The equation of the tangent line to the curve at the point (2,4) is y = (-1/2)x + 5.
To use implicit differentiation to find an equation of the tangent line to the curve at the given point (2,4), we need an implicit equation of the curve. Let's assume the curve is given by the equation:
x² + y² = 16
We can use implicit differentiation to find the slope of the tangent line at any point on this curve. Taking the derivative of both sides with respect to x, we get:
2x + 2y (dy/dx) = 0
Simplifying for (dy/dx), we get:
dy/dx = -x/y
Now we can substitute the given point (2,4) into this equation to find the slope of the tangent line at that point:
dy/dx = -2/4 = -1/2
So the slope of the tangent line at (2,4) is -1/2. We can use this slope and the point-slope form of the equation of a line to find an equation of the tangent line. The point-slope form is:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the given point. Substituting the values, we get:
y - 4 = (-1/2)(x - 2)
Simplifying, we get:
y = (-1/2)x + 5
Therefore, the equation of the tangent line to the curve at the point (2,4) is y = (-1/2)x + 5.
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Complete question:
Use implicit differentiation to find an equation of the tangent line to the curve at the given point (2,4)
0 / 1
It is November 1 of Year 1. Sales for Dee Company for November and December of Year 1 and January of Year 2 are forecasted to be as follows:
November, 400,000; December 600,000; January, 200,000
60% of sales are credit sales; the remaining sales are cash sales. Of these credit sales, 5% are collected during the month of sale, 25% in the following month, and 65% in the second following month; 5% are never collected. Total sales for September and October of Year 1 were 100,000 and 150,000, respectively.
What is the forecasted amount of total cash collections in November of Year 1?
Answer:
Step-by-step explanation:
To find the forecasted amount of total cash collections in November of Year 1, we first need to determine the credit sales for September, October, November, and December of Year 1, and January of Year 2.
Credit sales for September and October of Year 1 have already been given as 100,000 and 150,000, respectively.
For November, credit sales are 60% of 400,000 = 240,000.
For December, credit sales are 60% of 600,000 = 360,000.
For January of Year 2, credit sales are 60% of 200,000 = 120,000.
Now, we need to calculate the amount of credit sales that will be collected in November of Year 1.
5% of credit sales for November will be collected in November itself, which is 5% of 240,000 = 12,000.
25% of credit sales for November will be collected in December, which is 25% of 240,000 = 60,000.
65% of credit sales for November will be collected in January of Year 2, which is 65% of 240,000 = 156,000.
The remaining 5% of credit sales for November, which is 5% of 240,000 = 12,000, will never be collected.
Therefore, the total cash collections in November of Year 1 will be the sum of cash sales for November, and the amount of credit sales collected in November:
Cash sales for November = 40% of 400,000 = 160,000
Credit sales collected in November = 12,000
Total cash collections in November of Year 1 = 160,000 + 12,000 = 172,000.
Hence, the forecasted amount of total cash collections in November of Year 1 is $172,000.
Help what’s the answer
Answer:
Difference=£2.4
Step-by-step explanation:
Here in shop A
130 cm=£1.82
1 cm=£1.82/130
1 cm=0.014
Now
400 cm=0.014*400
=£5.6
Again, In shop B
235cm=£1.88
1 cm=£1.88/235
1 cm=£0.008
Now
400cm=0.008*400
=£3.2
Now,
Difference=£5.6-£3.2
=£2.4
10. Audry spends $600 per month on rent. She makes $25,000 per year. To the nearest percent, what percent of her income does she spend on rent? F 28% G 21% H 20% J 29%
Answer:
J 29%
Step-by-step explanation:
Monthly rent: $600.
There are 12 months in 1 year, so the total rent she pays in 1 year is
12 × $600 = $7200
We need to find what percent $7200 is of $25,000.
percent = part/whole × 100%
percent = 7200/25000 × 100%
percent = 28.8%
Rounded to the nearest percent, the answer is 29%.
The Venn diagram here shows the cardinality of each set. Use this to find the cardinality of the given set.
n(A ∩ B ∩ C^c) = 15 there are 15 elements in the intersection of sets A and B but not in set C.
What is a circle?
A circle is a two-dimensional geometric figure that consists of all the points in a plane that are equidistant from a given point called the center. The distance from the center to any point on the circle is called the radius, which is denoted by the letter "r".
To find the cardinality of n(A∩B∩C^c), we need to know the number of elements that are in the intersection of A and B but not in C.
One way to approach this is to use the principle of inclusion and exclusion. This states that:
n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(A ∩ C) - n(B ∩ C) + n(A ∩ B ∩ C)
We can rearrange this formula to solve for n(A ∩ B ∩ C^c):
n(A ∩ B ∩ C^c) = n(A ∩ B) - n(A ∩ B ∩ C) - n(B ∩ C) + n(A ∩ C) + n(B) + n(C) - n(A)
Plugging in the values we have been given, we get:
n(A ∩ B ∩ C^c) = 4 - 3 - 9 + 7 + 11 + 15 - 10
Simplifying this expression, we get:
n(A ∩ B ∩ C^c) = 15
Therefore, there are 15 elements in the intersection of sets A and B but not in set C.
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A water cooler springs a leak and empties in 2 minutes. The graph below shows the rate at which water leaks from the cooler as a function of time.
The amount of water that was in the cooler before it started leaking was 6 gallons.
Describe Integration?Integration is a mathematical process that involves finding the integral of a function. It is the reverse operation of differentiation, which involves finding the derivative of a function. The integral of a function is a measure of the area under the curve of the function, between two given limits of integration.
The graph shows the rate at which water leaks from the cooler as a function of time, which means that the y-axis represents the rate of leakage in gallons per minute (gal/min), and the x-axis represents the time in minutes.
Since we know that the cooler emptied in 2 minutes, we can integrate the leakage rate over the time interval [0, 2] to find the total amount of water that leaked out:
Total amount of water leaked = ∫[0,2] leakage rate(t) dt
The leakage rate is given by the graph, which consists of a straight line connecting two points: (0,6) and (2,0). We can express this line as a linear equation in slope-intercept form:
leakage rate(t) = mt + b
where m is the slope of the line and b is the y-intercept. To find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (0,6) and (x2, y2) = (2,0). Plugging in the values, we get:
m = (0 - 6) / (2 - 0) = -3
So the equation of the line is:
leakage rate(t) = -3t + 6
Now we can integrate this equation over the time interval [0, 2] to get the total amount of water leaked:
Total amount of water leaked = ∫[0,2] (-3t + 6) dt
= [-3t²/2 + 6t] from 0 to 2
= (-3(2)²/2 + 6(2)) - (-3(0)²/2 + 6(0))
= (6 - 0) - (0 - 0)
= 6 gallons
Therefore, the amount of water that was in the cooler before it started leaking was 6 gallons.
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The complete question is :
3.
h
b=32 inches
h = 22 inches
Find the area of the triangle above.
O242 sq. inches
O125 sq. inches
O 300 sq. inches
O 352 sq. inches
There are 352 square inches in the triangle's surface area. Hence, O 352 sq. inches is 's correct response.
The correct answer is 352 sq. inches
Which fundamental principle of a triangle is this?The triangle has the following characteristics: There are 180 angles in a triangle, thus they all sum up to 180. The lengths of the two sides of a triangle are greater than the length of the third side. Similar to this, the third side of a triangle has a shorter length than the angle between its 2 sides.
A = (1/2)bh if b is the quadrilateral base and h is its height.In this instance, the triangle's height is 22 inches, while its base is 32 inches. These values are substituted into the calculation to produce the following result: A = (1/2)(32)(22) A Equals 352 square inches
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Which equation defines y as a linear function of x?
Select all that apply.
□ A. y = 3x² +7
□ B. x - 4y = 5
□ C. 5x² + y = 3
OD. 2(x+3y) = 6
O E. y = 5x - 3x + 4
Among the given equations, the equation E. y = 5x - 3x + 4 is the only equation that is in the form y = mx + b.
What is linear equation ?
A linear function is defined as a function that has a constant rate of change, meaning that as x increases by a certain amount, y also increases by a certain amount. Therefore, the equation that defines y as a linear function of x is of the form y = mx + b, where m is the slope and b is the y-intercept.
Among the given equations, the equation E. y = 5x - 3x + 4 is the only equation that is in the form y = mx + b. By combining like terms, we can simplify it to y = 2x + 4. This equation has a constant rate of change of 2, which means that for every 1 unit increase in x, y will increase by 2 units.
The other equations are not linear functions because they either have an x² term, which causes a non-constant rate of change, or they have multiple variables, which means that changes in x will not produce a consistent change in y.
Therefore, the answer is E. y = 5x - 3x + 4.
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I need help I really don’t get this
The result of multiplying [tex]5,230[/tex] by [tex]25[/tex] is a quotient of [tex]209.2[/tex] rupees.
What in arithmetic is a quotient?In this example, the number being divided (15) is known as the reward, and the number being divided by (3 in this instance) is known as the divisor. The consequence of divide is the quotient.
What is the ratio between two numbers?When we divided one number by another, the result is a quotient. As an instance, when we divide 6 with 3, we obtain the answer 2, which corresponds to the division.This quotient may be either an integer or a decimal. For describing the presence or intensity of a quality in someone or something, the quotient is utilized.
25)5230(209.2
-50
--------------
230
-225
-----------------
50
-50
------------
0
-----------
So the quotient is [tex]209.2[/tex]
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How do you compute the sum of squared errors
Answer:
Relating SSE to Other Statistical Data
Variance = SSE/n, if you are calculating the variance of a full population.Variance = SSE/(n-1), if you are calculating the variance of a sample set of data.
What is 15426.82 rounded to the nearest hundredth
Answer:
Step-by-step explanation:
15426.80
Answer: 15426.82
Step-by-step explanation:
15426.82 is also 15426.82000
Since 2 is the hundredth number (behind the decimal point) and the next number is 0, it will be rounded down.
Therefore 15426.82 to the nearest hundredth is 15426.82
please answer question i cannot do it
The value of the height of the trapezium is 10.3 cm.
What is the area of a trapezium?The area of a trapezium is given by the formula:
Area = (1/2) x (sum of parallel sides) x (distance between the parallel sides)
The parallel sides of the trapezium are given as 18 cm and 13 cm
The area of the trapezium is given as 160 cm²
The height of the trapezium = h
The value of the height of the trapezium is calculated as follows;
160 = ¹/₂ (18 + 13) h
2 x 160 = (31)h
320 = 31h
h = 320 / 31
h = 10.3 cm
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5x+6/1/3=3x/0.4 HELP RSM.
Answer:
x = 0.8
Step-by-step explanation:
5x+6/1/3=3x/0.4
5x + 2 = 3x/0.4
2x + 0.8 = 3x
x = 0.8
Keekee bought a magazine for $6 and some binders for $9 each. She spent a total of $78. How
many binders did she buy? Step by step Please!!
Answer:
10 binders ........... .......... .....
Answer:
For this one I assigned y as the missing number
We know that $6 magazine plus $9 times a specific amount would equal $78
so 6 + 9(y) = 78
6 + 9(8) = 78
9(8)=72
72+6=78
So there were 8 binders bought at $9 each and a 1 magazine bought for $6.
Step-by-step explanation:
Estimate a 15% tip on a dinner bill of $58.12 by first rounding the bill amount to the nearest ten dollars.
Answer: an estimated 15% tip on a dinner bill of $58.12 would be $8.72.
Step-by-step explanation:
First, we can calculate 10% of $58.12 by moving the decimal point one place to the left, which gives us $5.81.
Then, we can calculate half of 10%, which is 5%, by dividing $5.81 by 2, giving us $2.91.
Finally, we add 10% and 5% to get the estimated tip amount:
$5.81 + $2.91 = $8.72
Therefore, an estimated 15% tip on a dinner bill of $58.12 would be $8.72.
The box plots show a random sample of wait times for two rides at a water park
The median wait time for Speed Slide is 2 minutes longer than the median wait time for Wave Machine and the IQR for both rides is 6 minutes.
Define the term box plot?A box plot, also known as a box and whisker plot, is a graphical representation of a data set that shows the distribution of the data along a number line.
In the box plots show a random sample of wait times for two rides at a water park is shown in figure.
If we compare the wait times in the box plots,
then for, Speed Slide: Median = 11
IQR= Q1 - Q3 (Calculation formula of IQR)
= 12 - 6
IQR = 6 minutes
for wave slide: median: 9
IQR= Q1 - Q3 (Calculation formula of IQR)
= 11 - 9
IQR = 2 minutes
The median wait time for Speed Slide is 2 minutes longer than the median wait time for Wave Machine and the IQR for both rides is 6 minutes.
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A type of wood has a density of 250 kg/m3. How many kilograms is 75,000 cm3 of the wood? Give your answer as a decimal.
write the equation for the relationship between x and y. x=1,2,4 y= 0,-5,-15
Answer:
y = -5x + 5
Step-by-step explanation:
y = mx + b
y = __x + __
To write the equation we need the slope (m) and the y-intercept (b).
Slope:
The is the change in y over the change in x. As the y is decreeing by 5, the x is increasing by 1. This gives us the slope -5/1 = -5
y-intercept:
The y intercept is the point (0,b). It is when x equals zero. If we start at 1 and go back to 0. That mean that the y increase by 5, so the intercept is at the point (0,5) which makes the y-intercept 5.
y = -5x + 5
Helping in the name of Jesus.
which is correct answer?
a (a value)
b
c
d
Indeed, the intermediate value theorem demonstrates that the equation [tex]x + sin(x) = -1[/tex] must have at least one solution on the interval [-/2, /4]. Thus option B is correct.
What is the intermediate valve theorem?The intermediate value theorem states that if a continuous function exhibits values with opposite signs at two places, there must be at least one location in the interval where it equals zero (or crosses the x-axis).
Note that x + sin(x) is a continuous function to see why. When x + sin(x) is evaluated at the interval's left endpoint, x = -/2, the result is [tex]-/2 + sin(-/2) = -/2 - 1[/tex] , which is less than -1.
The intermediate value theorem states that because x + sin(x) is continuous and can have values both less than and greater than -1 at either end of the range, it must also have a value of -1 somewhere in between.
Therefore, When x + sin(x) is evaluated at the interval's right endpoint, x = /4, the result is [tex]x + sin(x) = x + 2/2,[/tex] Which is greater than -1.
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what is the cost of sales
The expense incurred by a cοmpany tο prοduce the gοοds οr services sοld within a specific time periοd is knοwn as the cοst οf sales.
What dοes cοst cοmprise οf ?It cοmprises all cοsts that are directly related tο the prοductiοn prοcess, such as thοse fοr labοr, utilities, raw materials, and manufacturing equipment depreciatiοn.
Grοss prοfit, which is the amοunt οf mοney a firm makes frοm its cοre οperatiοns befοre deducting extra cοsts like marketing, administrative, and financing charges, is calculated by subtracting the cοst οf sales frοm revenue. Tο apprοpriately price their prοducts and assess the prοfitability οf their οperatiοns, firms must have a thοrοugh understanding οf their cοst οf sales.
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Complete question:
What is the definition of cοst οf sales?
Martin has a spinner that is divided into four sections labeled A, B, C, and D. He spins the spinner twice. PLEASE ANSWER RIGHT HELP EASY THANK UU
Drag the letter pairs into the boxes to correctly complete the table and show the sample space of Martin's experiment.
Answer:
going from left to right:
AA
BD
CB
DC
PLEASE HELP AND SHOW THE WORK
An equation of the line that goes through the point (-1, -3) and (3, 5) is y = 2x - 1.
An equation of the line in slope-intercept form that is perpendicular to the equation for obstacle 1 is y = -x/2 + 3.
How to determine an equation of this line?In Mathematics, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁) or [tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)[/tex]
Where:
m represent the slope.x and y represent the points.At data point (-1, -3), a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
[tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\\\\y - (-3) = \frac{(5- (-3))}{(3-(-1))}(x -(-1))\\\\y +3 = \frac{(5+3)}{(3+1)}(x +1)[/tex]
y + 3 = 2(x + 1)
y = 2x + 2 - 3
y = 2x - 1
In Mathematics, a condition that must be met for two lines to be perpendicular is given by:
m₁ × m₂ = -1
2 × m₂ = -1
m₂ = -1/2.
At point (-4, 5), an equation of the line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 5 = -1/2(x + 4)
y = -x/2 - 2 + 5
y = -x/2 + 3
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What is the perimeter of the football field without the end zones?
Answer:
30623 yards
Step-by-step explanation:
Answer:
In the NFL, the perimeter of a football field, excluding the end zones, is 30623 yards. The field is how many feet wide... A football field in the United States is 120 yards long (including the end zones).
Step-by-step explanation:
Brainliest pls
Hoang has worked as a nurse at Springfield General Hospital for 5 years longer than her friend Bill. Two years ago, she had been at the hospital for twice as long. How long has each been at the hospital?
5 years longer then Bill, 2x5=10.
10+2=12.
12-5=7
Hoang has be there for 12 years. Bill has for 7 years.
PLS HELP 40 POINTS AND BRAINLIEST!!
Step-by-step explanation:
All of the EXTERNAL angles of a polygon sum to 360 °
95 + 44 + 42 + 78 + p = 360°
p =101°
then q + p form a straight line = 180 °
so q = 79 °
The coordinates of three vertices of a parallelogram are (3,-2), (5,2) and (0,2). What are the coordinates of the fourth vertex?
The coordinate of fourth point of a parallelogram is (2,0)
We need to remember that the diagonals of a parallelogram intersect each other at a halfway point and the midpoint of each diagonal is the same.
A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram's adjacent angles add up to 180 degrees.
The midpoint formula
[tex]M=\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}[/tex]
AC=BD
We can find the coordinates of the fourth vertex (x,y) through this procedure:
For x
[tex]\frac{5-2}{2}=\frac{0+x}{2}\\\\x=2\\\\for\ y \\\frac{2-2}{2}=\frac{y+2}{2}\\\\y=0[/tex]
Hence the coordinate of fourth point is (2,0)
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The table represents some points on the graph of a linear function.
Which equation represents the same relationship?
y= -1.5x+3
y = 3x - 1.5
y= 1.5x -3
y= -3x+1.5
An equation that represents the same relationship include the following: D. y = -3x + 1.5.
How to determine an equation of this line?In Mathematics, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁) or [tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)[/tex]
Where:
m represent the slope.x and y represent the points.At data point (-3.5, 10.5), a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
[tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\\\\y - 10.5 = \frac{(3- 10.5)}{(-0.5 +3)}(x +3)[/tex]
y - 10.5 = -3(x + 3)
y = -3x - 9 + 10.5.
y = -3x + 1.5
In this context, we can reasonably infer and logically deduce that a linear function of the line that represents this table in slope-intercept form is y = -3x + 1.5.
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Find the surface area of the triangular pyramid. The side lengths of the base are equal.
The surface area of the triangular pyramid is the sum of the lateral surface area and the base area.
Lateral Surface Area: The lateral surface area of a triangular pyramid is equal to the product of the slant height and the perimeter of the base.
Slant height = √ ( (length of side)2 + (height)2 )
Perimeter of the base = 3 x length of side
Therefore, the lateral surface area = √ ( (length of side)2 + (height)2 ) x 3 x length of side
Base Area: The base area of the triangular pyramid is equal to one-half of the product of the three side lengths.
Therefore, the base area = 1/2 x (length of side) x (length of side) x (length of side)
Surface Area: The total surface area of the triangular pyramid = lateral surface area + base area
Therefore, the surface area = √ ( (length of side)2 + (height)2 ) x 3 x length of side + 1/2 x (length of side) x (length of side) x (length of side)
use the methods taught in this class to find the slope and y-intercept of the regression line. round your answers to 3 decimal places.
The slope and Y-intercepts of the regression lines can be found using the formulae: m = (nΣxy - ΣxΣy) / (nΣx² - (Σx)²) and b = (Σy - mΣx) / n
To find the slope and y-intercept of a regression line, you can use the formula y = mx + b, where m is the slope and b is the y-intercept. Regression Line is a method in which the dependent variable serves as the explanatory variable, and the former is utilized to infer information about the latter and create a forecast for it.
To calculate the slope of a regression line, you can use the formula m = (nΣxy - ΣxΣy) / (nΣx² - (Σx)²), where n is the number of data points, x and y are the variables, and Σ represents summation.
To calculate the y-intercept of a regression line, you can use the formula b = (Σy - mΣx) / n.
Once you have calculated these values, you can substitute them into the equation y = mx + b to get your regression line.
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Correct question is:
Use the methods taught in this class to find the slope and y-intercept of the regression line. Round your answers to 3 decimal places.
Can I please get help it's an EMERGENCY!
The number of hours it will take the same dog to run 26 1/10 miles is 7.2 hours
How long will it take the dog to run 26 1/10 miles?7 1/4 miles in 2 hours
26 1/10 miles in x hours
Equate miles ratio hours
7 ¼ miles : 2 hours = 26 ⅒ miles : x hours
7.25 / 2 = 26.10 / x
cross product
7.25 × x = 26.10 × 2
7.25x = 52.20
divide both sides by 7.25
x = 52.20 / 7.25
x = 7.2 hours
Ultimately, it will take 7.2 hours for the dog to run 26⅒ miles.
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6.) The sum of two numbers is 45.
The larger number y is 6 less than twice the smaller number
a.
Write a system of linear equations.
What is the smaller number?
Answer:
x= 13 =smaller number
Step-by-step explanation:
let x=smaller number
y=2x-6=larger number
x+y=45
x+2x-6=45 (equation)
3x=39
x=13
Answer:
[tex]x = 13[/tex] ..... smaller number
and
[tex]y = 32[/tex] ....... larger number
Step-by-step explanation:
Greetings!!!
Let the two numbers be X and Y
[tex]x + y = 45........ \:equation \: 1[/tex]
The larger number is y and is 6 less than twice the smaller number. which means:-
[tex](y - 6) = 2x........... \: equation \: 2[/tex]
so, now solve for y. from equation 2
[tex]y - 6 = 2x \\ y = 2x + 6[/tex]
Substitute equation 1 into equation 2
[tex]x + y = 45 \\ x + (2x + 6) = 45 \\ 3x + 6 = 45 \\ 3x = 45 - 6 \\ 3x = 39....divide \: both \: sides \: by \: 3 \\ x = 13[/tex]
To solve for y substitute x into the first equation
[tex](13) = + y = 45 \\ y = 45 - 13 \\ y = 32[/tex]
Finally, to be more sure make a cross check
[tex]y - 6 = 2x \\ 32 - 6 = 2(13) \\ 26 = 26[/tex]
If you have any questions tag it on comments
Hope it helps!!!