What are the solutions of the equation (x + 2)^2+ 12(x + 2)-14=0? Use u substitution and the quadratic formula to solve

Answers

Answer 1

Answer:

Step-by-step explanation:

Obviously, we are letting u = x + 2. So what we have when we rewrite using this substitution is

[tex]u^2+12u-14=0[/tex] and we plug that into the quadratic formula with

a = 1, b = 12, c = -14:

[tex]u=\frac{-12+-\sqrt{12^2-4(1)(-14)} }{2(1)}[/tex] which can be simplified to

[tex]u=\frac{-12+-\sqrt{144+56} }{2}[/tex] and a bit more to

[tex]u=\frac{-12+-\sqrt{200} }{2}[/tex] and a tiny bit more to

[tex]u=\frac{-12+-10\sqrt{2} }{2}[/tex] and finally to

[tex]u=-6+-5\sqrt{2}[/tex] and plug back in for u:

x + 2 = -6 ± 5√2 and then subtract the 2 to get

x = -8 ± 5√2


Related Questions

Select the correct answer.

For which system of inequalities is (3,-7) a solution?

A.
x + y < -4
3x + 2y < -5
B.
x + y ≤ -4
3x + 2y < -5
C.
x + y < -4
3x + 2y ≤ -5
D.
x + y ≤ -4
3x + 2y ≤ -5

Answers

Answer:

D

Step-by-step explanation:

3 - 7 = -4 and 3(3) + 2(-7) = -5, so D is the only choice that is correct for both inequalities.

please put the math too I really need it ;)

Answers

Answer:1) 32.  2).  3) 21.  4) 4

Step-by-step explanation: 1) 4*8=32m, 2) I don't know, 3) 6*7=42 for the area of a square but since a triangle half it so its 21, An the last is by 4 for example 4*10=40 but if doubled its 20*8 and that equals 160. and 160/40=4

b) Show that the points (1,1), (-1,-1) and ( -root3, root 3 ) are the vertices of an equilateral triangle.

Answers

Given:

The vertices of a triangle are [tex](1,1),(-1,-1),(-\sqrt{3},\sqrt{3})[/tex].

To prove:

The given vertices are the vertices of an equilateral triangle.

Solution:

Distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Let the vertices of the triangle are [tex]A(1,1),B(-1,-1),C(-\sqrt{3},\sqrt{3})[/tex]. Then, by using the distance formula, we get

[tex]AB=\sqrt{(-1-1)^2+(-1-1)^2}[/tex]

[tex]AB=\sqrt{(-2)^2+(-2)^2}[/tex]

[tex]AB=\sqrt{4+4}[/tex]

[tex]AB=\sqrt{8}[/tex]

Similarly,

[tex]BC=\sqrt{(-\sqrt{3}-(-1))^2+(\sqrt{3}-(-1))^2}[/tex]

[tex]BC=\sqrt{(1-\sqrt{3})^2+(1+\sqrt{3})^2}[/tex]

[tex]BC=\sqrt{(1)^2+(\sqrt{3})^2-2\sqrt{3}+(1)^2+(\sqrt{3})^2+2\sqrt{3}}[/tex]

[tex]BC=\sqrt{1+3+1+3}[/tex]

[tex]BC=\sqrt{8}[/tex]

And,

[tex]CA=\sqrt{(1-(-\sqrt{3}))^2+(1-\sqrt{3})^2}[/tex]

[tex]CA=\sqrt{(1+\sqrt{3}))^2+(1-\sqrt{3})^2}[/tex]

[tex]CA=\sqrt{(1)^2+(\sqrt{3})^2+2\sqrt{3}+(1)^2+(\sqrt{3})^2-2\sqrt{3}}[/tex]

[tex]CA=\sqrt{1+3+1+3}[/tex]

[tex]CA=\sqrt{8}[/tex]

Clearly, [tex]AB=BC=CA[/tex].

Since all sides of the given triangle are equal, therefore the given vertices are the vertices of an equilateral triangle.

Hence proved.

Which equation is a function of x?

Answers

Answer:

X=5

x=y2+9

x2=y

x2=y2+16

Step-by-step explanation:

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

A(n) ______________ is the act of uniformly turning in a clockwise or counter-clockwise direction around a center point.

Answer Choices:

Dilation

Translation

Reflection

Rotation

Answers

The answer is rotation
Rotation because you can rotate counter clockwise and clockwise. It can’t be reflection because it going to make another one similar.

CAN SOMEONE HELP THANKS 14 POINTS

Answers

Answer:

6,9,12

Step-by-step explanation:

A triangle cannot be considered a triangle unless the sum of the smaller two of the sides is greater than the larger side.

Answer:

(6, 9, 12)

Hope that this helps!

[tex]x^{2} +2000+15637=56 \\\\what is X\\\\PLEASE HELP[/tex]

Answers

Answer:

not defined

Step-by-step explanation:

[tex] {x}^{2} = 56 - 2000 - 15637 \\ {x}^{2} = - 1758[/tex]

Find the surface area and the volume of the composite figure

Answers

Answer:

See below

Step-by-step explanation:

Surface area of the figure:

S = 2(lw + lh + wh) + 1/2(4πr²) - πr² = 2(lw + lh + wh)  + πr² S = 2(6*10 + 6*6 + 6*10) + 3.14*(6/2)² = 340.26 cm²

Volume of the figure:

V = lwh + 1/2(4/3πr³) =  lwh + 2/3πr³ V = 6*10*6 + 2/3*3.14*(6/2)³ = 416.52 cm³

Answer:

> S = 340.26 cm²

> V = 416.52 cm³

Step-by-step explanation:

We need to find the surface area and the volume of the composite figure . The given figure is made up of a cuboid and a hemisphere . Let's Calculate them ,

Finding the Surface area :-

> S = 2(6*10 + 6*6 + 6*10) + 3.14*(6/2)

> S = 340.26 cm²

Volume of the figure:

> V = lbh + 1/2(4/3πr³)

> V = 6*10*6 + 2/3*3.14*(6/2)³

> V = 416.52 cm³

PLZZZ HELP
Find the average rate of change of h(x) = 2x² – 7x from x=2 to x=5.
Simplify your answer as much as possible.

Answers

Answer:

The average rate of change of h(x) in the given interval is 7.

Step-by-step explanation:

When we want to find the average rate of change of a function f(x), in an interval a < x < b, we just need to calculate:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

Here we have:

h(x) = 2*x^2 - 7*x

And we want to find the average rate of change between x = 2 and x = 5

This will be:

[tex]r = \frac{h(5) - h(2)}{5 - 2} = \frac{(2*5^2 - 7*5) - ( 2*2^2 - 7*2)}{3} = \frac{15 - (-6)}{3} = \frac{21}{3} = 7[/tex]

The average rate of change of h(x) in the given interval is 7.

What is the image point of (0, 8) after a translation right units and down 5 units?

Answers

Answer:

(5,3)

Step-by-step explanation:

1. Translation 5 units right, so the x-coordinates goes to 5.

2. Translation 5 units under, so the y-coordinates goes to 3.

So . the answer is (5, 3)

Pls help no files just type it in thank you

Answers

Answer:

I believe the correct answer is 49.

Step-by-step explanation:

If this answer is incorrect let me know and I will fix it. I'm sorry in advance if it is wrong.

Answer:

42 crickets

Step-by-step explanation:

6 x 7= 42

Simón y Carlos tienen una pista de autos iguales, pero cada uno de ellos tiene dos autos que corren a distintas velocidades. De los autos de Simón uno le da una vuelta completa a la pista en 31 segundos y el segundo lo hace en 17 segundos. De los autos de Carlos uno da una vuelta completa en 36 segundos y el segundo en 42 segundos. Proponen una competencia en la que todos los autos salen al mismo tiempo de la meta y el ganador será el primero en el que sus dos autos lleguen al mismo tiempo, de nuevo a la meta. ¿Quién ganará?

Answers

Answer:

Carlos.

Step-by-step explanation:

Dado que Simón y Carlos tienen una pista de autos iguales, pero cada uno de ellos tiene dos autos que corren a distintas velocidades, y de los autos de Simón uno le da una vuelta completa a la pista en 31 segundos y el segundo lo hace en 17 segundos, mientras que de los autos de Carlos uno da una vuelta completa en 36 segundos y el segundo en 42 segundos, si ambos proponen una competencia en la que todos los autos salen al mismo tiempo de la meta y el ganador será el primero en el que sus dos autos lleguen al mismo tiempo, de nuevo a la meta, para determinar quién ganará se deben realizar los siguientes cálculos:

Simón: 527 SEGUNDOS

A: 31 + 62 + 93 + 124 + 155 + 186 + 217 + 248 + 279 + 310 + 341 + 372 + 403 + 434 + 465 + 496 + 527

B: 17 + 34 + 51 + 68 + 85 + 102 + 119 + 136 + 153 + 170 + 187 + 204 + 221 + 238 + 255 + 272 + 289 + 306 + 323 + 340 + 357 + 374 + 391 + 408 + 425 + 442 + 459 + 476 + 493 + 510 + 527

Carlos: 252 SEGUNDOS

A: 36 + 72 + 108 + 144 + 180 + 216 + 252

B: 42 + 84 + 126 + 168 + 210 + 252

Por lo tanto, el ganador será Carlos.

On a map of a town a school is located (-6, 3) and a movie theater is located (-6, -15) what is the distance from the school to the theater

Answers

Answer:The distance from the school to the theater = 18 units

Step-by-step explanation:

Distance between (a,b) and (c,d) = [tex]\sqrt{(d-b)^2+(c-a)^2}[/tex] units.

Given: On a map of a town a school is located (-6, 3) and a movie theater is located (-6, -15).

So, distance between (-6, 3) and(-6, -15) = [tex]\sqrt{(-6-(-6))^2+(-15-3)^2}[/tex]

[tex]=\sqrt{0^2+(-18)^2}\\\\=\sqrt{18^2}\\\\=18\ units[/tex]

Hence, the distance from the school to the theater = 18 units

Write an inequality to describe the relationship between -1 2/3 and-1/4

Answers

Step-by-step explanation:

- 1⅔ <

__________________

Identify each line or segment that intersects ⊙ T. HELP PLEASE!!!

Answers

Answer:

The 2 option :)

Step-by-step explanation:

The Chords : QL ,SM , Secant : NR , Tangents : a  and b , Diameter : QL, ,radii: PT , QT and TL therefore the Option A is the correct answer.

What is a Circle ?

A circle is a round shaped figure , whose all points are in the same plane and at same distance from a single point known as center.

A secant is a segment that passes through 2 points on a circle, It is an infinite extension of a chord.

A tangent touches a circle at exactly one point and never enters the interior of the circle.

A chord is a line segment which connects two point on the circle.

A diameter is a chord that passes through the center of the circleThe radius is half of the diameter of the circle

Based on the above definitions

Chords : QL ,SM

Secant : NR

Tangents : a  and b

Diameter : QL

radii: PT , QT and TL

To know more about Circle

https://brainly.com/question/11833983

#SPJ2

For EASY BRAINLIEST!!!

Answer:
A.
B.
C.
D.

On both questions

Answers

Answer:

8a) 3x

8b) 3 × x

8c) (2/3)x

8d) x/2

8e) 1/x

9a) 4x - 7

9b) x + 1/x

9c) 5(x + 2)

9d) x/(x + 4)

9e) (x/8) + x

2 1 -5 4 3 2 -11 2 4 5 X -2 ب ا -5 a Write down the gradient of the graph.​

Answers

Answer:

Gradient = -3

Step-by-step explanation:

The gradient of the graph = change in y/change in x

Change in y = the vertical distance = 3 units

Change in x = the run/horizontal distance = 1 unit

The line slopes downward, so it's a negative gradient.

Thus:

Gradient = 3/1 = -3

Find RS. See image below

Answers

Step-by-step explanation:

since both cords are equal, so are arc length

4x + 18 = 7x - 51

3x - 21 = 0

x = 7

arc RS = 4(7) + 18

A system of equations has 1 solution. If 4x – y = 5 is one of the equations, which could be the other equation?

A- y = –4x + 5
B- y = 4x – 5
C- 2y = 8x – 10
D- –2y = –8x – 10

Answers

Answer:

D: 2y = 8x - 10  

Step-by-step explanation:

A:  y = 4x + 5. This has a slope of -4 Yes it could work.

B:  y = 4x - 5. No It does not work

C: 2y = 8x - 10. The slope is 8/2 = 4. So No it could not work.

D: -2y = 8x - 10. The slope is 8/-2 = -4. Yes This Does work!  :)

Q.No.1: A subset of {1,7,8 } is:

Answers

Step-by-step explanation:

you only need to provide an example ?

if your question here is complete, then the full set is

{1,7,8}

and these are all possible subsets (pick any one you like) :

{1}, {7}, {8}, {1,7}, {1,8}, {7,8}

and formally also

{}, {1,7,8}

the empty set is a subset of every set, and the whole set itself is also formally a subset.

Abel has a piece of string that is 7/10 of a meter long. He cuts off 1/2 of a meter of string. How many meters of string does Abel have now?

Answers

Answer:

1/5

Step-by-step explanation:

7/10-1/2=1/5

hope it helps:)))

which linear inequality is represented by the graph

Answers

Answer:

Step-by-step explanation:

In ΔLMN, MN = 15, NL = 20, and LM = 6. Which list has the angles of ΔLMN in order from smallest to largest?

Answers

Answer:

m<N, m<L, m<M

Step-by-step explanation:

The angle that sees the longest side length has the bigger angle measurement

so the angles would be listed as following :

from smallest to largest :

m<N, m<L, m<M

pls answer
. its urgent pls
an

Answers

Answer:

a

Step-by-step explanation:

Answer:

option c

Step-by-step explanation:

[tex]\frac{-4}{3} * y = \frac{-3}{4}[/tex]

shift -4/3 to the right hand side . when it shifts to other side miltiplication changes to division

y = [tex]\frac{-3}{4} /\frac{-4}{3}[/tex]

now do reciprocal

y = [tex]\frac{-3}{4} *\frac{3}{-4}[/tex]

y = [tex]\frac{-9}{-16}[/tex]

minus and minus gets cancel

y = [tex]\frac{9}{16}[/tex]

y = [tex]\frac{(3)^2}{(4)^2}[/tex]

y = [tex](\frac{3}{4})^2[/tex]

Find the volume of this cylinder.
_____ cubic inches​

Answers

Answer:

2355in³

Step-by-step explanation:

3.14(5)²×30=2355 in³

Answer:

Answer:94.2

Answer:94.2Step-by-step explanation:

Answer:94.2Step-by-step explanation:3.14(5)²×30

Answer:94.2Step-by-step explanation:3.14(5)²×303.14×25×30

Answer:94.2Step-by-step explanation:3.14(5)²×303.14×25×303.14×5×6

= 94.2

i am sorry if it is not correct

(PLEASE HELP)
Find measurement for angles for 1 and 2

Answers

Answer:

Angle 1 is = 54° ( vertically opposite angles)

Angle 2 is = Angle 1 (corresponding angles are equal)

therefore Angle 2 = 54°

Someone Helppp me please

Answers

Answer:

Step-by-step explanation:

diameter = 3.7

radius = diameter/2

=3.7/2

=1.85

area of circle = πr^2

=π*(1.85)^2

=3.4225π m^2

Evaluate 13 - 0.75w+8x when w=12 and x= 1 over 2

Answers

Answer:

8

Step-by-step explanation:

Given:

13 - 0.75w + 8x

where,

w = 12

x = 1/2

13 - 0.75w + 8x

Substitute the value of w and x into the equation

= 13 - 0.75(12) + 8(1/2)

= 13 - 9 + 8/2

= 13 - 9 + 4

= 8

Therefore,

13 - 0.75w + 8x = 8

please help me with this :)

Answers

Answer: 103 degrees

Step-by-step explanation: all angle of a regular triangle always add up to 180. so 62+15=77. and 180 - 77= 103

Answer:

A. 103 degrees

Step-by-step explanation:

In a triangle, the sum of angle measures is equal to 180 degrees, so by adding 62 & 15, & subtracting it from 180 you get the third angle measure of 103.

Which statement about the equation 3x ^ 2 + 9x - 12 = 0 is true ? 1 . The product of the roots is -12 . 2 The product of the roots is -4 . 3 The sum of the roots is 3 . The sum of the roots is -9 .

Answers

Answer:

Option : The product of the roots is - 4

Step-by-step explanation:

[tex]3x^2 + 9x - 12 = 0\\\\3x^2 + 12x - 3x - 12 = 0\\\\3x(x+4) -3(x+4) = 0\\\\(3x - 3) (x+ 4) = 0\\\\[/tex]

Therefore the roots are -4 and 1

The product of the roots are -4 x 1 = -4

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