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3 years ago

Write 54 + 63 as the product of the GCF of 54 and 63 and another sum

Mathematics

2 answers:

levacccp [35]3 years ago

8 0

Answer:

9*(6+7)

Step-by-step explanation:

First, we have to find the Greatest Common Factor (GCF), to do this we have to see all the factors of 54 and 63 and find the greatest factor that they have in common.

Factors of 54

1,2,3,6,9,18,27,54

Factors of 63

1,3,7,9,21,63

The GCF is 9 because is the greatest factor that is common to both numbers.

Now we have to divide 54/9 and 63/9

54/9 = 6

63/9 = 7

So now we can write the product of the GCF and another sum:

9*(6+7)

We can prove this by solving both expressions:

54+63 = 9*(6+7)

117 = 9*13

117 = 117

The results are equal so we prove it is right.

PolarNik [594]3 years ago

5 0

The GCF: 54: 1,2,3,6,9,18,27,54 63: 1,3,7,9,21,63 The common factors: 1,3,9 Greatest one: 9 Divided: 54 divide 9= 6 63 divided 9= 7 54+63= 9x(6+7)

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In quadrilateral ABCD,AB produced is perpendicular to DC produced.If A=44° and C=148°,calculate D and B.

7nadin3 [17]

Let AB extended intersect DC extended at point E
We now have right triangle BEC with E = 90 degrees 

For triangle BEC: 
Exterior angle at E = 90 
Exterior angle at C = 148 (given) 
Exterior angle of all polygons add up to 360 degrees 
Exterior angle at B = 360−148−90 = 122 

So in quadrilateral ABCD 
B = 122 
D = 360−44−148−122 = 46

5 0

3 years ago

There are 36 people in a fitness studio. What fraction represents the number of people running? • 3 8 of the people lifted weigh

klio [65]

Answer:

7/24

Step-by-step explanation:

3/8 is changed to 9/24 people lifting weights

1/3 is changed to 8/24 people cross training

17/24 people are not running

7/24 people are running

7/24 cannot be reduced

5 0

3 years ago

Factor the polynomial completely. Use synthetic division. F(x) = x^3-7x-6

aleksklad [387]

Answer:

The factors of given polynomial x =-1 , -2 and x =3

Step-by-step explanation:

Step(i):-

Given the polynomial

f(x) = x³ - 7x -6

put x =-1

f(-1) = (-1 )³- 7(-1) - 6 = -1+7-6=0

(x+1) is a one factor

By using synthetic division

x³ x² x constant

x=-1 ↓ 1 0 -7 -6

↓ 0 -1 1 6

1 -1 -6 0

The polynomial x² - x - 6

Step(ii):-

The factors ( x+1)(x² - x - 6 ) = 0

x = -1 and x² - x - 6 =0

x =-1 and x² - 3x + 2 x - 6 =0

x =-1 and x (x -3) + 2( x-3) =0

x =-1 and (x+2)(x-3) =0

Final answer:-

The factors of given polynomial x =-1 , -2 and x =3

6 0

3 years ago

What is the common ratio of 2, 10/3, 50/9

mojhsa [17]

The common ratio of 2, 10/3, 50/9 is $\frac{10}{6}$

Solution:

Given, series of elements are $2, \frac{10}{3}, \frac{50}{9}$

We have to find the common ratio of the above given series.

We know that, common ratio of an G.P is division of any number in that series with the previous number of the series.

So, now take $\frac{10}{3}$ and 2

$\text { Then, common ratio }=\frac{\frac{10}{3}}{2}$

$\begin{array}{l}{\text { Common ratio }=\frac{10}{3} \times \frac{1}{2}} \\\\ {\text { Common ratio }=\frac{10}{3 \times 2}=\frac{10}{6}}\end{array}$