what is the correct factorization of x^2 - 2x - 15?

Answer:

Step-by-step explanation: Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2".

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

p*(x)-((2*x^2-9*x+7)*(x-2))=0

STEP

1

:

Equation at the end of step 1

px - (((2x2 - 9x) + 7) • (x - 2)) = 0

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring 2x2-9x+7

The first term is, 2x2 its coefficient is 2 .

The middle term is, -9x its coefficient is -9 .

The last term, "the constant", is +7

Step-1 : Multiply the coefficient of the first term by the constant 2 • 7 = 14

Step-2 : Find two factors of 14 whose sum equals the coefficient of the middle term, which is -9 .

-14 + -1 = -15

-7 + -2 = -9 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and -2

2x2 - 7x - 2x - 7

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (2x-7)

Add up the last 2 terms, pulling out common factors :

1 • (2x-7)

Step-5 : Add up the four terms of step 4 :

(x-1) • (2x-7)

Which is the desired factorization

Equation at the end of step

2

:

px - (2x - 7) • (x - 1) • (x - 2) = 0

STEP

3

:

Equation at the end of step 3

px - 2x3 + 13x2 - 25x + 14 = 0

STEP

4

:

Solving a Single Variable Equation:

4.1 Solve px-2x3+13x2-25x+14 = 0

In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.

We shall not handle this type of equations at this time.

Supplement : Solving Quadratic Equation Directly

Solving 2x2-9x+7 = 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:

5.1 Find the Vertex of y = 2x2-9x+7

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, 2 , 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 2.2500

Plugging into the parabola formula 2.2500 for x we can calculate the y -coordinate :

y = 2.0 * 2.25 * 2.25 - 9.0 * 2.25 + 7.0

or y = -3.125

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = 2x2-9x+7

Axis of Symmetry (dashed) {x}={ 2.25}

Vertex at {x,y} = { 2.25,-3.12}

x -Intercepts (Roots) :

Root 1 at {x,y} = { 1.00, 0.00}

Root 2 at {x,y} = { 3.50, 0.00}

3 Solving 2x2-9x+7 = 0 by the Quadratic Formula .

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC

x = ————————

2A

In our case, A = 2

B = -9

C = 7

Accordingly, B2 - 4AC =

81 - 56 =

25

Applying the quadratic formula :

9 ± √ 25

x = —————

4

Can √ 25 be simplified ?

Yes! The prime factorization of 25 is

5•5

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 25 = √ 5•5 =

± 5 • √ 1 =

± 5

So now we are looking at:

x = ( 9 ± 5) / 4

Two real solutions:

x =(9+√25)/4=(9+5)/4= 3.500

or:

x =(9-√25)/4=(9-5)/4= 1.000

Answer:

Dilation

Step-by-step explanation:

Given

Main function: f(x)

Resulting function: 5f(x)

Required

Which transformation exists between both functions

The general explanation is that:

When a function f(x) is multiplied by a constant k, the resulting function g(x) is a dilation of f(x).

Mathematically, if the following relationship exists between f(x) and g(x)

g(x) = k.f(x)

Then g(x) is a dilation of f(x) and k is the constant of proportionality or dilation ratio

In this case:

g(x) = 5f(x)

So, the transformation that answers the question is dilation.

Answer: vertical | stretch | left

Step-by-step explanation:

Answer:

13). y = x² + 6x + 8

14). y = 2x² + 8x - 12  

Step-by-step explanation:

13). Vertex form of a parabola is given by,

     y = a(x - h)² + k

     Here (h, k) is the vertex of the parabola.

     Equation of a parabola with vertex (-3, -1) will be,

     y = a(x + 3)² - 1

     Since, y-intercept of the parabola is y = 8

     In other words, parabola is passing through (0, 8)

     8 = a(0 + 3)² - 1

     8 = 9a - 1

     9a = 9

     a = 1

    Therefore, equation of the parabola will be,

    y = (x + 3)² - 1

    y = x² + 6x + 9 - 1

    y = x² + 6x + 8

14). Equation of a parabola with vertex (-2, -20)

     y = a(x + 2)² - 20

     Since, y-intercept of the parabola is (0, -12),

    -12 = a(0 + 2)² - 20

    -12 + 20 = 4a

     4a = 8

     a = 2

    Therefore, equation of the parabola will be,

     y = 2(x + 2)² - 20

     y = 2(x² + 4x + 4) - 20

     y = 2x² + 8x + 8 - 20

     y = 2x² + 8x - 12  

There is no image posted though?

Answer: there is no image though

Step-by-step explanation:

Answer:

the domain is that x is a set of real numbers.

the range is y ≤ -3

Step-by-step explanation:

y = -|x + 3|

y is either positive or equal to zero.

Now, x is all real numbers because any value of x used will yield a valid value of y.

Thus, we can say that the domain is that x is a set of real numbers.

Now, for the range:

The minus sign in front of the absolute value indicates that the function has a maximum value.

Thus, the range is y ≤ -3

I think it is the first one

Answer:

Keep it simple: part one. D, part two. C

Step-by-step explanation:

Answer:pop

Step-by-step explanation:

Answer:

14:28

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Because 5/8×18 is 11 1/4

Answer:

what he said

Step-by-step explanation:

Answer:

you need to show or tell us the problem for us to be able to help you

Step-by-step explanation:

:/

Answer:

um

Step-by-step explanation:

can u show us the question bc we can't help if there's no question

Answer:

A sandwich costs $6

Answer:

0.2 +-4

Step-by-step explanation:

The required probability is 0.8826 that the number x of correct answers is fewer than 4.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

There are n equals 6 ​trials, each with a probability of success​ (correct) given by p equals 0.2.

This is a direct application of Binomial distribution with sample size (n) = 6 and P(success) = p = 0.35

Let X be a Binomial random variable.

X ~ Binomial (n = 6, p = 0.35)

We have to determine, P(X < 4)

Using Excel we discover this probability,

⇒ P(X < 4) = P(X ≤ 3) = BINOMDIST (3, 6, 0.35, 1) = 0.8826

⇒ P(X < 4) = 0.8826

Therefore, the required probability is 0.8826

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Answer:107.2

Step-by-step explanation:

Answer:

107.2

Step-by-step explanation:

6 x 16 = 96

.7 x 16 = 11.2

add them to get 107.2

Answer:

B

Step-by-step explanation:

600+125+175=900-400(deposit)=500

or

600-125-175-300-200=100+400=500

Brainliest Please :)

Answer:

20

Step-by-step explanation:

Given that the HCF of two numbers is 20 and the LCM of both numbers is a multiple of 14.

So, the LCM of both numbers = 14n where n can be any natural number.

As HCF of two numbers is always smaller than or equal to the smallest number among both the numbers.

Here, the HCF of two numbers is 20, so the smallest number is greater than of equal to 20.

Hence, the smallest possible number is 20.

Answer:I would believe it's the first choice. I'm not great with the inequalities though so it could be wrong. If you work 29 hours making $9.50, you make like $275 or something so it is greater than the $269.60 you need. :D

Answer:

nikki should quit her job

Answer:

The point (5, -8) is not in the solution area

Step-by-step explanation:

Answer:

The amount that would be in the account after 30 years is $368,353

Step-by-step explanation:

Here, we want to calculate the amount that will be present in the account after 30 years if the interest is compounded yearly

We proceed to use the formula below;

A = [P(1 + r)^t-1]/r

From the question;

P is the amount deposited yearly which is $4,500

r is the interest rate = 2.5% = 2.5/100 = 0.025

t is the number of years which is 30

Substituting these values into the equation, we have;

A = [4500(1 + 0.025)^30-1]/0.025

A = [4500(1.025)^29]/0.025

A = 368,353.3309607034

To the nearest whole dollars, this is;

$368,353

Answer:

1. you dont add before you multiply

2 they didnt do the parenthesis first...which was their mistake

Step-by-step explanation:

Four inches every four and a half pounds

The average rate of change of the length of the spring as the load varies from 5 pounds to 9 pounds is 0.5 inches per pound.

It is a measure of how much the function changes per unit, on average, over the given interval.

We have,

5 pounds loaded on a spring:

The length of the spring is 6 inches.

9 pounds loaded on a spring:

The length of the spring is 8 inches.

The average rate of change in the length of the spring as the load varies:

= (8 - 6) / (9 - 5)

= 2 / 4

= 1 / 2

= 0.5 inches per pound

Thus the average rate of change of the length of the spring as the load varies from 5 pounds to 9 pounds is 0.5 inches per pound.

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The given expression is :

1:2=3:x

To find,

The value of x.

Solution,

The ratio of LHS is 1:2 or 1/2

It should be same as in RHS.

If x = 6,

Then the ratio becomes :

1:2 = 3:6

or

1:2 = 1:2

Hence, the value of x = 6.

Given:

Player 1 is at (-7,5).

Player 2 is at (7,5).

To find:

The relationship between the positions of the two players.

Solution:

The two points are (-7,5) and (7,5).

Here, x-coordinates are different but y-coordinates are same. The absolute values of x-coordinates are equal but the signs are different.

The transformation is defined as

[tex](x,y)\to (-x,y)[/tex]

It means, the points are mirror image of each other with respect to y-axis.

Player 1's position is Player 2's position reflected across the y-axis; only the signs of the x-coordinates of Player 1 and Player 2 are different.

Therefore, the correct option is C.

Answer:

The last answer D

Step-by-step explanation:

Hope this helps. :) :D

The equation 3y + 1 = 3y + 1 has all real numbers as solutions becasuse 0 = 0 true for all real numbers option (D) is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The first equation:

3y = 3y + 1

0 = 1 (false)

The second equation:

3y = 3

y = 1 (one real solution)

The third equation:

3y = 0

y = 0 (one real solution)

The fourth equation:

3y + 1 = 3y + 1

0 = 0 (infinitely solution)

Thus, the equation 3y + 1 = 3y + 1 has all real numbers as solutions becasuse 0 = 0 true for all real numbers option (D) is correct.

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The number of people in the 25th annual parade in the town, can be found to be 203 people

The number of people that attend the town parade, has been increasing by 5% each year since the first year. In that first annual parade, 60 people showed up.

The number of people in the 25th parade can be found by the formula:

= Number of people in first parade x ( 1  + growth rate) ^ number of years

= 60 x ( 1 + 5% ) ²⁵

= 60 x 3.3863549408993848167083336666837

= 203 people

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Answer:

-5k - 10

Step-by-step explanation:

-k + 2 (-2k - 5)

-k - 4k - 10

-5k - 10

Answer:

-K+2(-2K-5)

-K-2K-10

-3K=10

K= 10÷(-3)

K=-3.333333

Given:

The recursive formula of a geometric sequence is

[tex]a_n=a_{n-1}\cdot (\dfrac{1}{8})[/tex]

[tex]a_1=-3[/tex]

To find:

The explicit formula of the given geometric sequence.

Solution:

We know that, first term of geometric sequence is [tex]a_1=-3[/tex].

Recursive formula of a geometric sequence is

[tex]a_n=a_{n-1}\times r[/tex]      ...(i)

where, r is common ratio.

We have,

[tex]a_n=a_{n-1}\cdot (\dfrac{1}{8})[/tex]    ...(ii)

On comparing (i) and (ii), we get

[tex]r=\dfrac{1}{8}[/tex]

The explicit formula of a geometric sequence is

[tex]a_n=a_1r^{n-1}[/tex]

Putting [tex]a_1=-3[/tex] and [tex]r=\dfrac{1}{8}[/tex], we get

[tex]a_n=-3\left(\dfrac{1}{8}\right)^{n-1}[/tex]

Therefore, the correct option is D.

Answer:

x=10

Step-by-step explanation:

add al the numbers that are alike so xes with xes blah blah

17x+10=180

-10 both sides

17x=170

divide 17 both sides

check

5(10)=50-1=49

80+5=85

40+6=46

49+85+46=180