Use the discriminant to determine how many and what kind of solutions the quadratic equation 2x^2 - 4x = -2 has.

Answers

Answer 1

Answer:

We can use three solution and they are

(1)completing the square

(2)quadratic formula

(3) factorisation method

Answer 2

The quadratic equation 2x^2 - 4x = -2 has  two values .

What is quadratic equation ?According to our definition, a quadratic equation is one with degree 2, implying that its maximum exponent is 2. A quadratic has the standard form y = ax2 + bx + c, where a, b, and c are all numbers and a cannot be zero. All of these are examples of quadratic equations: y = x^2 + 3x + 1.Kind of solutions -

   (1)completing the square

   (2)quadratic formula

   (3) factorization method

Given,

           quadratic equation 2x^2 - 4x = -2

                   2x² - 4x + 2 =0

Now solve this equation by factor,

                    2x² - 4x + 2 = 0

                    2x² - ( 2+2)x +2 = 0

                    2x² - 2x -2x + 2 = 0

                    2x(x- 1 ) -2 ( x -1) = 0

                    (2x - 2) ( x- 1) =0

                  2x - 2 = 0   or  x - 1 = 0

                   x = 1 or x = 1

So, this equation has 2 value of x.

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Related Questions

the sum of the first ten terms of an arithmetic progression consisting of positive integers is equal to the sum of the 20th, 21st and 22nd term. If the first term is less than 20, find how many terms are required to give a sum of 960

Answers

Answer:

The correct answer is = 15.

Step-by-step explanation:

Formula:

The sum of the first n terms of an arithmetic progression with first term a and constant difference d is

[tex]S_n=\dfrac{n}{2}[2a+(n-1)d[/tex]

using this formula in this problem

Solution:

The sum of the first ten terms is

[tex]S_{10}=\dfrac{10}{2}[2a+(10-1)d[/tex]

[tex]S_{10}=5(2a+9d)[/tex]

The sum of the 20th, 21st, and 22nd terms is three times the 21st term:

[tex]3a_{21}=3(a+(21-1)d)[/tex]

[tex]3a_{21}=3(a+20d)[/tex]

[tex]3a_{21}=3a+60d[/tex]

The problem then tells us

[tex]S_{10}=3a_{21}[/tex]

[tex]10a+45d=3a+60d[/tex]

[tex]7a=15d[/tex]

there are only positive integers and the first term a is less than 20 as given. Since 7 and 15 have no common factor, the only explanation of the requirements is a = 15 and d = 7. So the progression is

then, 15, 22, 29, 36, ...

The problem says to find the number of terms n for which the sum is 960:

putting value in the formula

[tex]30n+7n^{2}-7n=1920\\7n^{2}+23n-1920=0[/tex]

solving quadratic will give n = 15

thus, the correct answer is 15.

answer please don't skip plz answer

What is the value of x^2

-2xy+y^2

if x-y = 4 ?

please answer ​

Answers

Answer:

16

Step-by-step explanation:

[tex]x^2 - 2xy + y^2 = (x -y)^2 \\[/tex]

                   [tex]= 4^2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ given : x - y= 4 \ ]\\\\= 16[/tex]

The value of x^2-2xy+y^2

will be 16 .

Explanation is in the attachment .

hope it is helpful to you ☺️

In July 2014 one Mexican peso was worth 0.075 U.S. dollars. How many Mexican pesos was $133.00 U.S. dollars worth?

Answers

Answer:

1,773.33 Mexican pesos

Step-by-step explanation:

Create a proportion where x was how many Mexican pesos it was worth:

[tex]\frac{1}{0.075}[/tex] = [tex]\frac{x}{133}[/tex]

Cross multiply and solve for x:

133 = 0.075x

1773.33 = x

So, it was worth approximately 1,773.33 Mexican pesos

What is the probability that in a sample of 400 registered voters to at least 290 voted in their most recent local

Answers

Answer:

The probability that in a sample of 400 registered voters at least 290 voted in their most recent local elections is:

= 72.5%

Step-by-step explanation:

Sample of registered voters = 400

Sample of voters that actually voted = 290

Probability = 290/400 * 100

= 72.5%

b) This result above gives the statistic that for every 100 registered voters, 72.5 voters voted.  Probability measures the chance of an event occurring given other events.  Therefore, one can conclude that the voting was at least 72.5%.  Inversely, 27.5% of the registered voters did not participate or cast their ballots in the local elections.

Sidney's retirement party costs $28, plus an additional $1 for each guest she invites. What is the maximum number of guests there can be if Sidney can afford to spend a total of $44 on her retirement party?

Answers

Answer:

16 guests

Step-by-step explanation:

Firstly, we know Sidney's retirement party costs a starting amount of $28. We also know that she can only spend $44 on her retirement party. The easiest way to do it in my opinion is subtract 28 from 44, giving you 16. Since we know that each guest is only $1, we know that the maximum number of guests Sidney can afford is 16 guests. I hope this helped and please don't hesitate to ask for clarification!

$44-$28=$16

$16÷$1=16 guests at most

3.6 subtract by 1.487 is egual to ______.Pls write in step by step.​

Answers

Answer:

2.113

Step-by-step explanation:

 

               [tex]3.600\\1.487 \ -\\\overline{2.113}[/tex]

what is equivalent to x-2(3x-1)=3x

Answers

Answer:

1/4 = x

Step-by-step explanation:

x - 2( 3x - 1 ) = 3x

Step 1 :- Distribute 2

x - 2 × 3x - 2 × 1 = 3x

x - 6x + 2 = 3x

Step 2:- Combine like terms

-5x + 2 = 3x

Step 3 :- Add 5x to both sides

-5x + 5x + 2 = 3x + 5x

2 = 8x

Step 4 :- Divide both side by 8

2/8 = 8x / 8

1/4 = x

What is the area of triangle ABC? - OP 03 square units 0 7 square units o 11 square units 0 15 square units see pic​

Answers

The answers ir 15 square units

Answer:

7 sq unit

Step-by-step explanation:

Area of triagle ABC = Area of rectangle mnBp - Area of trangle AmC - Are of triangle CnB - Area of triangle ABp

Area of rectangle mnBp = 5x3 = 15 sq unit

Area of trangle AmC = 4x2 /2 = 4 sq unit

Are of triangle CnB = 5x1 /2 = 2.5 sq unit

Area of triangle ABp = 3x1 /2 = 1.5 sq unit

I believe you can work out thd answer from the above

helppp!! 21 - 3y = -18
3x+ y = -5

Answers

Answer:

(-3,4)

Step-by-step explanation:

A system of equations is given to us. The given equations are ,

[tex]\implies 2x - 3y = -18[/tex]

[tex]\implies 3x + y =-5[/tex]

We need to plot the graph and find the solution of the given system . For that refer to attachment . The point at which both the lines of the graph will intersect each other will be the solution of the given system of equations .

From the graph we can see that it intersect at (-3,4) . Therefore the Solution is ,

[tex]\longrightarrow \underline{\underline{ Solution = (-3,4)}}[/tex]

Answer: If you graphing it’s (-6, 13) or (3, 4)

Step-by-step explanation:

21 - 3y = -18- y = 13

3x + y = -5- x = -6

The slope of diagonal AB is ___ , and it’s equation is ___.

Answers

Answer:

The slope of diagonal AB is 0 and its equation is [tex]y=-2[/tex].

Step-by-step explanation:

Horizontal lines have zero slope. Since diagonal AB represents a horizontal line (same y-value regardless of x-value), the slope of diagonal AB is 0.

Horizontal lines can be expressed as [tex]y=n[/tex] where [tex]n[/tex] is some real number. In this case, diagonal AB sits on a line with only y-values of -2, and therefore the equation of the line the diagonal is on is [tex]\boxed{y=-2}[/tex].

Question 5 of 10
Select the correct answer.
The graph shows a line of best fit for data collected on the average temperature, in degrees Fahrenheit, during a month and the
number of inches of rainfall during that month.
Average Temp.
90
80
70
60
50
404
30
20
10
1 1 2 3 4 5 6
X
Inches of Rain
The equation for the line of best fit is y = -3.32x + 97.05.
Based on the line of best fit, what would be the prediction for the average temperature during a month with 13.25 inches of rainfall?

Answers

Answer:

53.06°F

Step-by-step explanation:

Given the equation of best fit :

y=-3.32x +97.05.

The average temperature for a month with 13.25 inches of Rainfall

Amount of Rainfall = x

Average temperature = y

To make our prediction ; put x = 13.25 in the equation and solve for y ;

y = -3.32x +97.05

Put x = 13.25

y = -3.32(13.25) +97.05

y = - 43.99 + 97.05

y = 53.06°F

please give full solutions
√8281​

Answers

Answer:

the answer is 91

Step-by-step explanation:

We have the number of emergency room admissions to SWTRHA hospital on 6 different Friday the 13ths along with the number of admissions to the same hospital on the previous Friday the 6th. Is there any difference between admissions on the 6th and the 13th. Conduct a depedent samples t-test to find out. What is the value of your t Stat

Answers

Answer:

Test statistic = - 2.71

Step-by-step explanation:

Table of the sample data is attached below :

Using a dependent sample t test :

H0 : μd = 0

H0 : μd ≠ 0

The difference in the 6th and 13th date data is :

Difference, d = -4, -6, -3, -1, 1, -7

The sample size, n = 6

The mean of d ; μd = Σd/ n = - 3.667

Standard deviation of difference, Sd = 3.011

The test statistic : μd/(Sd/√n)

Test statistic = - 3.33 / (3.011/√6)

Test statistic = - 3.33 / 1.2292356

Test statistic = - 2.709

Test statistic = - 2.71

What is the meaning proportion between 3 and 27?​

Answers

Answer:

you mean the mean not the meaning right?

The mean proportional of 3 and 27 = +√3×27 = +√81 = 9.

15. Which of the following is a rational number?
O A.V-
O B. 18
O C. T (3.141592...)
OD.3.59

Answers

Answer:

c

Step-by-step explanation:

non terminating recurring. i think option c must be the answer

an oil tank, which is a shape of a cylinder, is 3m high and has a diameter of 6m. the oil tank is two-thirds full. find the number of cubic meters of oil in the tank. use 3.14 for pi

Answers

Answer:

Step-by-step explanation:

The key is to find out the entire volume the tank can hold when it is full, then take 2/3 of that amount. The volume of a cylinder is

[tex]V=\pi r^2h[/tex] and filling in:

[tex]V=3.14(3)^2(3)[/tex] (if the diameter is 6 m, the radius is 3) so

V = 84.78 m³ when it is full all the way. If we need the amount that makes up 2/3 of that:

[tex]\frac{2}{3}(84.78)=56.52m^3[/tex]

Simplify 6/x^2−2x/x^2+3.

Answers

Answer:

3x2−2x+6/x2

Step-by-step explanation:

have a great day <33333

Which of the following best describes the relationship between angle a and angle bin the image below?

Answers

The answer is angle 2
angle 2 is the answer

Hello can anyone pls help with this multiple choice question

Answers

Answer:

The correct answer is the last one

Step-by-step explanation:

HELP ME PLEASE ASAP! So the answer for the question I got is 113.1. Is my answer correct or is it wrong? Please let me know how to solve this problem if the answer is wrong. Thank you for your time.

Answers

Answer: 113.01m - You are almost right

Step-by-step explanation:

Simply by using pir^2, you get the number you calculated, but it is asking for at least 2 decimal places. So it would be "113.01"

In order to test for the significance of a regression model involving 4 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are Select one: a. 3 and 43 b. 4 and 43 c. 4 and 42 d. 3 and 42

Answers

Answer:

c. 4 and 42

Step-by-step explanation:

Given

[tex]p = 4[/tex] -- independent variables

[tex]n = 47[/tex] ---- observations

Required

The numerator and denominator degrees of freedom

The denominator degrees of freedom is:

[tex]df =n - p - 1[/tex]

[tex]df =47 - 4 - 1[/tex]

[tex]df =42[/tex]

For the numerator, we have:

[tex]df = p[/tex]

[tex]df = 4[/tex]

Find the value for the side marked below.
Round your answer to the nearest tenth.
у
100
49°
y = [?]

Answers

Answer:

y = 75.5

Step-by-step explanation:

Reference angle (θ) = 49°

Hypotenuse = 100

Opposite = y

Apply trigonometric function, SOH. Which is:

Sin θ = Opp/Hyp

Plug in the values

Sin 49 = y/100

100*Sin 49 = y

y = 75.5 (nearest tenth)

solve the inequality x^3+4x>5x^2 please show steps and interval notation. thank you.​

Answers

Answer: [tex]x\in (0,1)\cup (4,\infty)[/tex]

Step-by-step explanation:

Given

In equality is [tex]x^3+4x>5x^2[/tex]

Taking terms one side

[tex]\Rightarrow x^3-5x^2+4x>0\\\Rightarrow x(x^2-5x+4)>0\\\Rightarrow x(x^2-4x-x+4)>0\\\Rightarrow x(x-4)(x-1)>0\\\Rightarrow (x-0)(x-1)(x-4)>0[/tex]

Using wavy curve method

[tex]x\in (0,1)\cup (4,\infty)[/tex]

What does point b represent on the graph ?

Answers

You need to add the photo

Answer:

Step-by-step B represents the $14 John earned in the 2 hours he worked.

explanation:

An ordinary fair die is a cube with the numbers one through six on the sides represented by painted that. Imagine that such a die is rolled twice in succession and that the face values of the two goals are added together. This song is recorded as the outcome of a single trial of a random experiment. Compute the probability of each of the following events. Event a: the sun is greater than six

Answers

Answer:

ok so what i think your trying to ask is if we roll two dice that the sum will be more then 6

Two dice

Assuming that the dice are unbiased or not " loaded".

Each side has the same probability, is 1/6 =0.16667, to turn up when rolled, if the die (D) is unbiased. The probability of a side turning up on D1 when 2 dice ( D1,D2) are rolled, is independent of the side turning up in D2. So this is an independent event.

How many ways can one get a sum total of 6 if D1 &D2 are rolled at the same time?

These are the possibilities

Case 1.

D1 =1 & D2=5

Or

D1= 5 & D2=1

Case 2.

D1 =2 & D2=4

Or

D1= 4 & D2= 2

Case 3. D1=3, D2=3

P3 =0.027778

Let's say, P 1 the probability for case 1 and P2 for case 2. There are no other cases.

The final probability P and is the sum total P = P1 + P2 + P3 the probability law of mutually exclusive events.

P1= 0.02778+ 0.02778 =0.055558

P2= 0.02778+0.02778 =0.055558

Same way,

P3=0.027778, when there is only one way to get the sum 6.

So, P = 0.138894

Based on truncating at the sixth decimal place.

A visual representation with two unbiased dice and the possible cases would also give the same result and is a short cut method. I like to derive from the basics.

Hope This Helps!!!

SCALCET8 3.11.501.XP. Find the numerical value of each expression. (Round your answers to five decimal places.) (a) sinh(ln(4)) (b) sinh(4)

Answers

sinh(ln(4)) = (exp(ln(4)) - exp(-ln(4)))/2 = (4 - 1/4)/2 = 15/8 = 1.875

sinh(4) = (exp(4) - exp(-4))/2 ≈ 27.28992

Write the equations for a line parallel to the line:
y=-4/3x-4
That goes through the point (-7,-6)
Write your equation in slope intercept form, using reduced fractions for the slope and intercept if necessary.

Answers

Answer:

y = -4/3x -46/3

Step-by-step explanation:

The question tells us to write an equation that is:

- parallel to the given line

- goes through the point (-7, -6)

Parallel lines will have the same slope, because if the slope was different, they would eventually intersect and not be parallel lines anymore.

We are going to use the point-slope form to find the other line.

Point-slope form uses a point that the graph will cross through and the slope of the graph to find the graph in y = mx + b form (also called slope-intercept form).

(I attached the point-slope form as an image below)

m = slope

x1 = x coordinate of the point

y1 = y coordinate of the point

We are going to substitute our slope into the form first:

y - y1 = (-4/3)(x - x1)

Next let's put in our point (-7, -6):

(Remember! -7 is our x coordinate & -6 is our y coordinate :-) )

y - (-6) = -4/3(x - (-7))

(cancel out the negatives to make them positive)

y + 6 = -4/3 (x +7)

Now solve for x using basic algebra:

y + 6 = -4/3 (x +7)

(distribue the -4/3)

y + 6 = -4/3x - 28/3

(subtract 6 from both sides)

y = -4/3x -46/3

That's your answer!

Hope it helps (●'◡'●)

Answer:

Step-by-step explanation:

y + 6 = -4/3(x + 7)

y + 6 = -4/3x - 28/3

y + 18/3 = -4/3x - 28/3

y = -4/3x - 46/3

Use the value of phi = 1.618 to predict the 23rd number in the Fibonacci sequence. The 22nd number in the sequence is 17,711.

- 10,946

- 17,711

- 22,897

- 28,656

Answers

Given:

[tex]\phi=1.618[/tex]

22nd number in Fibonacci sequence = 17,711

To find:

The 23rd number in the Fibonacci sequence.

Solution:

The nth term of a Fibonacci sequence is:

[tex]f_n=\dfrac{\phi^n-(1-\phi)^n}{\sqrt{5}}[/tex]

Substituting [tex]\phi=1.618, n=21[/tex], we get

[tex]f_{21}=\dfrac{(1.618)^{21}-(1-1.618)^{21}}{\sqrt{5}}[/tex]

[tex]f_{21}=\dfrac{(1.618)^{21}-(1-1.618)^{21}}{\sqrt{5}}[/tex]

[tex]f_{21}=10941.1724024[/tex]

[tex]f_{21}\approx 10941[/tex]

Now,

[tex]f_{23}=f_{21}+f_{22}[/tex]

[tex]f_{23}=10941+17711[/tex]

[tex]f_{23}=28652[/tex]

It is about 28,656. Therefore, the correct option is D.

A decorative wall in a garden is to be build using bricks that are 3 3/4 inches thick and mortar joints that are 1/4 inch. Use the diagram to find the height of the wall

Answers

Step-by-step explanation:

we cannot see the diagram, so we don't know how many layers of bricks are used. and therefore it is impossible to tell the height of the wall.

It is believed that students who begin studying for final exams a week before the test score differently than students who wait until the night before. Suppose you want to test the hypothesis that students who study one week before score less than students who study the night before. A hypothesis test for two independent samples is run based on your data and a p-value is calculated to be 0.2789. What is the appropriate conclusion

Answers

Answer:

The p-value is 0.2789 > 0.05, which means that the appropriate conclusion is that the students do not score differently.

Step-by-step explanation:

It is believed that students who begin studying for final exams a week before the test score differently than students who wait until the night before.

At the null hypothesis, we test if the two means are equal, that is, the subtraction of them is 0.

[tex]H_0: \mu_1 - \mu_2 = 0[/tex]

At the alternative hypothesis, we test if the two means are different, that is, the subtraction of them is different of 0. So

[tex]H_1: \mu_1 - \mu_2 \neq 0[/tex]

A hypothesis test for two independent samples is run based on your data and a p-value is calculated to be 0.2789.

Considering a standard significance level of 0.02789, the p-value is 0.2789 > 0.05, which means that the appropriate conclusion is that the students do not score differently.

Other Questions
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Suppose China also demands U.S. wheat (QDC) and that its demand is given by QDC = 2100 - 100PWhat is the total demand for U.S. wheat, assuming the only two sources of demand are domestic and Chinese? The total demand for U.S. wheat is:____.A. QD = 3530 - 155P for all P. B. QD = 1430 - 55P for all P. C. QD = 3530 - 155P for P < or = to $26 and QD = 2100 - 100P for P > $26. D. QD = 3530 - 155P for P < or = to $21 and QD = 2100 - 100P for P > $21. E. QD = 3530 - 155P for P < or = to $21 and QD = 1430 - 55P for P > $21. Lily owed Megan $129.42. So far, she has paid Megan $32.56.The remaining amount Lily has yet to pay Megan is $ Difference between developed and developing country. It is the highest level in the modern taxonomic classification system What's 70 x4 I just wanna see if its really going to help me Limestone, which contains the mineral calcite that fizzes in weak acid, may changedue to heat and pressure into the metamorphic rock marble. What characteristicswould you expect the marble to show?A: it would show fossils.B: It would not fizz in acid.C: It would have stripes.D: It would fizz in acid. Suppose that demand is unitary elastic at all points. When price is increased from a point on this demand curve, then total revenue will_____________. "Any government that is willing to assist in the task of recovery will find full cooperation, I am sure, on the part of the United States Government. Any government which maneuvers to block the recovery of other countries cannot expect help from us. Furthermore, governments, political parties, or groups which seek to perpetuate human misery in order to profit therefrom politically or otherwise will encounter the opposition of the United States." From the Marshall Plan, 1947 How does this excerpt reflect the U.S. position in the world in the post-World War II period? (7 points) 1. The United States was attempting to establish itself as a leading international power but lacked the resources and leadership to back up its stated goals.2. The United States was in a favorable economic position to help Europe recover, which gave it the political power to direct related International negotiations. 3. The United States was eager to restore productivity in its trading partners but did not want to appear discriminatory when it refused assistance to certain enemies. 4. The United States was firmly accepted as the leading nation of the world by that point, and other nations saw its statements as potential threats to their own future security. Read the following statement carefully[tex] \sqrt[ \sqrt{ \frac{? \times \frac{?}{?} }{?} } ]{?} \times \frac{?}{?} [/tex]No SeNsE rePoRt Stans Sporting Goods is a competitor that can manufacture seven soccer balls out of a possible ten, if it makes one soccer net. Which statement correctly compares the two businesses?Sabrinas Soccer has a comparative advantage over Stans Sporting Goods because Sabrinas Soccer has a lower opportunity cost.Stans Sporting Goods has a comparative advantage over Sabrinas Soccer because Stans Sporting Goods has a lower opportunity cost.Sabrinas Soccer has an absolute advantage over Stans Sporting Goods because Sabrinas Soccer has a lower production cost.Stans Sporting Goods has an absolute advantage over Sabrinas Soccer because Stans Sporting Goods has a lower production cost. What part of the joint cavity lubricates the joint, supplies nutrients, removes metabolic wastes, and absorbs shock In 2020, Susan had interest expense of $58,500 from her investments. Susan's has investment income of $46,500. Of this amount, interest is $15,000, qualified dividends are $9,000, and a net capital gain on the sale of securities is $22,500. What is the maximum amount of Susan's investment interest expense deduction for the current year if she decides to give up the capital gain preferential treatment Explain how sunlight is the primary source of energy for your own life 4. The Fox Trot was the most significant development in all of ballroom dancing.TrueFalse escribo lo que debe ir en cada de au estructura 1. Draw four illustrations of a globe and paper that are positioned to yield equatorial, transverse, oblique, and polar aspect projections. Label the equator in each. Use your textbook or lecture material if you need a reference.2. On any map, why is there distortion at areas that do not fall on lines of tangency or secancy? If a vulnerability is not fixed at the root cause, there is a possibility that another route of attack can emerge. This route is known as the ____________________. Solve: 4(x + 3) 44x 16x 16x 8x 8Please help Please help ASAP and please show work if possible.