The equation of the line in point-slope form, with slope equal to 5/6 and passing through the point located at (22 , 12), is (y - 12) = 5/6(x - 22).
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Using the point slope form, plug in the values to set up the equation.
(y - y1) = m(x - x1)
where m = 5/6 and (x1 , y1) = (22 , 12)
(y - 12) = 5/6(x - 22)
In slope-intercept form, the equation of the line is:
(y - 12) = 5/6(x - 22)
y - 12 = 5/6 x - 110/6
y = 5/6 x - 19/3
In standard form, the equation of the line is:
y = 5/6 x - 19/3
5/6 x - y = 19/3
Multiplying both sides by 6,
5x - 6y = 38
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Please do number 2 also don’t forget to explain how you got the answer.
Answer:
Step-by-step explanation:
FACTOR [tex]x^{2} y^{2}[/tex]
[tex]x^{2} y^{2} ( 5 -1 )= 4 x^{2} y^{2}[/tex]
The simplest possible explanation
The maximum upload size allowed for a file is 1.024x108 bytes. Write this number in standard
form.
It would be 0.00000001024 in standard form
Find the quotient: 8 ÷ 0.5
You can find the quotient by asking how many __ are in 8.
Think of the problem as __ items, each divided into 2 equal pieces.
The quotient is __
The quotient of 8 ÷ 0.5 is 16. This is done by finding out how many 0.5 are in 8.
What is quotient?A quotient refers to the number resulting from the division of one number by another. For instance, the quotient of 12 ÷ 3 is 4
A dividend is a number or expression that is to be divided by another. The dividend is 12
A divisor is a number or expression that another is to be divided by. The divisor is 3
Find the quotient: 8 ÷ 0.5
= 8 / 0.5
= 16
A problem as 24 items, each divided into 2 equal pieces.
The quotient is 12
So therefore, if there are 24 items, each divided into 2 equal pieces, the quotient is 12
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Answer:
1. Answer: You can find the quotient by asking how many Halves are in 8.
2. Answer: Think of the problem as 8 items, each divided into 2 equal pieces.
3. Answer: The quotient is 16.
( Answer on Edge. Sorry for answering late. Please mark me as brainliest.)
A plant is already 51 centimeters tall, and it will grow one centimeter every month. The plant's height, H (in centimeters), after m months is given by the
following function.
H(m)=51+m
What is the plant's height after 18 months?
M
the plants height would be 69cm
Find the center and the radius of each circle. (x+2)²+(y+4)²=50
The equation of the circle (x + 2)^2 + (y + 4)^2 = 50 has a radius of 5√2 and a center located at (-2 , -4).
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle, (x + 2)^2 + (y + 4)^2 = 50, is in standard form, then
h = -2
k = -4
r = 5√2
Hence, the equation of the circle (x + 2)^2 + (y + 4)^2 = 50 has a radius of 5√2 and a center located at (-2 , -4).
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What number must be placed in the box in the equation below to produce an equation that has more than one solution: 4x + 6 + 7x - 9 = 12x - 7 - x + ◼️? Please help, and thank you.
Step-by-step explanation:
4x+6+7x-9=12x-7-×
4x-3+7x=12x-7
11x-3=12x-7
add the numbers
11x=12x-4
x=4
Isaac saves 20% on a hard drive that costs $110 but must pay 6% sales tax. What is the total amount that he must pay at the store?
A. $93.28
B. $88.00
C. $106.00
D. $140.80
E. None of the above
Answer:
A. $93.28
Step-by-step explanation:
The reason why is because 110 - 20% would leave you only paying 88 dollars. but when you add the 6% sales tax you get $93.28
9,369 divided 53 help
Answer - 9,369 divided 53 = 176.773584906
How do i solve this?
Answer:
400,000,000 or [tex]4*10^{8}m[/tex]
Step-by-step explanation:
Put them both into standard form.
[tex]0.0001=1*10^{-4} and 4 trillion is 4*10^{2}[/tex]
Multiply them together.
[tex](1*10^{-4})*(4*10^{12}=4*10^{8}[/tex]
simplify -6(2+x) i need help
For a fundraising project, your math club is publishing a calendar. The cost of the digital images and the permission to use them is $125. In addition to these “one time” charges, the unit cost of printing each calendar is $3.25.
Part a: Write an equation for the total cost of the calendars.
Part b: Write a model that gives the average cost A per calendar as a function of the number of calendars printed.
Part c: Use the graph of the model shown below to estimate the number of calendars that must be sold before the average cost drops to $5 per calendar.
The require answers are,
Part a: The equation for the total cost of the calendars is C = 125 + 3.25*100 = 350
Part b: The model that gives the average cost A per calendar as a function of the number of calendars printed is A = 125 + 3.25x
Part c: The estimate number of calendars that must be sold before the average cost drops to $5 per calendar is 70.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .
Now it is given that,
Cost of the digital images and the permission = $125
“one time” charges = $3.25
Part a: The equation for the total cost of the calendars
THere are 100 calendars printed.
So, “one time” charge = 3.25*100
So, the total cost of the calendars C is given as,
C = 125 + 3.25*100
C = 125 + 325 = 450
Thus, the equation for the total cost of the calendars is given as,
C = 125 + 3.25*100 = 450
Part b: The model that gives the average cost A per calendar as a function of the number of calendars printed
Let there are x calendars printed
Total “one time” charges = 3.25x
So, Average cost is given as,
A = 125 + 3.25x
this is the model that gives the average cost A per calendar
Part c: The estimate number of calendars that must be sold before the average cost drops to $5 per calendar
Now from the graph it must be seen that the average cost drops to $ 5 per calender at 70.
Thus, number of calendars that must be sold before the average cost drops to $5 per calendar = 70
Thus, the require answers are,
Part a: The equation for the total cost of the calendars is C = 125 + 3.25*100 = 350
Part b: The model that gives the average cost A per calendar as a function of the number of calendars printed is A = 125 + 3.25x
Part c: The estimate number of calendars that must be sold before the average cost drops to $5 per calendar is 70.
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Solve negative one sixth times the quantity 3 minus 15 times the quantity one third squared end quantity end quantity.
two thirds
18 over 54
negative two ninths
negative two and 42 over 54
Negative one sixth times the quantity 3 minus 15 times the quantity one third squared end quantity end quantity will be C. negative two ninths
How to compute the expression?Based on the information given, the expression will be:
= 1/6 ×( 3 - 15 ) × (1/3)²
= -1/6 × -12 × 1/9
= -2 × 1/9
= -2/9
In conclusion, the correct option is D.
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A fair coin is tossed 16 times. (10 points) what is the mean number of heads? (5 points) what is the standard deviation for the number of heads? (5 points)
The mean number of heads is 8.
What is meant by Binomial distribution?In probability theory and statistics, the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success or failure, is known as the binomial distribution with parameters n and p. The probability of observing x successes in N trials is calculated using the binomial distribution, with p standing for the probability of success on a single trial. According to the binomial distribution, p is fixed throughout all trials.
The probability of success raised to the power of the number of successes and the probability of failure raised to the power of the difference between the number of successes and the number of trials are multiplied to create the binomial distribution. In mathematics and statistics, the binomial distribution is the likelihood that a specific outcome in a series will occur when there are only two possible outcomes: success or failure. Bi is the prefix for two.
Use the formula for the mean for the Binomial Distribution: μ = np
• n = 16
• p = ½
Therefore μ = 16 × ½ = 8
The mean number of heads is 8.
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a²b-b² if a = 3 and b = -4
this was to my last promt sorry
Answer:
21
Step-by-step explanation:
Answer:
The answer is -20
Step-by-step explanation:
This prblem calls for substitution. In this case, if a = 3 and b = -4, then
(3)²(-4) - (-4)²
Now we can solve using order of operations.
(9)(-4) + 16 << (two negatives make a positive)
-36 + 16
= -20
Hope this helps!
The Roebling Suspension Bridge extends over the Ohio River connecting Cincinnati, Ohio, to Covington, Kentucky. Describe the type of lines formed by the bridge and the river.
The Roebling Suspension Bridge extends over the Ohio River connecting Cincinnati, Ohio, to Covington, Kentucky, the lines formed buy the bridge and the river is skew lines
Given,
The situation, the Roebling Suspension Bridge extends over the Ohio River connecting Cincinnati, Ohio, to Covington, Kentucky.
The line formed by the bride and the river that do not intersect and are not coplanar
So, those are skew lines
Hence, the Roebling Suspension Bridge extends over the Ohio River connecting Cincinnati, Ohio, to Covington, Kentucky, the lines formed buy the bridge and the river is skew lines
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Write an equation of the line through the pair of points in slope-intercept form. (Lesson 3-4 )
(4,0) and (-3,-7)
y = x - 4 is an equation of the line in slope-intercept form passing through points (4 , 0) and (-3 , -7)
An equation of a line in slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept.
Given two points passed through by the line, you can use them to write the equation of the line in slope-intercept form.
1. Find the slope of the line using the two given points.
let Point 1(4 , 0) and Point 2(-3 , -7)
slope = m = (y2 - y1) / (x2 -x1)
m = (-7 - 0) / (-3 - 4)
m = -7/-7
m = 1
2. Use the value of the slope and one of the points to find the value of the y-intercept, b. Plug in these values in the formula for slope-intercept form.
y = mx+ b
y = 1x + b
Using Point 1,
0 = 1(4) + b
b = -4
3. Write the equation of the line in slope-intercept form.
y = mx+ b
where m = 1 and b = -4
y = x - 4
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Point D(2,4) is rotated 180 degrees about the origin. What are the coordinates of D'?
The coordinates of D' are D' = (-2, -4)
What are the coordinates of D'?The given paramaters are
D = (2, 4)
The rule is given as
180 degrees about the origin.
This is represented as
(x, y) = (-x, -y)
So, we have
D' = (-2, -4)
Hence, the coordinates of D' are D' = (-2, -4)
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Give measures for a, b , and an acute
b. exactly one triangle.
The measures for a = 10 cm , b = 12cm, and acute angle b =30°
A degree, is always denoted by ° (the degree symbol), known as a measurement of a plane angle in which one full rotation is 360 degrees.
Angle is the measure of the degree with which two lines are intersecting each other to form an orientation.
Acute angle is the measure of an angle which is greater than 0° and less than 90°. For example - 25°, 45° etc.
Triangle is the geometrical figure which is always made up of three sides aligning together to form a closed figure. There are various types of triangles like Acute angle triangle, Right angles Triangle, Obtuse angles triangle, etc.
Acute Angles Triangle is the triangle which consists of al three angles less than 90° but greater than 0°. And it can have any length of sides but the bar minimum condition is to have all three angles in acute form.
We need to find the measures of a, b, acute angle b to make exactly one triangle
As it is the necessary observation that, for one measurement there is only one and only one figure exists which is unique in nature.
Hence, the measure of a, b, c are a = 10 cm , b = 12cm, and acute angle b =30°
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(7.2 x 107) + (5.5 x 106) Express the result
in scientific notation
Answer:
1353.4 x 10^3
Step-by-step explanation:
(7.2 x 107) + (5.5 x 106) = 770.4 + 583 = 1353.4
Scientific Notation: 1353.4 = 1353.4 x 10^3
Answer: 1.3534x10^3
Step-by-step explanation:
(7.2 x 107) + (5.5 x 106) =6767/5 = 1353.4 = 1.3534x10^3
A rental car company charges $40.50 per day to rent a car and $0.12 for every mile driven. Sebastian wants to rent a car, knowing that: He plans to drive 400 miles. He has at most $210 to spend. Write and solve an inequality which can be used to determine dd, the number of days Sebastian can afford to rent while staying within his budget.
Considering the definition of an inequality, the number of days Sebastian can afford to rent while staying within his budget is less than or equal to 6.
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values called unknowns, in addition to certain known data.
Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
Inequality in this caseIn this case, you know that:
A rental car company charges $40.50 per day to rent a car and $0.12 for every mile driven. Sebastian plans to drive 400 miles. Sebastian has at most $210 to spend.Being "d" the number of days Sebastian can afford to rent while staying within his budget, the inequality that expresses the previous relationship is
40.50×d - 400×0.12 ≤ 210
Solving:
40.50×d - 48 ≤ 210
40.50×d ≤ 210 + 48
40.50×d ≤ 258
d ≤ 258÷ 40.50
d ≤ 6.37
Finally, the number of days Sebastian can afford to rent while staying within his budget is less than or equal to 6.
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Use multiplication to decide if the quotient is correct or incorrect.
116+7=21r7
A. Incorrect
B. Correct
SUBMIT
Answer: A, false
Step-by-step explanation:
The left side 123 does not equal to the right side 1801088541, which means that the given statement is false.
Find the inverse function for: f(x)=5x-15
Reduce your answer
F-1(x)=x/?+?
Answer:
[tex]f^{-1}(x)=\dfrac{x}{\boxed{5}}+\boxed{3}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=5x-15[/tex]
An inverse function is a reflection of the function in the line y = x.
To find the inverse of the given function, replace f(x) with y to get an equation for y in terms of x:
[tex]\implies y=5x-15[/tex]
Rearrange the equation to make x the subject:
[tex]\implies y+15=5x-15+15[/tex]
[tex]\implies y+15=5x[/tex]
[tex]\implies 5x=y+15[/tex]
[tex]\implies \dfrac{5x}{5}=\dfrac{y}{5}+\dfrac{15}{5}[/tex]
[tex]\implies x=\dfrac{y}{5}+3[/tex]
Replace x with f⁻¹(x) and y with x. This is the inverse function:
[tex]\implies f^{-1}(x)=\dfrac{x}{5}+3[/tex]
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Find the coordinates of Z if Y is the midpoint of XZ, X(-10, 9), and Y(-4, 8).
The coordinates of Z are (2,7).
What is coordinates in math?
A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).
The formula to calculate the midpoint between two points is equal to
[tex]Y = ( \frac{(x_{1} + x_{2}) }{2} , (\frac{y_{1} + y{2} }{2} )[/tex]
we have
X(-10,9),Y(-4,8)
Let
(x2,y2) ----> the coordinates of Z
substitute the values
( -4.8) = ( -10 + x₂ /2 , 9 + y₂/2)
Solve for x2
-4 = ( -10 + x₂/2
-8 = -10 + x₂
x₂ = -8 + 10
x₂ = 2
Solve for y2
8 = (9 + y₂)/2
16 = 9 + y₂
y₂ = 16 - 9
y₂ = 7
therefore, The coordinates of Z are (2,7)
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5years ago a woman was 4 times as old as her daughter.in four years time the woman will be two and a half times as old as her daughter.find their present age
At present, the age of the woman is 29 years, while the age of her daughter is 6 years.
In the question, we are given two characters, a woman and her daughter, and told to find their present age. We are also given some clues as to how we will arrive at the answer. Let's consider the first one.
In the first sentence, we are told that 5 years ago, the woman was 4 times as old as her daughter. We don't know the woman's age or her daughter's, so let's call the woman's present age x and her daughter's present age y for now. To know the age of the woman 5 years ago, we will subtract 5 from her current age, which will give us x - 5. Also, the woman was 4 times as old as her daughter 5 years ago, hence:
x - 5 = 4y
If we rearrange that; x = 4y + 5 (let's call this equation 1)
Now, on to the second clue.
In the second sentence, we are told that in four years time, the woman will be two and a half times as old as her daughter. The woman's age in 4 years time is x + 4, hence:
x + 4 = 2[tex]\frac{1}{2}[/tex]y
x + 4 = 5y/2
2x + 8 = 5y (let's call this equation 2)
Next, we will find the value of y (the daughter's present age) by substituting equation 1 into equation 2, that is, putting '4y + 5' in place of x in equation 2, thus:
2(4y + 5) + 8 = 5y
8y + 10 + 8 = 5y
8y - 5y = 18
3y = 18
y = 6
Therefore, at present, the daughter is 6 years old. To find the mother's age, we will substitute the daughter's age in place of y in equation 1:
x = 4y + 5
x = 4(6) + 5 = 29
Hence, the woman is 29 years old, and her daughter is 6 years old.
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Ben joins a book club. He pays $12 for each book and $5 for shipping and handling charges for each order. A. Name the quantities that change in this problem situation and the quantities that remain constant. Determine which quality is independent and which quantity is dependent. B. Create a table of values to represent the total cost if Ben orders 1 or 2 books or spends $41, $65, or $125
ignore question A
Ben joins a reading group. Each order costs him $12 for the book and $5 for postage and handling. A. Identify the variables that change and the variables that don't change in this issue. Identify the dependent and independent components of each quantity.
I can say that the price of the books is independent and the shipping and handling charges is dependent.
Given that Ben joins a book club.
Ben pays $12 for each book and $5 for shipping and handling charges for each order.
Shipping and handling quantities remain the same.
The amount he pays for each book quantities change every time so it is not constant.
Therefore, We can say that the price of the books is independent and the shipping and handling charges is dependent.
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4 A number generator produces two digits in boxes like this. Each digit is generated randomly. It can be any digit from 0 to 9. Find the probability that: a the first number is 4 b the second number is less than 8 numbered 1 to 4 4 6 c there are no Os.
a. The probability that a first number is 4 is 1/10
b. The probability that the second number is less than 8/10.
c. The probability that there will not be any zero's is 81/100
Given, a number generator produces two digits in a box, each of it is generated randomly from 0 to 9.
a. The probability that the first number is 4 = ?
probability of an event = favourable number of outcomes/ Total number of outcomes.
Total number of outcomes = 10
P(n) = 1/10
b. The probability that the second number is less than 8 = ?
probability of an event = favourable number of outcomes/ Total number of outcomes.
Total number of outcomes = 10
P(n) = 8/10
c. The probability that there are no zero's = ?
since there are two boxes, there is possibility of getting two zero's.
probability of an event = favourable number of outcomes/ Total number of outcomes.
9/10 × 9/10
= 81/100
Hence we get the required results.
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5 ( C - 3 ) = 10 find C
Answer: c=5
Step-by-step explanation:
5(c-3)=10
5c-15=10
5c=10+15
5c=25
c=5
Answer:
5(c-3)=10
(c-3) =10-5
(c-3)=5
c=5+3
c=8
what is the absoulte value of 0.75
Answer: 0.75
Step-by-step explanation:
please help me asap! ..
Answer:
B because there is no correlation
Step-by-step explanation:
hope this works :)
As seen in the diagram below, Sydney is building a walkway with a width of x feet to
go around a swimming pool that measures 8 feet by 7 feet. If the total area of the pool
and the walkway will be 240 square feet, how wide should the walkway be?
Answer: 4 feet
Step-by-step explanation:
[tex]Let\ width=x > 0\\Hence,\\(8+2x)(7+2x)=240\\(8)(7)+(2x)(7)+(8)(2x)+(2x)(2x)=240\\56+14x+16x+4x^2=240\\4x^2+30x+56=240\\4x^2+30x+56-240=240-240\\4x^2+30x-184=0\\[/tex]
Divide both parts of the equation by 4 :
[tex]x^2+7.5x-46=0\\x^2+11.5x-(4)(x)-(4)(11.5)=0\\(x)(x+11.5)-(4)(x+11.5)=0\\(x+11.5)(x-4)=0\\x+11.5=0\\x=-11.5\ feet\notin, \ hence\ x > 0\\x-4=0\\x=4\ feet\in,\ hence\ x > 0[/tex]
