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Helga [31]
4 years ago
11

Prove that: 25^9+5^17 is divisible by 30

Mathematics
1 answer:
diamong [38]4 years ago
7 0

25^9+5^17=

=2^18 +5^17

=5^17(5+1)

=5^17· 6

=5^16 ·30  is divisible by 30

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I need help with geometry.
Dahasolnce [82]
1.

In any trapezoid, the length of the midsegment is \frac{|base_1|+|base_2|}{2}

substituting the known values:

\frac{24+|base_2|}{2}=19

24+|base_2|=38

|base_2|=38-24=14

2.

Notice that since D and have the same y-coordinate, then DE is horizontal, and since F and D have the same x-coordinate, FD is vertical.

Thus FD and DE are perpendicular, so the triangle FED is a right triangle.

The median drawn from the right angle, is equal to half the hypotenuse.

That is, |DO|=1/2 |FE|, thus |OE|=|OF|=|OD|, are all radii of the circle centered at O.

O is the midpoint of EF, and is found by the Midpoint formula:

O=( \frac{1+7}{2} , \frac{5+1}{2} )=(4, 3)


Answer:

1. 14

2. (4, 3)

4 0
3 years ago
Sarah Kelly deposits four checks for $901.20, $3760.26, $655.79, and $252.00. Her cash consists of 30 one-dollar bills, 2 two-do
Olenka [21]

Answer:

जोडका लिखो

अवनेशवरी देवी

7 0
2 years ago
Brandy's Candies sells 250 types of candy, and 30% of them are lollipops. How many types of candy are lollipops?
Bas_tet [7]

Answer:

75

Step-by-step explanation:

When you have 100% of something, it's all of that one thing, right? So if you were to turn 100% into a decimal, it would be 1. This means you can divide any percentage by 100 to turn it into a decimal. So, 30%=.3. When you multiply something by 2, you get two of that thing, right? And just the same, when you multiply something by half, you get half of that thing. This means you can multiply 250 by .3 to get .3 of it, or, 30%.

250*.3=75

3 0
3 years ago
Applying properties of Exponents in exercise,use the properties of exponents to simplify the expression.See example 1.
evablogger [386]

Answer: a) 15625, b) 0.2, c) 625, d) 0.008.

Step-by-step explanation:

Since we have given that

a) (5^2)(5^3)

As we know that

a^m\times a^n=a^{m+n}

So, it becomes,

5^2\times 5^3=5^{2+3}=5^6=15625

(b) (5^2)(5^{-3})

So, it becomes,

5^2\times 5^{-3}=5^{2-3}=5^{-1}=\dfrac{1}{5}=0.2

(c) (5^2)^2

As we know that

(a^m)^n=a^{mn}

So, it becomes,

5^{2\times 2}=5^4=625

(d) 5^{-3}

a^{-m}=\dfrac{1}{a^m}\\\\5^{-3}=\dfrac{1}{5^3}=\dfrac{1}{125}=0.008

Hence, a) 15625, b) 0.2, c) 625, d) 0.008.

4 0
3 years ago
Use the unique factorization theorem to write the integer in standard factored form.<br><br> 1.5400
mash [69]

Answer:

Standard factor form of the integer : 15400 = 2³ × 5² × 7 × 11

Step-by-step explanation:

According to the unique factorization theorem, a given integer n (where, n>1), either is a prime number or can be represented as the product of the prime numbers.

Firstly, it is checked that the given integer is divisible by the smallest prime number 2 . If the integer is not divisible by 2, then the integer is checked for the next prime number 3 and then checked for 5 and so on until the remaining integers are prime numbers.

So, the standard factored form of the integer:

15400 = 2 × 770

15400 = 2 × 2 × 3850

15400 = 2 × 2 × 2 × 1925

15400 = 2 × 2 × 2 × 5 × 385

15400 = 2 × 2 × 2 × 5 × 5 × 77

15400 = 2 × 2 × 2 × 5 × 5 × 7 × 11

or,

15400 = 2³ × 5² × 7 × 11

Therefore, the standard factor form of the integer: 15400 = 2³ × 5² × 7 ×11

6 0
4 years ago
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