Based on this graph, what is the solution to the system of equations?
Answers:
A. There are an infinite number of solutions.
B. There is no solution.
C. (1, 3)
D. (2, 3)
E. (3, 2)
Answers
The solution is Option E.
The solution to the system of equations is the point of intersection of line and the lines intersect at the point A ( 3 , 2 )
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( -3 , -4 )
Let the second point be Q ( 7 , 6 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope m = 10 / 10 = 1
Now , the equation of line is y - y₁ = m ( x - x₁ )
y - 6 = 1 ( x - 7 )
y - 6 = x - 7
y = x - 1 be equation (1)
Now , the point of intersection of lines is at ( 3 , 2 )
Substitute the value of x and y in the equation , we get
when x = 3 , y = 2
2 = 3 - 1
2 = 2
Hence , the solution to the equation is ( 3 , 2 )
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Related Questions
Mrs. Harris has a piece of lumber that is 11 5/8 inches wide she plans to split the width of the lumber into three equal pieces how wide will each piece be
Answers
The size of width of each lumber piece will be 3.875 inches.
What is Algebra?Logic is the arrangement of all those concepts, whereas algebra is the study of abstract concepts.
Making something a little less complicated while both making it easier to attain or understand is the concept of clarity.
Mrs. Harris intends to divide the breadth of a piece of timber that is 11 ⁵/₈ inches broad into three equal pieces.
Convert the mixed fraction number to a decimal number. Then we have
11 ⁵/₈ = 11 + ⁵/₈
11 ⁵/₈ = 11.625 inches
The width of each lumber piece is given as,
⇒ 11.625 / 3
⇒ 3.875 inches
The size of width of each lumber piece will be 3.875 inches.
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Dr. Grumman got his first job in 2020. In that year, the government took out 6.2% of a person's
income for Social Security, until a person made $137,700. If Dr. Grumman earned $141,340 in
2020, how much did he pay to Social Security?
Answers
The amount paid to social security when Dr. Grumman earned $141,340 in 2020 is $8763.08.
What are percentages?A % in mathematics is a quantity or ratio that is stated as a fraction of 100 (from the Latin per centum, "by a hundred"). Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it.
We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.
Formula for percentages: (Value/Total value) * 100
Dr. Grumman earned $141,340 in 2020.
The social security he paid is:
(141340)(6.2/100) = 8763.08
Hence, the amount paid to social security when Dr. Grumman earned $141,340 in 2020 is $8763.08.
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What is | −34 |?
????
Answers
Answer:
34
Step-by-step explanation:
The absolute value of a real number [tex]a[/tex] is [tex]a[/tex] when [tex]a[/tex] ≥ 0, or −[tex]a[/tex] when [tex]a[/tex] < 0. The absolute value of −34 is 34.
Hope it helps and have a great day! =D
Help please Hurry
Based on the data, which of the following best describes the experimental probability of the arrow landing on a black or white section of the spinner? (1 point)
• a
O b
• c
• d
The spinner is equally likely to land on black or white.
The spinner is 3 times more likely to land on white.
The information cannot be concluded from the data.
The spinner is 3 times more likely to land on black.
Answers
Answer:
it's d. answer d. 57/76 is the probability of landing on black. that is roughly 3 times as much as the probability of landing in white 19/76. 19 X 3 = 60 which is roughly around the ballpark of 57.
how many times larger is a centigram than a milligram? 10times | 100 times| 1000 times| 0.1 time
Answers
Answer: 10 times
Step-by-step explanation:
Write down the percentage multiplier to find 53% of a price
Answers
The percentage multiplier to find the 53% of a price is 0.53
The given percentage value = 53%
Percentage of a quantity is defined as the number or the ratio, that can be expressed as the fraction of 100. To find the percentage of a number, divide the number by the whole quantity and multiply by 100. Percentage of a number is usually expressed as by using percentage sign "%"
Here we have to find the percentage multiplier
To find the percentage multiplier divide the given percentage by 100
The percentage value = 53%
The percentage multipler = 53 / 100
Divide the numbers
53 / 100 = 0.53
Therefore, the percentage multiplier is 0.53
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what is the correct decision in a hypothesis if the data produce a t-statistic that is in the critical region?
Answers
The correct decision in a hypothesis test when the data produces a t-statistic that is in the critical region is to reject the null hypothesis.
This is because a t-statics in the critical region indicates that the differences between the sample mean and the population mean are statistically significant. This means that the data indicates that the null hypothesis is wrong and that the alternative hypothesis is true. In a hypothesis test, the null hypothesis is what the researcher is trying to disprove. It is the general statement that suggests that there is no difference between the sample mean and the population mean. The alternative hypothesis is what the researcher is attempting to prove. It suggests that there is a difference between the sample mean and the population mean. Therefore, when the data produces a t-statistic that is in the critical region, it indicates that the alternative hypothesis is true. When a t-statistic is in the critical region, it means that the result is statistically significant. This means that the differences between the sample mean and the population mean are unlikely to have occurred by chance and that the alternative hypothesis is likely to be true. Therefore, when the data produces a t-statistic that is in the critical region, the correct decision is to reject the null hypothesis and accept the alternative hypothesis.
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Solve the following system of inequalities graphically on the set of axes below. State
the coordinates of a point in the solution set.
Y >1/2x-1
Y ≥-3/4x-6
Answers
The solution to the inequality are the region in the shaded area
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
Y >1/2x-1
Y ≥-3/4x-6
Represent properly
y > 1/2x - 1
y ≥ -3/4x - 6
Next, we make a plot of the system to determine the solution
The shaded area in the plot represent the solution to the inequality
In this case, one of the coordinates in the shaded area has a coordinate of (-4, -3)
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hal is asked to write an exponential function to represent the value of a $10,000 investment decreasing at 2% annually. what multiplicative rate of change should hal use in his function?0.020.981.021.98
Answers
If he want to write an exponential function to represent the value of a $10,000 investment decreasing at 2% annually, then the multiplicative rate will be 0.98
The initial investment = $10000
decreasing percentage = 2%
Therefore, the second term will be the 98% of the first term
The first term = 10000
The second term = 10000 × 98/100
= 10000 × 0.98
= 9800
The common ratio is the ratio of the second term to the first term
The common ratio = second term / first term
= 9800 / 10000
= 0.98
Therefore, the multiplicative rate of change should Hal use in his function is 0.98
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Calculate the length of the legs of the triangle.
Answers
Answer: 5
Step-by-step explanation:
The Vikings, who discovered Iceland, used Ravens to help find land.
True
False
Answers
Answer: TRUE Flóki reportedly released three ravens, and then sailed in the general direction that they flew, eventually discovering Iceland.
Step-by-step explanation:
What is the formula used to calculate the surface area for a square pyramid?
Answers
The formula used to calculate the surface area of a square pyramid is A = a^2 + 2a[tex]\sqrt{\frac{a^2}{4}+h^2 }[/tex]
The square pyramid is the geometric shape that has a square base and 4 lateral face. The total number of faces will be five. The base shape is square and the side shape will be triangle. Number of edges in the square pyramid is eight
The surface area is the amount space covered by the surface of the object
Here the surface area of the square pyramid is
A = a^2 + 2a[tex]\sqrt{\frac{a^2}{4}+h^2 }[/tex]
Where A is the surface area of the square pyramid
a is the base edge
h is the height of the square pyramid
Therefore, the surface area is A = a^2 + 2a[tex]\sqrt{\frac{a^2}{4}+h^2 }[/tex]
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complete the equation below by completing the square. x^2+6x+9=2
Answers
Answer:-3, 2
Step-by-step explanation:
a 5-card poker hand is dealt from a standard deck of cards (with 4 suits, and 13 kinds for each suit (2, 3, 4, 5, 6, 7, 8 , 9, 10, j, q, k, a). how many distinct ways are there to form a hand with two pairs?
Answers
A 5-card poker hand is dealt from a standard deck of cards and the number of distinct ways are there to form a hand with two pairs are 1326 ways.
To solve this problem, we got to use permutations and the combinations. Given that a 5-card poker hand is dealt from a standard deck of cards and with 4 suits and there are 13 different kinds for each and every suit and 13 different kinds are 2, 3, 4, 5, 6, 7, 8, 9, 10, j, q, k, a.
Here 4 suits with 13 different kinds for each and every suit , so number of total outcomes are 13*4 = 52
Here we use combinations, and given that a 5-card poker hand is dealt from a standard deck of cards and with 4 suits and there are 13 different kinds for each and every suit and 13 different kinds are 2, 3, 4, 5, 6, 7, 8, 9, 10, j, q, k, a.
The number of distinct ways are there to form a hand with two pairs are given by, C(52,2)
(52 * 51) / 2
(26 * 51)
1326 ways
Therefore, the number of distinct ways are there to form a hand with two pairs are 1326 ways.
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The reading group checked out 36 library books. 17 books are fiction, 10 are biographies, and some are science. How many books are science?
Answers
36-27= 9
so 9 books are science
Answer:
9 science books
Step-by-step explanation:
Step 1) 36 - 17 = 19
Step 2) 19 - 10 = 9
Which one of the following absolute value equations and inequalities have a solution set that is NOT the empty set?
O |2x-1|-7<-6
O |4x+5| -4=-5
O 3|x+2|-2=-3
O 2|x-5|-4 <-8
Answers
3x+4=-3
3x=-3-4
3x=-7
x=-7/3
Please solve the radical equation.
Please show work
Answers
Answer:
Step-by-step explanation:
Find common denominator.
1/x + x-1/9x = 1 => 9/9x + x-1/9x = 1 (The common denominator is 9x.)
Combine like terms.
9 + x - 1 / 9x = 1 => x + 8/ 9x = 1
Cancel out 9x from denominator. What you do to one side, you do to the other.
(9x)(x + 8/9x) = 1(9x) => x + 8 = 9x
Solve for x.
8 = 8x => x = 1 (subtract x from both sides at the beginning and then simplify.)
X=1
Showing how to find the answer:
Hope helps!
A leaky faucet is losing water and is filling a 5-gallon bucket every 20 hours. At that
rate, how many gallons of water will the faucet leak in
48 hours?
Show your
work.
Answers
gallons leaked per hour = 5 gallons / 20 hours = 5/20 gallons/hour
gallons leaked in 48 hours = (5/20 gallons/hour) * 48 hours = (5/20) * 48 gallons
gallons leaked in 48 hours = 12 gallons
So, the faucet will leak a total of 12 gallons in 48 hours.
Answer:
Step-by-step explanation:
We can start by finding the amount of water the leaky faucet loses in one hour:
5 gallons / 20 hours = 0.25 gallons per hour
This means that the leaky faucet loses 0.25 gallons of water every hour.
To find how many gallons of water the faucet will leak in 48 hours, we can multiply the rate of leakage per hour by the number of hours:
0.25 gallons/hour x 48 hours = 12 gallons
Therefore, the leaky faucet will lose 12 gallons of water in 48 hours.
If 10,000 is deposited into a savings account that pays 2. 3% annual interest, how much more would the
Answers
The account would contain 10,230.00 after 1 year.the amount in the account after 1 year, we can use the formula: [tex]P (1 + r/n)^nt[/tex]
To find the amount in the account after 1 year, we can use the formula:[tex]P (1 + r/n)^nt[/tex]
Where,
P = Principal Amount
r = Rate of Interest
n = Number of times the interest is compounded per year
t = Time in years
For this question,
P = 10,000
r = 2.3%
n = 1
t = 1
Therefore,
[tex]10,000 (1 + 0.023/1)^1*1\\10,000 (1.023)^1[/tex]
10,000 x 1.023
= 10,230.00
The complete question is:
If 10,000 is deposited into a savings account that pays 2.3% annual interest, how much more would the account contain after 1 year?
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Unit 5 Lesson 4 Practice Problems o
1. Match each equation with a description of the function it represents.
a. f(x) = 2x+4
b. g(x) = 2(x+4)
c. h(x) = 4x+2
d. k(x) = 4(x + 2)
14 Student
1.
To get the output, add 4 to the input, then multiply the
result by 2.
2.
To get the output, add 2 to the input, then multiply the
result by 4.
3. To get the output, multiply the input by 2, then add 4 to
the result.
4. To get the output, multiply the input by 4, then add 2 to
the result.
Answers
On solving the provided question, we can say that equation, k(x) = 4(x + 2) represents the function where you add 2 to the input, then multiply the result by 4.
What is equation?A mathematical equation is a formula that links two assertions and signifies equivalence with the equals sign (=). In algebra, a mathematical statement that proves the equality of two mathematical expressions is referred to as an equation. The equal sign, for instance, separates the variables 3x + 5 and 14 in the equation 3x + 5 = 14. There is a mathematical formula that explains the link between the two phrases that appear on either side of a letter. Frequently, the symbol and the single variable are the same. like in 2x - 4 = 2, for example.
a. f(x) = 2x+4 represents the function where you multiply the input by 2, then add 4 to the result.
b. g(x) = 2(x+4) represents the function where you add 4 to the input, then multiply the result by 2.
c. h(x) = 4x+2 represents the function where you multiply the input by 4, then add 2 to the result.
d. k(x) = 4(x + 2) represents the function where you add 2 to the input, then multiply the result by 4.
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ratio of heights of 2 triangles is 3:4, area 4:3, ratio of their base?
Answers
Ratio of the base of two triangles is 16:9 , if ratio of heights of two triangles is 3:4 and area 4:3.
It is given that the ratio of heights of two triangles is 3:4 and the ratio of area of two triangles is 4:3
We have to find the ratio of their base
The basic formula for the area of a triangle is equal to half the product of its base and height or [tex]\frac{1}{2} \times base \times height[/tex]
Let b₁ , b₂ are the base of two triangles respectively
So, ratio of areas of triangles : [tex]\frac{\frac{1}{2}\times b_{1} \times3}{\frac{1}{2}\times b_{2} \times4}[/tex]
[tex]\frac{4}{3} = \frac{\frac{1}{2}\times b_{1} \times3}{\frac{1}{2}\times b_{2} \times4}[/tex]
[tex]\frac{b{1}}{b_{2}} =\frac{16}{9}[/tex]
So, ratio of the base of two triangles is 16:9
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if m+1 is an even integer, which one of the flollowing must be add integer?
Answers
If m + 1 is an even integer, then 2m + 1 is an odd integer.
What do you understand by even and odd numbers?Even number: An even number is a number that is a multiple of 2. It can be said that any number that is completely divisible by 2 is an even number.
Odd number: Odd numbers are those numbers that are not completely divisible by 2.
let us understand by addition on different combinations of odd numbers and even numbers.
Odd number + Odd number = Even number
Even number + Even number = Even number
Even number + Odd number = Odd number
Odd number + Even number = Odd number
In subtraction
Even number - Even number = Even number
Even number - Odd number = Odd number
Odd number - Even number = Odd number
Odd number - Odd number = Even number
In multiplication
Even number × Even number = Even number
Even number × Odd number = Even number
Odd number × Odd number = Odd number
Given:
m + 1 is an even integer.
since alternate numbers are even.
Therefore, m must be an odd number.
If m is odd, then m - 1 is even.
2m is divisible by 2, so it is always an even number.
So,
2m - 2 is even.
2m + 1 is odd.
2m + 2 is even.
Since 2m + 1 is an odd number.
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Question 12Miple Choice Worth 4 pores)
(08.02 MC)
The expression 4x+13 represents the time it takes a commuter to travel in the morning to work. The expression 10x-2 represents the time it takes a commuter to
havel in the evening from work What is the total travel time?
Otx+18
Ox+11
06+21
Ox+15
Answers
If the functions be f(x) = 4x + 13 and g(x) = 10x − 2 then the expression (f + g)(x) be 4x + 11.
What is meant by functions?A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. The set X is known as the function's domain, while the set Y is known as the function's codomain. Initially, functions were just an idealized representation of the relationship between two changing quantities.
Given f(x) = 4x + 13 and g(x) = 10x − 2
We must add both functions to reflect the amount of time it takes to travel east and west in order to calculate the round-trip time.
Let the equation be (f + g)(x) = f(x) + g(x)
substitute the values in the above equation, we get
= (4x + 13) + (10x − 2)
simplifying the above equation, we get
= 4x + 13 + 10x − 2
= 4x + 10x − 2 + 13
= 4x + 11
Therefore, the expression (f + g)(x) be 4x + 11.
The completed question is:
The function f(x) represents the time it takes an airplane to travel east. The function g(x) represents the time it takes an airplane to travel west. Given f(x) = 4x + 13 and g(x) = 10x − 2, solve for (f + g)(x) to determine the total roundtrip time.
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The solution set of an equation of a circle is all of he points that lie on the circle.
A. True
B. False
Answers
question 10
What is the length of segment LN?
21.93
27.57
30.36
55.14
Answers
Which of the following expressions is equivalent to
x² +7x+12
÷
x+8x+15
for x>0 ?
Answers
The expression that is equivalent to x² +7x+12 ÷ x²+8x+15 is (x + 4) ÷ (x + 5)
How to determine the equivalent expressionFrom the question, we have the following parameters that can be used in our computation:
x² +7x+12
÷
x+8x+15
Express properly
So, we have
x² +7x+12 ÷ x²+8x+15
Factorize each expression
This gives
(x + 4)(x + 3) ÷ (x + 5)(x + 3)
Cancel out the common factor
(x + 4) ÷ (x + 5)
Hence, the expression is (x + 4) ÷ (x + 5)
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What is 4 3/5+5/6 as a mixed number in simplest form
Answers
PLEASE GIVE BRAINLIEST!
thank you and have a good day :)
Answer:
163/30
Step-by-step explanation:
4 3/5 in mixed number form would be 23/5
5/6 remains 5/6 as it is not greater than 1, therefore it cannot be simplified.
23/5 + 5/6
in order to add, we have to make the denominators alike. the least common multiple is 30. so we have to not just multiply the denominators by whatever results in 30, but also the numerators.
23 times 6 = 138
5 times 6 = 30
5 times 5 = 25
5 times 6 = 30
138/30 + 25/30
at this point, we can simply just add the numerators
163/30
i hope this helps
Help!! Math is really hard!!! Can someone explain how they got this?
Answers
Yes!
[tex](2^{2} )^{3}[/tex] = 2^6 = 64
(8-4)^2 = 4^2 = 16
then for the last part
4^-4 is the same as [tex]1/4^{4}[/tex] or 1/256
Then it is order of operations:
do 16 x 1/256 first which is 1/16
and then 64 - 1/16 to get 63 15/16 :)
which of the following continuous improvement tools is often used to initiate a root cause analysis effort? group of answer choices scatter plot. cause-and-effect (fishbone) diagram. pareto chart. swim lane process map.
Answers
Among the continuous improvement tools listed in the query, the cause-and-effect (fishbone) diagram is often used to initiate a root cause analysis effort. This tool helps identify potential causes of a problem by breaking down a complex issue into smaller and more manageable components.
The diagram is shaped like a fishbone, with the problem at the head and the potential causes in the "bones" of the fish. By examining the various factors that could contribute to a problem, a team can begin to isolate the most likely root causes and develop targeted solutions to address them. Other tools like scatter plot, Pareto chart, and swim lane process map can also be useful in continuous improvement efforts, but they may not be the best choice for initiating a root cause analysis
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If you help me with this your a hero:))) please help me
Answers
Answer:
x = -2, y = -4
Step-by-step explanation:
Take the first equation- -2y = 2 - 3x
Arrange it first-
-3x + 2y = -2
Multiply is by 5 on both sides
5(-3x + 2y) = 5(-2)
-15x + 10y = -10
Take the second equation- -5y = 10 - 5x
Arrange it-
-5x + 5y = -10
Multiply is by 2 on both sides
2(-5x + 5y) = 2(-10)
-10x + 10y = -20
Subtract second equation from the first one-
-15x + 10y = -10
- -10x + 10y = -20
= -5x = 10
-5x = 10
x = 10/(-5)
x = -2
Substitute the value of x in Equation 1
-2y = 2 - 3(-2)
-2y = 2 + 6
-2y = 8
y = 8/(-2)
y = -4
Hope it helps ;)
