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UNO [17]
2 years ago
8

The polynomial f(x) = x³-x²+px+q, where p and q are constants, has remainder 8 when divided by (x-1). If (x+1) is factor of f(x)

, find the values of p and q​
Mathematics
2 answers:
quester [9]2 years ago
7 0

Answer:p=-1 and q=1

Step-by-step explanation:

valentina_108 [34]2 years ago
3 0

Answer:

p=3, q=5

Step-by-step explanation:

f(x) = x³-x²+px+q

factor: x+1 = 0   x = -1

(-1)³ - (-1)² + p*(-1) + q = 0

-2 - p + q = 0

p = q-2

(x-1) is factor of f(x) - 8, root x = 1 : f(x) = x³-x²+(q-2)x+q-8

(1)³ - (1)² + (q-2)(1) + q - 8 = 0

q - 2 + q - 8 = 0

2q = 10     q = 5

p = q-2 = 3

check: x³-x²+3x+5 = <u>(x+1)</u>(x²-2x+5)

x³-x²+3x+5 = (x²+3)(x-1) + <u>8</u>

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Write in slope intercept form of the equation of a line passing through (-1,4) and perpendicular to y=x-5.
andrew11 [14]

Answer:

y=-x+3

Step-by-step explanation:

The general slope-intercept equation of a line is y=mx+b where m is the slope and b represents the y intercept. y and x are simply a point the line passes through. In this case, y=x-5, meaning m=1 and b=-5.

In order to find the perpendicular slope, we should take the current slope's <u>negative reciprocal</u>. We have:

-\frac{1}{1} =\\-1

Therefore, our perpendicular slope is -1. We now have equation:

y=-x+b

We can plug in the known values of the point (-1,4) to solve for b.

4=(-1)*(-1)+b\\4=1+b\\b=3

If we now put what we found together, we have equation

y=-x+3

<em>I hope this helps! Let me know if you have any further questions :)</em>

7 0
3 years ago
Please help me with this word problem!!!
Inessa [10]

Answer:

The number of customers needed to break even is

\simeq 6775.

Step-by-step explanation:

Rent per month = $ 7200

Rent per year, $ 7200 \times 12

                        = $ 86400 -------------(1)

Insurance per year = $ 4200 ---------(2)

Total  direct cost  for 2 servers (withoout  tax) per year,

= $ 2 \times 15 \times 8 \times 5 \times 50

= $ 60000

Total cost for helper ( without tax) per year,

= $ 4 \times 15 \times 5 \times \50

= $ 15000

Total cost for employees per year (without tax),

= $ (60000 +15000)  = $ 75000

Total cost per year for employees including tax,

$ \frac {(75000 \times (100 + 6.2 + 1.45)}{100}

= $ \frac {(75000 \times 107.65 }{100}

= $ 80737.5 -----------------------(3)

So,

total cost for running the restaurant (except food)

= (1) + (2) + (3) = $ (86400 + 4200 + 80737.5)

= $ 171337.5

Average total profit per customer,

= ( Average per customer payment - average cost of food per customer)

= $ (45.47 - 20.18)

= $ 25.29

So, total number of customer needed to break even,

= \frac {171337.5}{25.29}

\simeq   6775

7 0
3 years ago
Divya also wants to make fruit smoothies for dessert. She purchases
Slav-nsk [51]

Answer:

$17.97

Step-by-step explanation:

add everything up

- bananas: 6(0.75) = $4.50

- rice milk: $3.49

- strawberries: 2(4.99) = $9.98

5 0
3 years ago
Read 2 more answers
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Ann [662]

Answer:

146

Step-by-step explanation:

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3 0
2 years ago
Help!!!!!!!!!!!!!!!!!
ivann1987 [24]
I think it’s 700, but I’m not positive
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