The equation of the parabola which passes through the point (-3, -8) as described and has x-intercepts -7 and -4 as described is; y = -2 (x + 4) (x + 7).
Equation of a parabolaIt follows from the task content that the equation of the parabola whose x-intercepts are -7 and -4 and has the point, (-3, -8) on it be determined.
Since the equation of a parabola in the factored form usually takes the form;
y = a (x - f) (x - g) in which case when f and g are x-intercepts of the parabola.
Therefore, we have; y = a (x - (-4)) (x - (-7))
y = a (x + 4) (x + 7)
Hence, to find the value of a, we set y = -8 and x = -3 so that we have;
-8 = a (-3 + 4) (-3 + 7)
-8 = 4a
a = -2.
Therefore, the equation of the parabola is; y = -2 (x + 4) (x + 7).
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The table below shows a proportional relationship between h and j.
h
18
27
48
j
6
9
16
Find the constant of proportionality from h to j. Express
your answer as a fraction in reduced terms.
As per the proportional relationship, the constant of the proportionality is 1/3
Proportional relationship
A relationship is said to be proportional if each pair of data values are related in the same way, by multiplying by a factor.
The standard form of proportional relationship is written as.
y = k x
where k refers the constant of proportionality.
Given,
The table shows the proportional relationship between h and j.
Now, we need to find the constant of proportionality from h to j and we have to express the answer as a fraction in reduced terms.
We know that the standard form of the proportionality is written as,
y = k x
So, here y takes the value of j and x takes the values of h.
Then we have to take the points as (18, 6) and apply t on the standard form to get the value of k,
=> 6 = k (18)
Here we need the value of k, so move the number to the other side then we get,
=> k = 6/18
When we reduce this, then we get,
=> k = 1/3
Therefore, the constant of proportionality is 1/3.
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absolute value 2x - 6 less than 0
The solution set for the inequality is (-3, 3)
How to solve the absolute value inequality?Here we have the absolute value inequality
|2x| - 6 < 0
To solve this, we need to isolate the variable, which in this case is x.
Adding 6 in both sides we get:
|2x| -6 + 6 < 0 + 6
|2x| < 6
This can be decomposed in the inequality:
-6 < 2x < 6
Now to competely solve the inequality, we will divide both sides by 2, so we get:
-6/2 < 2x/2 < 6/2
-3 < x < 3
So the solution set is (-3, 3)
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1. (03.03 MC)
The subtotal for Abdiel's takeout order is $24.30. What will Abdiel's total be if he uses a coupon for 12% off the subtotal and leaves a 25% tip before the discount? (2 points)
O $26.73
$27.46
$33.02
$33.29
Abdiel's total if he uses a coupon for 12% off the subtotal and leaves a 25% tip before the discount is $27.46
The correct answer option is option B
What is Abdiel's total?Abdiel's subtotal = $24.30Abdiel's coupon = 12%Tip = 25%Amount of total after discount = 12% × $24.30
= 0.12 ×24.30
= $2.916
Amount of abdiel's tip = 25% × $24.40
= 0.25 × 24.30
= $6.075
Abdiel's total after discount before tip = (Amount of abdiel's tip + Abdiel's subtotal) - Amount of total after discount
= (6.075 + 24.30) - $2.916
= $30.375 - $2.916
= $27.459
Approximately,
$27.46
Therefore, the total amount Abdiel paid after discount before tip is $27.46
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Given f of x is equal to the quantity x plus 6 end quantity divided by the quantity x squared minus 9x plus 18 end quantity, which of the following is true?
f(x) is decreasing for all x < 6
f(x) is increasing for all x > 6
f(x) is decreasing for all x < 3
f(x) is increasing for all x < 3
The correct statement of the expression (x + 6) / ( x² - 9x + 18 ) is f(x) is increasing for all x > 6
How to determine the correct statementInformation given in the question
f of x is equal to the quantity x plus 6 end quantity divided by the quantity x squared minus 9x plus 18 end quantity
This is written as (x + 6) / ( x² - 9x + 18 )
factorizing the denominator gives
(x + 6) / {( x - 6)( x - 3)}
In the denominator
At x = 6 and at x = 3 the equation will result to infinity which is a very high value. hence:
f(x) is decreasing for all x < 6: contains x = 3 and result to a higher value
f(x) is decreasing for all x < 3: will result to negative numbers which will end up increasing
f(x) is increasing for all x < 3: contains values which will be decreasing like x = 4
Therefore the correct option is f(x) is increasing for all x > 6
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Once the fence is installed, Jason uses 6 gallons 3 quarts of paint. How many quarts does he use?
Answer:
Jason used 27 quarts of paintStep-by-step explanation:
We know that:
1 gallon = 4 quartsThen 6 gallons is:
6 gallons = 6*4 quarts = 24 quartsAdd 3 quarts to get total:
24 + 3 = 27 quartsAnswer:
27 quarts
Step-by-step explanation:
Now we have to,
→ find how many quarts does 6 gallons 3 quarts of paint measure.
Formula we use,
→ 1 gallon = 4 quarts
Now the required solution will be,
→ (6 × 4) + 3
→ 24 + 3
→ 27 quarts
Hence, the answer is 27 quarts.
Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
x < –3
x > –3
x < 3
x > 3
Answer: x < 3
Explanation: Once you reach step 3, you divide -2 on both sides. -2x cancels out, and -6 divided by -2 is 3
A restaurant has 60 menu items. Of these menu items, main dishes outnumber
appetizers by a ratio of 4:1. How many more appetizers would the restaurant have
to add to the menu to bring the ratio to 2:1?
Answer:
15 more appetizers
Step-by-step explanation:
A restaurant has 60 menu items. Of these menu items, main dishes outnumber appetizers by a ratio of 4:1. How many more appetizers would the restaurant have to add to the menu to bring the ratio to 2:1?
at a ratio of 4e:1a and having 60e: there are (60/4=15) 15 appetizers
at a ratio of 2e:1a and having 60e: there are (60/2=30) 30 appetizers
Because they already have 15 appetizers, they will need:
30 appetizers - 15 appetizers = 15 more appetizers
Year No. of cars sold
in (hundreds)
2000 45
2002 51
2004 53
2006 60
2008 77
A car manufacturer's sales figures for 2000 to 2008 are shown in the table. Estimate the average rate of change in the number of cars the manufacturer sold between 2002 and 2006.
A.
450 cars per year
B.
225 cars per year
C.
2,900 cars per year
D.
600 cars per year
Answer: In photo below
You're Welcome :)
The average rate of change in the number of cars the manufacturer sold between 2002 and 2006 is B. 225 cars per year.
What is the average rate of change?The average rate of change shows the slope line over the stated interval.
We can find the average rate of change by dividing the change in y-values by the change in x-values.
Year No. of cars sold
in (hundreds)
2000 45
2002 51
2004 53
2006 60
2008 77
The total number of cars sold between 2002 and 2006 = 16,400
The number of cars sold in 2002 = 5,100
The number of cars sold in 2006 = 6,000
The increase in car sold between 2002 and 2006 = 900 (6,000 - 5,100)
OR:
Increase in the number of cars sold in 2004 = 200 (5,300 - 5,100)
Increase in the number of cars sold in 2006 = 700 (6,000 - 5,300)
Total change in y-values = 900 (6,000 - 5,100)
Total change in x-values = 4 (2006 - 200)2
Average rate of change = 225 (900/4)
Thus, we can conclude that for 4 years, car sales increased on, average, by 225 each year.
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HELP!! WILL MARK BRAINLIEST!!
What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form in the box.
Answer:
1/4
Step-by-step explanation:
rise/run you can count it but it doesn't always work
If you want to know the mathematical way of doing it it's:
m(slope) = y2-y1/x2-x1 Choose any two points I chose (-4,5) & (0,6)
m = 6-5/0-(-4) Then subtract 6 - 5 and 0-(-4)
m = 1/4
The box plot shows the times for sprinters on a track team.
(A horizontal number line starting at 40 with tick marks every one unit up to 59. The values of 42, 44, 50, 54, and 56 are all marked by the box plot. The graph is titled Sprinters' Run Times, and the line is labeled Time in Seconds.)
Which of the following lists the range and IQR for this data?
The five number from the box plot is presented as follows:
Minimum value: 42.First quartile: 44.Median: 50.Third quartile: 54.Maximum value: 56.What does a box-and-whisker plot shows?A box and whisker plot shows five things of a distribution, listed as follows:
The data set's lowest value.The value that 75% of the measures are larger than is found in the first quartile, which is the median of the data set's lowest 50% of measurements.
50% of the data set is less than the median and 50% is more than the median, which is the midpoint value of the data set.The third quartile, which is the median of the data set's top 50% of measurements, is the value that 75% of the measures fall below.The data set's maximum value.
These numbers, which make up the five number summary, are the values highlighted on the box plot from left to right, from the minimum value to the greatest value, passing through the first quartile, the median, and the third quartile.
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Using front-end estimation, find a reasonable estimate of: 719x26=?
The estimation of 719 x 26 is 14,000
What is rounding off?Making a number simpler so that its value stays near to its original state is known as rounding. Although less exact, the outcome of rounding off a number is simpler to utilise.
Although the term "rounding" is a general one, we typically use the terms "round up" or "round down" to indicate whether the number has gone up or down after being rounded. The supplied number is said to be rounded up when the rounded number is increased, and it is said to be rounded down when the rounded number is dropped.
Given:
Estimation of 719 x 26
Now, Round off nearest hundred for 719 which is 700
i.e., Round 719 = 700
Now, Round off nearest hundred for 26 which is 20
i.e., Round 26 = 20
Hence, the estimation is 700 x 20 = 14,000.
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Solve for x.
giving 20 points for the right answer
Answer:
m∠D = 54°
Step-by-step explanation:
The sum of the measures of the interior angles of a triangle is 180°.
The sum of the measures of an interior angle and its corresponding exterior angle is 180°.
With this knowledge, we can construct the equation:
50° + (3x + 18)° + (180 - (8 + 8x))° = 180°
and solve for x.
50° + (3x + 18)° + (180 - 8 - 8x)° = 180°
(50 + 18 + 180 - 8)° + (3x - 8x)° = 180°
240° - 5x° = 180°
5x° = 240° - 180°
5x° = 60°
x° = 12°
Now, we can solve for m∠D by plugging in the x value that we solved for.
m∠D = (3x + 18)°
m∠D = 3(12)° + 18°
m∠D = 36° + 18°
m∠D = 54°
janet and andy bowled three games. Janets scores were 119, 96, and 145. Andys scores were 127, 74, and 88. How much greater was janets total score for the three games that andys total score
Answer:
64
Step-by-step explanation:
119+89+145=353-289=127+74+88
^
64
If you cut a sheet of paper in half, stack one piece on top of the other, cut those in half, stack all the pieces together, repeating this process 20 times, how high will the stack of paper be?
The stack of paper will have the height of 1048576 papers
How to determine how high the stack of paper will be?
The first cut will produce 2 papers, the second cut will produce 4 papers, the third cut will produce 8 papers and the fourth cut will produce 16 papers.
If you examine the stages of cut and the number of papers, the relationship between them is:
1st cut: number of papers = 2¹ = 2
2nd cut: number of papers = 2² = 4
3rd cut: number of papers = 2³ = 8
4th cut: number of papers = 2⁴ = 16
nth cut: number of papers = 2ⁿ
So if the process is repeated 20 times, the number of papers will be:
Number of paper = 2²⁰ = 1048576
Therefore, the stack of paper will be as high as 1048576 papers
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In an election for a corporation seat, there were two candidates. A total of 9,791 votes were polled. 116 votes were declared invalid. The successul candidate got 5 votes for every 4 votes his opponent had. By margin did the successful candidate win?
Margin did the successful candidate win is 5375 - 4300 = 1075.
Given:
In an election for a corporation seat, there were two candidates. A total of 9,791 votes were polled.
116 votes were declared invalid. The successful candidate got 5 votes for every 4 votes his opponent had.
Number of valid votes = 9791 - 116 = 9675.
Let the number of votes of successful candidate = 5x
Let the number of votes of opponent = 4x
5x + 4x = 9675
9x = 9675
divide by 9 on both sides
x = 9675/9
x = 1075
Hence the votes for successful candidate = 5*1075 = 5375.
votes for opponent = 4*1075 = 4300.
Margin by which the successful candidate wins = 5375 - 4300 = 1075.
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An object is launched directly in the air at a speed of 32 feet per second from a platform located 20 feet above the ground. The position of the object can be modeled using the function f(t)=−16t2+32t+20, where t is the time in seconds and f(t) is the height, in feet, of the object. What is the maximum height, in feet, that the object will reach?
Using differentiation, 36 feet is the maximum height, in feet, that the object will reach.
In the given question,
An object is launched directly in the air at a speed of 32 feet per second from a platform located 20 feet above the ground.
The position of the object can be modeled using the function [tex]f(t)=-16t^2+32t+20[/tex], where t is the time in seconds and f(t) is the height, in feet, of the object.
We have to find the maximum height, in feet, that the object will reach.
The given function is [tex]f(t)=-16t^2+32t+20[/tex].
To find the maximum height we differentiate the function with respect to t
[tex]\frac{df}{dt}=-32t+32[/tex]
As we know that at the maximum point the slope of the tangent is zero.
So df/dt = 0
So -32t+32=0
Subtract 32 on both side
-32t+32-32=0-32
-32t=-32
Divide by -32 on both side
-32/-32 t = -32/-32
t=1
Therefore at t=1 the function have maximum value. So we put t=1 in the given equation.
[tex]f(1)=-16(1)^2+32\times1+20[/tex]
f(1)=(-16)×1+32×1+20
Simplifying
f(1)=-16+32+20
f(1)=36 feet.
Hence, 36 feet is the maximum height, in feet, that the object will reach.
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the artist was hired to decorate 40 in 3 hours he completed 3/8 of the pots at that rate how long will it take the artist to decorate 25 clay pots?
The artist will take 5 hours to decorate 25 clay pots.
Given,
Number of pots to be decorated in 3 hours =40
Number of pots he decorated in 3 hours =[tex]\frac{3}{8}*40=3*5=15[/tex]
So, the artist took 3 hours to decorate 15 pots instead of 40 pots.
It means to decorate 1 pot he took time=[tex]\frac{Total time}{Number of pots decorated} =\frac{3}{15} =\frac{1}{15} hour[/tex]
So, to decorate 25 pots he need time,
[tex]time=\frac{1}{5}*25= 5 hours[/tex]
Thus, the artist need 5 hours to decorate 25 clay pots.
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Consider the equation and the following ordered pairs: (4,y) and (x,2).
y=−2x+4
Step 1 of 2 : Compute the missing x and y values so that each ordered pair will satisfy the given equation.
Answer
Keyboard Shortcuts
Complete the table below.
x y
row 14 Answer
row 2 Answer
2
The missing x and y values in the ordered pair of the equation are:
x = 1
y = -4
How to Find the Ordered Pairs of an Equation?Given the ordered pair (x, y) of an equation, y = mx + b, we can find their values by plugging in the given value of either of the x or y coordinates to find the other coordinate value.
The ordered pairs of y = -2x + 4 are given as:
(4, y) and (x, 2)
To find the value of y, substitute x = 4 into the equation y = -2x + 4:
y = -2(4) + 4
y = -8 + 4
y = -4
The value of y is -4.
To find the value of x, substitute y = 2 into the equation y = -2x + 4:
2 = -2x + 4
2 - 4 = -2x
-2 = -2x
-2/-2 = x
1 = x
x = 1
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A movie theater sends out a coupon for 54% off the price of a ticket. Write an equation for the situation, where y is the price of the ticket with the coupon, and x is the original price of the ticket. Use pencil and paper. Draw a graph of the equation and explain why the line should only be in the first quadrant.
The equation for the representation of the given situation will be
y = x - 0.54x, and the graph of the equation should only be in the first quadrant because x and y is representing a price which can't be negative.
What is an equation?An equation is a statement that says that the value of two mathematical expressions is equal.
Given that, a cinema sends out a coupon for 54% off the price of a ticket.
The equation for this situation will be y = x - 0.54x,
And the line of this equation will always lie in the first quadrant because values of x and y in the first quadrant are always positive, and here x and y are prices which can't be negative.
Hence, the graph of the equation should only be in the first quadrant because x and y is representing a price which can't be negative and The equation for the representation of the given situation will be
y = x - 0.54x
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D/dx(e^x)=e^x prove please
The differentiation of [tex]e^x[/tex] is [tex]\frac{d}{dx}(e^x) =e^x[/tex]. Hence, proved,
Given that, [tex]\frac{d}{dx}(e^x) =e^x[/tex].
What is the differentiation?The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.
Differentiate using the Exponential Rule which states that [tex]\frac{d}{dx}(a^x)[/tex] is [tex]a^xln(a)[/tex] where [tex]a=e.e^x[/tex]
So, now [tex]\frac{d}{dx}(e^x) =e^x[/tex]
The differentiation of [tex]e^x[/tex] is [tex]\frac{d}{dx}(e^x) =e^x[/tex]. Hence, proved,
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find the sum of the first 50 terms of the sequence
[tex]a(n)=3n+2[/tex]
The sum of first 50 terms of the sequence a(n) = 3n + 2 is 3925
In this question, we have been given a sequence a(n) = 3n + 2
We need to find the sum of the first 50 terms of the sequence
a(1) = 3 + 2
= 5
a(2) = 6 + 2
= 8
a(3) = 9 + 2
= 11
a(4) = 12 + 2
= 14
...
Given sequence is arithmetic sequence with common difference d = 3 and the first term a = 5
Using the formula for the sum of first n terms of AP
Sum of n terms of A.P. = n/2[2a + (n - 1)d]
For n = 50
S(50) = (50/2) * [2(5) + (50 - 1)3]
S(50) = 25 * [10 + (49 * 3)]
S(50) = 25 * 157
S(50) = 3925
Therefore, the sum of first 50 terms of the sequence a(n) = 3n + 2 is 3925
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Why should there be a number corresponding to the length of every line we draw?
Number lines are significant because they depict numbers as they appear in daily life.
What is number line?
A number line is a representation of a graduated straight line in elementary mathematics that serves as a visual representation of the real numbers. It is assumed that every point on a number line corresponds to a real number, and that vice versa.
Research has revealed that number lines are crucial because they foster sound mental number sense and arithmetic procedures.
They assist in providing a mental approach for addition and subtraction. Number lines are crucial, we can all agree on that.
Number lines are significant because they depict numbers as they appear in daily life.
Primarily because they make it possible for negative integers to be represented in a meaningful fashion.
The ability to display all real numbers, even enigmatic irrational numbers such π, -π, √2, -√ 2, etc., was a secondary but no less significant result.
Hence, number lines are significant because they depict numbers as they appear in daily life.
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I NEED HELP ASAP PLS!!
Answer:
7.8
Step-by-step explanation:
Switch 8 and 7, it round to 8 and end in tenths.
Answer:
7.8
Step-by-step explanation:
7.8 rounds to 8, because 8 is greater than 5, and then we end in the tenths place.
At a supermarket, oranges cost $1.30 per pound and pears cost $1.90 per pound. Misha spent less than $10.00 on 2 pounds of oranges and x pounds of pears. Which inequality represents this situation?
Answer:
kind423
Step-by-step explanation:
Answer: 2(1.9)+1.30x<10
Step-by-step explanation:
Orange= $1.30/lb
Pear= $1.90/lb
$1.30/lb = $y/2lb
y=1.30*2
y=$2.6 for 2lb of orange
So
She spent
2(1.30)+1.90x< $10
2.6+1.90x<10
1.90x<10-2.6
1.90x<7.4
x<7.4/1.90
x<3.89
According to 2(1.30)+1.90x< $10
2.6+1.90*3.89<10
9.991<10
assume that the box confains 11 balls: 5 red, 3 blues, and 3 yellow. as in the text, you draw one ball, note its color, and if its yellow rrplace it. if it is not yellow you do not replace it. you then draw a second ball and note its color
The probability that the second ball drawn is yellow is of:
0.2926 = 29.26%.
What is a probability?The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
In this problem, the possible outcomes to obtain a yellow ball on the second draw are:
Yellow (3/11 probability) then yellow (3/11 probability). -> yellow on the first is replaced.Non-yellow (8/11 probability) then yellow (3/10 probability) -> non yellow on the first is not replaced.Then the probability of an yellow ball on the second draw is given as follows:
p = (3/11) x (3/11) + (8/11) x (3/10) = 0.2926 = 29.26%.
Missing InformationThe problem asks for the probability that the second ball drawn is yellow.
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Find the Surface Area for the following:
(Use 3.14 for. Do not round and do not type your units.)
12 in.
5 in.
The surface area of the cone is 282.6 [tex]in^2[/tex].
What is surface area of cone?
The region that a cone's surface occupies in three dimensions is known as the surface area of a cone. The whole area a cone's surface covers is known as the cone's surface area. The overall surface area will include the cone's lateral and base surfaces. A three-dimensional solid construction with a circular base is referred to as a cone. A cone can be thought of as a collection of irregularly shaped circular discs that have been stacked on top of one another while maintaining a constant ratio between the radii of the adjacent discs. It is the total of the cone's lateral area and base area.
Here the given ,
=> Height h= 12in
=> Radius r = 5 in
Using surface area of cone formula,
=> Surface area SA = [tex]\pi[/tex]r(r+ [tex]\sqrt{r^2+h^2}[/tex]) square unit.
=> surface area SA = 3.14*5(5+[tex]\sqrt{12^2+5^2}[/tex])
=> surface area SA = 15.7(5+[tex]\sqrt{144+25}[/tex])=15.7(5+13)
=> surface area SA = 15.7*18=282.6 [tex]in^2[/tex]
Therefore surface area of the cone 282.6 [tex]in^2[/tex].
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Write the equation of the line in fully simplified slope-intercept form.
Answer: y = -x - 8
Step-by-step explanation:
Slope-intercept form is given in y = mx + b where m is the slope and b is the y-intercept.
We can see our b, the y-intercept, is -8 since the line intercepts the y-axis at (0, -8).
For our slope, we can see that the line moves down one and right one for a slope of 1/1=1. Since it's moving downwards, the slope is -1.
Now, we will write the full equation:
y = -x - 8
simplify your answer 5+2i/4i
1/2 - 5i/4 is the simplified form of the expression ( 5 + 2i ) / 4i.
What is the simplified form of the expression?Given the expression in the question;
( 5 + 2i ) / 4i
To simplify, multiply the numerator and denominator by the conjugate of 4i
( 5 + 2i ) / 4i
( 5 + 2i ) × i / 4i × i
( 5 + 2i )i / 4ii
Apply distributive property
( 5i + 2ii ) / 4ii
Not that i × i = i² = -1
( 5i + 2i² ) / 4i²
( 5i + 2( -1 ) ) / 4( -1 )
( 5i - 2 ) / -4
( -2 + 5i ) / -4
Split the fraction
-2/-4 + 5i/-4
1/2 - 5i/4
Therefore, the simplified form is 1/2 - 5i/4.
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A town's population is 43,200. About 125 people move out of the town each month. Each month, 175 people on average move into town. A nearby town has a population of 45,900. It has no one moving in and an average of 175 people moving away every month. In about how many months will the populations of the towns be equal? Write an equation to model the situation. Then solve the equation and answer the question.
The equation to model the situation is given below. And the months will the populations of the towns be equal will be 12.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A town's populace is 43,200. Around 125 individuals move out of the town every month. Every month, 175 individuals on the normal move into town. A close by the town has a populace of 45,900. It has nobody moving in and a normal of 175 individuals moving away consistently.
Let y be the total population and x be the number of months. Then the equations are given as,
y = (175 - 125)x + 43200
y = 50x + 43200 ...1
y = -175x + 45900 ...2
From equations 1 and 2, then we have
50x + 43200 = - 175x + 45900
50x + 175x = 45900 - 43200
225x = 2700
x = 2700 / 225
x = 12
The months will the populations of the towns be equal will be 12.
More about the linear equation link is given below.
https://brainly.com/question/11897796
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Huilan is 11 years older than Thomas. The sum of their ages is 61. What is Thomas's age?
Answer:
25
Step-by-step explanation:
Let the age of Thomas be x.
Huilan is 11 years older than Thomas,
Huilan = x + 11
The sum of their ages is 61.
x + x + 11 = 61
2x + 11 = 61
2x = 61 - 11
2x = 50
x = 50/2
x = 25
Hence,
Thomas's age is 25.
