what is the solution to the equation x² = 16?​

Answer:

x^2 +3x

Step-by-step explanation:

The outer rectangle has an area of

A = l*w = (4x)*(x+2) = 4x^2 +8x

The inner rectangle has an area of

A = (3x+5)*x = 3x^2 +5x

Subtract the inner rectangle from the outer rectangle

Shaded area = 4x^2 +8x - ( 3x^2 +5x)

Distribute the minus sign

                       =4x^2 +8x -  3x^2 -5x

Combine like terms

                       = x^2 +3x

[tex] \sf \: ( - 12 )\times( - 4) + (- 8 )+ (+ 3) \\ \sf \: = (- 12 \times - 4 )+ (- 8 + 3) \\ \sf \: = 48 - 5 \\ = 43[/tex]

Hope it helps.

RainbowSalt2222

Answer:

y = -4/11x + 75/11

Step-by-step explanation:

y2 - y1 / x2 - x1        1 - 5 / 6 - (-5)      -4/11

y = -4/11x + b

5 = -4/11(5) + b

5 = -20/11 + b

75/11 = b

Answer:

4i

Step-by-step explanation:

apply (a+b)^2 formula

Answer:

VOLUME OF RIGHT CIRCULAR CONE=≈74.93136cm^3

VOLUME OF SPHERE: ≈523.6cm^3

Solution :

Given data :

x = 65, n = 300

[tex]$\hat p = \frac{x}{n}[/tex]

  [tex]$=\frac{65}{300}$[/tex]

  = 0.2167

The hypothesis are :

[tex]$H_0: p \leq 0.3$[/tex]

[tex]$H_0: p> 0.3$[/tex]

The [tex]\text{level of significance}[/tex], α = 0.05

The test is right tailed.

The standard deviation is :

[tex]$\sigma = \sqrt{\frac{0.3(1-0.3)}{300}}$[/tex]

σ = 0.0265

The test statistics is :

[tex]$z=\frac{\hat p - p}{\sigma}$[/tex]

[tex]$z=\frac{0.2167 - 0.3}{0.0265}$[/tex]

  = -3.14

The critical value is 1.645

The rejection region is : If z > 1.645, then we reject [tex]H_0[/tex]

Decision :

Since the test statistics does not lie in the rejection, so we fail to . [tex]\text{reject the null hypothesis}[/tex].

P-value : [tex]$P(z > - 3.14)$[/tex]   = 0.9992

Therefore, the p-value is not less than the level of significance so we fail to [tex]\text{reject the null hypothesis}[/tex].

-4-3-2

1

2

3

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113.625 degrees is the answer

Answer:

x = [tex]-\frac{2}{3}[/tex]

Step-by-step explanation:

I used the FOIL method

[(2x + 3) (3x + 2)] − [(3x + 2) (2x− 3)] = 0

[tex](6x^{2} +4x+9x+6) - (6x^{2} -9x+4x-6)=0[/tex]

[tex](6x^{2} +13x+6) - (6x^{2} -5x-6)=0[/tex]

[tex](6x^{2} +13x+6) - 6x^{2} +5x+6=0[/tex]

combine like terms

[tex]6x^{2} -6x^{2} = 0[/tex]

[tex]13x+5x=18x[/tex]

[tex]6+6=12[/tex]

so, [tex]18x +12 = 0[/tex]

subtract 12 on both sides

[tex]18x=-12[/tex]

divide by 18 to isolate x

[tex]x=-\frac{12}{18}[/tex]

and simplifies to

[tex]x=-\frac{2}{3}[/tex]

Answer:

2440

Step-by-step explanation:

an=115

a=7

Sn=n/2(a+an) [Where n is no. of terms]

   = 40/2(7+115)

   = 20(122)

   = 2440

Answer:

T(n) = 4 + 12*n

Step-by-step explanation:

La pregunta completa se puede ver en la imagen de abajo.

En ella, podemos ver que:

La primera figura tiene: 16 palitos

la segunda figura, con n = 2, se añaden 3 palitos en cada extremo, por lo que tendremos 16 palitos + 4*3 palitos = (16 + 12) palitos

De manera similar, en la tercera figura se vuelven a añadir 3 palitos en cada extremo de la cruz, entonces esta figura tendrá:

(16 + 12) palitos + 4*3 palitos = (16 + 12 + 12) palitos.

Así, tenemos la relación:

T(1) = 16

T(2) = 16 + 12

T(3) = 16 + 12 + 12

Podemos asumir que la forma general será:

T(n) = 16 + 12*(n - 1)

podemos reescribir esto como:

T(n) = (12 + 4) + 12*(n - 1)

      = 4 + 12 + 12*(n - 1)

      = 4 + 12*n

La opción correcta es la primera.

Answer:

y = 4

Step-by-step explanation:

From the question given above, the following data were obtained:

Angle θ = 45

Hypothenus = 4√2

Adjacent = y =?

The value of y can be obtained by using cosine ratio as illustrated below:

Cos θ = Adjacent / Hypothenus

Cos 45 = y / 4√2

Cross multiply

y = 4√2 × Cos 45

Recall

Cos 45 = 1 / √2

Therefore,

y = 4√2 × 1/√2

y = 4

Answer:

38

Step-by-step explanation:

Put 2 in place of q

(34+18×2)-(5^2+7)

(34+36)-(25+7)

70-32=38

Answer:

I believ the answer is 6/12 or 1/2

Step-by-step explanation:

2x3 = 6 and 4x3 = 12 and 6/12 simplified would be 1/2

Answer:

I believe the answer is 6/12 or 1/2

Step-by-step explanation:

Answer:

4x( x^3 +3x+2)

Step-by-step explanation:

4x^4 + 12x^2 + 8x

Factor out 4x

4x( x^3 +3x+2)

Answer:

70+30i

Step-by-step explanation:

Answer:

x=-5

Step-by-step explanation:

[tex]\frac{x}{x+3} =\frac{5}{2} \\5x+15=2x\\5x-2x=-15\\3x=-15\\x=-15/3=-5[/tex]

Answer:

Step-by-step explanation:

The enlargement of a comic will be very similar to the original. Everything is larger but in the same proportion. The difference is if the original is enlarged so much that the individual pixel in the original comic becomes visible; causing the enlargement to be "pixelated."

If a comic is drawn using a grid, that may reduce pixelation because you can line up things with the grid.

If the comic's size is reduced, then again it will look similar but everything is smaller and in the same proportion. There will not be any pixelation effect.

Answer:

1,195,742.25 (final answer since instructions did not include rounding up or anything)

Step-by-step explanation:

n = 4

The given expression is:

9^8 ÷ 9n

USE PEMDAS order of operations and solve:

9^8 ÷ 9n

= 43046721 ÷ 9n

Substitue n with 4 and solve:

43046721 ÷ 9(4)

= 43046721 ÷ 36

= 1,195,742.25

Answer:

9^4

Step-by-step explanation:

We know that a^b ÷ a^c = a^ (b-c)

9^8 ÷ 9^4

9^(8-4)

9^4

Answer:

a) [tex]n = 4 + 7\cdot i[/tex], [tex]\forall\, i \in \mathbb{N}_O[/tex], b) [tex]n = 2 + (i+1)^{2}[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex]

Step-by-step explanation:

a) The sequence is representative for an arithmetic sequence, whose key characteristic is that difference is between two consecutive elements is the same. In particular, the sequence has a difference of 7 between any two consecutive elements and the initial element is 4. Hence, we can derive the following formula:

[tex]n = n_{o} + r\cdot i[/tex], [tex]\forall\, i \in \mathbb{N}_O[/tex] (1)

Where:

[tex]n_{o}[/tex] - Initial element.

[tex]r[/tex] - Difference between two consecutive elements.

[tex]i[/tex] - Index.

If we know that [tex]n_{o} = 4[/tex] and [tex]r = 7[/tex], then the expression for the n-th term of the sequence is:

[tex]n = 4 + 7\cdot i[/tex], [tex]\forall \,i\in\mathbb{N}_{O}[/tex]

b) In this case, we have a geometric sequence described by the following equation:

[tex]n = 2 + (i+1)^{2}[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex]  (2)

The constant element ([tex]2[/tex]) represents the two extreme squares, whereas the second order binomial represents the total of squares in the middle ([tex](i+1)^{2}[/tex]) and emulates the area formula of the square.

Answer:

Step-by-step explanation:

?

Answer:

34 : 6800000

Step-by-step explanation:

Answer:

13m

Step-by-step explanation:

volume of sphere = [tex]\frac{4}{3} * pi * r^{3}[/tex] = 3000π

4r^3/3 = 3000

r^3 =2250

r = ∛2250 = 13.10370 = 13

Answer:

Radius of the sphere is 13.1 m.

Step-by-step explanation:

Volume:

[tex]{ \boxed{ \pmb{volume = { \bf{ \frac{4}{3}\pi {r}^{3} }}}}}[/tex]

Substitute:

[tex]{ \tt{3000\pi = \frac{4}{3} \times \pi \times {( {r}^{3}) } }} \\ \\ { \tt{ {r}^{3} = \frac{3000 \times 3}{4} }} \\ \\ { \tt{r = \sqrt[3]{ \frac{3000 \times 3}{4} } }} \\ { \tt{r = 13.1 \: m}}[/tex]

Hi there!

[tex]\large\boxed{m = 2}[/tex]

Since the line is increasing (the y-values are increasing as x increases), we can automatically eliminate any answer choice containing a negative slope.

Thus, the only correct answer choice would be m = 2.

We could also solve using the slope formula:

m = y2-y1/x2-x1

Plug in given points:

m = 3-1 / 0 - (-1)

m = 2 / 1 = 2

Answer:

[tex]\sqrt[3]{x^{5}y} = x^{\frac{5}{3}}y^\frac{1}{3}[/tex]

Step-by-step explanation:

Given

[tex]\sqrt[3]{x^{5}y}[/tex]

Required

The equivalent expression

We have:

[tex]\sqrt[3]{x^{5}y}[/tex]

Rewrite as an exponent

[tex]\sqrt[3]{x^{5}y} = (x^{5}y)^\frac{1}{3}[/tex]

Open bracket

[tex]\sqrt[3]{x^{5}y} = x^{5*\frac{1}{3}}y^\frac{1}{3}[/tex]

[tex]\sqrt[3]{x^{5}y} = x^{\frac{5}{3}}y^\frac{1}{3}[/tex]

Step-by-step explanation:

We reflect We triangle across both axis so the x and y values will both switch.

Our triangle is originally in the second quadrant but then go to the 4the after we reflect it.

Second Quadrant are

^;8+1—](

Answer:

- 14x²y

Step-by-step explanation:

Given

- 7x² × 2y

= - 7 × 2 × x² × y

= - 14x²y

Answer:

Enterprises usually adopt some quality practices to control the product quality during the manufacturing process in order to assure the delivery of qualitative good products to customers. The quality practices or quality management systems adopted by industries will further evolve due to the changes of quality concepts as time goes by. This chapter discusses the change of quality concepts and the related revolution of quality management systems in the past century. The quality concepts were gradually changed from the achievement of quality standards, satisfaction of customer needs, and expectations to customer delight. Since merely satisfying customers is not enough to ensure customer loyalty, the enterprises gradually focus on customers’ emotional responses and their delight in order to pursue their loyalty. The emotion of “delight” is composed of “joy” and “surprise,” which can be achieved as the customers’ latent requirements are satisfied. Thus, the concept of “customer delight” and the means to provide the innovative quality so as to meet the unsatisfied customers’ latent needs are elaborated on. Finally, a framework of innovation creation is developed that is based on the mining of customer's latent requirements. This outline will manifest the essential elements of the related operation steps.

Answer: [tex]\frac{\sqrt{5}}{6}[/tex]

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Work Shown:

[tex]\frac{\sqrt{10}}{3\sqrt{8}}\\\\\frac{\sqrt{10}*\sqrt{8}}{3\sqrt{8}*\sqrt{8}}\\\\\frac{\sqrt{10*8}}{3\sqrt{8*8}}\\\\\frac{\sqrt{80}}{3\sqrt{64}}\\\\\frac{\sqrt{80}}{3*8}\\\\\frac{\sqrt{16*5}}{24}\\\\\frac{\sqrt{16}*\sqrt{5}}{24}\\\\\frac{4*\sqrt{5}}{24}\\\\\frac{\sqrt{5}}{6}\\\\[/tex]

Note: In the second step, I multiplied top and bottom by [tex]\sqrt{8}[/tex] to rationalize the denominator.

Answer:

square root of 5 over 6 or 0.37267799…

Step-by-step explanation:

Multiply the numerator and denominator by the conjugate.

Step-by-step explanation:

hope it helps you and please mark it brainliest answer