The distance between the line containing points (4, –1) and (4, 9) and point p (1,6) is of:
3 units.
Distance of point and lineThe standard equation of a line is given by the rule presented as follows:
ax + by + c = 0.
The coordinates of the points which we want to find the distance from the line are given as follows:
(x0,y0).
Then the shortest distance is given by the equation presented as follows:
D = |a(x0) + b(y0) + c|/sqrt(a²+b²).
The two points of the line are given as follows:
(4, –1) and (4, 9).
Since the x-coordinate is constant, the line has a slope of infinite, meaning that it is a vertical line defined as follows:
x = 4.
x - 4 = 0.
The point p has these following coordinates:
p(1,6).
Hence the distance between the point and the line is:
D = |a(x0) + b(y0) + c|/sqrt(a²+b²).
D = |1(1) + 0(6) - 4|/sqrt(1² + 0²).
D = |-3|
D = 3 units.
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Frank raises cattle for livestock. Last year, he sold exactly 30% of his cattle to a local rancher. If Frank has not gained or lost any cattle since last year, which of the following could be the total number of cattle he currently owns?
A) 610
B)520
C)350
D)300
The total number of cattle Frank currently owned could be C)350
How to find the total number of cattle Frank currently ownedThe problem is asking multiples of 7.
Multiples of 7 come into play after working the the percentage as follows
Frank sold 30%, the percentage left is
= 100% - 30%
= 70%
= 0.7
The multiple of 7 that is a number 7 will divide without remainder here is 350 and this is the correct answer.
= 350 / 0.7
= 500
This means Frank had 500 cattle sold
0.3 * 500 = 150
currently having
= 500 * 0.7 = 350
= 500 - 150 = 350
Remember that a cattle will always be in whole number
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-3x + 6 = 4 - 6x
I kept getting 1.5 But it's not correct. ???
Answer:
-2/3 or -0.6666
Step-by-step explanation:
-3x + 6 = 4 -6x
Let's move the x to one side
-3x +6x=4-6
Combine like terms
3x = -2
Divide both sides by 3
-2/3=x
or -0.666666
The assets and liabilities of a landscaping business are listed below.
Owned Inventory
$30,500
Cash
$75,420
Building Mortgage
$154,265
Savings Account
$28,000
Owned Equipment
$15,670
Small Business Loan
$25,652
Credit Cards
$11,450
Accounts Receivable
$11,560
Investments
$178,925
Which balance sheet correctly shows the assets, liabilities, and net worth of the landscaping business?
The total value of the ice cream shop owner's business assets would be; $286,898.
What are business assets?Business assets are the value of the assets of the Ice Cream Shop. The business assets consist of liabilities (amounts owed outsiders) and equity (the difference between assets and liabilities).
Business Assets:
Owned Inventory $30,500
Cash $75,420
Savings Account $28,000
Owned Equipment $15,670
Accounts Receivable $11,560
Property Value $125,768
Total assets = $286,898
Business Liabilities:
Small Business Loan $25,652
Other Debt $1,235
Building Mortgage $154,265
Total liabilities = $171,152
Equity = $115,746 ($286,898 - $171,152)
The total value of the ice cream shop owner's business assets would be; $286,898.
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Answer:
The net worth of the landscaping business is $148,708.
Step-by-step explanation:
Assets:
(Owned Inventory) $30,500
(Cash) $75,420
(Savings Account) $28,000
(Owned Equipment) $15,670
(Accounts Receivable) $11,560
(Investments) $178,925
30500+75420+28000+15670+11560+178925 = 340075
Liabilities:
(Building Mortgage) $154,265
(Small Business Loan) $25,652
(Credit Cards) $11,450
154265+25652+11450= 191367
Assets - liabilities = net worth
340075 - 191367 = 148708
So, the net worth of the landscaping business is $148,708.
2x + 4y = 4
number of solution
Given equation 2x + 4y = 4 has infinitely many solutions.
We have been given an equation 2x + 4y = 4
We need to find the number of solutions.
Above equation is a linear equation with two variables.
We know that, a linear equation in two variables has infinitely many solutions.
For any value real value of x we can find corresponding value of y.
Since x can takes infinitely many inputs the output would be infinitely many.
Therefore, given equation 2x + 4y = 4 has infinitely many solutions.
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use the figure below to solve for the missing value(s):
The missing values are:
m∠1 = 36°
m∠2 = 122°
m∠3 = 122°
m∠4 = 38°
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
The figure has two triangles.
58° and m∠3 is a straight angle.
58 + m∠3 = 180
m∠3 = 180 - 58
m∠3 = 122
Now,
m∠3 + m∠4 + 20 = 180
122 + m∠4 + 20 = 180
m∠4 = 180 - 122 - 20
m∠4 = 180 - 142
m∠4 = 38
m∠3 and m2 are opposite angles.
Opposite angles are equal.
m∠3 = m∠2 = 122
Now,
m∠1 + m∠2 + 22 = 180
m∠1 + 122 + 22 = 180
m∠1 = 180 - 144
m∠1 = 36
Thus,
The missing values are:
m∠1 = 36°
m∠2 = 122°
m∠3 = 122°
m∠4 = 38°
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The carousel on the national mall has four rings of horses. Kiran is running on the inner ring, which has a radius of 9 feet. Mai is riding on the outer ring, which is 8 feet farther out from the center then the inner ring is. And one rotation of the carousel, how much farther does mai travel from Kiran. One rotation takes 12 seconds. How much faster does mai travel than kiran?
Answer:
50.24
Step-by-step explanation:
so u subtract the distanse not 9-4 u have to find a porportional ratio it was 100 - 50 or something add u get 50.24
tbh i didnt knw i just searched it up and im only in 6th grade so im not the the smartest in the world
i have no clue what the second on is so good luck with that
Graph the following features:
Y-intercept=1
Slope- -2/3
The graph with the y-intercept of 1 and a slope of -2/3 is added as an attachment
What are linear equations?Linear equations are equations whose slopes are constant average rates of change.
How to graph the equation of the line?The given parameters are
y-intercept, c = 1Slope, m = -2/3A linear equation is represented as
y = slope * x + y-intercept i.e. y = mx + c
Substitute the known values in the above equation
So, we have the following equation
y = -2/3x + 1
Hence. the linear equation is y = -2/3x + 1
See attachment for the graph
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Suppose you have a complete, weighted graph with 8 vertices. How many Hamilton Circuits are there in this graph?
The number of Hamilton Circuits with 8 vertices are 5040.
Given that, a complete, weighted graph with 8 vertices.
What are Hamilton Circuits?A Hamiltonian circuit is a circuit that visits every vertex once with no repeats. Being a circuit, it must start and end at the same vertex. A Hamiltonian path also visits every vertex once with no repeats, but does not have to start and end at the same vertex.
For N vertices in a complete graph, there will be (n−1)!=(n−1)(n−2)(n−3)…3⋅2⋅1 routes. Half of these are duplicates in reverse order, so there are (n−1)!/2 unique circuits.
A complete graph with 8 vertices would have = 5040 possible Hamiltonian circuits. Half of the circuits are duplicates of other circuits but in reverse order, leaving 2520 unique routes.
Therefore, the number of Hamilton Circuits with 8 vertices are 5040.
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If 7-3(2x-1)=2x+26, then x=
The value of x in 7-3(2x-1)= 2x+26 is -4
What is linear equation?Linear equation is is a mathematical statement, which has an equal sign (=) between the algebraic expression. Linear equations are the equations of degree 1. It is the equation for the straight line. The solutions of linear equations will generate values, which when substituted for the unknown values, make the equation true. In the case of one variable, there is only one solution. For example, the equation x + 3= 0 has only one solution as x = -3.
To find x in 7-3(2x-1)= 2x+26 ,we solve the parentheses first which will give
7- 6x+3= 2x+26
collect the like terms
-6x-2x=26-3-7
-8x= 16
divide both side by -8
-8x/-8= 16/-8
therefore x= -2
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round this number to the hundredth 3.6432
Exponential test y =4
The function y = 4 is a straight line and not an exponential function.
Given, a function y = 4
now, we have to test the function is exponential or not
As, the function is a straight line graph i.e. y = 4.
Now, the function y = 4 is a straight line graph which is parallel to the x-axis.
So, the function y = 4 is not an exponential function
Hence, the function y = 4 is a straight line and not an exponential function.
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56% of the students at a collage are from in-state. aIf 4,620 students are from instate how many students attend the collage
A total of 2587 students attended the collage
How to determine the number of students in the college?From the question, the given parameters are:
Proportion of students = 56% are at the collage Total number of students = 4628The above parameters implies that
Number of students that attended = 56% x Total number of students
Represent the total number of students with x
So, we have the following representation
Number of students that attended = 56% * x
Where
x = 4620
So, we have
Number of students that attended = 56% x 4620
Evaluate the products
Number of students that attended = 2587.2
Approximate
Number of students that attended = 2587
Hence, 2587 of the students attended the collage
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he residence of a city voted on whether to raise property taxes the ratio of yes votes to no votes was 4 to 7 if there was a 5918 total votes how many yes votes were there
There is a total of 2152 yes votes
How to determine the number of yes votes?From the question, the statement is given as
The ratio of yes votes to no votes was 4 to 7
Mathematically, this can be represented as
Ratio = 4 : 7
Alternatively, we have
Yes : No = 4 : 7
Express the ratio as fraction
Yes = Yes/Yes + No
So, we have
Yes = 4/4 + 7
Evaluate the sum
Yes = 4/11
From the question, we have
Total votes = 5918
So, we have
Yes = 4/11 * 5918
Evaluate
Yes = 2152
Hence, the number of yes votes is 2152
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Thelma and Patrick went to a cafe
for lunch. One of them is a
vegetarian. Thelma ordered a
turkey sandwich with extra
mustard. Who is the vegetarian?
Patrick is vegetarian and Thelma is non vegetarian.
What are vegetarian?
The practice of not eating any meat is known as vegetarianism. It might also mean avoiding eating any leftovers from animal slaughter. There are several reasons to embrace a vegetarian diet. Due to their respect for sentient animal life, many people refrain from eating meat.
Main Body:
As Thelma ordered Turkey sandwich with extra mustard and turkey is an animal , which makes her non vegetarian so it is obvious that Patrick is a vegetarian and Thelma is non vegetarian.
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Find the LCM of 14 and 21. I need the explanation
Answer:
LCM = 42
Step-by-step explanation:
There are many ways to do this.
Listing Multiples:
Find and list multiples of each number until the first common multiple is found. This is the lowest common multiple.
Multiples of 14:
14, 28, 42, 56, 70
Multiples of 21:
21, 42, 63, 84
Therefore,
LCM(14, 21) = 42
Prime Factorization:
List all prime factors for each number.
Prime Factorization of 14 is:
2 x 7 => 21 x 71
Prime Factorization of 21 is:
3 x 7 => 31 x 71
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The new superset list is
2, 3, 7
Multiply these factors together to find the LCM.
LCM = 2 x 3 x 7 = 42
In exponential form:
LCM = 21 x 31 x 71 = 42
LCM = 42
Therefore,
LCM(14, 21) = 42
Cake / Ladder:
Divide your numbers by prime numbers as long as both numbers are evenly divisible by that prime.
Cake / Ladder
7 14 21
2 3
When there are no more primes that evenly divide into both numbers you are done.
The LCM is the product of the numbers in the L shape, left column and bottom row.
LCM = 7 x 2 x 3
LCM = 42
Therefore,
LCM(14, 21) = 42
Division Method:
Write your numbers in the top row.
Divide your numbers by prime numbers as long as at least one of your numbers is evenly divisible by a prime number.
Division Table
2 14 21
3 7 21
7 7 7
1 1
Bring down any numbers that are not evenly divisible by the prime number.
When the last row of results is all 1's you are done.
Find the product of the prime numbers in the first column to get the LCM:
LCM = 2 x 3 x 7
LCM = 42
Therefore,
LCM(14, 21) = 42
GCF Method:
LCM(14,21) = (14 × 21) / GCF(14,21)
= (14 × 21) / 7
= 294 / 7
= 42
Therefore,
LCM(14, 21) = 42
Venn Diagram:
Inside circle 14: 2
In between circles: 7
Inside circle 21: 3
Then, use prime factorization.
Find the set of prime factors for each number.
Prime Factorization Set for 14 is:
2, 7
Prime Factorization Set for 21 is:
3, 7
Identify the intersections of prime numbers and put them into the Venn Diagram where their circles intersect. Remove the numbers from the original sets.
14 ∩ 21
7
With the remaining prime numbers in each set, if any, put them into their respective circles, not in intersections.
14
2
21
3
Find the union of the sets in the Venn Diagram. This is the superset of all of the prime numbers in the diagram.
14 ∪ 21
The new superset list is
2, 3, 7
Multiply these factors together to find the LCM.
LCM = 2 x 3 x 7 = 42
LCM = 42
Therefore,
LCM(14, 21) = 42
PLEASE MARK AS BRAINLIEST!!!The measure of an obtuse angle is A: greater than 0 and less than 90 degrees B: 90 degrees C. greater than 90 and less than 180 degrees
The measure of an obtuse angle is greater than 90° but less than 180°
What is an obtuse angle?An obtuse angle is a type of angle that is always larger than 90° but less than 180°. In other words, it lies between 90° and 180°.
An angle is the space between two intersecting lines or surfaces at or close to the point where they meet.
Angles are mostly measured in degrees. But it can also be measured in radian. Examples of obtuse angle are 91°, 100°, 150° e.t.c
Other examples of angles are acute angle, reflex angle , right angle.
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Marco opened a savings account 10years ago. The account earns 5% interest,compounded annually. If the current balance is $400, how much did he deposit initially? Round your answer to the nearest cent.
Answer:
245.57
Step-by-step explanation:
[tex]P\left(1+0.05)^{10}=400 \\ \\ P=\frac{400}{(1.05)^{10}} \\ \\ P \approx 245.57[/tex]
Use your calculator to find the angle, to the nearest hundredth of a degree, whose tangent value is
O 0.35
O 18.43
O 0.32
O 71.57
Answer:18.43
Step-by-step explanation:
0.8421 as a fraction
Answer:
8421/10000
Step-by-step explanation:
8421/10000
The greatest temperature ever recorded in the United States occurred at an elevation of 178 feet below sea level. The greatest temperature ever recorded in Africa occurred at an elevation of 545 feet greater than in the United States. At what elevation, in feet, did the greatest temperature in Africa occur?
The greatest temperature in Africa occur is 367 feet.
What are integers?The collection of positive and negative integers is known as an integer. Integers, like whole numbers, do not include the fractional portion.
Zero (0)Positive Integers (Natural numbers)Negative Integers (Additive inverse of Natural Numbers)Given:
The greatest temperature ever recorded in the United States occurred at an elevation of 178 feet below sea level.
Using integers we represent it as (-178) feet.
and, greatest temperature ever recorded in Africa 545 feet greater than in the United States
= -178 + 545
= 367 feet.
Hence, The greatest temperature in Africa occur is 367 feet.
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Tammy must choose a number between 61 and 107 that is a multiple of 3,9 and 12. Write all the numbers that she could choose
Answer:
G LCM (least common multiple) of 3, 9, and 12. After doing that, find the number that is between 61 and 107.
Step-by-step explanation:
Least common multiple (lcm) is where g finds out the number that can be divided by all the numbers (3, 9, and 12 in this case) and still come out with a whole number.
Una grúa está elevando 5 /7 de los 224 kg que puede elevar como máximo ¿Cuántos kilos está elevando?
The number of kilograms that the crane is lifting, based on the maximum it can lift and the proportion being lifted is 160 kilos
How to find the number of kilos?The number of kilos that the crane is lifting can be found by the formula :
= Maximum kilogram capacity x Proportion of maximum being lifted
Maximum kilogram capacity = 224 kg
Proportion of maximum being lifted = 5 / 7
The kilos being lifted by the crane is therefore :
= 224 x 5/7
= 1, 120 / 7
= 160 kilos
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Write one quadratic equation that forms a graph through the points (−4,2) and (1,2) and has a
minimum value at the vertex.
Explain it in detail please
Quadratic equation that passes through the points (-4,2) and (1,2) and a form a graph of horizontal line y =2.
Graph is attached.
As given in the question,
Quadratic equation passes through the points (-4,2) and (1,2)
(x₁, y₁) =(-4,2)
(x₂ ,y₂) = (1,2)
(y-y₁)/ (x-x₁) = (y₂ -y₁)/(x₂ -x₁)
⇒(y-2)/(x +4) =(2-2)/)1+4)
⇒ (y-2)/(x+4) =0
⇒y -2 =0
⇒y =2
Quadratic equation formed from the given points (-4,2) and (1,2) is y =2.
which represents the horizontal line and does not have any vertex.
Graph of the quadratic equation y =2 is attached.
Therefore, quadratic equation that passes through the points (-4,2) and (1,2) and a form a graph of horizontal line y =2.
Graph is attached.
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If 10 ops are equal to 1.63 sals, how many sals are equal to a book that costs
12.25 ops?
Answer:
if the selling price of the radio is Arya 4321 and loss e79 find the cost price of the radio
Please solve :) and hurry!
The price for 7 bags of trail mix and 4 bananas is 15.45 dollars.
The expression for x trail bag and y bananas is 1.35x + 1.50y.
How to represent expression?In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)
Therefore, the cost of a bag of trail mix at the corner store is 1.35 dollars and the cost of a banana is 1.5 dollars.
The cost for 7 bags of trail mix and 4 bananas can be computed as follows;
let
x = bags of trail mix
y = number of banana
Therefore,
1.35x + 1.50y
1.35(7) + 1.50(4) = 9.45 + 6 = 15.45
Therefore, let's find the expression for x trail bag and y bananas.
Hence,
1.35x + 1.50y
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Ethan repairs household appliances like dishwashers and refrigerators. For each visit, he charges 25 plus 22 per hour of work. A linear equation that expresses the total amount of money Ethan earns per visit is y=25+22x .
The independent variable x is the hour of work.
The dependent variable y is the total money Ethan earn per visit.
The y-intercept is 25.
The slope is 22.
Ethan charges a one time fee of 25 dollars. For each visit Ethan earns 22 dollars for each hour of work.
How to solve linear equations?Ethan repairs household appliances like dishwashers and refrigerators. For each visit, he charges 25 plus 22 per hour of work.
A linear equation that expresses the total amount of money Ethan earns per visit is y = 25 + 22x.
Using slope intercept equation,
y = mx + b
where
m = slopeb = y-intercepty = 25 + 22x
The independent variable x is the hour of work.
The dependent variable y is the total money Ethan earn per visit.
The y-intercept is the value of y when x = 0. Therefore, the y-intercept is 25.
The slope is the change in the dependent variable with respect to the change in the independent variable. The slope is 22.
Ethan charges a one time fee of 25 dollars. For each visit Ethan earns 22 dollars for each hour of work.
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An auto insurance company charges males 16-18 years old a base price of $1100 for insurance in a given year. Their accuracies have determined that there is a 8.5% a claim will be made against such a policy and an average claim of $4900. What does the insurance company expect to make on average off of each policy holder?
If a claim will be made against such a policy and an average claim of $4900. the insurance company should make on average off of each policy holder is $683.5.
How to find the amount the company should make?Using this formula to find the amount
Amount = [Percentage claim × ( Base price - Average claim)] + [(1 - percentage claim) × Base price]
Let plug in the formula
Amount = [0.085 × ($1,100 - $4,900)] + [(1-0.085) × $1,100]
Amount = [0.085 × (- $3,800)] + [(0.915 × $1,100]
Amount = -$325+ $1,006.5
Amount = $683.5
Therefore the insurance company will make the amount of $683.5.
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need help asap please
Jada is planning a kayak trip. She finds an expression for the time, T(s), in hours it takes her to paddle 10 kilometers upstream in terms of s, the speed of the current in kilometers per hour. Jada gets if she allows s to take on any value between 0 and 7.5.
The domain of the function that represents Jada's trip is the set of input value the function can take
The appropriate domain is all real numbers except
x = 5.5
by looking at the graph, we can see that:
The x-value starts at negative infinity, and ends near 5.5
The x-value then continues near 5.5, and ends at positive infinity
This means that the input of the graph cannot be 5.5
Hence, an appropriate domain would be: x # 5.5
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Deduce the following in standard form: 3 −
The standard form of the given fractions are;
(i) −45/30
(ii) 16/−36
(iii) −3/−15
(iv) 68/−119
How to write fractions in standard form?
A fraction is said to be in standard form when both the numerator and denominator are co-prime numbers. Thus;
1) −45/30; Divide both numerator and denominator by 15 to get;
(−45 ÷ 15)/30
= -3/2.
(2) 16/−36; Divide both numerator and denominator by 4 to get;
(16 ÷ 4)/(−36 ÷ 4)
= -4/9
(iii) −3/−15; Divide both numerator and denominator by -3 to get;
(-3 ÷ 4)/(−15 ÷ 4)
1/5
(iv) 68/−119; Divide both numerator and denominator by 19 to get; -4/7
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Complete question is;
Reduce each of the following rational numbers in standard form:
(i) −45/30
(ii) 16/−36
(iii) −3/−15
(iv) 68/−119
Members of the student government are planning a movie night on campus. They have asked a random sample of students which of four movies the student would prefer. Here are the results Movie A- 31 students, Movie B- 27 students, Movie C- 34 students, Movie D- 28 students. There are 900 students total on campus. Based on the above information, how many students on campus would we expect to prefer Movie C? Round your answer to the nearest whole number. Do not round any intermediate calculations
There are 255 students who prefer Movie C.
In the given case, the total number of students in the campus = 900
Number of students in the random sample :
= 31 + 27 + 34 + 28
= 120
Number of students who prefer to watch movie C in the chosen sample:
= 34
To get number of students who would prefer to watch the movies C in the total population of 900, we can extrapolate the data from the chosen sample to the entire population.
Thus, number of students expected to prefer movie C in the campus =
34/120 × 900
= 255
Hence the expected number of students are 255.
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