1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
zlopas [31]
2 years ago
12

For which positive integer values of $k$ does $kx^2+20x+k=0$ have rational solutions? Express your answers separated by commas a

nd in increasing order.
Mathematics
1 answer:
Musya8 [376]2 years ago
3 0

Answer:

-10,10

Step-by-step explanation:

The given quadratic equation is

k {x}^{2}  + 20x + k = 0

The discriminant of this equation is given by;

D =  {b}^{2}  - 4ac

where a=k, b=20, c=k

For rational solutions, the discriminant must be zero.

{20}^{2}  - 4 \times k \times k = 0

Simplify to get:

400 - 4  {k}^{2}  = 0

This implies that:

400  = 4  {k}^{2}

100 =  {k}^{2}

Take square root to get:

k =   \pm\sqrt{100}

k =  \pm10

k =  - 10 \: or \: k = 10

You might be interested in
The radius of a circle is 4 feet. What is the area of a sector bounded by a 45° arc?
DIA [1.3K]

Answer:

Area = 6.28\  ft^2 or Area = 2  \pi\ ft^2

Step-by-step explanation:

Given

Radius, r = 4ft

Angle, \theta = 45

Required

Calculate the area of the sector

When angle is given in degrees, the area of sector is calculated as thus;

Area = \frac{\theta}{360} * \pi * r^2

Substitute\ r = 4\ and\ \theta = 45

Area = \frac{\theta}{360} * \pi * r^2 becomes

Area = \frac{45}{360} * \pi * 4^2

Area = \frac{45}{360} * \pi * 16

Area = \frac{45*16}{360} * \pi

Area = \frac{720}{360} * \pi

Area = 2 * \pi

Area = 2  \pi\ ft^2

The above is the area in terms of π

Solving further.... (Take π as 3.14)

Area = 2  \pi\ ft^2 becomes

Area = 2 * 3.14\  ft^2

Area = 6.28\  ft^2

Hence, the area of the sector is

Area = 6.28\  ft^2 or Area = 2  \pi\ ft^2

8 0
3 years ago
Instructions: Match each equations with correct type of event.
Mazyrski [523]

The question is incomplete. Below you will find the missing contents.

The correct match of events with order are,

  • P(A)P(B|A) - Dependent event
  • P(A)+P(B) - Mutually exclusive events
  • P(A and B)/P(A) - Conditional events
  • P(A) . P(B) - Independent Events
  • P(A)+P(B) -P(A and B) - not Mutually exclusive events.

When two events A and B are independent then,

P(A and B)=P(A).P(B)

when A and B are dependent events then,

P(A and B) = P(A) . P(B|A)

When two events A and B are mutually exclusive events then,

P(A and B)=0

So, P(A or B) = P(A) + P(B) - P(A and B) = P(A) + P(B)

P(A) + P(B) = P(A or B)

When events are not mutually exclusive then the general relation is,

P(A or B) = P(A) + P(B) - P(A and B)

If the probability of the event B conditioned by A is given by,

\mathrm{P(B|A)=\frac{P(A~and~B)}{P(A)}}

Hence the correct match are -

  • \mathrm{P(A)P(B|A)\rightarrow} Dependent event
  • \mathrm{P(A)+P(B)}\rightarrow Mutually exclusive events
  • \mathrm{\frac{P(A ~and ~B)}{P(A)}\rightarrow} Conditional events
  • \mathrm{P(A) . P(B)\rightarrow} Independent Events
  • \mathrm{P(A)+P(B) -P(A ~and ~B)\rightarrow} not Mutually exclusive events.

Learn more about Probability of Events here -

brainly.com/question/79654680

#SPJ10

5 0
1 year ago
Use pi=3 calculate the length of a cicumference of a circle with a radius of 5cm
8_murik_8 [283]
Circumference=2pir
r=5
pi=3
circumference=(2)(3)(5)
circumfernce=6(5)
circufmerence=30

answer is 30cm
5 0
3 years ago
Find the area of the circle with the given radius or diameter. Use 3.14.
elena55 [62]

Answer:

Step-by-step explanation:

If the radius, r, is given, then the area of the circle is A = πr².

If the diameter, d, is given, then the circle area is A = π(d/2)², or A = πd² / 4.

4 0
3 years ago
Triangle X Y Z is shown. Angle X Y Z is 51 degrees and angle Y Z X is 76 degrees. The length of X Z is 2.6, the length of X Y is
Novay_Z [31]

Answer:

3.2 units

Step-by-step explanation:

Use the law of sines

z/sin 76 = 2.6/sin 51

z = 2.6 sin 76/sin 51 = 3.2

4 0
2 years ago
Other questions:
  • What is the slope of a line parallel to the line
    7·1 answer
  • There are 45 new houses being built in a neighborhood. Last month, 1/3 of them were sold. This month, 1/5 of the remaining house
    12·2 answers
  • A sofa is on sale for
    6·1 answer
  • margery decided to purchase 4 points in order to lower her interest rate on her $150,000 mortgage. how much additional money doe
    9·2 answers
  • Guys I need help... will mark brannliest IF CORRECT
    6·1 answer
  • What is the value of x? Enter your answer in the box.
    14·1 answer
  • The graph shows a parabola and its focus. Write the equation of the parabola in vertex form.​
    7·1 answer
  • C= 5/9(F−32)
    11·1 answer
  • 4x - y = 10 i need all the steps and the answer
    15·1 answer
  • b. Write a complete program for the following situation related to setting the speed of a car to preset values before starting a
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!