Can anyone help with Discriminants in math??
(“number and types of solutions” is what the rest says)

Can Anyone Help With Discriminants In Math??(number And Types Of Solutions Is What The Rest Says)

Answers

Answer 1

#1

3x²-3x+2

D:-

b²-4ac(-3)²-4(3)(2)9-24-15

D<0 so unequal and un real roots

#2

b²-4ac(-10)²-4(1)(1)100-496

D>0 so unequal and real roots

#3

(-4)²-4(4)(1)16-160

Equal and real roots

Answer 2

Answer:

Discriminant

[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]

[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real solutions}[/tex]

[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real solution}[/tex]

[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real solutions}[/tex]

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

Question 5

Given function:  [tex]f(x)=3x^2-3x+2[/tex]

[tex]\implies a=3, \quad b=-3, \quad c=2[/tex]

Inputting these values into the discriminant:

[tex]\implies \textsf{discriminant}= (-3)^2-4(3)(2)=-15[/tex]

As -15 < 0 there are no real solutions

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

Question 6

Given function:  [tex]f(x)=x^2-10x+1[/tex]

[tex]\implies a=1, \quad b=-10, \quad c=1[/tex]

Inputting these values into the discriminant:

[tex]\implies \textsf{discriminant}= (-10)^2-4(1)(1)=96[/tex]

As 96 > 0 there are two real solutions

at [tex]x=5 \pm 2\sqrt{6}[/tex]

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

Question 7

Given function:  [tex]f(x)=x^2-4x+4[/tex]

[tex]\implies a=1, \quad b=-4, \quad c=4[/tex]

Inputting these values into the discriminant:

[tex]\implies \textsf{discriminant}= (-4)^2-4(1)(4)=0[/tex]

As 0 = 0 there is one real solution

at [tex]x=2[/tex]


Related Questions

Everyone I really need the answers now I know that the points I offer are not much but I need I really need someone to answer this. Thank you to whoever answers

Answers

Volume of cube = a³

Volume = 6³ dm³

Volume = 216 dm³

Volume of rectangular prism = L × W × H

Volume = 10 × 8 × 6 cm³

Volume = 480 cm³

Volume of pyramid = 1/3 base area × h

Volume = 1/3 × 14 × 17 × 12.86 cm³

Volume = 1020.226 cm³

Volume of Cylinder = πr²h

Volume = 3.14 ×6.5² × 5 m³

Volume = 663.325 m³

Volume of Cone = 1/3 πr²h

volume = 1/3 × 18.5² × 16 cm³

Volume = 1825.3 cm³

Volume of Sphere = 4/3 πr³

Volume = 4/3 ×3.14 × 7³ m³

Volume = 1436.026 m³

Mary had a 3-inch piece of ribbon. She cut it in half. How long were the new pieces?.

Answers

Half of 3 would be the new lengths of the pieces.
So 3/2=1.5
The pieces would each be 1.5 inches
given:

3 inch.

to find:

the length of the new pieces.

solution:

to find the length of the new piece's you'll have to divide 3 by 2.

3/2

= 1.5 inch

so, the length of the new pieces is 1.5 inch.

bro some one helpp lol
17 - q = 6
n-31/4 = 2
1 + 2r = 35
42 + 5t = 8t
4p - 3 = 17

Answers

Answer:

11

9.75

17

14

5

Step-by-step explanation:

q=17-6=11

4n-31=8

4n=31+8=39

n=9.75

2r=35-1=34

r=17

42=8t-5t=3t

t=14

4p=17+3=20

p=5

Please help!! Will mark brainlyest.

Answers

A reflection on the x-axis because it will become (-4,4) which is a reflection to (4,4) on the x-axis.

A small dog eats 3/4 of a cup of dog food twice a day. Using d for the numbers of days and f for the amount of food write an equation relating variables

Answers

Answer:

f = food variable

d = number of days

Equation: f = 1.5d

I don't understand this and serval people have got it wrong.

Answers

[tex]\stackrel{\textit{\Large morning rate}}{\cfrac{\stackrel{strawberries}{3}}{\underset{minutes}{4}}}~\hspace{7em}\stackrel{\textit{\Large afternoon rate}}{\cfrac{\stackrel{strawberries}{2}}{\underset{minutes}{3}}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\underline{3}}{4}~~ - ~~\cfrac{2}{3}\implies \cfrac{(3)\underline{3}~~ - ~~(4)2}{\underset{\textit{using this LCD}}{12}}\implies \cfrac{9-8}{12}\implies \cfrac{1}{12}\qquad \impliedby \textit{their difference}[/tex]

A cone has volume V, radius r, and a height of 12 cm.
Another cone has the same height and 1/3 times the
radius of the original cone. Write an expression for its
volume.

Answers

Answer:

I think it is 4/9 pi r

Step-by-step explanation:

according to the condition given:

2nd cone has:

Height = 12cm

r= 1/3r (cause it's given 1/3 of radius of the original cone)

We know that volume of a cone is = 1/3 pi (r)^2 h

Now substitute the values:

1/3 * pi* (1/3r)^2 * 12

when u simplify u will get

pi* 1/9*r*4 = 4/9 pi r

So, the answer is probably 4/9 pi r.

Plot the image of point A under a dilation about the origin (0,0) with a scale factor of 1/3

Answers

Answer:

Step-by-step explanation:

If the coordinates of A are (3,-6) then the coordinates if A after dilation by a factor 1/3 then the coordinates will be (9,-18).

What is dilation?

The dilation is the action or condition of becoming or being made wider, larger,or more open, point or figure. The area of shape will be area/ factor after dilation.

How to plot image?

We have been given point A whose coordinates are (3,-6). We have to plot the point A after dilation with factor 1/3,

The x value after dilation will be 3/1/3=9

The y value after dilation will be -6/1/3=-18.

Hence the coordinates of A after dilation are (9,-18).

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how many sides does a quadrillateral have

Answers

Answer: 4

Step-by-step explanation:In geometry a quadrilateral is a four-sided polygon, having four edges and four corners. The word is derived from the Latin words quadri, a variant of four, and latus, meaning side

Bob is thinking about leasing a car. the lease comes with an interest rate of 8%. determine the money factor that will be used to calculate bob’s payment. a. 0.00033 b. 0.00192 c. 0.00333 d. 0.01920

Answers

The money factor that will be used to calculate Bob's payment is 0.00333 if the annual percentage rate is 8% option (c) is correct.

What is money factor?

It is defined as the ratio of the annual percentage rate to 2400. Usually, it can be used to calculating the financing costs of a lease with monthly installments.

Bob is thinking about leasing a car, the lease comes with an interest rate of 8%.

The annual percentage rate(APR) = 8%

We know the formula for finding the money factor is given by:

[tex]\rm Money \ factor = \frac{APR}{2400}[/tex]

[tex]\rm Money \ factor = \frac{8}{2400}[/tex]

Money factor = 0.00333

Thus, the money factor that will be used to calculate Bob's payment is 0.00333 if the annual percentage rate is 8% option (c) is correct.

Learn more about the money factor here:

https://brainly.com/question/9583229

Can I have help on this? I will award brainliest to whoever gives me the correct answer.

Answers

I think it is the last one

The greatest common factors of the expressions 48ab² and 32a²bare,

⇒ 2⁴ ab

What is Greatest common factors?

The highest number that divides exactly into two more numbers, is called  Greatest common factors.

Given that;

The expressions are,

⇒ 48ab²

⇒ 32a²b

Now,

GCD of 32, 48 = 16

And, GCD of (ab²) and (a²b) = ab

Thus, The greatest common factors of the expressions 48ab² and 32a²b are,

⇒ 16 ab

⇒ 2⁴ ab

Hence, The greatest common factors of the expressions 48ab² and 32a²bare,

⇒ 2⁴ ab

Learn more about the Greatest common factors visit:

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Darin wants to put a fence around his garden how much fencing should he buy.

Answers

Answer:

I don't know. How much he wants I guess.

Step-by-step explanation:

There is really any information to help solve this problem

An art gallery sales 1400 paintings catalog states that 70% of the paintings by local painters how many of these paintings are by local painters

Answers

Answer:

the answer is 980 hope this helps

A bicycle has it listed price of $852.98 before tax if the sales tax rate is 6.75% find the total cost of the bicycle sales tax included

Answers

The answer would be $910.56

A triangular prism has a volume of 360 in.³ the area of the base of the prism is 24 in.² what is the height of the prism?

Answers

Answer:

15 in

Step-by-step explanation:

Volume / Area = missing length

360 / 24 = 15 in

angles of circles
find x and y

Answers

Answer:

no. 1

Step-by-step explanation:

visual brain cuz im on the moon

Find the surface area of the rectangular prism (above) using its net (below).

Answers

Answer:

48 units sq

Step-by-step explanation:

Find the area of each square/rectangle

2x2

2x5

2x5

2x5

2x2

2x5

Add all the parts together

4 + 10 + 10 + 10 + 4 + 10

= 48 units sq

Calculate the length below labeled x

Image above
Please help me with this ill give you brainlist answer

Answers

Answer:

2√30

Step-by-step explanation:

Since we have a right triangle, we first need to find the base of the big triangle, which is also the hypo of the smaller triangle.

We apply A²+B²=C²

We plug values in that we have

15²+B²=19²

Simplify

B²=136

B=√136=√2x2x2x2x17=4√17

Now that we have the hypo for the small triangle we apply the same formula to get X

4²+X²=√136

16+X²=136

X²=120

X=√120=√2x2x2x3x5=2√30

Answer:

11.0 mm (3sf)

Step-by-step explanation:

Let length of hypotenuse of smaller triangle be H mm. (this is referring to the only unlabelled length in the picture)

by the Pythagorean theorem (larger triangle),

19² = 15² + H²

H² = 361 - 225

H² = 136

by the Pythagorean theorem (smaller triangle),

H² = 4² + x²

136 = 16 + x²

x² = 120

x = 11.0 mm (3sf)

hope this helps!

Find the area of the semicircle. Round your answer to the nearest hundredth.

Answers

Answer:

452.39

Step-by-step explanation:

area of circle = [tex]\pi r^{2}[/tex]

area of semi circle is [tex]\pi r^{2}[/tex] divided by 2 (because a semi circle is half of a circle)

diameter = 2 x radius, and radius = half of diameter

so

radius = 24 / 2 = 12

[tex]12^{2}[/tex] x π = 452.389342

to nearest hundredth = 452.39

Hope this helps. If you need any further explanation, let me know!

- profparis

if i helped you, i would appreciate a brainliest :D

Answer:

266.19 in²

Step-by-step explanation:

[tex]\sf Area\:of\:a\:circle=\pi r^2[/tex]  (where r is the radius of the circle)

As a semicircle is half a circle

[tex]\implies \sf Area\:of\:a\:semicircle=\dfrac12\pi r^2[/tex]

From inspection of the diagram, we can see that the diameter (the widest part of a circle) is 24 in.

[tex]\sf Radius\:of\:a\:circle\:(r)=\dfrac12diameter[/tex]

Therefore, the radius of the circle = 24 ÷ 2 = 12 in

Substitute r = 12 into the equation for the area of a semicircle:

[tex]\begin{aligned}\implies \sf Area\:of\:a\:semicircle & =\dfrac12\pi 12^2\\ & =\dfrac12 \cdot \pi \cdot 144\\ & = 72\pi \\ & = 266.19\: \sf in^2 \:(nearest\:hundredth)\end{aligned}[/tex]

Open with
2 At Mount Rushmore, the sculpture of George Washington's head is approximately 60 feet in
height.
60 feet
Il George Washington's head was approximately foot in height and his nose was 2 inches
long, how long is the nose on the sculpture at Mount Rushmore?
A
22-feet
B
13 feet
C, 1
75 feet
6 feet
D.
og
Page 2 | 13
a +

Answers

Use up the computer and computer for computer and use the app for computer and work on it and then work to get a computer and then work out a few hours to do for the first few hours truism so I iiuttii get it for work and I will call tomorrow at work and I can get a

Consider the equation 3(x – 5)2
+ 6 = 54.
What value(s) of x makes the equation true? Enter one solution in each space
provided on your answer document. If there is only one solution, leave one space
blank

Answers

Answer:

if im not mistaken, x = 13!!

please help me I will give BRAINLY , 5 STARS and a THANKS

Answers

Answer:

12+y

Step-by-step explanation:

Given,

a=6

b=6

c=y

Perimeter of triangle= sum of all sides of triangle

= 6+6+y

= 12+y

Answer:

Step-by-step explanation:

Perimeter is the length of any closed figure. So for a triangle, the Perimeter is equal to P = a + b + c.

You are told that the triangle is isosceles which means it has 2 equal. You are to presume that the third side is not equal to the other 2.

a=  6

b = 6

c = y

Perimeter = a + b + y

Perimeter = 6 + 6 + y

Perimeter = 12 + y

You cannot go any further. There is no way to reduce it any further.

which expression is equivalent to 16 + 2 x 36?

Answers

Hey there!

16 + 2 * 36

= 16 + 36 * 2
= 16 + 36 + 36

= 16 + 2 * 6^2

= 16 + 72

= 88


Thus, your answers could possibly be:

• 16 + 36 * 2
• 16 + 72
• 16 + 2 * 6^2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Find the value of x. Round your answer to the nearest tenth

Answers

[tex]x=13.8[/tex]

Step-by-step explanation:

Since the triangle is right use the tangent ratio to solve for x

[tex]tan41^o=\frac{opposite}{adjacent}=\frac{12}{x}[/tex]

Multiply both sides by [tex]x[/tex]

x × [tex]tan41^o=12[/tex] ( divide both sides by [tex]tan41^o[/tex] )

x =  ≈  ( nearest tenth )

How am I supposed to do question 4???

Answers

Answer:

PQ= XY

QR=YZ

RP=ZX

/_P= /_X

/_Q= /_Y

/_R= /_Z

6 high school seniors choose from among 20 quotes for their yearbook. What is the probability that at least 2 of them choose the same quote

Answers

Using the binomial distribution, it is found that there is a 0.0328 = 3.28% probability that at least 2 of them choose the same quote.

What is the binomial distribution formula?

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.

In this problem, we have that:

There are 6 students, hence n = 6.There are 20 quotes, hence the probability of each being chosen is p = 1/20 = 0.05.

The probability of one quote being chosen at least two times is given by:

[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]

In which:

P(X < 2) = P(X = 0) + P(X = 1).

Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{6,0}.(0.05)^{0}.(0.95)^{6} = 0.7351[/tex]

[tex]P(X = 1) = C_{6,1}.(0.05)^{1}.(0.95)^{5} = 0.2321[/tex]

Then:

P(X < 2) = P(X = 0) + P(X = 1) = 0.7351 + 0.2321 = 0.9672.

[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.9672 = 0.0328[/tex]

0.0328 = 3.28% probability that at least 2 of them choose the same quote.

More can be learned about the binomial distribution at https://brainly.com/question/24863377

The parabola in the image has its focus at (4,3).Its directrix is the line y=1.The point (8,6) is on the parabola.

Answers

The statements that are true for this parabola are:

C. The point (8, 6) is the same distance from the point (4, 3) as it is from the line y = 1.

Option D.

Given the following data:

Vertex (h, k) = (4, 3).Point (x, y) = (8, 6).

How to determine the equation of the directrix?

Mathematically, the standard equation of the directrix line for a parabola is given by: y = a(x - h)² + 2.

Next, we would determine the distance where point (8, 6) lie on the parabola as follows:

y = a(x - h)² + 2

6 = a(8 - 4)² + 2

6 = a(4)² + 2

6 = 16a + 2

16a = 6 - 2

16a = 4

a = 4/16

a = 1/4.

Therefore, the parabolic equation becomes:

y = 1/4(x - 4)² + 2

When x = 2, we have:

y = 1/4(2 - 4)² + 2

y = 1/4(-2)² + 2

y = 1/4(4) + 2

y = 1 + 2

y = 3.

In conlusion, the statements that are true for this parabola in the image above include:

The point (8, 6) is the same distance from the point (4, 3) as it is from line (y = 1).The point (2, 3) is on the parabola.

Read more on directrix here: https://brainly.com/question/2346582

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At a high school, the ages of all employees during the last ten years are normally distributed. It has been calculated that 95.4% of the ages fall between 22.1 and 53.9 years. What is the standard deviation of the data?
A: 4.85 yr
B: 7.95 yr
C: 9.7 yr
D: 15.9 yr

Answers

Answer:

I'm sorry for trolling you, but ur mom

Step-by-step explanation:

Dr. Banner monitored the decay of a new type of recyclable material he developed for his
gamma radiation study. He noted that the decay of the material could be modeled by the
function f(x) = 100(0.98). What is the rate of decay of Dr. Banner's material?

Answers

Answer:

The rate of decay is: [tex]2\%[/tex]

Step-by-step explanation:

Exponential functions are modeled by:

[tex]f(x) = a(b)^x[/tex]

Where [tex]a[/tex] is the y-intercept and b is the growth or decay constant. If [tex]b[/tex] is less than one, the function decays. If [tex]b[/tex] is greater than 1, the function grows.

To calculate the percentage, subtract [tex]b[/tex] from 1:

[tex]\% = 1 - b\\\% = 1 - 0.98\\\% = 0.02[/tex]

Multiply the result by 100 to get the percentage.

[tex]0.02 * 100 = 2\%[/tex]

What is the equation, in slope-intercept form, of the line that is perpendicular to the line y – 4 = –two-thirds(x – 6) and passes through the point (−2, −2)? y = –two-thirdsx – ten-thirds y = –two-thirdsx ten-thirds y = three-halvesx – 1 y = three-halvesx 1

Answers

The equation, in slope-intercept form, of the line that is perpendicular to the line y – 4 = –two-thirds(x – 6) is y = 3/2x - 1

Equation of a line in slope-intecept form?

The equation of a lins is a linear equation and expressed as:

y = mx + b

m is the slope

b is the y-intercept

Determine the equation in point slope form

y - y1 = -1/m(x - x1)

y -(-2) = 3/2(x + 2)
y + 2 = 3/2(x+2)

Write in slope-intercept form

2(y+2) = 3(x+2)

2y + 4 = 3x + 6
2y = 3x - 2

y = 3/2x - 1

Hence the equation, in slope-intercept form, of the line that is perpendicular to the line y – 4 = –two-thirds(x – 6) is y = 3/2x - 1

Learn more on equation of aline here:  https://brainly.com/question/7098341

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