To find the two points having an x-coordinate of 3 whose distance from the point (-2, -1) is 13, you can use the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) is the coordinates of the first point, and (x2, y2) is the coordinates of the second point.
In this case, you can use the distance formula to find the y-coordinates of the two points having an x-coordinate of 3:
Distance = √((3 - (-2))^2 + (y - (-1))^2)
= √(5^2 + (y + 1)^2)
= √(25 + y^2 + 2y + 1)
= √(26 + y^2 + 2y)
= 13
If you set the distance equal to 13 and simplify the equation, you get:
y^2 + 2y + 12 = 0
This is a quadratic equation, which means it can be solved using the quadratic formula:
y = (-b ± √(b^2 - 4ac)) / (2a)
where a, b, and c are the coefficients of the quadratic equation.
Substituting the values into the quadratic formula, you get:
y = (-2 ± √(-2^2 - 4 * 1 * 12)) / (2 * 1)
= (-2 ± √(-4 - 48)) / 2
= (-2 ± √(-52)) / 2
Since the square root of a negative number is not a real number.
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please help, im sick and im having a mental breakdown right now.
Answer:
Step-by-step explanation:
SORRY CANT HELP YOU I AM ONLY IN 4 GRADE SO SORRY
I need help with this question
Please help with 17-20.
Answer:
17. VN ll OP
18. VN perp. TR
19. Yes because the both a straight line (m 180) and are not crossing at any point.
20. Yes because there crossing at an right angle.
Hope this helps!
A student ran a distance of 312 miles each day for 5 days. Then the student ran a distance of 414 miles each day for the next 5 days. What was the total distance in miles the student ran during these 10 days?
The total distance ran during these days, written as a mixed number, is (38 + 3/4)mi
What is the total distance that the student ran on the 10 days?We know that the student ran a distance of (3 + 1/2) miles each day for 5 days, so the amount that the student ran in these 5 days is given by the product:
5*(3 + 1/2) mi = (15 + 5/2) mi
Now, on the next 5 days, the student ran a distance of (4 + 1/4) miles, so the total distance that the student ran in these days is:
5*(4 + 1/4) mi = (20 + 5/4)mi
Now to get the total distance that the student ran on the 10 days we need to add the two distances above, we will get:
(15 + 5/2) mi + (20 + 5/4)mi
So we have a sum of mixed numbers, we can rewrite this as:
(15 + 5/2) mi + (20 + 5/4)mi = (15 + 20)mi + (5/2 + 5/4)mi
(15 + 20)mi + (5/2 + 5/4)mi = 35mi + (10/4 + 5/4) mi
35mi + (10/4 + 5/4) mi = 35mi + 15/4mi
35mi + 15/4mi = 35mi + 12/4 mi + 3/4 mi
35mi + 12/4 mi + 3/4 mi = (38 + 3/4)mi
That is the total distance that the student ran on the 10 days.
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The standard equation for the position s of a body moving with a constant acceleration a along a coordinate line is s = a/2 t^2 + v_0 t + s_0, where v_0 and s_0 are the body’s velocity and position at time t = 0. Derive this equation by solving the initial value problem Differential equation: d^2s/dt^2 = a Initial conditions: ds/dt = v_0 and s = s_0 when t = 0.
The standard equation for the position s of a body moving with a constant acceleration a along a coordinate line is proved below.
In statistics, the term equation refers the combination of variable and numbers.
Here we have to prove the the standard equation for the position s of a body moving with a constant acceleration a along a coordinate line.
While we looking into the given question, we have given the function
Here we are given that dt²/d²s = a (a constant), and when t=0,
dt/ds = v₀
and s = s₀.
And we need to show that s=a/2t²+v₀t+s₀.
While we differentiate the equation , then we get,
=> dt²/d²s = a
=> ds/dt = ∫a dt
=> ds/dt = at + c
Since ds / dt = v₀ when t = 0, we have
=> a(0) + C= C
Again we have to take the differentiation on the term, then we get,
=> s = ∫(at+v0)dt = a/2t²+v₀t+s₀.
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Every day, Aubrey's orange juice stand uses 2 bags of oranges. How many days will 4/5
of a bag of oranges last?
Answer:
please download the attached file and let me know if you need any further information about addmition in roots international and if so how to make food with clay
Step-by-step explanation:
ok inshallah and a have of safe Earth’s warm and and
[tex]85(94 + 611) < 64(85 - 54)[/tex]
it same like before the end
Answer: 2/5 days
Step-by-step explanation:
4 / 5 = 2d
4 / 10 = d
2 / 5 = d
Convert 251,000 to a scientific notation
Answer:
2.51 x 10^5
Step-by-step explanation:
Scientific notation gives you a number between 1 and 10 multiplied by a power of ten. In this case, you'll want to use the significant digits, 251, and divide or multiply by a power of ten to get a number between 1 and 10.
251,000 can become 2.51 (which is between 1 and 10) multiplied by 10 to a certain exponent. All you need to do is calculate the exponent.
2.51 x 10^(?) = 251,000
For each power of 10, the decimal moves a space. Since you want the decimal to move 5 spaces, you'll want to multiply 2.51 by 10^5.
2.51 x 10 = 25.1
2.51 x 10^2 = 251
2.51 x 10^3 = 2510
2.51 x 10^4 = 25,100
2.51 x 10^5 = 251,000
Suppose you are rounding to the nearest hundred. What is the greatest number that rounds to 800? What is the least number?
i have no idea how to do this can anyone help
The end behavior of the functions is obtained considering the limits of the functions as the input variable x goes to infinity.
For limits when x goes to infinity, only the term with the highest exponent of each of the numerator and of the denominator is considered, hence the functions are written as follows:
f(x) = x²/x³.g(x) = x³/x³.h(x) = x^4/x³.Applying the exponent properties, the equivalent expressions are given as the base x elevated to the subtraction of the exponents 2 and 3, hence:
f(x) = 1/x.g(x) = 1.h(x) = x.Which is how the functions behave as x goes to infinity.
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
1. m∠5 + m∠6 = 180° - Pair of linear angles
2. ∠ 2+ ∠ 3 = ∠ 6 - Exterior Angle Theorem.
3. m∠2 + m∠3 + m∠5 = 180° - Sum of angles of Triangle
Exterior and interior angles of Triangle:
The angles that are created outside of a triangle are its external angles. In other terms, the angle created between one of a triangle's sides and its neighboring extended side is the triangle's exterior angle.
Each exterior angle of the triangle and its corresponding interior angle will form a pair of linear angles i.e the Sum of an Exterior angle and its corresponding interior angle is 180°.
A triangle's exterior angle is equal to the sum of its two opposite interior angles. This property of the triangle is known as Exterior Angle Theorem.
Here we have
∠2, ∠3, and ∠5 are the interior angles of a triangle
∠1, ∠4, and ∠6 are exterior angles of the same triangle
Let's assume that the given triangle is ΔABC
Can be represented as given in the picture
As we know the sum of angles in a triangle = 180°
=> m∠2 + m∠3 + m∠5 = 180° will be true
If we observe the given picture,
From line BC, m∠5 + m∠6 = 180° [ Pair of linear angles ]
From Exterior angle Property
=> ∠ 2+ ∠ 3 = ∠ 6.
Therefore,
The correct statements are
1. m∠5 + m∠6 = 180° - Pair of linear angles
2. ∠ 2+ ∠ 3 = ∠ 6 - Exterior Angle Theorem.
3. m∠2 + m∠3 + m∠5 = 180° - Sum of angles of Triangle.
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Help me with this question please
Answer: x=±2/3
Step-by-step explanation:
The first thing we want to do is isolate the variable, x² in this case.
We can divide both sides by 9 which yields the equation x²=[tex]\frac{4}{9}[/tex].
Then we can take the square root of both sides, x=2/3.
Note: When the exponent is an even number both positive and negative x values will yield the same positive answer, so x=±2/3
f(x)=0.2 t
g(t)=0.5(x-6)
By the end. you will be able to solve
0.2 x=0.5(x+6)
The value of x when both the function give the same value is 10
Solution:
Given f(x) = 0.2x , g(x) = 0.5(x-6)
let x = 0 , f(x) = 0 , g(x) = -3
let x = 1 , f(x) = 0.2 , g(x) = -2.5
let x = 2 , f(x) = 0.4 , g(x) = -2
let x = 3 , f(x) = 0.6 , g(x) = -2.5
let x = 4 , f(x) = 0.8 , g(x) = -2 and so on till x=10
let x=10, f(x) = 2, g(x) = 2
∴ The value of x when both the values of the function are same is x = 10
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The value of x when both the function give the same value is 10
What are functions?
Function, in mathematics is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Solution:
Given f(x) = 0.2x , g(x) = 0.5(x-6)
let x = 0 , f(x) = 0 , g(x) = -3
let x = 1 , f(x) = 0.2 , g(x) = -2.5
let x = 2 , f(x) = 0.4 , g(x) = -2
let x = 3 , f(x) = 0.6 , g(x) = -2.5
let x = 4 , f(x) = 0.8 , g(x) = -2 and so on till x=10
let x=10, f(x) = 2, g(x) = 2
∴ The value of x when both the values of the function are same is x = 10
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hi someone do 13 if you can please thank u
Answer: y= 2x - 5
Step-by-step explanation: lmk if u need explanation to solve
Shape P is reflected in x = -1 to give P'.
a) What are the coordinates of A'?
Then P' is translated by (6)
b) What are the coordinates of A"?
Answer:
a) A' = (2, 4)
b) A'' = (1, -2)
Step-by-step explanation:
When reflecting a shape in a vertical line, each vertex of the shape will be the same distance from the vertical line but in the opposite direction.
Therefore, the x-values change but the y-values remain the same.
Part (a)To reflect point A in x = -1, determine the number of horizontal units the point is from x = -1. Count the same number of units on the other side of the vertical line (remembering that the y-value remains unchanged).
The x-value of point A is x = -4. This is 3 units to the left of x = -1.
Therefore, the x-value of point A' is 3 units to the right of x = -1.
The y-value of point A is y = 4, so the y-value of point A' is also y = 4.
Therefore, the coordinates of the point A' are:
A' = (2, 4)Part (b)To translate point A' by the given vector, translate the point:
1 unit to the left.6 units down.Therefore, the coordinates of the point A'' are:
A'' = (2-1, 4-6) = (1, -2)Answer:
-5
-9+5
Step-by-step explanation:
I need help solving so I will know how to do this thank you
Answer:
97.5/100
Step-by-step explanation:
To write 97.5% as a fraction in simplest form, we first convert the percentage to a decimal by dividing it by 100: 97.5% / 100 = 0.975. We can then express this decimal as a fraction by using the fact that any number can be represented as a fraction with the number as the numerator and a power of 10 as the denominator: 0.975 = 0.975/1. Finally, we simplify the fraction by dividing the numerator and denominator by the greatest common factor, which in this case is 1: 0.975/1 = 97.5/100. Therefore, 97.5% can be written as the fraction 97.5/100 in simplest form.
Answer:
39/40
Step-by-step explanation:
97.5/100
Step 1: Write down the percent divided by 100;
Step 2: If the percent is not a whole number, then multiply both top and bottom by 10 until you get an integer at the numerator.
Step 3: Simplify (or reduce) the fraction if it is not in the simplest form.
Please help asap need it now
Using fractions and mathematical operations, the number of students in the class are 53, the number of juniors are 21 and 16 seniors did not attend the field trip
What are FractionsA fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator.
A)
From the information given, 3/5 of the students are seniors
However, we know that he has 32 seniors currently
Let's use the concept of percentage here
3/5 = 0.6. Expressing this in percentage = 60%
This we can say 60% of the students are seniors
60/100 = 32/ x
x = total number of students
x = 32 / 0.6
x = 160/3 = 53 students
We have 53 students in the class
B) The number of juniors in the class are
53 - 32 = 21
C) The number of seniors that did not go will be
3/5 * 40 = 24
40 - 24 = 16
16 seniors did not go
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Bill jumps off a diving board that is 12 feet above the surface of a swimming pool. Jumping upward and outward, he reaches a maximum height of 18 feet above the surface of the water when he has jumped outward 4 feet. Find f(x) an equation for his parabolic path and when he hits the water, how far out has he reached, to to the nearest tenth of a foot.
The f(x) = -ax²+18 function equation for his parabolic path. x=√8 is he reached, to the nearest tenth of a foot.
What does "function equation" actually mean?A function is an equation that has just one answer for y for every possible value of x. When utilizing a function, each input of a certain type receives exactly one output.
Briefing:f(x) = -ax² + 18
f(2)= -a(2)²+18 = 12
-4a = 12-18
-4a = -6
a = -6/-4
a = 3/2
f(x) = (-3/2) x² + 12
f(0) = (-3/2) x² + 12
(3/2) x² = 12
x² = 8
x = √8
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help meeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
we need to find the value of x for which C(x) = 2200.
2200 = 270ln(x + 1) + 1900
300 = 270ln(x + 1)
300/270 = ln(x + 1)
10/9 = ln(x + 1)
e^(10/9) = x + 1
x = e^(10/9) - 1 = 2.037731778... ≈ 2.0 acres
for an average intake of 2200 calories per day the number of acres of land owned is approximately 2.0.
What linear equation does each graph represent?
Draw an equation into each box to match the graph with its equation.
The linear equation each graph is y = (1/5)x +3, y = 2x, y = -3x+5 and y = (1/3)x +5 respectively
How to determine what linear equation each graph represents?The equation of a line is of the form y = mx+c
Where m is the slope and c is the y-intercept
Graph 1
c = 3
m = 1/5 = 0.2
y = mx+c
Thus, the linear equation is y = (1/5)x + 3 or y = 0.2x + 3
Graph 2
c = 0
m = 2/1 = 2
y = mx+c
Thus, the linear equation is y = 2x+0 or y = 2x
Graph 3
c = 5
m = -3/1 = -3
y = mx+c
Thus, the linear equation is y = -3x+5
Graph 4
c = 5
m = 1/3 = 1/3
y = mx+c
Thus, the linear equation is y = (1/3)x+5 or y = 0.33x+5
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suppose that over a certain region of space the electrical potential v is given by the following equation. v(x, y, z)
12/√3 is the direction of the vector v .
What does a basic math vector mean?
A thing with both magnitude and direction is called a vector.
A vector can be visualized geometrically as a directed line segment, where the direction is indicated by an arrow and the length of the segment equals the magnitude of the vector.
Normalize (make length 1) the vector v = <1, 1, -1>.
||v|| = √(1^2 + 1^2 + (-1)^2) = √3.
So, the unit vector u is given by u = v/||v|| = <1, 1, -1>/√3.
To find the rate of change of the potential in the direction of the vector v, you should calculate the ∇f(6, 6, 5) and multiply by u.
=<df/dx, df/dy, df/dz>*u
= <4x-3y+yz, -3x+xz, xy> {at (6, 6, 5)} * u
= <36, 12, 36> · <1, 1, -1>/√3
= 12/√3.
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The complete question is -
Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 2x2 − 3xy + xyz (a) Find the rate of change of the potential at P(6, 6, 5) in the direction of the vector v = i + j − k.
Factor. 81x6 - 25y¹0 Enter your answer in the box.
Using difference of squares, [tex]81x^6-25y^{10}=\boxed{(9x^3-5y^5)(9x^3 + 5y^5)}[/tex].
You want to buy a $241,000 home. You plan to pay 15% as a down payment, and take out a 30 year loan for the rest.
The monthly payment will be 1,228.18.
What is principle amount?
The amount you owe at any one moment is the primary amount. When you first took out the loan, it is exactly your loan amount. The principle amount drops as you make EMI payments, and when it hits zero, your loan is closed.
The total price of the home is $241,000.
The down payment will be 15% among the total price.
Rest amount will be paid by taking loan for 30 years.
The down payment amount is
15% of $241,000 = $ 241,000×15/100 = $36,150.
Hence the loan amount is going to be the rest amount, that is,
$(241,000-36,150) =$204,850.
So the principle amount, P= $204,850.
Interest rate= 5% implies
interest, R= 5/100 = 1/20 = 1/12×1/20 (monthly) = 1/240.
Number of years, N= 30 years = 30×12 months = 360 months.
Hence the monthly payment will be
[ P × R × (1+R)N ] / [ (1+R)N - 1 ] = $1,099.68.
So the principle amount, P= $204,850.
Interest rate= 6% implies
interest, R= 6/100 = 1/12×6/100 (monthly) = 1/200.
Number of years, N= 30 years = 30×12 months = 360 months.
Hence the monthly payment will be
[ P × R × (1+R)N ] / [ (1+R)N - 1 ] = 1,228.18
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Identity the slope and y intercept of the graph then write the equation in slope intercept form
Answer:
m = -4
b =1
y = -4x+1
Step-by-step explanation:
We want to find the slope and y intercept
Given the two points ( -1,5) and ( 1,-3), we can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( -3 -5)/( 1 - -1)
= -8/( 1+1)
= -8/2
= -4
The y intercept is where it crosses the y axis
It crosses at 1
The slope intercept form of the line is
y = mx+b
y = -4x+1
Fred sells new and used kayaks.
He makes a 12.5% commission on every kayak he sells and he also gets paid $395.50 per week. a) Develop an equation for the way Fred is paid. b) Last month, the total value of the kayaks he sold was $17 400. Use the equation you’ve developed to find out how much Fred was paid for that month.
The total commission Fred was paid for that month is $2570.5.
Given that, Fred sells new and used kayaks.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Let the number of kayaks be x and the total amount of money Fred get paid per week be y.
A) An equation for the way Fred is paid.
So, equation is y =395.50 +12.5% of x
⇒ y=395.50 +0.125x
B) Last month, the total value of the kayaks he sold was $17400.
Here, x=17400
So, y=395.50 +0.125×17400
= $2570.5
Therefore, the total commission Fred was paid for that month is $2570.5.
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Write and graph the inverse of y=-x²+4.
Write the inverse of y=-x²+4
y=
(Simplify your answer. Use a comma to separate answers as needed.)
The inverse of y is [tex]\sqrt{4-x} ,-\sqrt{4-x}[/tex].
What is the inverse of a function?
A function whose inverse returns the initial value for the specified output is called an inverse function of the function. The inverse function of y, or[tex]f^{-1}[/tex] (y), will return the value x if f (x) produces an output of y.
Given equation is [tex]y=-x^{2} +4[/tex]
We find the inverse function f(x) by substituting x and y.
We compute the resulting equation for x. We change the variable to:
[tex]x=4-y^{2}[/tex]
Now, solve the equation [tex]x=4-y^{2}[/tex] for y
We get, y = [tex]\sqrt{4-x} ,-\sqrt{4-x}[/tex]
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a. What was the depreciation for the first year?
$637,362
b. Assuming the equipment was sold at the end of the fifth year for $ 138,700 determine the gain or loss on the sale of the equipment. Enter your answer as a positive amount.
Loss=____
c. Journalize the entry to record the sale. If an amount box does not require an entry, leave it blank.
(a) The depreciation for the first year is $99,732.40. (b) If the Machine was sold at the end of the fifth year, the gain or loss is $498,662
What is depreciation?We know that in accounting, depreciation is the loss on a fixed asset over the accounting period that benefited from it.
Using straight line method of depreciation,
Depreciation = [tex]\frac{Cost os asset-Residual value}{Estimated number of years}[/tex]
Applying the figures we have
Depreciation = [tex]\frac{637362-138700}{5}[/tex]
Depreciation= [tex]\frac{498662}{5}[/tex]
Depreciation= $99,732.40
(b) If the machine is sold at the end of the fith year, the loss is accumulated depreciation for 5 years
Loss= $(99,372.4*9) = $498,662
(c) The journal appears as follows
Journal
$ $
Coat of machine 637,362.00 Depreciation 498,662
Balance 138,700
Totals 637,362.00 637,362.
In conclusion, the depreciation for the first year and loss after the fifth year are $99,732 and $498,662 respectively.
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can someone help right quick????
Answer: x≥48
Step-by-step explanation:
The length of a rectangle is 2 ft more than twice the width. The area is 84 ft2. Find the length and width of the rectangle.
Lenght
Width
Answer:
let width=x
length = x + 2ft
Area = 82ft^2
Area= length×width
=(x+2)x
=x^2 +2x=82
x^2+2x-82=0
Use Quadratic Equation to get x.
x = -10.1(reject, length cannot be minus value or 8.11)
x = 8.11
width = 8.11ft
length = 10.11ft
Suppose XY has one endpoint at X(0, 0).
What are the coordinates of Y if (5, 12) is
1/3 of the way from X to Y?
Answer:
step By step
First multiply 5 by 3 and multiply 12 by 3
Which is 15,36
Add to x endpoint to determine y endpoint which is (15,36)
Explain:
This multiplication is used to find full distance from the endpoints of XY
An automobile uses 17 gal of fuel to go 570 mi. how many gallons are required to travel 890 mi? (round your answer to one decimal place.)
The automobile needs 26.5 gallons of gas to reach 890 miles.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, An automobile uses 17 gallons of fuel to go 570 mi.
∴ The automobile requires (17/570) gallons of gas to reach 1 mile.
∴ To reach 890 miles the automobile needs (17/570)×890.
= 26.5 gallons of gas.
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