log 30+ log 6 is not equivalent to log 36
What is equivalent expressions?Equivalent expressions are expressions that perform the same function not with standing their appearance. If two algebraic expressions are equivalent, they have the same value when the same value(s) for the variable are used (s).
The original phrase is as follows
Log 36
Following that, we write the alternatives (a) log 2+ log 18
Apply the logarithmic rule log 2+ log 18 log (218)
Log 2 plus log 18 log (36)
Remove the bracket
Log 2 plus log 18 log36
(a) Log 2+ Log 18 is the same as log 36.
(b) Log 30 plus log 6
Use the logarithms’ law. 30 logs or more 6 logs (30 x 6)
Log 30 plus log 6 Equals log (180)
Remove the bracket
Log 30-plus log 6-log180
Hence,
(c) Log 30+log 6 does not equal log 36.
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The function
h
defined by
h(t) = (49 + 4. 9t)(10 – t)
models the height, in meters, of an object
t
seconds after it is dropped from a helicopter.
1. Find or approximate the time when the object hits the ground. Explain or show your
reasoning
2. From what height is the object dropped? Explain or show your reasoning.
Answer:
55555555546776546567
Which of the following is correctly written in Standard Form?
Therefore , the solution to the given problem of equation comes out to be4x-3y = 6 as a standard equation in all the above options.
An equation's definitionAn equation is a representation of two identical variables in mathematics, one on either side of an equals sign. Common difficulties can be solved using equations. We frequently seek pre algebra help when faced with obstacles in real life. Lessons in pre-algebra cover the basics of mathematics.
Here,
Given : 4x-3y = 6
-4x + 2y =8
=> y = 4/5x + 4
=> 4/5x + 2y = 6
Thus ,
From the above following equations we get ,
4x-3y = 6
as a standard equation in all the above options.
Therefore , the solution to the given problem of equation comes out to be 4x-3y = 6 as a standard equation in all the above options.
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How do you calculate seed multiplication ratio?
The number of seeds produced from a single seed when it is sown and harvested is referred to as the seed multiplication ratio.
What is Seed?A seed is an undeveloped plant embryo and food reserve that is encased in a protective outer covering in botany. More broadly, "seed" refers to anything that can be sown, which could include seed and husk or tuber.
Seeds are the result of a ripened ovule being fertilised by sperm from pollen, resulting in a zygote. The embryo within a seed develops from the zygote, forming a seed coat around the ovule and growing to a certain size within the mother plant before growth stops.
The formation of the seed is a step in the reproduction process of seed plants (spermatophytes). Other plants, such as ferns, mosses, and liverworts, do not have seeds and must reproduce through water-based means.
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Airport Auto Leasing has a ratio of cars to trucks that is 5 to 3. If each leasing center has 24 trucks, which auto leasing company has more cars? Main Street Auto Leasing has more cars since it has cars while Airport Auto Leasing has cars only
If the ratio of cars to truck in Main Street Auto Leasing Company is 9 to 4 and in the airport Auto Leasing Company is 5 to 3 , then the Main Street Auto Leasing Company has more number of cars .
The Ratio of cars to truck in Main Street Auto Leasing Company is = 9:4 ;
the ratio of cars to truck in Airport Auto Leasing Company is = 5:3 ;
the number of trucks in each Leasing Company is = 24 trucks ;
Case (i) : Main Street Auto Leasing Company ;
Since the ratio is = 9:4 ,
So , the number of cars is = 9x and
the number of trucks = 4x ;
That means , [tex]4x = 24[/tex] ;
[tex]x = 6[/tex] ;
the number of cars in Main Street company is = [tex]9 \times 6[/tex] = 54 cars .
Case (ii) : Airport Auto Leasing Company ;
the ratio is = 5:3 ;
So , the number of cars is = 5x and
the number of trucks = 3x ;
That means , [tex]3x = 24[/tex] ;
[tex]x = 8[/tex] ;
the number of cars in Airport Auto company is = [tex]5 \times 8[/tex] = 40 cars .
Therefore , the Main Street Auto Leasing Company has more number of Cars .
The given question is incomplete , the complete question is
Main Street Auto Leasing has a ratio of cars to trucks that is 9 to 4. Airport Auto Leasing has a ratio of cars to trucks that is 5 to 3. If each leasing center has 24 trucks, which auto leasing company has more cars ?
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Angle J and Angle M are base angles of isosceles trapezoid JKLM. If angle j= 23x+5, and angle m = 13x+15 , find measure k .
The angle K for the Isosceles trapezoid is a supplementary angle to the angle J and the measure of angle K = 152°
What is an Isosceles trapezoidThis is a trapezoid in which the base angles are equal and therefore the left and right side lengths are also equal. The opposite angles are supplementary which implies they sum up to 180°.
angle J and angle M are base angles for the Isosceles trapezoid and are equal, so:
23x + 5 = 13x + 15
23x - 13x = 15 - 5 {collect like terms}
10x = 10 {divide through by 10}
x = 1
angle J = 23(1) + 5 = 28°
Angle K and angle J are supplementary so:
K = 180 - 28
K = 152°
Therefore, the measure of the angle K for the Isosceles trapezoid JKLM is equal to 152°
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Mrs Anderson has 185 pieces of wood he sold 25 peacas of wood to his neighbor and distract the rest of the world into piles around his house each pile of wood contained 40 pieces of wood which equation can be used to find peat the number of piles of wood Mr. Anderson made?
Answer: Let x be the number of piles of wood that Mr. Anderson made.
We know that he sold 25 pieces of wood to his neighbor, and the rest of the pieces of wood were divided into piles around his house, with each pile containing 40 pieces of wood.
Therefore, we can set up the equation:
185 pieces - 25 pieces = x * 40 pieces
Simplifying the equation:
160 = x * 40
To find the value of x, we need to divide 160 by 40
160/40 = x
x = 4
Therefore, Mr. Anderson made 4 piles of wood after he sold 25 pieces of wood to his neighbor.
It's worth noting that this equation was used to find the number of piles of wood Mr. Anderson made after selling 25 pieces to his neighbor, and assuming that he didn't use the rest of the wood for anything else except for making the piles.
Step-by-step explanation:
2 diagonals of a regular nonagon (a 9-sided polygon) are chosen. What is the probability that their intersection lies inside the nonagon
The probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
What is the probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event.
In this problem, the event of interest is the intersection of the two diagonals lying inside the nonagon. A nonagon is a 9-sided polygon, so there are 9 total corners, each of which can be one end of a diagonal. Therefore, there are 9 choose 2 = 36 total ways to choose two diagonals.
To find the number of favorable outcomes, we need to find the number of ways to choose two diagonals such that their intersection is inside the nonagon. To do this, we can notice that the diagonals that have an intersection inside the nonagon are the diagonals that connect non-adjacent corners of the nonagon. There are 8 non-adjacent corners, so there are 8 choose 2 = 28 ways to choose two non-adjacent corners.
So the probability of the intersection of the two diagonals lying inside the nonagon is:
P(intersection inside nonagon) = favorable outcomes / total outcomes = 28/36 = 2/3
Hence, the probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
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The probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
What is the probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event.
In this problem, the event of interest is the intersection of the two diagonals lying inside the nonagon. A nonagon is a 9-sided polygon, so there are 9 total corners, each of which can be one end of a diagonal. Therefore, there are 9 choose 2 = 36 total ways to choose two diagonals.
To find the number of favorable outcomes, we need to find the number of ways to choose two diagonals such that their intersection is inside the nonagon. To do this, we can notice that the diagonals that have an intersection inside the nonagon are the diagonals that connect non-adjacent corners of the nonagon. There are 8 non-adjacent corners, so there are 8 choose 2 = 28 ways to choose two non-adjacent corners.
So the probability of the intersection of the two diagonals lying inside the nonagon is:
P(intersection inside nonagon) = favorable outcomes / total outcomes = 28/36 = 2/3
Hence, the probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
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(25 points for the answer)
If John save 1/5 of his paycheck how much money would it take him to get to 14,500$ for his holiday trip? He earns $9062.5 each paycheck. (Unrealistic question unless you are under paid severely)
Use multiplication or division ONLY!
The amount of john would save 2900 rs
14500*1/5=2900
How much he earns on paycheck?A paycheck, also spelled paycheque, pay check or pay cheque, is traditionally a paper document issued by an employer to pay an employee for services rendered.a check used to pay an employee the amount of money the employee has earned.A paycheck can be an actual piece of paper (a check) that a person can take to the bank to deposit to their account or exchange for cash. Alternatively, a paycheck can be money a company electronically deposits directly into the employee's bank account.Take a look at how each common payroll interval works: Weekly: Once a week (52 paychecks per year) Biweekly: Once every other week (26 paychecks per year) Semimonthly: Twice per month (24 paychecks per yearTo learn more about paycheck refers to:
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what is the rate of decay f(x)=(.8)^x
9th grade AP algebra
The provided function, f(x)=(.8)^x, has a 20% rate of decay.
What is the Rate of decay or growth?
A rise in the resultant quantity for a given quantity is referred to as exponential growth, and a decrease in the resultant quantity for a given quantity is referred to as exponential decay.
given, a function f(x)=(.8)^x. To calculate the decay rate of this function.
The exponential decay formula aids in determining the exponential drop, which is a rapid reduction over time. To calculate population decay, half-life, radioactivity decay, and other phenomena, one uses the exponential decay formula. F(x) = a (1 - r)x is the general form.
Where
a = the initial amount
1-r is the decay factor
x = time span
from the given expression,
Decay factor = 0.8
That is also equal to 1 - r
1 - r = 0.8
r =0.2
Thus, rate of decay = r * 100%
rate of decay = 0.2 * 100 = 20%
therefore, The rate of the of the given function f(x)=(.8)^x is 20%.
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PLEASE HURRY!!
Find the value of x
Answer:
Step-by-step explanation:
3x=24
x=8
Using the graph below with the following point find the length of the two diagonals to determine if TUVW is a rectangle or not T(-5,0) U(7,3) V(9,-6) W(-3,-9)
The lengths of each diagonal are given as follows:
[tex]TV = \sqrt{232}[/tex][tex]WU = \sqrt{244}[/tex]As the lengths are different, the polygon TUVW is not a rectangle.
How to obtain the diagonals?The diagonal length is obtained using the formula for the distance between two points, presented as follows:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
In which [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of each point.
The first diagonal is TV, and the length is given as follows:
[tex]TV = \sqrt{(9 - (-5))^2 + (6 - 0)^2} = \sqrt{232}[/tex]
The second diagonal is WU, and the distance is given as follows:
[tex]WU = \sqrt{(-3 - 7)^2 + (-9 - 3)^2} = \sqrt{244}[/tex]
A rectangle has diagonals of equal length, hence the polygon for this problem is not a rectangle.
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Look at the graph, then select the correct answer.
Which distribution has the greatest spread?
A. Distribution 1
B. Distribution 2
C. Distribution 3
D. Distribution 4
The distribution has the greatest spread is
C. Distribution 3What is standard deviation?The term standard deviation refers to a measurement of the data's dispersion or spread from the mean.
A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed or spread out.
In the given problem the distribution that has a higher value of standard deviation is the one that has the highest spread spread
This is distribution 3 with a standard deviation of 7.2
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When can parallelism make your algorithms run faster when could it make your algorithms run slower?
When an algorithm necessitates extensive sharing of instantaneous results, parallelism slows it down. Because there are multiple independent parallel processes and the right number of threads, parallelism will speed up an algorithm.
What algorithm is parallelizable?The ones with data dependencies are the most challenging. It will be exceedingly challenging, for instance, if you are dealing with a vector and the input for the computation at point n depends on the output at position n-1.
When this occurs, you must comprehend what the original algorithm is doing and take an alternative approach. For the aforementioned case, it might be a difficulty with digital signal processing including a feedback-containing digital filter. These are challenging to parallelize, but that is not the sole solution. Instead, you might use the filter and signal's fast Fourier transforms, multiply them, and then perform the inverse transform. All of these operations can be partially parallelized.
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Write the answer to 3^4 x 3^7
(i) in the form 3^x
(ii) as an integer
Answer:
I)3^4 x 3^7=3^4+7(b/c the base is similar)
3^4 x 3^7=3^11
Ii) first 3^4=3x3x3x3=81
3^7=2187
then 81 x 2187=177147
3. ) Mary is the director of the Washington Performing Arts Center. Her employer offers a pension. Mary’s employer uses a formula to calculate the pension. Marina is planning on retiring at the end of this year after 30 years of employment. A retiring employee receives 1. 6% of his or her average salary for the last 5 years of employment multiplied by the number of years worked. Mary would receive this amount each year until her death. Her salaries for the last 5 years are $80,900; $90,200; $95,000; $99,000; and $104,000. Calculate Marina’s pension
Marina's pension amount is calculated by multiplying 1.6% of her average salary for the last 5 years by the number of years she has worked, which is 30.
1.6% x $80,900 = $1,282.40
1.6% x $90,200 = $1,444.32
1.6% x $95,000 = $1,520.00
1.6% x $99,000 = $1,584.00
1.6% x $104,000 = $1,664.00
Total = $7,604.72
Pension amount = $7,604.72 x 30 years
= $228,141.60
Marina's pension amount is determined using a formula set by her employer, the Washington Performing Arts Center. This formula takes into account her average salary for the last five years, which is $469,100, and multiplies it by 1.6%, then by the number of years she has worked for the Center, which is 30. This results in a pension amount of $228,141.60. This amount will be paid each year until her death. This pension amount is calculated based on the salaries she has earned over the past five years, which include $80,900; $90,200; $95,000; $99,000; and $104,000.
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Let ABC be a triangle, and
M, N, and K represent the midpoints of sides AB, BC, and AC respectively.
If area of the triangle ABC is 6.0 square feet, then what is the area of the triangle MAK?
Step-by-step explanation:
please refer to the sketch
4/5 + 3/4= asap PLEASEEE
A company has two manufacturing plants with daily production levels of 5x +14 items and 3x - 5 items, respectively. The first plant produces how many more items daily than the second plant?
Answer:
21x
Step-by-step explanation:
5x+14=19x
3x-5=-2x
-2x-19x=21x
Which of the following is the graph of y=-4 square root x
In the second graph, these points are located. As a result, the second graph is the function's correct graph.
what is function ?In mathematics, the term "linear function" refers to two different but related ideas. In calculus and related fields, a quadratic variable of grade 0 or 1 is a linear function if its graph is a direct line. A straight line on a reference system is a representation of a linear function. For instance, the linear function y = 3x - 2 is a straight line just on coordinate plane, hence it is a linear function. Since f(x) may be connected to y, the function can be represented by f(x) = 3x - 2.
given
The function provided is
This function is defined for any x values that are positive, including 0.
The radical expression x has a constant positive value. Given that is a function, it is always negative.
At x=0, = 0
At x=1, = -4
At x=4, = -8
This indicates that the graph of the specified function traveling through the points (0,0), (1,-4) and (4,-8).
In the second graph, these points are located. As a result, the second graph is the function's correct graph.
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√≈≈≈≈≈Which of the following is a one-to-one function? y = [[2x]], y = x^2, f(x) = { 4x + 1;x < -2
The one-to-one function is obtained as f(x) = 4x + 1 which is a linear function.
What is a function?A function y = f(x) is defined as a one to one relation between sets X and Y. The set X is called the domain while Y is called the range of f(x).
A function can either have one-to-one or many-to-one mapping.
One-to-one mapping implies unique element in the domain for each element in the range while for many-to-one mapping there are many elements in the domain for one element in the range.
The given functions are y = [2x] , y = x² and f(x) = 4x + 1 respectively.
They can be examined one by one as follows,
(a) y = [2x]
It is a greatest integer function.
At x = 1.1, y = [2 × 1.1] = [2.2] = 2
And, for x = 1.2, y = [2 × 1.2] = [2.4] = 2
It implies for different values of x, the function has same value.
Thus, it is not one-to-one function.
(b) y = x²
Find values of the function at two different x as,
x = -2, f(x) = (-2)² = 4
And, for x = 2, f(x) = 2² = 4.
It implies for different values of x, the function has same value.
Thus, it is not one-to-one function.
(c) f(x) = 4x + 1
It is a equation of a straight line.
Which implies it has different values for different values of x.
Thus, it is a one-to-one function.
Hence, out of the given functions only f(x) = 4x + 1 is one-to-one.
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The domain of y = √√√x-5-1 is
DONE
3 of 8
P
10
1000
098
7
6
5
4
3
12
y
2
19
Ð
6
8x
The function domain is X≥5 Or in interval notation [5, ∞)
What is Domain definition?The domain of a function is the set of input or argument values for which the function is real and definedThe domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limitedIn mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by {\displaystyle \operatorname {dom} } or {\displaystyle \operatorname {dom} f}, where f is the functionFind non-negative values for radicals x≥5solve x-5≥0:x≥5 function domain is X≥5 Or in interval notation [5, ∞)To learn more about Domain definition refers to:
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A neighbor of yours is getting ready to
plant a garden of flowers in his backyard.
He asks you for ideas on how to
conserve soil. You notice that his
backyard has a lot of hills. What do you
suggest?
In order to maintain soil fertility and productivity, soil must be protected from erosion and other forms of deterioration. Water use and watershed management are typically included.
What comes first in gardening?Eliminating the existing vegetation is the first step in making a garden bed. Weeds can be manually pulled. Just be certain to remove the roots to prevent regrowth. You might want to rent a gas-powered sod cutter to get rid of the grass if you're starting with a lawn.
What is an example of soil conservation?Better soil conservation techniques that affect both erosion and fertility include crop rotation, cover crops, conservation tillage, and installed windbreaks.
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forty children from an after-school club went to the field trip . this is 25% of the children in the club. how many children are in the club?
Answer: 25% of 40 is 40 times 25 divided by 100 which is 10 (number of children in the club)
there:)
Answer: 160 children
Step-by-step explanation: 25% times 4 is 100%. So, you'd multiply 40 by 4.
What is the value of sin cos theta?
If sinθ⋅cosθ = 1/2, then the value of sinθ + cosθ = √2
We know that the trigonometric sine function is nothinng but the ratio of the length of the opposite side of angle to that of the hypotenuse in a right triangle.
And cosine function (cos function) is the ratio of the length of the adjacent side of angle to that of the hypotenuse.
Given that sinθ⋅cosθ = 1/2
2(sinθ⋅cosθ) = 1 .........(1)
We know that trigonometric identity,
sin(2θ) = 2 sinθ cosθ
so equation (1) becomes,
sin(2θ) = 1
We know that sin(π/2) = 1
Comparing with equation sin(2θ) = 1 we get,
2θ = π/2
θ = π/4
Using trigonometric table,
sin(π/4) = 1/√2
and cos(π/4) = 1/√2
The value of sinθ+cosθ would be,
sin(π/4) + cos(π/4)
= (1/√2) + (1/√2)
= 2/√2
= √2
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The complete question is:
If sinθ⋅cosθ=1/2 find the value of sinθ+cosθ
which is the functions for increases 8.3%
Answer:
The US Consumer Price Index (CPI) increased 8.3% in the 12 months through August, with rent, food and healthcare accounting for the rise Excluding volatile food and gas prices, inflation climbed 6.3% year-on-year in July and 8.2% in September. US inflation ticked back up in August despite plunging gas prices.
citations: https://nypost.com/2022/10/13/inflation-hits-8-2-in-september-as-core-prices-surge/Step-by-step explanation:
Sergio purchased 4 items for $1.50 each. Sales tax was 8.25%. What was the total price?
please explain if you can, thxs!
Answer:
6.495.Step-by-step explanation:
The total cost of the items before tax was $1.50 * 4 = $<<1.54=6>>6.
The sales tax was $6 * 8.25% = $<<68.25*.01=0.495>>0.495.
So the total price was $6 + $0.495 = $<<6+0.495=6.495>>6.495.
The rate of growth dP / dt of a population of bacteria is proportional to the square root of t, where P is the population size and t is the time in days (0 ? t ? 10) as shown below.
dP/dt=k \sqrt{t}
The initial size of the population is 300. After 1 day the population has grown to 600. Estimate the population after 8 days. (Round your answer to the nearest whole number.)
The population of bacteria after 8 days is 7088
Here, we have been given an equation for the rate of growth of a population of bacteria
dP/dt = k√t
where P is the population size
and t is the time in days (0 ≤ t ≤ 10)
We rewrite above equation as,
dP = k√t dt
Integrating both sides, we get,
P = (2/3) × kt^(3/2) + C
We find the value of C.
For t = 0, P = 300 as the initial size of the population is 300.
Substitute t = 0 in above equation.
300 = 0 + C
C = 300
So, the above equation becomes,
P = 300 + (2/3) × kt^(3/2) .......(1)
Now we find the value of k.
After 1 day the population has grown to 600.
substitute t = 1, P = 600 in equation (1)
600 = 300 + (2/3) × k
(2/3)k = 300
k = 900/2
k = 450
So, the equation of population of bacteria after time t is:
P = 300 + [(2/3) × 450 × t^(3/2)]
P = 300 + 300 × t^(3/2)
P = 300 (1 + t^(3/2))
To find the population after 8 days, substitute t = 8
P = 300 (1 + 8^(3/2))
P = 7088.22
P ≈ 7088
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A pattern follows the rule "Starting with three, every consecutive line has 2 less than twice the previous line. "
1. How many marbles must be in the fifth line?
Therefore , the solution to the given problem of unitary method comes out to be 34 marbles are therefore on the sixth line.
Define the unitary method.The term unitary refers to a single or unique or variable unit. As a result, the purpose of this strategy is to construct values with regard to a single unit. For instance, if a car drives 44 kilometres on two litres of fuel, the unitary technique can be used to determine how many kilometers it will travel on one.
Here,
Every subsequent line, beginning with one, contains two less characters than the one before it.
This signifies that your starting line contains three marbles. The 3 marbles are multiplied by 2 to get 3x2=6, and the result is subtracted to get 6-2=4.
This implies that you will receive 4 marbles for the following line.
As a result, in order to determine the sixth line, you must first determine the fifth line by counting the number of marbles on the fourth line because your diagram does not include a fifth line.
(4) = ten marbles.
10×2=20
20-2=18
(5) line = (18)
18×2=36
36-2=34
Therefore , the solution to the given problem of unitary method comes out to be 34 marbles are therefore on the sixth line.
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Write a ratio of the following in three ways.
Write your answers on the blanks.
1) 6 Weeks to 12 days_____
2) 10 decimeters to 10 centimeters_______
3) 4 days to 36 hours___
4) 4 months to 8 weeks___
5) 30 seconds to 6 minutes__
6) 24 girls to 16 boys___
7) 12 mangoes to 36 fruits__
8) 2. Years to 36 months__
9) 45 points to 9 games__
10) 468 students for 9 classrooms___
Ratios express the relationship between two or more quantities, they can be expressed in different forms such as 6:12, 42:12 and 3:1, 10:10, 100:10, and 10:1, 24:36 and 2:3.
1. 6 Weeks to 12 days:
6:12 (using the same unit of measurement, weeks)42:12 (converting weeks to days, 6 weeks x 7 days/week = 42 days)3:1 (simplifying the ratio to its simplest form)2. 10 decimeters to 10 centimetres:
10:10 (using the same unit of measurement, decimeters)100:10 (converting decimeters to centimeters, 10 decimeters x 10 centimeters/decimeter = 100 centimeters)10:1 (simplifying the ratio to its simplest form)3. 4 days to 36 hours:
4:36 (using the same unit of measurement, days)24:36 (converting days to hours, 4 days x 24 hours/day = 96 hours)2:3 (simplifying the ratio to its simplest form)4. 4 months to 8 weeks:
4:8 (using the same unit of measurement, months)16:8 (converting months to weeks, 4 months x 4 weeks/month = 16 weeks)2:1 (simplifying the ratio to its simplest form)5. 30 seconds to 6 minutes:
30:6 (using the same unit of measurement, seconds)180:6 (converting seconds to minutes, 30 seconds x 6 minutes/60 seconds = 0.5 minutes)30:1 (simplifying the ratio to its simplest form)6. 24 girls to 16 boys:
24:16 (using the same unit of measurement, girls and boys)3:2 (simplifying the ratio to its simplest form)7. 12 mangoes to 36 fruits:
12:36 (using the same unit of measurement, mangoes and fruits)1:3 (simplifying the ratio to its simplest form)8. 2 years to 36 months:
2:36 (using the same unit of measurement, years and months)6:36 (converting years to months, 2 years x 12 months/year = 24 months)1:6 (simplifying the ratio to its simplest form)9. 45 points to 9 games:
45:9 (using the same unit of measurement, points and games)5:1 (simplifying the ratio to its simplest form)10. 468 students for 9 classrooms:
468:9 (using the same unit of measurement, students and classrooms)52:1 (simplifying the ratio to its simplest form)To learn more about the ratio, visit:
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write an equation in pint-slope form, slope-intercept, and standard form
Slope: -5 (-3,-7)
(-6,10), (-4,18)
(-4,9), (1,14)
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
to get the equation of any straight line, we simply need two points off of it, let's use (-6,10), (-4,18)
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{18}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{18}-\stackrel{y1}{10}}}{\underset{\textit{\large run}} {\underset{x_2}{-4}-\underset{x_1}{(-6)}}} \implies \cfrac{8}{-4 +6} \implies \cfrac{ 8 }{ 2 } \implies 4[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-6)}) \implies {\large \begin{array}{llll} y -10 = 4 ( x +6) \end{array}} \\\\\\ y-10=4x+24\implies -4x+y=34\implies \stackrel{standard~form}{{\Large \begin{array}{llll} 4x-y=-34 \end{array}}}[/tex]