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jeka94
2 years ago
7

Write each of the following numerals in base 10. For base twelve, T and E represent the face values ten and eleven, respectively

.
a. 421 five
b. 11101 two
c. 13Ttwelve
Mathematics
1 answer:
uysha [10]2 years ago
7 0

(a)

421₅ = 4×5² + 2×5¹ + 1×5⁰

… = 100 + 10 + 1

… = 111

(b)

11101₂ = 1×2⁴ + 1×2³ + 1×2² + 0×2¹ + 1×2⁰

… = 16 + 8 + 4 + 0 + 1

… = 29

(c)

13T₁₂ = 1×12² + 3×12¹ + 10×12⁰

… = 144 + 36 + 10

… = 190

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What is the measure of E
Verizon [17]

Answer:

The measure of angle E is:

m∠E = 80°

Step-by-step explanation:

Given

The triangle ΔDEF

It is stated that DE=EF and G is the midpoint of EF.

It means the midpoint G has converted the triangle into two equal right-angles triangles ΔDEG and ΔDFG with the right-angle at G.

Given

m∠GDE = 10°

As the right-angle triangle, ΔDEG lies at the right-angle G.

So, m∠DGE = 90°

as

m∠GDE = 10°

m∠DGE = 90°

m∠E = ?

We know that the sum of angles of a triangle is 180°.

m∠GDE + m∠DGE  + m∠E = 180°

10° + 90° + m∠E = 180°

100 + m∠E = 180°

m∠E = 180° - 100

m∠E = 80°

Therefore,

The measure of angle E is: m∠E = 80°

3 0
3 years ago
How many different license plates are possible if a license plate consists of 2 capital letters followed by 5 digits?
Alina [70]

The first letter can be any one of 26 letters.  For each one . . .
The second letter can be any one of 26 letters.  For each one . . .

The first digit can be any one of 10 digits.  For each one . . .
The second digit can be any one of 10 digits.  For each one . . .
The third digit can be any one of 10 digits.  For each one . . .
The fourth digit can be any one of 10 digits.  For each one . . .
The fifth digit can be any one of 10 digits.

The total number of possibilities is

                   (26 x 26 x 10 x 10 x 10 x 10 x 10) =

                   ( 26² x 10⁵) = (676 x 100,000) = <em>67,600,000</em> .


6 0
3 years ago
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Please help me somebody! &lt;3
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8 0
3 years ago
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There is a fire in the third floor of a building, 22 feet above the ground. The fire truck has a 16-foot tall ladder on top, and
Over [174]

Answer: Yes the ladder will reach the fire

Step-by-step explanation: Please refer to the attached diagram for details.

The fire is at point A, while the top of the truck is at point C. The fire is actually burning at 22 feet off the ground, but because the fire truck itself is already 6 feet off the ground, the point that would serve as the base of the building would be 16 feet from the third floor (which is 22 feet minus 6 feet). Hence, point A to point B is 16 feet. So we need to calculate if line AC (from the truck to the fire at the third floor, labeled as b) shall equal the length of the ladder which is 16-foot long.

The angle of the ladder with the top of the truck is 75 degrees. Therefore,

Sin 75 = opposite/hypotenuse

Sin 75 = 16/b

By cross multiplication we now have

b = 16/Sin 75

b = 16/0.9659

b = 16.56

If the distance from A to C is 16.56 feet, then the 16-foot long ladder would reach the fire.

8 0
3 years ago
Solve for x.<br> (7x - 1)•<br> (6x - 1)•
leonid [27]

Answer:

42x^2 - 7x - 6x + 1

42x^2 - 13x + 1 for FOIL method

To solve for x

7x - 1 = 0

7x = 1

x = 1/7

6x - 1 = 0

6x = 1

x = 1/6

Step-by-step explanation:

4 0
3 years ago
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