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Agata [3.3K]
3 years ago
13

The polynomial p(x) = 5x^3 – 9x^2 - 6x + 8 has a known factor of (x + 1).

Mathematics
2 answers:
alekssr [168]3 years ago
4 0

Answer:

(x+1)(5x-4)(x-2)

Step-by-step explanation:

We know that (x+1) is a factor, so we can use synthetic division to factor it out of 5x^3-9x^2-6x+8.

Once factored, we get (x+1)(5x^2-14x+8)

Now all we need to do is factor(5x^2-14x+8)

(5x^2-14x+8)=(5x-4)(x-2)

This gives us the answer (x+1)(5x-4)(x-2).

anzhelika [568]3 years ago
3 0

Answer:

(x+1)(5x-4)(x-2)

Step-by-step explanation:

You might be interested in
A - f(2x) <br> B - 1/2f(x) <br> C - f(1/2x) <br> D - 2f(x)
Ulleksa [173]

Answer:

A: f(2x)

Step-by-step explanation:

In this case it can be seen that the x values are being affected by this transformation. This means that we should look for points on f and g with the same y value but different x values. However in this case it is hard to pinpoint easy coordinates to work with. This is where process of elimination can help. We know it cant be B or C because if the dilation ratio is outside the function, the y values would be affected. That leaves it to A or D. We can see that g has shrunk from the original function. Shrinking along the x-values can be notated by the reciprocal of the factor of shrinking. In this case it looks like it shrunk down to half of the originals size. If we take the reciprocal of a half we get 2. Therefore if we plug that in we get:

f(2x)

3 0
3 years ago
The value of 3b2 – b when b = 5
Mila [183]

Answer:

70

Step-by-step explanation:

Evaluate 3 b^2 - b where b = 5:

3 b^2 - b = 3×5^2 - 5

Hint: | Evaluate 5^2.

5^2 = 25:

3×25 - 5

Hint: | Multiply 3 and 25 together.

3×25 = 75:

75 - 5

Hint: | Subtract 5 from 75.

| 7 | 5

- | | 5

| 7 | 0:

Answer:  70

6 0
3 years ago
43 coins, no nickels, $4.51 equal amount amount of pennies and dimes, how many of each coin
Sonbull [250]
Set up
Let the dimes = d
Let the pennies = p
Let the quarters = q

Equations
You cannot mean that the pennies and dimes have equal numbers. That would mean that each had 21.5 members. Now could you mean that the dime and penny amount could be the same with 43 coins that total 4.00. Four dollars means that you need 40 dimes alone. It must mean that you are including quarters. 

p + d + p = 43          (1)
p = d                        (2)
p +10d +25q = 451  (3)

Note how this last equation = was derived. You have to multiply the dimes by 10 and he quarters by 100 and the total by 100 to get the numbers all in pennies.

Put the results of 2 into 1.
2p  + q = 43                   (4)  
You need to modify equation 3 as well.
p + 10p + 25q = 451
11p + 25q  = 451           (5)

Solve the new equations
2p +  q = 43               (4)
11p + 25q = 451        (5)

Multiply 4 by 25
25(2p- + q = 43)
50p + 25q = 1075     (6)  Subtract (5) from (6)
<u>11p + 25q = 451
</u>39p = 624                        Divide by 39
p = 624 / 39
p = 16

Since the pennies and dimes are equal there are 16 dimes
p + d + q = 43
16 + 16 + q = 43
32 + q = 43
q = 11

Check
16 + 10*16 + 11*25 = ?
16 + 160 + 275  = ?
451 = ?

Nice problem. Thanks for posting.
3 0
3 years ago
Jana uses 20 cards to play a memory game the cards are either animal cards or fruit cards. The ratio of animal cards to fruit ca
Verdich [7]

Given that,

Total no of cards = 20

The ratio of animal cards to fruit cards is 2:3

No of animal cards = 20

Solution,

Let there are 2x animal cards and 3x fruit cards. ATQ,

2x+3x = 20

5x = 20

x = 4

Animal cards = 2x

= 2(4)

= 8

Fruit cards = 3x

= 3(4)

= 12

It is also mentioned that, of the cards, 1/3 have bananas on them. It means,

B=\dfrac{1}{3}\times 12\\\\=4

Hence, 4 cards have bananas on them.

5 0
2 years ago
Please help me with this math question!
barxatty [35]
1) Change radical forms to fractional exponents using the rule:
The n<span>th root of "</span>a number" = "that number" raised to the<span> reciprocal of n.
For example </span>\sqrt[n]{3} =   3^{ \frac{1}{n} }.

The square root of 3 (\sqrt{3}) = 3 to the one-half power (3^{ \frac{1}{2} }).
The 5th root of 3 (\sqrt[5]{3}) = 3 to the one-fifth power (3^{ \frac{1}{5} }).

2) Now use the product of powers exponent rule to simplify:
This rule says a^{m} a^{n} = a^{m+n}&#10;. When two expressions with the same base (a, in this example) are multiplied, you can add their exponents while keeping the same base.

You now have (3^{ \frac{1}{2} })*(3^{ \frac{1}{5} }). These two expressions have the same base, 3. That means you can add their exponents:
(3^{ \frac{1}{2} })(3^{ \frac{1}{5} })\\&#10;= 3^{(\frac{1}{2} + \frac{1}{5}) }\\&#10;= 3^{\frac{7}{10}}

3) You can leave it in the form 3^{\frac{7}{10}} or change it back into a radical \sqrt[10]{3^7}

------

Answer: 3^{\frac{7}{10}} or \sqrt[10]{3^7}
6 0
3 years ago
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