The linear equation that passes through these two points is:
y = -4x
How to find the equation for the line?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that the line passes through two known points (x₁, y₁) and (x₂, y₂), then we can write the slope as:
a = (y₂ - y₁)/(x₂ - x₁)
Here we know the two points (-2, 8) and (5, -20), so the slope is:
a = (-20 - 8)/(5 + 2) = -28/7 = -4
So the line is:
y = -4*x + b
To find the value of b, we can replace the values of the point (-2, 8), so we will get:
8 = -4*(-2) + b
Now we can solve this for b.
8 = -4*(-2) + b
8 = 4*2 + b
8 = 8 + b
8 - 8 = b
0 = b
Then the linear equation is:
y = -4*x
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Do the ratios 5/15 and 1/3 form a proportion?
Answer:
Step-by-step explanation:
We will check if 5/15 and 1/3 are in proportion or not by cross-multiplication.
5/15 = 1/3
5*3 = 15*1
15 = 15
as the left-hand side is equal to the right side. So, these fractions are in proportion.
A rare Pokemon trading card deck you have been wanting to buy costs 4500. You have earned 2485 from helping your mom in her online selling business. If you can save 155 weekly from your allowance, how many weeks would it take for your funds to reach 4500
It will take 13 weeks to gather funds that sum up to $4500.
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given: I have $2485 and I save $155 weekly
Thus amount left to be gathered is $4500-$2485=2015
If I save $155 weekly then we get = $2015/$155
=13 weeks
Hence, It will take 13 weeks to gather funds that sum up to $4500.
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What are the 3 steps to solving an equation?
Following are three steps 1. Isolate the variable: First, identify the variable you are trying to solve for and use the other terms in the equation to isolate that variable. This means using inverse operations to move any terms containing the variable to one side of the equation and any terms without the variable to the other side of the equation.
2. Simplify the equation: Once the variable is isolated, use the properties of equality and inverse operations to simplify the equation, if needed.
3. Solve the equation: Finally, use the inverse operations to solve the equation and find the value of the variable.
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Given the function p(x)=6x+2, compare and contrast p(-2) and p(4). Choose the statement that is true concerning these two values.
(A) The value of p(-2) is larger then the value of p(4).
(B) The value of p(-2) is smaller then the value of p(4).
(C) The value of p(-2) is the same as the value of p(4).
(D) The values of p(-2) and p(4) cannot be compared.
Given the function p(x)=6x+2, p(-2) is -10 while p(4) is 26, this shows that value of p(-2) is smaller than the value of p(4). The correct option is B.
What is a function?A function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). It is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets; mapping from A to B will be a function only when every element in set A has one end, only one image in set B.
p(x)=6x+2
for p(-2)
p(-2) = 6(-2) + 2
p(-2) = -12 + 2
p(-2) = -10
for p(4)
p(4) = 6(4) + 2
p(4) = 24 + 2
p(4) = 26
p(-2) < p(4)
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Answer:
(B) "The value of p(-2) is smaller then the value of p(4)" is True
Step-by-step explanation:
p(x)=6x+2
p(-2) = 6*(-2)+2
p(-2) = -12+2
p(-2) = -10
p(4) = 6*(4)+2
p(4) = 26
====
p(-2) = -10
p(4) = 26
===
(A) The value of p(-2) is larger then the value of p(4). False
(B) The value of p(-2) is smaller then the value of p(4). True
(C) The value of p(-2) is the same as the value of p(4). False
(D) The values of p(-2) and p(4) cannot be compared. False
What is the name of 3 side?
The three sides of a triangle are referred to as the base, the height, and the hypotenuse.
The base and height of a triangle can be used to calculate the area of the triangle using the formula:
Area = (Base x Height) / 2
To calculate the hypotenuse of a triangle, the Pythagorean Theorem is used. The theorem states that the sum of the squares of the lengths of the two sides of a right triangle is equal to the square of the length of the hypotenuse.
The formula for the Pythagorean Theorem is:
a2 + b2 = c2
where a and b are the two sides of the triangle and c is the hypotenuse.
To calculate the hypotenuse of a triangle, the following steps are taken:
1. Measure the length of each side of the triangle.
2. Square the length of each side (multiply the length by itself).
3. Add the two values together.
4. Find the square root of the sum. This is the length of the hypotenuse.
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Please answer quick! The question is in a file down below.
Answer:
perimeter= 9+9π cm
area= 40.5-10.125π cm²
Step-by-step explanation:
area of the square =9x9=81cm²
area of the two semicircles which have the same diameter =area of one circle
= (9÷2)²π =(81÷4)π
area of the whole shaded part = 81- (81÷4)π cm²
the area of each shaded part= (81-(81÷4)π)÷2
= 40.5-10.125π cm²
circumference of 2 semicircles= circumference of 1 circle = 2πr = 2x9xπ= 18π cm
then are perimeter of the whole shaded part = 18π+9+9= 18+18π cm
perimeter of each shaded part = (18+18π)÷2=
9+9π cm
Mike is saving money for a new bike that costs $180.00
If represents the amount of money he has saved so far, which expression represents the amount of money,in dollars, he still needs to save?
A
180+m180+m180+m
B
180−m180-m180−m
C
180×m180\times m180×m
D
180÷m180\div m180÷m
Answer: B
Step-by-step explanation:
B) 180−m180-m180−m
HELP !!!
write days in May and days in a year as a ratio
The ratio of days in May and days in a year is 31 to 365 or 31:365
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
We need to find the days in May and days in a year as a ratio
Therefore, Days in may = 31
Days in a year = 365
Thus, the expected ratio = 31/365
Or
31:365
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How many ways can a president, a vice-president and a secretary be chosen from 11 members of a club assuming that one person cannot hold more than one position
On solving the provided question, we can say that so, we apply permutation P(12,4) = 12!/ 8! = 11880
what is permutation?The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order. like in the case of.
so, we apply permutation
P(12,4) = 12!/ 8! = 11880
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WHAT IS 10000-22 CAN ANYONE HELP
Answer:
9978
Step-by-step explanation:
10000 - 22 = 9978
9978 is the answer
Answer: 9978
Step-by-step explanation:
Stack the numbers up like this 10000
22
borrow from the one make the zero a ten, and then borrow from that to make the next one and make it a nine and then do it to the last one and subtract. Hope this makes sense
The question is in the picture
Answer:
For the first line its distributive property
The 2nd is combining like terms
4th is simplifying it
Im not sure about the last one since its just the answer of the problem
Step-by-step explanation:
Please help asap!!!
Rotation of PQRS by 90 degree.
What does a math transformation mean?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's final shape and location. What are the four mathematical transformations?
In how many ways Transformations can be divided?Translation, rotation, reflection, and enlargement. You must be able to carry out each transformation and recognize which ones have already been done.
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Which expressions are equivalent to 8.5x + 0.5 + 3.5x -2x, A) 12x-2x, B) 10x + 0.5, C) 12-2x, D) 9x + 3.5 - 2x, E) 12x - 2x + 0.5
The given expression {8.5x + 0.5 + 3.5x - 2x} is equivalent to
10x + 0.5.
What are equations?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign "=".
Given is the expression as follows -
8.5x + 0.5 + 3.5x - 2x
The given expression is -
8.5x + 0.5 + 3.5x - 2x
(8.5x + 3.5x - 2x) + 0.5
12x - 2x + 0.5
10x + 0.5
Therefore, the given expression {8.5x + 0.5 + 3.5x - 2x} is equivalent to
10x + 0.5.
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I need to factor completely to get an answer for
n²-10n+24
I need to get factors in parenthesis like (n +/- #) (n +/- #)
I need it before tomorrow
Answer:
(n - 6)(n -4)
Step-by-step explanation:
Find two numbers that add to - 10 and multiply to +24.
In this case, -6 * -4 satisfies these requirements.
A lost tourist arrives at a point with 2 roads A and B. Road A leads to the city and takes either 4 or 8 hours, depending on traffic, with equal probability. Road B brings him to the city after 7 hours on average. Since there are no signs on the road, the tourist chooses a road with equal probability; what is the expected time until the tourist arrives to the city
The expected time until the tourist arrives in the city is 4.75 hours.
The expected time until the tourist arrives at the city can be calculated by using the formula for the expected value:
Expected value = (probability of outcome 1) x (value of outcome 1) + (probability of outcome 2) x (value of outcome 2) + ...
In this case, there are two possible outcomes: the tourist takes road A or road B.
If the tourist takes road A, the expected time until he arrives in the city is the average of the two possible travel times (4 hours and 8 hours). The probability of this outcome is 0.5 (the tourist has an equal chance of choosing either road). So, the expected value for this outcome is (0.5) x (4 + 8)/2 = 6 hours.
If the tourist takes road B, the expected time until he arrives in the city is 7 hours. The probability of this outcome is also 0.5. So, the expected value for this outcome is (0.5) x 7 = 3.5 hours.
To find the overall expected time until the tourist arrives in the city, we add up the expected values for each outcome:
Expected time = (0.5) x 6 + (0.5) x 3.5 = 4.75 hours
So the expected time until the tourist arrives in the city is 4.75 hours.
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(i) Six horses are each given 5 ml spoons of medicine three times each day.
Calculate the number of whole days a 2 L bottle of medicine will last.
Answer:22 days
Step-by-step explanation: since 6days are each given 5ml spoons of medicine three times a day,
Therefore consumption of each day is 90 ml and we have 2000 ml(2litre=2000 ml)
so, 2000/90 = we will get number of days
therefore 22.22 days
Which emplies 22 days.
Net of a square pyramid showing 4 triangles and the square base. The square base has side lengths of 3 inches. The height of each triangle attached to the square is 6 inches. The base of the triangle is the side of the square. What is the surface area of the solid? (1 point) a 18 square inches b 27 square inches c 36 square inches d 45 square inches
The correct option regarding the surface area of the solid is given as follows:
d. 45 square inches.
How to calculate the surface area?The surface area of a solid is composed by the sum of the areas of all the pars of the figure.
The composition of the figure in this problem is given as follows:
4 triangles of base 3 and height 6.One square of side length 3.Thea area of a triangle is given by half the multiplication of the base by the height, hence the area of the four triangles in this problem is given as follows:
At = 4 x 1/2 x 3 x 6
At = 36 square inches.
The area of a square is given by the square of the side length, hence:
As = 3³
As = 9 square inches.
Thus the surface area of the solid in this problem is given as follows:
S = At + As
S = 36 + 9
S = 45 square inches.
Meaning that option d is correct.
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what is 2.8 repeating as adecimal
Get the standard form and slope-intercept form
1. y -2 = 2/3 (x - 1)
2. y + 4 = - 4/5 (x+3)
Answer:
1. y-2=2/3(x-1) slope: y=2/3x+4/3 standard: 2x-3y=-4
Step-by-step explanation:
Identify a method of developing systems that is well-suited to traditional project management tools and technique
The waterfall model has equivalent flexibility to other approaches. suitable for conventional project management tools and methods.
The waterfall model of the software development life cycle is the greatest technique for creating systems.
This includes the following elements:
1. The requirements phase, which takes into account the needs needed to build the product
2. The product's design is created
3. The programmers who wrote the code to put the product into action built the product.
4. The product is examined and all flaws are fixed to ensure that it responds correctly to inputs.
5. The systems are periodically maintained to ensure continued operation and proper output
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Kayla had 20 candie. Kayla have 1/5 of the candie to her iter. Of the amount left , he gave 3/8 of her friend. How many candie doe Kayla have left for herelf ?
The candies left for Kyla were 10 based on the amount given to her sister and friend from total 20 candies.
Firstly we will calculate the remaining candies from twenty after giving to her sister. Next calculation will be the final answer representing candies left for Kyla herself.
Remaining candies = total number of candies - 1/5×total candies
Keep the values in formula
Remaining candies = 20 - 1/5×20
Remaining candies = 20 - 4
Remaining candies = 16
Total candies for Kyla = remaining candies - 3/8×remaining candies
Candies for Kyla = 16 - 3/8×16
Candies for Kyla = 16 - 3×2
Candies for Kyla = 16 - 6
Candies for Kyla = 10
Thus, Kyla received 10 candies.
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Tony performs a dilation on Figure R. He uses a scale factor of 4 with a center of dilation at the orgin.
What are the coordinates of the image of vertex P?
The x- coordinate of the vertex P is -4 and the y coordinate is -3. The coordinates of the image of vertex P is thus, (-4, -3).
What are coordinates?Coordinates are numbers describing the position of a point or shape in a line or particular space. We can represent a line or shape in the space between number lines with both positive and negative coordinates.
The vertical axis in the number line is called y-axis and the horizontal axis is called the x- axis. The coordinate of a point is written as (x, y). The x, y represents the numbers on x-axis and y -axis touched at which the point lies in the graph.
For the given vertex P, the vertex lies on the point -4 on x-axis and on -3 in y axis. Hence, the coordinate of P is (-4, -3).
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The Jackson family is planning a weekend vacation. They plan to rent a car from the ABC Car Rental Company. Let m represent the number of miles the family will drive. Let c represent the cost for renting a car. Write an equation that shows what the cost for renting a car will be.
Weekend Special: $40 + $0. 10 per mile
An equation that shows what the cost of renting a car will be: C=R+mc.
Let the rental cost = R
consider m to be the number of miles driven= m
let c be the cost per mile
And C is the total cost of renting;
Then C = R+mc
the given equation $40 + $0. 10 per mile
Now, in the above equation consider:
R =$40 ( the rental cost)
c = $0.10 ( the cost per mile)
The total cost is C = $40+$0.10m
Ex:
if m is known assume m=1000 miles
Then the total cost C = $40+($0.10/mile)(1000miles)
then C = $40+$100=$140
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What will be the output of 7 by 2?
The resultant output of the given question is 7 by 2 is 14.
This is because 7 multiplied by 2 is equal to 14
When you multiply two numbers, the result is the product of the two numbers. In this case, 7 multiplied by 2 is equal to 14.
Mathematicians use the process of multiplication to calculate the product of two or more given numbers. It is a fundamental mathematical operation in maths that is frequently utilised in everyday life. When we need to combine groups of similar sizes or values , we utilise multiplication.
Hence the correct answer to the given question is 14 .
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What is the best definition of a decimal?
A) Decimals are ratios out of one hundred
B) Decimals are whole counting numbers
C) Decimals are ratios relating one integer to another
D) Decimals are integers followed by a decimal point and a number less than one
Answer:
D
Step-by-step explanation:
I think it would be D hope this helps!
The best definition of a decimal is decimals are whole counting numbers.
How can we express numbers belonging to decimal numeral system?Suppose that the number is abcdefg and belongs to the decimal numerical system.
Remember one thing that the place on the left of decimal point is called ones. Move one-one places to right, and divide by 10 and 10 more and more.
Move one-one places to left, and multiply (un-divide) by 10 and 10 more and more.
Thus, we write abcd.efg as:
[tex]a \times 10^3 + b \times 10^2 + c \times 10^1 + d \times 10^{0} + e \times 10^{-1} + f \times 10^{-2} + g \times 10^{-3}[/tex]
We will call d as ones digit, c as tens digit (it get multiplied by 10), b as hundreds digit etc.
We call e as digit at 10th place (division by 10), f as digit at hundredth place and so on.
Therefore, the definition will be Decimals are whole counting numbers,
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Each root of x^2 - bx + c = 0 is decreased by 2. The resulting equation is x^2 - 2x + 1 = 0, then
(a) b= 6 , c = 9 (b) b = 3 , c = 5
(c) b=2 , c = -1 (d) b = -4 , c = 3
When the root of x²-bx+c = 0 is decreased by 2, the resulting equation is x²-2x+1, then b = 2 and c = 1
What is root of quadratic equation?The values of variables satisfying the given quadratic equation are called its roots.
if the roots of a quadratic equation ax²+bx+c = 0 are alpha and beta
alpha + beta = -b/a and
alpha × beta = c/a
when the roots are reduced by 2
alpha-2+ beta-2 = -b/a
(alpha+beta)-4 = -b/a
alpha+ Bata = -b/a + 4
the resulting equation is x²-2x+1 = 0
a = 1, b = -2 and c = 1
therefore alpha +beta = -b/a = -(-2)/1 = 2
therefore 2 = -b/a+4
a = 1
2 = -b+4
b = 4-2 = 2
alpha×beta = c/a = 1/1
(alpha -2)× ( beta -2) = (alpha)( beta) -2(alpha+beta) + 4 = 1-2(2)+4 = 1
therefore b = 2 , c = 1
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Graph the line that passes through the points (8, -3) and (4, 1) and
determine the equation of the line.
Answer:
y = -x + 5
Step-by-step explanation:
The equation is y= mx + b
m = the slope or rise/run or (y2 - y1) / (x2 - x1)
b = y-intercept
The slope here is -1, and the y-intercept is 5, so our equation is
y = -x + 5
Sangeeta divide R 40000 between her two daughterRimmy and Simmi in the ratio 3:5 Find the hare of each daughter
share of rimmy and simmi is rs15000 and rs25000.
this question is of ratio and proportion, and the solution is as follows,
total amount = rs 40000
Rimmy and Simmi in the ratio = 3:5
sum of shares= 3+ 5 = 8.
so,
share of Rimmy is = 3/8 X 40000
= 120000/8
= 15000
share of simmi is = 5/8 X 40000
= 200000/8
= 25000
so the share of rimmy and simmi is rs15000 and rs25000.
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The average monthly salary of 10 male staffs and 5 female staffs of a manufacturing company are Rs. 20,000 and Rs. 18,000 respectively. Find the average monthly salary of all staffs taken together.
The average monthly salary of all the staff is going to be 19,333.34 ₹.
Average is the value obtained by dividing the sum total of a set of figures by the number of figures. In this question, we have to find the average monthly salary of all the staff taken together,
So the sum total of the set of figures here will be (20,000 × no. of males + 18,000 × no. of males) ₹ and the number of figures here will be no. of males + no. of females. It's given that
No. of males=10
No. of females=5
So, the total no. of figures = 15
Sum total of set of figures = (20,000 × 10 + 18,000 × 5 )₹ and the average will be
=(20,000 × 10 + 18,000 × 5) ₹/15
=(200,000+90,000)/15₹
=290,000/15 ₹
=19,333.34 ₹
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Write the explicit formula for the sequence below:
The explicit formula for the sequence -28, -31, -34, -37, ..., is aₙ= -28 -3d.
What is an arithmetic sequence?A series of integers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.
Given:
-28, -31, -34, -37, ...
The general formula of an arithmetic sequence:
aₙ= a₁ + (n)d,
where a₁ is the first term and d is the common difference.
First, we will find the common difference between consecutive terms.
Here,
a₁ = -28
To find the common difference:
a₂ - a₁ = -31 + 28 = -3
a₃ - a₂ = -34 + 31 = 3
a₄ - a₃ = -37 + 34 = 3
Hence, d = -3.
Substitute the values to the formula,
aₙ= a₁ + (n)d,
aₙ= -28 + (-3)d,
aₙ= -28 -3d
Therefore, aₙ= -28 -3d is the required sequence.
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