Determine the number of real solutions for each of the given equations. Equation Number of Solutions y = -3x2 + x + 12 y = 2x2 - 6x + 5 y = x2 + 7x - 11 y = -x2 - 8x - 16

pppppppllllllleeeeaaaassssseeeee ANSWER FASRT

Answers

Answer 1

no. of real solns depends on the term b^2 - 4ac for y = ax^2 + bx + c
if its <0, no real soln
its =0, 1 real soln
its >0, 2 real solns

for
y = -3x2 + x + 12, 1^2-4(-3)(12) > 0, two solns
y = 2x2 - 6x + 5, -6^2-4(2)(5) < 0, no soln
y = x2 + 7x - 11, 7^2-4(1)(-11) > 0, two solns
y = -x2 - 8x - 16, -8^2-4(-1)(-16) = 0, one soln

Answer 2

According to the discriminant:

[tex]y = -3x^2 + x + 12[/tex] has two real solutions.[tex]y = 2x^2 - 6x + 5[/tex] has zero real solutions.[tex]y = x^2 + 7x - 11[/tex] has two real solutions.[tex]y = -x^2 - 8x - 16[/tex] has one real solution.

The number of real solutions of quadratic equation [tex]y = ax^2 + bx + c[/tex] depends on the discriminant [tex]\Delta = b^2 - 4ac[/tex].

If [tex]\Delta > 0[/tex], the equation has two real solutions.If [tex]\Delta = 0[/tex], the equation has one real solution.If [tex]\Delta < 0[/tex], the equation has zero real solutions.

Equation [tex]y = -3x^2 + x + 12[/tex]

The coefficients are: [tex]a = -3, b = 1, c = 12[/tex]The discriminant is: [tex]\Delta = 1^2 - 4(-3)(12) = 145[/tex].Positive, thus two real solutions.

Equation [tex]y = 2x^2 - 6x + 5[/tex]

The coefficients are: [tex]a = -2, b = -6, c = 5[/tex]The discriminant is: [tex]\Delta = (-6)^2 - 4(2)(5) = -4[/tex].Positive, thus zero real solutions.

Equation [tex]y = x^2 + 7x - 11[/tex]

The coefficients are: [tex]a = 1, b = 7, c = -11[/tex]The discriminant is: [tex]\Delta = (7)^2 - 4(1)(-11) = 93[/tex].Positive, thus two real solutions.

Equation [tex]y = -x^2 - 8x - 16[/tex]

The coefficients are: [tex]a = -1, b = -8, c = -16[/tex]The discriminant is: [tex]\Delta = (-8)^2 - 4(-1)(-16) = 0[/tex].Positive, thus one real solutions.

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Related Questions

The graph shows a probability distribution.

What is P(1.5≤X≤4.5)?

Enter your answer, as a decimal

P(1.5≤X≤4.5) =

Answers

Answer: 0.75

In the picture, the area that colored red is from x=5 till x=1, so the length would be: 5-1= 4 blocks. The height of all the block is the same, which is p=1. The total area of the red block would be: length * height = (5-1) * 1 = 4

The area of P(1.5≤X≤4.5) would be: length * height = (4.5-1.5) * 1= 3
The probability of P(1.5≤X≤4.5) would be: area/ total area= 3/4= 0.75

Select all that are undefined. sec (45°) csc (0°) sec (90°)

Answers

sec(45°) = 1/cos(45°) = 1/(rt(2)/2) = rt(2)

csc(0°) = 1/sin(0°) = 1/0 /undefined/

sec(90°) = 1/cos(90°) = 1/0 /undefined/

Final answer:

The sec(45°) and sec(90°) are defined, but csc(0°) is undefined.

Explanation:

To determine which of the given trigonometric functions are undefined, we need to understand the domains of these functions. In trigonometry, the secant and cosecant functions are undefined for angles where the cosine and sine functions are equal to zero, respectively.

For sec(45°), the cosine of 45° is equal to √2/2, which is not zero. Therefore, sec(45°) is defined.For csc(0°), the sine of 0° is equal to 0, which results in division by zero. Hence, csc(0°) is undefined.For sec(90°), the cosine of 90° is equal to 0, which again leads to division by zero. Thus, sec(90°) is undefined.

evaluate a = log(0.1) and b = ln(e^3)

Answers

[tex]log0.1=log\dfrac{1}{10}=log10^{-1}=-log10=-1\to a=-1\\\\lne^3=3lne=3\to b=3\\\\Used:\\\\a^{-1}=\dfrac{1}{a}\\\ loga^b=b\cdot loga\\\\log_aa=1[/tex]

Using sin^2x+ cos^2 x=1 and other trig properties, simplify the following: (cos^2Ø*tan^2Ø)/(1-cos^2 Ø.

Answers

[tex]\dfrac{\cos^2\O\cdot\tan^2\O}{1-\cos^2\O}=\dfrac{\cos^2\O\cdot\tan^2\O}{\sin^2\O}=\dfrac{\cos^2\O}{\sin^2\O}\cdot\tan^2\O\\\\=\dfrac{1}{\dfrac{\sin^2\O}{\cos^2\O}}\cdot\tan^2\O=\dfrac{1}{\left(\dfrac{\sin\O}{\cos\O}\right)^2}\cdot\tan^2\O=\dfrac{1}{\tan^2\O}\cdot\tan^2\O\\\\=\dfrac{\tan^2\O}{\tan^2\O}=1[/tex]

[tex]Used:\\\\\sin^2\O+\cos^2\O=1\to1-\cos^2\O=\sin^2\O\\\\\tan\O=\dfrac{\sin\O}{\cos\O}[/tex]

cos^2 x is the right answer.

Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. x - 2; 4x2 - 3x + 22

Answers

Answer:

[tex]x-2[/tex] is not a factor of [tex]p(x)=4x^2-3x+22[/tex].

Step-by-step explanation:

According to the factor theorem, if [tex]x-a[/tex] is a factor of [tex]p(x)[/tex], then [tex]p(a)=0[/tex].

Let [tex]p(x)=4x^2-3x+22[/tex]. If [tex]x-2[/tex] is a factor of [tex]p(x)=4x^2-3x+22[/tex], then [tex]p(2)=0[/tex].

Let us plug in [tex]x=2[/tex] in to the function to see if it will give us zero.

[tex]p(2)=4(2)^2-3(2)+22[/tex]

We simplify to obtain,

[tex]p(2)=4(4)-3(2)+22[/tex]

[tex]p(2)=16-6+22[/tex]

[tex]p(2)=10+22[/tex]

[tex]p(2)=32[/tex]

Since [tex]p(2)\ne0[/tex], [tex]x-2[/tex] is not a factor of [tex]p(x)=4x^2-3x+22[/tex].

Final answer:

According to the Factor Theorem, 'x - 2' is not a factor of the polynomial '4x^2 - 3x + 22'. This determination was made by plugging '2' into the second polynomial and finding that it does not result in zero.

Explanation:

For a polynomial P(x), the Factor Theorem states that if you plug a value 'a' into the polynomial and get zero (P(a) = 0), then x-a is a factor of that polynomial. In this case, you are asked to determine whether 'x - 2' is a factor of the quadratic function '4x^2 - 3x + 22'.

To do so, according to the Factor Theorem, plug the value '2' into the second polynomial function, so we have 4*(2)^2 - 3*(2) + 22 = 16 - 6 + 22 = 32. Because this does not equal zero, we can conclude that 'x - 2' is not a factor of the second polynomial '4x^2 - 3x + 22' based on the Factor Theorem.

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PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE HELP!! WILL GET BRAINIEST IF YOU SHOW WORK

1. Simplify the radical

2. Simplify the radical

3. Simplify the radical

4. Simplify the radical

Answers

the root of 27 is 3root3.

The simplification of the radical is c/3

What are radicals in math?

Radicals in math refer to expressions containing square roots or higher-order roots.

Represented by the radical symbol (√), they involve finding the root of a number. For example, √9 equals 3, as 3 * 3 equals 9.

Simplifying the surd;

√3c²)/√27

= √3 × √c²)/√9 × √3

= √3c/3√3

= c/3

Therefore the simplification of √3c²)/√27 is c/3.

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how many times greater is the value of the 2 in 204,936 than the value of the 2 in 124,936

A. 1/100

B. 1/10

C. 10

D. 100

E. 1,000

Answers

I believe it would be C.10

The value of the 2 in 204,936 is 10 times greater than the value of the 2 in 124,936. So the answer is C

A. 0
B. 4
C. 2
D. -2

Answers

The way to find the midpoint of a segment is to add the coordinates of the points you're trying to do the midpoint for and then divide by two (so it's the midpoint). Sine we're trying to find the midpoint of WQ, we need to add the coordinate of W and the coordinate of Q and then divide by 2. The coordinate of W is -8, and the coordinate of Q is 4. -8 + 4 = -4, divided by 2 is -2. That means that our answer is D, or -2.

Which of the following is equal to 7÷9/5
A: 9×7/5 B: 7×9/5 C: 9×5/7
D: 7×5/9

Answers

Final answer:

To find the value of 7÷9/5, we multiply 7 by the reciprocal of 9/5, which is 5/9, resulting in the expression 7×5/9. The correct answer is D: 7×5/9.

Explanation:

To solve the expression 7÷9/5, we must interpret the division as multiplication by the reciprocal. In other words, dividing by a fraction is the same as multiplying by its reciprocal. Therefore, 7 divided by 9/5 is equal to 7 multiplied by the reciprocal of 9/5, which is 5/9.

So, the calculation will be 7×5/9. Here's the math:

Identify the reciprocal of 9/5, which is 5/9.

Multiply 7 by the reciprocal of 9/5: 7 × 5/9.

Calculate the product: 7 × 5 = 35, and 35 ÷ 9 does not simplify further in this context.

The correct answer from the options provided is D: 7×5/9. The other options, A: 9×7/5, B: 7×9/5, and C: 9×5/7 do not represent the correct transformation from division to multiplication by the reciprocal.

Find the probability of drawing a heart or a black card from a standard deck of cards

Answers

75%

Hearts and black cards make up 3 of the 4 suits of cards. You could count the amount of them and then divide by 52 cards, or you can divide 3 by 4 since there are the same amount in every suit.

Final answer:

The probability of drawing a heart or a black card from a standard deck of cards is 3/4.

Explanation:

In a standard deck of cards, there are 52 cards in total. However, since we are interested in finding the probability of drawing a heart or a black card, we need to determine how many cards satisfy this condition.

There are 13 hearts in a deck, so the probability of drawing a heart is 13/52 or 1/4. Additionally, there are 26 black cards (13 spades and 13 clubs) in a deck, so the probability of drawing a black card is 26/52 or 1/2.

To find the probability of drawing a heart or a black card, we can add the probabilities together: 1/4 + 1/2 = 3/4.

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A student ate 3/20 of all candies and another 1.2 lb. Another student ate 3/5 of the candies and the remaining 0.3 lb. Altogether, what weight of candies did they eat?

Answers

let
x-------> total weight of candies
we know that

x=(3/20)*x+1.2+(3/5)*x+0.3
x=(3/20)*x+(3/5)*x+1.5----> multiply by 20----> 20x=3x+12x+30
20x=15x+30
20x-15x=30
5x=30
x=6 lb

the answer is
6 lb

David wants to rent a movie. He wants to watch either a comedy or a drama. The movie rental store has 18 comedies and dramas available for rent. Seven of the movies are comedies, and eleven of the movies are dramas. David has not seen two of the comedies, and he has not seen four of the dramas. If David selects a movie randomly, what is the probability the movie will be a comedy or a movie that he has not seen?

Answers

Let
A = number of ways to pick a movie David wants (either a comedy or a movie he hasn't seen)

B = number of movies total

There are 7 comedies and 4 dramas that David hasn't seen (note: the comedy movies that he hasn't seen are part of the "comedy movie" count, so there's no need to double count these). So there are 7+4 = 11 movies that David would want to rent. Therefore, A = 11.

There are 18 movies total for rent, so B = 18

Dividing the two values
A/B = 11/18 = 0.6111 approximately

The answer as a fraction is exactly 11/18
The answer in decimal form is roughly 0.6111
The answer in percent form is approximately 61.11%

[tex] |\Omega|=18\\
|A|=7+4=11\\\\
P(A)=\dfrac{11}{18}\approx61\% [/tex]

Maria needs to mail 3 letters. Each letter costs $0.41 to mail. How much change will she get back if she gives the clerk $2.00?

Answers

If Maria gives the clerk $2.00 then she will get $0.77 back in change.

I found this by using the expression x = 2.00 - 3(0.41) and solving for x.

Final answer:

Maria has to mail 3 letters, each costing $0.41, totaling to $1.23. She gives the clerk $2.00, so the change she will get back is $2.00 - $1.23 = $0.77.

Explanation:

This problem is about simple arithmetic and money management. Maria has to mail 3 letters, each costing $0.41. This means that the total expense that Maria has to pay is $0.41 * 3, which equals $1.23. Maria gives the clerk $2.00, so to find out the change, subtract the total cost of the letters ($1.23) from the amount she gave to the clerk ($2.00). So, the change Maria will get back is $2.00 - $1.23 = $0.77.

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Help
A survey was taken of 36 people to see if they owned a car and/or a truck. The results are shown in the Venn diagram.

Enter your answers in the boxes to complete the two-way table based on the given data.

Answers

Answer: The table should look like this

4 9 13

15 8 23

19 17 36

Step-by-step explanation:Happy to help

Based on the complete table, 19 people own a car, 13 people own a truck while 8 people neither own a car nor a truck.

How to complete the table

A survey was taken of 36 people to see if they owned a car and/or a truck. The results are shown in the Venn diagram.

own a car Dont own a car Total

Own a trcuk 4 9 13

Dont own a trcuk 15 8 23

Total 19 17 36

Those that own car 15 + 4 =19

those that own truck 9 + 4 = 13

Those that own car and truck 4 (Given)

Those that owns none = 36-15-9 - 4 = 8

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The area of a rectangular garden is given by the trinomial x2 + x – 42. What are the possible dimensions of the rectangle? Use factoring.

Answers

x^2 + x - 42 =

= x^2 + 1x - 42
             ^      ^
             |       |
             |      you need two numbers that multiply to -42
             |
           and add to 1

Find two numbers whose product is -42 and whose sum is 1.
The numbers are -6 and 7.

x^2 + x - 42 = (x - 6)(x + 7)

Final answer:

The dimensions of the rectangle given by the trinomial (x² + x – 42) are 7 and 6, which are derived by factoring the trinomial and applying the quadratic formula.

Explanation:

To find the possible dimensions of the rectangle, we start by factoring the trinomial that represents the area of the rectangle, namely x² + x – 42.

This can be factored as (x + 7)(x - 6), which are the roots of the quadratic equation when set to equal zero.

The roots, or solutions to this equation, can be calculated using the quadratic formula, -b ± √b² - 4ac 2a, which includes squaring the coefficient of the x-term, subtracting four times the product of the remaining coefficients, and dividing the result by twice the leading coefficient.

In this case, the dimensions that correspond to these roots, namely length and width, are 7 and -6. However, since dimensions cannot be negative, we disregard -6. Therefore, the possible dimensions of the rectangle are 7 and 6.

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please help. there is a picture below

Answers

Two triangles are similar if and only if all corresponding angles are equal (congruence), even if the corresponding sides are equal or not, therefore the answer is true because ΔJKL and ΔRST are similar and the statement above demands that "it must be", namely, this is a sufficient condition.

What are the minimum, first quartile, median, third quartile, and maximum of the data set?
12, 6, 8, 3, 10, 15, 18, 7

Answers

If we rearrange the given data set from lowest to highest, we have
[tex]3,\:6,\:7,\:8,\:10,\:12,\:15,\:18[/tex]

The minimum is 3.

The first quartile is the average of 6 and 7, which is 6.5

The median is the average of 8 and 10 which is 9.

The third quartile is the average of 12 and 15 which is 13.5.

The maximum is 18.

your mom is looking at he amount of sugar in two different drinks the apple juice has 216 grams sugar for every 8 serving the sprite 234 grams of sugar for every 9 serving which drink has more sugar

Answers

The apple juice has 27 grams per serving and the sprite has 26 grams per serving. So the apple juice has more. You just divide the total amount by the number of servings.

If nine people are in a room and every person shakes hands exactly once with each of the other people, how many handshakes will occur

Answers

The total number of handshakes = 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 36

Answer: 36 handshakes

A family of four (two kids and two parents) spend the day at an amusement park. At the end of the day, the family adds up all of the receipts from their meals: $16.25, $17.96, $3.58, $4.61, $5.23. What is the mean and median cost spent? What does the mean cost represent? Why is the mean cost significantly different from the median cost? Which measurement of central tendency is a better representation of the amount of money that the family spent at the amusement park?

Answers

A family of four spent the following for their meals $16.25, $17.96, $3.58, $4.61, $5.23.

Mean cost spent is calculated by:

Total Cost/Number of Meals

(16.25+17.96+3.58+4.61+5.23)/5

47.63/5

$9.53

Mean Cost represents the average amount per meal the family has spent.

Median cost is the cost that in the middle of the five costs which is $5.23.

The mean cost is significantly different from the median cost because it is higher.

Median cost is a better representation of the amount of money that the family spent because, with regard to meal costs, this means that exactly half of the meals in the amusement park are above this price ($5.23) and exactly half are below.

PLS HELP ME ASAP WITH 1 AND 2, THANK YOU!! SM!!

(Brainliest will be given hopefully!)

(Random answers gets moderated.)

Answers

I can't really help with 2) because I don't have my calculator on me, but I hope this helps :)

See the attachment for a table (1) and graph (2).

(3) The graph represents a function. The table has a domain of [0, 7] and a range of [170, 240].

The function might reasonably be used over a domain of [0, 24] and a range of [0, 240].

Which function represents a reflection of f(x) = 5(0.8)x across the x-axis? A. g(x) = 5(0.8)–x B. g(x) = –5(0.8)x C. g(x) = 1/5(0.8)x D. g(x) = 5(–0.8)x

Answers

If g(x) is a reflection of f(x) over the x axis, then g(x) = -1*f(x), which can be shortened to g(x) = -f(x). We stick a negative outside the entire f(x) function to flip the signs of each y coordinate. For example, if the point (1,2) was on f(x), then (1,-2) is on g(x).

So f(x) = 5(0.8)^x turns into g(x) = -5(0.8)^x

Answer: Choice B

Answer:

2nd option

Step-by-step explanation:

Which points in the scatter plot are outliers?

Point A

Point F

Point H

Point K

Point M

Answers

Hi there!

If you draw a line of best fit, you'll see that only two points lie way outside the line. These points are points K and F.

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!

Answer:

the points are k and f

Step-by-step explanation:

is it always true that trapezoids height is the distance between the 2 bases?

Answers

No. One side can be higher than the other side, therefore, a trapezoids height isn't always the distance between the 2 bases.

JK, KL, and LJ are all tangent to circle O. The diagram is not drawn to scale. If JA = 10, AL = 23, and CK = 9, what is the perimeter of ∆JKL
A.84
B.66
C.42
D.38

Answers

Answer: the perimeter of JKL is 84

ik this is rlly late but to help anyone else who gets this question:

This is an equilateral triangle, so the adjacent length is gonna be the same value as its corresponding length that was listed

JA = 10

JB = JA, JB is also 10

JA + JB (10+10) = 20

AL = 23

LC = AL, LC is also 23

AL + LC (23+23) = 46

CK = 9

KB = CK, KB is also 9

CK + KB (9+9) = 18

add all those up:

20 + 46 + 18 = 84

The sum of two numbers is 25, and the difference of their squares is 75. what are the two numbers?

Answers

x+y=25
14*14=196
11*11=121

196-121=75
the answer is x=14 and y=11

How many Liters of a liquid can be held in a barrel

Answers

a lot of water because it has to fill a barrel!!

Find the value of n such that x2-10x+n is a perfect square trinomial.

A. -5
B. 50
C. 100
D. 25

Answers

The answer is the last option (Option D), which is:

D. 25

The explanation is shown below:

1. You have that:

(a ± b)^2=a^2 ± 2ab + b^2

2. The expression given in the problem is:

x^2-10x+n

Where x^2=a and 2ab=10x

2b=10
b=10/2
b=5

3. Therefore, you have:

b^2=5
b^2=25

b^2=n
n=25

Answer:

the answer is 25!!

Step-by-step explanation:

I hope this is helpful to sum of y'all!!

find the point slope equation for (-2,-20) and (9,79)

Answers

Start by identifying your x1, x2, y1, and y2 values
x1: -2
x2: 9
y1: -20
y2: 79

The general form for writing a point slope equation is y-y1 = m(x-x1)
M is your slope.
To find the slope, plug the values you just identified into the equation y2-y1/x2-x1
This leaves you with 79+20/9+2
Which equals 9, so your slope (m) equals nine.
you can now plug everything into the general form which gives you:
y+20 = 9(x+2)

Final answer:

The point-slope equation for the points (-2,-20) and (9,79) is y + 20 = 9(x + 2).

Explanation:

To find the point-slope equation, we can use the formula: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Firstly, we calculate the slope using the formula: m = (y2 - y1)/(x2 - x1). Given the points (-2, -20) and (9, 79), the slope is (79 - (-20))/(9 - (-2)). Simplifying the expression, we get m = 99/11 = 9.

Next, we substitute one of the points and the calculated slope into the point-slope formula. Let's choose (-2, -20). So the equation becomes: y - (-20) = 9(x - (-2)). Simplifying further, we have: y + 20 = 9(x + 2).

This is the point-slope equation for the given points: y + 20 = 9(x + 2).

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What is the minimum value of the graph of y=sin x assumes

Answers

Short answer: - 1
The first thing you should do is draw this or get a program to do it. I use desmos. It is included. The graph shows one complete cycle every 2*pi intervals (or 360 degrees.)

You will find no lower value that y = - 1 (nor any value greater than y = 1)

Answer:

the answer is

negative one

- 1

Step-by-step explanation:

Other Questions

Determine the number of real solutions for each of the given equations. Equation Number of Solutions y = -3x2 + x + 12 y = 2x2 - 6x + 5 y = x2 + 7x - 11 y = -x2 - 8x - 16 pppppppllllllleeeeaaaassssseeeee ANSWER FASRT

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Determine the number of real solutions for each of the given equations. Equation Number of Solutions y = -3x2 + x + 12 y = 2x2 - 6x + 5 y = x2 + 7x - 11 y = -x2 - 8x - 16

pppppppllllllleeeeaaaassssseeeee ANSWER FASRT