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If G is the incenter of ∆ABC, then GD = GF = GE.

Given, GD is 3x + 5 and GF is 6x - 4.

According to the above statement,

GD = GF

or, 3x + 5 = 6x - 4

or, 5 + 4 = 6x - 3x

or, 9 = 3x

or, 9/3 = x

or, 3 = x

The value of x is 3.

By putting the value of x in GD or GF, we get

GD = 3(3) + 5 = 9 + 5 = 14

GF = 6(3) - 4 = 18 - 4 = 14

Therefore, GE = 14.

Answer:

A) 24 ( 4*6)

B) 15 ( 75%of 80 is 60...

60÷4 is 15)

Answer:

The answer is 30%

Step-by-step explanation:

4 times 6=24

24 divided by 80 times 100 is 30

(That's also how to find your percentage on a test)

Given:

A figure.

To find:

Whether the pair of angle 3 and angle 5 is adjacent, vertical, or neither.

Solution:

Adjacent angle: If two angles are adjacent to each other, it means they have a common vertex, one common side and they are not overlapping each other, then they are called adjacent angles.

Vertical angles: If two lines intersect each other then the opposite angles are known an vertical angles.

From the given figure it is clear that the angle 3 and angle 5 are neither adjacent nor vertical angles.

Therefore, the correct option is B.

Step-by-step explanation:

7equitacion h< y ⚽ de los siguientes dominios

Answer:

0.785 mile²

Step-by-step explanation:

First, find the area of the whole circle.  Then take 1/4 of that area:

A = πr² becomes A = 3.14(1 mile)²  = 3.14 mile²

1/4 of this result is 0.785 mile²

Answer:

140%

Step-by-step explanation:

Answer:

54

Step-by-step explanation:

1 inch is equal to 3 miles so if there's 18 inches, it's 18*3

Answer:

This is the answer:

=20

Answer:

1). All four triangles are right-angled.

3.) All four triangles are congruent.

4) Area of a rhombus = 4 x area of one triangle.

Step-by-step explanation:

If a rhombus is cut into four triangles using diagonals, the three statements that would apply to any rhombus would be that 'all those four triangles would be right-angled,' 'the triangles would be congruent to one another,' and 'area of one triangle * 4 would be equal to the area of the rhombus.'

As we know, the diagonals bisect one another in a rhombus at 90° and the angles opposite to one another are equal. This proves that all four triangles constructed through the diagonals would be ≅ through SSS congruency and perpendicular to one another because the corresponding edges of the congruent triangles are also ≅ . Since the rhombus is divided into four equal parts, the area of one triangle into four would be equals to the area of the rhombus. Thus, options 1, 3, and 4 are the correct answers.

Answer: -1

Step-by-step explanation:

Answer:

Base, b = 4.5 yards

Step-by-step explanation:

Given the following data;

Area of triangle = 45 square yards

Height = 20 yards

To find the base of the triangle;

Mathematically, the area of a triangle is given by the formula;

Area of triangle = ½ * b * h

Where;

b is the base of the triangle.

h is the height of the triangle.

45 = ½ * b * 20

90 = 20b

Base, b = 90/20

Base, b = 4.5 yards

Answer:

6+8

Step-by-step explanation:

Answer:

8=2x+8

8-8=2x

0=2x

0/2=x

0=x

Step-by-step explanation:

Hope it helps u!!

Answer:

The rate at which the tip of his shadow is moving down is [tex]\frac{24}{15} ft/sec[/tex]

Step-by-step explanation:

Given - A flood lamp is installed on the ground 200 feet from a vertical wall. A six-foot-tall man is walking towards the wall at the rate of 30 feet per second.

To find - How fast is the tip of his shadow moving down the wall when he is 50 feet from the wall ?

Proof -

From the given information, the figure becomes

Triangle ABC and Triangle DBE are similar triangle

AC/DE = BC/BE

⇒h/6 = 200/(200-x)

⇒h = 1200/(200 -x)

Now,

Differentiate h with respect to t, we get

[tex]\frac{dh}{dt} = 1200(-\frac{1}{(200-x)^{2} } )(-1)\frac{dx}{dt}[/tex]

⇒[tex]\frac{dh}{dt} = (\frac{1200}{(200-x)^{2} } )\frac{dx}{dt}[/tex]

Now,

If the rate of the tip is moving down the wall

At x = 50 feet, dx/dt = 30 feet per second

So,

⇒[tex]\frac{dh}{dt} = (\frac{1200}{(200-50)^{2} } )(30)[/tex]

⇒[tex]\frac{dh}{dt} = \frac{1200}{(150)^{2} } (30)[/tex]

⇒[tex]\frac{dh}{dt} = \frac{1200}{(150)(150) } (30)[/tex]

⇒[tex]\frac{dh}{dt} = \frac{24}{15 }[/tex]

So, we get

The rate at which the tip of his shadow is moving down is [tex]\frac{24}{15} ft/sec[/tex]

When you have a variable in an equation, you have to isolate it on one side. To do this, look for any other numbers and if they are added, multiplied, divided, or subtracted from x.

Next, you take that number and do the opposite of its operation to the other side.

In this example, you have x/5=20

So we first identify that x is being divided by 5

Then we take 5, and do the opposite of division to 20.

So x/5=20  turns into x = 5x20

Then we simplify, x = 100.

If your not sure your answer is write, you can always put the value of x back into the first equation and solve to see if its true:

X/5=20

100/5=20

20=20

Answer:cant seeStep-by-step explanation:

Answer:

[tex]Sales \ Tax \ Amount = Net \ Price \cdot \frac{Sales \ Tax \ percentage}{100}[/tex]

[tex]21.70 = 331.70 \cdot \frac{sales\ tax \ percentage}{100} \\\\\frac{21.70}{331.70} = \frac{sales\ tax \ percentage}{100}\\\\0.0654 = \frac{sales\ tax \ percentage}{100}[/tex]

Sales Tax Percentage  = 0.0654 × 100 = 6.54%

Answer:

Goodness of fit

Step-by-step explanation:

Given

The theoretical probabilities

See comment for complete question

Required

The type of test to be use

From the question, we understand that you are to test if the die is loaded or not using the given theoretical probabilities.

This test can be carried out using goodness of fit test because the goodness of fit is basically used to check the possibility of getting the outcome variable from a distribution. In this case, the outcome of the variables are the given theoretical probabilities.

In a nutshell, the goodness fit of test determines if the given data (in this case, the theoretical probabilities) is a reflection of what to expect in the original population.

Answer:

If cookies are for $1 and brownies are for $2, let number of cookies = x and number of brownies = y

∴ $1*(x*1) + $2*(y*1) = $13

Step-by-step explanation:

1) You can buy 4 brownies for $2 each = 2*4 = $8

The rest you can buy cookies = 5 cookies = $5

$8+$5=$13

2) You can buy 5 brownies and 3 cookies = $10+$3 = $13

3) You can buy 3 brownies and 7 cookies = $6+$7=$13

Equation: -

If cookies are for $1 and brownies are for $2, let number of cookies = x and number of brownies = y

∴ $1*(x*1) + $2*(y*1) = $13

9514 1404 393

Answer:

  {587, 1}

Step-by-step explanation:

The sum will be minimized when the second number is as close to zero as is allowed. If the numbers must be positive integers, the sum is minimized when the numbers are {587, 1}.

If the numbers may be real numbers, then the values that minimize the sum are {588-, 0+}

_____

The "cost" of taking a unit from the sum 588 and assigning it to the second number is that the sum of first and 3 times the second goes up by 3. In order to minimize that sum, the second number must be minimized.

№3

[tex]\sin C = \frac{AB}{AC} = \frac{27}{45} = \frac{3 * 9}{5 * 9} = \frac{3}{5}[/tex]

Answer: D (3/5).

№4

[tex]\cos A = \frac{AB}{AC} = \frac{24}{30} = \frac{3 * 4 * 2}{3 * 5 * 2} = \frac{4}{5}[/tex]

Answer: C (4/5).

№5

[tex]\tan C = \frac{AB}{BC} = \frac{32}{24} = \frac{2 * 2 * 2 * 4}{2 * 2 * 2 * 3} = \frac{4}{3}[/tex]

Answer: D (4/3).

Answer:

3.) Sin C = option D, [tex]\frac{3}{5}[/tex]

4.) Cos A = option C, [tex]\frac{4}{5}[/tex]

5.) Tan C = Option D, [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

3.) Sin C = [tex]\frac{opposite}{hypotenuse} = \frac{27}{45} = \frac{3}{5}[/tex]

4.) Cos A = [tex]\frac{adjacent}{hypotenuse} = \frac{24}{30} = \frac{4}{5}[/tex]

5.) Tan C = [tex]\frac{opposite}{adjacent} = \frac{32}{24} = \frac{4}{3}[/tex]

Hope this helps!

Answer:

$57.60

Step-by-step explanation:

40% of $96.00 is $38.40

$96.00 - $38.40 = $57.60

Answer:

60°

Step-by-step explanation:

If it a equilateral triangle

Answer:

49

Step-by-step explanation:

the number would simply be

14÷2=7

7²=49

9514 1404 393

Answer:

  (b)  28

Step-by-step explanation:

The total of the 3 numbers will be 3×15 = 45. Then the third number is ...

  45 -7 -10 = 28

Answer:

[tex]\boxed{\pink{\tt I = \dfrac{1}{3}sin(3x) - 3cos(x) + C}}[/tex]

Step-by-step explanation:

We need to integrate the given expression. Let I be the answer .

[tex]\implies\displaystyle\sf I = \int (cos(3x) + 3sin(x) )dx \\\\\implies\displaystyle I = \int cos(3x) + \int sin(x)\ dx [/tex]

[tex]\implies\displaystyle\sf I = \int cos\ u \dfrac{1}{3}du + \int 3sin \ x \ dx \\\\\implies\displaystyle \sf I = \int \dfrac{cos\ u}{3} du + \int 3sin\ x \ dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3}\int \dfrac{cos(u)}{3} + \int 3sin(x) dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3} sin(u) + C +\int 3sin(x) dx \\\\\implies\displaystyle \sf I = \dfrac{1}{3}sin(u) + C + 3\int sin(x) \ dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3}sin(u) + C + 3(-cos(x)+C) \\\\\implies \underset{\blue{\sf Required\ Answer }}{\underbrace{\boxed{\boxed{\displaystyle\red{\sf I = \dfrac{1}{3}sin(3x) - 3cos(x) + C }}}}}[/tex]