Find all values of k so that the trinomial x^2 + kx - 35 can be factored using integers

Answers

Answer 1

Answer: $(x-r_1)(x-r_2)=x^2-(r_1+r_2)x+r_1r_2$

So the trinomial $x^2+kx-35$ can be factored as long as

$\begin{cases}r_1+r_2=-k\nr_1r_2=-35\end{cases}$

has integer solutions for $r_1,r_2$ . Clearly, both have to be factors of -35, which leaves only a handful of cases:

$(r_1,r_2)=(1,-35)\implies r_1+r_2=-34$
$(r_1,r_2)=(-1,35)\implies r_1+r_2=34$
$(r_1,r_2)=(5,-7)\implies r_1+r_2=-2$
$(r_1,r_2)=(-5,7)\implies r_1+r_2=2$

So the possible values of $k$ are $\pm34$ and $\pm2$ .

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During a clothing store’s Bargain Days, the regular price for T-shirts is discounted by $5. There is a state sales tax of 5%, and the $5 discount is applied before the sales tax is calculated.a. Write an expression that shows the regular price r of a T-shirt minus the $5 discount.

b. Write a rule for the function p(r) that expresses the final price p of a T-shirt with the discount applied and sales tax added.

c. How much would you pay during Bargain Days for a shirt regularly priced at $15.50?

Answers

Answer:

Let the regular price of the t shirt be = r

Let the total cost of the t shirt be = t

So, we can say : $t=r-5$

$p(r)=1.05(r-5)$

Substituting r = 15.50

$p(r)=1.05(15.50-5)$

=> $p(r)=1.05(10.50)$

= $11.025

a) d = r - 5 where t is the full price
b) p = ( r - 5 ) * 1.05
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Find the area of a circle with a diameter of 22 inches?

Answers

$R=(Diameter)/(2)$

then

$R=(22~in)/(2)$

$\boxed{R=11~in}$

now we just need to apply this formula

$S=\pi*R^2$

$S=\pi*11^2$

$\boxed{\boxed{S=121*\pi~in^2}}$

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The clearance sale advertised 1/3 off the list price of clothes and 1/2 off the list price of luggage. Ramon bought a suitcase with a list price of $100 and a coat with a list price of $195. What was his total bill?A. $115
B. $150
C. $180
D. $295

Answers

The closest answer C, however the actual answer is $196.25.

price of the coat = 2/3*195 = 2*195/3 = 2*65 = 130
price of the luggage = 1/2*100 = 100/2 = 50
total bill = 130+50 = 180

(PLEASE HELP! WILL MARK BRAINLIEST!!!!) 1. Given any two angle measures and a side length you can always create a triangle. Is this statement true or false? Explain your answer.

2. What is the sum of the three angles inside of a triangle and how do you know?

Answers

Answer:

false and sum of the three angles of any triangle is equal to 180 degrees.

Step-by-step explanation:

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Answers

i have concluded the answer is a

it would be 200 if she used 5 over the limit. 30 x 5 = 150 150+50=200

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Answers

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