Decide whether this statement is always true, never true, or sometimes true, and explain why: In a quadratic equation of the form 0 = ax2 + bx + c, there will be two real solutions if a and c are of opposite signs

Answers

Answer 1

Answer:

Always true

Step-by-step explanation:

Here, we want to evaluate if the given statement is true

The discriminant D can be calculated using the formula;

b^2 - 4ac

if D is greater than 0, then we will have only real roots

In a case where a and c are of opposite signs;

then -4ac will always give a positive value which can be added to b^2

This positive value will ensure that D is greater than zero and hence we can have only real roots

So this assertion is always true if a and c are of opposite signs


Related Questions

Charlotte and Layla are workers in a factory making widgets. Layla can make 20
widgets per day in the factory. Charlotte is able to produce 10% fewer widgets per day
than Layla. How many widgets can Charlotte make per day?

Answers

Charlotte can make 18 widgets a day

identify an equation in slope-intercept form the line parallel to y=-3x+7that passes through (2,-4)

Answers

Answer:

y=-3x+2

Step-by-step explanation:

Same slope = parallel. You can aso double check this answer by either graphing using the desmos online graphing calculator or by plugging in the point into the equation y = -3(2) + 2 --> y = -6 + 2 --> y = -4, so we are correct.

Answer:

y=-3x+2

Step-by-step explanation:

In this equation the slope is the same as the original equation (-3), but has a different y-intercept meaning that this line is parallel. As for satisfying the requirement that the line is parallel and passes through (2,-4), I plugged the coordinates into the equation y=-3x+b to get  -4=-3(2)+b, and then found what b would have to equal to make the equation true.

(plus I put my answer into a graphing calculator to check my work)

Bobs new bike has 26 inch diameter wheels.what is the circumference of the new wheel.Give answer to 1 decimal place

Answers

Answer:

The circumference of Bob's new wheel is 81.7 inches

Step-by-step explanation:

Circumference of a circle

The circumference of a circle of radius r is given by:

[tex]C=2\pi r[/tex]

The radius is half the diameter:

r = d / 2 = 26 / 2 = 13

r = 13 inch

Now calculate the circumference:

[tex]C=2\cdot\pi\cdot 13[/tex]

Calculating:

[tex]C=81.7\ inch[/tex]

The circumference of Bob's new wheel is 81.7 inches

What is the slope intercept formula for a vertical line?

Answers

Answer:

there isnt one i dont think. since the line never has a slope and rarely a y-intercept would be not way for an equation to be made unless it wa  y=mx+b but that just slop intercept form. I dont know if that righ but ig u can try it

Step-by-step explanation:

Brainliest 5 stars and thank you! (correct answers only)

What is the qoutient?

Answers

Answer:     the answer is the first one

Step-by-step explanation:

Select all equations that have graphs with the same y-intercept.

Answers

Answer:

there ar no graphs. Wish i could help. To add a screenshot, select the paperclip icon when posting a question and add the image like that.

If you need to know how to take a screenshot on your device, tell me the brand and name of your device

Example: Brand; Acer, Name; Chromebook

Step-by-step explanation:

given that f(x)= x^2-6x and g(x)= x-8 calculate f•g(-2)

Answers

9514 1404 393

Answer:

   f•g(-2) = -160

Step-by-step explanation:

f(-2) = (-2)^2 -6(-2) = 4 + 12 = 16

g(-2) = -2 -8 = -10

f•g(-2) =  f(-2)•g(-2) = 16•(-10)

f•g(-2) = -160

Answer:

hope this pic helps.enjoy

What is the solution to this system of linear equations?

x + y = 4

x − y = 6

Answers

Answer:

x=5 , y= -1

Step-by-step explanation:

You can see that one of the y's is negative while the other is positive, so you can add them together.

Now, negative 1 + positive 1 = 0, so the y's cancel out leaving only the x's.

Remember you can't add one part without adding the other so x+x = 2x, and 4+6=10. This makes the final equation 2x=10.

You can simplify that into x=5. This gives you the answer for x

Then substitute x=5 into any of the two equations (doesn't matter) I'll use the first one. So if you substitute it you get 5+y=4.

Simplified, y= -1

Therefore, x= 5 and y=-1

Answer:

(5,-1)

Step-by-step explanation:

Got it right on edge cause of the guy above me

The question is number 12. URGENT PLEASE

Answers

Answer: Choice C

We have an expression in the form

[tex]\frac{f(x+\Delta x)-f(x)}{\Delta x}[/tex]

where the [tex]\Delta x[/tex] term is approaching 0, which is what the "lim" indicates (we're applying a limit).

Note how in [tex]f(x+\Delta x)[/tex], we effectively replace every copy of x with [tex]x+\Delta x[/tex]

Choice D is close, but it's missing the "lim" notation, so it's not 100% accurate.

CAN YOU HELP ME thank you 10pts

Answers

9514 1404 393

Answer:

  m∠CAB = 62°

  m∠CBG = 114°

Step-by-step explanation:

Given:

  the above figure

Find:

  What are the measures of angles CAB and CBG

Solution:

The total angle at C is 32°+52° = 84°. We know that "remote interior" angles ECB and EBE have a sum that matches angle CEF.

So, angle CBE = 150° -84° = 66°

Angle CBG is the supplement of this, so is ...

  m∠CBG = 180° -66° = 114°

That angle is the total of "remote interior" angles BCA and CAB. So angle CAB is ...

  m∠CAB = 114° -52° = 62°

n 2+ 7n + 15 = 5 show work

Answers

Answer: n2+7n+15−5=5−5

n2+7n+10=0

Step 2: Factor left side of equation.

(n+2)(n+5)=0

Step 3: Set factors equal to 0.

n+2=0 or n+5=0

n=−2 or n=−5

Answer:

n=−2 or n=−5

Step-by-step explanation: hope that helps

Point Q was rotated about the orgin (0,0) by 180

Answers

Answer:

Whats the question?..

Step-by-step explanation:

If
M
is the midpoint of AB¯¯¯¯¯¯¯¯
A
B
¯
. If A (4, 0)
A

(
4
,

0
)
and M(2, 1.5)
M
(
2
,

1.5
)
, then find the coordinates of B
B
.

Answers

Answer:

this question a little confusing but i think its b= when u multiply

there is a certain number. If you add 30 7 to it, then subtract 22 7 from the previous result, and then subtract that difference from 59/7, after that you will get 19 7. What is a certain number?

Answers

Step-by-step explanation:

59 / 7 - ( x + 30 / 7 - 22 / 7 ) = 19 / 7

59 / 7 - ( x + 8 / 7 ) = 19 / 7

59 / 7 - x - 8 / 7 = 19 / 7

- x = 19 / 7 - 59 / 7 + 8 / 7

- x = - 32 / 7

x = 32 / 7

A recipe for Chex mix calls for peanuts, m&ms, and Chex cereal in the ratio of 2:3:5. How many cups of cereal will you need if you use 1.5 cups of M&Ms

Answers

Answer:

1 cups of cereal will be needed

Step-by-step explanation:

The ratio is given as;

2:3:5

M&M takes 3 while cereal takes 2

This means the ratio of M&M to cereal is 3:2

So let us look at the ratio of the two

3/2 = 1.5/x

= 2 * 1.5 = 3 * x

3x = 3

x = 3/3

x = 1

Convert 147%, percent to a fraction in simplest form.

Answers

Answer:147/100

Step-by-step explanation:Convert the percentage to a fraction by placing the expression over  

100

. Percentage means 'out of  

100

1  47/100

That would be the answer uwu

I REALLY NEED HELP QUICK!

Answers

Answer:

y=1/2x-5

Step-by-step explanation:

From the picture you can see that (0, -5) is a point on the function and that (2, -4) is another point. Using these you can find the slope of the function with the equation

[tex](y_{2} -y_{1})/(x_{2}-x_{1} )[/tex]

We can substitute in the points so it looks like

[tex](-4--5)/(2-0)[/tex]  or  [tex]1/2[/tex] which is the slope of the function

Now, since the y-intercept is (0, -5) on the graph, the b part in the slope-intercept form of the equation would be -5, leaving us with the equation y=1/2x-5

SOMEBODY HELP ITS 30 POINTS
The distance in miles a car travels over time in minutes is shown in the table.

Distance (miles)
Time (minutes)
10
15
20
30
30
45
40
60

Kwame is not sure whether to use a line graph or a line plot to display the data. Which best explains which graph is a better representation of the data?
The line graph because it shows how the number of miles increases over the number of minutes.
The line graph because the numbers in the data table are equally spaced.
The line plot because numbers can be plotted on a number line.
The line plot because there are only a few data points.

Answers

Answer:

The line graph because it shows how the number of miles increases over the number of minutes.

Step-by-step explanation:

ake it or leave it

The best explanation graph is a better representation of the data below: "The line graph because it shows how the number of miles increases over the number of minutes."

What is a graph?

A graph can be defined as a visual representation or a diagram that represents data or values.

The distance in miles a car travels over time in minutes is shown in the table.

Distance (miles)    Time (minutes)

    10                                 15

   20                                 30

   30                                 45

   40                                 60

A line graph is a good choice for representing data that show a change in value over time. In this case, the value being measured is the distance in miles traveled, and the time is being used as the variable. A line graph is a good choice because it can show the change in distance over time, which is what the data represents.

Hence, the correct answer would be an option (A).

Learn more about the graphs here:

brainly.com/question/16608196

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PLEASE HELP This is solving Exponential and Logarithmic Equations I got the other ones, but I don’t even know what this says to be honest please help.

Answers

Answer:

Step-by-step explanation:

We have

[tex]e^\frac{x}{2}^l^n^3 = 5\\[/tex]

[tex]ln(e^\frac{x}{2}^l^n^3) = ln(5)\\\frac{x}{2}ln(3) = ln(5)\\\frac{x}{2} = \frac{ln(5)}{ln(3)} \\x = \frac{2ln(5)}{ln(3)}[/tex]

[tex]x = 2.929947041[/tex]

to the third decimal is 2.930 (i might be wrong on the rounding part)

Solving by substitution y=-7x+6 with 5x+y=2

Answers

Answer:

x=1/3,y=3

Step-by-step explanation:

y=7x+6_____equation1

5x+y=2_____equation2

substitute y into equation 2

5x+7x+6=2

12x+6=2

12x=2-6

12x=-4

x= -1/3

substitute X into equation 1

y=7x+6

y=7(-1/3)+6

y=-7/3+6

y=9/3

y=3

3a+6b-a-9b please help!

Answers

Answer: 2a - 3b
You can try rearranging it , it’ll be easier I think :)
3a + 6b - a - 9b
= 3a - a + 6b - 9b
= 2a - 3b

1(x-31)= 5(2+5)vvvvvb​

Answers

Answer:

1x-31=35

1x=35+31

1x=66

x=66

X-31=5*7
X-31=35
X=35+31
X=66

A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly and at a constant rate. After 888 months, he weighed 138138138 kilograms. He started at 909090 kilograms.

Answers

Given :

Initial weight of sumo wrestler, I = 90 kg.

Final weight of sumo wrestler, F = 138 kg.

Time taken, T = 8 months.

To Find :

Weight gain per month.

Solution :

Weight gain per month = ( Final weight - Initial weight ) ÷ Total number of month

[tex]W = \dfrac{138-90 }{8}\ kg/month\\\\W = 6 \ kg/month[/tex]

Therefore, weight gain per month is 6 kg/month.

Hence, this is the required solution.

Find the slope of line

Answers

Answer:

2/4

Step-by-step explanation:

rise/run

go up (rise) 2, run 4

2/4

From the information in the diagram, what is m PHOTO ABOVE

Answers

Answer:

107 degrees

Step-by-step explanation:

i just did it

rica walks to her friend Philip's house. The graph shows Erica's distance from home over time.




Find the rate of change from 1 minute to 2 minutes.

Answers

can you send a picture of the graph? there's no way to know the answer if we can't see the graph

A community center is collecting blankets. The director of the center has asked 135 families to donate 3 blankets each. If 20% of the families donated 3 blankets each, how many blankets did the center collect from these families?

81
27
115
50
Pls pls help

Answers

Answer: 81

Step-by-step explanation: 20% of 135= 27, and 27x3=81

Given the points A(-2, 5) and B(2, 3), find the coordinates of the point P on directed line segment AB that partitions AB in the ratio 4 to 1.

Answers

Answer:

The answer to your question is:  Point (-1/2 , 17/4)

Step-by-step explanation:

Data

A(-2, 5)

B (2, 3)

ratio 3:5    r = 3/5

Formula

Process

x =  

x = -1/2                                                           y = 17/4Data

A(-2, 5)

B (2, 3)

ratio 3:5    r = 3/5

Formula

Process

x =  

x = -1/2                                                           y = 17/4Data

A(-2, 5)

B (2, 3)

ratio 3:5    r = 3/5

Formula

Process

x =  

x = -1/2                                                           y = 17/4Data

A(-2, 5)

B (2, 3)

ratio 3:5    r = 3/5

Formula

Process

x =  

x = -1/2                                                           y = 17/4

The coordinates of the point P is (6/5, 17/5).

Given that, the points A(-2, 5) and B(2, 3) and the line segment divided in the ratio 4:1.

What is the section formula?

The Section formula is used to find the coordinates of the point that divides a line segment (externally or internally) into some ratio.

The section formula is [tex]P(x,y)=(\frac{mx_{2}+nx_{1} }{m+n}, \frac{my_{2}+ny_{1} }{m+n} )[/tex].

Here, m:n=4:1, (x1, y1)=(-2, 5) and (x2, y2)=(2, 3)

Now, P(x, y) = [tex](\frac{4\times 2+1 \times (-2)}{4+1} , \frac{4\times 3+1 \times 5}{4+1} )[/tex]

=(6/5, 17/5)

Therefore, the coordinates of the point P is (6/5, 17/5).

To learn more about the coordinate geometry visit:

https://brainly.com/question/18269861.

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Solve for z.

3 + 2z = 7

z =











Solve for z.

3 + 2z = 7

z =

Answers

Answer: z=2

Step-by-step explanation:

2 x 2 = 4 + 3 = 7

Answer: Okay, the answer is z=2.

Step-by-step explanation: Step 1: Simplify the both sides of the equation: 2z+3=7.

Step. 2: Subtract 3 from the both sides: 2z+3−3=7–3.

Last but not least is step 3. Divide the both sides by 2: 2z/2=4/2. So you get z=2. I hoped my step-by-step explanation formula substitution is very helpful, please mark me as Brainliest, and have a happy holidays!!!!!!! :D

I have like two more I don't understand, I'm in 4th and on my sisters account and I was sick while learning this so I don't know how please help will mark brainliest

Answers

1 1/2 x 12

Key: Keep, change, flip.

So 1 1/2 you have to make it into a improper fraction.

1 1/2 to 3/2 x 12/1 = 3/2 x 1/12 = 1/2 x 1/4 = 1/8

Hope this answer helps :)

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