please help with geometry homework

9514 1404 393

Answer:

  b.  A × B = GCF(A, B) × LCM(A, B)

  c. 15 = GCF × LCM / 20

Step-by-step explanation:

b. The products of the numbers in the table are 80, 108, 216, 45.

The products of the corresponding GCF and LCM are 80, 108, 216, 45.

Conjecture: the product of the numbers is equal to the product of the GCF and LCM.

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c. GCF×LCM = 5×60 = 300 = A×B = 20×B

  B = 300/20 = 15

The other number is 15, found by using the conjecture of part b.

_____

If you think for a minute about what the GCF and LCM are, you realize the relationship discussed in this problem must be the case. Consider the factors of two numbers A and B:

  A = (factors in common with B) × (factors unique to A)

  B = (factors in common with A) × (factors unique to B)

The GCF, by definition, are (factors in common between A and B).

The LCM, by definition, is the product of unique factors:

  (common factors) × (factors unique to A) × (factors unique to B)

__

Then the product of the LCM and the GCF is ...

  GCF × LCM =

  (factors in common) × ((factors in common) × (unique to A) × (unique to B))

Using the associative and commutative properties of multiplication, we can rearrange this product to be ...

  ((factors in common)×(unique to A)) × ((factors in common)×(unique to B))

  = A × B

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Personally, I use a kind of diagram to represent the factorization of A and B and their LCM and GCF:

  [unique to A (common] unique to B)

Then A = factors in [ ], and B = factors in ( ). The stuff in (common] is the GCF, and the overall product is the LCM.

Using the example of part c, this would look like [4 (5] 3), so A = 4·5 = 20 and B = 5·3 = 15. The GCF is 5, and the LCM is 4·5·3 = 60.

The end parts [unique to A( and ]unique to B) can have no common factors. Any common factors must reside in the (common] part.

[tex] \frac{10}{ \sqrt{7} - \sqrt{2} } \\ = \frac{10}{ \sqrt{7} - \sqrt{2} } \times \frac{ \sqrt{7} + \sqrt{2} }{ \sqrt{7} + \sqrt{2} } \\ = \frac{10( \sqrt{7} + \sqrt{2}) }{( \sqrt{7} - \sqrt{2} )( \sqrt{7} + \sqrt{2} )} \\ = \frac{10 \sqrt{7} + 10 \sqrt{2} }{( { \sqrt{7} )}^{2} - ( \sqrt{2} ) ^{2} } \\ = \frac{10( \sqrt{7} + \sqrt{2} )}{7 - 2} \\ = \frac{10( \sqrt{7} + \sqrt{2} ) }{5} \\ = 2( \sqrt{7} + \sqrt{2} ) \\ = 2 \sqrt{7} + 2 \sqrt{2} [/tex]

[tex]\frac{10}{\sqrt{7} } -\sqrt{2} =\frac{10\sqrt{7} -7\sqrt{2} }{7}[/tex]

( Decimal: [tex]2.36543...[/tex])

Steps:

1: Convert element to fraction.

[tex]\sqrt{2} =\frac{\sqrt{2}\sqrt{7} }{\sqrt{7} }[/tex]

[tex]=\frac{10}{\sqrt{7} } -\frac{\sqrt{2} \sqrt{7} }{\sqrt{7} }[/tex]

2: Since denominator are equal, combine the fractions.

[tex]\frac{a}{c}[/tex] ± [tex]\frac{b}{c} =\frac{a+b}{c}[/tex]

[tex]=\frac{10-\sqrt{2} \sqrt{7} }{\sqrt{7} }[/tex]

-----------------------

[tex]\sqrt{2} \sqrt{7} =\sqrt{14}[/tex]

[tex]=\frac{10-\sqrt{14} }{\sqrt{7} }[/tex]

Rationalize [tex]\frac{10-\sqrt{14} }{\sqrt{7} }[/tex] : [tex]\frac{10\sqrt{7} -7\sqrt{2} }{7}[/tex]

[tex]=\frac{10\sqrt{7}-7\sqrt{2} }7}[/tex]

9514 1404 393

Answer:

  D.  3.844 × 10^8 kilometers

Step-by-step explanation:

To write the number in scientific notation, put a decimal point after the most significant digits and write the rest of the significant digits after that. Multiply the number by the power of 10 that tells how many digits are between the most significant digit and the decimal point.

Here, the number has 8 digits between the most-significant digit (3) and the decimal point. Any trailing zeros are assumed to be not significant when the number is written without a decimal point. So, the number is written ...

  3.844 × 10^8 km

Hello there! The formula for finding the circumference of a circle is

[tex]C=\pi d[/tex]

We are given that the radius is 3.

Don't worry! We can find the diameter. The diameter is 2 times the radius, so the diameter is 6 yards.

Now multiply π by 6:

C=18.8 yards

Hope this helps you! Please mark Brainliest if it does!

~Just a joyful teen

[tex]SilentNature[/tex]

Answer:

Domain: {0,1,2,4}

Range: {0, 1, 4, -6}

Step-by-step explanation:

Hi there!

The domain is the set of all x-values in a relation.

{(0,0),(1,1),(2,4),4,-6)}

The x-values are 0, 1, 2, and 4.

Domain: {0,1,2,4}

The range is the set of all y-values in a relation.

{(0,0),(1,1),(2,4),4,-6)}

The y-values are 0, 1, 4 and -6.

Range: {0, 1, 4, -6}

A function occurs when there is only one y-value for every x-value. This is the case for this relation, so therefore it is a function.

I hope this helps!

Answer:

B)

Step-by-step explanation:

9.7×10⁵= 970000

Hope this helped you- have a good day bro cya)

Answer:

43%

Step-by-step explanation:

mark me as brainliest please

Answer:

71 m................

area =length *width

5864=84*width

width=5864/84

hence width is 71m

Answer:

9/11

Step-by-step explanation:

f(X)=-9/X

f(a) =-9/-11

f(a)= 9/11

Answer:

1)

Angle 1: 59

Angle 2: 88

Angle 3: 147

2)x =21

Step-by-step explanation:

1)

Angle on a straight line add up to 180 degrees and angles in a triangle add to 180 degrees

2)

Opposite angles are equal. (4x) and (2x+42) are opposite therefore equal, so

4x=2x+42

Minus 2x from both sides

2x = 42

Find 1x by dividing 42 by 2, therefore

X=21

Answer:

B-the cost of each pair of shoes

Step-by-step explanation:

This is because each pair of shoes cost $25 dollars more than each suit (which is represented by x)

x + 25, represents the cost of each pair of shoes. Option B is correct.

Given that,
This month Peter purchased 50 suits for his store. He also needed to buy 35 pairs of shoes, which cost $25 dollars more than each suit. The expression shows Peter's total expenses for this month
50 (x) + 35 (x + 25) + 450, What x + 25 represents the equation is to e determined.

A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the quadratic equation, cubic equation, etc. ax+b is a polynomial.

Here,
Let x be the rate of each suit,
and the cost of the shoe is $25 dollars more than each suit. So,
50 (x) + 35 (x + 25) + 450
In the equation, x + 25  represent the cost of each pair of shoe.

Thus, x + 25, represents the cost of each pair of shoes. Option B is correct.

Learn more about polynomial function here:

https://brainly.com/question/12976257
#SPJ2

Answer:

567898765

Step-by-step explanation:

Answer:

Part A:  A) [tex]\frac{4y^{10}}{3w}[/tex]

Part B:

C) Quotient Rule of Powers (explained in Part A of this post).

D) Zero Exponent Rule (explained in Part A of this post, in solving for base z).

Step-by-step explanation:

[tex]\frac{28y^{15}w^{3} z^{7}}{21y^{5}w^{4} z^{7}}[/tex]

Use the Quotient Rule of Exponents:

[tex]\frac{a^{m}}{a^{n}} = a^{m-n}[/tex]

The 28 and 21 can be reduced by dividing both of them by 7.  For the exponential expressions with the same base, you could subtract their exponents.  I'll do each base separately so it doesn't get confusing.

[tex]\frac{28y^{15}w^{3} z^{7}}{21y^{5}w^{4} z^{7}}[/tex]

[tex]y^{15-5}[/tex] = [tex]y^{10}[/tex] (in the numerator).

[tex]w^{4-3}[/tex] = w (in the denominator. The "w" in the numerator cancels out).

[tex]z^{7-7}[/tex] = [tex]z^{0} = 1[/tex]  We used the Zero Exponent Rule here, were it states: [tex]a^{0} = 1[/tex]. (unnecessary to include in the final answer).

Altogether, you'll have:

Option A: [tex]\frac{4y^{10}}{3w}[/tex]

C) Quotient Rule of Powers (explained in Part A of this post).

D) Zero Exponent Rule (explained in Part A of this post, in solving for base z).

Answer:

104.364

Step-by-step explanation:

Product means multiplication so:

44.6×2.34 = 104.364

Answer:

1/8

Step-by-step explanation:

First convert 1/2 to eighths:

1/2 = 4/8

5/8-4/8= 1/8

Hope this helps! :)

The value of m in the fourth equation does not tend to zero, hence the function that has a maximum value of m, where m is a positive constant is[tex]f(x)=-(m+x)^2[/tex]: Option D is correct.  

For any function to have a maximum, the differential of the function must be equal to zero.

If the functions in options A and B and C are differentiated and equated to zero, the values of m in each function will tend to zero as well.

For the function [tex]f(x)=-(m+x)^2[/tex]

[tex]f'(x) = -2(m+x)\times 1\\f'(x)=-2(m+x)\\0 = m+x\\m = -x[/tex]

Since the value of m in the fourth equation does not tend to zero, hence the  function that has a maximum value of m, where m is a positive constant is[tex]f(x)=-(m+x)^2[/tex]  

Learn more here: https://brainly.com/question/12185438

Answer :

1 one, it's one hoped this help !

The HCF (Highest Common factor) also called the GCF (Greatest Common Factor) of two consecutive odd numbers is 1. Hope this helps!

~Just a joyful teen

[tex]GraceRosalia[/tex]

Answer:

A

Step-by-step explanation:

because > means more than the other number

Answer:

lol no34532534

Step-by-step explanation:

Answer:

option b

Step-by-step explanation:

have a great day

pls mark as brainliest

Answer:

B

Step-by-step explanation:

Answer:

b. 254.34

c. 3.33

that is the answer I suppose

Answer:

f(- 7) = 0

Step-by-step explanation:

Substitute x = - 7 into f(x) , that is

f(- 7) = 2(- 7 - 5)(- 7 + 7)

       = 2 × - 12 × 0

      = - 24 × 0

     = 0

Answer:

20 million vehicles in total

Step-by-step explanation:

25%=1/4

5 million vehicles = 25%

100%/25%=4

5 million * 4 = 20 million vehicles in total

Step-by-step explanation:

The sum of the interior angles of a triangle is equal to 180° so we can write

[tex]y + 2y + 3y = 180° \Rightarrow 6y = 180°[/tex]

Solving for y, we get

[tex]y = 30°[/tex]

So the other two angles of the triangle are

[tex]2y = 2(30°) = 60°[/tex]

and

[tex]3y = 3(30°) =90°[/tex]