If one of the roots of the equation x²- 4x + k=0exceeds the other by 2, then find the roots and determine the value of k

Answers

Answer 1

Answer:

roots: 1 and 3

k = 3

Step-by-step explanation:

2 roots: p and p+2

(x-p) (x-p-2) = x² - 4x + k

x² -2px -2x + p² + 2p = x² - 2 (p+1)x + (p² + 2p) = x² -4x + k

-2 (p+1) = -4

p+1 = 2

p = 1   ... root 1

p' = 1+2 = 3   ... root 2

k = p² + 2p = 3

check: (x-1) (x-3) = x² - 4x + 3 = x² - 4x + k


Related Questions

[AB] is a diameter of center C(O, 3cm). M is a point on (C) such that MA=MB. D is the symmetric of A with respect to M.
What is the nature of triangle AMB? Justify. ​

Answers

Answer:  I dont know AZ

Ab and cd intersects at e, aec=5x+12 and deb=8x-3

Answers

Answer:

x = 5

Step-by-step explanation:

Angles DEB and AEC are vertical angles, so they are congruent, and their measures are equal.

8x - 3 = 5x + 12

3x = 15

License plates in the tiny country of Venn follow a unique pattern. The first character is one of 41 Egyptian hieroglyphs, the second is one of 39 emojis, and the third character is one of 10 polygons. How many 3 character license plates are available to the people of Venn?

Answers

Answer:

12710 license plates

Step-by-step explanation:

Given that :

First character = one of 41 different hieroglyphs

Second character = one of 31 emojis

Third character = one of 10 polygons

A license plate consists of 3 characters

Number of 3-character license plates available :

Number of hieroglyphs * Number of emojis * number of polygons

41 * 31 * 10 = 12710 license plates.

A survey was conducted on 800 students regarding the number of automobiles in their household. The population mean is 2.7 automobiles with a standard deviation of 0.7.

Which statement is true?
A.
There is a 95% certainty that the sample mean will fall within the interval 2.68 to 2.72.
B.
There is a 95% certainty that the sample mean will fall within the interval 2.67 to 2.73.
C.
There is a 95% certainty that the sample mean will fall within the interval 2.62 to 2.77.
D.
There is a 95% certainty that the sample mean will fall within the interval 2.65 to 2.75.

Answers

I can’t say much but I guess C

((will give brainliest)) What is the output of the function y = 12 + 3x if the input is 5.​

Answers

Answer:

y = 27

Step-by-step explanation:

The output is the value of y when x = 5

Substitute x = 5 into the function , that is

y = 12 + 3(5) = 12 + 15 = 27 ← output

output is 27

to solve you plug in the input into x and rewrite the equation as y=12+3(5) then you add 12+15 and get y=27

In a random sample, 3 of 400 computer chips are defective. Based on
the sample, how many chips out of 100,000 would you expect to be
defective?

Answers

Answer:

750 of 100,000 chips would be expected to be defective.

Step-by-step explanation:

(3/400) and (?/100,000)

100,000 ÷ 400 = 250.

Multiply 250 by 3 to find the number of defective chips.

250 x 3 = 750.

The base of a 14-foot ladder is 2 feet from a building. If the ladder reaches the flat roof , how tall is the building

Answers

the building is around 14.14 feet tall

a^2 + b^2 = c^2
14^2 + 2^2 = 200
squareroot 200 is abt 14.14

Answer:

Step-by-step explanation:

The height of the building is 8 rad 3

Approximately 13.9 ft

QUESTION 6 / 10
Which of the following is not a source of income?

A. Your monthly student loan payment.

B. The stipend you receive for doing an internship.

C. Your annual salary for doing your job.

D. The wages you receive after a work shift.

Answers

Answer:

b. The stipend you receive.

Step-by-step explanation:

It would say paid intern if they were paid.

Can someone help me with this??

Answers

Answer:

A

Step-by-step explanation:

When dilating an object, you multiply the x and y values by whatever scale you want to dilate the object by. It cannot be C because 2/5 is less than 1, which means that the object would shrink. So the answer must be A

Simplify the expression to standard form

-2.5(-3+ 4n+8)

Answers

Answer:

-12.5-10n

Step-by-step explanation:

jjjjjjjvuvubibuvuvuvibibivi

Answer:

distribute to get:

7.5 -10n -20

-10n - 12.5

1. What is the decimal equivalent of 3/
9? 0.2 0.3 0.4 0.5​

Answers

0,3 is the decimal equivalent of 3/9

Which expressions are equivalent to this exponential expression?
6-10
6-4
06-6
0 66
0
1
0
O
1
36

Answers

Answer:

6*6=36

Step-by-step explanation:

6*6. 6 with exponent of 2=36

Please look at the picture and answer my question I need help!

Answers

Answer:

64oz=4lb

Step-by-step explanation:

When converting ounces to pounds there is a 16:1 ratio, or there is 16 ounces in every pound.

To solve this, simply do 64/16 and you'll get your answer of 64oz=4lb.

64/16=4

64oz=4lb

An interior designer wants to place this bed in a home, and she is especially concerned about the headboard, which is 6 feet wide and 5 feet tall. She’ll place the headboard on a wall that is 7 feet wide and 9 feet tall. She needs to know the area of the space that will remain after she places the bed against the wall

Answers

Answer:

Step-by-step explanation:

Area of the Wall minus the Area of the headboard      

Area = length x width      in  this use tall as length and wide as width

Area Wall - Area Headboard  =  (Tall wall)(Wide wall)  -  (Tall head)(Wide head)

                 =  (9)(7) - (5)(6) feet

                 =    63 - 30  feet

                 =   ????                      I'll let you finish it

The area of the space that will remain after she places the bed against the wall is 30 feet².

What is Area?

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area.

We have,

The headboard, which is 6 feet wide and 5 feet tall.

The headboard on a wall that is 7 feet wide and 9 feet tall.

So, Area of remaining space

= Area of the Wall - Area of the headboard      

= (9)(7) - (5)(6) feet

= 63 - 30  

= 30 feet²

               

Learn more about Area here:

https://brainly.com/question/27683633

#SPJ5

If a car has tires with a diameter of 28 inches and is traveling at 55 mph, how fast are its tires spinning, in rpm^ prime s (revolutions per minute)? [There are 63,360 inches in 1 mile) Round your final answer to 2 decimal places .

Answers

Answer:

The tires are spinning at 660.49 revolutions per minute.

Step-by-step explanation:

The speed of the tires (v) is the same that the speed of the car, so to find the angular velocity of the tires we need to use the equation:

[tex] \omega = \frac{v}{r} [/tex]

Where:

r: is the radius of the tires = d/2 = 28 inches/2 = 14 inches

[tex]\omega = \frac{55 mph}{14 inches*\frac{1 mile}{63360 inches}} = 2.49 \cdot 10^{5} \frac{rad}{h}*\frac{1 h}{60 min}*\frac{1 rev}{2\pi rad} = 660.49 rpm[/tex]              

Therefore, the tires are spinning at 660.49 revolutions per minute.

   

I hope it helps you!          

EXPLAIN YOUR WORK PLZ

AJ worked 48 hours last week. He earns $15.40 per hour plus overtime, at the usual rate, for hours exceeding 40 hours. What was his gross pay?
A $644.80
B$739.20
C$800.80
D$1,108.80

Answers

Answer:

D

Step-by-step explanation:

It will be $1,108.0 Because if you devide 40 by the hours, Plus the pay which is 15.40 You will get D

Carlos has 2.6 meters of wire. He has 3 projects for which he needs 0.9 meters each. Does carlos have enough wires?

Answers

Answer: Carlos does not have enough wires by 0.1 meters

Step-by-step explanation:

To determine if Carlos has enough wires, you need to find out the total amount of wires needed and then compare this to the amount of wires that Carlos has already.

= 0.9 + 0.9 + 0.9

= 2.7 meters

Carlos has 2.6 meters of wire but needs 2.7 meters.  

Carlos therefore, does not have enough wires.

A 30 year fixed rate mortgage at 4.5% with principal of $150,000 has a monthly payment of $760 per month. After
30 years, what is the total amount spent on interest?
A) $6,750
B) $123,600
c) $156,750
D) $273,600

Answers

Answer:

A 30 year fixed rate mortgage at 4.5% with principal of $150,000 has a monthly payment of $760 per month. After

30 years, what is the total amount spent on interest?

A) $6,750

B) $123,600

c) $156,750

D) $273,600

Step-by-step explanation:

Plz, answer this question plz!

Answers

c. that is da answer swag

what is the sum of -4/7 and 6/7

Answers

Answer:

2/7

Step-by-step explanation:

Since the denominators are the same, we need to add the numerators and place it over the common denominator

-4+6 = 2

so

-4/7 + 6/7 = 2/7

2/7

Answer:

B

Step-by-step explanation:

Is parallelogram BCDE a rectangle?

Answers

No, all lines should be equal considering that rectangles have 4 of the same right angles

can someone help please ​

Answers

half of the triangle is a right angle triangle, so we use the phythagoras theorem and multipy our answer by 2

plz help me I only have 5 minutes left winner gets brainliest
In what year did the Apartheid Laws in South Africa end?



1990


1972


1994


1958

Answers

They ended in the early 1990s

Answer:1994.

Step-by-step explanation:I need brainliest I helped with your other questions in comments pls

Analyze: 30 + 11 when c=4

Answers

It would be 23 because 3(4) + 11 would convert to 12 + 11 giving you 23

Answer:

23

Step-by-step explanation:

3c + 11

3(4) + 11

12 + 11

23

Help, Help, Please
[tex] \sf find \: the \: value \: of \: \theta \: when \: \theta \: is \: acute\: angle[/tex]
[tex] \sf \cos^{2}(\theta) - \sin^{2}(\theta) =2-5 \cos(\theta) [/tex]
[tex]\text{note:explanation is a must}[/tex]

Answers

Answer:

θ = [tex]\frac{\pi }{3}[/tex] (60° )

Step-by-step explanation:

Using the identity

sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x

Given

cos²θ - sin²θ = 2 - 5cosθ

cos²θ - (1 - cos²θ) = 2 - 5cosθ

cos²θ - 1 + cos²θ = 2 - 5cosθ

2cos²θ - 1 = 2 - 5cosθ ( subtract 2 - 5cosθ from both sides )

2cos²θ + 5cosθ - 3 = 0 ← in standard form

(cosθ + 3)(2cosθ - 1) = 0 ← in factored form

Equate each factor to zero and solve for θ

cosθ + 3 = 0

cosθ = - 3 ← not possible as - 1 ≤ cosθ  ≤ 1

2cosθ - 1 = 0

cosθ = [tex]\frac{1}{2}[/tex] , so

θ = [tex]cos^{-1}[/tex] ([tex]\frac{1}{2}[/tex] ) = [tex]\frac{\pi }{3}[/tex] ( or 60° )

Answer:

[tex] \huge \boxed{ \boxed{\blue{ { \theta = 60}^{ \circ} }}}[/tex]

Step-by-step explanation:

to understand thisyou need to know about:trigonometryPEMDASlet's solve:[tex] \sf \: rewrite \: \sin ^{2} ( \theta) \: as \: 1 - \cos ^{2} ( \theta) : \\ \sf \implies \: \cos ^{2} ( \theta) - (1 - \cos ^{2} ( \theta)) = 2 - 5 \cos( \theta) [/tex][tex] \sf \: remove \: parentheses \: and \: change \: its \: sign : \\ \sf \implies \: \cos ^{2} ( \theta) - 1 + \cos ^{2} ( \theta)) = 2 - 5 \cos( \theta) [/tex][tex] \sf \: add : \\ \sf \implies \: 2\cos ^{2} ( \theta) - 1 = 2 - 5 \cos( \theta) [/tex][tex] \sf \: move \: left \: hand \: sides \: expression \: to \: right \: hand \: sides \: : \\ \sf \implies \: 2\cos ^{2} ( \theta) + 5 \cos( \theta) - 1 -2 = 0[/tex][tex] \sf \: rewrite \: 5\cos( \theta) \: as \: 6 \cos( \theta) - \cos( \theta) : \\ \sf \implies \: 2\cos ^{2} ( \theta) + 6 \cos( \theta) - \cos( \theta) - 3 = 0[/tex][tex] \sf \:factor \: out \: 2 \cos( \theta) \: and \: - 1 : \\ \sf \implies \: 2\cos ( \theta)( \cos( \theta) + 3 ) -1( \cos( \theta) + 3) = 0[/tex][tex] \sf \: group: \\ \sf \implies \: (2\cos( \theta) - 1) ( \cos( \theta) + 3 ) = 0[/tex][tex] \sf \: rewrite \: as \: two \: seperate \: equation: \\ \sf \implies \: \begin{cases}2\cos( \theta) - 1 = 0\\ \cos( \theta) + 3 = 0 \end{cases} [/tex][tex]\sf add \: 1 \: to \: the\: first \: equation \: and \: substract \: 3 \: from \: the \: second \: equation: \\ \sf \implies \: \begin{cases}2\cos( \theta) = 1\\ \cos( \theta) = - 3 \end{cases} [/tex]

[tex] \sf the \: second \: eqution \: is \: false \: \\ \sf because \: - 1 \leqslant \cos( \theta) \leqslant 1 \: \\ \sf but \: we \: can \: still \: work \: with \: the \: second \: equation[/tex]

[tex] \sf substract \: both \: sides \: by \: 2 : \\ \implies\frac{ 2\cos( \theta) }{2} = \frac{1}{2} \\ \implies\cos( \theta) = \frac{1}{2} \\ \therefore \: \theta \: = {60}^{ \circ} [/tex]

The local movie theater charges $13 for adult tickets and $7 for children’s tickets. Yesterday they sold 115 tickets and made $943. How many adult and children tickets did they sell?

Answers

Answer:

i need more info

Step-by-step explanation:

At the craft store, Amelia bought a bag of purple and yellow marbles. She received 75 marbles in all. 15 of the marbles were purple. What percentage of the marbles were purple?

Answers

Answer: 20%

Step-by-step explanation:

Given

Total marbles are 75

Out of this 15 are purple

Percentage of purple marbles is given by

[tex]\Rightarrow \dfrac{15}{75}\times 100=20\%[/tex]

So, purple marble constitutes of 20%

Find the values of x and y that make these triangles congruent by the HL Theorem

Answers

Answer:

number 3

because because because because because because because because because

Step-by-step explanation:

because because because because

Complete the following equation <, >, or = 3.20_ 3.02

Answers

Answer:

Step-by-step explanation:

Complete the following equation using , or = 3.20 ___ 3.02 A.

The following equation 3.20 > 3.02

The equation shown has an unknown number ⍰÷3/4=4/9

Answers

Answer:

9

Step-by-step explanation:

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