which expression correctly represents the area of triangle EFG?
a. 1/2 gf sin (F)
b. 1/2 ef sin (E)
c. 1/2 gf sin (G)
d. 1/2 ef sin (G)

The variable x of the equation is 9.6.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

We have to solve the equation for the variable x .

A variable is a number represented with a letter in an equation.

Therefore, let's find the variable x in the equation.

-8 + 2x - 9 + 3x - 10 = 21

combine the like terms

-8 + 2x - 9 + 3x - 10 = 21

- 8 - 9 - 10 + 2x + 3x = 21

-27 + 5x = 21

add 27 to both sides of the equation

-27 + 5x = 21

-27 + 27  + 5x = 21 + 27

5x = 48

divide both sides by 5

5x / 5 = 48  /5

x = 48 / 5

Therefore,

x = 9.6

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Answer: $68.99

Step-by-step explanation:

12% of 61.60 is 7.39200, if you simplify the total, you would get 7.39. Then, you add the total with the sale price to get the original price. Which in this case is $68.99.

The measure of missing line segments will be:

DG = 26; GE = 26; DF = 15; CH = 14; CE = 28

The centroid of a triangle is the place where the three medians of the triangle connect. It is sometimes defined as the point at where the three medians cross. A median line connects the middle of a side to the opposing vertex of a triangle. The centroid of a triangle is the point at where the triangle's three medians coincide (each median connecting a vertex with the midpoint of the opposite side).

Here,

IF If J is the centroid of CDE, this means that J divides CG, FE, DC, CE and DH into two equal parts.

The following expressions are therefore true

DG + GE = DE and DG = GE

Substituting

DG + DG = DE

2DG = DE

Given DE = 52

2DG = 52

DG = 52/2

DG = 26

Since DG = GE, hence GE = 26

Also DF + FC = DC and DF = FC

Since FC = 15, hence DF = 15

Also CH + HE = CE and CH = HE

Since HE = 14, hence CH = 14

CE = 14+14

CE = 28

The missing line segment count will be: DG = 26; GE = 26; DF = 15; CH = 14; CE = 28.

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The equation of the graph is f(x) = |x - 3| + 5

Given that the graph is an absolute value graph

We start by calculating the vertex of the graph

In this case, the graph has it minimum point located at the coordinate (3, 5)

This coordinate can then be interpreted as

(h, k) = (3, 5)

As a general rule, the general representation of the equation of an absolute value function is f(x) = |x - h| + k

Substitute the known values in the above equation

So, we have the following equation

f(x) = |x - 3| + 5

Hence, the equation of the graph represented by the figure is f(x) = |x - 3| + 5

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The unit price for a 7-meter roll of blue ribbon costs $12.04 is $1.72.

The unit price is simply used to calculate the price that's paid for each good.

In this case, the 7 -meter roll of blue ribbon costs $12.04. Therefore, to get the unit price goes thus:

= Total amount paid / Number of meters

= $12.04 / 7

= $1.72

The unit price is $1.72.

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The pit [2, 2]'s prior probability tends to be 0 and its posterior probability tends to be 1.

Compute the probabilities of Pits Each square in the Wumpus world do consist of a pit with the probability of 0.01 and consist of independent contents of the squares.

As suppose there are total of N/2 pits that are scattered randomly among the total of N squares. To compute the probabilities of the pits in [1, 3] and [2,2], consider that the probabilities of the assignments to complete where the other assignments doesn't gets off.

Thus, the total number of the 3-pit assignment rather remains consistent with the three assigned partial assignments here P 1,3 =true.Thus, in 21 assignment completes when the P 1,3 =true. Next the 55 assignment completes when the

P 1,3, = false.

Thus, it gives P(P 1.3 ) = a' (0.01(0.0001+0.0099+0.0099), 0.99(0.0001+ 0.0099)) = (0.1674, 0.8326)

While when the value of Pay = true, then there are basically four assignments that are partialenough with the total value of 0.0001, 0.0099, 0.0099, 0.9801, through the assignment gets completed.

Next when the value of Pa, = false, then there is only a single assignment that is partial with the value of 0.0001 that completes the assignments. Thus, then the final value of P (P2.2 ) is given asP(P2.2) = a' (0.01(0.0001+ 0.0099+0.0099+0.9801), 0.99x 0.0001) = (0.9902, 0.0098

Thus, the prior probability of the pit [2, 2] tends to be 0 and the posterior probability tends to be one (1).

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The values of x, y and z are 4, 1 and - 6 respectively.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied

We have the following equations -

8x + y + 4z = 9

4x - 3y + z = 7

8x - 4y + 5z = - 2

We have -

4x - 3y + z = 7

z = 7 - 4x + 3y

We can write -

8x + y + 4z = 9

as -

8x + y + 4(7 - 4x + 3y) = 9

8x + y + 28 - 16x + 12y = 9               ...Eq[1]

and we can write -

8x - 4y + 5z = - 2

8x - 4y + 5(7 - 4x + 3y) = -2

8x - 4y + 35 - 20x + 15y = - 2         ...Eq[2]

Plot the graph of equation [1] and [2]. We will will get -

x = 4

y = 1

Now -

z = 7 - 4x + 3y

z = 7 - 16 + 3

z = - 6

Therefore, the values of x, y and z are 4, 1 and - 6 respectively.

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Answer:   17/2578  (Decimal: 0.006594)

Step-by-step explanation:

That's the answer :)

The equation of line in slope-intercept form is y = 2x + 1

Q. What is Equation of line ?

 A straight line's general equation is y = mx + b, where m denotes the   gradient or slope and y = b denotes the point at which the line crosses the y-axis. On the y-axis, this value b is referred to as the intercept.

We know the equation of line is

y = mx + b

where,

m = slope

b = y - intercept

To form an equation we need to find 'b' and 'm'.

so, first find 'b' i.e, y - intercept

For that, you just need to see the red line cuts the y-axis at its sharp grid means not in middle of the grid.

So, by observing the graph we see y = 1 where the red line cuts the y-axis

so we get, b = 1 means y-intercept

Now, we need to find slope (m).

For that, we know slope = rise / run

So take any point on graph which is easily to recognize the (x,y) points on graph.

Here I take the point (2, 5).

Now mark that point and find rise and run values.

rise = 4 (count from y = 1 to y = 5 )

run = 2 (count from x = 0 to x = 2)

Now, put the values and get the slope.

slope (m) = 4 / 2

               = 2

Now, put the y-intercept and slope values in equation of line .

y = mx + b

y = 2x + 1

Hence, the equation of line in slope-intercept form is y = 2x + 1

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The probability that Sam gets only one of the two guessess correct is 3/16.

Probability is the likelihood of the occurence of an event.

The probability of guessing correctly = 1/4

The probability of guessing incorrectly = 3/4

Therefore, the probability that only one guess is correct will be:

= probability of guessing correctly × probability of guessing incorrectly

= 1/4 × 3/4

= 3/16

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The rate of change of the area of the square when the side length is 8 inches is 224 inches per hour.

Let s be the side of the given square.

A = s²

dA/dt = d (s²)/dt

dA/dt = 2s × ds/dt

Given ds/dt= 14 inches per hour, s = 8 inches

dA/dt = 2×14×8

dA/dt = 224 inches per hour

The area of the square is s². Since we need to find the rate of change we need to differentiate the area with respect to time which will give us  2s × ds/dt. Once we replace the given values with their respective positions we will get the desired answer. Hence the rate of change in the area of the square is 224 inches per hour.

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Answer: 41.18% or 7/17

Step-by-step explanation:

7 + 4 + 6 = 17

7/17 (fraction)

41.18%

Juan wants to buy a video game for $63  He saves  every Friday $12.

An equation to represent Juan’s total savings, , in dollars, after  Fridays y is  

Part A is

y =12x

Fridays will it take for Juan to save up enough money for the video game is .

Part B

y >  63

12 x > [tex]5\frac{1}{4}[/tex]

x  =  6

so

That means 6 fridays

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For figure 4, The perimeter is 9 cm and the area is 3.5 square cm.

For figure 5, The circumference is 8π ft. and the area is 16π square ft.

For figure 6, The perimeter is 56 yards and the area is 196 square yards.

For figure 7, The perimeter is 12 cm and the area is 6 square cm.

What is the perimeter?

Perimeter is the distance measured around the edge of any geometrical shape.

The perimeter of a square having side "a" is = 4 ×a.

The perimeter of a triangle having sides "a", "b", and "c" is = a+b+c.

What is the Circumference of a circle?

In geometry, the circumference is the perimeter of a circle.

To find the circumference of a circle, we can use the formula.

                Circumference of a circle = 2×π×r

Where "r" is the radius of a circle.

What is the Area of a circle?

In geometry, the area of a circle is the space occupied by the circle.

To find the area of a circle having radius "r", we can use the formula.

                Area of a circle = π×r².

What is the Area of a triangle?

The area of a triangle is defined as the space enclosed within the three given sides of a triangle.

The formula for finding the area of a triangle for a given height "h" and base "b" is

                  Area of a Triangle = [tex]\frac{1}{2} *b *h[/tex]

What is the area of a square?

The area of a square is defined as the space occupied by the square.

To find the area of a square having side "a" is

                  Area of a Square = (a)²

For figure 4,

The sides of the given triangle are 2.5 cm, 3 cm, and 3.5 cm.

The height of the triangle is given as 2 cm.

Then, the perimeter of a triangle = 2.5 + 3 + 3.5

                                                       = 9 cm.

and the area of a triangle [tex]=\frac{1}{2}*3.5*2[/tex]

                                          = 3.5 square cm.

For figure 5,

The radius of the given circle is 4 ft.

so, the Circumference of a circle = 2×π×r

                                                       = 2×π×4

                                                       = 8π ft.

and the area of the circle = π×r²

                                          = π×(4)²

                                          = 16π square ft.

For figure 6,

The side of the given square is 14 yd.

so, the perimeter of a square = 4×side

                                                 = 4×14

                                                 = 56 yards.

and the area of a square = (side)²

                                          = (14)²

                                          = 196 square yards.

For figure 7,

The sides are 3 cm, 5 cm, and 4 cm.

so, the perimeter of a triangle = 3+5+4

                                                  = 12 cm.

The height of a triangle is 3 cm and the base is 4 cm.

and the area of a triangle = [tex]\frac{1}{2}[/tex] × h × b

                                          = [tex]\frac{1}{2}[/tex] × 3 × 4

                                          = 6 square cm.

Hence,

For figure 4, The perimeter is 9 cm and the area is 3.5 square cm.

For figure 5, The circumference is 8π ft. and the area is 16π square ft.

For figure 6, The perimeter is 56 yards and the area is 196 square yards.

For figure 7, The perimeter is 12 cm and the area is 6 square cm.

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The probability of the next flip result in a trail is 0.5.

Given that,

If you flip a coin 100 times and receive 80 heads and 20 tails.

We have to find what is the probability that the upcoming flip will result in a tail based on these findings.

Probability refers to potential. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events.

Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty.

One is the probability of every event in a sample space.

Next flip result is independent of the past results.

P(Next flip result is tail) = 1/2 = 0.5

Therefore, The probability of the next flip result in a trail is 0.5.

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The cost of a soft taco is $1.25 and the cost of a burrito is $2.50.

Let the cost of a soft taco would be t and,

The cost of a burrito would be b

As per the given question, the equations would be as

3t+3b=11.25   ...(i)

4t+2b=10       ...(ii)

With the two equations in that form, an elimination solution is probably the simplest.

Multiply each equation by a constant so that the coefficients of b are opposite so that when the two equations are joined, b is eliminated.

-6t-6b = -22.50

12t+6b = 30.00

_____________

6t   =  7.50

t = 7.50/6 = 1.25

Substitute the value of t = 1.25 in equation (ii), and solve for b

4(1.25)+2b=10

5+2b=10

2b=5

b=2.50

Thus, the cost of a soft taco is $1.25 and the cost of a burrito is $2.50.

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Answer:

3/2x

Step-by-step explanation:

For a proportional relationship between the volume of flour used (in cups), x, and the number of baked muffins, y, the constant of proportionality is 4.

Constant of proportionality, also known as constant ratio or constant rate, refers to is the ratio that relates two given values in a data set that is represented as a proportional relationship. When two parameters are proportional, either directly or indirectly, the relationship is expressed as a = kb or a = k/b, where k indicates the relationship between the two variables and is known as the proportionality constant. In the given data, the proportionality constant is:

k =b/a = 8/2 =12/3 = 16/4 = 20/4 = 4

Hence, the proportionality constant for the given data is 4.

Notes: The question is incomplete. The complete question is: Brian loves to bake blueberry muffins for his friends and family. There is a proportional relationship between the volume of flour brian uses (in cups), x, and the number of muffins he bakes, y. What is the constant of proportionality. (Refer to the table).

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The attendant at a parking lot compared the number of hybrid vehicles to the total number of vehicles in the lot over a weekend.

Day      hybrids    total

Fri           5             9

sat                         63

sun         40            

we need to find number of hybrids in sat and total in sun.

Number of hybrids in sat = 5*7 = 35(ratios are equal)

Total in sum = 9*8 = 72.

Day      hybrids    total

Fri           5             9

sat          35           63

sun         40           72

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Answer:

  38 units

Step-by-step explanation:

You want the perimeter of pentagon ABCDE with vertices at A(4, -2), B(4, 10), C(7, 10), D(15, 4), E(7, -2).

The perimeter of a plane figure is the sum of the lengths of its sides.

By counting grid squares, or subtracting coordinates, you can find the lengths of the vertical and horizontal segments easily:

  AB = 12, BC = 3, EA = 3

The lengths of the diagonal segments can be found using the distance formula or your knowledge of Pythagorean triples. Counting grid squares (or subtracting coordinates), you see that each diagonal side has a vertical distance of 6 and a horizontal distance of 8. These correspond to twice the lengths of the sides in a 3-4-5 triangle, so you know the diagonal length is twice the hypotenuse: 2·5 = 10.

The Pythagorean theorem, or the distance formula, will tell you the same thing:

  c² = a² +b² . . . . . . Pythagorean theorem for sides a, b, hypotenuse c

  c = √(a² +b²)

  diagonal length = √(6² +8²) = √100 = 10

Then the remaining two sides are ...

  CD = 10, DE = 10

The perimeter is ...

  perimeter = AB +BC +CD +DE +EA

  = 12 +3 +10 +10 +3 = 38 . . . units

The perimeter of pentagon ABCDE is 38 units.

The correct answer is (A) I and IV. The first and fourth quantities are discrete.

What is discrete quantity?

A discrete quantity has a limited range of possible values. For instance, the number of students in a classroom is a discrete quantity because the range of possible values is not continuous and can only be a positive integer.

It can only have certain values, not just any value, according to the definition of discrete. One discrete quantity is the number of sheep in a field.

Consider, the first statement

"The number of students who passed the English test".

In this quantity a certain value is considered.

Hence this quantity is discrete.

In second and third statement there is no certain quantity is considered.

Hence, these quantities are not discrete quantities.

Also in the last statement there is come quantity of pages is considered.

Hence, this quantity is discrete quantity.

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The height of building has shadow 47.75m long is 95.5m

The angle of elevation is defined as the angle which is formed by angle between horizontal line of sight and object.

let the height of building be h. we have given height of another building is 3.2m and shadow is 1.6m long.

we know that

tan(∅) = perpendicular/base = 3.2/1.6 =2

As question says at same time, another building of height h and shadow is 47.75m long.then angle will be same.

⇒ tan(∅) = perpendicular/base = h/47.75

⇒ h/47.75 = 2

⇒ h = 2(47.75) = 95.5m

Thus, required height of building is 95.5.

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The correct statements regarding the scatter plot are given as follows:

The scatter plot is used to give the points needed to build the linear regression equation relating the output variable of the vertical axis as a function of the input variable represented by the horizontal axis.

In the context of this problem, these points are given as follows:

(0, 4), (2, 5), (7,7), (9, 10), (14, 12), (15, 15), (21, 17).

Inserting these points into a linear regression calculator, the equation is listed as follows:

y = 0.6529x + 3.65758

On each day listed on the options, the predicted weights are given as follows:

From these numeric values, the correct options are selected.

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Answer:

To do percentages with fractions,

divide the numerator by denominator to get a decimal,

so for example, 12/40.

12/40 is 0.3 decimal, and then to make it percent,

we multiply by 100,

how does that work?

you move two places to the right because 100 has two zeros

so 0.3 would be 30,

therefore the percent of 12/40 would be 30%

number two same thing

33/60=0.55

0.55x100=55

so 55%

have a good day! <3

Answer:

Step-by-step explanation:

Answer:

x=-4

Step-by-step explanation:

-3x-18=-6

-3x=12

x=-4

Answer:  x=-4

Step-by-step explanation:

Start off with the equation: -3x-18=-6

Add 18 to both sides: -3x=12

Divide by -3: x=-4

Hope this helped!

(a) Equation is 8x - 2x = 36

(b) By solving equation we get the value of x = 6

(c) The length of the rectangle is 14

Given,

In the question:

A square and a rectangle have same perimeter.

The square (2x,2x) and the rectangle (10, x+8) have perimeters of the same length.

Now, According to the question:

We know that the formula of Perimeter of rectangle and square.

Perimeter of square = 4 x side

Perimeter of rectangle = 2(length + breadth)

Perimeter of a square = 4(2x) = 8x

Perimeter of rectangle = 2(x + 8) + 20

Now,

8x = 2x + 16 + 20

6x = 36

x = 6

Hence, (a) Equation is 8x - 2x = 36

(b) By solving equation we get the value of x = 6

(c) The length of the rectangle is 14 .

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The statements that are always true about Isosceles Trapezoids:

One pair of opposite sides are parallel.

One pair of opposite sides are congruent.

The sum of the angles is 360°.

Diagonals are congruent.

Diagonals intersect perpendicularly.

What is an isosceles trapezoids?

A convex quadrilateral having one pair of opposite sides divided by a line of symmetry is known as an isosceles trapezoid. It is a particular instance of a trapezoid. Alternately, it can be described as a trapezoid whose base angles and both legs are identical in size.

The true statements are:

One pair of opposite sides are parallel.

One pair of opposite sides are congruent.

The sum of the angles is 360°.

Diagonals are congruent.

Diagonals intersect perpendicularly.

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The required value of t according to the given question is - 8.

Given points are (-2,t) and (-1,-6)

Now let these two points be considered as

A and B that is let the points be A(-2,t) and B(-1,-6)

To find the slope of the graph we will use the formula m = y - y₁ / x - x₁

Given y = ty₁ = - 6x = - 2 x₁ = - 1

Thus on substituting these values in the above mentioned formula we will get m = t + 6 / - 1

Also given slope or m = 2Thus 2 = - t - 6 t = - 6 - 2 t = - 8

Thus the required value of t is - 8.

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