The equation of the line parallel to [tex]\(5x + 2y = 12\)[/tex] and passing through the point (-2, 4) is given as [tex]\(y = -\frac{5}{2}x - 1\).[/tex]
To find the equation of a line parallel to [tex]\(5x + 2y = 12\)[/tex] and passing through the point (-2, 4), we need to follow these steps:
1. Convert the given equation[tex]\(5x + 2y = 12\)[/tex] into slope-intercept form [tex]\(y = mx + b\).[/tex]
2. Determine the slope of the given line.
3. Use the slope and the given point to find the equation of the parallel line using the point-slope form.
4. Convert the equation into slope-intercept form if needed.
Let's start with step 1:
1. Convert [tex]\(5x + 2y = 12\)[/tex] into slope-intercept form [tex]\(y = mx + b\):[/tex]
Subtract [tex]\(5x\)[/tex] from both sides:
[tex]\[2y = -5x + 12\][/tex]
Divide both sides by 2:
[tex]\[y = -\frac{5}{2}x + 6\][/tex]
Now, we know that the slope of the given line is [tex]\(-\frac{5}{2}\)[/tex] . Since the line we're looking for is parallel to this line, it will have the same slope.
2. The slope [tex](\(m\))[/tex] of the parallel line is [tex]\(-\frac{5}{2}\).[/tex]
Next, we use the point-slope form[tex]\(y - y_1 = m(x - x_1)\),[/tex]where [tex]\((x_1, y_1)\)[/tex] is the given point (-2, 4) and [tex]\(m\)[/tex] is the slope.
3. Substitute the values into the point-slope form:
[tex]\[y - 4 = -\frac{5}{2}(x - (-2))\][/tex]
[tex]\[y - 4 = -\frac{5}{2}(x + 2)\][/tex]
Now, distribute[tex]\(-\frac{5}{2}\):[/tex]
[tex]\[y - 4 = -\frac{5}{2}x - 5\][/tex]
4. Convert to slope-intercept form:
Add 4 to both sides:
[tex]\[y = -\frac{5}{2}x - 5 + 4\][/tex]
[tex]\[y = -\frac{5}{2}x - 1\][/tex]
So, the equation of the line parallel to [tex]\(5x + 2y = 12\)[/tex] and passing through the point (-2, 4) is [tex]\(y = -\frac{5}{2}x - 1\).[/tex]
Complete question:
What is the equation of the line that is parallel to the line 5x+2y=12 and passes through the point (-2, 4)?
whats the chance to not get 33% chance 3 times in a row
You have 2 types of bread, 3 types of meat, and 2 types of cheese. How many different sandwiches can you make if each sandwich has 1 type of bread, 1 type of meat, and 1 type of cheese?
branliest offered
what is solution of 7v-(6-2v)=12 show work
A -3.6
B -2
C 2
D 3.6
What shape has 4 congruent sides but is not a square?
in 1996,Donovan Bailey of Canada ran the 100 meter dash in 9.84 seconds.How fastis that to the nearst second?to the nearst tenth of a second
40% of a certain number is 80 what is that number ?
Sarah washes cars at the car wash. She makes $8.25 per hour and earns $30 in tips per day. Give an expression that Sarah could use to calculate her daily earnings.
you would need to multiply 8.25 by the number of hours worked (x) and then add the tips
so it would be A. 8.25x+30
What geometric formula relates the radius of a circle to its area?
The geometric formula for the radius of a circle to its area will be;
A = πr²
Where, A is area of circle , r is radius of circle.
What is Circle?
Circle is a closed two dimensional figure in which the set of all points in the plane is equidistance from the center of circle.
Let radius of a circle = r
And, Area of a circle = A
Then, The geometric formula for the radius of a circle to its area will be;
A = πr²
Thus, The geometric formula for the radius of a circle to its area will be;
A = πr²
Where, A is area of circle , r is radius of circle.
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Find the value of a.
What is surface area
Problem page a delivery truck is transporting boxes of two sizes: large and small. the large boxes weigh 45 pounds each, and the small boxes weigh 15 pounds each. there are 120 boxes in all. if the truck is carrying a total of 3300 pounds in boxes, how many of each type of box is it carrying?
Can somebody help me please?
Which is the graph of 4x – 3y = 12?
Answer:
its the last graph pictured
The graph of 4x - 3y = 12 is given below.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
The given linear equation is 4x - 3y = 12.
Rearranging it into slope intercept form, we get,
y = 4/3 x - 4
In order to find the points through which it passes, put some of the values of x.
When x = -3, y = -4 - 4 = -8
When x = 0, y = 0 - 4 = -4
When x = 3, y = 4 - 4 = 0
When x = 6, y = 8 - 4 = 4
...........
So the graph passes through (-3, -8), (0, -4), (3, 0) and (6, 4).
Hence the graph of the given equation is given below.
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What is the area of the trapezoid shown? (1) angle a = 120 degrees (2) the perimeter of trapezoid abcd = 36?
Neither statement alone is sufficient to determine the area of the trapezoid.
Explanation:The area of a trapezoid can be found using the formula:
Area = (1/2) * (sum of parallel sides) * height
To find the area of the trapezoid, we need the lengths of the parallel sides and the height.
(1) The given angle does not provide information about the lengths of the sides, so it is not sufficient to find the area.
(2) The perimeter of the trapezoid does not directly give information about the lengths of the sides, so it is also not sufficient to find the area.
Therefore, neither statement alone is sufficient to determine the area of the trapezoid.
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what is sin 30?......
Answer:
The correct option is D) [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
we need to find sin 30° with the reference of provided figure
Since, [tex] sin\theta=\frac{perpendicular}{hypotenuse}[/tex] .....(1)
In fig , perpendicular is 1 and hypotenuse is
now put [tex]\theta=30\degree[/tex] in (1)
[tex] sin\theta=\frac{1}{2}[/tex]
Hence, The correct option is D) [tex]\frac{1}{2}[/tex]
An urn contains six chips, numbered 1 through 6. two are chosen at random and their numbers are added together. what is the probability that the resulting sum is equal to 5?
Final answer:
The probability of drawing two chips from an urn numbered 1 through 6 such that their sum is 5 is 4/15, since there are four favourable outcomes (1,4), (2,3), (3,2), and (4,1) out of the total 15 possible combinations.
Explanation:
The question involves calculating the probability of drawing two chips from an urn, each numbered 1 through 6, such that their sum equals 5. To solve the problem, let's consider all possible combinations of two different chips that can be drawn at random:
(1, 4)(2, 3)(3, 2)(4, 1)There are 4 favourable combinations that result in a sum of 5. As each chip can be drawn only once, the total number of pairs can be given by the combination formula C(n, k) = n! / (k!(n-k)!)), where n is the total number of chips and k is the number of chips drawn. In this case, C(6, 2) = 6! / (2!4!) = 15, and so there are 15 possible pairs that can be drawn from our urn.
Therefore, the probability of getting a sum of 5 is the number of favourable outcomes divided by the total number of outcomes, which is 4 favourable combinations divided by 15 possible combinations, resulting in a probability of 4/15.
Find the difference quotient please
What has 6 wheels and flies ?
Answer:
A garbage truck
Step-by-step explanation:
Please help guys!!
What set of transformations is performed on LMNO to form L'M'N'O'?
A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left
A 270-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left
A translation 1 unit to the left followed by a 270-degree counterclockwise rotation about the origin
A translation 1 unit to the left followed by a 90-degree counterclockwise rotation about the origin
Answer:
Its b and can you give me the brainlist
Step-by-step explanation:
Simplify the expressions. (use only positive exponents in your answers.) (a) (9x4)(-9x-3) = incorrect: your answer is incorrect.
Given two points on the graph of the line, the equation of the line can be found.
True
False
Why is it incorrect
HELP PLEASE!! 30 POINTS!!
John's credit card company calculates a finance charge based upon a periodic rate of 1.75% on all unpaid balances. If John has an unpaid balance of $475, determine the finance charge that he will be assessed.
A. $8.31
B. $349.00
C. $346.30
D. $469.33
Final answer:
The finance charge for John is calculated by multiplying his unpaid balance by the periodic rate. The calculation results in a finance charge of $8.31, which is option A.
Explanation:
John's finance charge on his credit card, based on a periodic rate of 1.75% on an unpaid balance of $475, can be calculated using the formula: Finance Charge = Periodic Rate × Unpaid Balance. To find the finance charge, multiply 1.75% (or 0.0175 in decimal form) by $475. Therefore, the finance charge would be 0.0175 × $475 = $8.3125. When rounded to the nearest cent, this is $8.31, which corresponds to option A.
how can i turn 7/2 into a decimal
Which temperature conversion is correct? °c = k - 273 k = 273 x °c k = °c - 273 °c = k + 273?
Answer: The formula to convert kelvin to degree celsius is:
°C=K-273
First option: °C=K-273
How many kilograms are in 5500 g? Show all work
When converting gram to kilogram (smaller unit to larger unit), you must divide by 10. This means that you must move each unit to the left. For example:
Kilo, hectogram, decagram, gram... you must move 3 steps to the left which means 5500 grams is equal to 5.5 Kilograms
Which of the following illustrates the truth value of the following mathematical statements? 6 + 3 = 9, and 5 • 5 = 20
A. T T → T
B. F T → F
C. T F → F
D. F F → F
Write an equation that represents a vertical translation 7 units down of the graph of g(x)=|x|
Translation involves changing the position of a function.
The equation that represents the new function is: [tex]\mathbf{g'(x) = |x| - 7}[/tex]
The parent function is given as:
[tex]\mathbf{g(x) = |x|}[/tex]
The rule of translating a function down is:
[tex]\mathbf{(x,y) \to (x,y-h)}[/tex]
Where: h is the number of units translated down
i.e. h = 7
So, we have:
[tex]\mathbf{g'(x) = g(x) - h}[/tex]
Substitute [tex]\mathbf{g(x) = |x|}[/tex]
[tex]\mathbf{g'(x) = |x| - h}[/tex]
Substitute 7 for h
[tex]\mathbf{g'(x) = |x| - 7}[/tex]
Hence, the required function is: [tex]\mathbf{g'(x) = |x| - 7}[/tex]
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The equation that represents the given situation is g(x) = |x|-7
To write an equation that represents a vertical translation 7 units down of the graph of g(x) = |x|, we need to modify the original function accordingly.
A vertical translation can be represented by adding or subtracting a constant to the function. In this case, since we are translating the graph downward by 7 units, we subtract 7 from the original function:
g(x) = |x| - 7
Thus, the equation that represents this vertical translation is g(x) = |x| - 7.
This results in each point on the graph of g(x) = |x| shifting 7 units downward, creating the new graph of g(x) = |x| - 7.
simplify
(-6i)(-7-6i)-(7i)(3-2i)
Closest integer to the square root 75