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dangina [55]
3 years ago
9

Find the remainder when f(x) is divided by (x - k) f(x) = 5x4 + 8x3 + 4x2 - 5x + 67; k = 2

Mathematics
2 answers:
yan [13]3 years ago
8 0

It is to be solved by reminder thorem
f(x)/(x-k) will have reminder f(k), 
so, f(2) = 5*(2^4) + 8 *(2^3) +4* (2^2) -5(2) +67

             =5*16 + 8*8 +4*4 -5*2 +67
             =80 + 64 + 16 -10 +67

             = 217


nirvana33 [79]3 years ago
8 0

Answer: The remainder when f(x) is divided by (x-2) is 217.

Step-by-step explanation:

Since we have given that

f(x) = 5x^4 + 8x^3 + 4x^2 - 5x + 67

And it is divided by g(x)=(x-k)

Here, k= 2

So, g(x)= x-2

So, we need to find the remainder .

By using "Remainder theorem ":

Put\ g(x)=0\\\\x-2=0\\\\x=2

Now,

f(2)=5(2)^4 + 8(2)^3 + 4(2)^2 - 5(2) + 67\\\\f(2)=80+64+16-10+67\\\\f(2)=217

Hence, the remainder when f(x) is divided by (x-2) is 217.

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Two lines have a slope of 3 and different y-intercepts how many solutions will this system have
Taya2010 [7]

Answer:

0 solutions / no solutions

Step-by-step explanation:

If two lines have the same slope but different y-intercepts, it means that they are parallel.

For example, we have two lines:  

y = x

y = x + 1

Both lines have the same slope of 1, but different y - intercepts. Because each equation increases the x and y at the same right (slope) but started at different points, the two equations will never touch.

It's similar to two runner who run at the same pace. If one runner started 50 meters ahead, that runner will always be ahead 50 meters (y-intercept) because they both run at the same rate.

6 0
2 years ago
If x and ​(19x+30​) are the measures of complementary​ angles, what is the measure of each​ angle?
Alisiya [41]

Answer:

3° and 87°

Step-by-step explanation:

<em>here's</em><em> your</em><em> </em><em>solution</em>

<em> </em><em>=</em><em>></em><em> </em> we know that measure of complementary angle is 90°

=>. one angle is. = x

=> other angle is .= (19x + 30)

=> so, x + 19x + 30° = 90°

=> 20x + 30° = 90°

=> 20x = 60°

=> x = 60/20

=> x = 3°

hence one angle is 3° and other is 87°

hope it helps

7 0
3 years ago
1. $17.04 for 4 packages
yan [13]

answer

they are each $4.26

5 0
3 years ago
GEOMETRY PROBLEM THAT IS SOO HARD FOR ME <br> PLEASE HELP ME!!!!
12345 [234]
59.5 feet
Work:
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3 0
3 years ago
La funcion que representa el beneficio obtenido por una empresa si vende x unidades de uno de sus productos es f(x)= -70x^2+2800
DerKrebs [107]

Answer:

20

Step-by-step explanation:

La función es

f(x)=-70x^2+2800x-45000

Diferenciando con respecto a x obtenemos

f'(x)=-140x+2800

Igualar con cero

0=-140x+2800\\\Rightarrow x=\dfrac{2800}{140}\\\Rightarrow x=20

Doble derivada de la función

f''(x)=-140

Entonces, la función es máxima cuando el número de unidades vendidas,  x=20,

3 0
2 years ago
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