6 (x + 2)^12 - 8 = 64

[tex]12 = \frac{1+a}{1-a} => 12(1-a)= 1+ a \\=> 12 -12a = 1 + a => 12a+1 = 12-1 \\=> 13a = 11 => a= \frac{11}{13}[/tex]

ok done. Thank to me :>

The expression that represents the area of the gray region, the area of the land remaining in the backyard is 3x²+10x-17 square yards. The correct option is B.

The area of the gray region is the area of the rectangular backyard minus the area of the circular pond.

The area of the rectangular backyard is given as 6x+14x-12 square yards, which simplifies to 20x-12 square yards.

The area of the circular pond is given as 3x²-4x+5 square yards.

So, the area of the gray region is:

(20x-12) - (3x²-4x+5)

= 20x-12 - 3x²+4x-5

= 3x²+10x-17

Therefore, the expression that represents the area of the gray region, the area of the land remaining in the backyard is 3x²+10x-17 square yards.

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Answer:

84 = g  

Step-by-step explanation:

(16 ÷ 4)(3 × 7) = g       Divide

   4(3 × 7) = g              Multiply

    4 × 21 = g               Multiply

        84 = g                Simply

Answer:

AC is perpendicular to BD.

Further explanation

We observe that both the ABC triangle and the ADC triangle have the same AC side length. Therefore we know that  is reflexive.

The length of the base of the triangle is the same, i.e., .

In order to prove the triangles congruent using the SAS congruence postulate, we need the other information, namely . Thus we get ∠ACB = ∠ACD = 90°.

Conclusions for the SAS Congruent Postulate from this problem:

∠ACB = ∠ACD

- - - - - - - - - -

The following is not other or additional information along with the reasons.

∠CBA = ∠CDA no, because that is AAS with ∠ACB = ∠ACD and  

∠BAC = ∠DAC no, because that is ASA with  and ∠ACB = ∠ACD.

no, because already marked.

- - - - - - - - - -

Notes

The SAS (Side-Angle-Side) postulate for the congruent triangles: two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle; the included angle properly represents the angle formed by two sides.

The ASA (Angle-Side-Angle) postulate for the congruent triangles: two angles and the included side of one triangle are congruent to two angles and the included side of another triangle; the included side properly represents the side between the vertices of the two angles.  

The SSS (Side-Side-Side) postulate for the congruent triangles: all three sides in one triangle are congruent to the corresponding sides within the other.

The AAS (Angle-Angle-Side) postulate for the congruent triangles: two pairs of corresponding angles and a pair of opposite sides are equal in both triangles.  

Learn more

Which shows two triangles that are congruent by ASA?  brainly.com/question/8876876  

Step-by-step explanation:

Answer:

x > 2 or  x < 1/2  

Step-by-step explanation:

|4x - 5| > 3

         Case 1                         Case 2

  4x - 5 > 3                           - (4x - 5) > 3

  4x > 5 + 3                          - 4x + 5 > 3

   4x > 8                               -4x > - 5 + 3

      x > 2                               -4 x  > - 2

                                               -x > -2/4   multiply by -1  to make "x" positive and

                                                                this action with change all signs :  

                                                                 any negative becomes positive and

                                                                 > becomes <

                                               x < 2/4

                                                x < 1/2              

Answer:

B

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

y + 4 = [tex]\frac{1}{3}[/tex] (x - 1) ← is in point- slope form

with m = [tex]\frac{1}{3}[/tex] and (a, b ) = (1, - 4 ) → B

The volume of a cone is (1/3)πr2h.

In this problem r=2h or h=(1/2)r

Hence V = (1/6)πr3

dV/dt = (1/2)πr2 dr/dt

With this information you should now be able to answer the question. Remember the relation between r and h!

never mind i was right

im also so sorry if you dont understand or its not one of the answers

Answer:

t a sand and gravel plant, sand is falling off a conveyor, and onto a conical pile at a rate of 10 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate is the height of the pile changing when the pile is 15 feet high?

Step-by-step explanation:

Answer:

D : 0

Step-by-step explanation:

f(0) = 0

Answer:

Negative 12

Step-by-step explanation:

-10 ≥ 2x + 14

-24 ≥ 2x [subtract 14 from both sides]

2x ≤ -24 [read right to left]

x ≤ -12  [divide both sides by 2]

Chad had 96 M&Ms left when he arrived at school.

Chad initially collected 256 M&Ms.

However, he lost 5/8 of them on his way to school through a hole in his bag.

To determine how many M&Ms Chad had left when he arrived at school, we need to calculate the fraction that represents the M&Ms he did not lose.

If Chad lost 5/8 of the M&Ms, it means he kept 1 - 5/8 = 3/8 of them.

To find the number of M&Ms Chad had left, we multiply 3/8 by the total number of M&Ms he initially collected:

(3/8) [tex]\times[/tex] 256 = (3 [tex]\times[/tex] 256) / 8 = 768 / 8 = 96.

Therefore, Chad had 96 M&Ms left when he arrived at school.

In summary, Chad initially collected 256 M&Ms but lost 5/8 of them, leaving him with 3/8 of the total.

Multiplying 3/8 by 256 gives us 96 M&Ms, which is the number of M&Ms Chad had left when he arrived at school.

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Answer:

then whats the point

Step-by-step explanation:

Answer:

9,600

Step-by-step explanation:

100-4 is 96

96 times 100 is 9600

Answer:

[tex]2.5y^{3}x[/tex]

Answer:

Step-by-step explanation:

Line A:

Mark two points in line A.

(1,3) & ( 2 , 5)

[tex]Gradient =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\\\=\dfrac{5-3}{2-1}=\dfrac{2}{1}\\\\\\= 2[/tex]

Line B:

(0,5) ; (5,0)

[tex]Gradient = \dfrac{0-5}{5-0}=\dfrac{-5}{5}=-1[/tex]

Answer:

As no graph is provided you can only solve it.Steps provided below

Yes you have done it

The first one it's the first image, and the second one is the second image.

Answer:

y=b+2x/5 in slope- intercept form.

Step-by-step explanation:

Hope this helps :)

Answer:

Step-by-step explanation:

If the same line holds the hypotenuse of two right triangles, both of the triangles are similar.

This is because they have same ratio of corresponding sides.

Yes .

Let's check your graph

In ∆ADE and ∆ABC

Hence both triangles are similar

The answer is:

y=2x+3

Answer:

1/3(p + 45)

Step-by-step explanation:

1/3 p + 15 is the same as 1/3(p + 45)

-Chetan K

Answer:

-3

Step-by-step explanation:

slope formula is y2-y1 over x2-x1

if we plug in the values and solve, that gets you -3.

Answer:

-3

Explanation:

1-(-2) divided by 3-4

Answer:

YES

Step-by-step explanation:

You just need to plug in the numbers

x=2

y=5

5=2+3

5=5

So it is yes.

Answer:

A=7c/5 + 8d/5

Step-by-step explanation:

Answer:

A = [tex]\frac{7c+8d}{5}[/tex]

Step-by-step explanation:

7c + 8d = 5A ( isolate A by dividing both sides by 5 )

[tex]\frac{7c+8d}{5}[/tex] = A

lol no

just give up in life

The function is used to model real life situation

(a) The value of a

The function is given as:

[tex]\mathbf{y = a(x - 100)(x - 200) }[/tex]

The profit on 120 computers is 3200000.

So, we have:

[tex]\mathbf{3200000 = a(120 - 100)(120 - 200) }[/tex]

[tex]\mathbf{3200000 = -1600a}[/tex]

Divide both side by -1600

[tex]\mathbf{a = -2000}[/tex]

Hence, the value of (a) is -2000

(b) The maximum profit

The function becomes

[tex]\mathbf{y = -2000(x - 100)(x - 200)}[/tex]

Expand

[tex]\mathbf{y = -2000(x\² - 200x - 100x + 20000)}[/tex]

[tex]\mathbf{y = -2000(x\² - 300x + 20000)}[/tex]

Expand

[tex]\mathbf{y = -2000x\² + 600000x - 40000000}[/tex]

Differentiate

[tex]\mathbf{y' = -4000x + 600000}[/tex]

Set to 0

[tex]\mathbf{-4000x + 600000 = 0}[/tex]

Collect like terms

[tex]\mathbf{4000x = 600000}[/tex]

Divide both sides by 4000

[tex]\mathbf{x = 150}[/tex]

Substitute 150 for x in [tex]\mathbf{y = -2000(x - 100)(x - 200)}[/tex]

[tex]\mathbf{y = -2000(150 - 100)(150 - 200)}[/tex]

[tex]\mathbf{y = 5000000}[/tex]

150 computers must be produced to maximize the profit of $5,000,000  

c) Range when the target is at least $4,800,000

This means that:

[tex]\mathbf{y \ge 4800000}[/tex]

So, we have:

[tex]\mathbf{-2000x\² + 600000x - 40000000 \ge 4800000}[/tex]

Collect like terms

[tex]\mathbf{-2000x\² + 600000x - 40000000 - 4800000 \ge 0}[/tex]

[tex]\mathbf{-2000x\² + 600000x - 44800000 \ge 0}[/tex]

Divide through by -2000

[tex]\mathbf{x\² - 300x +22400 \le 0}[/tex]

Factorize

[tex]\mathbf{(x - 140)(x - 160) \le 0}[/tex]

Express as inequality

[tex]\mathbf{140 \le x \le 160}[/tex]

A range of 140 to 160 computers would give the company at least $4,800,000

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[tex]\pink{Answer}[/tex]

[tex]\\ \sf\longmapsto2x + 3x + 4x = 180 \\ [/tex]

[tex]\\ \sf\longmapsto9x = 180 = > x = 20[/tex]

[tex]\\ \sf\longmapsto \: a = 2x = 2 \times 2 0 = 4 0 [/tex]

[tex]\\ \sf\longmapsto \: b \: = 3x = 3 \times 20 = 60[/tex]

[tex]\\ \sf\longmapsto \: c = 4x = 4 \times 20 = 80[/tex]

hence , angles of the triangle are 40 , 60 and 80

The angles of a triangle are in the ratio 2 : 3 : 4 . find the angles of the triangle .

40° , 60° and 80°

We know that sum of all the angles of a triangle adds to 180° .

Let the angles be 2x , 3x and 4x

Now,

=> 2x + 3x + 4x = 180°

=> 9x = 180°

=> x = 180/9

=> x = 20°

(The value of x is 20)

Answer:

y=x^2 is a parabola when y is x squared

y=-x^2 is the first one but when it is flipped over the x axis

y=x^2+2 is the first one shifted two up

y=x^2-2 is the third one but shifted 4 units down

y=2x^2 is the first one but two times the square of x

Step-by-step explanation:

Existe un mayor porcentaje de bonos convertibles sobrevalorados comparado con el porcentaje de bonos de ingresos sobrevalorados, con lo cual la afirmación de Danny es correcta.

Dado que Danny Whitman, un analista de valores de Your Bottom Dollar, Inc. siempre ha considerado que es más probable que los bonos convertibles se sobrevaloren más que los bonos de ingresos, y de 312 bonos convertibles del año anterior, Danny encontró que 202 estaban sobrevalorados, mientras que 102 de los 205 bonos de ingreso estaban sobrevalorados, para determinar si estos datos confirman la posición de Danny se debe realizar el siguiente cálculo:

Por lo tanto, existe un mayor porcentaje de bonos convertibles sobrevalorados comparado con el porcentaje de bonos de ingresos sobrevalorados, con lo cual la afirmación de Danny es correcta.

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