Rewrite equation in standard form

The equation of this circle in standard form include the following: D. (x + 7)² + (y - 10)² = 11².

In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;

(x - h)² + (y - k)² = r²

Where:

Based on the information provided, we have the following parameters:

By substituting the given parameters into the equation of a circle formula, we have the following;

(x - h)² + (y - k)² = r²

(x - (-7))² + (y - 10)² = 11²

(x + 7)² + (y - 10)² = 11²

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Answer:

[tex]m = \frac{ - 1 - 2}{3 - 0} = \frac{ - 3}{3} = - 1[/tex]

We know that b, the y-intercept, is 2, so:

[tex]y = - x + 2[/tex]

(a) The total number of ways to distribute the apples and pears subject to the conditions is = 135,124 ways.

(b) The total number of ways to distribute the apples and pears subject to the conditions is: 3 \times 10 \times [tex]3^7[/tex] = 34,650 ways.

Combinatorics is a branch of mathematics that deals with counting and arranging the possible outcomes of different arrangements and selections of objects.

a) To distribute seven identical apples and six identical pears to three distinct people such that each person has at least one pear, we can use the principle of inclusion-exclusion. Let's denote the three people as A, B, and C.

First, we can distribute the six pears in[tex]{6+3-1 \choose 6} = {8 \choose 6} = 28[/tex] ways using stars and bars.

Next, we can distribute the seven apples to the three people without any restrictions, which can be done in [tex]3^7[/tex] ways.

However, this overcounts the cases where one or more people receive no pears. There are [tex]{3 \choose 1}[/tex] ways to choose one person who does not receive a pear, and then [tex]2^7[/tex] ways to distribute the apples among the remaining two people.

Similarly, this also overcounts the cases where two people receive no pears. There are [tex]{3 \choose 2}[/tex] ways to choose two people who do not receive a pear, and then [tex]1^7[/tex] way to distribute the apples among the remaining person.

Finally, we need to add back the cases where all three people receive no pears, which is just one way (each person receives no pears).

Thus, the total number of ways to distribute the apples and pears subject to the conditions is:

[tex]28 \times - {3 \choose 1} \times + {3 \choose 2} \times - {3 \choose 3} \times = 135,124 ways.[/tex]

b) To distribute seven distinct apples and six distinct pears to three distinct people such that each person has at least one pear, we can first choose the person who receives the remaining pear in [tex]{3 \choose 1} = 3[/tex] ways. Then we can distribute the pears in [tex]{6-1 \choose 3-1} = {5 \choose 2} = 10[/tex] ways, leaving one pear for the chosen person and distributing the other two pears among the remaining two people using stars and bars.

Next, we can distribute the seven distinct apples to the three people without any restrictions, which can be done in [tex]3^7[/tex] ways.

Thus, the total number of ways to distribute the apples and pears subject to the conditions is:

[tex]3 \times 10 \times 3^7[/tex] = 34,650 ways.

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The value of the missing side lengths such as b and d would be = 3.5 and 11.3

To calculate the side length of the given triangle, the sine rule must be obeyed. That is;

a/sinA= b/sin B

For the first triangle;

b = ?

B = 30°

a = 6

A = 60°

That is ;

b/ sin30° = 6/sin60°

Make b the subject of formula;

b = sin30×6/sin60

= 0.5×6/0.866025403

= 3.5

For second triangle:

a/sinA= d/sin D

where;

a = 8

A = 45°

d = ?

D = 90°

That is;

8/sin45° = d/sin90°

d =8×1/0.707106781

= 11.3

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The equation represents the proportional relationship between the number of bag and cost of cereal bag is y = 7.25x

Number of bags = 3

Cost of three bags of cereal = 21.75

Let the number of bags of cereal bought = x

The cost paid for the bag = y

They both are directly proportional

3/x = 21.75/y

3y = 21.75x

on dividing both side with 3 we will get cost of one bag of cereals

3y/3 = 21.75x/3

y = 7.25x

The proportional relationship between a number of bags of cereal and the cost of cereal is y = 7.25

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The graph is attached, from the graph the zeros are

x = -7, 1 and 3

The polynomial in factored form. P(x) = (x + 7) (x - 1) (x - 3)

The zeros of the polynomial function given as P(x) = x³ + 3x² − 25x + 21 is solved using graphical method

From the graph are deduced to be

x = -7, x = 1 and x = 3

From the zeros the factored form of the equation is written as

x = -7, x + 7 = 0

x = 1, x - 1 = 0

x = 3, x - 3 = 0

hence factored form of the polynomial is, P(x) = (x + 7) (x - 1) (x - 3)

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Note that the answers to the above transformation prompt is above as follows:

1. Angle PQR

2. Segment PS

3. Scale factor =  3/2 = 1.5

1. Angle PQR in the scaled copy corresponds to angle ABC in polygon ABCD in polygon PQRS. In the two separate figures, they are both in the same position. They complement each other.

2. In the scaled copy, segment PS is the section in polygon PQRS that corresponds to segment AD in polygon ABCD. They are similar in appearance and appear in the same location.

3. The scale factor is the ratio of any of the segment lengths.

Let's consider segments lengths of AD in ABCD, which corresponds to segment PS in PQRS.

AD = 2 units

PQ = 3 units

Scale factor from ABCD to PQRS = PQ/AD = 3/2 = 1.5

The whole number tells us that ABCD is scaled up or enlarged to given a bigger polygon, PQRS

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The equation to complete the square for x² + 3x = 6 is 3/2 (option a)

To complete the square for the equation x² + 3x = 6, we need to add a specific number to both sides of the equation. The number we need to add is half of the coefficient of x, squared. In other words, we need to find (b/2)², where b is the coefficient of x.

In this equation, b is 3, so (b/2)² is (3/2)², which simplifies to 9/4. Therefore, to complete the square, we need to add 9/4 to both sides of the equation:

x² + 3x + 9/4 = 6 + 9/4

Now, we can rewrite the left side of the equation as a perfect square:

(x + 3/2)² = 33/4

Finally, we can solve for x by taking the square root of both sides of the equation:

x + 3/2 = ± √(33/4)

x = -3/2 ± √(33/4)

Therefore, the answer to the question is a) 3/2.

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The proportion is 12/20 = n/165 and we can estimate that 99 seventh graders out of the 165 attending Monique's school participate in after-school activities.

To estimate the number of seventh graders who participate in after-school activities, we can set up a proportion using the given data. Let n be the number of seventh graders who participate in after-school activities out of the total number of seventh graders attending Monique's school, which is 165.

The proportion can be written as:

12/20 = n/165

To solve for n, we can cross-multiply and simplify:

12 × 165 = 20n

1980 = 20n

n = 1980/20

n = 99

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Answer:

$20

Step-by-step explanation:

25% off of 100% = 75%
0.75x=15, where x is the original bill

x=20

Statements (iii) and (iv) are not equivalent, as they also have different truth values for some combinations of p and q.

What are proportions?

In mathematics, a proportion is a statement that two ratios are equal. It expresses the relationship between two or more quantities that are directly proportional to each other. A proportion can be represented as an equation of the form:

a/b = c/d

To construct the truth tables, we assign a truth value of either true or false to each statement. We use "T" to represent true and "F" to represent false. Then, we evaluate the truth value of each statement for all possible combinations of truth values for the variables involved. In this case, there is only one variable, which is whether or not someone knows CPR.

Let's use the variable p to represent the statement "someone knows CPR" and q to represent the statement "someone is a paramedic".

Then, the statements can be rewritten as follows:

i. p is necessary for q.

ii. p is sufficient for q.

iii. not p is necessary for not q.

iv. not p is sufficient for not q.

The truth tables for each statement are as follows:

i.

p q p is necessary for q

T T T

T F F

F T T

F F T

ii.

p q p is sufficient for q

T T T

T F F

F T T

F F T

iii.

p q not p is necessary for not q

T T F

T F T

F T F

F F T

iv.

p q not p is sufficient for not q

T T F

T F T

F T F

F F T

From the truth tables, we can see that statements (i) and (ii) are not equivalent, as they have different truth values for some combinations of p and q. Similarly, statements (iii) and (iv) are not equivalent, as they also have different truth values for some combinations of p and q.

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The length of the curve is [tex]e^ \pi[/tex] - 1 units.

To find the length of the curve [tex]x = e^t cos(t), y = e^tsin(t)[/tex], where 0 ≤ t ≤ π.

In this case, the curve is defined by the equations [tex]x = e^t cos(t)[/tex] and [tex]y = e^t sin(t)[/tex], where t is the variable that represents the parameter along the curve.

To find the length of this curve, we can use a formula known as the arc length formula.

L = ∫[a,b] √〖[dx/dt]〗² + 〖[dy/dt]² dt

where L represents the length of the curve, a and b are the starting and ending values of the parameter, dx/dt and dy/dt are the derivatives of x and y with respect to t.

To find the derivatives dx/dt and dy/dt. Using the product rule and chain rule of differentiation, we get:

[tex]dx/dt = e^tcos(t) - e^t sin(t) dy/dt = e^t sin(t) + e^t cos(t)[/tex]

Substituting these expressions into the arc length formula and simplifying, we get: L = ∫[0,π] [tex]e^tdt[/tex]

Integrating this expression with respect to t, we get: L = [tex]e^\pi[/tex]- 1

So the length of the curve is [tex]e^ \pi[/tex] - 1 units.

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Step-by-step explanation:

a)

with step 1 to 3 we see that the numbers of squares serving the length of the sidelines is following the step number 1:1.

so, step 1 has a side length of 1 square.

step 2 has a side length of 2 squares.

step 3 has a side length of 3 squares.

so, we expect step 4 to have a side length of 4 squares.

but the first statement says "5-by-5", so, the side length is 5.

therefore, this statement is false.

and yes, we expect step 15 to have a side length of 15.

and the shift of the single square from the bottom left to the top right is also correct.

therefore, the statement is true.

b)

step 4 = 4×4 = 16 squares

step 15 = 15×15 = 225 squares

c)

no.

just look at step 1.

y = 1² - 1 = 1 - 1 = 0.

but I can clearly see that there is 1 square.

d)

it makes an n×n array. which is the same as n².

The value of g(-5) is 7.5, g(-2) is 4, and g(5) is 7.5 if the value of function g(x) = 1/2x²-5 if x≠-2 and g(x) = 4 if x = -2.

A function is a rule that associates each element in a set (called the domain) with a unique element in another set (called the range). A function takes an input from the domain and produces an output in the range.

To find the value of g(-5), substitute the value in given function

g(-5) = 1/2×(-5)² - 5

= 1/2×25 - 5

= 12.5 - 5 = 7.5

The value of g(-2) is 4 as it is defined in the question only.

To find the value of g(5), substitute the value in given function

g(5) = 1/2×(5)² - 5

= 1/2×25 - 5

= 12.5 - 5 = 7.5

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The probability that the mean of a sample of 55 families will be between 17 and 18 pounds is approximately 71.55%.

σ_sample = σ / sqrt(n)

σ_sample = 2.5 / sqrt(55)

σ_sample ≈ 0.336

Now, we can standardize the values of 17 and 18 pounds using the Z-score formula. This will tell us how many standard deviations away from the population mean these values are:

Z = (X - μ) / σ_sample

Z_17 = (17 - 17.2) / 0.336 ≈ -0.595

Z_18 = (18 - 17.2) / 0.336 ≈ 2.381

Now we will use the standard normal distribution (Z-distribution) to find the probabilities corresponding to these Z-scores. You can use a Z-table, statistical software, or an online calculator to find these probabilities.

P(Z < -0.595) = 0.2760

P(Z < 2.381) = 0.9915

To find the probability that the mean of a sample of 55 families will be between 17 and 18 pounds, we will find the difference between the probabilities corresponding to the two Z-scores:

P(17 < X < 18) = P(Z < 2.381) - P(Z < -0.595)

P(17 < X < 18) = 0.9915 - 0.2760

P(17 < X < 18) ≈ 0.7155

So, the probability that the mean of a sample of 55 families will be between 17 and 18 pounds is approximately 71.55%.

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ItI > teritical I.p value <0.05, we fail to reject num hypothesis

Test statistic , t= x1-x2/s1.s1/n1+s2.s2/n2

=26-32/3.3/18+2.2/24

=-6/0.815=-7.3484

iti=7.2484

Teritical at >=0.05 I df=n1+n2+n3=40

Static testing is the process of reviewing the code and creating documents and requirements before it is performed to detect errors instead of actually running the code. The major objective is to identify faults early in the development process because it is typically simpler to identify the potential causes of failures in this way.

A sort of testing called static testing is done on a piece of software without running the actual code. We examine and validate the product and its supplementary materials during testing.

Dynamic testing, in contrast, is a sort of testing done on software while the code is being executed.A test statistic is a figure obtained from a statistical analysis. It explains how far your observed data is from the null hypothesis, which states that there is no correlation between the variables or distinction between the sample groups.

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The expression equals to the fraction of squared that is shaded blue is 3/8

Fraction is defined as the parts of a whole the number is expressed as a quotient, in which the numerator is divided by the denominator

The whole part here is the total number of boxes and its blue shaded part is defined as the part of it.

The Numerator represents the shaded part = 3

The Denominator represent the whole squared boxes = 8

The total number of square boxes is 8

the number of blue shaded boxes is 3

Fraction of the square = 3/8

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The question is incomplete the complete question is :

Which expression equals the fraction of the square that is shaded blue?

To divide exponents with different bases and powers, you need to first factor out the common factors from the exponents. This will help you simplify the expression and make it easier to solve.

For example, let's say you have the expression 4x^3 / 2x^2. To divide these exponents, you need to factor out the common factors. In this case, the common factor is x^2, so you can simplify the expression as follows:

4x^3 / 2x^2 = (4/2) * (x^3/x^2) = 2x^(3-2) = 2x

So the answer is 2x.

In general, to divide exponents with different bases and powers, you need to:

1. Factor out the common factors from the exponents
2. Divide the coefficients (if there are any)
3. Subtract the exponents of the common factors

By following these steps, you can easily divide exponents with different bases and powers.
To divide exponents with different bases and powers, follow these steps:

1. Convert the bases to their prime factorization (if needed).
2. Divide the exponents with the same base by subtracting the exponent in the denominator from the exponent in the numerator.
3. Combine the results back together as a simplified expression.

Remember, you can only directly divide exponents with the same base. If bases are different, you'll need to factorize them to find common factors.

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Answer:

can you tell me the options please so I can answer it thank you

The length of a wave does not directly determine its depth. The depth of a wave is influenced by various factors, including the shape and size of the seafloor,

The temperature and salinity of the water, and the strength and direction of the current. Therefore, without additional information about these factors, it is impossible to accurately determine the depth of a wave based solely on its length. I suggest seeking the advice of an expert in oceanography or physics for a more comprehensive explanation.

The length of a wave is the distance between two successive points in the same phase, such as from crest to crest or trough to trough. In your case, the wave length is given as 30 feet. However, without additional information about the wave, we cannot determine its depth solely based on its length.

Depth refers to the vertical distance from the surface to the lowest point of a wave (trough), and it's not directly related to the wave length. Therefore, we cannot accurately choose an option (a, b, c, or d) for the depth based on the provided information.

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The calculated length of the segment EF is (c) 5

from the question, we have the following parameters that can be used in our computation:

The trapezoid

The length of segment EF can be calculated using

EF = 1/2 * Sum of BC and AD

using the above as a guide, we have the following:

EF = 1/2 * (3.3 + 6.7)

Evaluate

EF = 5

Hence, the length of segment EF is (c) 5

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There are 7776 possible 5-number license plate combinations utilizing the numbers 0, 1, 2, 3, 4, and 5, with repetitions allowed.

The number of 5-number license plates that can be made using the digits 0, 1, 2, 3, 4, and 5, with repetitions allowed, can be found by using the multiplication principle. Since there are 6 digits to choose from for each of the 5 positions, the total number of possible license plates is:

6 x 6 x 6 x 6 x 6 = 6⁵

= 7776

Therefore, there are 7776 possible 5-number license plate combinations utilizing the numbers 0, 1, 2, 3, 4, and 5, with repetitions allowed.

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Answer:

x = 8

Step-by-step explanation:

-4x + 10 = -2x - 6

-4x + 2x = -6 - 10 (Calculate)

-2x = -16 (Divide both sides by -2)

x = 8

Have a nice day! :D

Answer:

x=8

Step-by-step explanation:

-4x+10=-2x-6   original equation

-4x+16=-2x      add 6 both sides

16=2x              add 4 both sides

x=8                 divide 2 both sides

The mean change in heart rate is 0.28 , around to 2 decimal places.

What is mean?

In statistics, the mean is nothing but  the measures of central tendency, apart from the mode and median. Mean is the average of the given set of values or data. It denotes the equivalent distribution of values for a given data set. To calculate the mean of given data, we need to add the total values given in a datasheet and  then divide the sum by the total number of values.

The change in heart rate for the 10 individuals are as follows

(1.8, -0.4, -0.6, 0.4, 0.2, -1.0, 1.6, 0.8, 2.0, -2.0).

So the data is given by,

(1.8, -0.4, -0.6, 0.4, 0.2, -1.0, 1.6, 0.8, 2.0, -2.0).

Mean of the given data = sum of all data/ number of data

Mean = (1.8-0.4 -0.6+0.4+ 0.2 -1.0+1.6+ 0.8+2.0-2.0)/10

         = 2.8/10

         =0.28

Hence, the mean change in heart rate is 0.28 , around to 2 decimal places.

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So the probability distribution function for X is:

- P(X = 0) = 0.46

- P(X = 1) = 0.46

- P(X = 2) = 0.08

Probability is a measure of how likely an event is to occur. Many events are impossible to predict with absolute certainty.

(a) Using the tree diagram:

- P(RR) = (9/13) * (8/12) = 0.46

- P(RL) = (9/13) * (4/12) = 0.23

- P(LR) = (4/13) * (9/12) = 0.23

- P(LL) = (4/13) * (3/12) = 0.08

So the probabilities for the simple events are:

- P(RR) = 0.46

- P(RL) = 0.23

- P(LR) = 0.23

- P(LL) = 0.08

(b) The possible values for X are 0, 1, or 2.

- P(X = 0) = P(RR) = 0.46

- P(X = 1) = P(RL) + P(LR) = 0.23 + 0.23 = 0.46

- P(X = 2) = P(LL) = 0.08

So the probability distribution function for X is:

- P(X = 0) = 0.46

- P(X = 1) = 0.46

- P(X = 2) = 0.08

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By solving differential equation for [tex]du/dt = e^5u + 3t.[/tex] The u =[tex](-1/5) ln[25t + e^{-5u} - 26].[/tex]

We have to separate variables first:

[tex]du/e^5u = dt + 3t/e^{5} u du[/tex]

Now, we will integrate sides to their variables:

∫ du/[tex]e^{5u}[/tex]= ∫ (dt + 3t/[tex]e^{5u}[/tex]) du

Using substitution:

let w = 5u, then du = dw/5:

1/5 ∫ dw = [tex]e^{-w}[/tex]∫ (dt + 3t/[tex]e^w[/tex] (du/5)

Integrating both sides:

-1/5 [tex]e^{-w}[/tex]= t + (1/25) [tex]e^{-w}[/tex] + C

Substituting back w = 5u:

-1/5 [tex]e^{-5u}[/tex]= t + (1/25) [tex]e^{-5u}[/tex] + C

Using initial condition, u(0) = 5:

-1/5 [tex]e^{-25}[/tex] = 0 + (1/25) [tex]e^{-25}[/tex] + C

C = -26/25

The solution to differential equation with initial condition is:

-1/5 [tex]e^{-5u}[/tex] = t + (1/25) [tex]e^{-5u}[/tex]- 26/25

When we solve for u, we have:

u = (-1/5) ln[25t + [tex]e^{-5u}[/tex]- 26].

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Solution of a system of equations involving quadratic functions, required to calculate the values of the variables that satisfy both equations simultaneously.

Write down the equations in standard form.

A quadratic equation can be written in the form ax² + bx + c = 0, where a, b, and c are constants.

Similarly, a system of quadratic equations can be written in the form.

a₁x² + b₁x + c₁= 0

a₂x² + b₂ x + c₂ = 0

Rearrange one of the equations so that one of the variables is expressed in terms of the other.

Then substitute this expression into the other equation to obtain a single quadratic equation in one variable.

Solve the resulting quadratic equation using any of the available methods.

Such as factoring, completing the square, or using the quadratic formula.

Once you have found the values of the variables.

Substitute them back into one of the original equations to find the corresponding values of the other variables.

Check the solutions by plugging them into both equations and verifying that they satisfy both equations.

If the two equations do not have any real solutions, then the system has no real solutions.

If the two equations have infinitely many solutions, then the system is dependent.

And one of the equations is a multiple of the other.

Here, the solution set is given by the equation of the dependent line.

If the two equations have a unique solution, then the system is independent.

And the solution set is given by the coordinates of the intersection point of the two graphs.

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A one-sided significance test provides a p-value of 0.4, which helps us make decisions about the null hypothesis in a statistical analysis. The p-value represents the probability of obtaining results as extreme or more extreme than the observed data, assuming the null hypothesis is true. In most cases, a significance level (alpha) of 0.05 is used as a threshold for determining statistical significance.

When we compare the p-value of 0.4 to the significance level of 0.05, we notice that the p-value is greater than the alpha value. This indicates that we do not have sufficient evidence to reject the null hypothesis. In other words, the results of the study are not statistically significant, and we cannot conclude that there is a significant effect or relationship between the variables of interest.

It is important to remember that failing to reject the null hypothesis does not necessarily mean that there is no effect or relationship between the variables; it merely suggests that the evidence is not strong enough to make such a claim. Further research or larger sample sizes might be needed to explore the relationship between the variables more accurately.

In conclusion, a one-sided significance test with a p-value of 0.4 suggests that we cannot reject the null hypothesis, as the results are not statistically significant at the commonly used alpha level of 0.05.

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The dimensions of the street sign are 10 inches by 4 inches.

What is the perimeter?

The perimeter is a mathematical term that refers to the total distance around the outside of a two-dimensional shape. It is the length of the boundary or the sum of the lengths of all the sides of a closed figure.

Let's assume that the length of the rectangular street sign is L, and the width is W.

We know that the perimeter of the sign is 28 inches, which can be expressed as:

2L + 2W = 28

Simplifying this equation, we get:

L + W = 14 (dividing both sides by 2)

We also know that the area of the sign is 40 square inches, which can be expressed as:

L * W = 40

Now we have two equations with two unknowns (L and W). We can use substitution or elimination to solve for the dimensions.

Using substitution, we can rearrange the first equation to solve for one variable in terms of the other:

L = 14 - W

Then we can substitute this expression for L in the second equation:

(14 - W) * W = 40

Expanding and rearranging terms, we get:

W² - 14W + 40 = 0

This is a quadratic equation that we can solve using the quadratic formula:

W = (-(-14) ± √((-14)² - 4(1)(40))) / 2(1)

W = (14 ± √(36)) / 2

W = 7 ± 3

We can reject the negative value of W since it doesn't make sense for a length or width. Therefore, we have:

W = 10 or W = 4

If W = 10, then L = 14 - W = 4, which gives us a perimeter of 28 inches, but an area of only 40 square inches, so this solution doesn't work.

If W = 4, then L = 14 - W = 10, which gives us a perimeter of 28 inches and an area of 40 square inches, so this is the correct solution.

Therefore, the dimensions of the street sign are 10 inches by 4 inches.

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For an integral value of [tex]I_1 = \int_{ -2}^{3} [2f(x) + 2] dx = 18 \\ [/tex] and

[tex]I_2 = \int_{ 1}^{-2} f(x)dx = -10 \\ [/tex], the computed value of integral [tex]\int_{ 1}^{3} f(x)dx[/tex] is equals to the -6. So, option(c) is right one.

In mathematics, an integral is the continuous process of a sum, which is used to calculate areas, volumes, and their properties. Integration is a way to sum up parts to the whole.

We have an integral say [tex]I_1 = \int_{ -2}^{3} [2f(x) + 2] dx = 18 \\ [/tex]

[tex]I_2 = \int_{ 1}^{-2} f(x)dx = 10 \\ [/tex]

We have to determine value of [tex]\int_{ 1}^{3} f(x)dx[/tex].

Using the properties of integral, consider integral [tex]I_1 = \int_{ -2}^{3} [2f(x) + 2] dx = 18\\ [/tex]

from distribution property, [tex]I_1 = \int_{ -2}^{3} 2f(x) dx + \int_{ -2}^{3} 2 dx = 18 \\ [/tex]

[tex]2 \int_{ -2}^{3} f(x) dx + [ 2x]_{ -2}^{3} = 18[/tex]

[tex]2 \int_{ -2}^{3} f(x) dx + 10 = 18[/tex]

[tex]2 \int_{ -2}^{3} f(x) dx = 8[/tex]

[tex]\int_{ -2}^{3} f(x) dx = 4[/tex]

Now, consider the required integral and rewrite, [tex]\int_{ 1}^{3} f(x)dx = \int_{ 1}^{-2} f(x)dx + \int_{ -2}^{3} f(x)dx \\ [/tex]

Substitute all known values of integrals

[tex]\int_{ 1}^{3} f(x)dx = 10 + 4 = 14 [/tex]

Hence, required value is 14.

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