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3 years ago

Need help with 26 & 27

Mathematics

1 answer:

Sphinxa [80]3 years ago

5 0

26. Angle ABC = 22+14 = 36 degrees

27. x +117 = 180 (linear pair)

x = 180 - 117 = 63 degrees

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Factor f(x) = 15x^3 - 15x^2 - 90x completely and determine the exact value(s) of the zero(s) and enter them as a comma separated

Illusion [34]

Answer:

$x=-2,0,3$

Step-by-step explanation:

We have been given a function $f(x)=15x^3-15x^2-90x$ . We are asked to find the zeros of our given function.

To find the zeros of our given function, we will equate our given function by 0 as shown below:

$15x^3-15x^2-90x=0$

Now, we will factor our equation. We can see that all terms of our equation a common factor that is $15x$ .

Upon factoring out $15x$ , we will get:

$15x(x^2-x-6)=0$

Now, we will split the middle term of our equation into parts, whose sum is $-1$ and whose product is $-6$ . We know such two numbers are $-3\text{ and }2$ .

$15x(x^2-3x+2x-6)=0$

$15x((x^2-3x)+(2x-6))=0$

$15x(x(x-3)+2(x-3))=0$

$15x(x-3)(x+2)=0$

Now, we will use zero product property to find the zeros of our given function.

$15x=0\text{ (or) }(x-3)=0\text{ (or) }(x+2)=0$

$15x=0\text{ (or) }x-3=0\text{ (or) }x+2=0$

$\frac{15x}{15}=\frac{0}{15}\text{ (or) }x-3=0\text{ (or) }x+2=0$

$x=0\text{ (or) }x=3\text{ (or) }x=-2$

Therefore, the zeros of our given function are $x=-2,0,3$ .

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3 years ago

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harvey collects rare marbles. He has 125 marbles in collection 1, 36 fewer marbles in collection 2, and 53 more marbles than col

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Collection 1, no of marbles = 125

Collection 2, no of marbles =36 fewer = 125-36 =89

Collection 3, no of marbles = 53 more =125+53 =178

Hence total marbles = 125+89+178

= 392

Given that he uses 14 trays to hold all the marables

Let us assume that he distributes equally all 392 marbles in 14 trays

Then marbles in each tray = 392/14 = 27

Thus division is used for finding out the no of marbles in a tray.

For finding out no of marbles in 3 trays, we get = 3x27 = 81 marbles

(Here direct variation is used)

Answer is 81 marbles

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