today) ASAP
Question 6(Multiple Choice Worth 1 points)
(08.07 LC)
The table represents a quadratic function C(t).
t C(t)
−2 7
−1 4
0 3
1 4
2 7
What is the equation of C(t)?
C(t) = −(x − 3)2
C(t) = (x − 3)2
C(t) = −x2 + 3
C(t) = x2 + 3
C(t equation )'s is thus: [tex]C(t) = (t - 0)^2 + 3[/tex] or condensed, [tex]C(t) = t^2 + 3[/tex] as the vertical stretch or compression factor and (h, k) is the vertex.
what is parabola ?A parabola is a symmetry U-shaped plane curve. This graph represents a quadratic function using the formula y = ax2 + bx + c. The parabola's direction and shape are determined by the nonzero integers a and b in this equation, whereas the parabola's location on the x-axis is affected by the linear coefficient b and the constant coefficient c. A parabola has a vertex, or the location where the curve changes direction, and it can open upward or downward.
given
We can start by noting that since the vertex of a parabola always lies in the centre of the two x-intercepts for a quadratic function, the parabola's vertex must be at the coordinates (0, 3).
The equation can be expressed in the vertex form of a quadratic function as follows:
[tex]C(t) = a(t-h)^2 + k[/tex]
where "a" is the vertical stretch or compression factor and (h, k) is the vertex. Using the values from the table as inputs, we obtain:
[tex]C(t) = a(t - 0)^2 + 3[/tex]
We still need to determine what "a" is worth. To do this, we can utilise a different table row, for instance (1, 4):
[tex]4 = a(1 - 0)^2 + 3[/tex]
1 = a
C(t equation )'s is thus: [tex]C(t) = (t - 0)^2 + 3[/tex] or condensed, [tex]C(t) = t^2 + 3[/tex] as the vertical stretch or compression factor and (h, k) is the vertex.
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Which equation could be solved using this application of the quadratic formula?
-3√32-4(1)(24)
2(1)
H=
O A.
O B.
O C.
C.
O D.
x² + 6x + 24 = 3x
3x² + 3x + 24 = 3
x² + 3x - 24 3
-
x² + 3x + 24 = 3
Answer:
Option A
Step-by-step explanation:
Solving using quadratic formula:
Use the quadratic formula to determine the coefficient of the quadratic equation.
Option A:
x² + 6x + 24 = 3x
x² + 6x + 24 - 3x = 0
x² + 3x + 24 = 0
Compare with ax² + bx + c = 0,
a = 1 ; b = 3 and c = 24
[tex]\boxed{\bf x= \dfrac{-b \± \sqrt{b^2-4ac}}{2a}}[/tex]
[tex]= \dfrac{-3 \±\sqrt{3^2-4(1)(24)}}{2(1)}[/tex]
This equation could be solved using the application of the quadratic formula.
Option B:
3x² + 3x + 24 = 3
3x² + 3x + 24 - 3 = 0
3x² + 3x + 21 = 0
a = 3 ; b = 3 and c = 21
Here, co-efficients are different.
Option C:
x² + 3x - 24 = 3
x² + 3x - 24 - 3= 0
x² + 3x - 27 = 0
a = 1 ; b = 3 and c = -27
Here, co-efficients are different.
Option C:
x² + 3x + 24 = 3
x² + 3x + 24 - 3 = 0
x² + 3x + 21 = 0
a= 1 ; b = 3 and c = 21
Here, co-efficients are different.
Determine the interval(s) on which the function Is constant.
Write your answer as an interval or list of intervals.
When writing a list of Intervals, make sure to separate each interval with a comma and to use as few intervals as possible.
Click on "None* if applicable.
The list of intervals on which the function is constant is:
A(-4,-3) and B(3,6).
What is a constant function?A constant function is a function that returns the same value regardless of the input. In other words, for every value of x, the output of the function is the same constant value. For example, the function f(x) = 2 is a constant function because no matter what value of x is plugged into the function, the output will always be 2. Constant functions are often represented by horizontal lines on a graph.
What does a list of intervals mean in the graph?A list of intervals in a graph typically indicates the range of values or intervals on a given axis. For example, on the x-axis of a graph, a list of intervals might represent the range of values from a lower bound to an upper bound, with each interval indicating a range of values that falls between two specific points on the axis. On the y-axis, the intervals might represent the range of possible values for the dependent variable or data being plotted. In general, the intervals on a graph provide a visual representation of the range of values being considered or plotted.
According to the given informationThe given function in the graph on intervals A(-4,-3) and B(3.6) is a horizontal line which means there is no change in output. So the function is constant.
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Find the value of y in 3/5 y=6
since 3/5 y is 6 to find what 1/5 y is we divide 6 by 3 which is 2 so 1/5 y=2. Now to find the value of y we multiply that by 5 and since 2*5=10 y=10. Also pls mark as brainliest answer
Identify the values of a, b, and c in the following quadratic equation: 2x^2 −3x−5
Explain why the empty set is a subset of every set
The empty set (also known as the null set) is a subset of every set because it does not contain any elements that are not in the set. In other words, if A is any set, then every element of the empty set is also an element of A, since the empty set contains no elements. This satisfies the definition of a subset, which states that for any two sets A and B, A is a subset of B if every element of A is also an element of B. Therefore, the empty set is a subset of every set.
~~~Harsha~~~
2. Mrs. Cooper created a triangular shaped vegetable garden and needs to put down fertilizer to cover the space. If the garden has a base of 8m and a height of 10m, how much fertilizer will she need?
Answer:
40 m²
Step-by-step explanation:
Area of triangle:
To find the area of triangle, multiply the base and area and then divide it by 2.
base = b = 8 m
height = h = 10m
[tex]\boxed{\bf Area \ of \ triangle = \dfrac{1}{2}*b*h}[/tex]
[tex]= \dfrac{1}{2}*8 * 10\\\\= 4 * 10\\\\= 40 \ m^2[/tex]
Oliver and Mike each place some apples and oranges into the same bowl.
• The ratio of apples to oranges Oliver places in the bowl is 2:3
• The ratio of apples to oranges Mike places in the bowl is 1:2
• They each place 6 oranges in the bowl.
Write the total number of apples and oranges they place in the bowl.
Answer: 5 * 5 = 20
20 divided by 1 = 20
If there are 5 apples with an apple:orange ratio of 1:4, there are 20 oranges.
please answer in detail
Answer:
AB: y = 2x + 4
Step-by-step explanation:
Line AB is parallel to the line y = 2x + 3
When 2 lines are parallel they have the same coefficient of x.
=> AB: y = 2x + m (1)
Because line AB passes through the point (0, 4)
Replace x = 0; y = 4 into (1) => 2 × 0 + m = 4 => m = 4
So AB: y = 2x + 4
Evaluate. Write your answer as a whole number or as a simplified fraction.
Answer:
[tex]\frac{64}{25}[/tex]
Step-by-step explanation:
[tex]\frac{4^{3} }{5^{2} }[/tex]
4³ = 64
5² = 25
[tex]\frac{64}{25}[/tex] is already in simplest form, so it is the answer.
Lastly, let’s consider the alternative method of paying for college: paying with loans. You take out a loan in the amount of your tuition and fees cost for 5 years rounded up to the nearest thousand dollars (for example if the total cost is $55,787 the loan would be for $56,000). The loan has a monthly interest rate of 0.25% and a monthly payment of $250. How long will it take you to pay off the loan? Use the formula N= (-log(1-i*A/P))/(log(1+i)) to determine the number of months it will take you to pay off the loan. Let N represent the number of monthly payments that will need to be made, i represent the interest rate in decimal form, A represent the amount owed (total amount of the loan), and P represent the amount of your monthly payment. Be sure to show your work for all calculations made.
With given compound interest, it will take 27.25 years to pay off the loan.
What is Compound interest?
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, the interest that is earned on both the principal amount and any previously accumulated interest. In other words, it is interest that is calculated not only on the original amount of money but also on any interest that has been earned previously. This can result in significant growth of an investment or loan balance over time, as the interest earned on the accumulated interest can compound exponentially. Compound interest can be calculated using a specific formula that takes into account the principal amount, the interest rate, and the compounding frequency.
Now,
First, we need to calculate the total amount of the loan. We round up the tuition and fees cost for 5 years to the nearest thousand dollars:
Total cost = $70,000
Rounded up to nearest thousand = $70,000
So, the amount of the loan is $70,000.
Next, we can use the formula N= (-log(1-i*A/P))/(log(1+i)) to calculate the number of monthly payments needed to pay off the loan.
N = (-log(1-0.0025*70000/250))/(log(1+0.0025))
N = (-log(1.75))/(log(1.0025))
N = 326.45
Rounding up to the nearest whole number, it will take 327 monthly payments to pay off the loan.
So, it will take 327/12 = 27.25 years to pay off the loan.
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find the measure of angle A
Answer:
do 5x-27+7x-26=10x-23 because sum of two interior angle of a triangle is equal to the sum of one exterior angle and don't forget because it comes daily in exam
Primary Level 2 3 4 5 6 7. 8 children/funny monkeys thin/rake strong/ox eagle/aeroplane my room/ clean/ whistle swimmer/fish Exercise 2 Read the story. Look for the simile (as/like) When Mr. Bumble is angry, he shouts as loud as thunder. His eyes look like fire. He bangs his hands which feel as heavy as lead. Mr. Bumble stamps his feet like an et All the pupils keep as quiet as lambs when Mr. Bumble behaves like e
The similes in the story are:
"shouts as loud as thunder""eyes look like fire""hands feel as heavy as lead""stamps his feet like an et""quiet as lambs"What is a Simile?A simile is a figure of speech that compares two things using the words "like" or "as." It is a type of metaphor that helps to create a vivid and engaging image in the reader or listener's mind.
Similes are often used in literature, poetry, and everyday language to make a comparison more relatable and understandable. For example, "He is as brave as a lion" or "She sings like an angel." These similes help to convey a certain quality or trait by comparing it to something else that is well-known or familiar.
Note: It seems there may be a typo in the last sentence of the story, where the word "e" appears instead of "elephant" or another word that would make sense in context.
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Please help me solve and show my work
The degree measure of the angles are;
1. 5π/3 = 300°
2 3π/4 = 135°
3. 5π/6 = 150°
4. -3π/2 = 90°
What is degree and radian?A degree is a unit of measurement which is used to measure circles, spheres, and angles while a radian is also a unit of measurement which is used to measure angles.
A circle has 360 degrees which are its full area while its radian is only half of it which is 180 degrees or one pi radian.
therefore π = 180°
1. 5π/ 3 = 5×180/3 = 300°
2. 3π/4 = 3× 180/4 = 540/4 = 135°
3. 5π/6 = 5×180/6 = 150°
4. - 3π/2 = -3 × 180/2 = -270° = 90°
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Which graph represents the hyperbola x2/52-y2/42 = 1?
For the given equation we have horizontal length of 5 and vertical width of 4 units. The graph that depicts this hyperbola is: Option B.
What is a hyperbola?A hyperbola is a particular kind of conic section in mathematics, which is a curve created by the intersection of a cone and a plane. The collection of all points in a plane that have a constant difference between them and two fixed points, known as the foci, is referred to as a hyperbola. The distance between the foci is referred to as this consistent difference and is represented by the symbol 2a.
Two separate branches that are mirror reflections of one another make up a hyperbola. The vertices are the two locations where the two branches of a hyperbola are joined.
For the given equation of the parabola, the value of a and b = 5 and 4.
Thus, we have horizontal length of 5 and vertical width of 4 units
The graph that depicts this hyperbola is: Option B.
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The complete question is:
You can afford a $1000 per month mortgage payment. You've found a 30 year loan at 5.3% interest.
a) How big of a loan can you afford? (Round to the nearest cent, as needed.)
$
b) How much total money will you pay the loan company? (Round to the nearest cent, as needed.)
$
c) How much of that money is interest? (Round to the nearest cent, as needed.)
Answer:
a) To find out how big of a loan you can afford, we can use the formula for the monthly payment of a mortgage:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]
where M is the monthly payment, P is the principal (the amount borrowed), i is the monthly interest rate (which is the annual interest rate divided by 12), and n is the number of monthly payments (which is the number of years times 12).
In this case, we know that M = $1,000, i = 0.053/12, and n = 30 x 12 = 360. We want to solve for P, the principal we can afford.
Substituting these values into the formula, we get:
$1,000 = P [ 0.004416(1 + 0.004416)^360 ] / [ (1 + 0.004416)^360 - 1 ]
Simplifying and solving for P, we get:
P = $183,928.72
Therefore, you can afford a loan of approximately $183,928.72.
b) The total money paid to the loan company will be the monthly payment multiplied by the number of payments over the life of the loan. In this case, we have:
Total money paid = $1,000 x 360 = $360,000
Therefore, the total amount of money paid to the loan company will be $360,000.
c) To find out how much of that money is interest, we can subtract the principal from the total amount paid. In this case, we have:
Interest paid = Total money paid - Principal = $360,000 - $183,928.72 = $176,071.28
Therefore, the amount of money paid in interest will be $176,071.28.
Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
The equations that can be used to solve for y are y(y + 5) = 750, y² – 5y = 750 and y(y – 5) + 750 = 0
What is quadratic equation?
it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form.
The equations that can be used to solve for y, the length of the room are:
1. y(y + 5) = 750
2. y² – 5y = 750
3. y(y – 5) + 750 = 0
Option 1 and 2 are quadratic equations that can be solved by factoring, completing the square, or using the quadratic formula. Option 3 is also a quadratic equation but it requires rearranging to the standard form before applying the same methods. The last option, (y + 25)(y – 30) = 0, is not a quadratic equation but it can be easily solved using the zero product property.
To learn more about quadratic equation from the given link:
brainly.com/question/30098550
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