How can you use the graph of a quadratic equation to determine the number of real solutions of the equation?​

Answers

Answer 1

Answer:

Step-by-step explanation:

The number of real solution of a quadratic equation can be found from the number of x-intercepts on the graph. If the curve passes through the x-axis twice, (2 x-intercepts), then the equation has two real solutions.

If it passes through once, (the vertex is on x-axis), then there is one real solution, and if it does not touch the x-axis at all (floating above it or below it), then it has no real solutions.

Hope this helped!


Related Questions

Can someone help me with these questions.

Answers

Answer:

C ( x = 2 (multiplicity of 2), x = -2, x = -4)

A ( x = 5 (crosses), x = -3 (touches))

Step-by-step explanation:

Here are a couple of rules that helped me come to these answers.

1. When finding a zero, you flip the value inside of the parenthesis. For example (x + 2) would have the zero of x = -2.

2.The multiplicity of something is how many times the same zero is there. It is the exponent outside of the equation. For the first question, the (x - 2) has an exponent of 2, thus it has the multiplicity of 2.

3. The multiplicity determines whether the line just touches (or "bounces" off) the x axis or crosses the x axis. If the multiplicity is odd, it crosses the axis. If the multiplicity is even, it just touches the axis. A good way to remember this is with linear and quadratic equations. A linear is commonly know as only having an exponent of 1 (an odd) number and would cross the x axis. A quadratic equation has an exponent of two (an even number) so the line "bounces" on a graph.

Simplifying your answer

Answers

Answer:

  -49

Step-by-step explanation:

In order to fill in the given expression, we need to know ...

f(-2) = -4f(-3) = 5f(-4) = 7g(0) = -7g(-3) = 3

Then the expression is ...

  √(5 -(-4)) -(-7)² +7÷(-7)·(3) = √9 -49 +7/(-7)(3)

  = 3 -49 +(-1)(3) = 3 -49 -3

  = -46 -3 = -49

Mark is going to work, he drives 70 miles at 35 mph, how many minutes does it take Mark to get to work?

Answers

Answer:

time = 120 minutes

= 120 min

= 02:00:00

= 2 hours, 0 minutes, 0 seconds

Help me please as soon as possible

Answers

Answer:

x=8

Step-by-step explanation:

Triangles

An isosceles triangle is a triangle with two equal sides. The angles the equal sides form with the third side are also equal.

The triangle shown in the figure is isosceles and the angles marked as '2' and 67° are equal. But we are also given that the angle '2' equals 8x+3, thus:

8x+3=67

Reducing:

8x=67-3=64

Solving:

x=64/8

x=8

Could someone help ASAP? every answer I put is apparently wrong so I’d appreciate some help

Answers

Answer:

235 cm²396 cm²

Step-by-step explanation:

Figure 1

Area is

20*14 - (20 - 11)(14 - 9) = 280 - 9*5 = 280 - 45 = 235 cm²

Figure 2

Area is

24*27 - (24 - 10 )( 27 - 9) = 648 - 14*18 = 648 - 252 = 396 cm²

The population of Centerville is 1,600 people to the nearest 50 people. What are the upper and lower bounds of the population?
The lower bound is 1,575 people, and the upper bound is 1, 625 people.
The lower bound is 1,550 people, and the upper bound is 1, 650 people.
The lower bound is 1, 650 people, and the upper bound is 1, 700 people.
The lower bound is 1,500 people, and the upper bound is 1, 700 people.​

Answers

Answer:

Not positive but im pretty sure it is the first one.

Step-by-step explanation:

Billy's Boat Rental Company charges a yearly fee of $105 and $9.50 each time a member wants to rent a boat. Lisa's Boat Rental Company does not charge a yearly fee, but charges $14.75 every time a member rents a boat. How many times does a person have to rent a boat for the cost to be the same amount at both rental companies?

Answers

Step-by-step explanation:

we can proceed to model the cost of Billy's Boat Rental Company

let y be the cost

let x be the number of rentals

y=105+9.5x----1

Also, the cost of Billy's Boat Rental Company

y=14.75------2

the question is "How many times does a person have to rent a boat for the cost to be the same amount at both rental companies"

we have to equate the two cost and solve for x

105+9.5x=14.75

105-14.75+9.5x=0

90.25+9.5x=0

9.5x=-90.25

divide both sides by 9.5 we have

x=-90.25/9.5

x=9.5

Approximately 10 times

Carnival M charges an entrance fee of $5.00 and $0.65 for each ride. Carnival P charges an entrance fee of $10.00 and $0.45 for each ride. How many rides will the cost for carnivals be the same

Answers

Answer:

your mom

Step-by-step explanation:

Given and Prove Information
Given: PR = QS
Prove: PQ = RS
Diagram
Proof
Statements
1.PR = QS
2.
3.
4.
5.
6.
7.
Reasons
1. Given
2.
3.
4.
5.
6.
7.
5. What is Statement :
Your answer
6. What is Reason
Your answer
- What is Statement ?
Your answer

Answers

Answer:

I hope this helps you

Step-by-step explanation:

The answer is A

Answer:

I agree the answer is A

Step-by-step explanation:

A = A

A != B

AA = 2A

A = A

(26 POINTS) !Based On the information in the table, is the cost of the apples proportional to the weight of apples ?

Answers

Answer:

Where is the table? Where

Answer:

Step-by-step explanation:

the point (12,5) is on the graph, what do the coordinates tell you about the water in the bucket?

I WILL MAKE YOU BRAINLESS WHOEVER HAS THE BEST EXPLAINATION
Simplify the expression. 1.7 – 2.7 – 1.34 + 4.9 – 1.48
explain im lost

Answers

Answer:

0.08

Step-by-step explanation:

1.7 – 2.7 – 1.34 + 4.9 – 1.48

 2.7

- 1.7       (subtract 1.7 from 2.7)

--------

-1.0      [2.7 is greater than 1.7 and 2.7 is negative(in the ques) , therefore  1.0 is negative]

-1.0-1.34

we know that  (-) (-) is (+)

therefore add -1.34 with -1.0

   1.34

+  1.0

-----------

  -2.34 [since 1.34 is greater and it is negative]

-2.34+4.9

we know that (-)(+) is (-)

therefore subtract -2.34 from 4.9

  4.90  ← (we put zero so that we can subtract without getting confused)

-  2.34

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

  1.56 [1.56 is positive because 4.9 is greater and it is positive]

1.56-1.48

here, digit before the decimal point is same but  after decimal point .56 is greater than .48  therefore subtract 1.48 from 1.56

  1.56

-  1.48

-----------

  0.08

therefore,  1.7 – 2.7 – 1.34 + 4.9 – 1.48 = 0.08

hope it helps you!

Triangle ABC is a right triangle.

Triangle A B C is a right triangle. Angle A C B is 90 degrees, angle C B A is 31 degrees, and angle B A C is 59 degrees.
What is the relationship between angles A and B?

They are congruent.
They are complementary.
They are supplementary.
There is no relationship between them.

Answers

Answer:

B JUST DID THE QUIZ

Step-by-step explanation:

FOR FUTURE PPL ON EDGE 2022!!

The relationship between angles A and B is B. They are complementary.

What are the 3 sides of the triangle?

In a proper triangle, the hypotenuse is the longest aspect, an "opposite" aspect is the only across from a given attitude, and an "adjacent" side is subsequent to a given angle. We use special words to describe the perimeters of proper triangles.

What are the elements of a triangle?

All triangles have three aspects and three corners (angles). The point at which two sides of a triangle meet is known as a vertex. the base of a triangle may be any one of its 3 aspects, but it also includes the lowest one.

Learn more about Triangle here https://brainly.com/question/17335144

#SPJ2

5/9 - (-1/6)
Subtract fractions

Answers

Answer:

7/18 is what I got.

Step-by-step explanation:

pic below

Write in Slope Intercept form: x-3y=-15

Answers

Answer:  Slope = 0.667/2.000 = 0.333

 x-intercept = -15/1 = -15.00000

Step-by-step explanation: y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  x-3y+15  = 0 and calculate its properties

Notice that when x = 0 the value of y is 5/1 so this line "cuts" the y axis at y= 5.00000

 y-intercept = 15/3  =  5

When y = 0 the value of x is -15/1 Our line therefore "cuts" the x axis at x=-15.00000

 x-intercept = -15/1  = -15.00000

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 5.000 and for x=2.000, the value of y is 5.667. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 5.667 - 5.000 = 0.667 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     =  0.667/2.000 =  0.333

 Slope = 0.667/2.000 = 0.333

 x-intercept = -15/1 = -15.00000


19
1 point
17) For each of the following, identify the type of angle pair, and solve for 'x'.
(12x-3)
(7x+12)

Answers

x=3
12x-3=7x+12= (x=3)
explanation: isolate the variables

help pls pointssssssssss​

Answers

Answer:

the second one i believe:)

Step-by-step explanation:

i literally just did this in algebra lol...hope this helps:))

Answer:

A

Step-by-step explanation:

Jamil found that he reads 1/5 of his 115 - page book in 1/4 of an hour. At this rate how many pages does he read in an hour.

Answers

Answer:

Step-by-step explanation:

1/5 of 115= 23

so in 15mins he reads 23 pages.

15mins x 4=60mins

23x4=92

Have a nice day sunshine

PLEASE HELP ME I REALLY NEED TO KNOW THIS

Answers

Answer:

I think it might be D. 15, Im not sure though, If its not im very sorry.

Step-by-step explanation:

Which set of ratios below is equivalent to 5:6?

Answers

the correct answer is c 10:12

Jenny has a bag of lollipops leftover from Halloween.
There are 6 cherry
, 5 lemon, 2 grape,
3 orange and 4 lime. What is the probability that
Jenny randomly chooses a cherry lollipop?
3

Answers

Answer:

kinda low kinda high because there is also 5 lemon

Answer: probably low because you have a lot of lemon lollipops

Step-by-step explanation:

Trinity sold candles for $7 each after she paid a $10 setup fee. The equation f(x)=7x-10 shows the profit Trinity will make from selling candles where x is the number of candles and f(x) is the profit she will make. If Trinity has 30 candles to sell, find the domain and range of the function.

Answers

Domain: 200

Range: 200

What value is needed to complete the square x^2-6x+

Answers

Answer:

9

Step-by-step explanation:

Take half of the coefficient of x and square it.

-6/2 = -3

Square -3 to get 9.

Answer: 9

Answer:

9 and 9

Step-by-step explanation:

yeah its only 9 and 9

70 Points question!!!! Answer ASAP
sec pi/3=2=

Answers

Answer:

pi/6

Step-by-step explanation:

take away the "=" and pretend its a parenthesis and    combined  

the two, the answer would be pi/6.

Answer:

2

Step-by-step explanation:

To Find :-

sec ( π / 3 ) sec ( 180°/3) sec 60° 2

Solve for x;
|x+0.5|= -5
A. x= -5.5
B. x= -5.5 OR 4.5
C. No solution
Please answer asap. Thank you ❤

Answers

Answer:

your answer will be A

Step-by-step explanation:

Answer:

C. No solution

Step-by-step explanation:

Solve for x:

|x+0.5|= -5

As we know an absolute value is always positive

So there is no solution to this equation as | x + 0.5 | ≥ 0 and the right side is negative

Correct option is C


A ribbon 105 centimeters long is cut into two pieces. One of the pieces is four times longer than the other. What is the length, in centimeters of the shorter piece
of ribbon?
Type your answer as the number ONLY.

Answers

Answer:

  21 cm

Step-by-step explanation:

The two pieces have a length ratio of 1 : 4, so the shorter piece is 1/(1+4) = 1/5 of the total length.

 105 cm/5 = 21 cm

The shorter piece is 21 cm.

_____

We assume you can figure out how to write only the digits of the number.

Solve for x if AC =33

Answers

Answer:

6.2

Step-by-step explanation:

can i hae brailiezt plzz

The answer of x if AC=33 is 6.20

3. The Green family is going on vacation. They rent a car that costs $139 for the week plus
plus $0.20 per mile. If the total bill is $168, how many miles did they drive?
PLEASE HELPP!!!

Answers

Answer:

168 divided by 0.20 is 840 Equalling the mileage.

Answer:

145 miles

Step-by-step explanation:

168 = .20m + 139

-139             - 139

29 = .2m

/.2     /.2

145 = m

(3,4)(4,-3)(7,4)(3,8)
Is it a function ?

Answers

Answer:

yes

Step-by-step explanation:

The Lake of Distress is contaminated with flesh-eating bacteria!! The lake started with only
4 square feet infected, but as time has gone on, the bacteria are growing by a factor of 3
every hour. Assume that the relationship between hours and square feet of bacteria is
continuous.

What is the domain of the function in set notation?

Answers

Given:

The lake started with only  4 square feet infected.

The bacteria are growing by a factor of 3  every hour.

To find:

The domain for this situation.

Solution:

Initial value = 4 square feet

Growth factor = 3

Using exponential growth model, we get

[tex]y=ab^t[/tex]

where, a is initial value and b is growth factor.

So, square feet of bacteria after t hours is

[tex]y=4(3)^t[/tex]

Here, domain is set of values of time and range is square feet of bacteria.

Above equation is defined for all values of t but we know that, time cannot be negative.

As the relationship between hours and square feet of bacteria is  continuous, therefore the value of t can be any real number greater than or equal to 0.

[tex]Domain=\{t|t\in R\text{ and }t\geq 0\}[/tex].

Therefore, the domain is [tex]\{t|t\in R\text{ and }t\geq 0\}[/tex].

Jose's batting average is 0.250 after 160 times at bat, which means he made a hit 40 of the times he was at
bat. He wants to improve his batting average to 0.333. If he makes a hit the next x times at bat, which
equation can be used to calculate the number of hits needed to obtain this improved batting average?
A. +40
160
.333
B.
160
= .333
2+40
C.
2+40
2+160
.333
O
D.
3+160
= .333
+40

Answers

Answer:

The correct option is;

[tex]\dfrac{x + 40}{x + 160} = 0.333[/tex]

Which is of the form of option C with 2 replaced by x and the characters formatted

Step-by-step explanation:

The given parameters are;

Jose's present batting average = 0.250

The number of times he was at bat = 160

The number of times he made a hit = 40

The batting average he wants to improve to = 0.333

If he makes a hit the next x times he was at bat is represented as if he makes a hit each time, for the next x time he was at bat. We have;

The number in times he makes a hit the next x times he was at bat = x

Therefore, we get;

New total number of hits Jose makes = 40 + x = x + 40

New total number of time Jose was at bat = 160 + x = x + 160

Therefore, given that Jose intends to improve his batting average to 0.333, and that the batting average is given by the relation;

[tex]Batting \ average = \dfrac{The \ number \ of\ hits}{The \ number \ of\ at \ bat }[/tex]

To find x, we have;

[tex]0.333 = \dfrac{x + 40}{x + 160}[/tex]

Therefore, the correct option is most likely C. where the 2 is supposed to be x.

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