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Sergeu [11.5K]
3 years ago
7

Find the values of k so that each remainder is three. 10. (x^2+ 5x + 7) = (x + k)

Mathematics
1 answer:
Goryan [66]3 years ago
5 0

Answer:

k=1\text{ or } k=4

Step-by-step explanation:

We can use the Polynomial Remainder Theorem. It states that if we divide a polynomial P(x) by a <em>binomial</em> in the form (x - a), then our remainder will be P(a).

We are dividing:

(x^2+5x+7)\div(x+k)

So, a polynomial by a binomial factor.

Our factor is (x + k) or (x - (-k)). Using the form (x - a), our a = -k.

We want our remainder to be 3. So, P(a)=P(-k)=3.

Therefore:

(-k)^2+5(-k)+7=3

Simplify:

k^2-5k+7=3

Solve for <em>k</em>. Subtract 3 from both sides:

k^2-5k+4=0

Factor:

(k-1)(k-4)=0

Zero Product Property:

k-1=0\text{ or } k-4=0

Solve:

k=1\text{ or } k=4

So, either of the two expressions:

(x^2+5x+7)\div(x+1)\text{ or } (x^2+5x+7)\div(x+4)

Will yield 3 as the remainder.

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15.5 decimeters but in meters
ivanzaharov [21]

Answer:

There are 10 decimeters in one meter so the answer is 15.5 / 10 = 1.55 meters.

3 0
2 years ago
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A solution of salt and water is 20% salt. If 25% of the water is removed, what is the percentage of salt in the new solution?
Ratling [72]
So lets say that this salt and water solution consists of 100 liters.

Then that means 20 liters is salt, and 80 liters out of the 100 is water.



Now, we remove 25% of the water. 25% of 80 liters is 20 liters. So, we are left with 80-20, or 60 liters.



Now in all we have 20 liters of salt, and 60 liters of water.

The percentage of salt in the new mixture will be 20/(20+60) = 20/80 = 25%.



Your answer is 25%
4 0
3 years ago
What is x square minus x minus 12=0?
bonufazy [111]
I believe it's 12=0

Hope I helped! ( Smiles )

6 0
3 years ago
What is the multiple zero and multiplicity of f(x) = x3 + 10x2 + 25x?
elena-s [515]

Answer:

The multiple zero is x=-5.

The multiplicity is 2

Step-by-step explanation:

The given function is

f(x)=x^3+10x^2+25x

To find the zero of this function, we equate it to zero.

\Rightarrow x^3+10x^2+25x=0

We factor to obtain;

x(x^2+10x+25)=0

Observe that; the expression within the parenthesis is a perfect square.

This implies that;

x(x+5)^2=0

This implies that;

Either x=0 or (x+5)^2=0

(x+5)^2=0 has a multiple zero which is

x=-5 and its multplicity is 2.

3 0
3 years ago
Fast please!!
Lostsunrise [7]

Answer:

Part 1) The price of a USB memory, stick selling at a 21% discount of its market price (m) ------> 0.79m

Part 2) The price or a CD that sells for 21% more than the amount (m) needed to manufacture the CD -----> 1.21m

Part 3) The final value of a painting after its initial value m, increases by 2/5 -----> \frac{7}{5}m

Part 4) The total number of markers that Nancy has if she gives away 2/5 of her m markers to Amy ----->  \frac{3}{5}m

Step-by-step explanation:

Part 1) The price of a USB memory, stick selling at a 21% discount of its market price (m)

we know that

100% is the market price m

100%-21%=79%

79%=79/100=0.79

so

The price of a USB memory with a 21% discount of its market price is equal to multiply m by 0.79

(0.79)*m=0.79m

Part 2) The price or a CD that sells for 21% more than the amount (m) needed to manufacture the CD

we know that

100% is the amount m

100%+21%=121%

121%=121/100=1.21

so

The price or a CD that sells for 21% more than the amount (m) is equal to multiply m by 1.21

(1.21)*(m)=1.21m

Part 3) The final value of a painting after its initial value m, increases by 2/5

we know that

100% is the initial value m

2/5=0.40=40%

100%+40%=140%

140%=140/100=1.4

Convert to fraction

1.4=14/10=7/5

so

The final value is equal to m multiplied by 7/5  

\frac{7}{5}m

Part 4) The total number of markers that Nancy has if she gives away 2/5 of her m markers to Amy

we know that

100% is the number of makers m

2/5=0.40=40%

100%-40%=60%

60%=60/100=0.6

Convert to fraction

0.6=6/10=3/5

The total number of markers that Nancy has is equal to multiply m by 3/5

so

\frac{3}{5}m

5 0
2 years ago
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