The equation of a line in the point-slope form that has a slope of 1/3 and passes through the point (6,-2) is [tex]y+2 =\frac{1}{3} (x-6 )[/tex].
What is point-slope form?A straight line is represented using its slope and a point on the line using point slope form. In other words, the point-slope form is used to determine the equation of a line whose slope is "m" and passes through the point ([tex]x_{1}, y_{1}[/tex]). The equation of a straight line can be expressed in various ways, Point slope shape is one of them. The point slope form's equation is as follows:[tex]y-y_{1} =m(x-x_{1} )[/tex]where (x, y) is a chance point on the line that should be treated as a variable when using the formula.A fixed point on the line is ([tex]x_{1}, y_{1}[/tex]).The slope of the line is m.Calculation
[tex]y-y_{1} =m(x-x_{1} )[/tex]
[tex]y-(-2) =\frac{1}{3} (x-6 )[/tex]
[tex]y+2 =\frac{1}{3} (x-6 )[/tex]
Therefore, the equation of a line in the point-slope form that has a slope of 1/3 and passes through the point(6, -2) is [tex]y+2 =\frac{1}{3} (x-6 )[/tex]
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Solve the inequality for x. Show each step of the solution for full credit. (3 points - 2 points showing work, 1 point correct answer)
7x+1/2 >4
The value of x in the Inequality (7x + 1)/2> 4 is x > 1.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤.
In this case, the inequality is given as:
(7x + 1)/2> 4
Cross multiply
7x + 1 > 2 × 4
7x + 1 > 8
Collect like terms
7x > 8 - 1
7x > 7
Divide
x > 7/7
x > 1
Therefore, x > 1.
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Help needed with this equation thx
The geometric system has a length of f = 4 cm and a length of g = 6 cm.
How to find the missing lengths of a geometric systemHerein we find a geometric system formed by two rectangles, the rectangle ABCD has an area of 60 square centimeters and the rectangle APQD has an area of 24 square centimeters. The area of a rectangle is equal to the product of the lengths of its base (b) and its height (h), both in centimeters.
First, describe the area formulas for the rectangles ABCD and APQD, both in square centimeters:
Rectangle ABCD
(g + 9) · f = 60 (1)
Rectangle APQD
g · f = 24 (2)
Where:
g - Length of the side QD, in centimeters. f - Length of the side BC, in centimeters.Second, use distributive property in (1):
By (1):
g · f + 9 · f = 60
Third, use substitution by (2) on (1) and determine the value of f:
(2) in (1):
24 + 9 · f = 60
9 · f = 36
f = 4
Fourth, determine the value of g:
By (2):
g = 24 / f
g = 24 / 4
g = 6
The lengths of f and g are 4 and 6 centimeters, respectively.
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the numbers 1, 2, 3, 4, 5 are to be arranged in a circle. an arrangement is badbad if it is not true that for every nn from 11 to 1515 one can find a subset of the numbers that appear consecutively on the circle that sum to nn arrangements that differ only by a rotation or a reflection are considered the same. how many different bad arrangements are there?
There are 2 different bad arrangements possible.
We see that there are 5! absolute ways of orchestrating the numbers. Nonetheless, we can constantly turn these numbers so that, for instance, the number 1 is dependably at the highest point of the circle. Consequently, there are just 4! ways under turn, which is easy to drill down. We methodically list out every one of the 24 cases.
Presently, we should inspect assuming they fulfill the circumstances. We can see that by selecting each number, in turn, we can continuously acquire subsets with aggregates 1, 2, 3, 4, and 5. By picking the round trip, we can get 15. By selecting everything aside from 1, 2, 3, 4, and 5, we can get subsets with amounts of 10, 11, 12, 13, and 14.
This implies that we presently just have to check for 6, 7, 8, and 9. Be that as it may, whenever we have found a set adding to 6, we can pick all the other things and get a set adding to 9, and comparably for 7 and 8. Hence, we just have to check each case for whether we can acquire 6 or 7.
We observe that there are just 4 arrangements that fulfill these circumstances. In any case, each of these is an impression of another. We divide by 2 for these reflections to get the final answer of B = 2.
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given that the probability of a family owning a dog is 0.91, and the probability of a family owning a cat and a dog is 0.15, what is the probability of a family owning a cat given that the family owns a dog?
The probability of a family owning a cat given that the family owns a dog is 0.164
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event has already occurred.
Here
probability of a family owning a dog is 0.91,
P(dog) = 0.91
probability of a family owning a cat and a dog is 0.15,
P(dog ∩ cat) = 0.15
according to conditional probability
the probability of occurring of B after event A takes place is
P(A|B)=P(A∩B)/P(A)
so, the probability of a family owning a cat given that the family owns a dog is
P(dog | cat) =P(dog∩cat)/P(dog)
= 0.15/0.91
=0.164
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rove by induction that 3n < n! for all integers n greater than 6. state whether you are using regular or strong induction
We can use both regular and strong induction.
The Fundamentals of Inductive Mathematics (i.e., Regular Induction). If any of the following statements involving a positive number, n, are accurate: The claim is true if and only if n is 1. If the assertion is true for n=k, then it must also be true for n=k+1(x).
In a variation of induction known as strong induction, we make the assumption that the assertion is true for all values before k. This provides us with more information with which to work.
Regular Induction form
N>6 = n=7 in basic case
3n = 37 = 2187
N! = 7! = 5040
For n= 7 3n<n! is true
Induction hypothesis
Let for n= k and k>6
Assume 3k<k! is true
We prove that for k = k+1 the assumption holds true then the assumption must be true for k
K = k+1
3k+1 < (k+1)!
3k. 3 < (k+1) k!
3k < (k+1)/3.k!
For k>6
(k+1)/3 >1 and let (k+1)/3 = p
3k < P.k!
But we assumed that 3k < k! for k > 6 then 3k must be less than p.k1 since P>1
Therefore 3k<k! for k>6
3n < n! for all integers n greater than 6.
Therefore we can use both regular and strong induction
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At the 2004 athens olympics, the ration of canadas gold medals to greeces gold medals was 1:2. together,canada and greece won. 9 gold medals.how many did canada and greece win
The total number of medals won by Canada is 3 and Greece's 6,
Here we have to find the number of medals won by Canada and Greece.
The ratio of medals won by Canada and Greece is 1: 2.
The total number of medals won = is 9
The common number is x.
Medal won by Canada = x
Medal won by Greece = 2x
So we get the equation:
x + 2x = 9
3x = 9
x = 3
So the total medal won by Canada = 3
The total medal won by Greece = 2 × 3= 6
Therefore the number of medals won by Canada and Greece is 3 and 6 respectively.
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Q8.
Solve the simultaneous equations
2x + 3y = 5p
y = 2x + p
where p is a constant.
Give your answers in terms of p in their simplest form.
Answer:
x = 1/4p
y = 3/2p
Step-by-step explanation:
2x + 3y =5p__________________equ 1
y = 2x + p____________________equ 2
sub equ 2 for y in equ 1
2x + 3(2x + p) = 5p_______________open brackets
8x = 2p______________________divide both sides by 8
x = 1/4p
sub 1/4p for x in equ 2
y = 2(1/4p) + p___________________open brackets
y = 3/2p
Please help I will give the brainiest for the fastest answer.
Answer: Campbell to Hillsboro to Richmond to Winchester
(Note: Not taking the Washington route)
Step-by-step explanation:
Form Campbell all the way to Richmond have no other choices, From Richmond to Winchester has two choices, 12.2 mi +5.2 mi or 15.7 mi
12.2+5.2=17.4 mi while the other choice is only 15.7 mi
So taking the 15.7 mi option is faster
Lena made $60 babysitting for 3 hours on Sunday. He made $140 for 7 hours
on Tuesday. What is the rate of change?
Answer:20 dollars per hour
Step-by-step explanation:60/3 = 20
20 dollars per hour
7 x 20 = 140
a box contains tiles. each tile has certain properties: each tile is made of wood or plastic. each tile is red, yellow, or blue. each tile is a triangle, square, pentagon, or circle. there is exactly one tile for each combination of properties. for example, there is one red circle that is made of wood. steve chooses one tile, and ellen chooses a different tile. what is the probability that the two chosen tiles differ with respect to all three properties?
1/24 is the probability that the two chosen tiles differ with respect to all three properties
1/2 chance that the tiles materials will be different (wood or plastic). 1/3 chance exists that the tiles will have different colors (r, y or b) 1/4 chance where the tile shapes will change (t, s, p or c)the probability that all three attributes of the two tiles will be different.1/2 * 1/3 * 1/4 = 1/24 The probability of an event occurring is a measure of its likelihood. It assesses the likelihood of an event. P(E) = Number of Favourable Outcomes/Total Outcomes is the probability formula.
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18=0.125 . Which calculation is NOT a way to find 58?
The calculation that is not a way to find a fraction of 5/8 is:
1 - 0.125.
What is a fraction?A fraction is a numerical representation of the division of the two terms x and y, as follows:
Fraction = x/y.
The terms are classified as follows:
The top term x is the numerator of the fraction.The bottom term y is the denominator of the fraction.Hence the numeric value of the fraction 5/8 presented in this problem is given as follows:
5/8 = 0.625.
The calculation that is not a way to find the fraction of 5/8 is the only expression that has a different value than 5/8.
The expression with a different value is of:
1 - 0.125 = 0.875.
As the value of 0.875 is different than the value of 0.625 equivalent to the fraction of 5/8.
Missing InformationThe complete problem is given by the image at the end of the answer.
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Question 1 of 10
Identify the type of function represented by f x = 2 1/2
The function represented by the f(x) =[tex]2(\frac{1}{2})^x[/tex] is an exponential decay function
The function is
f(x) =[tex]2(\frac{1}{2})^x[/tex]
The function is defined as the expression that represents the relationship between one variable and another variable.
The function is in the form of
f(x) = a × [tex]b^x[/tex]
Such functions are called exponential function
Here
The value of a = 2
The value of b = 1/2
If the value of b > 1, the function is called exponential growth function.
If the value of b < 1, the function is called exponential decay function.
Here b < 1
Therefore it is exponential decay function
Hence, the function represented by the f(x) =[tex]2(\frac{1}{2})^x[/tex] is an exponential decay function
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What are the roots of the equation x 2 + 16 x + 80 = 0 x 2 +16x+80=0 in simplest a + b i a+bi form?
The quadratic equation x² + 16 · x + 80 has two roots: x₁ = - 1 / 10 + i (4 / 5), x₂ = - 1 / 10 - i (4 / 5).
How to determine the roots of a quadratic equation
In this question we find a quadratic equation of the form a · x² + b · x + c = 0, whose roots can be found by using the quadratic formula:
x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c)
Where b² - 4 · a · c is the discriminant of the quadratic formula, which offers three cases of solutions:
b² - 4 · a · c > 0: Two different real roots. b² - 4 · a · c = 0: Two equal real roots. b² - 4 · a · c < 0: Two conjugate complex roots.If we know that a = 1, b = 16 and c = 80, then the roots of the quadratic equation are, respectively:
x = - 16 / 160 ± (1 / 160) · √(16² - 4 · 1 · 80)
x = - 1 / 10 ± (1 / 10) · √(- 64)
x = - 1 / 10 ± i (4 / 5)
The roots are - 1 / 10 + i (4 / 5) and - 1 / 10 - i (4 / 5).
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Which equation represents this sentence?
Half the difference of a number and 5 is−2.
Responses
12(5−x)=−2
1 half left parenthesis 5 minus x right parenthesis equals negative 2
12x−5=−2
1 half x minus 5 equals negative 2
12(x−5)=−2
1 half left parenthesis x minus 5 right parenthesis equals negative 2
5−12x=−2
The equation which represents the sentence given; Half the difference of a number and 5 is−2 is; 1/2(x - 5) = -2; 1 half left parenthesis x minus 5 right parenthesis equals negative 2.
Word phrases from Algebraic expressions.It follows from the task content that the expression which best represents the given algebraic expression is to be determined.
First, the difference of a number, x and t is represented as; (x - 5).
Hence, the word phrase; Half the difference of a number and 5; is best represented algebraically as; 1/2(x - 5).
Ultimately, the whole word phrase; Half the difference of a number and 5 is -2 can best be represented as; 1/2(x - 5) = -2.
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Container A has 600 mL of water and is being filled at a rate of 12 mL per minute. Container B has 1500 mL of water and is being drained at 12 mL per minute. How many minutes, m, will it take for the two containers to have the same amount of water?
Answer:
It will take 37.5 minutes for both containers to reach the same amount of water which is 1050 mL
Step-by-step explanation:
1500 - (12 × 37.5) = 1050
600 + (12 × 37.5) = 1050
Answer two questions about Equations A and B:
A. 3(x+2) = 18
B. x+2=6
1) How can we get Equation B from Equation A?
Choose 1 answer:
Add/subtract the same quantity to/from both sides
Add/subtract a quantity to/from only one side
Multiply/divide both sides by the same non-zero constant
Multiply/divide only one side by a non-zero constant
2) Based on the previous answer, are the equations equivalent? In other words, do they have
the same solution?
Part A
We can get equation B from A by Multiply/divide both sides by the same non-zero constant.
Part B
The two equations are equivalent, they have same solution
The equations are
3(x+2) = 18
x + 2 = 6
Part A
Consider the first equation
3(x + 2) = 18
Divide both side of the equation by 3
3(x+2) / 2 = 18/3
x + 2 = 6
We will get equation B from equation A, if we divide both side of the equation by 3
Part 2
The first equation
3(x+2) = 18
x + 2 = 6
x = 6-2
x = 4
The second equation
x+2 = 6
x = 6-2
x = 4
Both the equation has same solution
Hence,
Part A
We can get equation B from A by Multiply/divide both sides by the same non-zero constant.
Part B
The two equations are equivalent, they have same solution
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Lola received $522.50 when she cashed her paycheck. Why is this important to us?
Because you can also cash a check at a bank if you have an account there.
If you have a checking account, you can write and mail a check to pay your bills. The bank will withdraw the money from your account.
As long as you have enough money in your account (as much or more than what you're trying to cash), you can cash a check and get money back immediately.
You can deposit money into a savings account. A savings account is a good way to save your money and earn money called interest.
Banks also offer electronic services. You can use these services even when the bank is closed.
Some banks have more than one branch or office. Use the branch closest to you if you are in a different town or state. All branches will have access to your account information.
Monica cashed her paycheck at Ready Cash. The fee at Ready Cash to cash a check is 10% of the amount of the check. Her paycheck was $538. how much was the fee for Monica to cash her paycheck
Answer:
$53.8.
Step-by-step explanation:
10% of $538 is like saying 538 times .10. After you multiply, you get $53.8 as the fee that Monica had to pay.
What is the equation of the line that passes through the point (−2,−7) and has a slope of 6?
The equation of the line in slope intercept form is y = 6x + 5
How to determine the equation of the line?The given parameters are
Slope, m = 6
Points, (x₁, y₁) = (-2, -7)
A linear equation can be represented as
y = slope * x + y-intercept
i.e.
y = m(x - x₁) + y₁
Substitute the known values in the above equation
So, we have the following equation
y = 6(x + 2) - 7
Expand
y = 6x + 12 - 7
Evaluate the like terms
y = 6x + 5
Hence. the linear equation is y = 6x + 5
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At the beginning of the lesson, Jacob determined that there was a problem with the sail length measurements of 7.5 meters, 4.8 meters, and 2.5 meters. Explain how Jacob was able to determine there was a problem with the specifications of the triangular sail.
Answer:
Jacob was able to determine there was a problem with the specifications of the triangular sail because of the Pythagorean theorem.
Step-by-step explanation:
Assume the triangular sail is a right triangle.
The Pythagorean theorem says: [tex]A^{2} + B^{2} = C^{2}[/tex]
If A = 4.8, B = 2.5, and C = 7.5, then [tex]4.8^{2} + 2.5^{2} = 7.5^{2}[/tex].
[tex]4.8^{2} + 2.5^{2} = 23.04 + 6.25 = 29.29[/tex]
[tex]7.5^{2} = 56.25[/tex]
In conclusion, [tex]29.29 \neq 56.25[/tex], so there is a problem with the sail.
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
there is probably a way to do this w/o calculus, but I cheated and used that.
A = Length * Width
A = x * ( 650 -2x)
A = 650x -2[tex]x^{2}[/tex]
d/dx ( A = 650x -2[tex]x^{2}[/tex])
0=650 -4x
4x = 650
x = 135 m
A= 650*135 -2*[tex]135^{2}[/tex]
A = 51,300 [tex]m^{2}[/tex]
pls hurry and thanks 40 pts
The angle of x in the triangle is 75 degrees.
How to find the angles of triangle?The sum of angles in a triangle is 180 degrees. The triangle is a an isosceles triangle.
An isosceles triangle is a triangle that has any two sides equal in length and angles opposite to equal sides are equal in measure.
Therefore, the base angles are equal.
The third angle of the triangle is 30 degrees(vertically opposite angles)
Hence,
x + x + 30 = 180
2x + 30 = 180
2x = 180 - 30
2x = 150
x = 150 / 2
x = 75 degrees
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Bryan paid $144.00 for an item at the store that was 20% off the original price. What was the original price?
Answer:
$180
Step-by-step explanation:
[tex]P\times{(1-0.20)}=144[/tex]
[tex]P\times{0.80}=144[/tex]
[tex]P=\frac{144}{0.80}[/tex]
[tex]P=180[/tex]
Determine the intercepts of the line
x int
y int
Answer:
Y-int = -45, X-int =-11.25
Step-by-step explanation:
Please read this before moving on :)
An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+b, where m is slope and b is the y-intercept.
We know that equation of a line is y=mx+b. To find the value of the x-intercept of the line we simply need to put the value of the y as 0.
Using the Slope Equation : Pick two points on the line and determine their coordinates. Determine the difference in y-coordinates of these two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).
1 - Finding the Slope
2 points; (0,-40), (-10,0)
0-(-40)/(-10)-0 = 40/-10 = -4
2 - Y-INTY=MX+B
Y=MX+(-45)
Y=MX-45
Y-int = -45
3 - X-INTY=MX+B
0=(-4)x+-45
45=-4x
X-int =-11.25
1. Of the three lines in the graph, one has slope 1, one has slope 2, and one has slope
Label each line with its slope. HELP IM REALLY STUCK ON THIS
Guys, what is the answer to 5-x=12?
Answer:
x= -7
Step-by-step explanation:
here you go.....
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if a seed is planted, it has a 95% chance of growing into a healthy plant. if 9 seeds are planted, what is the probability that exactly 3 don't grow?
If 9 seeds are planted, what is the probability that exactly 3 don't grow will be 1/5832000 as 5% chance are there that plant will not grow.
What is probability?The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.
Here,
The chances of seed to be not growing is 1–0.95 =0.05.
For 3 seeds not to grow being simultaneous occurring events have the probability = 0.05×0.05x0.05=0.000125
As 9 seeds being planted the probability of selecting 1 out of 9 is (1/9).
So for 3 mutual occurring case is (1/9)×(1/9)x(1/9)= 1/729
So the probability will be (1/729)×1/8000=1/58,32,000
The likelihood that exactly 3 seeds out of 9 will not germinate is 1/5832000, or 5%, so there is a chance that the plant won't grow.
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Find the solution for −0.5x − 3.69 = x − 1.9 − 2.39. x = 0.4 x = −0.4 x = 2.5 x = −2.5
The solution for the given expression -0.5x-3.69=x-1.9-2.3 is x= 0.34
The given problem is related to an algebraic expression which is the thought of expressing numbers utilizing letters or letter sets without indicating their real values, which is made up of factors and constants, at the side of logarithmic operations (expansion, subtraction, etc.). Expressions are made up of terms.
since the given expression is :
-0.5x-3.69=x-1.9-2.3
=>-0.5x-x=-1.9-2.3+3.69
=>-1.5x=-0.51
=>x=0.34
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Which equations are true? Select all that apply.
Answer:
The equation that is true is equation two
9. (-1kw-1z-2)-3
- (-1)-³³₂
11, 9-648
h2
These are the questions here is the photo
Using the simplification of power, [tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}=-64w^{-3}z^{6}[/tex] and [tex]\frac{g^{-6}h^8}{h^2}=g^{-6}h^{6}[/tex].
In the given question,
We have to simplify the given expression.
Before simplifying the expression we first learn that the negative power can be positive after changing their position from numerator to denominator.
We use the method of adding the power of expression to solve the expression.
(1) The given expression is [tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}[/tex].
We firstly simplifying the power after the bracket by multiplying the power to each variable.
[tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}=(-\frac{1}{4})^{-3}(w^{-1})^{-3}(z^{-2})^{-3}[/tex]
Simplifying the expression.
[tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}=(-1)^{-3}(\frac{1}{4})^{-3}(w^{-3})(z^{6})[/tex]
Now we make the power positive by changing their position
[tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}=(-1){4}^{3}(w^{-3})(z^{6})[/tex]
Simplifying
[tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}=-64w^{-3}z^{6}[/tex]
(2) The given expression is [tex]\frac{g^{-6}h^8}{h^2}[/tex].
Simplifying the expression.
As we know that the power with same base get subtracted when they are in division.
So [tex]\frac{g^{-6}h^8}{h^2}=g^{-6}h^{8-2}[/tex]
[tex]\frac{g^{-6}h^8}{h^2}=g^{-6}h^{6}[/tex]
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Graph the function f(x)=−14x−2.
Use the line tool and select two points to graph.