The equation
(p-1)x^2 + 4x + (p-5)=0, where p is a constant,
has no real roots.
(a) Show that p satisfies p^2 - 6p+1>0.

Answers

Answer 1

Answer:

Proof is shown below.

Step-by-step explanation:

Use quadratic Formula, where from the standard form ax^2 + bx + c = 0, where a is not zero, we identify a = p-1, b=4, c = p-5, and since the given equation has no real roots, the discriminant b^2 - 4ac < 0, so that substituting we have that,

4^2 - 4(p-1)(p-5) < 0

16 - 4(p^2 - 6p + 5) < 0

16 - 4p^2 +24p - 20 < 0

-4p^2 + 24p - 4 < 0,

p^2 - 6p + 1 > 0, by dividing both sides of the inequality by -4.  


Related Questions

Plz help I need help

Answers

Answer:

The ratios are proportional ratios

Answer:

Step-by-step explanation:

The ratios are proportional

[tex]\dfrac{5}{12}=\dfrac{5*2}{12*2}=\dfrac{10}{24}[/tex]

Tristan is ordering a taxi from an online taxi service. The taxi charges $3 just for the pickup and then an additional $1.50 per mile driven. How much would a taxi ride cost if Tristan is riding for 9 miles? How much would a taxi ride cost that is mm miles long?

Answers

Answer:

$ 16.50

y = 1.50m + 3

Step-by-step explanation:

1.50(9) + 3 = $16.50

Convert 5 over 9 into a decimal

Answers

Answer: 0.556

Step-by-step explanation:

Answer:

5/9 as a decimal is .5 repeating. I hope this helps.

MATH WEEK 5 DISCUSSION

Answers

5 ————————————————————————-

solve pls brainliest

Answers

Answer: (a.) +3 meters each second   (b.) +80 Celsius

Step-by-step explanation:

(a.) 18/6 =+3 meters each           (b.) 4*20=+80 Celsius

(b.) 4*every hour=

HELP HELP EASY
Use a calculator to approximate cos 43° and round to
four decimal places.

Answers

Answer:

0.731353701619170483287543608275622403378...

Step-by-step explanation:

cos((43 π)/180)

UwU

It's verified you can trust

0.7315

Is what you needed

Solve x2+12x=82 using completing the square. Answer the questions below.

Answers

Answer:

exact form : x =  ± √ 118 − 6

Decimal form :  x =  4.86278049 or − 16.86278049

Step-by-step explanation:

Use the formula  ( b /2 ) ^2  in order to create a new term. Solve for  x  by using this term to complete the square.

(I'LL GIVE BRAINLIEST) Carson wanted to buy a cowboy hat that cost $49.95 (with tax) at a souvenir shop. He knew he had $18 at home already, and he could earn $10 per lawn by mowing lawns for his neighbors. He came up with the following expression to figure out how many lawns he would need to mow in order to purchase the hat: M = 10w + 18 with "w" being the number of lawns he would need to mow and "M" being the total amount of money he has.
Carson then determined he would need to mow 3 lawns by completing the follow steps:
50 = 10w + 18
32 = 10w
3.2 = w

Identify Carson's error. Explain the steps to correctly solve for how many lawns Carson needs to mow. Be sure to clearly state the correct answer.

Answers

Answer:

so Carson's problem was at the end, since the neighbors are paying 10$ PER DAY, and 3 days work would only earn him 30$ meaning at the end he would be a dollar short, technically, he needs to work exactly 3.2 days, or...

let's say he works 4 hrs a day

1 Day = 4Hr

3.2 Days = X

X = 3.2 × 4

= 12.8 Hrs

so Carson needs to work 3 days and an extra 48 Minutes

2x2=6 %234664. I don’t mean

-6.4x + 3.5y = 7? what is the slope

Answers

6.4/3.5, OR about 1.83

First job is to isolate the y.

3.5y=6.4x+7

Now divide both sides by 3.5 to get the equation into y=mx+b form.

That leaves a rounded equation of y=1.83x+2

In y=mx+b, the m is the slope. This means the slope of this line is 1.83, or 6.4/3.5

Ai chỉ cách làm cho mk vs ạ

Answers

I don’t understand sorry

f(x)=[tex]x^{2}[/tex]-6x+9

Answers

Answer:

x equals three by multiplicity two

Step-by-step explanation:

that's the correct answer hope it's help.

How many pints of blood does a person have for every 14 lbs of body weight?

Answers

Answer:

1 pint(of blood) for every 14 lbs of weight

Step-by-step explanation:

Answer:

One pint.

Step-by-step explanation:

A person has approximately one pint of blood for every 14 pounds of body weight.

Hope this helps! :D

According to the Rational Root Theorem, which statement about f(x)=8x3−4x2+6x+3 is true?

Group of answer choices

Any rational root of f(x) is a multiple of 8 divided by a multiple of 3.

Any rational root of f(x) is a factor of 8 divided by a factor of 3.

Any rational root of f(x) is a multiple of 3 divided by a multiple of 8.

Any rational root of f(x) is a factor of 3 divided by a factor of 8.

Answers

The rational root theorem is used to determine the possible roots of a function.

The true statement is: (d) Any rational root of f(x) is a factor of 3 divided by a factor of 8.

The function is given as:

[tex]\mathbf{f(x) = 8x^3 - 4x^2 + 6x + 3}[/tex]

The possible roots of a function

[tex]\mathbf{f(x) = qx^n + ax^{n-1} +.....+ p}[/tex]

are

[tex]\mathbf{Roots = \pm\frac{Factors\ of\ p}{Factors\ of\ q}}[/tex]

By comparison: p = 3 and q = 8

So, we have:

[tex]\mathbf{Roots = \pm\frac{Factors\ of\ 3}{Factors\ of\ 8}}[/tex]

Hence, the true option is (d) Any rational root of f(x) is a factor of 3 divided by a factor of 8.

Read more about rational root theorem at:

https://brainly.com/question/9353378

solution needed step by step ​

Answers

Answer:

I am doinnnng ok just wait

Answer:

Points again!!!

Step-by-step explanation:

Hey thanks

Triangle ABC, with A = (-2,3) B = (-4,1) and C = (-3,5), is rotated 90- clockwise about the origin to make Triangle A'B'C'. What are the y-coordinates of B'?

Answers

Answer:

Step-by-step explanation:

-1

Carson has a smart phone data plan that costs $35 per month that includes 10 GB of data, but will charge an extra $15 per GB over the included amount. How much would Carson have to pay in a month where he used 3 GB over the limit? How much would Carson have to pay in a month where he used went over by x GB?

Answers

Answer:

3 GB over: $80 x GB over: $35+$15x

Step-by-step explanation:

3 GB over is 3 times 15 plus 35, which equals 80, x GB over is x times 15 plus 35. Boom, answer.

Your welcome!

Answer:

$80

Step-by-step explanation:

530÷34= ? Write answer as a whole number and remainder.

Answers

Answer:

15 with a remainder of 20

Step-by-step explanation:

hope it helps :)

Answer:

168 and the remainder is 7

Step-by-step explanation:

if is wrong i'm sorry

1) Eight times the difference between a number and seven, is the same as when five times
the number is increased by four. Find the number.

Answers

Tip: Go step-by-step

Let the number = x

Eight times the difference between a number and seven.. = 8(x-7)

is the same as... =

the number increased by 4.. x+4

8(x-7)=x+4

Distribute

8x-56=x+4

Subtract x from both sides

7x-56=4

Add 56 to both sides

7x=60

x=60/7

Joseph takes his little brother to the local frozen yogurt shop. he doesn't want his brother to spoil his dinner, so he can get no more than three ounces bought. the function consists only of the ordered pairs (0, 0.35), (1,1.35), (2,2.35) and (3,3.35) what is the domain and range of the function?

Answers

Answer:

Domain: (0,1,23)

Range: (0.35,1.35,2.35)

Step-by-step explanation: The domain is the set of all the first components of the ordered pairs, and the range is the set of all the second components of the ordered pairs.

What is
(1/2)^2- 1/2 -6








.

Answers

Answer:

-6.25 tI am not sure if this can help you but this is what I got

I need the answer ASAP

Answers

Answer:

It would be 120 inches squared.

Step-by-step explanation:

12 x 8 = 96

6 x 4 = 24 / 2 = 12

12 x 2 = 24

96 + 24 = 120 inches squared

Answer: 80 in 2 cm

Step-by-step explanation: so if you add you can find it but add you answer you get 2 times and round to the nearest ten and you have your answer.

Need help with number 10

Answers

Answer:

d

Step-by-step explanation:

the answer is d, tan = (cateto opuesto / cateto adyascente)

D.

Tan is opposite/adjacent
Tan35 = .7002
.7002 = opposite/60
.7002*60=42.012
Opposite = width of river = 42.0

Correct answer gets brainiest

Answers

Answer:

[tex]x + 2x + a + 90 \degree = 360\degree \\ x + 2x + 132\degree + 90 \degree = 360\degree \\ 3x + 222\degree = 360\degree \\ 3x = 360\degree - 222\degree \\ 3x = 138\degree \\ x = \frac{138\degree}{3} \\ \boxed{ x = 46\degree}[/tex]

There are three sizes of pizza, three of crust, and ten toppings. If you Order one size, one type of crust, and one topping, how many pizza choices are there?

Answers

3 Sizes
3 crusts
10 top
3x3=9
9x10=90
90 different pizza choices

_
Write 0.34 as a fraction using the steps below.

Answers

Answer:

31/90

Step-by-step explanation:

3.1 x 10 = 31 which is the numerator

9x10 = 90 which would be the denominator

Answer:

It would be 17/50 hope that helps

For the simple linear equation below, what is the y-coordinate of the ordered pair when the x-coordinate is -15? y=4/5x Enter your answer in the box.(-15, )​

Answers

Answer:

The answer is -12

Step-by-step explanation:

90000 1000 + 7000 + 7 =​

Answers

Answer:

900,008,007

Step-by-step explanation:

first add 90000,1000 +7000=900,008,000

then add 7 with 900,008,000

Answer =900,008,007

What did James earn this pay period? (use pay stub) *
1 point
$1451.28
$1000.00
$709.74

Answers

make a purchase, then the statement is true.
If you just leave the balance <> to 0 and don't purchase anything more, the interest just keeps on building up. It is the surest way to get into financial trouble.

What is 6 tens = ? Ones

Answers

6 tens would be 60 ones

Round 171,936 to the nearest ten thousand

Answers

Answer:

Rounding = 170,000

Your answer is →  170,000

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