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Dimas [21]
3 years ago
14

Trevor solved the system of equations below. What mistake did he make in his work? 2x + y = 5 x − 2y = 10 y = 5 − 2x x − 2(5 − 2

x) = 10 x − 10 + 4x = 10 5x − 10 = 10 5x = 0 x = 0 2(0) + y = 5 y = 5 He should have substituted 5 + 2x He combined like terms incorrectly, it should have been 4x instead of 5x He subtracted 10 from the right side instead of adding 10 to the right side He made no mistake
Mathematics
1 answer:
patriot [66]3 years ago
6 0
The correct answer is "He did not distribute correctly". The correct incomplete-worked expression is x - 10 + 4x = 10

I hope this helps!
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18 points - Qu. If 16 whole numbers factor into 120. You will see how 32 whole numbers factor into 1200 what does the same princ
alexandr402 [8]

Explanation:

<em>Your premise and conclusion are both incorrect</em>.

120 has the prime factorization ...

  120 = 2³ × 3 × 5

The exponents of the prime factors are {3, 1, 1}. The number of divisors of 120 is the product of the increments of these numbers: (3+1)(1+1)(1+1) = 4·2·2 = 16.

120 has 16 natural-number divisors

__

1200 has the same prime factor and two more: 2·5, so the factorization is ...

  1200 = 2⁴ × 3 × 5²

These exponents are {4, 1, 2} and the product of their increments is 5·2·3 = 30.

1200 has 30 natural-number divisors.

__

When a number is multiplied by 2, its number of natural-number divisors will be (n+1)/n times the previous number of divisors, where n is the increment of the exponent of 2 that is a factor of the original number.

For 120, 2^3 is the power of 2 that is a factor. So, multiplying the number by 2 multiplies the number of divisors by (4+1)/4 = 5/4.

240 will have 20 divisors versus the 16 that 120 has.

Likewise, multiplying this number (240) by 5 will multiply its number of divisors by (2+1)/(1+1) = 3/2, where 1 is the power of 5 that is a factor of 240.

1200 will have 20(3/2) = 30 divisors, versus the 20 that 240 has, or the 16 that 120 has.

__

<em>Summary</em>

The number of divisors of an integer is the product of the increments of the exponents of its prime factors.

_____

<em>For reference</em>

Here are the divisors of 120:

  1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

Here are the divisors of 240:

  1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240

Here are the divisors of 1200:

  1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200

7 0
3 years ago
The graphs below have the same shape. What is the equation of the blue graph?
postnew [5]

Answer:

<h2>C. G(x) = (x - 1)² - 3</h2>

Step-by-step explanation:

f(x) + n - shift the graph of f(x) n units up

f(x) - n - shift the graph of f(x) n units down

f(x - n) - shift the graph of f(x) n units to the right

f(x + n) - shift the graph of f(x) n units to the left

===================================

Look at the picture.

The graph of F(x) shifted 1 unit to the right and 3 units down.

Therefore the equation of the function G(x) is

G(x)=(x-1)^2-3

4 0
3 years ago
Solve triangle ABC if AB=24.6, BC=29.7, and CA=30
PtichkaEL [24]
Triangle ABC equals 84.3
8 0
3 years ago
A box of marbles can be shared equally among 6,7,or 8 students with 4 marbles left over each time.what is the least possible num
elena-s [515]

168 is the least common multiple of 6,7,and 8


8 0
3 years ago
a certain shark has triangular teeth with a height that is 1 centimeter shorter than the base. if the area of one tooth is 1 squ
Advocard [28]

The Shark's teeth has a base of 2 cm and height of 1 cm.

Step-by-step explanation:

Step 1 :

Given,

the area of the shark's triangular teeth = 1 sq cm

Let b be the base and h be the height of the shark's triangular teeth.

We have the teeth's height is 1 cm short than the base

So  h = b - 1

Step 2 :

Area of Triangle  = (\frac{1}{2}) × b × h = 1

Substituting h = b -1

(\frac{1}{2}) × b × (b-1) = 1

=> b² - b = 2 = > b²-b-2 = 1

Solving for b we have

(b-2)(b+1) = 0

b = 2 or b = -1

Since b is the base , we take the positive value as length/distance cannot be negative.

So b = 2

h = b - 1 = 2 - 1 = 1

h = 1

Step 3 :

Answer :

The Shark's teeth has a base of 2 cm and height of 1 cm.

6 0
3 years ago
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