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

Answers

Answer 1

Answer:3

Step-by-step explanation:

Given

Quadratic equation is [tex]x^2-4+k=0[/tex]

if one root exceeds the other by two

suppose one of the roots is a, then the other is a+2

The Sum of roots is

[tex]=\dfrac{-\text{coefficient of x}}{\text{coefficient of }x^2}[/tex]

[tex]\therefore a+a+2=-\dfrac{-0}{1}\\\\\Rightarrow 2a+2=0\\\Rightarrow a=-1[/tex]

Product of roots

[tex]\Rightarrow (a)(a+2)=\dfrac{k-4}{1}\\\Rightarrow (-1)(1)=k-4\\\Rightarrow k=4-1=3[/tex]


Related Questions



Jessica paid $23,000 for her car. The value of the car depreciates at a rate of 15% each year. Which function represents the value of her car each year?

Answers

Answer:

Step-by-step explanation:

DOES ANYONE KNOW THE ANSWER

HELPPPP HELPPP IM GOING TO FAILLL

Answers

Answer: A is the answer

Step-by-step explanation:

ANSWER: y = (4/3)x + 4

The slope of the line is 4/3 and it crosses the y-axis at 4

A customer buys a CD for $15 and a video game. The customer pays a total of $42.80 for the two items, which includes 7% sales tax. Which equation can be used to find x, the cost of the video game before tax? 0.07 (15 + x) = 42.80 0.07 (42.8 minus 15) = x 1.07 (15 + x) = 42.80 1.07 (42.8 minus 15) = x

Answers

Answer:

1.07 (15 + x) = 42.80

Step-by-step explanation:

Given data

CD= $15

Let the cost of the video game be x

The total cost= 15+x

Hence the equivalent expression is

1.07 (15 + x) = 42.80

open bracket

16.05+1.07x= 42.80

42.80-16.05= 1.07x

26.75=1.07x

x= 26.75/1.07

x= 25

Check

7% tax for CD

=0.07*15

=1.05

total =1.05+15

=$16.05

7% tax for Video game

=0.07* 25

=1.75

total =1.75+25

=$26.75

In all

=26.75+16.05

=$42.8

PLEASE HELPPPPPPP ASAPPP
Using PT in the Coordinate System
Find the length of the legs.
(4.4)
(-2,-2)
[?]
Enter the number that
belongs in the green box.

Answers

Answer:

6 units

Step-by-step explanation:

distance between (-2,-2) and (4,-2)

distance formula,

√(x2-x1)²+(y2-y1)²

x2=4

x1=-2

y1=-2

y2=-2

putting the values,

√(4+2)²+(-2+2)²

√6²+0²

6 units

question in pic! will give brainliest! help asap

Answers

Answer:

(5x^2+1)(4x-1) is the answer

A company donates to charity every year as its contribution to society. If the company makes a profit in that year, 2/9 of the profit will be allocated for donation. If the company incurs a loss, the company will also allocate 0.05 of the loss for donation. If the company makes a profit of RM43.2 million in a certain year
and incurs a loss of RM2.5 million and RM6.5 million respectively in two consecutive years, calculate the total donations the company would have allocated for charity in those three years.


can someone please help meee

Answers

Answer:

RM10.05 million

Step-by-step explanation:

year 1 profit= RM 43.2m yr 2 loss =RM 2.5 myr 3 loss=RM 6.5 m

therefore:

2/9 of 43.2

=9.6m

5/100 of 2.5m

=125,000

5/100 of 6.5m

=325,000

therefore total donations are :

9,600,000+125,000+325,000

=10,050,000

I tried... hope it helps

1. How many goldfish do you have if 30% of the entire population of 20 fish in your tank are goldfish?

Answers

Answer:

6 Goldfish

Step-by-step explanation:

Answer:

66.6 becuz you divide it

Helllohello help please if you want -

Answers

3(7d + 4e) = 3 • 7d + 3 • 4e = 21d + 12e

True or False: If two parallel lines are cut by a transversal, each pair of supplementary angles are congruent

Answers

Answer:

this is a true. hdudndjfnfjfndbf9

Find the area of AABC with A = (1,3), B = (5, 7), and
C = (6,3).

Answers

Answer:

A=L×B

A=1×3

A=3cm²

B=L×B

B=5×7

B=35cm²

C=L×B

C=6×3

C=18cm²

Due today!!!!!!! Help!!!!!!

Select all of the quadratic expressions in vertex form.

Group of answer choices

(x−2)2+1


x2−4


x(x+1)


(x+3)2


(x−4)2+6

Answers

Answer:

All except x2-4 and x(x+1)

Step-by-step explanation:

Standard Form: ax^2 + bx + c

Vertex Form: a(x - h)^2 + k

Hope that helps you!!

find area will mark brainlist

Answers

Answer:

I hope this helps you

Step-by-step explanation:

A = 1/2 h (a+b)

= 1/2 × 8 (15+21)

= 1/2 × 36 × 8

= 36×4

= 144

Answer:

29

Step-by-step explanation:

18+15=23 8+21=29

Factor the expressions using the GCF 54-30

Answers

I'm sorry, but what exactly are the expressions?

If you comment the expression under my answer, I'll edit my answer and actually answer it.

But nobody can answer an expression that doesn't exist-

how do you solve for exterior angle therom

Answers

Answer:

The interior angles of a triangle add to 180°:a + b + c = 180°

Angles c and d make a straight angle, which is 180°:d + c = 180°

So d + c equals a + b + c:d + c = a + b + c.

Subtract c from both sides:d = a + b.

Step-by-step explanation:

HELP ME PLEASE (no links)

Answers

Answer:

y = 1.5x

Step-by-step explanation:

We are to find the equation of the straight line

Using the coordinate (0, 0) and (200, 300)

Slope m = 300-0/200-0

m = 300/200

m = 1.5

Since the line pass through the origin, the y intercept is 0

Substitute m = 1.5 and b =0 into y = mx+b

y = 1.5x + 0

y = 1.5x

This gives the required equation

Sandra runs A new personal best in the hundred meter dash her average speed is 7.4 m/s how long to the nearest hundredth does it take her to run the race

Answers

Answer:

[tex]13.51\ \text{s}[/tex]

Step-by-step explanation:

[tex]s[/tex] = Average speed of Sandra = [tex]7.4\ \text{m/s}[/tex]

[tex]d[/tex] = Distance Sandra ran = [tex]100\ \text{m}[/tex]

Time is given by

[tex]t=\dfrac{d}{s}[/tex]

[tex]\Rightarrow t=\dfrac{100}{7.4}[/tex]

[tex]\Rightarrow t=13.51\ \text{s}[/tex]

The time it takes Sandra to run the given distance is [tex]13.51\ \text{s}[/tex].

A roll of ribbon is used to tie 12 gifts which will be given to teachers on Teacher's
Day. Every gift requires a length of 1.85 m. After tying all the gifts, it was found that
2
of the ribbon had been used. The remaining ribbon was cut into 12 pieces of the
3
same length. Calculate the length of each piece of ribbon that had been cut.​

someone please help me with this question

Answers

Answer:

22.2m

Step-by-step explanation:

1 roll to 12 gifts

one gifts uses 1,85m of ribbon

1,85m is the length

12 × 1.85 = 22.2m

Jordan baked 4 apple pies. She wants to share them equally among 3 of her neighbors. What fractional part of the pies will each neighbor get?


A. 3/7

B. 3/4

C. 1 1/3

D. 2 1/3

Answers

Answer:

C.

Step-by-step explanation:

1 1/3 as an improper fraction is 4/3.

Please make me the brainliest

Please help ASAP i don’t know how to do this

Answers

Answer:

c = 74

d = 122

a = 58

b = 48

Step-by-step explanation:

C: a triangle always equals to 180, so 48 + 58 - 180 = 74

D: Angels next to each other on a line always equal to 180, so 180 - 58 = 122

A: Alternating interior angles of a parallel line equal to each other, so it would also be 58

B: A line is 180, so C + A - 180 = B, 74 + 58 - 180 = 48

Which data set could be represented by the box plot shown below?

Choose 1 answer:

A 2,3,5,5, 7, 7, 8, 10, 11


B 2,3,5,5,6,7,8,8,11

C 2,3,5,5, 6, 7, 8, 10, 11

D 3,3,5,5, 6, 7, 8, 9, 11

Answers

A data set which could be represented by the box plot shown above include the following: B. 2, 3, 5, 5, 6, 7, 8, 8, 11.

What is a box plot?

In Mathematics, a box plot is sometimes referred to as a box-and-whisker plot and it can be defined as a type of chart that is used for the graphical or visual representation of the five-number summary of a data set with respect to locality, skewness, and spread.

By using the box-and-whisker plot (box plot) shown in the image attached above, the five-number summary for the given data set include the following:

Minimum = 2.First quartile = 4.Median = 6.Third quartile = 8.Maximum = 11.

By critically observing the box-and-whisker plots (see attachment), we can logically deduce that it represents all of the five-number summary for 2, 3, 5, 5, 6, 7, 8, 8, and 11.

Read more on box plot here: brainly.com/question/14277132

#SPJ1

Lin and Kal's ages add up to 41 Lin is 5 years older than Kal. Use the equation from the to find their ages.​

Answers

Kal is 18 Lin is 23 divide then subtract

Helpppp me pleaseee

Answers

Answer:

1 st questions answer is  third option

while the answer of other question is  3

Step-by-step explanation:

2nd qestions explanation

put value of x=2 in equation as x-2=0 from equation

(2)^3-6(2)^2+a2+10=2

8-24+a2+10=0

2a=-18+24

2a=6

a=3

A fun park charges $10 for admission and then two dollars for every ride. Write a function that determines the amount of money spent, Y, based on the number of rides ridden, X.!! please help ahhh

Answers

Answer:

x is I think 5

Step-by-step explanation:

dndjdudjndndjdjdjjd

a recipe requires 2/3 cup of sugar to make one cake what is the maximum number of cakes that can be made using 4 1/2 cups of sugar​

Answers

Answer:

6

Step-by-step explanation:

2/3, 1 1/3, 2, 2 2/3, 3 1/3, 4

A pole that is 12 feet tall casts a shadow
that is 9 feet long. At the same time of
day, how long is the shadow cast by a tree
that is 4 5 feet tall?

Answers

3.375 because 9 is 3/4th of the 12 so you would divide 4.5 by 4 and multiply by 3 and it gives you 3.375

Plzzzzzzzzzzzzz help me giving 30 points i asked this question too much.

Answers

Answer:

$1.90  1 9/10

Step-by-step explanation:

5 1/2= $5.50

5.50+2.60= 8.10

10-8.10= $1.90

If three the coordinates of a quadrilateral are at A(3,2), B(-4, 2), and C(-4, -1). What are the coordinates of the 4th corner, point D?

Answers

(3,-1)

it should shape like a square or rectangle when you plot it

hope it helps !

1½–¾ what is the answer to this fraction ​

Answers

Answer:

0.75 or 3/4

Step-by-step explanation:

~Convert the mixed numbers into improper fractions

~Then find the LCD (Least Common Denominator) and combine

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

GL.

Answer:

3/4

Step-by-step explanation:

1½ = 3/2

3/2 _ 3/4 =

[tex] \ \frac{3 \times 2}{2 \times 2} - \frac{3}{4} [/tex]

[tex] \frac{6}{4} - \frac{3}{4} = \frac{6 - 3}{4} = \frac{3}{4} [/tex]

i need help with this..​

Answers

Answer:

a = 9

Step-by-step explanation:

sin45 = a/9√2

a = 9√2(sin45)

a = 9

Please help due in 15 minutes!!!!!

Answers

Answer:

44ft

Step-by-step explanation:

The formula for circumference is 2 * π * radius and in this case we want to use 3.14 for π and so we do 2 x 3.14 x 7 because the radius is half of the diameter (14) and once you do that you end up getting 43.96 and once you round you get 44ft so you are correct.

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