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3 years ago

One root of f(x)=x^3-4x^2-20x+48 is x = 6. What are all the factors of the function? Use the Remainder Theorem.

Mathematics

1 answer:

luda_lava [24]3 years ago

7 0

Answer:

(x - 6)(x + 4)(x - 2)

Step-by-step explanation:

since x = 6 is a root then (x - 6) is a factor

x³ - 4x² - 20x + 48 ÷ (x - 6)

= (x - 6)(x² + 2x - 8)

= (x - 6)(x + 4)(x - 2) ← factors of f(x)

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klio [65]

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3 years ago

What is the product? (9 t minus 4)(negative 9 t minus 4) negative 81 t squared minus 16 negative 81 t squared + 16 negative 81 t

liraira [26]

The product is negative 81 t squared + 16 ⇒ 2nd answer

Step-by-step explanation:

The product of two binomials (ax + b)(cx + d), where a, b, c, and d are constant

Multiply (ax) by (cx) ⇒ 1st × 1st
Multiply (ax) by (d) and (b) by (cx) ⇒ ext-reams and nears
Add the two products ⇒ like terms
Multiply (b) by (d) ⇒ 2nd × 2nd

Let us find the product of (9 t - 4) and (-9 t - 4)

Multiply the 1st two terms

∵ (9 t)(-9 t) = -81 t²

Multiply the ext-reams

∵ (9 t)(-4) = -36 t

Multiply the nears

∵ (-4)(-9 t) = 36 t

Add the like terms

∵ -36 t + 36 t = 0

Multiply the 2nd two terms

∵ (-4)(-4) = 16

Write the answer

∴ (9 t - 4)(-9 t - 4) = -81 t² + 0 + 16

∴ (9 t - 4)(-9 t - 4) = -81 t² + 16

The product is -81 t² + 16

Learn more:

You can learn more about the product of algebraic expressions in brainly.com/question/1617787

#LearnwithBrainly

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3 years ago

Read 2 more answers

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tino4ka555 [31]

i forgot hiw to do that

Step-by-step explanation:

8 0

3 years ago

Help. Solving Multi Step Ratio Problems!

Romashka-Z-Leto [24]

Answer:

Part 1) $30\ coupons$

Part 2) $12\ sandwiches$

Part 3) $60\ push-ups$

Part 4) $96\ minutes$

Part 5) $\$95$

Part 6) $1\frac{7}{8}\ cups\ of\ pretzel$

Step-by-step explanation:

Part 1) we know that

At the Green House of Salad , you get a $1 coupon for every 3 salads you buy

Using proportion

Find out the number of salads you could buy to get $10 in coupons

$\frac{1}{3}=\frac{10}{x} \\\\x=3(10)\\\\x=30\ coupons$

Part 2) we know that

Kim orders catering for $35

She spend $5 on a large order of potato salad and the rest on turkey sandwiches

Each sandwich is $2.50

How many sandwiches does Kim buy?

step 1

Find out how many Kim spent on turkey sandwiches

Subtract $5 from $35

35-5=$30

step 2

Using proportion, find out the number of sandwiches

$\frac{1}{2.50}=\frac{x}{30}\\\\x=30/2.50\\\\x= 12\ sandwiches$

Part 3) we know that

Molly does 10 push-ups at the same time as Liza does 15 push-ups

Using proportion

Find out how many push-ups Liza does when Molly does 40 push-ups

$\frac{10}{15}=\frac{40}{x}\\\\x=15(40)/10\\\\x=60\ push-ups$

Part 4) we know that

A shark swim at a speed of 25 miles per hour

The shark rest after 40 miles

How long in minutes, does the shark swim before resting?

Using proportion

Find out how long in minutes the shark swim 40 miles

Remember that

$1\ h=60\ min$

$\frac{25}{60}\ \frac{miles}{minutes}=\frac{40}{x}\ \frac{miles}{minutes}\\\\x=60(40)/25\\\\x=96\ minutes$

Part 5) we know that

For every bar of soap that Aly sells, she earns $5

For every mug that Janet sells, she earns twice as much as Aly

Aly sells 5 bars of soap and Janet sells 7 mugs

How much money did they make altogether?

step 1

Find out the amount earned by Aly

using proportion

$\frac{1}{5}=\frac{5}{x}\\\\x=5(5)\\\\x=\$25$

step 2

Find out the amount earned by Janet

Remember that

For every mug that Janet sells, she earns twice as much as Aly

For every mug that Janet sells, she earns 2($5)=$10

using proportion

$\frac{1}{10}=\frac{7}{x}\\\\x=10(7)\\\\x=\$70$

step 3

Adds the amount earned by Aly plus the amount earned by Janet

$25+70=\$95$

Part 6) we know that

Ted is making trail mix for a party

He mixes 1 1/2 cups of nuts, 1/4 cup of rising and 1/4 cup of pretzel

How many cups of pretzel does Ted need to make 15 cups of trail mix?

Adds the quantities

$1\frac{1}{2}+\frac{1}{4} +\frac{1}{4}=2\ cups\ of \ trail\ mix$

That means

For every 2 cups of trail mix we need 1/4 cup of pretzel

using proportion

Find out how many cups of pretzel does Ted need to make 15 cups of trail mix

$\frac{2}{(1/4)}=\frac{15}{x}\\\\x=15(1/4)/2\\\\x=\frac{15}{8}\ cups\ of\ pretzel$

Convert to mixed number

$\frac{15}{8}=\frac{8}{8}+\frac{7}{8}=1\frac{7}{8}\ cups\ of\ pretzel$

6 0

3 years ago

Find the number of elements in A1 ∪A2 ∪A3 if there are 100 elements in A1, 1000 in A2, and 10,000 in A3 if a) A1 ⊆ A2 and A2 ⊆ A

Stella [2.4K]

Answer:

Step-by-step explanation:

Given that there are 3 sets such that there are 100 elements in A1, 1000 in A2, and 10,000 in A3

a) If A1 ⊆ A2 and A2 ⊆ A3

then union will contain the same number of elements as that of A3

i.e. $n(A1 ∪A2 ∪A3)=n(A3) =10000$

b) If the sets are pairwise disjoint.

union will contain the sum of elements of each set

$n(A1 ∪A2 ∪A3) = 100+1000+10000=11100$

c) If there are two elements common to each pair of sets and one element in all three sets

We subtract common elements pairwise and add common element in 3

i.e. $n(A1 ∪A2 ∪A3) = 100+1000+10000-2-2-2+1\\= 10995$

5 0

2 years ago