if [tex]f(x)=\frac{1}{3} - \frac{1}{2}x [/tex] and [tex]g(x) = 2x^{2} + x + 4[/tex] find [tex] (f+g)(x) [/tex]

Both of these are linear equations with different y-intercepts and different slopes.

Let's analyze the lines:

y = 2x:

This is a linear equation with a slope of 2 and a y-intercept at the origin (0,0). This means that for every unit increase in x, y increases by 2. The graph is a straight line that passes through the origin.

y = 2 - x:

This is also a linear equation, but with a slope of -1 and a y-intercept at (0,2). This means that for every unit increase in x, y decreases by 1. The graph is a straight line that intersects the y-axis at the point (0,2).

Now, let's consider their relationship:

Both equations are linear, so their graphs are straight lines.

Therefore, the graphs of these two equations are lines with different slopes. The line represented by y = 2x slopes upwards, while the line represented by y = 2 - x slopes downwards.

Answer: C

Step-by-step explanation:

plug in y=8 to

x+y=3

x+8=3

x=-5

There is no need to look at the other answer choices since they do not have x equaling to -5.

So,

[tex]x+y=3\Rightarrow y=3-x[/tex]

Then,

[tex]8=3-x\Rightarrow x=-5[/tex]

The ordered pair is therefore,

[tex]C(-5,8)[/tex]

Hope this helps.

r3t40

Answer:

(23,-4):[tex]\sqrt{545}[/tex] units

Step-by-step explanation:

We are given that M(-19,4)and P(4,0)

We have to find the ordered pair that represents MP and find the magnitude of MP.

MP=P-M

MP=(4,0)-(-19,4)=(4+19,0-4)

MP=(23,-4)

Magnitude of MP=[tex]\sqrt{(23)^2+(-4)^2}[/tex]

Magnitude of MP=[tex]\sqrt{529+16}[/tex]

Magnitude of MP=[tex]\sqrt{545}[/tex] units

Hence, .option c is true.

Answer:c.(23,-4):[tex]\sqrt{545}[/tex] units

Answer:

A 2021

Step-by-step explanation:

The formula h=2A/b indicates a combined variation. As the values of A and B change, the value of H also changes accordingly. Understanding its concept helps in solving related problems.

The formula h=2A/b is a representation of combined variation. Combined variation, or joint variation, occurs when a quantity varies directly with the product of two or more other quantities. In other words, as the values of A and B change, the value of h will also adjust accordingly. Let's break it down:

By understanding the concept of combined variation, solving problems involving such formula will become much easier.

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The equation h=2A/b represents combined variation where h varies directly with area (A) and inversely with width (b). The formula indicates how changing one variable affects another in the context of proportional relationships. The mention of molecular cohesion and size pertains to a different scientific context and is not directly related to this mathematical formula.

The formula h=2A/b describes a scenario of combined variation, where h varies directly as the area A and inversely as the width b. Direct variation means that as one variable increases, the other variable increases as well, while inverse variation indicates that as one variable increases, the other decreases. In this case, if the area doubles, h will also double if b remains constant, and if b is halved, h will double, assuming A stays constant.

The provided information about the parameter a describing inter-molecular cohesion and the parameter b describing the effect of molecular size seems to be associated with a completely different context, likely a scientific or chemical formula, rather than the combined variation formula presented in the question. This formula might be relevant to the Born-Oppenheimer surfaces as depicted in Figure 3.1c, which describes a chemical interaction.

Answer:

The correct answer to this problem is the final option, angle BTA is congruent to angle ATC.

Step-by-step explanation:

To solve this problem, we first have to unpack the meaning of the given information.  First, let's remember that CPCTC means that corresponding parts of congruent triangles are congruent.  This means that the same parts of two different triangles that are stated to be congruent (the same) are thus also congruent (the same).

In this case, triangle BAT and triangle CAT are stated to be congruent. This means that line segment BA and CA are congruent, angles BAT and CAT are congruent, and more because of CPCTC (explained above).

The correct answer to this problem is the final option, angle BTA is congruent to angle ATC. We can figure this out simply by looking at the triangle names.  Angle ATC is the same as angle CTA (the letters are just in reverse order).  From the congruence statement, we can tell that BTA and CTA are congruent angles due to the fact that triangle BAT and CAT are congruent using CPCTC.  Looking at the figure, this makes sense because these two angles appear to be the same measure.

Also, we can eliminate the other answer choices, since they are not corresponding parts of the two triangles (the line segments and angles do not represent two congruent pieces of the triangle - they are not matched up correctly).

Hope this helps!

Answer:

1/3

Step-by-step explanation:

If there are 12 sections and Lia paints 8, then Kira paints 4.

The fraction that represents how much Kira has painted of the wall is

4/12.

4/12 can be reduced.

4 and 12 have a common factor of 4 so we will divide top and bottom of 4/12 by 4 giving us 1/3.

Answer:

-6

Step-by-step explanation:

f(g(-1)) means we need to find g(-1) and then plug that result into f(x).

So let's start:

g(-1) means to replace the input variable in g(x)=x^2 with -1.

So we replace x with -1.  

g(-1)=(-1)^2

g(-1)=1

Now that we have g(-1) can be replaced with 1, we can further evaluate f(g(-1)).

So let's do that:

f(g(-1))

f(1)=1-7   ; I replaced the x in f(x)=x-7 with 1 to find f(1).

f(1)=-6

----

Putting altogether

f(g(-1))=f((-1)^2)=f(1)=1-7=-6.

Answer:

f(g(-1)) = -6

Step-by-step explanation:

* Lets explain how to solve the problem

- The problem is about the composite function

- A composite function is a function that depends on another function.

- A composite function is created when one function is substituted into

 another function.

- Ex: f(g(x)) is the composite function that is formed when g(x) is

 substituted for x in f(x)

* lets solve the problem

∵ f(x) = x - 7

∵ g(x) = x²

- We want to find f(g(-1))

* At first lets find g(-1) by substitute x in the function g(x) by -1

∵ g(x) = x²

∵ x = -1

∴ g(-1) = (-1)² = 1

* Now we want to find f(g(-1)), then we will substitute x in f(x) by

 the value of g(-1)

∵ g(-1) = 1

∵ f(x) = x - 7

∴ f(g(-1)) = f(1)

∵ f(1) = 1 - 7 = -6

∴ f(g(-1)) = -6

If an image of a triangle is congruent to the pre-image, the scale factor of the dilation is 1

From the question, we understand that the images are congruent

This means that, the shape is not dilated.

Instead, the shape is translated, reflected or rotated.

When a shape is not dilated, the scale factor is 1

Hence, the scale factor of the dilation is 1

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Let the length = x and the width = y

For the length of fence we have x +x + y = 48 = 2x +y = 48

Rewrite as y = 48 - 2x

For the area we have x * y  = 254

Replace y in the are equation:

x * 48 -2x = 254

Simplify the left side:

48x - 2x^2 = 254

Subtract 254 from both sides:

48x - 2x^2 - 254 = 0

Using the quadratic formula solve for x:

a = -2, b = 48 and c = -254

x = -48 + 4√17/-4

x = 16.123 m.

The length = x = 16.123 meters.

The width = 48 - (16.123*2) = 15.754 meters

Rounding to the nearest centimeter:

Length = 16.1 ( 16 meters and 1 cm)

Width = 15.8 ( 15 meters and 8 cm)

Answer:

d

Step-by-step explanation:

Answer:

D.  (4, -4).

Step-by-step explanation:

y = -x is a line that has a negative slope of  -1 ( rising to the left)  and passing through the origin. It makes an angle of 45 degrees with the x-axis.

So, for example the point ( 0,1 )will map onto( -1 , 0).

Any point which maps on to itself across this line will have to lie on the line.

If x = 4 y = -x = -4.

Answer:

[tex]\sqrt{13}[/tex]

Step-by-step explanation:

The median from B intersects the midpoint of AC

Find the midpoint using the midpoint formula

midpoint = [ 0.5(1 - 5), 0.5(- 1 + 3) ] = (- 2, 1 )

Calculate the length using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = - 2, 1 ) and (x₂, y₂ ) = (0, 4 )

d = [tex]\sqrt{(0+2)^2+(4-1)^2}[/tex]

  = [tex]\sqrt{2^2+3^2}[/tex]

  = [tex]\sqrt{4+9}[/tex] = [tex]\sqrt{13}[/tex] ≈ 3.6 ( to 1 dec. place )

Answer:

-6

Step-by-step explanation:

To find the slope, plug any two of your points into the slope formula.

I'll use your first two; (-2, 8) and (-1, 2).

[tex]\frac{y2-y1}{x2-x1}[/tex]

Your y1 term is 8, your y2 term is 2.

Your x1 term is -2, your x2 term is -1.

[tex]\frac{2-8}{-1-(-2)} \\\\\frac{-6}{-1+2} \\\\\frac{-6}{1} \\\\-6[/tex]

Your slope is -6.

Answer:

The slope is [tex]\huge \boxed{-6}[/tex].

Step-by-step explanation:

Slope formula:

[tex]\displaystyle \frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]

[tex]\displaystyle \frac{2-8}{(-1)-(-2)}=\frac{-6}{1}=-6[/tex]

Therefore, the slope is -6, and the correct answer is -6.

Answer:

The measure of arc c is 86°

Step-by-step explanation:

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

so

86°=(1/2)[arc c+arc a]

see the attached figure with letters to better understand the problem

In this problem

Triangles ABO and CDO are congruent by SSS postulate theorem

∠AOB=∠COD

∠AOB=arc a -----> by central angle

∠COD=arc c -----> by central angle

therefore

The measure of arc a is congruent with the measure of arc c

arc a=arc c

so

86°=(1/2)[2arc c]

86°=[arc c]

arc c=86°

Answer:

1.45

Step-by-step explanation:

Percent is the same as putting the number over 100. In this case that would be 145/100 which as a decimal is 1.45.

Answer: is 1.45

Step-by-step explanation:

first you would take 145 percent and divide it by 100 then the answer would be 1.45 or 145/100=1.45

hope this helps

Step-by-step explanation:

i have answered ur question

The Perimeter of the given polygon can be calculated using the distance formula for each of its sides. The calculated distances are added to give a total perimeter of approximately 18.5 units.

The Perimeter of a polygon is calculated by adding the lengths of all its sides. Here, we need to calculate the distance between each pair of points, which gives the length of the sides of the polygon.

The distance between two points (x1, y1) and (x2, y2) is given by the formula sqrt((x2-x1)² + (y2-y1)²) .

To find the Perimeter of the polygon, we calculate the distances between each pair of vertices and then add them up:

Adding these distances, we get a perimeter of approximately 5 + 4.1 + 3.2 + 4.2 + 2 = 18.5 units, rounded to the nearest tenth of a unit.

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Answer:

[tex]4x^5\sqrt[3]{3x}[/tex]

Step-by-step explanation:

The product will be written as:

[tex]\sqrt[3]{16x^7}*\sqrt[3]{12x^9}[/tex]

As both the radicals have same root 3 so,

[tex]= \sqrt[3]{16x^7 * 12x^9}[/tex]

The powers of x will be added as the base is same

[tex]=\sqrt[3]{16*12 * x^{(7+9)}}\\=\sqrt[3]{192x^{16}}\\[/tex]

We have to break the terms so that the powers can be written as a multiple of 3

[tex]=\sqrt[3]{64*3*x^{15}*x}\\ =\sqrt[3]{(4^3)*3*(x^{3*5})*x}\\ Applying\ cube\ root\\= 4x^5\sqrt[3]{3x}[/tex]

Answer:

Step-by-step explanation:

The question is to evaluate the natural logarithm of 5. Natural logarithms are logarithms with base e.

e is the irrational number equal to 2.71828182845904523536028747 ... (being irrational the decimals do not end and do not have a repetition period).

Logarithms are evaluated using tables or scientific calculators.

ln (5) = 1.6094379... it is also an irrational number, so it has infinite decimals with no repetition period.

So, rounding to two decimal numbers, ln (5) = 1.61, which is the option C).

Answer:c

Step-by-step explanation:test

Answer: 6

Step-by-step explanation: 8 times 3/4 equals to 6.

Answer:

6 teaspoons

Step-by-step explanation:

Number of teaspoon in 1 batch = 3/4

Number of teaspoon in 8 batches = ?

We know the quantity of teaspoon of  vanilla for one batch. To find the quantity for 8 batches we will simply multiply the quantity of teaspoon  of vanilla for one batch by 8

=3/4 * 8

=3*2

=6

Therefore 6 teaspoons will be needed....

The expression will be x=y-4

The less than expression implies that one number x is lower than another number b by some constant d i.e. it implies that b is greater than a. If we subtract a from b it will give the constant d.

Here, given that,

x is 4 lesser than a number,

let's assume that number is y

from the above, it is clear that As y is greater than x, if we subtract 4 from y we will get x.

so the expression can be written as

y-x=4

⇒x=y-4

Therefore The expression will be x=y-4.

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The expression 'x is 4 less than a number' can be represented algebraically by the equation 'x = n - 4', where n is the unknown number.

If you're asked to represent a situation involving x as an algebraic expression, you should analyze all the provided facts. According to the question, x is 4 less than a certain number. This situation can be represented by the expression x = n - 4, where n is the number being referred to. In this expression, we made sure to account for the fact that x is 4 less than this number, so we subtract 4 from n to find the value of x.

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Answer:

Answer is

b = (8)tan(30°) - first choice

Step-by-step explanation:

Steps:

tan 30=b/8

b= 8tan30°

Option (a) is correct,  b = (8)tan(30°) is the equation which can be used to solve for b

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles

In a  right angle triangle the three sides are represented by the letters a, b and c .

a represents the side adjacent with given angle .

b represents the side opposite to the given angle.

c represents the hypotenuse of the triangle .

Check the attached image for clear picture of the right angle triangle with angle 30 degrees .

Using the trigonometric ratio we can write the ratio as

b/a = tan 30

Multiplying both sides by a , we get

b= a tan 30

since a=8 so

b =8 tan (30)

Hence, b = (8)tan(30°) is the equation which can be used to solve for b

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Answer:

B

Step-by-step explanation:

If C is the correct answer and if the final result is multiplied out, where does the minus sign in a^4 - b^4 come from? All pluses don't make a minus. A is incorrect.

If D is correct, then a^2 - b^2 should be further factored producing a different kind of answer, like (a + b)^2(c-d)^2 which is not the same as a^4 - b^4. So D is not correct.

The first step in factoring a^4 - b^4 is (a^2 + b^2)(a^2 - b^2) A doesn't lead you anywhere. A is incorrect. The answer must be B.

a^4 - b^4 = (a^2 -  b^2)(a^2 + b^2)  The first term factors.

a4 - b^4 = (a + b)(a - b) (a^2 +b^2)

Answer:

Step-by-step explanation: THE ANSWER IS B

Answer:

the volume of a cube by 5cm is going to be a 5x6=30

Answer:

scalene and obtuse all sides are different and bigger than 90 degree angle

Answer: D. 0.8125

Step-by-step explanation: His expenses is $975, and his salary is $1200. Divide the expenses by the salary to find the debt-to-income ratio.

975/1200 = 0.8125

The debt-to-income ratio is 0.8125.

Answer:

d) 0.8125

Step-by-step explanation:

Malcolm’s debt-to-income ratio is 0.8125 if his monthly expenses are $975 and his monthly salary is $1200.

All you have to do is divide monthly expenses by the monthly salary.

975 ÷ 1200 = 0.8125

Answer:

True.

Step-by-step explanation:

Let's use the picture I made.

I used degrees instead...

tan(90-x)= b/a   .  I did opposite over adjacent for the angle labeled 90-x which is that angle's measurement.

cot(x)=b/a    .  I did adjacent over opposite for the angle labeled 90 which is that angle's measurement.

Now this is also known as a co-function identity.

[tex]\tan(\frac{\pi}{2}-x)[/tex]

Rewrite using quotient identity for tangent

[tex]\frac{\sin(\frac{\pi}{2}-x)}{\cos(\frac{\pi}{2}-x)}[/tex]

Rewrite using difference identities for sine and cosine

[tex]\frac{\sin(\frac{\pi}{2})\cos(x)-\sin(x)\cos(\frac{\pi}{2})}{\cos(\frac{\pi}{2})\cos(x)+\sin(\frac{\pi}{2})\sin(x)}[/tex]

sin(pi/2)=1 while cos(pi/2)=0

[tex]\frac{1 \cdot \cos(x)-\sin(x) \cdot 0}{0 \cdot \cos(x)+1 \cdot \sin(x)}[/tex]

Do a little basic algebra

[tex]\frac{\cos(x)-0}{0+\sin(x)}[/tex]

More simplification

[tex]\frac{\cos(x)}{\sin(x)}[/tex]

This is quotient identity for cotangent

[tex]\cot(x)[/tex]

Answer:

True

Step-by-step explanation:

tan( pi/2 -x)

We know that tan (a-b) = sin (a-b) / cos (a-b)

tan (pi/2 -x) = sin (pi/2 -x)

                       --------------

                      cos (pi/2 -x)

We know that

sin (a-b) = sin(a) cos(b) - cos(a) sin(b)

and cos (a-b) = sin(a) sin(b) + cos(a) cos(b)

tan (pi/2 -x) = sin (pi/2) cos (x) - cos (pi/2) sin (x)

                       ----------------------------------------------

                      sin(pi/2) sin(x) + cos(pi/2) cos(x)

We know sin (pi/2)=1

                cos (pi/2) = 0

tan (pi/2 -x) = 1 cos (x) - 0 sin (x)

                       ----------------------------------------------

                      1 sin(x) +0 cos(x)

tan (pi/2 -x) =  cos (x)

                      ------------------

                      1 sin(x)

We know cos(x)/ sin (x) = cot(x)

tan (pi/2 -x) = cot(x)

Answer:

Divide and express 2.7/1.1 to the nearest tenth.

Step-by-step explanation:

Answer:

27) 18 < P ≤ 18 + 6√2 ⇒ answer D

28) The sum of the degree measures these angles is 1080° ⇒ answer B

29) 3E minutes before A ⇒ answer B

30) The difference between the greatest possible values is 0 ⇒ answer E

31) r divided by s = 1/3 ⇒ answer A

Step-by-step explanation:

* Lets explain each problem

27)

∵ BE is a quarter circle

∵ The radius of the circle is 6

∵ Point c is on the arc BE

∴ The distance from D to C = 6 ⇒ not depends on the position of c

   because DC is a radius in the quarter circle BE

- In Δ BDE

∵ m∠ D = 90°

∵ DB = DE = 6 ⇒ radii of the quarter circle

- By using Pythagoras Theorem

∴ BE = √ (6² + 6²) = √(36 + 36) = √72 = 6√2

- The perimeter of the quadrilateral ABCD is the sum of the sides

∵ AB = 6 , AD = 6 , CD = 6

- Point C can move from B to E

∴ The length of side BC can b greater than 0(it can not be 0

   because the quadrilateral has 4 sides

∴ The length of BC can not exceed the length of BE because the last

   position of point C to be on the arc BE is point E

∴ The length of BC ⇒ 0 < BC ≤ 6√2

  equal 6√2

∵ P is the perimeter of the quadrilateral ABCD

∴ P = 6 + 6 + 6 + (0 < BC ≤ 6√)

∴ P = 18 + (0 < BC ≤ 6√)

- Add 18 to 0 and 18 to 6√2

∴ 18 < P ≤ 18 + 6√2

28)

- In the figure we have a quadrilateral

- All the arrows represent the exterior angles of the figures

- Use the fact that:

 The sum of all angles around a points is 360°

∵ There are 4 vertices (points) on the quadrilateral

∴ The sum of the all angles around the 4 vertices = 4 × 360 = 1440°

- Use the fact that:

 The sum of the interior angles of any quadrilateral is 360°

∵ The sum of the angles represented by the arrows is the difference

  between the sum of all angles around the 4 vertices and the sum

  of the interior angles of the quadrilateral

∴ The sum of these angles = 1440° - 360° = 1080°

* The sum of the degree measures these angles is 1080°

29)

- In any watch the short arrow-hand represents the hours and the long

 arrow-hand represents the minutes

- The numbers of the hours in the watch from 1 to 12

- The number of minutes between each two hours is 5 minutes, then

  at 1 o'clock the minutes number is 5 , at 6 o'clock the number of

  minutes is 30 , at 9 o'clock the number of minutes is 45 , so we can

  find the number of minutes at any number of hour by multiply the

  number of hour by 5

∵ The number of hours have been replaced by letters

∵ The time on the watch is 45 minutes after 12 o'clock OR

  15 minutes before 1 o'clock

∵ The short arrow-hand pointed between L and A

∵ L is the replacing of 12 o'clock and A is the replacing of 1 o'clock

∵ The long arrow-hand pointed at I

∵ I is the replacing of  9 o'clock

∵ The hour number 9 means 5 × 9 = 45 minutes

∴ The hour hand I has 5I minutes

∴ The time in letter is 5I minutes after L

- This answer is not in the choices

- But the answer of 3E minutes before A means:

∵ E is the replacing of 5 o'clock

∴ 3E = 3 × 5 = 15 minutes

∵ A is the replacing of 1 o'clock

∴ 3E minutes before A means 15 minutes before 1 o'clok

* The answer is ⇒ 3E minutes before A

30)

∵ r² = 9

∴ r = ± √9 = ± 3

∴ r has two values -3 and 3

∵ s² = 25

∴ s = ± √25 = ± 5

∴ s has two values -5 and 5

- To find the greatest value of s - r put s greatest and r smallest

∵ The greatest value of s is 5

∵ The smallest value of r is -3

∴ The greatest value of s - r = 5 - (-3) = 5 + 3 = 8

- To find the greatest value of r - s put r greatest and s smallest

∵ The greatest value of r is 3

∵ The smallest value of s is -5

∴ The greatest value of r - s = 3 - (-5) = 3 + 5 = 8

∴ The difference between the greatest possible values of s - r

   and r - s = 8 - 8 = 0

* The difference between the greatest possible values is 0

31)

- There are 27 cubes each of side length r

- The 27 cubes are arranged to form on single large cube of side

  length s

∵ The volume of any cube is V = L³ , where L is the length of its side

∵ The large cube formed from the 27 small cubes

∴ The volume of the large cube = the volume of the 27 small cubes

∵ The side of the small cube is r

∴ The volume of the small cube is r³

∵ The side of the large cube is s

∴ The volume of the large cube is s³

∴ s³ = 27 r³

- Divide both sides by s³ and 27

∴ s³/(27 s³) = (27 r³)/(27 s³)

∴ 1/27 = r³/s³

- Take ∛  for both sides

∴ ∛(r³/s³) = ∛(1/27)

- The cube root canceled by the power 3 and the cube root of

  1/27 is 1/3

∴ r/s = 1/3

* r divided by s = 1/3

Answer:

[-∞, 3)

Step-by-step explanation:

We are given the following inequality which we are to express as a set using the interval notation:

[tex] - 2 x + 3 0 > 4 x + 1 2 [/tex]

Rearranging the inequality by adding the like terms together to get:

[tex] - 2 x - 4 x < 1 2 - 3 0 [/tex]

[tex] - 6 x < - 1 8 [/tex]

[tex]x<\frac{-18}{-6}[/tex]

[tex]x<3[/tex]

Since the values of [tex]x[/tex] are lesser than [tex]3[/tex] so we can express this in interval notation as:

[-∞, 3)

Answer:

x = 8

Step-by-step explanation:

Angle bisector splits an angle into two equal angles

4x + 1 = 33

4x = 33 - 1

4x = 32

x = 32/4

x = 8

Answer:

x=8

Step-by-step explanation:

If AB is a bisector, that means  angles CAB and BAD are equal

<CAB = <BAD

33 = 4x+1

Subtract 1 from each side

33-1 = 4x+1-1

32 = 4x

Divide each side by 4

32/4 = 4x/4

8 =x

Answer:

193.8

Step-by-step explanation:

The 'mean' of a set is the set's average.

To find the average, add the terms together and divide by the number of terms.

[tex]108+305+252+113+191\\413+252+113+191\\665+113+191\\778+191\\969[/tex]

Divide by your number of terms (5).

[tex]\frac{969}{5} =193.8[/tex]

Answer:

193.8

Step-by-step explanation:

You add up all of the numers and get 969. Then you have to divide by the amount of numbers there are so divide by 5 and get 193.8