What are the solutions to this quadratic equation? x2+6x-5 A. B. C. D.

Answers

Answer 1
Factoring x2-6x+5

The first term is, x2 its coefficient is 1 .
The middle term is, -6x its coefficient is -6 .
The last term, "the constant", is +5

Step-1 : Multiply the coefficient of the first term by the constant 1 • 5 = 5

Step-2 : Find two factors of 5 whose sum equals the coefficient of the middle term, which is -6 .

-5 + -1 = -6 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and -1
x2 - 5x - 1x - 5

Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-5)
Add up the last 2 terms, pulling out common factors :
1 • (x-5)
Step-5 : Add up the four terms of step 4 :
(x-1) • (x-5)
Which is the desired factorization

Equation at the end of step
1
:

(x - 1) • (x - 5) = 0
STEP
2
:
Theory - Roots of a product

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2 Solve : x-1 = 0

Add 1 to both sides of the equation :
x = 1

Solving a Single Variable Equation:

2.3 Solve : x-5 = 0

Add 5 to both sides of the equation :
x = 5

Supplement : Solving Quadratic Equation Directly

Solving x2-6x+5 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

3.1 Find the Vertex of y = x2-6x+5

Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 3.0000

Plugging into the parabola formula 3.0000 for x we can calculate the y -coordinate :
y = 1.0 * 3.00 * 3.00 - 6.0 * 3.00 + 5.0
or y = -4.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = x2-6x+5
Axis of Symmetry (dashed) {x}={ 3.00}
Vertex at {x,y} = { 3.00,-4.00}
x -Intercepts (Roots) :
Root 1 at {x,y} = { 1.00, 0.00}
Root 2 at {x,y} = { 5.00, 0.00}

Related Questions

What is the equation of this line?

Answers

Answer:

y = 1/2x - 3

Step-by-step explanation:

HELP ME OUT PLEASE!!!!!!!

Which equation could represent the relationship shown in the scatter plot?​

A) y = -3x - 2

B) y = 9x - 1/2

C) y = -3/4x + 10

D) y = -2/3x + 1​

Answers

Answer:

option C is correct.

according to me..

hope it helpful for you.

Lauren is going to invest in an account paying an interest rate of 3.4% compounded
annually. How much would Lauren need to invest, to the nearest cent, for the value of
the account to reach $13,000 in 8 years?

Answers

The answer would be 7615.7
Suppose x needs to be invested
So x.(1+3.4%)^8=13000
X. 1.034^8=13000
X=13000
———-
1.034.8
X= 7615.7

Albert is 5 years 6 months. How old is Albert in months​

Answers

Answer:

5x12=60,+6=66

Step-by-step explanation:

Answer:

66 months

Step-by-step explanation:

12months x 5= 60

60 + 6= 66

plsss answer questions guys


just answer number 5. plsss​

Answers

Answer:

B.{c}

Step-by-step explanation:

Answer:

Hey mate.....

Step-by-step explanation:

This is ur answer.....

B. c

Hope it helps!

Brainliest pls!

Follow me! :)

PLEASE NEED THIS ASAP

Answers

Answer:

The answer is in the above attachment.

A ticket for a show costs ​$114.50. A parking pass costs ​$13.00. Let x represent the number of tickets and y represent the cost. How much does it cost for 2 tickets and a parking​ pass?

Answers

Answer:

X multiplied by Y is $229 plus a parking pass being $242

Step-by-step explanation:

X = 2 (2tickets)

Y = $114.50 (cost of one)

multiplying the tickets by the cost of one will give you $229 and the cost for the parking pass being $13.00 well 29 + 13 = 42 adding 42 to the 200 we left gives you $242 for 2 tickets and a parking pass

Write a linear function f
with f(5)=−1
and f(0)=−5
.

Answers

Answer:

f(x) = 4/5x - 5

Step-by-step explanation:

y-mx+b

m=-5-(-1)/0-5=4/5

y = 4/5x + (-5)

y = 4/5x - 5

PLEASE HELP ME I AM CONFUSED
Sara bought 3 4 of a pound of bananas and 3 5 of a pound of pears. How much fruit did Sara buy?

Answers

Answer:

69

Step-by-step explanation:

because 34plus 35 will give you 69

Please look at picture for question.

Answers

Answer:

Amount spent on breakfest each day: 2B+J

Amount spent on granola bars each day: 2B

Amount spend on juice each day: J

Number of days buys breakfast: 7

y is inversely proportional to
[tex]x {3}^{?} [/tex]
y=44 when x=a
Find y when x=2a

Answers

[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\stackrel{\textit{"y" is inversely proportiional to }x^3}{y = \cfrac{k}{x^3}}\qquad \textit{we also know that} \begin{cases} y = 44\\ x = a \end{cases} \\\\\\ 44 = \cfrac{k}{a^3}\implies 44a^3=k~\hfill \boxed{y=\cfrac{44a^3}{x^3}} \\\\\\ \textit{when x = 2a, what is "y"?}\qquad y = \cfrac{44a^3}{(2a)^3}\implies y = \cfrac{44a^3}{8a^3}\implies \blacktriangleright y = \cfrac{11}{2} \blacktriangleleft[/tex]

In one week, a computer shop sold 13 laptop computers and
7 desktop computers. What was the ratio of laptop computers to all
computers that were sold in the week? Describe the ratio using words.

Answers

Answer:

13:7

Step-by-step explanation:

This ratio would be 13 laptop computers for every 7 desktop computers; 13:7

Ashley received a $24 discount on a radio she bought for $98.00. What is the percent of discount she saved?

Answers

Answer:

24.49

Step-by-step explanation:

Answer:

24.489%, but most of the time they only go to 2 decimal places so 24.49%

Step-by-step explanation:

What is 6 3/4 percent of 800

Answers

Answer:

319973/400

Step-by-step explanation:

800 - 27/4%

800 - ( 27/4 × 1/100)

800 - 27/400

= 319973/400

Don’t totally understand it

Answers

Answer:

A.1 B.2 E.5 F.6

Step-by-step explanation:

Hope it helps brainliest awnser pls

what is The greatest common factor of 42 and 96? I need it to be broken down for me to understand. thanks

Answers

Answer:

GCF is 6

Step-by-step explanation:

42 :

2 | 42

3 | 21

7 | 7

  | 1

; 42 = 2 x 3 x 7

96 :

2 | 48

2 | 24

2 | 12

2 | 6

3 | 3

  | 1

; 96 = 2 x 2 x 2 x 2 x 2 x 3

here, common factors are 2 x 3 = 6

Hence, the GCF of 42 and 96 is 6.

The perimeter of the figure below is 32.6 m. Find the length of the missing side.

Answers

Answer: 4.6

Step-by-step explanation: let the missing length be x

2+2+4.8+4.8+4.8+4.8+.4.8+x=32.6

28+x=32.6

x=32.6-28

x=4.6

A group of 4 friends went out for a special dinner. the items they ordered are listed below
24.95+18.96+17.55+23.14+12.00=96.60
Part B: The four friends decided to split the bill evenly. How much does each friend owe

Answers

My friends the answer is 3.

  24.95 + 18.96 + 17.55 + 23.14 + 12.00 + 96.60

  4 divided by 12 is 3

       

Based on the table below, find the input and output values of the function.

Answers

Answer:

the inputs are: 0,1,2,8,12

the outputs are: 19,9,7,16,17

(Put them in order if needed)

**inputs are x values and outputs are the y values**

-7+0.3(-4x+20)+8.8x
Help me plz
This is 8th grade math btw

Answers

Answer:

7.6x−1

Step-by-step explanation:

Expand by distributing terms

−7−1.2x+6+8.8x

Collect like terms.

(−7+6)+(−1.2x+8.8x)

Simplify

−1+7.6x

Regroup terms.

7.6x−1

Suppose that a risk-free investment will make three future payments of $250 in 1 year, $250 in 2 years, and $250 in 3 years. Instructions: Round your answers to 2 decimal places. a. If the Federal Reserve has set the risk-free interest rate at 4 percent, what is the proper current price of this investment? $ b. What is the price of this investment if the Federal Reserve raises the risk-free interest rate to 6 percent? $

Answers

Answer:

la théorie des plaques est

The total present value will be $693.75

The total present value will be $668.23

What is Future Value?

Future value is the value of an asset or investment as of some future date. In other words, the future value is the sum of money that an investment will be worth, assuming a certain rate of return, after a specific amount of time (interest rate).

First, i= 4/100 = 0.04

n= 1, 2, 3

Amount= $250

So, Present Value = 250/ (1 + 0.04) +  250/ (1 + 0.04)² +  250/ (1 + 0.04)³

=  250/ 1.04 + 250/ 1.04² + 250/ 1.04³

= 240. 38 + 231.13 + 222.24

= $693.75

So, The total present value will be $693.75

Second,  i= 6/100 = 0.06

n= 1, 2, 3

Amount= $250

So, Present Value = 250/ (1 + 0.06) +  250/ (1 + 0.06)² +  250/ (1 + 0.06)³

=  250/ 1.06 + 250/ 1.06² + 250/ 1.06³

= 235. 84 +  222.49 + 209.90

= $668.23

So, The total present value will be $668.23

Learn more about Future Value here:

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(Score for Question 2: of 27 points) 2. Two sidewalks in a park are represented by lines on a coordinate grid. Two points on each of the lines are shown in the tables. Sidewalk 1 х y 2 17 0 5 Sidewalk 2 х у 1 20 3 26 (a) Write the equation for Sidewalk 1 in slope-intercept form. (b) Write the equation for Sidewalk 2 in point-slope form and then convert to slope-intercept form. (c) Is the system of equations consistent independent, coincident, or inconsistent? Explain. a. Note: Review 2.11 Strange Solutions and 5.05 Classifying Systems if you're not sure where to start. (d) Use the substitution or elimination method to solve your system, and explain which one you picked. If the two sidewalks intersect, what are the coordinates of the point of intersection?


PLS HURRRRRRY i need this answer the real one and step by step pls if u dont know it dont try​

Answers

Answer:

Step-by-step explanation:

From the question, I couldn't really tell what the chart looks like, so I am guessing it looks like this:

Sidewalk 1:

x  |  y

2  |  17

0  | 5

Sidewalk 2:

x  |  y

1  |  20

3  | 26

Part a.

Now, we have to write the equation for sidewalk 1 in slope-intercept form.

Slope-intercept form is represented as this: [tex]y=mx+b[/tex], where m is the slope and b is the y-intercept. Because this is true for all values on the line, we can plug in values of the chart for Sidewalk 1.

[tex]17=2m+b\\5=0m+b[/tex]

Subtracting the second equation from the first, we have

[tex]12=2m[/tex], and [tex]m = 6[/tex].

Now, we can just plug 6 back into the first equation to get:

[tex]17=2(6)+b[/tex]  to get [tex]17 = 12 + b[/tex], and then [tex]b = 5[/tex].

Now, we can just rewrite slope intercept form for Sidewalk 1 to have

[tex]y=6x+5[/tex].

Part b.

Point-slope form is represented as [tex]y-y_1=m(x-x_1)[/tex], where x and y are the coordinates of one point, and x1 and y1 are the coordinates of another point on the line. Because the chart represented for Sidewalk 2 includes a point, namely [tex](1, 20)[/tex] and [tex](3, 26)[/tex], we can plug this in and solve for the slope:

[tex]26-20=m(3-1)[/tex]

This is it in point-slope form. Because the second part of the question asks us to convert to slope-intercept form, we must solve for the slope, or m.

Expanding, we have [tex]26-20=3m-m[/tex]

Combining like terms, we have [tex]6 = 2m[/tex], and then [tex]3 = m[/tex]. Now, we need to plug a point and the slope back into point-slope form, not needing another point. We choose [tex](1, 20)[/tex], even though [tex](3, 26)[/tex] works just as well.

[tex]y-20=3(x-1)[/tex]

Expanding, we have [tex]y-20=3x-3[/tex]

Adding 20 to both sides, we have [tex]y=3x+17[/tex]

Part c. and d.

We see that both equations do not have the same slope, so then they are not parallel, meaning they don't have no solutions. If they have a solution, we can set them equal to each other.

[tex]3x+17=6x+5[/tex]

Subtracting 3x, we have [tex]17=3x+5[/tex]

Subtracting 5, we have [tex]12 = 3x[/tex]

Dividing by 3, we have [tex]x = 4[/tex].

Because there is no x = x, or anything like that, the solution does not have infinite solutions and therefore has one solution, meaning it is consistent independent.

-2 5/12 - (-10 8/9)

Answers

-13.30

that might be the answer

8.47222222222

:D Hope this helps! I apologize if I’m wrong.

select all the ways you can describe the given polygon

Answers

Answer:

Isoceles and obtuse

Step-by-step explanation:

PLEASE HELP!!!!
On a Saturday, a library checked out 117 books. If 36 of the books were fiction, what is the ratio
of non-fiction books to fiction books checked out?

Answers

36:81

117 - 36 = 81
Answer:

4/9

Solution:

117-36 = 81
So out of the 117 books checked out, 36 of them were fiction and 81 were non-fiction, 36/81 simplified to lowest terms is 4/9

Please help and only answer if correct!

Answers

Answer: So last time it was 1/4 and 4 so it's no different it just going down by one so it's 1/3 and 3 if it's not I give up.

Step-by-step explanation:

Add or subtract. Write fractions in simplest form.

-9.24 + (-2.89)

how do i do this problem? please help, i will mark you brainliest!!

Answers

Answer:

-12.13

Step-by-step explanation:

To add two negative numbers, drop the negative signs and add the two positive numbers. Then make the answer negative.

-9.24 + (-2.89) =

We are adding two negative numbers, -9.24 and -2.89.

Step 1: ignore the negative signs and add the number 9.24 + 2.89

9.24 + 2.89 = 12.13

Step 2: the answer is negative, so add a negative sign to the sum above.

-9.24 + (-2.89) = -12.13

A researcher estimates that a fossil is 3200 years old. Using carbon-14 dating a procedure used to determine the age of an object the researcher discovers that the fossil is 3600. Find the percent error

Answers

Answer:

11.1

Step-by-step explanation:

The percentage error for the given data will be 12.5%

What is the percentage?

According to its definition, a percentage is any number relative to 100. It is shown with the sign %. "Out of 100" is what the percentage means. Consider dividing any quantity or item into 100 identical bits.

The percentage error will be calculated as:-

percent error = (|experimental value - theoretical value| / theoretical value) x 100

In this case, the experimental value is 3600 years (from carbon-14 dating) and the theoretical value is 3200 years (from the researcher's estimate). Plugging these values into the formula:

percent error = (|3600- 3200| / 3200) x 100 = (400/ 3200) x 100 = 12.5%

Learn more about percentage error on:

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4. Find the sum of all the numbers from 100 to 199 that are not divisible by 13.
What is the formula for
this?

Answers

There are 100 numbers in the range 100-199. Find the smallest and largest multiple of 13 in this range. We have

104 = 8•13

195 = 15•13

so there are 15 - 8 + 1 = 8 multiples of 13 between 100 and 199.

Then the sum we want is

[tex]\displaystyle \sum_{k=100}^{199} k - \sum_{\ell=8}^{15}13\ell[/tex]

or equivalently,

(100 + 101 + 102 + … + 199) - 13 (8 + 9 + … + 15)

To compute these sums, recall the following formula:

[tex]\displaystyle \sum_{i=1}^n i = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2[/tex]

Then

[tex]\displaystyle \sum_{k=100}^{199} k = \sum_{k=1}^{199} k - \sum_{k=1}^{99} k = \frac{199\cdot200}2 - \frac{99\cdot100}2 = 14,950[/tex]

and

[tex]\displaystyle \sum_{\ell=8}^{15} 13\ell = 13 \left(\sum_{\ell=1}^{15} \ell - \sum_{\ell=1}^7 \ell\right) = 13 \left(\frac{15\cdot16}2 - \frac{7\cdot8}2\right) = 1,196[/tex]

which means the sum we want is 14,950 - 1,196 = 13,754.

Find the domain of the function.



f(x) = -5x + 3

Answers

Enter a problem...

Calculus Examples

Popular Problems Calculus Find the Domain and Range f(x)=5x-3

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The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

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)

Set-Builder Notation:

{

x

|

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R

}

The range is the set of all valid

y

values. Use the graph to find the range.

Interval Notation:

(

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)

Set-Builder Notation:

{

y

|

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R

}

Determine the domain and range.

Domain:

(

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)

,

{

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Range:

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