When solving the equation x2 – 8x - 7 = ( by completing
the square, which equation is a step in the process?

Step-by-step explanation:

m(x) = x+3

y = x+3

=> x = y-3

m`¹(x) = x-3

Answer:

Option A

Step-by-step explanation:

[tex] \frac{12}{25} \times \frac{11}{24} \times \frac{10}{23} \times \frac{9}{22} [/tex]

we start with 12 red marbles out of 25 marbles, that's the probability for the first.

in the second step we have one red marble less, wich also means one marble less overall

and so on

[tex] \frac{12 \times 11 \times 10 \times 9}{25 \times 24 \times 23 \times 22} [/tex]

[tex] = \frac{11880}{303600} [/tex]

can be reduced by 1320 (step by step) to

[tex] \frac{9}{230} [/tex]

Answer:

A

Step-by-step explanation:

The slope is -1/2 and the y-intercept is 14

Given:

The expression is:

[tex]\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^7+4a^3b^4}{b^8-a^8}[/tex]

To find:

The simplified form of the given expression

Solution:

Formula used:

[tex]x^2-y^2=(x-y)(x+y)[/tex]

We have,

[tex]\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^7+4a^3b^4}{b^8-a^8}[/tex]

It can be written as:

[tex]=\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^3(a^4+b^4)}{(b^4)^2-(a^4)^2}[/tex]

[tex]=\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^3(a^4+b^4)}{(b^4-a^4)(b^4+a^4)}[/tex]

[tex]=\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^3}{(b^2-a^2)(b^2+a^2)}[/tex]

[tex]=\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^3}{(b-a)(b+a)(b^2+a^2)}[/tex]

Taking LCM, we get

[tex]=\dfrac{1(b-a)(b^2+a^2)+2a(b-a)(b+a)+4a^3}{(b-a)(b+a)(b^2+a^2)}[/tex]

[tex]=\dfrac{b^3+a^2b-ab^2-a^3+2a(b^2-a^2)+4a^3}{(b-a)(b+a)(b^2+a^2)}[/tex]

[tex]=\dfrac{b^3+a^2b-ab^2-a^3+2ab^2-2a^3+4a^3}{(b-a)(b+a)(b^2+a^2)}[/tex]

[tex]=\dfrac{b^3+a^2b+ab^2+a^3}{(b-a)(b+a)(b^2+a^2)}[/tex]

Using the grouping method factories the numerator.

[tex]=\dfrac{b(b^2+a^2)+a(b^2+a^2)}{(b-a)(b+a)(b^2+a^2)}[/tex]

[tex]=\dfrac{(b+a)(b^2+a^2)}{(b-a)(b+a)(b^2+a^2)}[/tex]

Cancel out the common factors.

[tex]=\dfrac{1}{b-a}[/tex]

Therefore, the value of the given expression is [tex]\dfrac{1}{b-a}[/tex].

Answer:

tienes que pensar

Step-by-step explanation:

put bralinyns

Answer:

Distance from point AA to point BB = 189.3 feet

Step-by-step explanation:

Let the distance from point AA to the base of the lighthouse be represented by x, and the distance from point BB to the base of the lighthouse be represented by y. So that;

distance from point AA to point BB = x - y

To determine the value of x, applying the required trigonometric function;

Tan θ = [tex]\frac{opposite}{sdjacent}[/tex]

Tan 13 = [tex]\frac{102}{x}[/tex]

x = [tex]\frac{102}{Tan 13}[/tex]

  = 441.81 feet

x = 441.8 feet

To determine the value of y;

Tan 22 = [tex]\frac{102}{y}[/tex]

y = [tex]\frac{102}{Tan 22}[/tex]

  = 252.46

y = 252.5 feet

Thus,

distance from point AA to point BB = 441.8 - 252.5

                                                           = 189.3 feet

Answer:

none

Step-by-step explanation:

No choice is correct.

The original expression has 560 x 70, the product of 560 and 70 inside the parentheses.

(560 x 70) ÷ 10 is 10 times smaller than 560 x 70

None of the choices show 560 x 70. They show 560 + 70 and 560 - 70.

Answer: none

Answer:

23.6 units

Step-by-step explanation:

If we have a circle of radius R, the perimeter of the arc is given by:

P = 2*pi*R

Now, if we only want to find the length of an arc defined by an angle "a", it will be:

L = (a/2*pi)*2*pi*R = a*R

In this case, we know that DA = 10, so we can think that this is a circle of radius R = 10 units

And for the arc DE, we have the angle:

a = 2.36 rad

replacing these two in the formula, we get:

L = 2.36*10 units = 23.6 units

Answer:

A. 112.5°C

Step-by-step explanation:

Use the inverse variation equation, y = [tex]\frac{k}{x}[/tex]

Replace y with T, and replace x with V:

T = [tex]\frac{k}{V}[/tex]

Plug in 90 as T and 25 as V, then solve for k:

T = [tex]\frac{k}{V}[/tex]

90 = [tex]\frac{k}{25}[/tex]

2250 = k

So, the equation is T = [tex]\frac{2250}{V}[/tex]

Plug in 20 as V and solve for T:

T = [tex]\frac{2250}{V}[/tex]

T = [tex]\frac{2250}{20}[/tex]

T = 112.5

So, the temperature will be A. 112.5°C

Answer:

[tex]a^3 + 1 = 0[/tex]

Step-by-step explanation:

We start with the equation:

[tex]a + \frac{1}{a} = 1[/tex]

We want to find the value of:

[tex]a^3 + 1 =[/tex]

We can start with our previous equation and multiply both sides by a:

[tex](a + \frac{1}{a})*a = 1*a\\a^2 + 1 = a[/tex]

Now we can rewrite our initial expression as:

[tex]a = 1 - \frac{1}{a}[/tex]

Replacing that in the right side, we get:

[tex]a^2 + 1 = a = 1 - \frac{1}{a}[/tex]

Now again, let's multiply both sides by a

[tex]a*(a^2 + 1) = a*(1 - \frac{1}{a} )\\a^3 + a = a - a/a\\a^3 + a = a - 1\\a^3 = -1\\a^3 + 1 = 0[/tex]

So we can conclude that:

[tex]a^3 + 1 = 0[/tex]

Answer:

again, barely readable.and you didn't provide the picture for this problem.

but if the are of the triangle if just half of the square, it's one of the options that got 1/2 in it as a fraction.

but if it's 1/2 * 2 * 2

or 1/2 * 4 * 4

really depends on the square. either the area of the square is 2*2 or 4*4, and the triangle is just half of it. at least that's most likely.

can't really tell what's going on here without the missing picture

Answer:

A.  fraction 1 over 2 ⋅ 4 ⋅ 4 or 1/2 ⋅ 4 ⋅ 4

Step-by-step explanation:

Hope I helped!!

Answer: its 180 , because it dont matter if its up or side .

Answer:

13°

Step-by-step explanation:

the lines are parallel so

82 + 85 = 167

167 - 180 = 13

x = 13°

Step-by-step explanation:

Hey there!

From the given figure;

An exterior angle is 127°.

To find: value of"X"

Now;

x+127° = 180°. [Being linear pair]

or, X = 180° - 127°

or, X = 53°

Therefore, the value of "X" is 53°.

Hope it helps!

Answer:

53°

Step-by-step explanation:

the extended line(the base and the line that extends past the triangle) is 180°. With an extended line that is 180°, the inside angle must be 180° - the outside angle, and the outside angle must be 180° - the inside angle. if the angle on the outside is 127°, then the inside angle(x) should be 180° - 127° or 53°.

to verify: all the inside angles must equal to 180°

the angle on the top is 90°( when there is that square thing on an angle it means it is 90°) and the angle on the right is 53°, so the remaining angle is 180 - (90° + 53°) or 37°.

90° + 53° + 37° = 180 °

Answer:

150.83 (cm²).

Step-by-step explanation:

1) the area of the bottom and top is: A₁=π*r²*2=2*3.1415*4≈25.13 (cm²);

2) the length of the circle in the bottom/top side is: l=2*π*r=2*3.1415*8≈12.57 (cm);

3) the area of the side surface of the cylinder is: A₂=l*h=12.57*10=125.7 (cm²);

4) the required area of the cylinder is:

A=A₁+A₂=25.13+125.7=150.83 (cm²).

Answer:

São todas planas.

Step-by-step explanation:

São todas planas.

Answer:

Hello,

Please, see the attached file.

Thanks.

Step-by-step explanation:

The remaining steps can be ∆ABC ∼ ∆DBA AA criterion for similarity Corresponding sides of similar triangles are proportional, AB/AC = AD/AB, and AB2 = AC × AD.

Triangles are closed two-dimensional geometric figures with three straight sides and three angles. The sum of the three angles in any triangle is always 180 degrees.

The first 10 steps to prove that AB2 + BC2 = AC2 are given in the table. The remaining steps to their correct sequence in the proof are:

These steps follow logically from the previous statements in the proof. In step 11, the Pythagorean Theorem is applied to the right triangle ADB.

Thus, this can be the match for the given scenario.

For more details regarding triangles, visit:

https://brainly.com/question/2773823

#SPJ7

Answer:7.25 feet

Step-by-step explanation:

6.25+6.5=12.75

20-12.75=7.25

Answer:

453.3203125

Step-by-step explanation:

I hope it's right just use it. If it's wrong, I'll try again.

Answers:

===========================================================

Explanation:

The tickmarks show that WZ and XY are the same length. The arrows show that WX is parallel to ZY. This is an isosceles trapezoid.

For any isosceles trapezoid like this, the diagonals are the same length. We can prove it using the SAS congruence theorem.

So,

WY = XZ

15x-2 = 9x+10

15x-9x = 10+2

6x = 12

x = 12/6

x = 2 .... first answer

Use that value of x to find the length of each diagonal.

Both diagonals are 28 units long, which helps confirm we have the right x value.

Answer:162 might be wrong tho so dont mark as brainlyest

Step-by-step explanation:

[tex]answer = 3 {x}^{2} {e}^{ {x}^{3} } [/tex]

Answer:

[tex] \displaystyle f'(x) = 3x^2 {e}^{ {x}^{3} } [/tex]

Step-by-step explanation:

we would like to figure out the first derivative of the following:

[tex] \displaystyle f(x) = {e}^{x ^{3} } [/tex]

to do so take derivative In both sides:

[tex] \displaystyle f'(x) = \frac{d}{dx} {e}^{x ^{3} } [/tex]

to differentiate the above we can consider composite function derivation given by

[tex] \rm\displaystyle \frac{d}{dx} f(g(x)) = \frac{d}{dx} f'(g(x)) \times \frac{d}{dx} g'(x)[/tex]

let

g(x)=u

so we obtain:

[tex] \displaystyle f'(x) = \frac{d}{dx} {e}^{u} \times \frac{d}{dx} u[/tex]

substitute back:

[tex] \displaystyle f'(x) = \frac{d}{dx} {e}^{ {x}^{3} } \times \frac{d}{dx} {x}^{3} [/tex]

by using derivation rule we acquire:

[tex] \displaystyle f'(x) = 3x^2 {e}^{ {x}^{3} } [/tex]

and we are done!

Answer: 40°

Step-by-step explanation: The formula for calculating the size of an exterior angle is: exterior angle of a polygon = 360 ÷ number of sides. So it's 360°÷9=40°

Answer:

hope it is helpful to you

Answer:

4(7a+3)

Step-by-step explanation:

28a+12

take common

4 is the common number for both the terms because it divides 28 and 12 exactly.

4(7a+3)

Answer:

Step-by-step explanation:

2.5

Answer:

x = 15 and y = 7

Step-by-step explanation:

x = 2y + 1

x + y - 8 = 14

Let's substitute the value of x in the second equation:

(2y + 1) + y - 8 = 14

3y -7 = 14

3y = 14 + 7

3y = 21

y = 21/3

y = 7

And now you substitute the value of y in the first equation:

x = 2•7 + 1

x = 14 + 1

x = 15

Answer:

[tex]\frac {x^{3}-4x^{2}-20x+32}{x^{3}+2x^{2}-4x-8}[/tex]

Step-by-step explanation:

make the denominator same

[tex]\frac{(x^{2}-4)(x-2)}{(x^{2}-4)(x+2) }-\frac{(2x+20)(x+2)}{(x^{2}-4)(x+2)}[/tex]

then expand

[tex]\frac {x^{3}-2x^{2}-4x+8}{x^{3}+2x^{2}-4x-8} - \frac {2x^{2}+24x+40}{x^{3}+2x^{2}-4x-8}[/tex]

join

[tex]\frac {x^{3}-4x^{2}-20x+32}{x^{3}+2x^{2}-4x-8}[/tex]

i think but not sure

Answer:

[tex] \frac{x - 2}{x + 2} - \frac{2x + 20}{ {x}^{2} - {2}^{2} } \\ \frac{x - 2}{x + 2} - \frac{2x + 20}{(x + 2)(x - 2)} \\ = \frac{ {(x - 2)}^{2} - (2x + 20)}{(x + 2)(x - 2)} \\ = \frac{ {x}^{2} - 4x + 4 - 2x - 20 }{(x - 2)(x + 2)} \\ = \frac{ {x}^{2} - 6x - 16 }{(x2)(x + 2)} \\ = \frac{(x - 8)(x + 2)}{(x + 2)(x - 2)} \\ = \frac{(x - 8)}{(x - 2)} [/tex]

Answer:

The answer is 3366 cubic feet.

Step-by-step explanation:

To find the volume of the rectangular prism, use the formula for a rectangular prism, which is V= LWH. Next, plug in the information given from the question, and the formula will look like V= (18ft) (11ft) (17ft).

Then, solve the equation for the answer, and the answer will be 3366 cubic feet.

Answer:3366

Step-by-step explanation:

Answer:

y/x

Explanation:

The constant of proportionality defines two directly proportional quantities that decrease or increase proportionally/same rate.

Given constant of proportionality= k

Side of the square= x

Perimeter of the square= y

constant of proportionality=k=y/x

For example if perimeter of square is 8 and side of square is 2, constant of proportionality is 8/2=4

Answer:

The answer is 32

Step-by-step explanation:

A right triangle has a total of 180 degrees. As they give you 58 degrees and 90 degree, you just do 180 degrees - 58 degrees - 90 degrees.

Answer: 32

Step-by-step explanation:

Subtract the angle 58 and 90 since it is a right angle

Answer:

f^1(x)= (1/2)x-(1/2)

hope this helped