The turning points of the given equation are:
(3, 27 + 1/45) and (-3, 27 + 1/45), and (4, 27 + 4/243) and (-4, 27 + 4/243).
How did we get the values?The turning point of a parabolic equation in the form of y = ax^2 + bx + c can be found by setting the derivative equal to zero and solving for x. The derivative of the given equation y = 4/(4x^2 + 27x + 27) + 27 is:
dy/dx = -16x/(4x^2 + 27x + 27)^2 + 27
Setting the derivative equal to zero, we can solve for x:
-16x/(4x^2 + 27x + 27)^2 + 27 = 0
-16x = (4x^2 + 27x + 27)^2 - 27 * (4x^2 + 27x + 27)
-16x = 16x^4 + 216x^3 + 1044x^2 + 729x + 729 - 108x^2 - 729x - 729
8x^4 - 288x^3 - 336x^2 = 0
x = ±3, ±4
For these values of x, we can find the corresponding y-values using the original equation:
y = 4/(4x^2 + 27x + 27) + 27
At x = 3, y = 4/(4 * 9 + 27 * 3 + 27) + 27 = 4/180 + 27 = 27 + 1/45
At x = -3, y = 4/(4 * 9 + 27 * -3 + 27) + 27 = 4/180 + 27 = 27 + 1/45
At x = 4, y = 4/(4 * 16 + 27 * 4 + 27) + 27 = 4/243 + 27 = 27 + 4/243
At x = -4, y = 4/(4 * 16 + 27 * -4 + 27) + 27 = 4/243 + 27 = 27 + 4/243
So, the turning points of the given equation are:
(3, 27 + 1/45) and (-3, 27 + 1/45), and (4, 27 + 4/243) and (-4, 27 + 4/243).
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PLEASE HELP MEEEEEE
thank you <3
The value of the varaible 'x' will be 4. And the value of the varaible 'y' will be 7.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.
a) The equation is given as,
4 / 8 = 3 / (y - 1)
1/2 = 3 / (y - 1)
y - 1 = 6
y = 7
b) The equation is given as,
5 / (7 + 2x) = 2 / (x + 2)
5(x + 2) = 2(7 + 2x)
5x + 10 = 14 + 4x
5x - 4x = 14 - 10
x = 4
The value of the varaible 'x' will be 4. And the value of the varaible 'y' will be 7.
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seven people are going to share an 84-ounce bottle of soda. how many ounces of soda will each person get to dink
Answer:
Each person will get 12 ounces of soda
Step-by-step explanation:
84 ounces divided by 7 people is 12 ounces per person
Answer:
each person will get 12oz
Step-by-step explanation:
84oz divided by the 7 people will get 12oz per person
100 POINTS WILL PLEASEEEEEE HELP
Answer:
b
Step-by-step explanation:
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
8. Use long division to find (2x³ - 7x² + 7x - 2) /(x - 2). Show your work
Answer:
2x² - 3x + 1
Step-by-step explanation:
x - 2 | 2x³ - 7x² + 7x - 2
-- 2x³ - 4x² <== 2x²
- 3x² + 7x - 2
-- - 3x² + 6x <== -3x
x - 2
-- x - 2 <== 1
0 | 2x² - 3x + 1
Thus, the quotient is 2x² - 3x + 1
Answer:
Hello! :)
Answer:
Solved using long polynomial division: [tex]2x^{2} -3x + 1[/tex]
Solved using polynomial division: (2x-1)(x-1)
Sorry I was in a hurry and didn't type out the whole step-by-step.
Find x rounded to one decimal place.
x =
The value of x rounded to one decimal place is 176. 0 units
How to determine the valuesUsing the trigonometric identity, sine, let's find the value of the hypotenuse for the smaller triangle, we have;
sin 60 = 88/x
find the value of sin 60
0. 8660x = 88
Divide both sides by 0. 8660
x = 101. 62
Then to determine the value of x, we have;;
tan 30 = 101.62/x
Find the value of the trigonometric identity, we have;
0. 5774x = 101. 62
divide both sides by the coefficient of x
x = 101. 62/0. 5774
divide the values
x = 175. 99 units
Hence, the value is 176. 0 units
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el perimetro de un patio rectangular es de 204 pies si el ancho del patio es de 45 pies cual es el largo del patio
The length of the rectangular patio is 57 ft.
What is a Parallelogram?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
Given is that the perimeter of a rectangular patio is 204 feet and the width of the patio is 45 feet.
We can write -
2(L + B) = 204
L + B = 102
L = 102 - 45
L = 57
Therefore, the length of the rectangular patio is 57 ft.
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{Question in english -
The perimeter of a rectangular patio is 204 feet if the width of the patio is 45 feet what is the length of the patio}
Which equation has the roots a = 1 and = -7/5
The solution is Option C.
The value of the quadratic equation is 5x² + 2x = 7
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
5x² + 2x = 7
On simplifying the equation , we get
Subtracting 7 on both sides of the equation , we get
5x² + 2x - 7 = 0 be equation (1)
Now , the roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
Substituting the values in the equation , we get
x = [ -2 ± √ ( 4 - 4 ( 5 ) ( -7 ) ] / 10
x = [ -2 ± √ ( 144 ) ] / 10
x = ( -2 ± 12 ) / 10
So , the two roots of the equation are
x = ( -2 + 12 ) / 10
x = 10/10 = 1
And , x = ( -2 - 12 ) / 10
x = -14/10
x = -7/5
Hence , the roots of the quadratic equation are 1 and -7/5
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2. Calculate the volume of the prism.
(Hint: 2 inches is just half the length of
the triangular base. What is the length of
the base?)
It cost $1,230 to carpet a 10 ft by 6 ft room. If the same type of carpet is used, how much would it cost to carpet a 7 ft by 8 ft room?
a.$20.50
b. $76.85
c. $1,148
d. $1,318
The required cost of carpet is $1,148.
Hence option (c) is correct.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
Cost of carpet of dimension 10 ft x 6 ft = $1230
Then cost of carpet of area 60 ft² = $1230
The cost of carpet per unit area = 1230/60
= $20.5
Area of carpet 7 ft x 8 ft = 56 ft²
Then the cost of this carpet
= 56x20.5
= 1,148
Therefore, the cost of carpet of dimension 7 ft x 8 ft = $1,148
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A party venue charges an event fee of $70 in addition to charging $20 per person at the party.
Use the Ray tool to make a graph that shows C, the total cost of a party at this venue for p people at the party. Graph the ray by plotting two points. The first point selected must be the endpoint of the ray. The second point can be any other point on the ray.
Therefore , the solution of the given problem of equation comes out to be another point on the line would be (3, 110).
What is equation?In arithmetic equations, the identical sign (=) is used to denote the equivalence of two assertions. It is demonstrated that using mathematical methods, which have acted as manifestations of reality, it is feasible to compare different numerical factors. For fact, the equal sign splits the number 12 into two separate parts, even if the answer is y + 6 = 12. It is possible to determine how many letters are also present on either end of this character.
Here,
The equation for the total cost of a party at this venue for p people is:
C = 20p + 70
To graph this equation, you can plot two points and draw a line passing through them.
One point can be the y-intercept (0, 70), which represents the fixed event fee charged by the venue.
The second point can be any other point on the line. For example, when there are 3 people at the party, the total cost would be:
C = 20(3) + 70 = 110
So another point on the line would be (3, 110). Plotting these two points and drawing a line passing through them will give you the graph of the total cost as a function of the number of people at the party.
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State whether the data described below are discrete or continuous, and explain why. The times required by students to complete a statistics test Choose the correct answer below. O A. The data are discrete because the data can take on any value in an interval. O B. The data are discrete because the data can only take on specific values. O C. The data are continuous because the data can take on any value in an interval. OD. The data are continuous because the data can only take on specific values.
The data are discrete because the data can only take on specific values, So correct option is B.
What do you mean by discrete data?Discrete data refers to data that can only take on specific, separate values. It is a type of data that can be counted or enumerated, but not measured. In other words, the values can't be expressed as fractions or decimals between two whole numbers. Some examples of discrete data include the number of siblings in a family, the number of pets owned by an individual, and the number of correct answers on a test. Discrete data is distinct from continuous data, which can take on any value within a certain range.
The data are discrete because the data can only take on specific values (e.g. a time of 20 minutes, 21 minutes, 22 minutes, etc.). They cannot take on any value in an interval, such as 20.5 minutes. Discrete data represent a countable number of values, while continuous data can take on any value within a given range.
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A 2-column table with 5 rows. Column 1 is labeled Minutes with entries 1, 2, 3, 4, 5. Column 2 is labeled Words with entries 250, 500, A, 1,000, B. Use the relationship between quantities to calculate the missing values in the table. A = B =
By using the relationship between quantities, the missing values in the table are:
A = 750
B = 1,250.
What is a proportional relationship?In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be represented by this mathematical expression:
y = kx
Where:
k is the constant of proportionality.y and x represent the variables in a proportional relationship.Next, we would determine the constant of proportionality (k) for the data points contained in this 2-column table as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 250/1
Therefore, a linear equation for this proportional relationship can be correctly written as follows:
y = kx
y = 250x
When x = 3, the value of A is given by:
y = 250(3) = 750.
When x = 5, the value of A is given by:
y = 250(5) = 1,250.
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The diagram below shows a rectangle with side lengths 4 and 8 and a square with side length 5. Three vertices of the square lie on three different sides of the rectangle, as shown. What is the area of the region inside both the square and the rectangle?
Answer:
The area of the region inside both the square and the rectangle is 37 square units.
Step-by-step explanation:
The area of the region inside both the square and the rectangle can be found by subtracting the areas of the four triangles outside the square from the area of the rectangle.
The area of the rectangle is 4 * 8 = 32 square units. The area of each triangle can be found using the formula for the area of a triangle, which is (base * height) / 2. The base of each triangle is half the length of the side of the square, which is 5 / 2 = 2.5 units. The height of each triangle is the difference in height between the rectangle and the square, which is 4 - 5 = -1 unit. The area of each triangle is (2.5 * -1) / 2 = -1.25 square units. The area of the four triangles outside the square is 4 * -1.25 = -5 square units.
The area of the region inside both the square and the rectangle is 32 + 5 = 37 square units.
9yr 12yr what is the lateral the area of the cone to the nearest whole number
Answer: 678.58
Step-by-step explanation:
Use the graph at the right to graph the following equations:
y = 1/2x + 3
y = 2x
Do the graphed equations have any points in common? If so, where?
✓CHECK: Use the space below to prove
that the point is a solution to both equations.
Answer: Yes at x = 2.
Step-by-step explanation: There are two ways to do it. Graph the function or solve it. Since im on a computer solving would be easiest for me to explain. To find a point where the two lines meet, you should set the two equations equal to each other. When you solve by subtracting 1/2x on both sides, the result is 3/2x = 3. This means that x=2. When you graph you should see that when x =2 the answer is right.
Find the center of the circle that can be circumscribed about the triangle.
A - (0, 0)
B - (0, 1)
C - (-1, 3)
D - (2, 0)
Answer:
A. (0, 0)
Step-by-step explanation:
To find the center of the circle that can be circumscribed about the given triangle, find the triangle's circumcenter.
A circumcenter of a triangle is:
The center of a circle that passes through each vertex of a triangle.The point at which the perpendicular bisectors of the sides of the triangle intersect.A perpendicular bisector is a line that divides another line segment into two equal parts at a right angle.
Add perpendicular bisectors to the sides of the triangle (shown in green on the attached diagram).
The point of intersection of the perpendicular bisectors is (0, 0).
Therefore, the center of the circle that can be circumscribed about the triangle is (0, 0).
7x - y = 7
x + 2y = 6
The work done by the force 4i−3j+2k in moving a particle along a straight line from the point (3,2,−1) to (2,−1,4) is:A. 0 unitsB. 4C. 15D. 19
The work done by the force 4i−3j+2k is the scalar product of the force vector and the displacement vector between the two points. In this case, the displacement vector is (3−2, 2−(−1), −1−4) or (1,3,−5). The scalar product of these two vectors is (1)(4)+(3)(−3)+(−5)(2) = 15 units.
Work is the scalar product of the force and displacement vectors. The force vector in this problem is given as 4i−3j+2k, while the displacement vector (the vector from the starting point to the end point) is (3−2, 2−(−1), −1−4) or (1,3,−5). The scalar product of these two vectors is (1)(4)+(3)(−3)+(−5)(2) = 15 units. This means that the work done by the force is 15 units.
The work done by a force is the energy transferred to an object by the force. It is calculated by taking the scalar product of the force and displacement vectors. This scalar product gives the magnitude of the work done by the force, which in this case is 15 units. This means that the force transferred 15 units of energy to the object by moving it from the starting point to the end point.
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Dan went to a craft fair where he spent a total of 16.00 he spent 6.00 on admission and went to 8 tables he spent the same ammount of money (m) at each table the following number sentence can be used to find how much money he spent at each table
Dan spent 1.25 at each table.
The formula used to solve this problem is m = 16 - 6/8. The calculation is as follows: 16 is the total amount of money Dan spent, 6 is the admission fee, and 8 is the number of tables. The equation is set up to find the amount of money Dan spent at each table. Taking the total amount of money spent, 16, and subtracting the admission fee, 6, leaves us with 10. We then divide this amount, 10, by the number of tables, 8, to find the amount of money spent at each table, which is 1.25. Therefore, Dan spent 1.25 at each table.
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does anybody know the anwser to 47,61 : 15,87 =
whoever helps wil be crownd as brainliest
The quotient of 47.61 and 15.87 has the result given as follows:
47,61 : 15,87 = 3.
How to obtain the result of the operation?The operation for this problem is defined as follows:
47,61 : 15,87 =
The : symbol means that the operation is a division, that is, we must obtain the quotient of dividing 47.61 by 15.87.
Using a calculator, we have that 47.61 is three times 15.87, hence the result of the quotient is given as follows:
47,61 : 15,87 = 3.
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Need help solving this problem
The value of cot(θ - π/2) is 1.52.
What are trigonometry ratios?
The trigonometric functions in mathematics are real functions that relate the right-angled triangle's angle to the ratios of its two side lengths. They are extensively used in all fields of geometry-related science, including geodesy, solid mechanics, celestial mechanics, and many others.
There are six trigonometric ratios used in trigonometry: sine, cosine, tangent, secant, and cotangent. The abbreviations for these ratios are sin, cos, tan, sec, cosec(or csc), and cot. Look at the below-displayed right-angled triangle. Any two of the three sides of a right-angled triangle can be compared in terms of their respective angles using trigonometric ratios.
Given that tan θ = -1.52.
The given expression is
cot(θ - π/2)
= - cot(π/2 - θ)
Now applying the trigonometry identity cot(π/2 - θ) = tan θ:
= - tan θ
Now putting the value of tan θ = -1.52:
= - (-1.52)
= 1.52
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Mirta has a savings account which gathers compound interest each year. She opened the account with a deposit of 3000
. After 4 years there is 3690.37
in the account. Work out the annual interest rate of the savings account. Give your answer as a percentage to 1 d.p.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 3690.37\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{each year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}[/tex]
[tex]3690.37 = 3000\left(1+\frac{\frac{r}{100}}{1}\right)^{1\cdot 4} \implies \cfrac{3690.37 }{3000}=\left(1+\cfrac{r}{100} \right)^4 \\\\\\ \sqrt[4]{\cfrac{3690.37 }{3000}}=1+\cfrac{r}{100}\implies \sqrt[4]{\cfrac{3690.37 }{3000}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[4]{\cfrac{3690.37 }{3000}}=100+r\implies 100\sqrt[4]{\cfrac{3690.37 }{3000}}-100=r\implies \boxed{5.3\approx r}[/tex]
Answer:
5.3 is about r
Step-by-step explanation:
and, this question too? plese
The model product, P(16), predicts the number of moose to be 3545 in 1997 and 2970 in 2009.
what is probability ?The odds that a happening will happen or a claim will be true is measured by probability theory, a branch od arithmetic. The probability of an item is a number between 0 but also 1, where about 0 represents how frequently the event is to occurring and 1 represents certainty. A risk is a numerical illustration of the possibility that a specific occurrence will take place. Probabilities may be expressed as percentages ranging from 0percent to 100% as well as from 0 to 1. the ratio of the number of outcomes to the proportion of occurrences in a whole set of equally plausible options that lead to a specific occurrence.
given
We'll choose x on the graph to represent the number of years since 1990 and y to represent the number of moose.
On the graph, there are two points: (4, 4290) and (8, 3850)
We can determine the slope of this line using the slope formula (m = [y2 - y1]/[x2 - x1]):
Replacement: m = (3850 - 4290)/(8 - 4)
m = -440/4 Solve the parenthesis's subtraction puzzles.
m = -110 Reduce the percentage
Since we know the line's slope, we can apply the point-slope formula (y - y1 = m[x - x1]) to determine the line's equation.
P(16) = 2970
The model product, P(16), predicts the number of moose to be 3545 in 1997 and 2970 in 2009.
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You flip a fair coin 3 times, and get a different amount of money depending on how many heads you get. • For O heads, you get $0. • For 1 head, you get $2. • For 2 heads, you get $4. Another piece of information is also flashing at you as you stand before the lights: • Overall, across all possible outcomes your expected winnings from the game are $6. 1. (3 points) How much do you get paid if the coin comes up heads 3 times? 2. (3 points) Write down a complete expression for the cumulative probability function for your winnings from the game.
The amount of money you get paid if the coin comes up heads 3 times is $12.
You flip a coin 3 times,
If you get o heads then $0
If you get 1 heads then $2
If you get 2 heads then $ 4
So if you toss the coin 3 times and 3 heads come up then
1 heads = $2
2 heads = $ 4
3 heads = $ 6
So , amount of money you get paid if the coin comes up heads 3 times is $12.
The probability function that X will have a value less than or equal to x is known as the Cumulative Distribution Function (CDF) of a real-valued random variable X, assessed at x. It is employed to describe a table's random variables' probability distribution. And with this data, we can quickly make a CDF graphic on an Excel spreadsheet.
So, CDF determines the cumulative probability for the specified value.
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According to a survey, 40% of adults watch a particular television show. Six adults are selected at random. The binomial distribution below shows the probability that k out of 6 adults watch the television show. P(k = 0) = 0.0467 P(k = 1) = 0.1866 P(k = 2) = 0.3110 P(k = 3) = 0.2765 P(k = 4) = 0.1382 P(k = 5) = 0.0369 P(k = 6) = 0.0041 The distribution is symmetric. skewed. both symmetric and skewed.
The distribution is b) skewed.
The sum of the probabilities is: 1
How to find the answerIn a binomial distribution, p represents the probability of success. Success in the sense that the event of interest happens. In the model presented, the probability of success p is 0.4 since we are informed that 40% of adults watch a particular television show.
The next quantity of significance in a binomial model is the number of independent trials, n.
In our case there are 6 independent trials since we are told that 6 adults were selected at random. If we let the random variable K denote the number of adults out of the 6 who watch the television show, then K is a binomial random variable with parameters;
n = 6 and p = 0.4
A binomial distribution is only symmetric when either p is 0.5 or n is large. In the presented scenario none of these conditions is met since p is 0.4 while n is just 6 which is relatively small.
Thus we conclude that the distribution is not symmetric but rather skewed.
The sum of the probabilities is any discrete probability distribution such as the Bernoulli, binomial, negative binomial, Poisson, or the geometric distribution is always equal to 1. That's a rule of thumb.
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Use the definition of Ax to write the vector equation as a matrix equation. z_1 [5 0] + z_2 [5 2] + z_3 [-3 3] + z_4 [4 -2] = [-3 19] The vector equation written as a matrix equation is
the matrix equation for the given vector equation is:
[tex][ [5 0] [5 2] [-3 3] [4 -2] ] [z_1, z_2, z_3, z_4]^T = [-3 19]^T[/tex]
What is matrix equation?An equation of the form Av = b, in which A is a m by n matrix known as the coefficient matrix, v is a n by 1 column vector, and b is a m by 1 column vector, is known as a matrix equation (also known as a matrix-vector equation).
According to question:Given the vector equation:
[tex]z_1 [5 0] + z_2 [5 2] + z_3 [-3 3] + z_4 [4 -2] = [-3 19][/tex]
We can write this as a matrix equation by defining a matrix A and a vector x, such that:
A = [ [5 0]
[5 2]
[-3 3]
[4 -2] ]
[tex]x = [z_1, z_2, z_3, z_4]^T[/tex]
The vector equation then becomes:
[tex]Ax = [-3 19]^T[/tex]
So the matrix equation for the given vector equation is:
[tex][ [5 0] [5 2] [-3 3] [4 -2] ] [z_1, z_2, z_3, z_4]^T = [-3 19]^T[/tex]
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solve 2x/\2 - 5x -3 is greater than or equal to zero algebraically
The solution to the given inequality 2x/2 - 5x -3 ≥ 0 is x ≤ - 3/8.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
We have to solve 2x/2 - 5x -3 is greater than or equal to zero algebraically.
As per the question, we have inequality as follows:
2x/2 - 5x -3 ≥ 0
2x/2 - 5x ≥ 3
Multiply by 2 on both sides of the inequality,
4x - 20x ≥ 6
-16x ≥ 6
Divided by -16 and flip the sign of the above inequality,
x ≤ - 6/16
x ≤ - 3/8
This is the solution to the given inequality.
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Please help I will give brainly
By solving the equation 3x = x² - 4, we know that the positive solution of the given problem is x = 4.
What are equations?Using the equal symbol, they are linked.
For instance, a formula might be 3x - 5 = 16. After solving this equation, we learn that the value of the variable x is 7.
So, using the given information, form the following equation:
3x = x² - 4
Now, solve this equation as follows:
3x = x² - 4
0 = x² - 3x - 4
0 = (x-4)(x+1)
Then, x = 4 and x = -1
Therefore, by solving the equation 3x = x² - 4, we know that the positive solution to the given problem is x = 4.
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Find an ordered pair (x,y) that is a solution to the equation
Answer:
(3, -11)
Step-by-step explanation:
Rearranging the equation becomes a slope-intercept form:
[tex]y = 2 - 3x[/tex]
where m = slope of equation = [tex]-3[/tex]
and c = intercept = [tex]2[/tex]
Substitute any value of x into the above slope-intercept equation to determine it's corresponding y value. Together these x and y values will form an ordered pair.
For example:
Take x = 3 and substitute in the above mentioned equation:
[tex]y = 2 - 3(3)[/tex]
[tex]= 2 - 9[/tex]
y = [tex]-11[/tex]
∴ An ordered pair that is a solution to the equation: (3, -11)
what's the answer to this
Answer:
84.8 squared centimeters
Step-by-step explanation:
You know the height is 8 cm
You know one of the bases has a length of 15.5 cm
You know one of the bases has a length of 5.7 cm
Formula to find a trapezoid:
[tex]\frac{b_{1}+b_{2}}{2}[/tex]×h
so...
substitute!!!!!