What is the result of x + 2x - 6 = 21?

Answer:

-2,7

Step-by-step explanation:

[tex]\huge\bold\red{Answer:-}[/tex]

Step by step solution :

STEP 1 : Trying to factor by splitting the middle term

1.1 Factoring x2+5x-14

The first term is, x2 its coefficient is 1 .

The middle term is, +5x its coefficient is 5 .

The last term, "the constant", is -14

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

Step-2 : Find two factors of -14 whose sum equals the coefficient of the middle term, which is 5 .

-14 + 1 = -13

-7 + 2 = -5

-2 + 7 = 5 That's it

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

x2 - 2x + 7x - 14

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

x • (x-2)

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

7 • (x-2)

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

(x+7) • (x-2)

Which is the desired factorization.

Equation at the end of step 1 :

(x + 7) • (x - 2) = 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+7 = 0

Subtract 7 from both sides of the equation :

x = -7

Solving a Single Variable Equation:

2.3 Solve : x-2 = 0

Add 2 to both sides of the equation :

x = 2

Supplement : Solving Quadratic Equation Directly

Solving x2+5x-14 = 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+5x-14

For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is -2.5000

Plugging into the parabola formula -2.5000 for x we can calculate the y -coordinate :

y = 1.0 * -2.50 * -2.50 + 5.0 * -2.50 - 14.0

or y = -20.250

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = x2+5x-14

Axis of Symmetry (dashed) {x}={-2.50}

Vertex at {x,y} = {-2.50,-20.25}

x -Intercepts (Roots) :

Root 1 at {x,y} = {-7.00, 0.00}

Root 2 at {x,y} = { 2.00, 0.00}

Solve Quadratic Equation by Completing The Square

3.2 Solving x2+5x-14 = 0 by Completing The Square .

Add 14 to both side of the equation :

x2+5x = 14

Now the clever bit: Take the coefficient of x , which is 5 , divide by two, giving 5/2 , and finally square it giving 25/4

Add 25/4 to both sides of the equation :

On the right hand side we have :

14 + 25/4 or, (14/1)+(25/4)

The common denominator of the two fractions is 4 Adding (56/4)+(25/4) gives 81/4

So adding to both sides we finally get :

x2+5x+(25/4) = 81/4

Adding 25/4 has completed the left hand side into a perfect square :

= x2+5x+(25/4)

= (x+(5/2)) • (x+(5/2))

= (x+(5/2))2

Things which are equal to the same thing are also equal to one another. Since

x2+5x+(25/4) = 81/4 and

x2+5x+(25/4) = (x+(5/2))2

then, according to the law of transitivity,

(x+(5/2))2 = 81/4

We'll refer to this Equation as Eq. #3.2.1

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

= (x+(5/2))2 is

= (x+(5/2))2/2

= (x+(5/2))1

=x+(5/2)

Now, applying the Square Root Principle to Eq. #3.2.1 we get:

x+(5/2) = √ 81/4

Subtract 5/2 from both sides to obtain:

x = -5/2 + √ 81/4

Since a square root has two values, one positive and the other negative

x2 + 5x - 14 = 0

has two solutions:

x = -5/2 + √ 81/4

or

x = -5/2 - √ 81/4

Note that √ 81/4 can be written as

√ 81 / √ 4 which is 9 / 2

Solve Quadratic Equation using the Quadratic Formula

3.3 Solving x2+5x-14 = 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 = 1

B = 5

C = -14

Accordingly, = B2 - 4AC

=25 - (-56)

= 81

Applying the quadratic formula :

-5 ± √ 81

x = —————

2

Can √ 81 be simplified ?

Yes! The prime factorization of 81 is

3•3•3•3

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).

√ 81 = √ 3•3•3•3 =3•3•√ 1

= ± 9 • √ 1

= ± 9

So now we are looking at:

x = ( -5 ± 9) / 2

Two real solutions:

x =(-5+√81)/2=(-5+9)/2= 2.000

or:

x =(-5-√81)/2=(-5-9)/2= -7.000

Two solutions were found :

Answer:

well u should go to sleep and get u some rest

Answer:

Perpendicular

Step-by-step explanation:

Remember that:

So, let's find the slope of QR and ST.

QR)

We can use the slope formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Let Q(-6, 11) be (x₁, y₁) and R(2, -1) be (x₂, y₂). Substitute:

[tex]m=\frac{-1-11}{2-(-6)}[/tex]

Subtract:

[tex]m=-12/8=-3/2[/tex]

So, the slope of QR is -3/2.

ST)

Let S(-4, 8) be (x₁, y₁) and T(-1, 10) be (x₂, y₂). Substitute:

[tex]m=\frac{10-8}{-1-(-4)}[/tex]

Subtract:

[tex]m=2/3[/tex]

So, the slope of ST is 2/3.

The negative reciprocal of -3/2 is 2/3.

And the negative reciprocal of 2/3 is -3/2.

So, the slopes are indeed negative reciprocals of each other.

So, QR and ST are perpendicular.

Perpendicular     hope this helped

Answer:

The answer is True.

Step-by-step explanation:

-3x - 10 > -31

-3(5) - 10 > -31

-15 - 10 > -31

-25 > -31

True.

The number of rectangles in the paintings shown is: 7 rectangles.

A rectangle is a quadrilateral shape with four sides and four angles.

A rectangle has two opposite sides that are equal to each other and are parallel as well. Also, the interior angles formed by the sides are right angles.

Thus, from the paintings there are:

Therefore, the number of rectangles in the paintings shown is: 7 rectangles.

Learn more about rectangles on:

https://brainly.com/question/166401

Answer:

The integers are the whole numbers, both positive and negative. The next integer after 5 is 6, so there is no integer between them. Since 5 and 6 are consecutive numbers, it is not possible to squeeze another integer between them. So, the answer is none.

Step-by-step explanation:

please mark me brainliest

Hey there!

-5 between (-6)

= -5 - (-6)

= -5 + 6

= 1

Therefore, your answer is: 1

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

$17.54

Step-by-step explanation:

Given the following question:

25% of 70.16

To find the answer we simply use the formula to calculate percentages to find 25% of 70.16. Of course, round if needed.

[tex]\frac{p\times n}{100}[/tex]
[tex]\frac{25\times70.16}{100} =1754\div100=17.54[/tex]
[tex]=17.54[/tex]

The sleeping bags shipping, and handling will cost "$17.54."

Hope this helps.

well, the original price was "x", which oddly enough is the 100%, we also know that 25% off that is 30 bucks, so namely 100% - 25% = 75%, is 30 bucks, so

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 30&75 \end{array}\implies \cfrac{x}{30}=\cfrac{100}{75}\implies \cfrac{x}{30}=\cfrac{4}{3} \\\\\\ 3x=120\implies x=\cfrac{120}{3}\implies x=40[/tex]

Answer:

3

explanation:

[tex]\rightarrow \sf \sf \dfrac{36}{3a}[/tex]

[tex]\rightarrow \sf \sf \dfrac{36}{3(4)}[/tex]

[tex]\rightarrow \sf \sf \dfrac{36}{12}[/tex]

[tex]\rightarrow \sf \sf 3[/tex]

Answer:

C: (4,5)

Step-by-step explanation:

The solution is where the two lines intersect.

Answer:

g(x) = - 16x² + 100

Step-by-step explanation:

Given the model:

First drop:

h(x) = - 16x² + 4

Second drop hits the ground 2 seconds later

Function g(x) to model the second drop:

-16t² + V0t + h0

h(x) = - 16x² + 4

0 = - 16x² + 4

16x² = 4

x² = 4/16

x² = 1/4

x = 1/2

2 seconds later :

X = 1/2 + 2

x = 2.5

0 = - 16(2.5)² + 0 + h0

0 = - 100 + h0

h0 = 100

Hence,

g(x) = - 16x² + 100

Answer:

x=33/5

Step-by-step explanation:

Let's solve your equation step-by-step.

2x+4/5 −6=8

Step 1: Simplify both sides of the equation.

2x+4/5−6=8

2x+4/5+−6=8

(2x)+(4/5+−6)=8(Combine Like Terms)

2x+−26/5=8

2x+−26/5=8

Step 2: Add 26/5 to both sides.

2x+−26/5+26/5=8+26/5

2x=66/5

Step 3: Divide both sides by 2.

2x/2=66/5/2

x=33/5

Answer:

$ 8902.72

Step-by-step explanation:

We would like to calculate the money which we need to invest at 3.3% rate compounded annually for two years . We know that ,

[tex]\longrightarrow \boldsymbol{ A = P \bigg(1+\dfrac{R}{100}\bigg)^n } [/tex]

where the symbols have their usual meaning . So here ,

[tex]\longrightarrow \$ 9500 = P \bigg( 1+\dfrac{3.3}{100}\bigg)^2\\ [/tex]

Simplify RHS ,

[tex]\longrightarrow \$ 9500 = P \bigg(\dfrac{100+3.3}{100}\bigg)^2\\[/tex]

Simplify Nr . in RHS ,

[tex]\longrightarrow \$ 9500 =P\bigg(\dfrac{103.3}{100}\bigg)^2\\ [/tex]

Isolate P ,

[tex]\longrightarrow P = \dfrac{ \$9500\times 100\times 100}{103.3\times 103.3}\\[/tex]

Simplify ,

[tex]\longrightarrow \underline{\underline{\boldsymbol{ P = \$ 8902.72 }}}{} [/tex]

And we are done !

[tex]\bold{Formula: A = P(1 + \frac{r}{100})^{(n)}}[/tex]

Where

[tex] \bold{Solution : } \\ \\ \: \: \: \: \tt \: A = 9,500(1+\frac{3.3\%}{100})^{(2)} \\ \: \: \: \: \: \: \tt \: A = 9,500(1+ 0.033)^{(2)} \\ \tt \: A = 9,500(1.033)^{(2)} \: \: \\ \tt \: A = 10,137.34 \qquad \: \: \: [/tex]

therefore,I need $10,137.34 if would like to purchase the car.

Answer:

the answer is 4

Step-by-step explanation:

Answer:

13+5-14 is equaled to 4 so if i do 18-14 is will still give me 4 because 13+5 is 18 so 18- 14 is 4

Perimeter:

[tex]6y + 12[/tex]

Area:

[tex] {2y}^{2} + 12y[/tex]

Step-by-step explanation:

Perimeter of a rectangle : P= 2( L + w)

in this case it would be 2(y+6) + 2(2y)

= 2y+12 + 4y

simplified to 6y +12

Area of a rectangle : A= LW

=(y+6)(2y)

We foil and get

[tex] {2y}^{2} + 12y[/tex]

Answer:

The answer is A.

Step-by-step explanation:

3+6=9

-5-9=-14

-14/2

Hope this helps! :)

Answer:

Answer is A. -7

Step-by-step explanation:

-5-(3+6)/2. PEMDAS (Parenthesis)

-5-9/2 Add/Subtract & Slash and dash = -5 + -9 = -14

-14/7= -7/1 which is just -7

Answer:

$530

Step-by-step explanation:

6% of 500 is 30. Add 500 and 30.

Answer: 28 feet and 4.5 inches

8 meters = 26.24...

.650 meters = 25 inches.

25 inches = 2 feet 1 inch

28 and 4.5 inches is your answer.

Answer:

A: 2/3, B: 5, C: Yes because the slope is consistent.

Step-by-step explanation:

Answer:

a = 8/3b or b = 3/8a

Step-by-step explanation:

The fractions present in the table, 24/9 and 40/15, are equivalent to 8/3, showing a linear relationship between the variables a and b. Knowing this, reducing any of the 3 fractions to its lowest form will allow you to find the information necessary to develop an equation. As 8/3 turns out to be the simplest form of any of the fractions, the equation is a = 8/3b, or, if you decide to reverse the variables, b = 3/8a.

Using the slope concept, it is found that the medic was 370.5 ft from the shelter.

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

In this problem:

Hence:

[tex]\tan{65^\circ} = \frac{794.5]{d}[/tex]

[tex]d = \frac{794.5}{\tan{65^\circ}}[/tex]

[tex]d = 370.5[/tex]

The medic was 370.5 ft from the shelter.

More can be learned about the slope concept at https://brainly.com/question/18090623

Answer:

c, d, and h are parallel

Step-by-step explanation:

parallel lines are when the slope is the same and the y-intercept is different

a. y = 2x - 3

b. y = -3x + 7

c. y = -2x + 4

d. y = -2x + 2

e. y = 1/3x - 3

f. y = x/2 + 7/2

g. y = -x/3 + 8/3

h. y = -2x + 5

c, d, and h all have the same slope of -2 and contain different y-intercepts

Answer:

£ 45.6

Step-by-step explanation:

Number of adults ⇒ 12

Number of children ⇒ 26

Total cost of tickets ⇒ £ 1804.80

Cost of an adult's ticket ⇒ £ 51.60

Cost of a ticket for child ⇒ ?

Let the cost of a ticket for child be x.

Therefore,

Total cost = cost of tickets for adults + cost of tickets for children

Total cost = (No. children × Cost of a ticket) + (No.adults × Cost of a ticket)

£ 1804.80 = 26x + 12 × £51.60

1804.80  = 26x + 619.2

1804.80 - 619.2 = 26x

1185.6 = 26x

Divide both sides by 26.

45.6 = x

So,

Cost of a ticket for child is £45.6

Step-by-step explanation:

12 x 51.60 you get the total cost for the adult tickets and all thats left is the total cost - adult ticket cost and then you get the child ticket wirth now all thats left is childs ticket cost % 26

Answer:

x = 11

y = 17

Step-by-step explanation:

We know that opposite angles (or vertical angles) are equal.

So

8x + 7 = 9x - 4

Subtract 8x from both sides of the equation

8x - 8x + 7 = 9x - 8x - 4

7 = x - 4

Add 4 to both sides of the equation

7 + 4 = x - 4 + 4

11 = x

Looking at the other 2 angles,

5y = 7y - 34

Subtract 7 y from both sides of the equation

5y - 7y = 7y - 7y - 34

-2y = -34

Divide both sides by -2

-2y/-2 = -34/-2

y = 17

Answer:

Step-by-step explanation:

Vertically opposite angles are equal.

8x + 7     = 9x - 4          {Add 4 to both sides}

8x + 7 + 4 = 9x

    8x  + 11  = 9x           {Subtract 8x from both sides}

            11 = 9x - 8x

x = 11

7y - 34 = 5y        {Add 34 to both sides}

        7y = 5y + 34          {Subtract 5y form both sides}

  7y - 5y = 34

         2y = 34                {Divide both sides by 2

            y = 34/2

y =17

Answer:

im not sure but i could try and work it out

Given the number of firefighters and the average salary, the total salary altogehter is about $1.35 x 10^10

Scientific notation is used simplify large numbers into smaller numbers. In order to transform a number into a scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.

3 x 10^5 x 4.5^4 = 13.5 x 10^9

= 1.35 x 10^10

To learn more about scientific notation, please check: brainly.com/question/25334755

30% of the final exam

70% of final exam:-

Answer:

=12x+28

Step-by-step explanation:

Answer:

exact form:

x=±√5+1

decimal form:

x = 3.23606797..., -1.23606797...

Step-by-step explanation:

Use the formula (b/2)^2 in order to create a new term. Solve for x by using this term to complete the square. ---- :))

Answer:

x = √5 + 1, x = -√5 + 1

Step-by-step explanation:

We want the coefficient of x^2 to be 1, so let's divide either side by 3;

3x^2 - 6x - 12 = 0 => Divide either side by 3

3x^2/3 - 6x/3 - 12/3 = 0/3 => Simplify

x^2 - 2x - 4 = 0

Let's try to form a perfect square;

(x^2 - 2x + ? ) - 4 = 0

          |

         1/2(- 2) = (- 1)^2 = 1

(x^2 - 2x + 1) + 4 - 1 = 0

(x - 1)^2 - 5 = 0

(x - 1)^2 = 5

For x - 1 = √5 : x = √5 + 1

For x - 1 = - √5 : x = -√5 + 1

Answer:

y= - x + 4

Step-by-step explanation:

The point-slope form of the equation of a line is:

y= m ( x - h )+ k

Where m is the slope and (h,k) is a point through which the line passes.

The slope of the line is m=-1 and it passes through (-1,5), thus the equation of the line is:

y=(-1) ( x - (-1) ) + 5

Operating:

y= - ( x + 1 ) + 5

y= - x - 1 + 5

Simplifying:

y= - x + 4