The expression to find the number of cups of water Katrina drinks in a week is 0.5 gallons/day x 16 cups/gallon x 7 days/week = 56 cups/week.
To find the number of cups of water Katrina drinks in a week, we need to convert the given information from gallons to cups and then multiply it by the number of days in a week.
Given that Katrina drinks 0.5 gallons of water per day, we know that there are 16 cups in a gallon. Therefore, Katrina drinks 0.5 x 16 = 8 cups of water per day.
To calculate the number of cups of water she drinks in a week, we multiply the daily consumption by the number of days in a week, which is 7.
Therefore, the expression to find the number of cups of water Katrina drinks in a week is: 8 cups/day x 7 days/week = 56 cups/week.
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Casho needed to get her computer fixed, she tooled it to the repair store. The technician at the store worked on the computer for 5 hours and charged her 102$ for parts the total 627 write and solve an equation which can be used to determine x
The cost of the labor per hour
The cost of the labor per hour is $105. the equation can be used to determine x. The cost of labor per hour is $105. the total amount paid by Casho was $627 - $102 (the cost of the parts) = $525. The technician charged her $105 per hour for his labor.
Given, The technician at the store worked on the computer for 5 hours and charged her 102$ for parts a total 627.
Since Casho needed to get her computer fixed, she took it to the repair store. Therefore, the cost of labor per hour can be calculated.
To find the cost of labor per hour, we can use the following formula; Total Cost = Cost of Parts + Labor Cost * Hours Worked Given, Total Cost = 627Cost of Parts = $102 Labor Cost = x (unknown)Hours Worked = 5Thus, the equation can be written as;
Total Cost = Cost of Parts + Labor Cost * Hours Worked$627 = $102 + x * 5Solving the above equation for x; Let's first subtract $102 from both sides,$627 - $102 = x * 5$525 = x * 5Then, divide both sides by 5 to isolate x,$\frac{525}{5} = x$105 =
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I want to write an equation for a line that passes through 2 of the data points collected. The points are (8,5) and (-12, -9). Is 7x - 10y = 3 a good model? Why?
Answer:
No
Step-by-step explanation:
Slope is [tex]\frac{-9-5}{-12-8}=\frac{-14}{-20}=\frac{7}{10}[/tex]
[tex]y-y_1=m(x-x_1)\\y-5=\frac{7}{10}(x-8)\\y-5=\frac{7}{10}x-\frac{28}{5}\\10y-50=7x-56\\10y+6=7x\\6=7x-10y[/tex]
Therefore, 7x-10y=3 would not be a good model, but it's very close
please see photo thank you
Answer:
[tex]37in^2[/tex]
Step-by-step explanation:
We can break up this figure into two bits, the longer rectangle at the top, and the smaller square at the bottom.
To find area if a rectangle, you do length x width. You can do this with the square, too. For the area of the square, you would do:
[tex]3 * 3=9in^2[/tex]
For the area of the bigger rectangle, we know the length of it (7 at the top), so we now have to find the width. The only width number that is available to us is the 7 at the right, and the 3 at the left side of the square.
We can subtract these two numbers to get 4 for the width. We just have to multiply our length (7) by our width (4):
[tex]7*4=28in^2[/tex]
Now that we have our areas of our smaller figures, we just need to add them together:
[tex]9in^2 + 28in^2 = 37in^2[/tex]
The area of the figure is [tex]37in^2[/tex]
Drag the tiles to the correct boxes to complete the pairs.
Match each percent amount to its correct value.
15% of 30
30% of 45
60% of 7
23% of 20
13.5
arrowBoth
4.5
arrowBoth
4.6
arrowBoth
4.2
arrowBoth
The correct matches are as follows:
15% of 30 ➔ 4.5
30% of 45 ➔ 13.5
60% of 72 ➔ 43.2
3% of 201 ➔ 6.03
Here is the correct matching of the percent amounts to their respective values:
15% of 30 ➔ 4.5
30% of 45 ➔ 13.5
60% of 72 ➔ 43.2
3% of 201 ➔ 6.03
To determine the values, we multiply the given percent amounts by their corresponding numbers.
For example, to find 15% of 30, we multiply 0.15 (which is the decimal form of 15%) by 30. The result is 4.5.
Similarly, 30% of 45 is obtained by multiplying 0.30 by 45, resulting in 13.5.
60% of 72 is calculated by multiplying 0.60 by 72, giving us 43.2.
Finally, 3% of 201 is obtained by multiplying 0.03 by 201, resulting in 6.03.
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Pls help it’s for my homework l
Answer:
2997 cm²
Step-by-step explanation:
If the scale factor of linear dimensions of 2 figures is k, then the scale factor of the surface areas is k².
The linear scale factor of the figures is 9.
k = 9
k² = 9² = 81
The area of the big pot is 81 times the area of the small pot.
37 cm² × 81 = 2997 cm²
Hence, The Surface Area of the Larger Pot is: 2997 cm^2
Step-by-step explanation:
MAKE A PLAN:
We need to find the Ratio of the Surface Areas of the TWO POTS, based on the given Height Ratio, And then, Calculate the Surface Area of the Larger Pot:
SOLVE THE PROBLEM:1) - The Height Ratio is Given as ( 9:1 ), So, the Linear Ratio is ( 9 )
2) - The Ratio of Surface Areas is the Square of the Linear Ratio:
9^2 = 81
3) - Calculate the Surface Area of the LARGER POT:
h1 / h2 = 1/9
Now:S1 / S2 = 1/81
S2 = 37 * 81 = 2997 cm^2
37 cm^2 * 81 = 2997 cm^2
Draw the conclusion:Hence, The Surface Area of the Larger Pot is: 2997 cm^2
I hope this helps you!
Given the image below. Solve for y.
Answer:
y = 3[tex]\sqrt{5}[/tex]
Step-by-step explanation:
using the Altitude- on- Hypotenuse theorem
(leg of big Δ )² = (part of hypotenuse below it ) × (whole hypotenuse)
y² = 3 × (3 + 12) = 3 × 15 = 45 ( take square root of both sides )
y = [tex]\sqrt{45}[/tex] = [tex]\sqrt{9(5)}[/tex] = [tex]\sqrt{9}[/tex] × [tex]\sqrt{5}[/tex] = 3[tex]\sqrt{5}[/tex]
Will 5 divided by 0.4 be rational or irrational and why
Answer:
Step-by-step explanation:
no
If your grocery bills over the last four weeks were &203, $195,$180 and $238 what was the average bill?
Answer:
204
Step-by-step explanation:
Sum: 816
Count: 4
Median: 199
Geometric Mean: 202.92942642991
Largest: 238
Smallest: 180
Range: 58
For problems 6-7, state the postulate or theorem you would use to prove the triangles are similar.
Answer:
AA Postulate
Step-by-step explanation:
To prove that two triangles are similar in problem 6-7, we would use the Angle-Angle (AA) postulate. This postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
System A -x-27-8=0 x-27= 8
The system has no solution.
O The system has a unique solution:
(x,7) =
O The system has infinitely many solutions.
They must satisfy the following equation: y =
The system has infinitely many solutions, and they can be expressed in the form (x, y) = (x, x - 27), where x can take on any real value.
The given system of equations is:
x - 27 - 8 = 0
x - 27 = 8
To solve this system, let's start by simplifying the second equation:
x - 27 = 8
Adding 27 to both sides, we get:
x = 35
Now we can substitute the value of x into the first equation
x - 27 - 8 = 0
35 - 27 - 8 = 0
8 - 8 = 0
0 = 0
We see that the equation is satisfied, which means that the system is consistent. However, the system is not unique because it has infinitely many solutions. This is because when we simplified the second equation, we obtained a value for x (x = 35) that satisfies both equations.
The system can be represented by the equation y = x - 27. Since x can take on any value, y will also vary accordingly. Therefore, the solutions to the system can be written as (x, y) = (x, x - 27), where x is any real number.
In summary, the system has infinitely many solutions, and they can be expressed in the form (x, y) = (x, x - 27), where x can take on any real value.
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A triangle has two sides of lengths 5 and 13. What value could the length of
the third side be? Check all that apply.
A. 5
B. 24
C. 8
D. 2
O E. 19
F. 10
>
SUBMIT
Answer:
Answer is simple
Step-by-step explanation:
just apply the Pythagoras theorem if u have Hypo nd perpendicular given than B(base) square will be B²=5²-13²
B²=✓144
=12
Which of the following statements best describes the graph of x + y = 2? (5 points)
Group of answer choices
It is a line which intersects the x-axis at (2, 2).
It is a line which intersects the y-axis at (2, 2).
It is a line joining the points whose x- and y-coordinates add up to 2.
It is a line joining the points whose x- and y-coordinates add up to 4.
The best description of the graph is option B) It is a line which intersects the y-axis at (2, 2). This is because the line has a y-intercept of 2 and intersects the y-axis at the point (0, 2). Option B
To determine the best description of the graph of the equation x + y = 2, we can rearrange the equation into slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Rearranging the equation, we have:
y = -x + 2
From this equation, we can see that the slope is -1, meaning that for every unit increase in x, y decreases by 1. The y-intercept is 2, indicating that the line intersects the y-axis at the point (0, 2).
Therefore, the best description of the graph is option B) It is a line which intersects the y-axis at (2, 2). This is because the line has a y-intercept of 2 and intersects the y-axis at the point (0, 2).
Option A) It is a line which intersects the x-axis at (2, 2) is incorrect because the line intersects the x-axis at the point (2, 0), not (2, 2).
Option C) It is a line joining the points whose x- and y-coordinates add up to 2 is incorrect because the equation represents a line and not a set of points.
Option D) It is a line joining the points whose x- and y-coordinates add up to 4 is incorrect because the equation represents a line where the x- and y-coordinates add up to 2, not 4.
Option B
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Solve for the measure of the indicated arc.
O Saved 41°
O
49°
45°
51⁰
131
M
?
K
45°
The value of x and the measure of the intercepted arc of the circle is 2 and 140 degrees respectively.
What is the value of x and the measure of the indicated arc?An inscribed angle is simply an angle with its vertex on the circle and whose sides are chords.
The relationhip between an an inscribed angle and intercepted arc is expressed as:
Inscribed angle = 1/2 × intercepted arc.
From the image:
Inscribed angle Q = 70 degrees
Intercepted arc = 69x + 2
Value of x = ?
To solve for x, plug the given values into the above formula and solve for x:
Inscribed angle = 1/2 × intercepted arc.
70 = 1/2( 69x + 2 )
Multiply both sides by 2
2 × 70 = 2 × 1/2( 69x + 2 )
140 = 69x + 2
140 - 2 = 69x
138 = 69x
x = 138/69
x = 2
Now, to find the value of the intercepted arc:
Intercepted arc = 69x + 2
Plug in x = 2
Intercepted arc = 69( 2 ) + 2
Intercepted arc = 138 + 2
Intercepted arc = 140 degrees.
Therefore, the Intercepted arc measure 140 degrees.
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To pay for a $15,500 motorcycle, Jane made a down payment of $3300 and took out a loan for the rest. On the loan, she paid monthly payments of $219.23 for 5 years. What is the total amount Jane ended up paying for the motorcycle (including down payment and monthly payments)
Answer:
$16,453.80
Step-by-step explanation:
5 × 12 months = 60 months (the time she payed the monthly payments in months)
219.23 × 60 = 13, 153.8
13,153.8+3,300= $16,453.80.
Type the correct answer in each box. Use numerals instead of words for numbers. Consider this function: . To determine the inverse of the given function, change f(x) to y, switch and y, and solve for . The resulting function can be written as f -1(x) = x2 + , where x ≥ .
The inverse of the given function is f -1(x) = \[\frac{x+2}{3}\], where x is greater than or equal to -2/3.
Consider the function, f(x) = 3x - 2. To find the inverse of the function, follow the steps given below:
Step 1: Replace f(x) with y. y = 3x - 2
Step 2: Interchange x and y. x = 3y - 2
Step 3: Solve for y. Add 2 to both sides. x + 2 = 3y Divide both sides by 3. \[\frac{x+2}{3}=y\]
Step 4: Replace y with f -1(x).
Hence, f -1(x) = \[\frac{x+2}{3}\] The resulting function can be written as f -1(x) = \[\frac{x+2}{3}\], where x is greater than or equal to -2/3.
Note that the domain of f(x) is all real numbers, which means that the range of f -1(x) is also all real numbers.
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Point C has a coordinate of (-4, -6) and point D has a coordinate of (1, -6), how far are they apart?
The distance between points C and D is given as follows:
5 units.
How to calculate the distance between two points?Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The coordinates for this problem are given as follows:
(-4, -6) and (1, -6).
Hence the distance is given as follows:
[tex]D = \sqrt{(-4 - 1)^2 + (-6 - (-6))^2}[/tex]
D = 5 units.
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What numbers are missing from the pattern below? Enter your answer, using
a comma to separate each number.
9, 18, 27, 36, ?, ?, ?, ?, 81, 90, 99, 108
Answer here
SUBMIT
Answer:
45,54,63,72
Step-by-step explanation:
d=9
36+9
45+9
54+9
Answer: 45, 54, 63, 72
Step-by-step explanation
just look at each number and go up in the tens and down in the ones and once you get to 0 you start at 9 again
Solve the equation. -3x+1+10x=x+4
Answer:
x = 1/2
Step-by-step explanation:
-3x + 1 + 10x = x + 4
7x + 1 = x + 4
6x + 1 = 4
6x = 3
x = 3/6
x = 1/2
Answer:
the solution to the equation is x = 1/2.
Step-by-step explanation:
To solve the equation -3x + 1 + 10x = x + 4, we can start by simplifying both sides of the equation:
Combine like terms on the left side:
(-3x + 10x) + 1 = x + 4
7x + 1 = x + 4
Next, we want to isolate the x term on one side of the equation. We can do this by subtracting x from both sides and subtracting 1 from both sides:
7x - x + 1 - 1 = x - x + 4 - 1
6x = 3
Finally, to solve for x, we divide both sides of the equation by 6:
6x/6 = 3/6
x = 1/2
So, the solution to the equation is x = 1/2.
Do the ratios
6/5 and 8/7 form a proportion
The ratio of 6/5 and 8/7 is 21/20
What is ratio?A ratio is a relationship between two things when it is expressed in numbers or amounts.
For example if the ratio of boys to girls In a class is 4: 5 , this means that there are 4 boys to 5 girls in the class , i.e for every 4 boys there are 5 girls.
For example if two boys are to share 10 mangoes in the ratio 1:4 , this means one will take 2 and the other will take 8
2:4 can also be expressed as 2/4 = 1/2
Similarly, 6/5 : 8/7
= 6/5)/8/7
= 6/5 × 7/8
= 42/40
= 21/20
Therefore the ratio of 6/5 : 8/7 is 21/20
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Joseph has been assigned a reading that will help him understand the physical laws that keep airplanes in the air. He's a bit
nervous about flying, too, so he really wants to understand how flight works. In addition to taking a deep breath and clearing
away distractions, how should be start making sense of the the reading?
O a.
Joseph needs to think about why this is an important article to him. Then he needs to keep reading it over and over until he
knows it well.
O b. Joseph needs to read the whole thing once, then bring questions to his professor during the next class period.
c. Joseph needs to determine the thesis and topic sentences. Each topic sentences will explain one aspect of the thesis.
Joseph needs to determine the thesis and topic sentences. Each topic sentences will explain one aspect of the thesis. Option C
To start making sense of the reading on the physical laws that keep airplanes in the air, Joseph can follow a systematic approach to enhance his understanding and alleviate his nervousness about flying. While options (a) and (b) might have some merit, option (c) is a more effective strategy for comprehending and synthesizing the information.
Option (a) suggests repeatedly reading the article until Joseph knows it well. While repetition can help reinforce understanding, it might not be the most efficient method for Joseph.
Reading the same material multiple times without actively engaging with the content may not result in deeper comprehension. It's important for Joseph to actively process the information and apply critical thinking.
Option (b) suggests reading the entire article once and then bringing questions to his professor during the next class period. While seeking clarification from the professor is beneficial, reading the article only once might not provide a solid foundation for asking insightful questions. Joseph could benefit from a more comprehensive understanding of the material before seeking clarification.
Option (c) is a more effective approach. Joseph should begin by identifying the thesis and topic sentences of the article. The thesis statement will outline the main idea or argument, while the topic sentences will provide an overview of the key points discussed in the article.
Once Joseph has identified the thesis and topic sentences, he can focus on each topic sentence individually. By breaking down the content into manageable segments, Joseph can ensure that he comprehends each aspect of the thesis before moving on to the next.
Moreover, Joseph can actively engage with the material by taking notes, summarizing each section in his own words, and making connections to real-world examples or personal experiences. This active approach will enhance his understanding and help him internalize the concepts.
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A rectangular tank measuring 40 cm long, 30 cm wide and 35 cm high was filled with water to a hight of 15 cm. 4800 cm3 of water were poured into water. find the new height of water
answer ASAP
A rectangular tank measuring 40 cm long, 30 cm wide and 35 cm high was filled with water to a hight of 15 cm. 4800 cm3 of water were poured into water ,The new height of the water in the tank is approximately 19.83 cm.
To find the new height of water in the tank after pouring in 4800 cm³ of water, we can use the concept of ratios.
First, let's calculate the initial volume of water in the tank before pouring in the additional water. The initial volume can be calculated as the product of the length, width, and initial height:
Initial volume = 40 cm * 30 cm * 15 cm = 18,000 cm³
Next, we add the volume of the water poured in:
Total volume = Initial volume + Volume poured in = 18,000 cm³ + 4800 cm³ = 23,800 cm³
To find the new height, we divide the total volume by the base area of the tank (length * width):
New height = Total volume / (Length * Width) = 23,800 cm³ / (40 cm * 30 cm) = 19.83 cm (rounded to two decimal places)
As a result, the tank's new water level is roughly 19.83 centimetres high.
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Pls help it’s for my homework
a. The value of y when x = 4 is 13.
b. The correct point using part a is point B.
How to find the value of the output in a graph?The graph is represented with x and y axis. If y = x² - 3 let's find the value of y when x = 4.
Therefore,
a.
y = x² - 3
y = 4² - 3
y = 16 - 3
y = 13
b
Some point on the graph of y = x² - 3 have been plotted. Using the part a answer, the point B is the correct point of the equation.
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44. Farheen's salary is three times Saima's, which is
one-third of Atika's salary. If their total salary is Rs.
35.000, Find Farheen's salary.
A. 10,000
C. 15,000
B. 5,000
D. 12,500
Let's start by using variables to represent the salaries of Saima and Atika. Let S be Saima's salary, and A be Atika's salary. Then, we can write:
Saima's salary: SFarheen's salary: 3SAtika's salary: 9S (since S is one-third of A, we can write A = 3S, and then multiply both sides by 3 to get A = 9S)We know that their total salary is Rs. 35,000, so we can write an equation:
S + 3S + 9S = 35,000
Simplifying the left side, we get:
13S = 35,000
Dividing both sides by 13, we get:
S = 2,692.31 (rounded to two decimal places)
Now that we know Saima's salary, we can find Farheen's salary:
Farheen's salary = 3S = 3 × 2,692.31 ≈ Rs. 8,076.92
Therefore, the closest answer choice is A. 10,000, which is not the exact value but is the closest option to the calculated value.
In this math problem, using the given ratios and total salary, we find Saima's salary is Rs. 5000. As Farheen's salary is three times Saima's, Farheen earns Rs.15,000.
Explanation:According to the problem, Farheen's salary is three times Saima's salary, and Saima's is one-third of Atika's. Let's denote Saima's salary as 'x'. Hence, Farheen's salary is '3x' and Atika's salary is '3x'. All their salaries add up to Rs.35,000 as per the question. Therefore, the equation becomes as follows:
x + 3x + 3x = 35000. This reduces to 7x = 35000 after adding the like terms on the left hand side of the equation. Dividing each side by 7, we find 'x = 5000', which is Saima's salary.
Therefore, Farheen's salary is three times Saima's, so it equals '3 * 5000 = 15000', which matches with option C from the list. So, Farheen's salary is Rs. 15,000.
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Janes printing services charges 29.95 to print 200 high quality copies of a one page resume . Each additional set of 100 copies cost 14$ regardless is you use all 100 copies or not . What is the cost for 425 copies ?
Answer:
$71.95
Step-by-step explanation:
$29.95- 200 copies
$14- 100 copies
$14- 100 copies
$14- 25 copies
so 14[3] + 29.95 = $71.95
Write 135 as a product of its prime factors. Write your answer in index form need answer quickly URGENT
135 as a product of its prime factors is written as 3 × 3 x 3 x 5
What are prime factors?The prime factors are those prime digits that can divide a particular digit evenly and without leaving any remainder. To put it differently, these are the main digits that, when multiplied with one another, result in the initial number.
In mathematics and number theory, prime factors hold significant value as they enhance comprehension of number properties and interconnections. In addition, they are utilized in a range of mathematical calculations and algorithms.
From the information given, we have the value as;
135
The prime factors are 3 × 3 x 3 x 5
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when the function f(x) is divided by x-1, the quotient is 3x^2-9x+7 and the remainder is 5. Find the function f(x) and write the result in standard form?
The function f(x) in standard form is 3x³ - 12x² + 16x -2
How to find the function f(x) and write the result in standard form?A function is an expression that shows the relationship between the independent variable and the dependent variable. A function is usually denoted by letters such as f, g, etc.
We have:
The function = f(x)
dividend = (x-1)
quotient = 3x²-9x+7
remainder = 5
Thus, the function f(x) in standard form will be:
f(x) = (x - 1)(3x² - 9x + 7) + 5
Expand the left-hand side:
f(x) = (3x³ - 9x² + 7x - 3x² + 9x - 7) + 5
f(x) = 3x³ - 12x² + 16x -7 + 5
f(x) = 3x³ - 12x² + 16x -2
Therefore, the function f(x) in standard form is 3x³ - 12x² + 16x -2.
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The table below shows the number of days, y, needed to complete a project as a function of the number of full-time staff,
x, working on the project. Which rational function best models the data in the table?
People Working, x
36
18
8
6
Days, y
2
4
9
12
The rational function that best models the data in the table is: y = 72/x.
To determine the rational function that best models the given data, we can analyze the relationship between the number of full-time staff (x) and the number of days needed to complete the project (y).
Let's examine the data in the table:
People Working, x: 36, 18, 8, 6
Days, y: 2, 4, 9, 12
Based on the data, we can observe that as the number of full-time staff increases, the number of days needed to complete the project decreases. This suggests an inverse relationship between x and y.
One rational function that represents an inverse relationship is of the form y = k/x, where k is a constant. This function implies that as x increases, y decreases, and vice versa.
To find the specific value of k, we can use one of the data points from the table. Let's use the first data point (x=36, y=2):
2 = k/36
To solve for k, we can cross-multiply:
2 * 36 = k
k = 72
Therefore, the rational function that best models the data in the table is:
y = 72/x
This function suggests that the number of days needed to complete the project is inversely proportional to the number of full-time staff. As the number of staff increases, the number of days decreases, following a hyperbolic trend.
Please note that while this rational function provides a reasonable approximation of the data, it may not perfectly fit all the data points. Further analysis and additional data points could refine the model for greater accuracy.
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If electricity is billed at a rate of $0.75 per KWH and you used on average 120 KWHs per month, what would you expect to pay each month?
You would expect to pay $90 each month for electricity based on an average usage of 120 KWHs per month.
How to find the expected monthly payTo calculate the monthly cost of electricity, you can multiply the average number of kilowatt-hours (KWH) used per month by the cost per KWH.
Given:
Cost per KWH: $0.75
Average monthly usage: 120 KWHs
To find the monthly cost, you can multiply the cost per KWH by the average monthly usage:
Monthly Cost = Cost per KWH * Average monthly usage
Plugging in the values, we have:
Monthly Cost = $0.75/KWH * 120 KWHs
Calculating the result:
Monthly Cost = $90
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Please help me out id appreciate it
The division between the functions f(x) = ∛(4 · x) and g(x) = 2 · x + 3 is equal to (f / g) (x) = ∛(4 · x) / (2 · x + 3), x ≠ - 3 / 2. (Correct choice: D)
How to perform an operation between two functions
In this problem we find two functions, with which we must perform a division between two functions, whose definition is shown below:
(f / g) (x) = f(x) / g(x)
If we know that f(x) = ∛(4 · x) and g(x) = 2 · x + 3, then the division between the two functions is:
(f / g) (x) = ∛(4 · x) / (2 · x + 3)
The restrictions on the domain is represented by every x when 2 · x + 3 = 0:
2 · x + 3 = 0
2 · x = - 3
x = - 3 / 2
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Write the equation of the line in slope-intercept form. m=−2 , passes through the point (1,8)
Answer:
y = -2x+10
Step-by-step explanation:
Slope-intercept form of the equation for a line is
y = mx+b where m is the slope and b is the y intercept
We know the slope is -2
y = -2x+b
Substituting the point in for x and y and solving for b.
8 = -2(1) + b
8 = -2+b
10 =b
Now
y = -2x+10
Answer:
y = - 2x + 10
Step-by-step explanation:
The equation of a line in slope-intercept form is given by:
y = m x + c
Here,
m → slope of the line
c → y-intercept
In this case, the slope (m) is given as -2, and the line passes through the point (1, 8). We can substitute these values into the equation to find the y-intercept (c)Using the point-slope form of a line, we have:
( y - y₁ ) = m ( x - x₁ )
Substituting the coordinates ( x₁, y₁ ) = ( 1, 8 ), and the slope m = -2:
( y - 8 ) = - 2 ( x - 1 )
Expanding and rearranging the equation:
y - 8 = - 2x + 2
Adding 8 to both sides:
y = - 2x + 10
