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maksim [4K]
2 years ago
6

1-4) What is the point of intersection?

Mathematics
1 answer:
Irina18 [472]2 years ago
3 0

Answer:

Step-by-step explanation:

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SOLVE THE EQUATION<br> −9(x + 6) + 60 = 13 − 10x
yuradex [85]

Answer:

x=7

Step-by-step explanation:

−9(x + 6) + 60 = 13 − 10x

Distribute

−9x -54 + 60 = 13 − 10x

Combine like terms

-9x +6 = 13 -10x

Add 10x to each side

-9x+10x +6 = 13-10x+10x

x +6 = 13

Subtract 6 from each side

x+6-6=13-6

x = 7

7 0
3 years ago
Points E, F, and D are on circle C, and angle G measures 60°. The measure of arc EF equals the measure of arc FD.
galben [10]

Answer:

∠EFD ≅ ∠EGD ⇒ A

Arc ED ≅ arc FD ⇒ C

m arc FD = 120° ⇒ E

Step-by-step explanation:

Let us revise some facts

  1. Equal chords subtended equal arcs
  2. The measure of an inscribed angle is one-half the measure of the central angle which subtended by the same arc
  3. The measure of a central angle is equal to the measure of its subtended arc
  4. If one angle of an isosceles triangle measure 60° then the triangle is equilateral
  5. The sum of the measures of the interior angles of any quadrilateral is 360°

In the quadrilateral  CDGE

∵ m∠G = 60°

∵ m∠GDC = m∠GEC = 90°

- By using the 5th rule above

∴ m∠G + m∠GDC + m∠DCE + m∠GEC = 360°

∴ 60 + 90 + m∠DCE + 90 = 360

∴ 240 + m∠DCE = 360

- Subtract 240 from both sides

∵ m∠DCE = 120°

In circle C

∵ ∠DCE is a central angle subtended by arc DE

∵ ∠DFE is an inscribed angle subtended by arc DE

- By using the 2nd rule above

∴ m∠DFE = \frac{1}{2} m∠∠DCE

∵ m∠DCE = 120°

∴ m∠DFE = \frac{1}{2} (120)

∴ m∠DFE = 60°

- That means ∠EFD ≅ ∠EGD because their measure is 60°

∴ ∠EFD ≅ ∠EGD

In Δ EFD

∵ EF = FD

∵ m∠DFE = 60°

- By using the 4th rule above

∴ Δ EFD is an equilateral triangle

∴ ED = FD = FE

In circle C

∵ Side ED subtended by arc ED

∵ Side FD subtended by FD

∵ Side ED ≅ side FD ⇒ proved

- By using the 1st rule above

∴ Arc ED ≅ arc FD

∵ m∠ECD = 120°

∵ ∠ECD is a central angle subtended by arc ED

- By using the 3rd rule above

∴ m∠ECD = m arc ED

∴ m of arc ED = 120°

∵ Arc ED ≅ arc FD

∴ m arc ED = m arc FD

∴ m arc FD = 120°

5 0
3 years ago
Read 2 more answers
The sum of the ages of Mr Lin and his son Ethan is 38 years. In three years' time, Mr Lin will be three times as old as his son.
Sati [7]

Answer:

Mr.Lin's present age is 30 years now. His son is 8 years old now.

Step-by-step explanation:

Let L = Mr.Lin's present age,

   S = his son's present age.

First equation  is

L + S = 38.       (1)

The second equation is  

L + 3 = 3*(S+3)   (2)   ("In three years' time, Mr.Lin will be three times as old as his son.")

From (1), express S = 38-L and substitute it into (2). You  will get

L + 3 = 3*((38-L)+3),   or

L + 3 = 114 - 3L + 9,

4L = 114 + 9 - 3,  

4L = 120,

L = 30.

8 0
3 years ago
What slope would a line have to be perpendicular to a line with a slope of 1/4 ?
denpristay [2]

Answer:

A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line. The negative reciprocal of the original line is –2, and is thus the slope of its perpendicular line.

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
What is the equation of the line passing through the points (3,6) and (2,10)
andrezito [222]

Answer: y= - 4x+18

Step-by-step explanation:

Equation: y=mx+b

***remember: b is the y-intercept and m is the slope.

m=\frac{y2-y1}{x2-x1}

3= x1

2= x2

6= y1

10=y2

m=\frac{10-6}{2-3}= \frac{4}{1}= -4

m=-4

Now we have y=-4x+b , so let's find b.

You can use either (x,y) such as (3,6) or (2,10) point you want..the answer will be the same:

   (3,6). y=mx+b or 6=-4 × 3+b, or solving for b: b=6-(-4)(3). b=18.

   (2,10). y=mx+b or 10=-4 × 2+b, or solving for b: b=10-(-4)(2). b=18.

Equation of the line: y=-4x+18

3 0
3 years ago
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