Mathematics High School

please help with question 3

Answers

Answer 1

Answer:

p = - [tex]\frac{2}{3}[/tex] , p = 2

Step-by-step explanation:

Using the discriminant to solve for p

Δ = b² - 4ac

The condition on the discriminant for 2 eeal and equal roots is

b² - 4ac = 0

Given

p²x² - (p + 2)x + 1 = 0

with a = p² , b = - (p + 2) , c = 1 , then

(- (p + 2) )² - 4p² = 0

(p + 2)² - 4p² = 0

p² + 4p + 4 - 4p² = 0

- 3p² + 4p + 4 = 0 ( multiply through by - 1 )

3p² - 4p - 4 = 0 ← in standard form

(3p + 2)(p - 2) = 0 ← in factored form

Equate each factor to zero and solve for p

3p + 2 = 0 ⇒ 3p = - 2 ⇒ p = - [tex]\frac{2}{3}[/tex]

p - 2 = 0 ⇒ p = 2

Related Questions

Supply the missing reasons to complete the proof.

Answers

Answer:

3. ASA

4. Corresponding sides of congruent triangles are congruent

Step-by-step explanation:

I marked this in the attached image. ∠B ≅∠E, ∠ACE ≅ ∠DCE, and the side between them BC ≅ EC, so the the triangles ΔACB and ΔDCE are congruent by ASA.

If the triangles are congruent, then all corresponding angles and sides are also congruent.

1. Kristina took out a bank loan for $60,000 that must be repaid with regular monthly payments of $1100. The bank charges her an interest rate of 3.0% compounded monthly a) How many payments will Kristina have to make to pay off the loan. N=? I= ?PV = ?PMT= ? FV=? P/Y = ?C/Y =? END BEGIN b) How much interest will Kristina Pay?

Answers

Answer:

See below

Step-by-step explanation:

Given:

Loan amount PV = $60000Interest rate r = 3% PATime t = x yearsNumber of compounds n = 12Monthly payment PMT = $1100

FV is:

60000*(1 + (3/100)/12)^(12x) = 60000*(1.0025)^(12x)

Which is same as total payment:

1100*12*x

Solve the following by graphing:

60000*(1.0025)^(12x) = 1100*12*x

See attached

The solution is:

x = 5.333 = 5 1/3 years = 5 years 4 months = 64 months

Total payment:

FV = $70 395.95

The amount of interest:

I = FV - PV = 70395.95 - 60000 = $10395.95

The wallaby is essentially a small kangaroo that is native to Australia. To monitor the wallaby population, scientists catch 88 and tag them. A month later, they capture 600 wallabies and notice that 44 have tags. To the nearest viole number, what is the best estimate for the TOTAL wallaby population using ratios?

Answers

The best estimate for the total wallaby population is 1200.

Since to monitor the wallaby population, scientists catched 88 and tag them, already a month later, they captured 600 wallabies and noticed that 44 had tags, to determine what is the best estimate for the total wallaby population using ratios, the following calculation must be done:

44 = 600 88 = X 88 x 600/44 = X 1200 = X

Therefore, the best estimate for the total wallaby population is 1200.

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What point located in quadrant IV has an x-value that is 3 units from the origin and a y-value that is 4 units from the origin?

Answers

(3, -4) has to be 20 lettered doodle doo

PLS HELP.

7) Find RQ

Answers

Answer:

are we doing ur homework

Step-by-step explanation:

Im doing an extra credit assignment and I need someone to help me solve by substitution method
y=x+3
y=2x+5

Answers

Answer:

(-2,1)

Step-by-step explanation:

that is where the two graphs intersect

What common side does ΔABC share with ΔADC?

BC

AD

BD

AC

Answers

I think it’s AC, but I may be wrong

Answer:

it's a and c

luk closely

The hypotenuse of a right triangle is 6 feet long. One leg is 2 feet longer than the other. Find the length of each leg to the nearest hundredth of a foot.

Answers

Here is a diagram explaining the information

find the side of square whose perimeter. is 24.8cm.

Answers

Answer:

6.2

Step-by-step explanation:

What is 3/10 of 2560

Answers

Answer:

768

3/10 times 2560 simply equals 768 after the calculations are done

5. Name the side included by

AB
AC
BC
none of these.

Answers

Answer:

Step-by-step explanation:

Side AB is in between angle A and angle B. We can tell this because angle A is at one point, and angle B is at the other.

Have a nice day!

I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

if a necklace was on discount 10% and the original price was $20 what was the amount of discount?

Answers

Answer:

10$

Step-by-step explanation:

dollars hope it helps

Answer:

its 10$

Step-by-step explanation:

hari drags a load of 60 kg along a distance of 12 m. what amount of work does he do?also mention the type of work

Answers

Answer:

----->

Step-by-step explanation:

The weight of the 60kg load is (m g) = 588 Newtons. (Force x distance) = (588 N) x (12 m) = 7,056 Joules of work.

how many real square roots does -1 have?

Answers

It is 0 because there are no square roots for negitive numbers

There are no real square roots does -1 have.

-1 is negative, it does not have a real square root.

Here, we have,

we know that,

The number -1 does not have any real square roots.

In the real number system, a square root of a number is a value that, when squared, gives the original number.

However, when we square any real number, the result is always non-negative.

Since -1 is negative, it does not have a real square root.

It is 0 because there are no square roots for negative numbers.

Hence, There are no real square roots does -1 have.

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How do you work x+1-2=4 and x-1=2

Answers

Answer:

Simplify x+1-2x+1−2 to x-1x−1.

x-1=4

x−1=4

2 Add 11 to both sides.

x=4+1

3 Simplify 4+14+1 to 55.

x=5

Add 11 to both sides.

x=2+1

2 Simplify 2+12+1 to 33.

x=3

MEDIUM) Ana gave Bill and Clare as much money as each had. Then Bill gave Ana and Clare as much money as each had. Then Clare gave Ana and Bill as much money as each had. Then each of the three people had $24. How much money did each have to begin with

Answers

Answer:

At the very end, the amounts of money are:

A -- 24

B -- 24

C -- 24

If A and B received as much as they had just prior to the last transaction, they must each have received 12 and they must have received it from C, so at the end of the previous step, the situation must have been:

A -- 12 (24 minus 12)

B -- 12 (24 minus 12)

C -- 48 (24 plus 12 plus 12)

Before that, A and C got half of what they had above from B, so:

A -- 6 (12 minus 6)

B -- 42 (12 plus 6 plus 24)

C -- 24 (48 minus 24)

And initially, B and C got half of what they had above from A, so:

A -- 39 (6 plus 21 plus 12)

B -- 21 (42 minus 21)

C -- 12 (24 minus 12)

Step-by-step explanation:

Do Now 13.2:
Green light has a frequency of 5.71 x 10' Hz.
Calculate the energy of a green light photon.
(SHOW ALL WORK for FULL CREDIT!)

Answers

Answer:

Not Step-by-step explanation:

Not enough info

Help please!!
A small party balloon has a maximum volume of 500 cm3. Unfortunately, it has a leak that allows 10 cm of air to escape every second. a Write down an equation for the volume (v cm) of the party balloon, t secs after it starts to leak.

Answers

Step-by-step explanation:

I think you mean that 10 cm³ of air are escaping every second.

and we start with a volume of 500 cm³.

V = 500 - 10t 0 <= t <= 50

because negative t (seconds) don't make any sense, and neither does a negative volume (for t > 50).

Two parallel lines are crossed by a transversal. Vertical and parallel lines h and i are cut by transversal g. At the intersection of lines h and g, the uppercase right angle is 70 degrees and the bottom left angle is x degrees.

Answers

Answer:

x = 70

Step-by-step explanation:

DETERMINE WHICH OF THE LINES ARE PARALLEL OR PERPENDICULAR thx sm

Answers

Answer:

Parallel: a and b

Perpendicular: none

Step-by-step explanation:

You are given the coordinates of each line.

To check if they are parallel or perpendicular, need to find slope.

In this case we can use :

m = (y2 - y1) / (x2 - x1)

So for line a:

(1,5) and (-2, -4)

slope = (-4 - 5) / (-2 - 1)

slope = -9/-3

slope = 3

Line b:

(3, 2) and (1, -4)

slope = (-4 - 2)/(1 - 3)

slope = -6/-2

slope = 3

Line C:

(6, 1) and (-4, 2)

slope = ( 2 - 1) / ( -4 -6)

Slope = 1/ -10

slope = - 1/10

Line A and B are parallel because their slopes are the same.

To check if they are perpendicular, we need to know if their slopes are reciprocals.

Here none of them are perpendicular to each other

(test question) If you're good at geometry please help me

Answers

Step-by-step explanation:

this is a rectangle. so, all things are symmetric.

EI = IG = FI = IH

IGF = IFG = IEH = IHE

therefore, since EI = FI

2x + 8 = 6x - 20

28 = 4x

x = 7

now,

EG = EI + IG = 2×EI = 2×(2×7 + 8) = 2×22 = 44

IFE is a complementary angle to IFG (together they have 90°).

and because IFG = IGF = 30°

IFE = 90 - 30 = 60°

a 260$ suit is marked down by 30%. find the sale price

Answers

Answer:

182

Step-by-step explanation:

If the suit itself is originally 260 and it lowered by 30% of itself, then we need to find 30% of 260, which would be 78. Since we are lowering the price, we subract 260 - 78 and get 182 as our final answer.

I hope this answer helped. Please let me know if I am incorrect. Thank you!

Your math grade is a 68%.You turn in some late work, and now your grade is an 82%.What is the percent change?

Answers

Answer:

your grade increased by 14%

Given 4 < x < 9 and 5 - y< 4 , where x and y are integers. Find the maximum value of x-y.

Answers

Answer:

You want to maximize x and minimize y

Maximum y = 8

Minimum y = 10

8-10= -2

James makes $44,059 per year, how much would he make monthly?

Answers

Answer:

$3671.58

Step-by-step explanation:

Take the annual salary and divide it by the number of months

On New Year’s Day 2021, your uncle put $3 dollars in his safe for you that he says will grow exponentially until you decide to take it out. If you take the money out on New Year’s Day 2023, the money will have grown to $18.75. You decide that you will ask for the money on New Year’s Day 2031. How much money will you receive then?

Answers

if 18.75 - 3 = 15.75

if every 2 years you get 15.75

if from 2023 to 2031 is 8 years

then 8 divided by 2 = 4

so 15.75 * 4 = 63

then the answer is 63

Please I really need help
15 POINTS..15 POINTS

ONLY ONE QUESTION
ANSWER IT WITH EXPLANATION

PLEASE I NEED IT NOW

Answers

yes the slope is constant

NEW ANSWER

Lupita is correct because when there is a constant of proportiantilly the line will start at the origin and it will be straight all the way. No curves, bends, etc. Another way you can tell is because when the line gets to "2" it lines up with 300 when the line gets to "4" it lines up with 600. That shows that the line is equal all the way through.

thanks for brainly (:

glad I could help!

2x + 3 for x=3
PLEASE I NEED A ANSWER

Answers

Answer:

Step-by-step explanation:

2 times 3 = 6

6+3=9

Luis has 3 pounds of ground turkey to make turkey burgers. He uses 3/8 pound per burger to make 6 burgers. How many 1/4 pound burgers can Luis make with the remaining turkey?

Answers

Answer: he can make 3 1/4 pound burgers.

Step-by-step explanation: we know that he starts with 3 lbs of burger meat, and uses some of the meat to make 6 burgers that each weigh 3/8 lbs. If you take the 3/8 lbs and multiply by 6 burgers, you get 18/8, which is how much has been used so far. If you subtract 18/8 from the 3 lbs that Luis has originally started with, you get 6/8 lbs, which is how much he has after his first 6 burgers. Then you can take the 1/4 and see how many times it fits into 6/8 (1/4=2/8, 6/8 divided by 2/8 = 3 burgers that each weigh 1/4 lbs)

***WILL GIVE BRAINLIEST***
A triangular garden is to be split so that the angle at vertex B is bisected. This diagram was supplied by the landscape architect, but you do not have a way to measure the angles at B. You do have the given side lengths, so what is the length of side AD that will allow the angle at B to be bisected?

A.
5 m
B.
4 m
C.
2 m
D.
3 m

Answers

The length of side AD that will allow the angle at B to be bisected is 3m, the correct option is D.

What is Angle Bisector Theorem?

According to the angle bisector theorem, the angle bisector of an angle of a triangle bisects the opposite side into two parts that are proportional to the other two sides.

The sides of the triangle are 5,7 and (x+4) m.

The BD will be the angle bisector of angle B only if

x/4 = 5/7

x = 5 *4 / 7

x = 20/7 = 2.85 ≈ 3m

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