Consider the system of quadratic equations
y = 3x^2 - 5x,
y = 2x^2 - x - c,
where c is a real number.

(a) For what value(s) of c will the system have exactly one solution (x,y)?

(b) For what value(s) of c will the system have more than one real solution?

(c) For what value(s) of c will the system have no real solutions?

Solutions to the quadratics are (x,y) pairs. Your answers will be in terms of c, but make sure you address both x and y for each part.

Answers

Answer 1

9514 1404 393

Answer:

  (a)  c = 4

  (b)  c < 4

  (c)  c > 4

Step-by-step explanation:

(a) The solutions to the system of equations can be found by substituting one expression for y into the other equation:

  3x^2 -5x = 2x^2 -x -c

  x^2 -4x +c = 0 . . . . . . . subtract the right side expression

The discriminant is

  d = b^2-4ac = (4)^2 -4(1)(c) = 16-4c.

The system will have exactly one solution when d = 0.

  16 -4c = 0

  4 -c = 0

__

(b) There will be more than one real solution when d > 0

  4 -c > 0

  c < 4 . . . . two real solutions

__

(c) There will be no real solutions when d < 0.

  4 -c < 0

  c > 4 . . . . no real solutions

_____

Additional comment

The question posed here simply asks for a value of c. It does not ask for the solutions (x, y). We can count them without knowing exactly what they are.


Related Questions

I Need help with this

Answers

The answer is B. I hope this helps with your work. For next time just match the frequency with how tall the line is.

Answer:

it would be choice B

Step-by-step explanation:

the frequencies in the chart are 4,5,9,8, and 4 so you look at which graph's bars go up to those numbers

I am STRESSED. Please answer the following questions below that are HIGHLIGHTED.

Answers

Answer:

1.5 tons and 256 pounds OR 1 ton and 1256 pounds

Step-by-step explanation:

what is the smallest subset of the number -8,546,999 belong to

Answers

Answer:

its 4

Step-by-step explanation:

jamal wants to draw a right triangle and label it JKL​

Answers

The answer is B: (-4,-2)

Answer:

Calm down jamal don't go pulling out the nine

Step-by-step explanation:

this is just a joke

i put 15 i think it’s wrongs please help

Answers

Answer:

[tex] \sqrt{( {0 - 12}) {}^{2} + (1 - 10) {}^{2} } \\ = \sqrt{0 + 81} \\ = \sqrt{81} \\ = 9[/tex]

[tex] \huge\mathfrak\pink{A} \huge\mathfrak\purple{n} \huge\mathfrak\blue{s} \huge\mathfrak\red{w} \huge\mathfrak\green{e} \huge\mathfrak\orange{r}\ [/tex]

9 is the correct answer

What is the perimeter of the track, in meters? Use tt 3.16 and round to the nearest hundredth of a meter

Answers

Answer:

The perimeter of the track is of 317 meters.

Step-by-step explanation:

Perimeter:

The perimeter of a figure is the sum of all its dimensions.

In this question:

The track is composed by two straights of 80m, and two half circles with a diameter of 50m.

Perimeter of a circle:

The perimeter of a circle with diameter d is of:

[tex]P = \pi d[/tex]

Track:

Two half circles, each with a diameter of 50m, plus two straight lines of 80m. So

[tex]P = \frac{2\pi}{2}(50) + 2*80) = 50\pi + 160 = 50*3.14 + 160 = 317[/tex]

The perimeter of the track is of 317 meters.

PLS HELP DUE SOON!!!

Answers

Answer:

its both.

Step-by-step explanation:

RNA and DNA are made up of nucleotide(s).

Answer: Both DNA and RNA

Step-by-step explanation:

Simplfy completely (6x − 2)(6x + 2). Show all work for full credit.

Answers

Answer:

there you go. hope this helps out

Answer:

36[tex]x^{2}[/tex] - 4

Step-by-step explanation:

(6x - 2)(6x + 2)

= (6x)(6x) + (6x)(-2) + (2)(6x) + (-2)(2)

= 36[tex]x^{2}[/tex] - 12x + 12x - 4

= 36[tex]x^{2}[/tex] - 4

need help w this thanks

Answers

Answer:

a

Step-by-step explanation:

Here is my question.

Answers

Answer:

I'm sorry no one answered this in time. I know it sucks. Have great day! Owa Owa!

Step-by-step explanation:

Pls answer its khan academy I really need it

Answers

Answer:

Step-by-step explanation:

Note the f(0) = 9

and f(1) = 15

Since, f(x) = abˣ substituting for x, we get:

9 = f(0) = a . b⁰ = a

⇒ a = 9

Now, f(1) = 15

⇒ 15 = a . b¹

⇒ 15 = 9 . b

⇒ b = 15/19

Therefore,

f (r) = 9. (5/3)

Hence, the answer.

Multiply.


−3.6(−5.4)(3)

Answers

Answer:

-3.6(-5.4)(3)

=58.32

hope it helps.

Answer:

it's answer is 58.32

hope it is helpful to you

solve for k. a/b=b/a+1k

Answers

Answer:

[tex]\frac{(a+b)(a-b)}{ab}[/tex]

Step-by-step explanation:

[tex]\frac{a}{b}=\frac{b}{a} +k[/tex]

[tex]k=\frac{a}{b}-\frac{b}{a}=\frac{a^2-b^2}{ab}=\frac{(a+b)(a-b)}{ab}[/tex]

Estimate:
8 3/5 + 8 4/9

Answers

The answer is 17.04 .......

Answer:

17

Step-by-step explanation:

You know that 8+8=16, and adding the fractions would result in something close to 17.

Please answer it’s due at 3

Answers

Answer:

1134mm

Step-by-step explanation:

Emily made fruit punch for a party. The list shows the fruit juices she had
available. Emily picked 3 of the juices and used the entire amount of all
3 to make 4.65 liters of punch.

0.25 liters of grape juice
1.05 liters of cranberry juic
1.15 liters of apple juice
3.35 liters of orange juice
1.00 liters of grapefruit juic


Which 3 juices did Emily use if she made 4.65 liters of punch?

A. Grape, apple, and orange

B. Grape, apple, and grapefruit

C. Cranberry, apple, and orange

D. Grape, cranberry, and orange


Answers

Answer:

D: grape, cranberry, and orange

Step-by-step explanation:

Jason drew a triangle to explain the Triangle Sum Theorem and labeled the angles 1, 2, and 3

He tore each angle off the triangle so he could move the three angles around.

What should Jason do next to explain the Triangle Sum Theorem?

Jason should line up the angles next to each other as adjacent angles to show that the 3 angles together form a straight angle.

Jason should create a new triangle by moving the angles closer together to show that the 3 angles can create other triangles.

Jason should fold each angle in half to show each angle with one half of the measure it had in the triangle.

Jason should stack the angles on top of each other to show that the 3 angles have the same measures.

Answers

Answer:

A

Step-by-step explanation:

Well B is strange. You might get them to make one complementary angle, but that has nothing to do with the Triangle sum theorem.

C is true. He is getting similar triangles, but that does not prove the Triangle sum theorem.  So -- don't choose C

D is just taking up space so you get 4 choices.

The answer should be A but the problem is the tips of the angles should all come to the same place. I think it does mean A, but it is a bit awkwardly worded.

Answer:A

Step-by-step explanation:

smart person above

Jana wants to buy a shirt at the store. The shirt is normally $24, but today it is on sale for 15% off.
How much will she save?

Answers

Answer:

She will save $3.60

Step-by-step explanation:

10% of 24= 2.4

5% of 24 = 1.2

2.4 + 1.2= 3.6

This means she is saving $3.60 because 15% of $24 is $3.60! :)

Jana save $3.6 to buy a shirt.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

The shirt is normally $24, but today it is on sale for 15% off.

Now,

Since, The shirt is normally $24, but today it is on sale for 15% off.

Hence, The save money = 15% of 24

                                       = 15/100 × 24

                                       = $3.6

Thus, She save $3.6 on the shirt.

Learn more about the percent visit:

https://brainly.com/question/24877689

#SPJ2

A cylinder has a radius of 5 m and a height of 11 m. Identify the volume of the cylinder to the nearest tenth.

Answers

Answer:

86,405 cm³

Step-by-step explanation:

V = cross-sectional area × height = πr²h = 3.142 × 5² × 1100cm

= 86,405 cm³

Answer:

863.9 m³

Step-by-step explanation:

Cylinder volume is V = πr²h.  Here the height, h, is 11 m and the radius, r, is 5 m.  Thus we have:

V = π(5 m)²(11 m), or

V = π(275) m³, or approximately 863.9 m³

What is the prime factorization of 48?
O A. 2x3x8
OB. 2x2x3 x4
OC. 2x2x2x3
OD. 2x2x2x2x3
O E. 2x2x2x3 x3

Answers

Answer:

D

Step-by-step explanation:

2 x 2 = 4

4 x 2 = 8

8 x 2 = 16

16 x 3 = 48

Please help I'll mark you as brainiest

Answers

Answer: A is the answer good luck :)

Answer is A most likely

Jason inherited a piece of land from his great-uncle. Owners in the area claim that there is a 45% chance that the land has oil. Jason decides to test the land for oil. He buys a kit that claims to have an 80% accuracy rate of indicating oil in the soil. What is the probability that the land has ol and the test predicts it?

A) 0.09

B) 0.11

C) 0.36

D) 0.44​

Answers

I think the answer is A I hope I’m right.

Use the graph below to find the indicated function Value. y=f(x); f(4)

Answers

From the graph at f=4
then y=3

The value of f(4) is 3 if the graph of the function is shown in the picture, the answer is 3.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The graph of the function is shown in the picture.

From the graph the value of f(4) can be evaluated as follows:

y = f(x)

Plug x = 4

y = f(4)

From the graph:

Draw a vertical line from point 3 on the x-axis and when it cuts the curve draw a horizontal line when the line cuts the y-axis note the point.

y = f(4) = 3

Thus, the value of f(4) is 3 if the graph of the function is shown in the picture, the answer is 3.

Learn more about the function here:

brainly.com/question/5245372

#SPJ2

In the finger above what is m

Answers

Answer:

ABE is 180-64.5= 115.5

EBE is 90-64.5= 25.5

HELP PLEASE !!

a teacher asks five students to write an equation with a solution of x= 4 . the students and their equations are shown below. which of the following students correctly wrote an equation with x= 4 as the solution ? select three that apply .

Answers

Bert, Camille, Etsuko

A gift box has the dimensions shown below. 16 in x11 in. What is the perimeter of the box in feet

A. 4 feet 1/2 inch
B. 4 feet 6 inches
C. 54 inches
D. 4 feet

Answers

The formula for perimeter is 2l+ 2w so 2(16)+ 2(11)= 54 and since there are 12 inches in 1 ft, you have to divide 54 by 12 to get 4.5 feet (or 4 feet 6 inches)
So, you answer is B

whats the answer for this

Answers

Answer:

1 should be 90 degrees because if u look at the angle its a right angle

2 its an obtuse angle so those angles are more than 90 degrees but less than 180 so its 150 degrees

Add (-2x + 4) + (4x + 6)
A) 2x + 10
B 6x + 10
C) 2x - 2
D) 6x-2​

Answers

Answer:

A. 2x + 10

Step-by-step explanation:

Amelia purchased a new mattress when it was on sale. The sale price was 25% less than the regular price. If the sale price was $481, what was the original price? (Round your answer to the nearest dollar).

Answers

Answer:

$641

Step-by-step explanation:

Let $p be the original price.

[tex](1 - 25\%)p = 481 \\ \frac{75}{100} p = 481 \\ p = 641[/tex]

p = 641 (cor. to the nearest dollar)

∴ The original price was $641.

18 a exactement 6 diviseurs

Answers

Answer:

18 is divisible by 6

Step-by-step explanation:

Because 6 can divide 18, 3 times

Vrai

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