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ankoles [38]
3 years ago
6

A rectangle has an area of 100 square centimeters. The base of the rectangle is 25 centimeters.

Mathematics
2 answers:
Fed [463]3 years ago
6 0

Answer:

The height of the rectangle is 4 cm.

Step-by-step explanation:

You find area by multiplying base and height.

The formula is  A=bh

so 100=25h

25 times 4 is 100

100=25*4

4cm is your answer

Lena [83]3 years ago
6 0
The height of the rectangle is 4 cm.
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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
2 years ago
Read 2 more answers
Need help ASAP! Giving Brainliest!
allsm [11]

ok thats cool ig what do you need help with

4 0
2 years ago
Read 2 more answers
Find the area of the figure. If needed, round to the nearest tenth.
Umnica [9.8K]

Answer:

18 \:ft^2

Step-by-step explanation:

The area of a trapezoid.

(a+b)h\frac{1}{2}

(8+4)3 \times \frac{1}{2}

(12)3 \times \frac{1}{2}

36 \times \frac{1}{2}

=18

6 0
3 years ago
P=-30h+74 The variable h represents the number of hours he has spent reading, the variable p represents the number of pages left
olchik [2.2K]

Answer: Ethan will have to spend 2 hours reading if 14 pages are left to read

Step-by-step explanation:

Given the equation

P=-30h+74

where p =number of pages left to read and

h= the number of hours he has spent reading

Therefore , if Ethan has 14 pages left to read, then the number of hours Ethan will have to read will be

P=-30h+74

14= -30h + 74

30h= 74-14

30h= 60

h = 60/30

h =2 hours

Ethan will have to spend 2 hours reading if 14 pages are left to read

6 0
2 years ago
Create an equivalent system of equations using the sum of the system and the first equation. x + 4y = 8 4x + y = 2
qaws [65]

Answer:

Equivalent systems of equations review

Step-by-step explanation:

We're given two systems of equations and asked if they're equivalent.

x + 4y = 8 (1)

4x + y = 2 (2)

Interestingly, if we sum the equations in System A, we get:

x + 4y = 8 \\4x + y = 2 \\

5x+5y=10

Replacing the first equation in System A with this new equation, we get a system that's equivalent to System A:

5x+5y=10

4x + y = 2

This is System B, which means that System A is equivalent to System B.

5 0
3 years ago
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