The solutions to these system of equations are given as follows:
1. x = 1, y = 7.
2. x = 0.5, y = 2.
3. x = 6, y = -2.
4. x = 3, y = 3.
What is a system of equations?A system of equations is a set of equations involving multiple variables that are related, and then operations are made to solve these equations and identify the numeric value of each variable in the context of a problem.
For item 1, it is already stated that the solution for x is x = 1, hence the solution for y is obtained as follows:
y = 2(1) + 5 = 7.
For item 2, we are given two equations for y, hence the solution for x is obtained as follows:
2x + 1 = 6x - 1
4x = 2
x = 2/4
x = 0.5.
Hence the solution for y is:
y = 2(0.5) + 1 = 1 + 1 = 2.
For item 3, from the second equation, we have that:
y = 4 - x.
Then the solution for x will be of:
2(x - 7) = 4 - x
2x - 14 = 4 - x
3x = 18
x = 18/3
x = 6.
The solution for y is:
y = 4 - 6 = -2.
For item 4, from the first equation, we have that:
y = 3x - 6.
Then, replacing on the second equation, the solution for x is obtained as follows:
x + 3(3x - 6) = 12
x + 9x - 18 = 12
10x = 30
x = 3.
Then the solution for y is:
y = 3x - 6 = 3(3) - 6 = 9 - 6 = 3.
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ASAP I NEED THIS QUESTION DONE DUE TODAY!!!! 2/3p + 3; p=3/5
Answer: 17/5 or 3.4
Step-by-step explanation:
Substitute p for 3/5 so it would be 2/3(3/5)+3
2/3(3/5)= 2/5
2/5+3=17/5 or 3.4
Hope this helps :)
Answer:
Step-by-step explanation:
Substitute p for 3/5 so it would be 2/3(3/5)+32/3(3/5)= 2/52/5+3=17/5 or 3.4
Find an equation for the perpendicular bisector of the line segment whose endpoints are (4,6) and (8,-6)
The equation of the perpendicular bisector for the line is y = 1/3(x) - 2
How to determine the equation of the perpendicular bisector?
Given: the endpoints of the line (4,6) and (8,-6)
The bisector of the line will divide the line into two i.e. the bisector will be at the point of the line.
The coordinate of the midpoint can be calculated using the formula below:
Xm = (X1 +X2)/2 and Ym = (Y1 +Y2)/2
Where X1 = 4, Y1 =6 and X2= 8, Y2= -6
Xm = (4+8)/ 2 = 12/2 = 6 and Ym = (6+(-6))/2 = 0/2 = 0
Thus, midpoint(6, 0)
slope = y2-y1 / x2-x1
Thus, the slope of the line segment (m₁) = -6-6 / 8-4 = -12/4 = -3
When the two lines are perpendicular, the product of their slope is -1 i.e.
m₁ × m₂ = -1
where m₁ and m₂ represent the slope of the lines
Let the slope of the bisector be m₂
-3 × m₂ = -1
m₂ = 1/3
Equation of perpendicular bisector with coordinate (6,0):
y - 0 = 1/3(x-6)
y = 1/3(x-6)
y = 1/3(x) - 2
Therefore, the equation for the perpendicular bisector of the line segment is y = 1/3(x) - 2
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in need of help!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
2 pairs of parallel sides
The formula W=0.86g^2-0.01g+5.9 models the weight, W, in ounces, for a cat who is fed g grams per day of a special food. According to the formula, how much will a cat weigh when it is fed 13 grams of the special food per day? Round to the nearest hundredth.
Weight of cat when 13 grams food is fed is 151.11 ounces.
Explain equationEquations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. LHS = RHS (left hand side = right hand side) appears in all mathematical equations. You can solve equations to determine an unknown variable's value, which corresponds to an unknown quantity.
Given, the formula for weight,
W = 0.86[tex]g^{2}[/tex] - 0.01g + 5.9
= 0.86[tex](13^{2} )[/tex] - 0.01*13 + 5.9
= 0.86*169 - 0.13 + 5.9
= 145.34 - 0.13 + 5.9
= 151.11 ounces
Therefore, the weight of the cat will be 151.11 ounces.
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Which graph represents the solution of -3m < 15?
There are 4 squares and 16 triangles. What is the simplest ratio of squares to
triangles?
Answer:
1 : 4
Step-by-step explanation:
There are 4 squares and 16 triangles.
That is,
Squares : Triangles
4 : 16
To write it in its simplest ratio, divide both by 4.
Squares : Triangles
1 : 4
After arriving in Australia, Jason exchanged $750 of US currency for $1,041.67 Australian
dollars. Complete the two statements based on this currency exchange. Round to the
nearest hundredth.
9. What is the exchange rate of US dollars per Australian dollar?
What is the exchange rate of Australian dollars per US dollar?
The exchange rate of US dollars per Australian dollar is 0.72
The exchange rate of Australian dollars per US dollar is 1.39
Exchange rate
Exchange rate is the price of a country's money in relation to another country's money and it is “fixed” when countries use gold or another agreed-upon standard, and each currency is worth a specific measure of the metal or other standard.
Given,
After arriving in Australia, Jason exchanged $750 of US currency for $1,041.67 Australian dollars. Complete the two statements based on this currency exchange.
Here we need to find the exchange rate of US dollars per Australian dollar and Australian dollars per US dollar then round it to the nearest hundredth.
According to the given details,
Total amount in US dollars = $750
Converted amount in Australian dollar = $1,041.67
When we divide the US dollar by the Australian dollar then we get the value of one dollar rate,
=> 750/1041.67
=> 0.719
When we round off it to the nearest hundredth then we get the exchange rate of $1 is 0.72
Similarly, now we have to divide the Australian dollar by the US dollar then we get the value of one dollar rate,
=> 1041.67/750
=> 1.388
When we round off it to the nearest hundredth then we get the exchange rate of $1 is 1.39.
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find the Doubling time for a city who is population is growing by 17% per year
The doubling time will be 4.4 years for a city is population is growing by 17% per year.
What is the doubling time?It's time to double down on the time-doubling equation (pun intended). On the assumption that the growth in amount remains constant from one period to the next, the equation is as follows:
Doubling time = log 2 / log (1 + increase)
It has given that the population of the city is growing back 17% per year.
Doubling time = log 2 / log (1 + increase)
Doubling time = log 2 / log (1 + 17/100)
[tex]\mathrm{Apply\:log\:rule}:\quad \frac{\log _c\left(b\right)}{\log _c\left(a\right)}=\log _a\left(b\right)[/tex]
[tex]=\log _{1+\frac{17}{100}}\left(2\right)[/tex]
Doubling time = 4.41484
Round to the nearest tenth decimal.
Doubling time = 4.4
Thus, the doubling time will be 4.4 years for a city is population is growing by 17% per year.
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Write the equation of a line passing through the point (6, 4) that is parallel to the line 2x + 3y = 9.
The equation of line parallel to 2x +3y = 9 and passing through the point (6,4) is 3y + 2x = 24
What is gradient ?Gradient or slope is the ratio of the change in y to the change in x between two points in a line.
Gradient tells how steep a line is. A perfectly vertical or horizontal line has no slope.
2x + 3y = 9
making y the subject,
3y = 9 - 2x
y = 9/3 -2x/3
Comparing the above equation, with equation of a straight line, y = mx + c
m, which is slope = -2/3
The new line will also have a slope of -2/3 because they are parallel.
Equation for new line,
y-[tex]y_{1}[/tex] / x - [tex]x_{1}[/tex] = slope
The new point is (6,4)
y - 4 / x -6 = -2/3
By cross multiplying
3(y-4) = -2(x - 6)
3y - 12 = -2x + 12
3y + 2x = 24
In conclusion, the equation o the new line is 3y + 2x = 24
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5. On a cattle farm, the ratio of beef cattle to dairy cattle is 4:3.
3
(a) Interpret the ratio: For every
beef cattle, there are
cattle.
dairy
(b) If there are 24 dairy cattle, how many
beef cattle would there be? Show your
work.
For every 4 beef cattle there is 3 dairy cattle. For 24 dairy cattle there will be 32 beef cattle as per the given ratio of 3:4.
What is ratio?An ordered pair of numbers a and b, written as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls). The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two things.
Here,
a. No for every 4 beef cattle there is 3 dairy cattle.
b. 4/3=x/24
x=4*24/3
x=32 beef cattle
There are 3 dairy cattle for every 4 beef cattle. According to the stated ratio of 3:4, there will be 32 beef cattle for every 24 dairy cattle.
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Given: AB=BC AC < bisector of
Considering the given figure we have that
< BAC = < CAD definition of angle bisection
< BAC = < BCA base angles of isosceles triangle
What is angle bisection?This refers to when angles are being shared or divided into two equal parts.
In the given problem, line AC is the bisector of < BAC. creating wo equal angles in the process. hence
< BAC = < CAD definition of angle bisection
Triangle BAC is an isosceles triangle, since the sides BA and BC are equal. the angles are also equal therefore
< BAC = < BCA base angles of isosceles triangle
Line AC is also a transversal line, connecting the two parallel lines BC and AD. This creates opportunity for alternate angle theorem
< BCA = < CAD alternate internal angle theorem
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A town has a population of 16000 and grows at 2.5% every year. To the nearest tenth of a year, how long will it be until the population will reach 24300?
After 16.9 years the population will reach to 24300.
What do you mean by exponential growth and decay?
Quantities that fluctuate quickly are subject to exponential growth and decay. The idea of geometric progression has been used to infer exponential growth and decay. Exponential growth or exponential decay are terms used to describe quantities that vary exponentially rather than continuously. Studying bacterial growth, population expansion, and money growth schemes all use exponential growth.
It is given that a town has a population of 16000 and grows at 2.5% every year.
Now we need to find the time period when the population will reach 24300
So, [tex]24300 = 16000(1+0.025)^{t}[/tex]
24300/16000 = [tex](1+0.025)^{t}[/tex]
24300/16000 = [tex]1.025^{t}[/tex]
1.51875 = [tex]1.025^{t}[/tex]
Taking log on both sides we get,
log(1.51875) = t log(1.025)
0.18148 = t (0.01072)
t = 0.18148/0.01072 = 16.9
Therefore, after 16.9 years the population will reach to 24300.
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You pick a card at random.
5678
What is P(not divisor of 45)?
Write your answer as a percentage.
%
The percentage of card which is not divisor of 45 is 23.077%
Always write the things that need to be estimated on the right side and the variables that are known on the left side to simplify the task. In the important in the current, the number of apples is known, but it is unclear what they are worth. It should be highlighted that issues with this method are addressed using the concepts of ratio and proportion.
What does the term "percent" mean?
A fraction of one hundred is used to express a quantity or ratio as a percentage. The acronyms "pct," "pct," and occasionally "pc," as well as the percent symbol, "%," are also frequently used.
A % is a numeric expression that lacks both dimensions and a measurement system. The formula to determine the proportion of one number to another is percentage = (Original number/Another number) x 100.
In mathematics, a percentage is a number or ratio that represents a portion of 100. In percentages, 100% is meant. It contains no units.
A %, also known as a decimal or a fraction, is a figure that indicates how many out of 100 we are discussing. For example, "three for the price of one" is a percentage.
Given That:
In the deck of 52 cards You pick randomly 5 , 6 , 7 , 8
so each card has 4 variant
now for getting probability of not getting a divisor of 45 is
total outcomes = 52
observable outcomes = 4+4+4 = 12
its because 5 is a divisor so we didn't include it
hence the probability is 12/52
Percentage of this probability is 0.23077 x 100 = 23.077%
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What is the equation of this line in slope intercept form?
2x+3y=−6
The function g(x)=3x^3+x is an odd function.Which transformation of g(x) would result in odd functions?Check all that apply
The transformations of g(x) that would result in odd functions are (a)-g(x) , (b)g(2x) and (d)g(–x) ,
In the question ,
it is given that,
the function is g(x) = 3x³ + x
We know that the function f(x) is called an odd function if f(-x) = -f(x) .
Option(a)
the transformation is given as -g(x)
-g(x) = -(3x³ + x) = -3x³ - x
g(-x) = 3(-x)³ + (-x) = -3x³ - x
so , this is odd function .
Option (b)
the transformation is given as g(2x)
g(-2x) = 3(-2x)³ + (-2x) = -24x³ - 2x
-g(2x) = -{3(2x)³ + (2x)} = -( 24x³ + 2x ) = -24x³ - 2x
so , this is odd function .
Option (c)
the transformation is given as g(x)-3
(g(-x) - 3) = 3(-x)³ + (-x) - 3 = -3x³-x-3
-(g(x) - 3) = -{(3x³ + x) -3} = -3x³ - x +3
So, so , this is not an odd function
Option (d)
the transformation is given as g(-x)
g(-(-x)) = g(x) = 3x³+x
-g(-x) = -(3(-x)³ + (-x)) = -(-3x³ - x) = 3x³+x
so , this is odd function .
Therefore, the odd transformations are -g(x) , g(2x) and g(–x) ,
The given question is incomplete , the complete question is
The function g(x)=3x³+x is an odd function. Which transformation of g(x) would result in odd functions? Check all that apply
(a) -g(x)
(b) g(2x)
(c) g(x) − 3
(d) g(–x)
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-5ax6(2ax4 + 7x2)
what might be the answer to this?? (pleasee!! it’s for my semester final.)
The solution of the given expression -5ax⁶(2ax⁴ + 7x²) is equal to -10a²x¹⁰-35ax⁸.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The given expression is -5ax⁶(2ax⁴ + 7x²). The solution of the expression will be done as,
E = -5ax⁶(2ax⁴ + 7x²)
E = -10a²x¹⁰-35ax⁸.
Therefore, the solution of the given expression -5ax⁶(2ax⁴ + 7x²) is equal to -10a²x¹⁰-35ax⁸.
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I need the answer quick
In which quadrant does the point (10, -9) lie?
Answer:Qadrant 4
Step-by-step explanation:
Which number has a 6 whose value is
10 times greater than the value of the
6 in 237,629?
A. 328,564
B. 426,579
C. 519,638
D. 618,402
Answer: B
Step-by-step explanation:
For 237,629 the 6 is located in the hundreds section so its value is approx. 600.
Now when you multiply 600 by 10 you get 6000
So the number of 6 should be located in the 6,000 range which is only in answer B 426,579
Answer:
B- 426,579
Step-by-step explanation:
The value of 6 in 237,629 is 600
600×10=6,000
Which answer has 6,000 as the value of 6?
- Answer B: 426,579
Which graph represents the function f(x) = –|x + 3|?
Answer:
The answer would be A. (Not sure if its A B C or D question but I will have picture below)
Step-by-step explanation:
Hope this helps you! :))
the variables x and y are related such that each time x decreases by 5 , y increases by 2 .if y is a positive value when x=0. which of the following equations could express the relationship between x and y
The linear function that could express the relationship between x and y is given as follows:
y = -0.4x + b, b > 0.
What is a linear function?The slope-intercept representation of a linear function is given by the rule presented below as follows:
y = mx + b
The coefficients of the function, along with their meaning, are listed as follows:
m is the slope of the function, being obtained by the division of the change in y by the change in x.b is the y-intercept of the function, representing the values of the output variable y when the input variable x assumes a value of zero.In the relationship, we have that each time x decreases by 5 , y increases by 2, hence the slope is obtained as follows:
y = -2/5 = -0.4.
The y-intercept is positive, hence the definition of the function is given as follows:
y = -0.4x + b, b > 0.
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Divide negative 7 and 4 over 7 ÷ negative 8 and 1 over 5.
265 over 287
negative 265 over 287
36 over 35
negative 36 over 35
The division of negative 7 and 4 over 7 ÷ negative 8 and 1 over 5 is A. 265 over 287
What is a division?A division simply shows the separation of the number that is given. It should be noted that division is illustrated by the symbol / or ÷.
In this case, negative 7 and 4 over 7 ÷ negative 8 and 1 over 5 will be:
= (- 7 4/7) ÷ (- 8 1/5)
= - 53/7 ÷ (-41 / 5)
= -53/7 × -5/41
= 265 / 287
Therefore the correct option is A.
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Answer: 265/287
I'm not an average brain like other people.
Bahir is h cm tall. Sienna is 4 cm taller than Bahir.
Write down an expression, in terms of h, for Sienna’s height.
Answer:
.
Step-by-step explanation:
Leila bought a suit on sale for 331.20 . This price was 64% less than the original price. What was the original price?
Answer:
$920
Step-by-step explanation:
You want to know the original price of a suit on sale for $331.20, if that price represents a 64% discount.
Discounted priceThe discounted price is found by subtracting the amount of the discount from the original price. That amount is the product of the original price and the rate of the discount.
discounted price = price - (discount)·(price)
discounted price = price · (1 - discount)
The the original price is ...
price = (discounted price)/(1 - discount) = $331.20/(1 -0.64)
price = $920
The original price of the suit was $920.00.
<95141404393>
Alisha used her bank card to buy a bus pass 3 times. Each time she bough
a pass it cost her $13.75. She then deposited $30 into her bank account. Write
an expression to find the change in Alisha's bank account in dollars as a result
these transactions. Also, evaluate the expression to find the change in the
account balance.
The answer will be A-3*13.75+30 using arithmetic operation.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
Alisha used her bank card to buy a bus pass 3 times.
Each time she bought a pass it cost her $13.75,
She then deposited $30 into her bank account.
So the expression A-3*13.75+30
A is the initial value.
Hence this will be the expression A-3*13.75+30
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Find the distance from the point (1,2) to the line-y= 1/2x-3. Round your answer to the nearest tenth.
Answer:
the graphical explanation please
how many different outcomes are possible when flipping a coin and rolling a die
The total possible outcome when a coin is flipped and a die is rolled is 12
What is Probability?The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favourable Outcomes/Number of total possible outcomes.
For example if a coin is flipped, a coin only has two faces, this means that it will have 2 Total possible outcome. When a die is rolled, a die has 6 faces which means that it will Total outcome of 6. When both a coin is flipped and a die is rolled the total possible outcome is 6×2 = 12 outcomes.
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A clinical trial was conducted to test the effectiveness of a drug used for treating insomnia in older subjects. After treatment with the drug, 23 subjects had a mean wake time of 92.1 min and a standard deviation of 40.5 min. Assume that the 23 sample values appear to be from a normally distributed population and construct a 98% confidence interval estimate of the standard deviation of the wake times for a population with the drug treatments. Does the result indicate whether the treatment is effective?
A 98% confidence interval estimate of the standard deviation of the wake times for a population with the drug treatments is
70.9 min < x-bar < 113.3 min
Yes, the result indicate that the treatment is effective
How to get the confidence intervalConfidence interval gives the probability that the unknown parameter will fall within a stated range
The confidence interval is constructed using the formula
confidence interval = x-bar ± z(s/√n)
Definition of variables
mean, x-bar = 92.1 min
standard deviation, s = 40.5 min
sample size, n = 23
confidence level = 98%
z score, z
For sample size less than 30, n < 30. t scores are used
degree of freedom, df = n - 1 = 23 - 1 =22
t score for 98% confidence level and dt of 22 = 2.509
substituting into the formula
= x-bar ± t(s/√n)
= 92.1 ± 2.509 (40.5 / √23)
= 92.1 ± 21.188
= 70.9112 < x-bar < 113.288
Effectiveness of the treatment
when a test a test more than 2 standard deviations away from mean it is considered unusual. The usual range is
= 92.1 ± 2 * 40.5
= 11.5 < x-bar < 173.5
Hence the treatment is effective
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You have a loan for $1000 at 7.65 APR 100 of the loan is due each month and there is a penalty of 2% on the original amount were not paid If you do not pay anything on that loan during the year and assuming there is no compounding how much will you owe in total
If you do not pay anything on that loan during the year and assuming there is no compounding, the total sum owing is $1,216.50.
What does a loan simply mean?When money is given to someone else with the knowledge that it would be returned with interest, it is referred to as a loan. . Lenders will consider a borrower's income, credit rating, and level of debt before deciding to grant a loan.
Money borrowed from a bank or other financial organization is known as a loan. The borrower consents to repay the loan's principal plus interest. There are many different kinds of loans, such as auto loans, student loans, and mortgages.
The amount is 1000(1 + 0.0765), or 1000 x 1.0765, or 1,076.50.
Punishment equals 12(0.02 x 1000) = 12(20) = 240.
The total sum owing is $1,216.50 (1,076.50 plus 240).
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At a carnival game, it cost Noah $12 to toss 30 rings. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
The table of the equivalent ratios is:
Toss Dollars
5 2
30 12
45 18
The points are plotted in the diagram below.
How to Create a Table of Equivalent Ratios?Applying the knowledge of ratios we can create a table of equivalent ratios, given that it cost $12 to toss 30 rings.
Therefore, the ratio of dollars to toss is: 12:30 = 2:5.
Number of toss = x
Amount in dollars = y
Substitute k = 2/5 into y = kx to derive an equation to use to create a table of equivalent ratios:
y = 2/5x.
Therefore, wheny = 2:
2 = 2/5(x)
10 = 2x
x = 5 toss
When x = 45:
y = 2/5(45)
y = 18 dollars
The table of equivalent ratios is completed as:
Toss Dollars
5 2
30 12
45 18
(5, 2), (30, 12), and (45, 18), which are the points of the equivalent ratio table are plotted as shown in the diagram below.
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