The coordinates of K are (3, 1).
What is the coordinate point?
The coordinates of a point are a pair of numbers that define its exact location on a two-dimensional plane. Recall that the coordinate plane has two axes at right angles to each other, called the x and y-axis. The coordinates of a given point represent how far along each axis the point is located.
Point K is 1/n of the way from J(4,5) to L(0,-7). To find the coordinates of K, we can use the concept of linear interpolation.
Given two points J(x1,y1) and L(x2,y2) and a value of t, such that 0<=t<=1, the coordinates of the point K(x,y) that is t of the way from J to L is given by:
x = (1-t)x1 + tx2
y = (1-t)y1 + ty2
In this case, we know that n=4 and t = 1/4.
So the x and y coordinates of K are:
x = (1-1/4)x1 + (1/4)x2 = (3/4)x1 + (1/4)x2 = (3/4)(4) + (1/4)(0) = 3
y = (1-1/4)y1 + (1/4)y2 = (3/4)y1 + (1/4)y2 = (3/4)(5) + (1/4)(-7) = 1
Hence, the coordinates of K are (3, 1).
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What is the distance between points − 6 − 7 and − 1 5 on the coordinate plane?
The distance between the points (-6, 7) and (-1, -5) is 13 units.
What is the distance?The complete velocity of an object, regardless of direction, is its distance.
Distance is the amount of space an object has traveled, regardless of where it began or concluded.
Knowing an object's distance from us allows us to calculate its true size.
Typically, the following formula is used to determine the distance between two points:
d=((x2 - x1)2 + (y2 - y1)2)
So, the following is the distance formula:
d=((x2 - x1)2 + (y2 - y1)2)
Points are: (-6, 7) and (-1, -5)
Now, put in the values in the above formula and calculate as follows:
d=((x2 - x1)2 + (y2 - y1)2)
d=((-1+6)2 + (-5-7)2)
d=√25+144
d=√169
d=13 units
Therefore, the distance between the points (-6, 7) and (-1, -5) is 13 units.
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See screenshot. something bout a decagon
The area of the regular decagon is 496.7 squared unit.
What is a decagon?In geometry, a decagon is a ten-sided polygon or 10-gon. The total sum of the interior angles of a simple decagon is 1440°. Regular decagon.
To calculate the area of the decagon, we use the formula below.
Formula:
A = 5r²sin∅............................ Equation 1Where:
A = Area of the decagonr = length of the decagon from the vertex to the center = 13∅ = Angle at the center of the decagon = 360/10 = 36°Substitute these values into equation 1
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Your bill at a restaurant is $45.
You have a coupon for 25% off the
total. What will be your bill be
with the discount? Help asap
Answer:
Price after discount: $33.75
You saved: $11.25
Step-by-step explanation:
Is ½ a whole number?
1/2 is not a whole number.
We know that the whole numbers are numbers that include natural numbers and zero.
That is the set of whole numbers is denotes by W = N ∪ {0},
here N represents the set of natural numbers.
And we know that the natural numbers are nothing but the numbers which can be counted and start from 1 and ends at infinity.
i.e., the set of natural numbers N = {1, 2, 3, . . ., ∞}
and the set of whole numbers W = {0, 1, 2, 3, . . ., ∞}
A set of whole numbers do not include fractions, decimals, or negative integers.
Here, 1/2 is a fraction (number of the form p/q where q ≠ 0)
So, given number 1/2 is not a whole number.
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Which expression represents the measure of segment RS?a. 7x – 3b. 7x + 5c. x + 5d. x – 3
Option C better choice, the measurement of the line segment RS is equal to x+5.which is difference of segment TR and TS.
A line segment is a part of a straight line that is bounded by two distinct end points and contains every point on the line that is between its endpoints. The length of a line segment is given by the Euclidean distance between its endpoints. A closed line segment includes both endpoints, while an open line segment excludes both endpoints.
There is a point S between the line segments T and R, measure of segment TR is 4x+1 and the measure of segment TS is 3x-4.
we shall find out the measure of RS.
so, length of RS is equal to difference of TR and TS.
Mathematically,
RS=TR-TS
RS=(4x+1) -(3x-4)
RS=4x+1-3x+4
RS=x+5
Hence the length of RS is equal to x+5.
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I need help please!!!!!
Answer:
For f(1), it's -14. For determining x, x = -1.
Step-by-step explanation:
For f(1), just plug in 1 to x. -6(1) is -6, + -8 is -14.
For determining x, if you plug in -1, you get -6(-1), which is +6. +6 -8 is -2.
what is the solution set of the following system of equations
y=3x+6
y=(x+4)^2-10
a.{(-5,-9)}
b.{(5,21)}
c.{(0,6),(-5,-9)}
d.{(0,6),(6,21)}
Answer:
c) (0,6) and (-5,-9)
Step-by-step explanation:
if you graph the system you will get a line and a parabola
the two points at which they intersect will be (0,6) and (-5,-9)
Find the cube root. 3√64/343
Step-by-step explanation:
3√64/343
3√4^3/7^3
3√(4/7)^3
4/7
Answer:
4/7
Step-by-step explanation:
[tex]\sqrt[3]{\frac{64}{343} }[/tex]
[tex]\frac{\sqrt[3]{64}}{ \sqrt[3]{343} }[/tex]
[tex]\sqrt[3]{64}[/tex] = 4
[tex]\sqrt[3]{343}[/tex] = 7
[tex]\frac{4}{7}[/tex]
In a race, you run 3 kilometers east in 21 minutes. What is your velocity in km/min?
Answer:7
Step-by-step explanation: 21/3 = 7
Answer:
1/7 km/min
Step-by-step explanation:
Divide/simplify the two values, 3/21 = 1/7
PLEASE HELPPP PLEASE HELPP
Answer:
Step-by-step explanation:
Firstly, divide the figure into 2
You will have a rectangle on the bottom and a triangle on top. Let's name your shapes by saying that the rectangle is FIG -1 and your triangle is FIG -2
FIG -1
b x h
8 x 11
88 cm^2
FIG -2
b x h / 2
7 x 11 / 2
77/2
38.5 cm^2
Total = 88 + 38.5
= 126.5 cm^2
How many non negative integer solutions are there to the equation 2x1 2x2 x3 x4 12?
There are 20 non-negative integer solutions to the equation 2x1 + 2x2 + x3 + x4 = 12.
NON NEGATIVE INTEGER SOLUTIONSThe number of non-negative integer solutions to the equation 2x1 + 2x2 + x3 + x4 = 12 is equivalent to the number of solutions to the equation x1 + x2 + x3 + x4 = 6, which is the number of ways to place 6 distinguishable balls into 4 distinguishable boxes. This is equivalent to the number of ways to choose 3 balls to not place in the first box, which is (6 choose 3) = 20. Therefore, there are 20 non-negative integer solutions to the equation 2x1 + 2x2 + x3 + x4 = 12.
The equation 2x1 + 2x2 + x3 + x4 = 12 is equivalent to the equation x1 + x2 + (x3/2) + (x4/2) = 6. The variables x1, x2, x3 and x4 are non-negative integers, thus (x3/2) and (x4/2) are also non-negative integers.
The number of solutions to x1 + x2 + (x3/2) + (x4/2) = 6 is equivalent to the number of ways to place 6 distinguishable balls into 3 distinguishable boxes. This is equivalent to the number of ways to choose 3 balls to not place in the first box, which is (6 choose 3) = 20.
Because each of x1 and x2 are integers and (x3/2) and (x4/2) are integers, it ensures x1, x2, x3, and x4 are also integers. Therefore, there are 20 non-negative integer solutions to the equation 2x1 + 2x2 + x3 + x4 = 12.
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Use substitution to solve the system of equations. Show your work. Check your answer to show proof that the solution works in each equation
3x+y=10
y=6x+1
(If you can, please put a step by step explanation!)
Answer:
x=1
Step-by-step explanation:
If y=6x+1, we can substitute that into the original equation, so it would look like 3x+6x+1=10.
Now we just solve for x. Add 3x and 6x to get 9x, and subtract 1 from both sides of the equation, now we have
9x=9, divide both sides by 9 and we end up with x=1.
PS. sorry for the bad handwriting but i attached a photo of how i solved it.
I think of a number, multiply it by four, and subtract three. I get eleven.
a) Using the statement above, form an equation.
Use the letter 'x' for the unknown number.
7
b) Solve the equation.
Answer: (x*4) - 3= 11. X = 3.5
Step-by-step explanation
(4x) - 3 = 11 or (x*4) - 3 = 11.
11 + 3 = 14
So then,
14 = x * 4 (or 4x)
14 / 4 = 3.5
so,
X = 3.5
What are the rules of logarithm?
The rules of logarithms are as:
1. Rule of product.
2. Rule of division.
3. The Power/Exponential Rule.
4. A new fundamental rule.
The alternate format for writing exponents is with logarithms. A number appears base-based logarithm is approximately equivalent to another number. A logarithm performs exponentiation's exact opposite function.
1. Rule of product: According to this rule, adding the individual logarithms of two logarithmic values results in the multiplication of those values.
[tex]Log_b (mn)= log_b m + log_b n[/tex]
2. Rule of division: The difference between each logarithm is equivalent to the division of two logarithmic values.
[tex]Log_b \left(\frac{m}{n}\right)= log_b m - log_b n[/tex]
3. The Power/Exponential Rule: According to the exponential rule, the exponent times the logarithm of m's logarithm is equivalent to m's logarithm with a reasonable exponent.
[tex]Log_b (m^n) = n log_b m[/tex]
4. A new fundamental rule:
[tex]Log_b m =\frac{log_a m}{log_a b}[/tex]
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What is it called when a system of equations has no solution?
The phrase "inconsistent pair of linear equations" refers to a set of linear equations that cannot be solved.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
What makes an equation linear?
When a linear equation is graphed, it always produces a straight line since each term in the equation has an exponent of 1. This is the basis for the term "linear equation" being used to describe it.
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Solve by completing the square 1) x² + 16x + 24 = 0. could y'all do the step to step I just need and example
Answer:
(x+8)^2=40
Step-by-step explanation:
x^2+16x+24=0.
Well, to solve for this, you do:
1. (16/2)^2 to find what number should be in place of 24.
That, by the way, is 64.
2. There's no 64! We have to add 64-24 on both sides, which makes the equation
x^2+16x+64=40.
3. Since we know that (16/2)=8, using the completing the square formula, you know that it's going to be a variation of (x+8)^2 or (x-8)^2.
As we are adding for the middle term, it must be (x+8)^2.
4. Answer: (x+8)^2=40.
Sorry if this is too late :)
How do you convert a quadratic function to vertex form?
The process of converting a quadratic function to vertex form.
In math quadratic function is defined as a polynomial where the highest degree of any variable is 2.
Here we have to write the steps to convert the a quadratic function to vertex form.
Here we have to convert quadratic equation from standard form to vertex form
Let us consider that the given quadratic equation is given as,
=> y = ax² + bx + c { a, b, c € R, a ≠ 0}.
Here from the above equation we have to take a as common from the terms containing x.
then the equation is rewritten as,
=> y = a(x² + bx/a) + c
In order to Complete the square inside the bracket by adding and subtracting (b/2a)², then we get,
[tex]y=a[x^2+\frac{bx}{a} +(\frac{b}{2a})^2 - (\frac{b}{2a})^2 ]+ c[/tex]
When we factorize it, then we get,
[tex]y=a[(x+\frac{bx}{a})^2 - (\frac{b}{2a})^2 ]+ c[/tex]
Rewrite it as follows:
[tex]y=a[x+\frac{bx}{a}]^2 - (\frac{b}{2a})^2+ c[/tex]
Let us consider that the value of
=> h = -b/2a and k = c - b²/4a
Then we get the vertex form of the expression as,
=> y = a(x - h)² + k.
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convert 7 pounds 12 ounces to grams
Answer:
3515.3443 grams
can someone help me before 11:59 pls
Answer: can you help me i cant put a q i have to points
Step-by-step explanation: plssssssssssssssss
A customer wanted to purchase a video game and realized that they were short $4.28 to be able to pay. Which value is the opposite of being short $4.28
values of x are solutions to the equation below?
Check all that apply.
10x²-64 36+6x²
□ A. x= -√√5
B. x = 5
C. x = -5
O D. x = √√√5
E. x=-10
F. x= 10
The values of x that are solutions to the equation 10x²-64 36+6x² are x = 5, x = -5, x = -10, and x = 10.
What is Equation?Equation is a statement of equality between two expressions that states that they have the same value. Equations can be used to solve problems, model real world situations and describe relationships between different quantities. Equations can be expressed in many different forms, such as linear equations, quadratic equations, exponential equations and more. Equations are a powerful tool for understanding and describing the world around us.
The solutions to the equation 10x²-64 36+6x² are B. x = 5, C. x = -5, E. x=-10, and F. x= 10. These values represent the x-coordinates of the points in which the equation cuts the x-axis. The equation does not have a solution for x= -√√5 or x = √√√5, so these answers are incorrect.
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Use a formula to find the surface area of the square pyramid. (H.6ft.)(W.3ft.)(L.3ft.)
A. 45 ft
B. 81 ft
C. 36 ft
D. 72 ft
The surface area of a square pyramid with base length of 3 ft. and height of 6 ft. is 45 square ft. (option A)
The formula for the surface area of a square pyramid is given by:
A = a² + a √(a² + 4h²)
Where:
A = surface area
a = base length
h = height of the pyramid
In the given problem, the side length of the base = W = L = 3 ft.
Hence,
a = 3 ft.
h = 6 ft.
Plug these parameters into the formula:
A = 3² + 3 x √(3² + 4x6²)
A = 9 + 3 x √153
A = 45 ft². (option (A)
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What is the type of system of linear equation which has no solution notice that the two lines are parallel and will never intersect?
Inconsistent Pair of Linear Equations is the type of system of linear equation which has no solution notice that the two lines are parallel and will never intersect.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
What makes an equation linear?
When a linear equation is graphed, it always produces a straight line since each term in the equation has an exponent of 1. This is the basis for the term "linear equation" being used to describe it.
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How do you graph y 2x²?
To plot the graph of the given quadratic function y = 2x², evaluation the value of the function for several values of x at the left and right side of the origin, then plot the data.
The standard form of a quadratic function is:
y = f(x) = ax² + bc + c
Steps to plot the graph of a quadratic function includes:
Find x-interceptFind y-interceptFind the extreme pointHowever, in the given function y = 2x², x-intercept, y-intercept, and the extreme point are all (0,0) or the origin. Hence, we need to use auxiliary points.
Evaluate the value of y for several values of x in the left and right of the extreme value, (0,0). The results are given in the following table.
x y
-5 50
-4 32
-3 18
-2 8
-1 2
0 0
1 2
2 8
3 18
4 32
5 50
Plot the data and we get the graph of y = 2x² ( as in the attached picture)
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what is the answer in history of world religions
Answer:
C. Functional
Step-by-step explanation:
I hope I helped you,
Alex Martin :)
Consider the following.
Point
Line
(-3,5), x+6=0
(a) Write the slope-intercept form of the equation of the line through the given point and parallel to the given line.
(b) Write the slope-intercept form of the equation of the line through the given point and perpendicular to the given line.
The given point and parallel to the given line is: y - 5 = 0 (Slope is 0)perpendicular to the given line is: y - 5 = -1/6x (Slope is -1/6).
What is slope-intercept?Slope-intercept is a form of linear equation which is written in the form y = mx + b, where m is the slope of the line and b is the y-intercept. This form of equation is useful for graphing linear equations, as it allows the user to quickly determine the slope and the y-intercept of the equation, which makes it much easier to plot on a graph. It is also helpful for solving linear equations, as the slope and the y-intercept can quickly be determined.
(a) The slope-intercept form of the equation of the line through the given point and parallel to the given line is y = 5. This is because the given line has a slope of 0 and the given point has a y-coordinate of 5, which is the same as the y-intercept of the parallel line.
(b) The slope-intercept form of the equation of the line through the given point and perpendicular to the given line is y = -6x + 5. This is because the given line has a slope of 0 and the line perpendicular to it has a slope of -1/0, which is -infinity. This means that the slope of the perpendicular line is -6 and its y-intercept is 5, which is the same as the given point's y-coordinate.
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Prove that the square root of 2 is irrational.
The proof that the square root of 2 is irrational can be shown using proof by contradiction.
Assume that the square root of 2 is rational, meaning that it can be expressed as the ratio of two integers (p/q, where p and q are integers and q is not equal to zero).
This means that:
√2 = p/q, where p and q are integers and q is not equal to zero.
Squaring both sides of the equation:
2 = p^2/q^2
multiply both sides by q^2
2q^2 = p^2
Now, since p and q are integers, p^2 and q^2 are also integers.
Therefore, 2q^2 is an even integer.
However, if 2q^2 is an even integer, q^2 is also an even integer, which means that q is even.
Therefore, p and q have a common factor of 2. But, this contradicts the assumption that p and q have no common factors other than 1.
Therefore, our assumption that the square root of 2 is rational must be false.
Hence, we can conclude that the square root of 2 is irrational.
Answer:
To prove that the square root of 2 is irrational, we will use a proof by contradiction. Suppose that the square root of 2 is rational, which means that it can be expressed as a fraction a/b, where a and b are integers with no common factors. Then, we can square both sides of this equation to get:
2 = (a/b)^2 = a^2 / b^2
Multiplying both sides by b^2, we get:
2b^2 = a^2
This means that a^2 is an even number, because it is equal to 2 times b^2. Therefore, a must be an even number, because the square of an odd number is always odd. Let a = 2c, where c is an integer. Substituting this into the previous equation, we get:
2b^2 = (2c)^2 = 4c^2
Dividing both sides by 2, we get:
b^2 = 2c^2
This means that b^2 is an even number, and therefore b must also be an even number. However, this contradicts our original assumption that a and b have no common factors. Therefore, our assumption that the square root of 2 is rational must be false, and the square root of 2 is indeed an irrational number.
Which lemonade mixture Will taste the most lemony? Show your work to support your answer. Mix A: 2 cups of concentrate 3 1/2 cups of water. Mix b: 5 cups of concentrate 8 cups of water. Mix c: 1/2 of concentrate 2 cups of water
Answer:B
Step-by-step explanation: To solve this, we first need to find the ratio of concenrate to water for each mixture. A is 2:3.5, B is 5:8, and C is 0.5:2. Now, we can roughly estimate them. C is .25, B is around .6, and A is around .57. This means that B is the most lemony.
The graph below shows the temperature in Paula’s house over time after her mother turned on the air conditioner. Describe the relationship between the two quantities.
We can see from the graph that the temperature decreases with increasing time. As a result, the two quantities temperature and time are inversely proportional to one another. The necessary relationship between these quantities is x ∝ 1/y or x = k(1/y)
What is inversely proportional?The two are said to be inversely proportional when one quantity's value increases relative to another's decline or vice versa. It suggests that in nature, the two quantities behave in opposite ways. Taking time and speed as an example, they are inversely related. Speed increases result in a shorter amount of time.
Other names for this type of proportion that are also used in this context are reciprocal proportion, inverse proportion, varying inversely, inverse variation, and inverse variation. Let's use the example of x and y to illustrate the relationship between the two variables.
x ∝ 1/y or x ∝ y⁻¹
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Write 48 as a percentage of 200
Answer: 24%
Step-by-step explanation: 48 out of 200 is 24%, meaning that 48 is 24% of 200. To find our answer, we follow two simple steps before we add the percentage symbol, though there can be three steps if we have to round a decimal in a percentage to two digits after the decimal point.
Answer:24%
Step-by-step explanation:
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Find mZ1 and mZ3 in the kite. The diagram is not drawn to scale.
The values of angles are m∠1 = 39° and m∠2 = 51° from the given kite.
What is triangle ?
triangle can be defined in which it consists of three sides , three angles and sum of the angles is 180 degrees
Given figure is a kite.
The diagram is not drawn to scale.
We have to find the measure of angle 1 and 3 in the kite.
From the figure,
Kites have two sets of equivalent adjacent sides and one set up of congruent opposite angles.
So, sides AB and AD are equivalent adjacent sides.
m∠1 = 39°
AC and BD are diagonals.
Diagonals of a kite always meet at right angles.
Let the diagonals intersect at point O.
From right triangle AOB,
m∠1 + m∠2 + m∠O = 180°
39° + m∠2 + 90° = 180
m∠2 = 180° - 90° - 39°
m∠2 = 90° - 39°
m∠2 = 51°
Therefore, m∠1 = 39° and m∠2 = 51°.
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