Algebra 2 Math question Grade 11
Can anyone please help me with this question? Soon as possible!
Write an equation for the line that passes through the points (3,5) and (-2, 1).
All work must be shown for full credit. Be sure to include slope calculation.
Answers
Answer:
\(\displaystyle y=\frac{4}{5}x+\frac{13}{5}\)
Step-by-step explanation:
The equation of the line in slope-intercept form is:
y=mx+b
Where m the slope of the line and b the y-intercept.
When two points are given, it's convenient to calculate the slope first.
Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:
\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)
The points are (3,5) and (-2,1):
\(\displaystyle m=\frac{1-5}{-2-3}=\frac{4}{5}\)
The equation is now:
\(\displaystyle y=\frac{4}{5}x+b\)
To calculate b, we use any of the given points and solve for b. Use (3,5):
\(\displaystyle 5=\frac{4}{5}3+b\)
Operate:
\(\displaystyle 5=\frac{12}{5}+b\)
Solve:
\(\displaystyle b=5-\frac{12}{5}=\frac{13}{5}\)
The required equation of the line is:
\(\boxed{\displaystyle y=\frac{4}{5}x+\frac{13}{5}}\)
Related Questions
HELP PLEASE!! WILL THANK AND MARK BRAINLIEST!
Answers
The analysis of the tables based on the first difference values indicates
1 a. The function is a linear function
b The reason the function is linear is because the rate of change in the x and y-values are constant, such that the rate of change of the function is also constant
2. a. The function is not linear
b. This is so because the changes in the consecutive terms of the x-values is not constant while the change in the y-values is constant making the overall rate of change of the function (the slope of the function) to vary
3. a. The table is not a linear function
b. The reason why the table does not represent a linear function is because the change in the terms of the y-values is not constant
4. a. The table is a linear function
b. The reason why it is a linear function is because the changes in the x and y-values are constant
What is a linear function?A linear function is a function that when plotted on a graph, forms a straight line.
1) The changes in x-values are;
Δx₁ = -2 - (-3) = 1
Δx₂ = -1 - (-2) = 1
Δx₃ = 0 - (-1) = 1
Δx₄ = 1 - 0 = 1
The changes in y-values are;
Δy₁ = 2 - 1 = 1
Δy₂ = 3 - 2 = 1
Δy₃ = 4 - 3 = 1
Δy₄ = 5 - 4 = 1
a. Is it a linear function? Yes
b. Why it is a linear function is because the first difference of the y-values and the change between consecutive x-values are both constant
2. The changes in x-values are;
Δx₁ = -2 - (-5) = 3
Δx₂ = -1 - (-2) = 1
Δx₃ = 2 - (-1) = 3
Δx₄ = 5 - 2 = 3
The changes in y-values are;
Δy₁ = 4 - 2 = 2
Δy₂ = 6 - 4 = 2
Δy₃ = 8 - 6 = 2
Δy₄ = 10 - 8 = 2
a. Is it a linear function? No
b. The reason why it is not a linear function is because the rate of change in the y-values is constant while the rate of change in the x-values varies, which indicates that the rate of the function also varies resulting in a non linear function.
3. The changes in x-values are;
Δx₁ = -5 - (-10) = 5
Δx₂ = 0 - (-5) = 5
Δx₃ = 5 - 0 = 5
Δx₄ = 10 - 5 = 5
The changes in y-values are;
Δy₁ = 4 - 9 = -5
Δy₂ = 2 - 4 = -2
Δy₃ = 0 - 2 = -2
Δy₄ = -3 - 0 = 2
a. Is it a linear function? No
b. The reason why the table of values does not represent the values of a linear function is that the first difference, which is the change in the consecutive y-values is not constant, such that the rate of changes of the ordered pairs of the function function is not constant and the graph therefore does not follow a straight line pattern
4) The changes in x-values are;
Δx₁ = 3 - (-1) = 4
Δx₂ = 7 - 3 = 4
Δx₃ = 11 - 7 = 4
Δx₄ = 15 - 11 = 4
The changes in y-values are;
Δy₁ = -4 - (-9) = 5
Δy₂ = 1 - (-4) = 5
Δy₃ = 6 - 1 = 5
Δy₄ = 11 - 6 = 5
a. Is it a function? yes
b. The reason why it is a function is because the first difference in the y-values is constant and the difference between consecutive x-value terms is also constant
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There are 40% more black balls than white balls in a bag.
Work out the ratio of black balls to white balls.
Give your answer in its simplest form.
Answers
Answer:
there are 40% black ball a
white ball we don't know
so, we let = x
40\100 × x
now we cutting
ans is 10x
pls help asap if you can!!
Answers
The ∆ABC is an isosceles triangle and have the base angles m∠A and m∠C equal to 51° and the angle m∠B is equal to 78°.
What is an Isosceles triangleAn isosceles triangle have the measure of its base angles to be equal, and the sum of the interior angles sum up to 180°.
Given that sides AB ≅ BC, then the triangle ∆ABC has two sides with similar length and base angles so;
angles m∠A and m∠C are the base angles are both equal to 51°
m∠B = 180° - (51 + 51)° {sum of interior angles of a triangle}
m∠B = 180° - 102°
m∠B = 78°
Therefore, the isosceles triangle ∆ABC have the base angles m∠A and m∠C equal to 51° and the angle m∠B is equal to 78°.
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What is the remainder when the two-digit, positive integer x is divided by 3?
(1) The sum of the digits of x is 5
(2) The remainder when x is divided by 9 is 5
Answers
Answer:
22Step-by-step explanation:
You want the remainder of a number when divided by 3 if (1) the sum of digits is 5, and (2) the remainder from division by 9 is 5.
(1) Digit sum is 5The sum of digits of a 2-digit number will be 5 if that number is one of ...
{14, 23, 32, 41, 50}
In every case, the remainder when divided by 3 is 2. Effectively, it is the remainder of 5 when that is divided by 2.
(2) Mod 9 value is 5In addition to the numbers listed above, 2-digit numbers with a sum of digits of 14 will also have a remainder of 5 when divided by 9. This adds five more numbers to the list:
{59, 68, 77, 86, 95} . . . . have remainders of 5 when divided by 9
The remainders when divided by 3 are all 2 for these numbers as well.
__
Additional comment
The process of (recursively) summing the digits of a positive integer is called "casting out 9s". It effectively finds the modulo 9 value of the number, with the exception that a sum of 9 corresponds to a modulo 9 value of 0.
Since 9 is divisible by 3, the modulo 3 value of a number will be the modulo 3 value of the modulo 9 value. In other words, if the sum of digits is 5, or the remainder from division by 9 is 5, then the mod 3 value is 5 mod 3 = 2.
Can you help me with this? I don't get it
Answers
Given:
Hugo plans to buy packs of baseball cards until he gets the card of his favourite player.
He has enough money to buy at most 4 packs.
The probability of each pack containing the desired card is 0.2.
The probability distribution is,
X 1 2 3 4
P(X) 0.2 0.16 0.128 512
Required:
The probability that Hugo buys at most 3 packs of cards.
Explanation:
The probability that Hugo buys at most 3 packs of cards.
\(\begin{gathered} P(X\leq3)=P(X=1)+P(X=2)+P(X=3) \\ P(X\leq3)=0.2+0.16_+0.128 \\ P(X\leq3)=0.488 \end{gathered}\)Final Answer:
The probability that Hugo buys at most 3 packs of cards is 0.488.
b
It takes 4 workers 6 days to build a shed.
How many sheds could 2
of the workers make in 36
days, if all of the workers
work at the same rate?
Answers
2z-1/3- 3z+1/5=1
z=?
Have a good Earth day!
Answers
Answer:
Z=23
Step-by-step explanation:
Multiply both sides of the equation by 15, the least common multiple of 3,5.
Use the distributive property to multiply 5 by 2z−1.
Use the distributive property to multiply −3 by 3z+1.
Combine 10z and −9z to get z.
Subtract 3 from −5 to get −8.
Add 8 to both sides.
Add 15 and 8 to get 23.
Which equation justifies why 10 1/3 = 3 square root 10?
Answers
Answer:For this case we must find the justification of:
By definition of properties of powers and roots we have to meet:
So, if we have:
Other property states that:
So, the expression: "Ten to the one third power all raised to the third power" is represented as:
Step-by-step explanation: b
Answer:
B
Step-by-step explanation:
2) After fuel prices rose by 15%, a
family's annual heating bill was £1654.
What would the bill have been without
the price increase?
Answers
Therefore , the solution of the given problem of percentage comes out to be the initial annual heating cost was about £1438,26 before the 15% increase.
What precisely is a percentage?A number or statistic that is stated as an amount of 100 is referred to as "a%" in statistics. The forms "pct," "pct," or "pc" are additionally uncommon. The common way to indicate it is with a representation "%," though. The ratio to the total sum is flat, and there are no indicators. Percentages are actually integers because they almost always add up to 100. To suggest that a number indicates a percentage, either the word "fraction" or a representation for percentage (%) must come before the number.
Here,
Assume that the annual heating expense was x prior to the 15% increase.
=> x + 0.15x = 1.15x was the new bill after the 15% price rise.
We can write: Because we are aware that the new price following the increase is £1654:
=> 1.15x = 1654
We must find x in order to determine the initial bill before the increase:
=> x = 1654/1.15
=> x ≈ 1438.26
Therefore, the initial annual heating cost was about £1438,26 before the 15% increase.
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Which situation is best represented using a negative integer?
Answers
Answer:
a
Step-by-step explanation:
Solve.
−0.65p − 4 = 0.35p
The solution is p =
Answers
Answer:
Step-by-step explanation:
Solution,
p=-4
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In the group of 2000 people 40 persent reads science and 30percent reads maths.If 100 people read both then how many people don't read both
Answers
Answer: 500 people don't read both.
Step-by-step explanation:
30% of 2,000 = 600 people read math.40% of 2,000 = 800 people read science.800 + 100 + 600 = 1,500 people either read science, math, or both.2,000 - 1,500 = 500 people don't read math and science.The angles of a hexagon are each a° and each of the others is 1/2 times a°. Find the angles
Answers
Answer:
this question is weirdly worded. i think you meant to type "three angles of a hexagon....." I'll do my best.
Step-by-step explanation:
sum of angles in a polygon: (n-2) 180° where n=#of sides of the polygon
(6-2) 180°
(4) 180°
720°
1a + 1a + 1a + 0.5a + 0.5a + 0.5a = 720°
4.5a = 720°
a = 720°/4.5
a = 160
0.5a = 80
Check
3(160) + 3(80)
480 + 240 = 720
Dusty has a summer lawn-mowing business. In one week, he mows 20 lawns and earns a total of $450. If he charges the same amount for each lawn, how much does Dusty charge to mow a lawn?
Answers
Answer:
Step-by-step explanation:
Write in slope-intercept form,
y=mx + b. − mowing, week, 20, 450
what is the difference between union set and universal set
Answers
Answer:
Universal set is a set which contains all values
Union of Sets : The joining of two or more sets .
Step-by-step explanation:
What is the relationship between the points on the line and solutions to the linear equation?
Answers
The relationship between the points on the line and solutions to the linear equation is, the equation has a solution at each point along the line.
In the given question, we have to find the relationship between the points on the line and solutions to the linear equation.
The equation has a solution at each point along the line. This simply means that it is easy to tell whether an ordered pair is a solution to an equation. The ordered pair is a solution to the equation if it lies on the line drawn by the linear equation.
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The area of the floor is (x2-169) sq units. Find the width of the floor if the length is (x - 13) units.
Answers
The width of the floor if the length is (x - 13) units is (x+13) units.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that area of the floor is (x²-169) sq units.
We have to find the width of the floor when length is (x - 13) units.
Area=Length×Width
x²-169=(x-13)width
We know that (a²-b²)=(a+b)(a-b)
(x-13)(x+13)=x-13width
Divide both sides by (x-13)
x+13=width
Hence, the width of the floor if the length is (x - 13) units is (x+13) units.
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13.The difference between two numbers is 14. The smaller number is b.
Write an expression that represents the greater number.
Answers
Answer:
b=6
Step-by-step explanation:
The greater number is 8
x+ 9 = 9 + x is an example of which property?
Answers
Answer: Commutative property of multiplication: Changing the order of factors does not change the product.
Step-by-step explanation: For example, 4 × 3 = 3 × 4 4 \times 3 = 3 \times 4 4×3=3×44, times, 3, equals, 3, times, 4.
a varies jointly with b and c. a=10 b=5 and c=15. find c when a=15 and b=10
Answers
Let's begin by identifying key information given to us:
\(\begin{gathered} a\alpha bc\Rightarrow a=kbc \\ a=kbc \\ a=10,b=5,c=15 \\ \text{Substitute these into the equation, we have:} \\ 10=k\cdot5\cdot15 \\ 10=75k\Rightarrow75k=10 \\ 75k=10 \\ k=\frac{10}{75}=\frac{2}{15} \\ k=\frac{2}{15} \\ \\ When;a=15,b=10 \\ a=kbc \\ 15=\frac{2}{15}\cdot10\cdot c \\ 15=\frac{2\cdot10}{15}c \\ 15=\frac{20}{15}c \\ 15\cdot15=20c\Rightarrow225=20c \\ 20c=225 \\ c=\frac{225}{20}=11.25 \\ c=11.25 \end{gathered}\)Question 4 (3 mark) : Write a program called Powers to calculate the first 4 powers of a given number. For example, if 3 were entered, the powers would be \( 3,9,27 \) and \( 81\left(3^{1}, 3^{2}, 3^{
Answers
Here's a Python program called "Powers" that calculates the first four powers of a given number:
```python
def powers(number):
power_list = []
for exponent in range(1, 5):
result = number ** exponent
power_list.append(result)
return power_list
# Example usage
input_number = int(input("Enter a number: "))
result_powers = powers(input_number)
print("The first 4 powers of", input_number, "are:", result_powers)
```
When you run this program and enter a number, it will calculate the powers for that number and display them as a list. For example, if you enter 3, it will output:
```
Enter a number: 3
The first 4 powers of 3 are: [3, 9, 27, 81]
```
Feel free to customize the program as needed or incorporate it into a larger project.
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a coffee company wants to bring out a new holiday flavor and decide to conduct a study to see what their customers prefer. in which situation could they use a hypothesis test for matched pairs?
Answers
The null hypothesis for the test would be that there is no difference between the ratings for the existing coffee flavors and the newly introduced holiday flavor. The alternative hypothesis would be that there is a significant difference between the ratings.If the p-value of the test is less than the level of significance, the company can reject the null hypothesis and conclude that there is a significant difference between the ratings for the two sets of flavors. This would indicate that the holiday flavor is preferred more than the existing flavors and the company can introduce it as a new flavor for the holiday season.
The coffee company can use a hypothesis test for matched pairs in a situation where they want to compare the preferences of their customers for the existing coffee flavors with the newly introduced holiday flavor. By conducting a matched-pairs hypothesis test, the company can determine whether the holiday flavor is preferred more than the existing flavors.Matched-pairs hypothesis test is a statistical test used to determine the difference between two related variables. In this case, the related variables are the preferences of the customers for existing coffee flavors and the newly introduced holiday flavor. The test involves measuring the differences between the paired variables and determining whether the differences are significant enough to indicate a preference for one flavor over the other.
For instance, the coffee company can conduct a survey among its customers to determine their preferences for the different coffee flavors. The survey can involve asking the customers to rate the existing coffee flavors and the newly introduced holiday flavor on a scale of 1 to 10. The company can then compare the ratings for each customer to determine whether the holiday flavor is preferred more than the existing flavors.After collecting the data, the company can use a paired t-test to determine whether the differences in the ratings are significant.
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Please help!Calculate the slope and in your notebook graph the rates of change for the three cars.
Car C travels at the rate indicated in the table.
The unit rate is _____ miles per hour
Answers
Answer:
52 mph
Step-by-step explanation:
Manoj and Tamar are arguing about a number trick they heard.
Tamar tells Andrew to think of a number, multiply it by five and
subtract three from the result. Then Manoj tells Andrew to think
of a number, add five and multiply the result by three. Andrew
says that whichever way he does the trick he gets the same
answer.
a. What was the number Andrew started with?
b. What was the result Andrew got both times?
c. Name another set of steps that would have resulted in the
same answer if Andrew started with the same nu
Answers
Answer:
a . Andrew's started with number 9
b. 42
c. 4x + 6 = (x+12)*2
Step-by-step explanation:
Let the Andrew's number is x
Tamar tells Andrew to think of a number, multiply it by five andsubtract three from the result
5x - 3
Manoj tells Andrew to think of a number, add five and multiply the result by three.(x +5)*3
as he was getting the same answer so both the numbers will be equal
5x -3 = (x+5)*3
5x - 3 = 3x + 15
2x = 18
x = 9
a. Andrew's started with number 9
b. (1) 5x- 3 = 5*9 - 3
= 42
(2) (x + 5)*3
= 14*3 = 42
c. Think of a number, then multiply it with 4 then add 6 in it
Think of a number add 12 in it then then double it.
4x + 6 = (x+12)*2
x = 9
9. What is the length of QR?
Answers
Answer:
48
Step-by-step explanation:
definition of very similar triangles hope the answer is correct
To conserve water, many communities have developed water restrictions. The water utility charges a fee of $34, plus an additional $1.36 per hundred cubic feet (HCF) of water. The recommended monthly bill for a household is between $60 and $85 dollars per month. If x represents the water usage in HCF in a household, write a compound inequality to represent the scenario and then determine the recommended range of water consumption. (Round your answer to one decimal place.
Answers
60 ≤ 1.36x + 34 ≤ 85; To stay within the range, the usage should be between 19.1 and 37.5 HCF.
Hown to write the inequalityThe correct compound inequality to represent the scenario is:
60 ≤ 1.36x + 34 ≤ 85
To solve for x, we need to isolate it in the middle of the inequality:
60 - 34 ≤ 1.36x ≤ 85 - 34
26 ≤ 1.36x ≤ 51
Finally, we divide by 1.36 to isolate x:
19.12 ≤ x ≤ 37.5
Therefore, the recommended range of water consumption is between 19.1 and 37.5 HCF. The answer is (D) 60 ≤ 1.36x + 34 ≤ 85; To stay within the range, the usage should be between 19.1 and 37.5 HCF.
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complete question
To conserve water, many communities have developed water restrictions. The water utility charges a fee of $34, plus an additional $1.36 per hundred cubic feet (HCF) of water. The recommended monthly bill for a household is between $60 and $85 dollars per month. If x represents the water usage in HCF in a household, write a compound inequality to represent the scenario and then determine the recommended range of water consumption. (Round your answer to one decimal place.)
60 ≤ 1.36x − 34 ≤ 85; To stay within the range, the usage should be between 69.1 and 87.5 HCF.
60 ≤ 1.36x − 34 ≤ 85; To stay within the range, the usage should be between 44.1 and 87.5 HCF.
60 ≤ 1.36x + 34 ≤ 85; To stay within the range, the usage should be between 37.5 and 44.1 HCF.
60 ≤ 1.36x + 34 ≤ 85; To stay within the range, the usage should be between 19.1 and 37.5 HCF.
An airplane traveling with the wind flies 450 miles in 2 hours. On the return trip, the plane takes 3 hours to travel the same distance. Find the speed of the airplane if the wind is still.
Answers
Answer:
150mph
Step-by-step explanation:
URGENT
Which of the following expressions will work to find z.
7(cos(60))
7(cost(30))
2y
y√ 2
7(tan(60))
7(tan(30))
7(sin(30))
y√ 3
Answers
The value of x and z in the right triangle are 7√3 and 14 units.
How to find the side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a right triangle is 180 degrees.
Therefore, let's find the side x and z using trigonometric ratios.
Hence,
tan 30 = opposite / adjacent
tan 30 = y / x
tan 30 = 7 / x
cross multiply
x = 7 / tan 30
x = 7 × √3 / 1
x = 7√3 units
Let's find z as follows:
sin 30 = opposite / hypotenuse
sin 30 = 7 / z
cross multiply
z = 7 / sin 30
z = 7 / 0.5
z = 14 units
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20. The table below shows the results of a survey on
students' favorite school lunches. What fraction of
the students surveyed said that grilled cheese is
their favorite school lunch?
What Is their Favorite
School Lunch?
Answers
Answer:
I believe it would be 3/10 simplified, 30/100 not simplified
Step-by-step explanation:
because it is 30%, 30% in a fraction form is 3/10, or 30/100
Troy is dreaming that the gas station that he works at is being robbed. in the dream, he feels a mixture of fear and anger. functional magnetic resonance imaging (fmri) of his brain activity at this time would show that the _____ is/are activated, which is connected to these and other emotional states.
Answers
In multiple brain imaging investigations employing positron emission tomography (PET) and other techniques, it has been discovered that frightened stimuli, such as frightening faces, frightening images, and fear conditioning cues, activate the amygdala (fMRI)
What is functional magnetic resonance imaging?(fMRI) detects the minute variations in blood flow that accompany mental activity. It may be used to determine which brain regions are in charge of crucial functions, assess the consequences of a stroke or another illness, or direct brain treatment.
It demonstrates actual brain activity and identifies the regions of the brain that are involved during behavior or cognitive processes. Furthermore, it uses variations in blood flow and oxygen concentration as a gauge of neuronal activity.
Therefore, Troy is dreaming that the gas station that he works at is being robbed. He has a mix of fury and dread in the dream. Functional magnetic resonance imaging (fmri) of his brain activity at this time would show that the (amygdala). Is/are activated, which is connected to these and other emotional states.
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