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

one of the acute angles of a right angle triangle is 35 degree find the measure of the acute angle.​

Answers

Answer:

55°

Step-by-step explanation:

One triangle = 180° Therefore 90°+35°+ Unknown acute angle = 180°

125°+ Unknown acute angle = 180°

Unknown acute angle = 180°-125°

Unknown acute angle =55°

Answer:

55°

Step-by-step explanation:

One triangle 180° 90+35 =125-180=55°

Could I get help on this?

Answers

Answer:

returning the collateral

If you paid $160 in interest to a loan company for the use of $10000 of or 30 days, what annual simple interest rate did they charge?

Answers

Answer:A loan company charges $30 interest for a one month loan of $500. Find the annual interest rate they are charging.

Step-by-step explanation:You will earn $160 interest total over the four years. Try it Now 1. A loan company charges $30 interest for a one month loan of $500. Find the annual interest ...

Help please im struggling fighting demons rn

Answers

It’s up then to the left

Solve for m.

35m>−30


a. m>−50

b. m<−50

c. m>−18

d. m<−18

Answers

Answer:

A.

m>-50

i asked for all the quizzes answers on my questions and i will tell you!

Step-by-step explanation:

k12

Answer:

m<-50

Step-by-step explanation:

Calculate the perimeter of a square with a side length of 3ft

Answers

The perimeter of a square is the length of one side multiplied by 4 ( the number of sides)

3 ft x 4 sides = 12 ft.

Perimeter = 12 ft.

geomtry plz help me 15 pointz

Answers

Answer:

m∠R=76°

Step-by-step explanation:

∠STR=∠RST=(2x+2)° (base angles of isos triangle)

2(2x+2)+(3x+1)=180 (angle sum of triangle)

      4x+4+3x+1=180

               7x+5=180

                    7x=180-5

                        =175

                      x=175÷7

                        =25

Hence, m∠R = (3x+1)°

                     = [3(25)+1]°

                     = (75+1)°

                     = 76°

Answer:

m∠R=76º

Step-by-step explanation:

All angles in a triangle add up to 180º.

The triangle given is an isosceles triangle.

(2x+2)+(3x+1)+(2x+2)=180

Remove parentheses.

2x+2+3x+1+2x+2=180

Collect like terms.

7x+2+1+2=180

Add.

7x+5=180

Subtract 5 from both sides of the equation.

7x=175

Divide 7 from both sides of the equation.

x=25

m∠R=(3x+1)º

3x25+1=76º

m∠R=76º

Hope this helps :)

how is 7 square root 2 is equal to 49?

Answers

Answer:

Square root is how many times your multiply the number by itself. So 7 square root 2 is 7x7 which is 49.

What's the kinetic energy of an object that has a mass of 12 kilograms and moves with a velocity of 10 m/s?

Answers

Answer:

Step-by-step explanation:

Assuming it has no spin

KE = ½mv²

KE = ½(12)10²

KE = 600 J

Where , the distance between the points ( a, c) and ( b, c) is ( ) units

Answers

Answer:

I would love to help but there is no upload. Would you mind creating a new question with a picture or data of the graph

Step-by-step explanation:

Write the ratio as a ratio of whole numbers using fractional notation.
39 days to 15 days

Answers

Solution:

[tex] \frac{39 \: \: days}{15 \: \: days} \\ = \frac{39}{15} \\ dividing \: \: \: both \: \: \: numerator \: \: \: and \: denominator \: \: \: by \: \: \: 3 \\ = \frac{13}{5} \\ = 13 : 5[/tex]

Answer:

13:5

Hope it helps.

Do comment if you have any query.

PLZ HELP ASAP IS FOR IMPORTANT ASSIGNMENT Find the function that represents the relationship shown in the
table below and explain how you determined the equation by
showing your solution and adding statements to explain your
steps.
X
0
1
2
3
4
ON
у
-5
9
16
23
N
Edit
View
Insert
Format
Tools
Table

Answers

Answer:

Step-by-step explanation:

Choose the correct answer to 97 ÷ 4.
24 R1
24
23 R5
24 R3

Answers

Answer:

24 R1

Step-by-step explanation:

   

24R1 is the answer. H

Mr. Morton sold
bird houses to stores he started the week with 60 he sold 10 to one store and divided the rest between five other stores how many bird houses he’s so to each of the other five stores

Answers

Answer:

10

Step-by-step explanation:

Classify: −4m+21(m−1)≤15m+2(m−1).

Answers

Answer:

[tex]\boxed{\sf All\: real\: numbers}[/tex]

Step-by-step explanation:

[tex]\star \:\sf Classify\: -4m+21\left(m-1\right)\le \:15m+2\left(m-1\right)\: \star[/tex]

Apply Distribution law:

[tex]\sf -4m+21m-21\le \:15m+2\left(m-1\right)[/tex]

Combine like terms:

** [tex]\sf \hookrightarrow -4m+21m=17m[/tex]

[tex]\longmapsto\sf 17m-21\le \:15m+2\left(m-1\right)[/tex]

[tex]\sf 2(m-1)[/tex]

[tex]\hookrightarrow 2m-2[/tex]

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

[tex]\longmapsto\sf 17m-21\le \:15m+2m-2[/tex]

Combine like terms:

** [tex]\sf 15m+2m=17m[/tex]

[tex]\longmapsto\sf 17m-21\le \:17m-2[/tex]

Add 21 from both sides:

[tex]\longmapsto\sf 17m-21+21\le \:17m-2+21[/tex]

[tex]\longmapsto\sf 17m\le \:17m+19[/tex]

Subtract 17m from both sides:

[tex]\longmapsto\sf 17m-17m\le \:17m+19-17m[/tex]

[tex]\longmapsto\sf 0\le \:19[/tex]

Therefore, the solution of the inequality: All real numbers

_____________________________________________

find four rational numbers between -5 and 8​

Answers

Answer:

4.3, 4,5, 5.4, and 5.5

Step-by-step explanation:

A man walks for 2 hours at a certain speed. He then cycles at three times that speed for 4 hours. He goes 77 km altogether. Find the speed at which he walks.

Answers

The speed at which he walks is 7.7km/hr

The formula for calculating the distance is expressed as;

distance = speed * time

Let the speed moved by the man be x

If the  man walks for 2 hours at a certain speed, his distance will be 2x km

If he then cycles at three times that speed for 4 hours, the new the speed at which he walks is 7.7km/hr

If he goes 77km altogether, hence;

2x + 4(2x) = 77

2x + 8x = 77

10x = 77

x = 77/10

x =7.7km/hr

Hence the speed at which he walks is 7.7km/hr

Learn more here: https://brainly.com/question/13262646

can someone pls help me … I really need help

Answers

Answer:

It's the last one!

Step-by-step explanation:

Natalie completed 56 sit-ups. Natalie completed 4 times as many sit-ups as Matthew.

How many sit-ups did Matthew complete?

Answers

Mathew completed 14 sit-ups.

find the zscore which the area to the left is 0.46

Answers

Answer:

  Z ≈ -0.100

Step-by-step explanation:

A suitable calculator, spreadsheet, or table of the normal distribution can tell you the answer. Attached in the result using a spreadsheet. The function arguments are (area, mean, standard-deviation).

  Z ≈ -0.100

find an equation for the line below

Answers

Answer:

y = 1/3 x + 14/3

Step-by-step explanation:

We can identify the two points shown easily.

They are (-2, 4) and (4, 6).

First, we find the line of the slope of the line that contains those two points.

slope = m = (y2 - y1)/(x2 - x1) = (6 - 4)/[4 - (-2)] = 2/6 = 1/3

Now we use one point and the slope to find the y-intercept.

y = mx + b

Let's use point (4, 6) and the slope, 1/3.

6 = (1/3)(4) + b

18/3 = 4/3 + b

b = 18/3 - 4/3

b = 14/3

The equation is

y = mx + b

y = 1/3 x + 14/3

3.) Write the equation of a quadratic function that is shifted down 4 and horizontally compressed by 1/5

Answers

Answer:

[tex]5x^2 - 4[/tex]

Step-by-step explanation:

For shifted down a function you have to follow the next structured:

[tex]f(x) - c[/tex]

In our case is:

[tex]x^2 - 4[/tex]

Now for compressed or shrink a graph you have to multiply by a factor in the input something like this:

[tex]f(cx)[/tex]

In our case is:

[tex]5x^2[/tex]

Maybe you can think, why 5 and not [tex]\frac{1}{5}[/tex] instead?. Well, when you multiply by [tex]\frac{1}{5}[/tex] this dilate or stretch the graft because the output of each value is smaller, example:

[tex]f(x) = x^2\\g(x) = \frac{1}{5} x^2[/tex]

Then evaluate for a number, for example 5:

[tex]f(5) = 25\\g(5) = 5[/tex]

the output of [tex]g(x)[/tex] is 5 steps a far from the answer of [tex]f(x)[/tex] this in a graph is illustrate as a stretching.

So the opposite happen when you multiply by a integer number, the graph is compressed because the output take the "faster steps".

So combine the two transformation and get [tex]5x^2 - 4[/tex]

consider the system of equations. which shows an equivalent system of equations?
see attatched

Answers

Answer:

A.

Step-by-step explanation:

All choices show the first original equation.

Each choice shows a different second equation.

Take the second original equation:

6x + 5y = 30

Multiply both sides by -5.

-30x - 25y = -150

Answer: A.

Suppose that you take 1000 simple random samples from a population and that, for each sample, you obtain a 95% confidence interval for an unknown parameter. Approximately how many of those confidence intervals will contain the value of the unknown parameter?

Answers

Using the interpretation of a confidence interval, it is found that approximately 950 of those confidence intervals will contain the value of the unknown parameter.

A x% confidence interval means that we are x% confident that the population mean is in the interval.

Out of a large number of intervals, approximately x% will contain the value of the unknown parameter.

In this problem:

95% confidence interval.1000 samples.

0.95 x 1000 = 950

Hence, approximately 950 of those confidence intervals will contain the value of the unknown parameter.

A similar problem is given at https://brainly.com/question/24303674

Abigail earned $10.26 for babysitting her cousin for 3 hours. How much did she earn in each hour?

Answers

Divide total earned by number of hours:

10.26/3 = $3.42

She earned $3.42 per hour

Each hour she earns $3.42

Which expression is equivalent to 3.5 B +4.5+0.5 B -0.5-1.5 B?

Answers

Answer:

+4.5B+0.5B-1.5B+0.5‐0.5+0.5

Solve for x in terms of y if 3x - 5 = y.

Answers

Answer:

5/3

Step-by-step explanation:

y= 3x - 5

Replace y with 0

0 = 3x -5

Rewrite the equation as

3x−5=0

Add 5 to both sides of the equation.

3x=5

Divide each term by 3 and simplify.

x = 5/3

Hope this helped :)

pls help i’ll mark brainliest!!
Interpret the slope of the function in the terms of the problem.
25 ml of water are lost every hour
5 ml of water are lost every hour
10 ml wat are lost every hour
2mL of water are lost

Answers

2 ML lost every hour that’s what I think

What equation represents this graph?

Answers

it should be d. y=2/3x+2
The answer is d. y=2/3x+2

Suppose y varies directly with x. If y=16 when x= 8, find x when y=10

Answers

Answer:

5

Step-by-step explanation:

By question,

=> y = kx

When y = 16 , x = 8

=> 16 = x(8)

=> x = 2

When y = 10 ,

=> 10 = 2x

=> x = 5

Answer:

5

it is the correct answer

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