(a) state the value of cos(30°)<br> (b) state the value of sin(30°)

Given collinear points E, F and G such that point F is the midpoint of segment EG. Find the new length of EG given that EF =5x+9

Veseljchak [2.6K]

Answer:

The length of EG is 58 units

Step-by-step explanation:

The midpoint of a segment divides it into two equal part

Let us use this rule to solve our question

∵ E, F, and G are collinear points

∵ Point F is the midpoint of segment EG

→ That means F divides EG into 2 equal segments EF and FG

∴ EF = FG

∵ EF = 5x + 9

∵ FG = 3x + 17

→ Equate them

∴ 5x + 9 = 3x + 17

→ Subtract 3x from both sides

∵ 5x - 3x + 9 = 3x - 3x + 17

∴ 2x + 9 = 17

→ Subtract 9 from both sides

∴ 2x + 9 - 9 = 17 - 9

∴ 2x = 8

→ Divide both sides by 2 to find x

∵ $\frac{2x}{2}=\frac{8}{2}$

∴ x = 4

→ Substitute x by 4 in EF and FG to find their lengths

∵ EF = 5(4) + 9 = 20 + 9 = 29

∵ FG = 3(4) + 17 = 12 = 17 = 29

∵ EG = EF + FG

∴ EG = 29 + 29 = 58

∴ The length of EG is 58 units

6 0

2 years ago

What’s the mean of 18 23 10 39 22 17 16 15

prohojiy [21]

It would be 20
To get this answer you would add up all the answer then divide it by how many numbers there are
18+23+10+39+22+17+16+15= 160
160/8 = 20

6 0

2 years ago

In a school there are 600 teachers ad 1200 students

8_murik_8 [283]

Answer:

Can you please give a clearer explanation of what is your question?

Step-by-step explanation:

8 0

3 years ago

Write 3x^2-18x-6 in vertex form

Vedmedyk [2.9K]

The standard form of a quadratic equation is $\displaystyle{ y=ax^2+bx+c$ , while the vertex form is:

$y=a(x-h)^2+k$ , where (h, k) is the vertex of the parabola.

What we want is to write $\displaystyle{ y=3x^2-18x-6$ as $y=a(x-h)^2+k$

First, we note that all the three terms have a factor of 3, so we factorize it and write:

$\displaystyle{ y=3(x^2-6x-2)$ .

Second, we notice that $x^2-6x$ are the terms produced by $(x-3)^2=x^2-6x+9$ , without the 9. So we can write:

$x^2-6x=(x-3)^2-9$ , and substituting in $\displaystyle{ y=3(x^2-6x-2)$ we have:

$\displaystyle{ y=3(x^2-6x-2)=3[(x-3)^2-9-2]=3[(x-3)^2-11]$ .

Finally, distributing 3 over the two terms in the brackets we have:

$y=3[x-3]^2-33$ .

Answer: $y=3(x-3)^2-33$

6 0

3 years ago

Find the surface area of the cylinder use 3.14 for pi

elena55 [62]

Answer:

351.658 square in

Step-by-step explanation:

First find the circumference of the circle

C = 25.13

Find area of the circle

A = 50.27

Multiply the circumference by the height

25.13 × 10 = 251.3

Add 251.3 with 50.27 twice

251.13 + 50.27 + 50.27 ≈ 351.658

Therefore your answer is D) 351.658 square in

8 0

2 years ago

(a) state the value of cos(30°) (b) state the value of sin(30°)