Consider this system of equations: y = x2 y = x + k For which value of k does the system have no real number solutions? For which value of k does the system have one real number solution? For which value of k does the system have two real number solutions?

Answers

Answer 1

Final answer:

For the given system of equations, the value of k determines the number of real number solutions.

Explanation:

In order to determine the number of real number solutions for the system of equations y = x^2 and y = x + k, we need to analyze the discriminant of the quadractic equation x^2 - (x + k) = 0.

If the discriminant is negative (less than zero), the system has no real number solutions.If the discriminant is zero, the system has one real number solution.If the discriminant is positive (greater than zero), the system has two real number solutions.

The discriminant of the quadratic equation x^2 - (x + k) = 0 can be calculated as b^2 - 4ac, where a = 1, b = -1, and c = -k.

For no real number solutions: b^2 - 4ac < 0

For one real number solution: b^2 - 4ac = 0

For two real number solutions: b^2 - 4ac > 0

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Related Questions

everyday on her way home from school, Minnie usea $1 to buy a bag of chips. The bag cost $0.75, and she saves the remaining quarter in her change jar. Minnie buys 5 bags of chips per week. At this rate, how long will it take her to save $10.00

Answers

If she saves $1.25 a week ,divide it by 10 and you get 8 weeks. It would take her 8 weeks to save $10.00 hope this helped :)

Lucy is a dress maker. She sews 4/7 of a dress in 3/4 hour. Lucy sews at a constant rate. At this rate, how many dresses does Lucy sew in one?

Answers

To find out how many dresses she can sew in one hour, divide the fraction of the dress she makes by the number of hours it takes for her to make the dress.

[tex]\sf\dfrac{4}{7}\div\dfrac{3}{4}[/tex]

When dividing fractions we flip the one we're dividing by and multiply:

[tex]\sf\dfrac{4}{7}\times\dfrac{4}{3}[/tex]

Multiply the numerators and denominators together:

[tex]\boxed{\sf\dfrac{16}{21}}[/tex]

So she sews 16/21 of a dress in one hour.

Need help! Easy!! 7th grade Pre-algebra! Easy!

Answers

7. The sign of -10 tells you the signs of the roots are different, leaving only B and C as viable choices. It is easiest to evaluate the quadratic using the integer root. When we use -2, we find the equation is satisfied.

B is the appropriate selection.

_____
8. The vertex form will be
.. y = a(x +1)² -10 . . . . . matching selections F and H
When we substitute x=1, we get 4a-10 = 2; a=3

H is the appropriate selection

The answers are B and H

a 20 foot ladder leans against a wall so that the base of the ladder is 8 feet from the base of the building. what angle does the ladder make with the ground?

Answers

66.42° you can just do 66.4°

use cos(x)8/20

The ladder makes an angle of 63.43 degrees with the ground.

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given that 20 foot ladder leans against a wall so that the base of the ladder is 8 feet from the base of the building

We need to find the angle which the ladder make with the ground.

tan(x) = opposite side / adjacent side

In this case, the opposite side is the height of the building, which is 20 feet.

The adjacent side is the distance from the wall to the base of the ladder, which is 8 feet.

Plugging in the values:

tan(x) = 20 / 8

x=tan⁻¹(20/8)

x=63.43 degrees

x is the angle

Hence, the ladder makes an angle of 63.43 degrees with the ground.

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The ratio of the number of boys to the number of girls in the class is 1:6. Which statement must describe the class?

A) There are exactly 7 students in the class.

B) There is 1 boy for every 6 girls in the class.

C) There are 5 more girls than boys in the class.

D) There is 1 boy out of the 6 students in the class.

Answers

Your answers either A or B but im leaning more towards A

: ) have a nice day

Answer: B

Step-by-step explanation: If it is asking the ratio from boys to girls the boy would be 1 and the girl would be 6 so the ratio is for every one boy is six girls. So it would be B.

what is yhe best approximation of the value of w?
A) 1.4 cm
B) 4.0 cm
C) 6.0 cm
D) 7.3 cm

Answers

b 4.0 cm because if you think about it the one that says 3.3 cm is actually just slightly shorter than w so it has to be 4.0cm

Answer

B) 4.0 cm

Explanation

First, we can adapt the law of sines to the notation of our triangle:

[tex]\frac{sin(W)}{w} =\frac{sin(U)}{u}[/tex]

Now, we can infer from our diagram that [tex]W=39[/tex], [tex]U=31[/tex], and [tex]u=3.3[/tex], so we can replace the values in our previous expression:

[tex]\frac{sin(W)}{w} =\frac{sin(U)}{u}[/tex]

[tex]\frac{sin(39)}{w} =\frac{sin(31)}{3.3}[/tex]

Finally, we can solve for [tex]w[/tex]:

[tex]\frac{3.3sin(39)}{w} =sin(31)[/tex]

[tex]3.3sin(39)=wsin(31)[/tex]

[tex]\frac{3.3sin(39)}{sin(31)} =w[/tex]

[tex]w=\frac{3.3sin(39)}{sin(31)}[/tex]

[tex]w=4.03224[/tex]

Which rounds to [tex]w=4.0[/tex]

We can conclude that the best approximation of w is 4.0 cm

th original price of a computer was reduced by $250. if p= the computer original price in dollars. which algebraic expression represents the reduced price

Answers

the algebraic expression would be p-250

The original price is p, it was reduced by $250 so your expression should be

p-250

4(2.1k-4)=6(3.4k-2) what does (K) equal?

Answers

Hey there.

4(2.1k - 4) = 6(3.4k - 2); apply the distributive property to remove the parenthesis.
8.4k - 16 = 20.4k - 12; Get the variable to one side, so subtract 8.4k.
-16 = 12k - 12; isolate the variable by adding 12.
-4 = 12k; divide by 12 to solve for our variable.
k = -1/3

I hope this helps!

HEEEEEEELP ASAP Janette went to Tire Mart and paid $122.57 per tire for 4 tires and a flat rate fee for installation for a total of $555.28 before taxes. Monique went to Fast Wheels and paid $136.71 per tire for 4 tires and a flat rate fee for installation for a total of $585.34 before taxes. The difference in the amount that they paid in installation charges is $____ WILL GIVE YOU BRAINLIEST

Answers

$122.57 • 4 + $555.28 = $1,045.56

$136.71 • 4 + $585.34 = $1,132.18

$1,132.18 - $1,045.56 = $86.62

The ratio of plates to napkins is 3:12. Write the ratio in simplest form.

Answers

The ratio 3:12 in simplest form would be 1:4. We can figure this out by dividing the ratio by 3 which would leave 1 plate to 4 napkins.
I hope this helped! :-)

1:4 is the answer.

The common factor of 3 and 12 is 3.

3 divided by 3 is 1

12 divided by 3 is 4

So you get 1:4

Hope this helped! ♡

Gene has a gasoline budget of $275 per month. He uses an average of $7 of gasoline each day he drives. Which of the following equations represents how much money is left in his gasoline budget after x days of driving?

Answers

Final answer:

The equation to represent how much money is left in Gene's gasoline budget after driving for x days is y = 275 - 7x, where x is the number of days Gene drives and y is the money left in the budget.

Explanation:

The equation representing how much money is left in Gene's gasoline budget after driving for x days can be expressed as y = 275 - 7x. Here, 275 represents the monthly gasoline budget, 7 is the cost of gasoline each day, and x is the number of days. If we plot y against x, we can visualize how Gene's monthly gasoline budget decreases by $7 for each day he drives.

This equation is a simple example of a linear equation, which describes a straight line in a coordinate system. The variable x is the independent variable (number of days driven) and y is the dependent variable (money left in the budget). The slope of the line (-7) represents the rate at which the budget decreases each day.

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What is 2x2 ? Plz I need the answer .

Answers

the answer is to the question you asked is 4

2x2 is 4.
All you are doing is multiplying 2 by 2, doubling it.
Hope this helped<3

Can someone please help me??

Answers

I believe your answer should be 8, I am sorry if I am wrong, please mark mine with a low star rating if I am false

In ABC what is the measure of C

Answers

C = 36

To solve this equation, you know what each angle is equal to, and all triangles add to equal 180 degrees, so you can set it up like so:

6x + 2x + 2x = 180 Then combine all the x's and simplify by dividing.

Answer:

36 °

Step-by-step explanation:

Hello

In geometry an interior angle or an internal angle is an angle formed by two sides of a polygon that sharing a common end is contained within the polygon, and the sum of these angles is given by

sum=(n-2)*180°

where n is the number of sides of the polygon,in our case n= 3 (a triangle)

Step 1

find the sum o internal angles

sum=(3-2)*108°

sum=1*180°

(1)sum=180°

step 2

find x

now, according to the graph the sum of internal angles is

sum(graph)=6x+2x+2x

(2)sum=10x

(1) must be equal to (2)

180°=10x

isolating x

x=18

Step 3

find C

by the graph ,we know

C=2x

and x=18

replacing

C=2(18)

C=36°

Have a great day

Thirty five is what fraction of 80

Answers

The fraction is 7/16
35/80= 7/16

The answer is (35/80=7/16) hope it helps and have a great day!

if the selling price is $18.00 and the markup is 33%.what is te dollar markdown?

Answers

the answer is 16.67 hope this helps

Good night. How ru?

If the markup is 33%, then the markdown is 67%

(18*67)/100 = x
1.206/100 = x
100x = 1.206
x = 1.206/100
x = 12,06$

Help with 3 and show all work

Answers

x<=50.

< is less than
> is greater than

Without him paying the extra fee is <=50
x is pounds.
Now, you have x<=50.

Hope this helped☺☺

Hi there!

The answer should be x<=50, or x is less than or equal to 50.

Your previous answer was almost correct, but the inequality actually has a less than or equal to sign since Michael could still be at exactly 50 pounds without having to pay extra. The charge only applies when the weight is more than 50 pounds.

Hope this helps!

Can anyone help me? Or at least explain how you solved the problem

Answers

2/3.3/1=6/3
Answer is 2.

The answer would be 2 because 2/3/1/3 is the same as 2/3 multiplied by 3/1 because you are dividing fractions so you keep change flip.

Please help me !!! Easy math

Answers

the first one is $10 , the second one is $22

Answer:

i agree with answer above mine

Step-by-step explanation:

What is the surface area of this design/

Answers

A=lxw so 640in that is your answer

Find the total surface area of the cube box below

Answers

The surface area of the cube is 24 feet.

We know a cube has 6 equivalent sides. One side has an edge of 2 ft so the other edges are all 2 ft so 6(2 x 2) or 2 x 2 + 2 x 2 + 2 x 2 + 2 x 2 + 2 x 2 + 2 x 2 = 24ft.

I need the answers to 5&6 explain how you found the answer and I'll give brainliest

Answers

I found the answer to 5, but I couldn't see the rest of worksheet to solve 6 thoroughly.

Both of these problems can be solved through substitution using the variables that you know equal a number.

For example #5: 5(3)(3)-7(3)+4
45-21= 24, and 24+8=28

That is how you solve number 5 and can also solve 6 the same way using the same method.

The volume of a right rectangular shipping carton is 948.75 cubic meters. The height of the shipping carton is 11 meters, and the width is 7.5 meters. What is the length of the shipping carton? Enter your answer as a decimal in the box.

Answers

11.5 meters I think.. took teh test

If volume of a right rectangular shipping carton is 948.75 cubic meters and the height of the shipping carton is 11 meters, and the width is 7.5 meters then length is 11.5 meters.

What is Three dimensional shape?

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that volume of a right rectangular shipping carton is 948.75 cubic meters.

The height of the shipping carton is 11 meters, and the width is 7.5 meters.

We have to find the length of the shipping carton

V=Length × width × height

V= Length x 7.5 x 11

948.75 = 82.5 length

Divide both sides by 82.5

Length = 948.75/82.5

Length = 11.5 meters

Hence, if volume of a right rectangular shipping carton is 948.75 cubic meters and the height of the shipping carton is 11 meters, and the width is 7.5 meters then length is 11.5 meters.

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What is the answer to 2/5 + 7/20 and 6/15 + 14/40

Answers

2/5+7/20=3/4

6/15+14/40=3/4

2 times 5=10 7 times 20 is 140 6 times 15 is 90 and 14 times 40 is 560 and all the anwsers to that and that’s what you get

Students in a class were asked to name their favorite sport they like to watch on television. The results are shown in the circle graph. How many times more students prefer to watch basketball than prefer to watch soccer? Soccer- 3% Basketball- 25.5%

Answers

25.5 / 3 = 8.5

8.5 times more student prefer basketball over soccer

Using the divison operation, we can conclude that students prefer Basksetball 8.5 times more than soccer.

Percentage who prefer soccer = 3%Percentage who prefer Basksetball = 25.5%

To obtain the number of times basket ball preference is greater than soccer :

We use the division operation :

(percentage of basketball) ÷ (percentage of soccer)

(25.5) ÷ 3 = 8.5

Therefore, students prefer basketball 8.5 times more than soccer.

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Congruency means that two figures or items are exactly the same size and shape. Where in life would it be vitally important for two or more items to be congruent?

Answers

money and the wheels of a car

I agree with Awesome5864. Wheels should be congruent...You need at least 2 of the same size and shape because if you dont the car is going to have one side taller than the other one.
Hope this helps!
Brainliest? Please?

show your work and simplify the expression (x – 2) (3x-4)

Answers

The answer is 3x^2-10x+8.

(x - 2)(3x - 4)

Remember F.O.I.L

First
Outside
Inside
Last

First: x * 3x = 3x^2

Outside: x * -4 = -4x

Inside: -2 * 3x = -6x

Last: -2 * -4 = 8

3x^2 - 4x -6x + 8

Now, combine like terms.

3x^2 - 10x + 8

Hope I helped!

I'd be very happy to help if you need anything else!

~ Zoe

"write an equation in slope-intercept form of the line satisfying the given conditions."

The line passes through (-3,2) and is parallel to the line whose equation is y = 4x + 1.

How do I do this problem? Show all work.

Answers

The given line has a slope of 4.
This is because y = 4x+1 is in the form y = mx+b (m = 4 is the slope)

Any line parallel to the given line is also going to have the same slope of m = 4

Plug in m = 4 and (x,y) = (-3,2) and then solve for b
y = mx+b
2 = 4(-3)+b
2 = -12+b
2+12 = -12+b+12
14 = b
b = 14

So m = 4 and b = 14 means that y = mx+b turns into y = 4x+14

----------------------------------------

Final Answer: y = 4x+14

7.2 = 8t
t = ???
I need a little help with this one
sorry...

Answers

You have to get t alone so you divide both sides by 8
7.2/8= 0.9 and 8t/8=t
T=0.9

Hey!
There is no problem with needing a little help, no need to apologize. To solve this use the inverse operation of multiplication (division) to solve. See photo :D

Cheers,
Izzy

Charlene records the number of pieces of red colored candies in ten bags of candy of assorted colors. find and interpret the mean absolute deviation of the data
6,6,7,7,8,8,10,10,11

Answers

To calculate the mean absolute deviation, you first must find the mean of the data and then find the difference between each piece of data and the mean.

Please see the attached picture for the work.

The mean absolute deviation is approximately 1.48.

This means that the numbers of candies in the 10 bags are all very close to one another. There is not much variation.

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