The slope of line containing the points (-2, 5) and (4, -4) is [tex]\frac{-3}{2}[/tex].
What is slope of the line?A slope of a line is the change in y coordinate with respect to the change in x coordinate.
What is the formula for finding the slope of line from two points?[tex]m = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
Where,
m is the slope of line.
[tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2},y_{2})[/tex] are the two points.
According to the given question.
We have two points (-2,5) and (4,-4).
Therefore, the slope of the line containing the points (-2, 5) and (4, -4) is given by
[tex]m = \frac{-4-5}{4-(-2)}[/tex]
⇒[tex]m = \frac{-9}{6}[/tex]
⇒[tex]m =\frac{-3}{2}[/tex]
Hence, the slope of line containing the points (-2, 5) and (4, -4) is [tex]\frac{-3}{2}[/tex].
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What is the solution of the equation when solved over the complex numbers?
x^2+24=0
x =
or x =
Find the 5th term of the expansion of (x + y)9.
What is a equation of the graph of the equation below translated down 3 units y=-x^2
if -7k=-42, then k=6
Identify the graph of 4+2i. Is the point at (2,4), (4,2), (4,-2), or (-4,2)?
The graph of the complex number 4 + 2i corresponds to the point (4, 2) on the complex plane, with 4 as the real part and 2 as the imaginary part.
To identify the graph of the complex number 4 + 2i, you can think of it as a point on the complex plane. In the complex plane, the horizontal axis represents the real part of a complex number, and the vertical axis represents the imaginary part. So, for the complex number 4 + 2i, the real part is 4, and the imaginary part is 2.
Now, let's locate this point on the complex plane:
The real part (4) corresponds to the horizontal axis.
The imaginary part (2) corresponds to the vertical axis.
So, the point (4, 2) on the complex plane represents the complex number 4 + 2i. Therefore, the correct answer is (4, 2).
In summary, the graph of the complex number 4 + 2i corresponds to the point (4, 2) on the complex plane, where 4 is the real part, and 2 is the imaginary part.
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A rose garden is designed by joining a rectangle and a semicircle, as shown below. The rectangle is 24ft long and 18ft wide. If the gardener wants to build a fence around the garden, how many feet of fence are required?
According to the given rectangle, approximately 112.27 feet of fence are required to enclose the rose garden.
The perimeter of a rectangle is the sum of all its sides. In this case, the rectangle has two sides of length 24 feet and two sides of length 18 feet.
Therefore, the perimeter of the rectangle can be calculated as follows:
Perimeter of rectangle = 2 * (Length + Width)
= 2 * (24 ft + 18 ft) = 2 * 42 ft = 84 ft.
The circumference of a circle can be calculated using the formula:
Circumference = π * Diameter.
Diameter of the Semicircle: The diameter of the semicircle is equal to the width of the rectangle, which is 18 feet.
Circumference of the Semicircle: Using the formula mentioned above:
Circumference = π * 18 ft
≈ 56.5487 ft (rounded to four decimal places).
Perimeter of the Semicircle: As it is a semicircle, we only need half of the circumference:
Perimeter of semicircle = Circumference / 2
≈ 56.5487 ft / 2 ≈ 28.2744 ft (rounded to four decimal places).
Total Fence Length Required: Now, we add the perimeter of the rectangle and the semicircle to find the total length of fence required to enclose the rose garden:
Total fence length = Perimeter of rectangle + Perimeter of semicircle
= 84 ft + 28.2744 ft ≈ 112.2744 ft (rounded to four decimal places).
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Suppose your friend says the line y=-2x +3 is perpendicular to the line x+2y=8. Do you agree? Explain.
-19.78 is rational or irrational
Tarting at home, Emily traveled uphill to the hardware store for 60 minutes at just 6 mph. She then traveled back home along the same path downhill at a speed of 12mph. What is her average speed for the entire trip from home to the hardware store and back?
to construct a line parallel to a given line m to a point not on m, you need to know how to construct_______angles?
A. right
B. acute
C. congruent
D. obtuse
The hypotenuse of a right triangle is 20 centimeters, and the shorter leg is 12 centimeters. Find the length of the other leg. 2 cm 4 cm 16 cm
The length of the other side is : 16cm
What is a right-angled triangle?A right-angled triangle is a triangle with one of its angle 90 degrees and has two adjacent sides and a hypotenuse which is the longest side.
Analysis:
Since it is a right-angled triangle, we use Pythagoras theorem
[tex]hypotenuse^{2}[/tex] = [tex]opposite^{2}[/tex] + [tex]adjacent ^{2}[/tex]
hypotenuse = 20cm, opposite = 12cm, adjacent = xcm
[tex]20^{2}[/tex] = [tex]x^{2}[/tex] + [tex]12^{2}[/tex]
[tex]x^{2}[/tex] = 400 - 144
[tex]x^{2}[/tex] = 256
x = [tex]\sqrt{256}[/tex] = 16cm
In conclusion, the length of the other side is 16cm
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What does y=mx+b the m mean?
A man invested $500 in the stock market. During the first week, he gained $200. During the second week, the market was strong and the man doubled his money. During the third week, stocks fell, and the man lost $650. How much money did the man have at the end of three weeks?
What is the answer to John bought a video game on sale for $35. The original price of the game was 3 times that amount. John also bought video game controllers on sale for $28. The original price of the game controllers are 5 times that amount. Together how much money did the video game and controllers cost before they went on sale?
What is the value of the function at x=−3?
Answer:
correct answer is 4
Step-by-step explanation:
Can someone please explain the concept of Algebra? Just give me some basic tips so I can solve questions like the ones in the picture. Thanks in advance!
HELLO,
FORMULA: Ax+By=C
The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, $5,050 is collected. If 1,000 adults attended the fair, write and solve a linear equation to find the number of children that attended
ANSWER IN STANDARD FORM!
AND IF YOU ARE GOING TO ANSWER JOSEPH OR JURGEON I NEED AN HONEST ANSWER WITH EXPLANATION!
x = children
y = adults
1.50x +4.00y =5050
y = 1000
1.50x + 4.00(1000) = 5050
1.50x +4000.00 = 5050
1.50x= 1050
x = 1050 / 1.50 = 700 children atttended
The prime factorization of a number n can be written as n=pr whose p and r are distinct primes. how many factors does n have not including 1.
The total number of factors for a number 'n' with prime factorization [tex]n = p^r * q^s * ... * z^w[/tex] (where 'p', 'q', ..., 'z' are distinct primes and 'r', 's', ..., 'w' are their respective powers) is equal to (r + 1) * (s + 1) * ... * (w + 1).
When we have the prime factorization of a number, determining its total number of factors is a straightforward process. The number of factors of 'n' can be found by considering the powers of its prime factors.
Let's take an example to illustrate this. Consider the number 'n' with prime factorization:
[tex]n = p^r * q^s * ... * z^w,[/tex]
where 'p', 'q', ..., 'z' are distinct prime numbers, and 'r', 's', ..., 'w' are their respective powers.
To find the total number of factors for 'n', we need to consider all possible combinations of its prime factors. For any factor of 'n', we can choose to include 'p' raised to a power ranging from 0 to 'r', 'q' raised to a power ranging from 0 to 's', and so on, for all the distinct primes.
The total number of factors can be calculated using the formula:
(r + 1) * (s + 1) * ... * (w + 1)
This formula works because for each prime factor 'p', we have 'r + 1' options for its power, and similarly for other prime factors. By multiplying all these options, we get the total number of factors.
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What’s the measure of LMF
LMF = 17x
so 17x + 3x =180
20x = 180
x = 180/20 = 9
17 *9 = 153
angle LMF = 153 degrees
In an isometric transformation, the preimage and image must not __________. A. change size B. rotate C. preserve angle measures D. reflect across the x axis Please select the best answer from the choices provided A B C D
Frank and Latoya each ran every day as part of an exercise routine. Frank ran
3 miles each day for x days. Latoya ran 5 miles each day for y days.
The total number of miles that Frank ran is at least the total number of miles that Latoya ran. Write an inequality describing this relationship.
What is the area of The shaded sector of the circle
Answer: 27[tex]\pi[/tex] [tex]unit^{2}[/tex]
Step-by-step explanation: area of circle =[tex]\pi r^{2}[/tex]
where r is the radius of circle
here r=9
to find the area of circle we cover an angle of 360° but here we have to cover only 120°=360°÷3
so area of shaded region =area of circle÷3
=[tex]\pi[/tex]×9×9÷3
=27[tex]\pi[/tex] [tex]unit^{2}[/tex]
For what values of k does the function y = cos kt satisfy the differential equation 4y'' = −9y? (enter your answers as a comma-separated list.)
The values of k that satisfy the equation 4y'' = -9y for the function y = cos kt are k = ±3/2.
Explanation:This is a question in differential equations, where we are given a cosine function y = cos kt and asked to find values of k that satisfy the given equation 4y'' = −9y.
Recall, the second derivative of cos kt is -k²cos kt which is equivalent to -k²y.
Substituting that into the differential equation, we get 4(-k²y) = -9y. If we simplify this, we get k² = 9/4. Therefore, the values of k which satisfy the given equation are k = ±3/2.
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The values of k that satisfy the differential equation 4y'' = −9y are k = ±3/2.
We can find the values of k that satisfy the differential equation 4y'' = −9y by solving for k.
First, we can rewrite the differential equation in its general form:
ay'' + by' + cy = 0
where a = 4, b = 0, and c = -9.
Next, we can find the characteristic equation:
ar^2 + br + c = 0
Plugging in the values of a, b, and c, we get:
4r^2 + 0r - 9 = 0
Solving for r, we get:
r = ±3/2
Therefore, the general solution to the differential equation is:
y = Acos(3t/2) + Bsin(3t/2)
where A and B are arbitrary constants.
Finally, we can substitute y = cos kt into the original differential equation and solve for k:
4k^2cos kt + 9cos kt = 0
Dividing both sides by cos kt, we get:
4k^2 + 9 = 0
Solving for k, we get:
k = ±3/2
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Evaluate 4-(3+2)^2
A. -21
B. -9
C. 5
D. 1
A prepaid cell phone charges a preset number of minutes to use text messaging. The graph represents y, the number of minutes used for x, the number of text messages sent and received. Is there a direct variation? Which equation represents the relationship? Yes, y = 2x. Yes, y = 20x. No, y = x + 10. No, y = x + 20.
Answer:
Yes, y = 2x
Step-by-step explanation:
I took it on edge and got it right!!!
There will be definitely a direct relation and the relation will be y = 2x.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b, will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Proportion is very useful to set relations between variables.
Given that the prepaid cell phone charges a preset number of minutes to use text messaging. The graph represents y, the number of minutes used for x, and the number of text messages sent and received
so it is clear that cell phone charge upon the number of minutes to use text messaging hence y = 2x will be the correct answer.
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After the police track the monkey and his kidnapper for a while, something changes. After one hour, the location is 32 miles away from the zoo. But after 70 minutes, or 76 hours, the location is still 32 miles away. Write an equation in point-slope form that represents the distance of the monkey and kidnapper, assuming they are still traveling in a linear pattern.
What is the least possible integer value for which 40% of that integer is greater than 9.6?
A recipe for a batch of cookies calls for 2 1/3 cups of flour for 24 cookies. Manuel wants to make 72 cookies. How many cups of flour does he need
Simplify the expression shown.3x + 2 – 3x + 7 +5xwhat is the coefficient in the simplified expression?
The expression 3x + 2 - 3x + 7 +5x simplifies to 5x
when the terms containing variable 'x' are combined. Therefore, the coefficient in the simplified expression is 5.
Explanation:The given expression is 3x + 2 – 3x + 7 +5x.
To simplify this expression, we need to combine like terms, which in this case are terms with x.
The like terms are 3x, -3x, and 5x. When added together, they simplify to: 3x - 3x + 5x = 5x.
The number part of the term, excluding x, is referred to as the coefficient. So the coefficient of x in this simplified expression is 5.
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Lori sold 3 times as many raffle tickets as tony. lori sold 24 tickets. how many more raffle tickets did lori sell than tony?
Answer:
Your Answer is C) 16
Step-by-step explanation:
Step 1: Find the number Tony sold.
24 ÷ 3 = 8
Step 2: Find how many more tickets were sold by Lori than Tony.
24 - 8 = 16
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