1.find the slope between these 2 points:(5,-5) and(3,-5)
2.find the slope between these two points:(2,3)and (4,5)
3.find the slope between the two points (-5,5)and (3,-5)
4.find the slope between these two points (9,9) and (12,15)
Answers
2. 2√2
3. 2√14
4. 3√5
I provided the distance formula and and example for you.
Final answer:
To find the slope between two points, use the formula m = (Y2 - Y1) / (X2 - X1) where (X1, Y1) and (X2, Y2) are the coordinates of the two points. The slopes for the given point sets are: 0, 1, -5/4, and 2.
Explanation:
To find the slope between two points, we can use the formula:
m = (Y2 - Y1) / (X2 - X1)
where (X1, Y1) and (X2, Y2) are the coordinates of the two points.
For the first set of points (5, -5) and (3, -5), the slope is:
m = (-5 - (-5)) / (3 - 5) = 0 / -2 = 0
For the second set of points (2, 3) and (4, 5), the slope is:
m = (5 - 3) / (4 - 2) = 2 / 2 = 1
For the third set of points (-5, 5) and (3, -5), the slope is:
m = (-5 - 5) / (3 - (-5)) = -10 / 8 = -5/4
For the fourth set of points (9, 9) and (12, 15), the slope is:
m = (15 - 9) / (12 - 9) = 6 / 3 = 2
Related Questions
Hazel has an assortment of red, blue, and green balls. The number of red balls is the number of blue balls. The number of green balls is more than the number of blue balls. In total, she has balls.
An equation created to find the number of blue balls will have?
Answers
When finding the number of blue balls in the scenario described, the equation will have x + x + x + 1 = 9, where x represents the number of blue balls.
An equation created to find the number of blue balls will have:
Let x be the number of blue balls.
The equation will be x + x + x + 1 = 9.
Solving the equation, we get x = 2.67.
Jimmy is a partner in an internet-based coffee supplier. The company offers gourmet coffee beans for $14 per pound and regular coffee beans for $7 per pound. Jimmy is creating a medium-price product that will sell for $9 per pound. The first thing to go into mixing bin was 18 pounds of the gourmet beans. How many pounds of the less expensive regular beans should be added?
Answers
To create a blend that sells for $9 per pound, when Jimmy has already added 18 pounds of the gourmet beans, he needs to add approximately 36 pounds of the regular coffee beans.
Explanation:This is a problem of mixtures in mathematics. Jimmy is attempting to create a new blend of coffee for his business that will have a price point between the regular beans and the gourmet beans.
First, let's understand the goal: A new blend worth $9 per pound. He has already added 18 pounds of gourmet beans which costs $14 per pound. To bring the overall cost down to $9 per pound, we need to add cheaper beans, worth $7 per pound.
Let's denote the weight of the regular beans needed as 'x'. We set up the equation based on weights and costs:
(18*$14 + x*$7) / (18 + x) = $9
Solving this equation, we find x to be around 36 pounds. So, Jimmy should add approximately 36 pounds of the regular beans to his mixture to reach the target price of $9 per pound.
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Jaws made his figure from six congruent squares the edge of each square was 8 inches which figure did Josh construct what is the surface area of his figure
Answers
Equipment was acquired at the beginning of the year at a cost of $75,720. The equipment was depreciated using the straight-line method based on an estimated useful life of six years and an estimated residual value of $7,920. What was the depreciation expense for the first year?
Answers
Final answer:
The annual depreciation expense for the equipment is calculated by subtracting the estimated residual value from the cost to find the depreciable base, and then dividing by the useful life. The first-year depreciation expense is $11,300.
Explanation:
To calculate the depreciation expense for the first year using the straight-line method, we first need to determine the depreciable base of the equipment. The depreciable base is the cost of the asset minus its estimated residual value. For the equipment mentioned, the cost is $75,720 and the estimated residual value is $7,920.
Depreciable base = Cost - Residual Value
= $75,720 - $7,920
= $67,800
Next, we divide the depreciable base by the useful life of the asset to calculate the annual depreciation expense:
Depreciation Expense = Depreciable base / Useful life
= $67,800 / 6 years
= $11,300 per year
Therefore, the depreciation expense for the first year is $11,300.
Why do the functions f(x) = sin−1(x) and g(x) = cos−1(x) have different ranges?
Answers
For a function to have an inverse function, it must be one-to-one—that is, it must pass the Horizontal Line Test.
1. On the interval [–pi/2, pi/2], the function y = sin x is increasing
2. On the interval [–pi/2, pi/2], y = sin x takes on its full range of values, [–1, 1]
3. On the interval [–pi/2, pi/2], y = sin x is one-to-one
sin x has an inverse function on this interval [–pi/2, pi/2]
On the restricted domain [–pi/2, pi/2] y = sin x has a unique inverse function called the inverse sine function. f(x) = sin−1(x)
the range of y=sin x in the domain [–pi/2, pi/2] is [-1,1]
the range of y=sin-1 x in the domain [-1,1] is [–pi/2, pi/2]
1. On the interval [0, pi], the function y = cos x is decreasing
2. On the interval [0, pi], y = cos x takes on its full range of values, [–1, 1]
3. On the interval [0, pi], y = cos x is one-to-one
cos x has an inverse function on this interval [0, pi]
On the restricted domain [0, pi] y = cos x has a unique inverse function called the inverse sine function. f(x) = cos−1(x)
the range of y=cos x in the domain [0, pi] is [-1,1]
the range of y=cos-1 x in the domain [-1,1] is [0, pi]
the answer is
the values of the range are different because the domain in which the inverse function exists are different
In this exercise we want to explain why two more similar functions have different ranges, like this:
the values of the range are different because the domain in which the inverse function exists are different .
In this exercise we know that we are dealing with two distinct functions, like this:
What is the function of sine?The sine function is considered an odd function, as there is a symmetry in the graph with respect to the bisector of the odd quadrants. When a function is considered odd, we have that f (x) = -f (x), that is, sin (-x) = -sin (x).
What is the function of cosine?Cosine is a trigonometric function, used in a right triangle to define the ratio of the side adjacent to and the hypotenuse of this triangle.
So we can see that the reason the two functions have different ranges is associated with them having different domains.
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What is the equation of this circle in general form?
x² + y² + 8x + 10y + 25 = 0
x2+y2−8x−10y+25=0
x2+y2−8x−10y+37=0
x² + y² + 8x + 10y + 37 = 0
Answers
The equation of a circle is:
[tex](x - xo) {}^{2} + (y - yo) {}^{2} = r {}^{2} [/tex]
(x+4)²+(y+5)²=4²
x²+8x+16+y²+10y+25=16
Simplify 16:
x²+y²+8x+10y+25=0
Tis the actual answer :)
In a certain class 40% of students are girls and 20% of the girls wear glasses what percent of the children in the class a girl who wear glasses?
Answers
40/100 students are girls.
20% of those 40 girls wear glasses.
So that's 20/40.
20/100
The percentage of the children in the class who is a girl and wears glasses is 8%.
Given that:
Total students in the class = 100%
Percentage of students in the class who are girls = 40%
Percentage of girls who wear glasses = 20%
It is required to find the percentage of students in the class who are girls wearing glasses.
This can be found as:
P = 40% × 20%
= 0.4 × 0.2
= 0.08
Now 0.08 in terms of percentage is 0.08 × 100 = 8%.
Hence the percentage of girls who wear glasses is 8%.
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Jenny has $25 and she earns $10 for each lawn that she mows. Jenny wants to buy a concert ticket that costs $65. Enter the minimum number of lawns Jenny needs to mow to be able to buy the concert ticket. $$
Answers
Answer:
4 Lawns
Step-by-step explanation:
Jenny wants to buy a concert ticket that costs = $65.00
Jenny has $25.00.
She needs more to buy a concert ticket = 65 - 25 = $40.00
For each lawn that she mows she earns = $10.00
For $40 she needs to mow = 40 ÷ 10 = 4 lawns
Jenny needs to mow 4 lawns to be able to buy the concert tickets.
Need the rate of change!!!
Two points: (30, 14) and (34, 17)
Answers
rate of change is 3/4
The lines shown below are parallel. If the green line has a slope of -2, what is the slope of the red line?
Answers
therefore their slope is the same.
If the green line has a slope of -2, then the red line must have a slope of -2 too.
Ans: -2
A class has 50 students. use the third row of digits in the random number table below to select a simple random sample of three students. if the students are numbered 01 to 50, what are the numbers of the three students selected
Answers
To select a simple random sample of three students from a class of 50 students using the third row of digits in the random number table, you would use the digits in the third row to determine the numbers of the selected students.
Explanation:To select a simple random sample of three students from a class of 50 students using the third row of digits in the random number table, you would start by numbering the students from 01 to 50.
Then, you would use the digits in the third row of the random number table to select the students.
For example, if the digits in the third row are 579362814, you would select the students with the corresponding numbers: 05, 79, and 36.
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simplify the expression given below
Answers
Photomath is a great app to use for algebra problems.
Step 1:
Cross product for sum of fractions.
Step 2:
Rewrite the expression Adding and subtracting terms from the same grade.
Step 3:
Simplify expression.
Answer
Option 4
See attached image.
Lamar purchased n notebooks. They were 5 dollars each. Write an equation to represent the total cost c that Lamar paid.
Answers
Where N = notebooks bought and C = total cost
A building in san fransico is shaped like a square pyramid. It has a slant height of 856.1 feet and each side of its base is 145 feet long. Find the lateral area of the building.
Answers
where
l is base length
w base width
h is height
given that the slant side of our pyramid is 856.1 ft with square base of 145 ft, the height of the pyramid will be found by Pythagorean theorem.
c²=a²+b²
hence:
856.1²=a²+72.5²
a=853.025 ft
The Lateral area is therefore going to be:
A=145√[(145/2)²+856.025²+145]+145√[(145/2)²+856.025²]
A=249,136.0025 ft²
Does the graph represent a function that has an inverse function?
A. Yes
B. No
Answers
Answer: A. Yes.
Step-by-step explanation:
To find out if the function represented in the graph has an inverse function, you must apply the Horizontal Line Test, which is used to know if a function is a One-to-one function.
A one-to-one function is that function where each x value has an unique y value.
Therefore, if in the Horizontal Line Test, the horizonal intersects the graph of the function at only and only one point, then the function has an inverse function.
As you can see in the graph attached, the horizontal lines intersect the function at only one point, therefore, you can conclude that it is a One-to-one function and it has an inverse function.
TRUE. The graph represents a function that has an inverse function because it passes the horizontal line test.
Explanation:The graph represents a function that has an inverse function if and only if each horizontal line crosses the graph at most once. This is known as the horizontal line test. If a function passes the horizontal line test, then it has an inverse function. If it fails the horizontal line test, then it does not have an inverse function.
In this case, we can see that the graph passes the horizontal line test because each horizontal line intersects the graph at most once. Therefore, the graph represents a function that has an inverse function.
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Find equations for the tangent plane and the normal line at point upper p 0(3 comma 5 comma 0) on the surface negative 7 cosine left parenthesis pi x right parenthesis plus 3 x squared y plus 5 e superscript xz baseline plus yz equals 147.
Answers
Which shows a correct order to solve this story problem? Kent and Curtis went to the state fair. They had to pay a total of $7.18 sales tax on everything they bought. They spent $22.50 for each admission ticket and $35.50 altogether for food. They split all the costs evenly. How much did each boy pay? A. Step 1: Calculate the price of 2 admission tickets. Step 2: Add that amount to the amount spent on food and the tax. Step 3: Divide by 2. B. Step 1: Double the amount for 1 admission ticket. Step 2: Take half of the amount spent on food and add the total from Step 1 plus the tax. Step 3: Divide by 2. C. Step 1: Add $22.50 and $35.50. Step 2: Divide the total by 2. Step 3: Add the amount of the tax.
Answers
S = Sales Tax = $ 7.18 per any purchase
A = Admission Ticket = $ 22.50 entry price for one person (no tax applied)
F = Food = $ 35.50 purchases for two people
We know the cost for one person was: (22.50) + [(35.50/2) + 7.18] =
$ 47.43 per person. Now we can check each method and see which one is the correct algorithm:
Method A)
[2A + (F + 2S)] / 2 = [ (2)(22.50) + [35.50 + (2)(7.18)] ]/ 2 = $47.43
Method A is the correct answer
Method B)
[(2A + (1/2)F + 2S) /2 = [(2)(22.50) + 35.50(1/2) + (2)7.18] / 2 = $38.55
Wrong answer. This method is incorrect because the tax for both tickets bought are not being used in the equation.
Method C)
[(A + F) / 2 ]+ S = [(22.50 + 35.50) / 2 ] + 7.18 = $35.93
Wrong answer. Incorrect Method. The food cost is being reduced to the cost of one person but admission price is set for two people.
suppose a triangle has two sides of length 2 and 3 and that the angle between these two sides is pi/3. what is the length of the third side of the triangle
Answers
c²=b²+a²-2ba cosC
C= pi/3 = 180/3 = 60 degrees
cosine 60 deg = 0.5
c²=2²+3²-[2×2×3×0.5]
c²=7
c=√7
c=2.645 ;length of third side of angle
The length of the third side of the triangle will be 2.65 units.
What is law of cosine?Let there is a triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle C, then we have:
a² + b² – 2ab cos(C) = c²
A triangle has two sides of length 2 and 3 and that the angle between these two sides is π/3.
Then the length of the third side of the triangle will be
c² = 2² + 3² – 2 x 2 x 3 x cos(π/3)
c² = 4 + 9 – 12 x (1/2)
c² = 13 – 6
c² = 7
c = √7
c = 2.65 units
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In 33,294 how is the value of the 3 in the ten thousands place related to the value of the 3 in the thousands place ?
Answers
in the number 33,294
3 3 2 9 4
║ ║ ║ ║ ║
ten thousands thousands hundreds tens ones place
place place place place
therefore
3 in the ten thousands place is---------------> 30000
3 in the thousands place is----------------> 3000
so
30000/3000=10
the answer is 10 times higher
The value of the 3 in the ten thousands place is 30,000, while the value of the 3 in the thousands place is 3,000. The value of a digit in a place depends on its position in the number.
Explanation:The value of the 3 in the ten thousands place in 33,294 is 30,000. The value of the 3 in the thousands place is 3,000. The value of a digit in a place depends on its position in the number. In this case, the 3 in the ten thousands place is ten times greater than the 3 in the thousands place.
A trading token is in the shape of a trapezoid and has an area of 25 square centimeters. If the bases are 3 and 7 centimeters, What is the height of the token
Answers
Answer:
5 cm
Step-by-step explanation:
The formula for the area of a trapezoid gives a relation that can be used to find the height.
A = 1/2(b1 +b2)h . . . . b1, b2 are base lengths, h is the height
__
Filling in the given information, we have ...
25 cm² = 1/2(3 cm +7 cm)h
25 cm²/(5 cm) = h = 5 cm . . . . . . . divide by the coefficient of h
The height of the token is 5 cm.
find the mean and median of these numbers 14, 3, 15, 4, 3, 11
Answers
what is the perimeter of a right trianglr whose hypotenuse is the line segment A(-6,4) B(2,-1)
Answers
[tex]\text { Length of hypotenuse = } \sqrt{(-6-2)^2 + (4-(-1))^2} [/tex]
[tex]\text { Length of hypotenuse = } \sqrt{64 + 25} [/tex]
[tex]\text { Length of hypotenuse = } \ 9.43 \text { units}[/tex]
height = | 4 - (-1)|= 5 units
Base = |-6 -2| = 8 units
Perimeter = 9.43 + 5 + 8 = 22.43 units
---------------------------------------------
Answer: Perimeter = 22.43 units
---------------------------------------------
A jogger ran 3 miles due east of his house. then he ran 5 miles at a heading of 30o east of north (or 30o ne). how far is he from his house after running 8 miles
Answers
We want to find how far is the jogger from his house after he runs a total of 8 miles, we will see that the distance is equal to 7 miles.
So we need to define a coordinate axis, the point (0, 0) will be the jogger's house (where he/she starts). North is the positive y-axis and East is the positive x-axis.
Then the jogger starts at (0, 0).
Then he ran 3 miles due East, so the new position is:
(0, 0) + (3mi, 0) = (3mi, 0)
Then he ran 5 miles at 30° East of North (or 60° North of East).
The components are:
x-component = 5mi*cos(60°) = 2.5 miy-component = 5mi*sin(60°) = 4.33 miThen the new position is:
(3mi, 0) + (2.5mi, 4.33 mi) = (5.5mi, 4.33 mi)
The distance to the jogger's house is just the magnitude of that final vector, which is:
|| (5.5mi, 4.33 mi) || = √( (5.5mi)^2 + (4.33mi)^2) = 7mi
So the jogger is at 7 miles from his/her house.
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The jogger is approximately 5.83 miles away from his house at a heading of 51.83° northeast after running 8 miles.
Explanation:To find how far the jogger is from his house after running 8 miles, we need to calculate the resultant displacement. The jogger ran 3 miles due east, so his displacement in the east direction is 3 miles. Then, he ran 5 miles at a heading of 30° east of north (or 30° NE). We can split this displacement into the north and east components. The east component can be calculated as 5 miles * cos(30°) = 5 miles * 0.866 = 4.33 miles. The north component can be calculated as 5 miles * sin(30°) = 5 miles * 0.5 = 2.5 miles.
To calculate the resultant displacement, we can use the Pythagorean theorem. The east and north components form a right triangle, with the resultant displacement as the hypotenuse. The magnitude of the resultant displacement can be found as √(3^2 + 4.33^2 + 2.5^2) = √(9 + 18.7489 + 6.25) = √33.9989 = 5.83 miles. The direction of the resultant displacement can be found using trigonometry. tan(θ) = opposite/adjacent = (2.5 miles + 3 miles)/(4.33 miles) = 5.5/4.33. Taking the arctan of both sides, θ = arctan(5.5/4.33) = 51.83°. Therefore, the jogger is approximately 5.83 miles away from his house at a heading of 51.83° northeast.
lindsey earn $70 for working 5 hours. how much does she earn for working 12 lawns?
Answers
Answer $ 168
as per the question,
money earned for working 5 hours = 70
money earned for working 1 hour = 70/5= 14
money earned for working 12 hours = 12 * 14
money earned for working 12 hours = $168
Factorise x^2 + 3x -40
Answers
[tex]\bf x^2\stackrel{8-5}{+3}x\stackrel{(8)(-5)}{-40}\implies (x+8)(x-5)[/tex]
Math question
Algebra 2, Fundamental Theorem of Algebra, Stste the number of complex roots and the possible number of real and imaginary roots for each equation. Then find all roots. One root has been given.
x^6 - 3x^5 + 2x^4 - 6x^3 - 15x^2 + 45x = 0; 3
(if possible please provide work)
Answers
The signs from the original equation are: + - + - - +. 3 sign changes mean that there are either 3 or 1 positive roots.
If we change the signs of the odd-powered terms: + + + + - -. This 1 sign change means that there is exactly 1 negative root.
All roots:
We can immediately factor out x from the equation:
x (x^5 - 3x^4 + 2x^3 - 6x^2 - 15x + 45) = 0
Factor out (x-3) since x = 3 is a root:
x (x - 3) (x^4 + 2x^2 - 15) = 0
Factor the last term further:
x (x - 3) (x^2 - 3) (x^2 + 5) = 0
This allows us to determine the rest of the x-values:
x = 0, 3, sqrt3, -sqrt3, i*sqrt5, i*-sqrt5
Will someone please do number 8 for me ?
Answers
18/16 = 1.125
they are not similar
A farmer wishes to fence a rectangular area behind his barn. The barn forms one end of the rectangle and the length of the rectangle is three times the width. How many linear feet of fence must he buy if the perimeter of the rectangle is 320 feet?
Answers
Final answer:
The farmer needs to buy 320 linear feet of fence to enclose the rectangular area behind his barn.
Explanation:
Let's represent the width of the rectangle as x. Since the length is three times the width, we can represent the length as 3x. The perimeter of a rectangle is calculated by adding up all four sides, so we have the equation:
2(x + 3x) = 320
Simplifying, we get:
2(4x) = 320
8x = 320
x = 40
So the width of the rectangle is 40 feet, and the length is 3 times that, which is 120 feet. The perimeter is calculated by adding up all four sides: 40 + 120 + 40 + 120 = 320 feet. Therefore, the farmer needs to buy 320 linear feet of fence.
The sun is 25 degrees above the horizon. find the length of a shadow cast by a building that is 100 feet tall. round your answer to two decimal places. the length of the shadow is ____ feet.
Answers
214.45 feet
Explanation
The sun is 250 above the horizon. This means that the angle of elevation is 25o.
Since you have been given the height of the building, you can use the trigonometric ratio (tangent) to find the length of the shadow (l).
tan〖= 〗 oposite/adjacent
tan25=100/l
l=100/tan25 =214.4506921
Length of the shadow = 214.4506921 feet
Answer:
214.45 feet.
Step-by-step explanation:
Please find the attachment.
Let x be the length of building's shadow.
We have been given that the sun is 25 degrees above the horizon. The length of the building is 100 feet tall.
We can see from our attachment that the length of the building is opposite side and the length of the shadow is adjacent side for the angle of 25 degrees.
Since tangent relates the opposite side of right triangle with adjacent side, so we can set an equation to find the length of building's shadow as:
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
[tex]\text{tan}(25^{\circ})=\frac{100}{x}[/tex]
[tex]x=\frac{100}{\text{tan}(25^{\circ})}[/tex]
[tex]x=\frac{100}{0.466307658155}[/tex]
[tex]x=214.45069\approx 214.45[/tex]
Therefore, the length of shadow cast by the building is 214.45 feet.
when is a rectangle a square?
a) when its sides are parallel
b) when its angles are right angles
c) when its sides are congruent
d) when its angles are convex angles
Answers
A rectangle becomes a square when all of its sides are congruent, which is the defining characteristic that differentiates it from a rectangle. While rectangles do share other attributes such as parallel sides, right angles, and convex angles, these do not specifically define a square.
A rectangle becomes a square when all of its sides are congruent. This by definition means that all four sides of the shape are of equal length. While rectangles do have parallel sides and right angles, these characteristics alone do not suffice to differentiate a square from a rectangle, as rectangles also have these attributes. In the case of convex angles, both squares and rectangles have angles that are convex, so this also cannot be used to distinguish a square from a rectangle.
To specifically address the options provided:
a) when its sides are parallel: This is true for both rectangles and squares, but it doesn't make a rectangle a square.b) when its angles are right angles: Again, both shapes share this characteristic so it doesn't define a square specifically.c) when its sides are congruent: This is the defining characteristic of a square compared to a rectangle.d) when its angles are convex angles: Both rectangles and squares have convex angles, so this does not define a square.Therefore, the most accurate answer is (c) when its sides are congruent.