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harkovskaia [24]

3 years ago

10

On a January day in Michigan, the low temperature was 5 degrees colder than 2℉ and the high temperature was 5 degrees warmer tha

n 2℉.

1 answer:

aliya0001 [1]3 years ago

8 0

Answer:

-3 was the low and the high temp. is 7

Step-by-step explanation:

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

Goryan [66]

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.

5 0

3 years ago

Savannah bought a book for 85% of the original price. By what percent of the price was the book reduced

agasfer [191]

Answer:

15%

Step-by-step explanation:

100-85=15

100%= the total cost of the book

85%= price she bought it for

15%= the percentage the book was reduced by

7 0

3 years ago

Read 2 more answers

Find the difference between 430 and 144

nata0808 [166]

286. you just subtract the two numbers

5 0

3 years ago

Read 2 more answers

Verify that P = Ce^t /1 + Ce^t is a one-parameter family of solutions to the differential equation dP dt = P(1 − P).

NemiM [27]

Answer:

See verification below

Step-by-step explanation:

We can differentiate P(t) respect to t with usual rules (quotient, exponential, and sum) and rearrange the result. First, note that

$1-P=1-\frac{ce^t}{1+ce^t}=\frac{1+ce^t-ce^t}{1+ce^t}=\frac{1}{1+ce^t}$

Now, differentiate to obtain

$\frac{dP}{dt}=(\frac{ce^t}{1+ce^t})'=\frac{(ce^t)'(1+ce^t)-(ce^t)(1+ce^t)'}{(1+ce^t)^2}$

$=\frac{(ce^t)(1+ce^t)-(ce^t)(ce^t)}{(1+ce^t)^2}=\frac{ce^t+ce^{2t}-ce^{2t}}{(1+ce^t)^2}=\frac{ce^t}{(1+ce^t)^2}$

To obtain the required form, extract a factor in both the numerator and denominator:

$\frac{dP}{dt}=\frac{ce^t}{1+ce^t}\frac{1}{1+ce^t}=P(1-P)$

3 0

3 years ago

Joanne has a scale drawing of her backyard that includes a garden bed that measures 26 inches long and 16 inches wide.

SIZIF [17.4K]

1, 12 2.16 it should be right because i got the same question before

4 0

3 years ago