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3 years ago

In the diagram, GB = 2x + 3.. What is GB?

Mathematics

1 answer:

tia_tia [17]3 years ago

6 0

Answer:

GB = 15

Step-by-step explanation:

DC, EB and FA are the medians of the triangle.

The point G where the medians intersect is the centroid.

On each median the distance from the vertex to the centroid is twice as long as the distance from the centroid to the midpoint, hence

FG = 2GA, that is

5x = 2(x + 9)

5x = 2x + 18 ( subtract 2x from both sides )

3x = 18 ( divide both sides by 3 )

x = 6

Hence

GB = 2x + 3 = (2 × 6) + 3 = 12 + 3 = 15

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A bike ramp is shown in the figure. What is theta, the bike ramp's angle of elevation? Round your answer to the nearest degree.

AysviL [449]

Answer:

Ф = 14° ⇒ to the nearest degree

Step-by-step explanation:

* Lets revise the trigonometry functions

- Assume that we have a right triangle ABC

∵ m∠B = 90°

∴ AC is the hypotenuse ⇒ opposite to the right angle

∴ AB and BC are the legs of the right angles

- Let angle ACB called Ф

∵ sinФ = opposite/hypotenuse

∴ sinФ = AB/AC

∵ cosФ = adjacent/hypotenuse

∴ cosФ = BC/AC

∵ tanФ = opposite/adjacent

∴ tanФ = AB/BC

* Now lets solve the problem

- We will consider the bike ramp is the ΔABC

∵ AB = 1.5 feet

∵ ∠ACB is Ф

∵ The length of the ramp is the hypotenuse

∴ AC = 6 feet

- W have the length of the opposite to Ф and the hypotenuse

∴ We will chose the sin function

∵ sinФ = AB/AC

∴ sinФ = 1.5/6 ⇒ use the inverse of sin to find Ф

∴ Ф = sin^-1 (1.5/6) = 14.47 ≅ 14° ⇒ to the nearest degree

3 0

3 years ago

Read 2 more answers

6x-y in a verbal expression

Zolol [24]

Answer:

six x minus y.

Step-by-step explanation:

In changing it to verbal expression, you are essentially changing all the signs into words. Write it like how you will say it.

8 0

3 years ago

Can someone please Help me?

Mila [183]

9514 1404 393

Answer:

see below

Step-by-step explanation:

It is easiest to compare the equations when they are written in the same form.

The first set can be written in slope-intercept form.

y = 2x +7

y = 2x +7 . . . . add 2x

These equations are identical, so have infinitely many solutions.

The second set can be written in standard form.

y +4x = -5

y +4x = -10

These equations differ only in their constant, so have no solutions.

The third set is already written in slope-intercept form. The equations have different slopes, so have exactly one solution.

5 0

3 years ago

How do you determine whether a sum will be positive, negative, or 0 when adding a positive and a negative integer?

professor190 [17]

If the integers have the same absolute value ... they're the same number
but with different signs ... then their sum is zero.

Example: (plus) 927 added to (negative) 927 = zero

If the integers have different absolute values ... they're different numbers with different
signs ... then their sum has the same sign as the one with the bigger absolute value.

Examples:

==> (plus) 92 added to (negative) 91
   92 and 91 are 1 number apart on the number line.
   The positive number is bigger than the negative number.
   So the sum is +1 .

==> (plus) 35 added to (negative) 37
      35 and 37 are 2 numbers apart on the number line.
      The negative number is bigger than the positive one.
So the sum is -2 .

3 0

3 years ago

1. The Senior Class of Great Ridge High School and Ann Arbor High School are planning a trip to Six Flags Theme Park. Great Ridg

Zanzabum

Answer:

A)14v + 16b = 1152

10v + 13b = 925

B)Number of students in a van = 8

Number of students in each bus = 65

C) Elimination method was easier.

Step-by-step explanation:

Let v be the number of students in a van

Let b be number of students in a bus

A) We are told the first school can fill 14 vans and 16 buses with 1152 students

Thus;

14v + 16b = 1152 - - - - - (eq 1)

Also,we are told that the second school can fill 10 vans and 13 buses with 925 students.

Thus;

10v + 13b = 925 - - - - (eq 2)

B) To solve this we will use elimination method.

Multiply eq (1) by 5 and multiply eq (2) by 7 to give;

70v + 80b = 5760 - - - - eq(3)

70v + 91b = 6475 - - - - - eq(4)

Subtract eq(3) from eq(4) to give;

91b - 80b = 6475 - 5760

11b = 715

b = 715/11

b = 65

Put 65 for b in eq(3) to give;

70v + 80(65) = 5760

70v = 5760 - 80(65)

70v = 560

v = 560/70

v = 8

Number of students in a van = 8

Number of students in each bus = 65

C) Elimination method was used because in both equations, we had different digits attached and so it would have been more tedious to use substitution method or graphical method. Thus, elimination method was more easier.

7 0

3 years ago