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Answer:

a =b = [tex]\frac{5\sqrt{5} }{5}[/tex]

Step-by-step explanation:

[tex]a^{2} +b^{2} = 5 ^{2}[/tex]

a = b

[tex]2a^{2} = 5 ^{2}[/tex]

[tex]2a^{2} = 25\\[/tex]

[tex]a^{2} = \frac{25}{5}[/tex]

a = [tex]\frac{5}{\sqrt{5} }[/tex]

must rationalize...

a =b = [tex]\frac{5\sqrt{5} }{5}[/tex]

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

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: [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.

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:

4i

Step-by-step explanation:

apply (a+b)^2 formula

Answer:

E. 248

Step-by-step explanation:

1 to 500 in set A, 250 to 750 in set B

500 - 250 = 250

100 and 200 are divisible by 100.

250 - 2 = 248

Step-by-step explanation:

Hello!

In order to graph this, a point would have to go through (-6, 1). Then, since it says it needs a slope of 5 (or, to make things a bit easer, we could see it as 5/1) we'd need the next point to be 5 up and 1 across.

One possible solution:

(-6, 1) -> (-5, 6)

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:

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]

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:

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:

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:

- 14x²y

Step-by-step explanation:

Given

- 7x² × 2y

= - 7 × 2 × x² × y

= - 14x²y

3rd step

Solution:-

[tex]\\ \sf\longmapsto -2x+8-3x=7[/tex]

[tex]\\ \sf\longmapsto -2x-3x+8=7[/tex]

[tex]\\ \sf\longmapsto -5x+8=7[/tex]

[tex]\\ \sf\longmapsto -5x=7-8[/tex]

[tex]\\ \sf\longmapsto -5x=-1[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{-1}{-5}[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{1}{5}[/tex]

-4-3-2

1

2

3

4

5 6

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Answer:

34 : 6800000

Step-by-step explanation:

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: [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

tangent of ∠PLM = [tex]\frac{opposite}{adjacent} =\frac{4}{3}[/tex]

Answer:

PLM=4/3

Step-by-step explanation:

The sum of the interior angles in a triangle is 180 degrees.

72 + 35 + <1 = 180

107 + <1 = 180

<1 = 73 degrees

Hope this helps!

Answer:

<1 = 73

Step-by-step explanation:

The sum of the angles of a triangle is 180 degrees

72+ 35+ <1 = 180

Combine like terms

107 + <1 =180

Subtract 107 from each side

<1 = 180-107

<1 = 73

Answer:

VOLUME OF RIGHT CIRCULAR CONE=≈74.93136cm^3

VOLUME OF SPHERE: ≈523.6cm^3

Answer:

x + y = -5

Step-by-step explanation:

2x - x - y + 2y = -1 - 4

x + y = -5

Answer:

23

Step-by-step explanation:

[tex]2 y + 7[/tex]

Replace y with 8

[tex]= 2 (8) + 7\\= 16+ 7\\= 23[/tex]

Therefore, the value of the expression when y=8 is 23.

I hope this helps!

Answer:

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

Step-by-step explanation:

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

Factor out 4x

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

We must understand that certain standards has been layed down for the conversions of measuring units. A summary of such standards are discussed below:

1. Option A. 1 L = 1 dm³

2. Option A. 1 mL = 1 cm³

3. Option B. 0 K = −273 °C

4. Option B. 1000 g = 1 kg

5. Option A. 400 cm = 4.0 m

6. Option B. 1 dm = 0.10 m

7. Option A. 100°C = 373 K

1. Option A. 1 L = 1 dm³

Option B. 1 L = 1 cm³

From standard measurement,

1 L = 1 dm³

1 L = 1000 cm³

From the measuring standard, we can see that 1 L  ≠ 1 cm³.

Hence, option A gives the correct answer.

2. Option A. 1 mL = 1 cm³

Option B. 1 cm³ = 1 L

Hence, option A gives the correct answer.

From standard measurement,

1 mL = 1 cm³

1000 cm³ = 1 L

Thus, option A gives the correct answer.

3. Option A. 0°C = –273 K

Option B. 0 K = −273 °C

Recall:

T (K) = T(°C) + 273

T (K) = Temperature in Kelvin

T(°C) = Temperature in decree celcius

Next, we shall convert 0°C to K

T(°C) = 0°C

T (K) = T(°C) + 273

T (K) = 0 + 273

T (K) = 273 K

Thus, 0°C is equivalent to 273 K

Next, we shall convert 0 K to °C

T(K) = 0

T (K) = T(°C) + 273

0 = T(°C) + 273

Collect like terms

0 – 273 = T(°C)

T(°C) = –273°C

Thus, 0 K is equivalent to –273°C

Therefore, option B gives the correct answer.

4. Option A. 1 kg = 100 g

Option B. 1000 g = 1 kg

From standard measurement,

1 Kg = 1000 g

1000 g = 1 Kg

Hence, Option B gives the right answer

5. Option A. 400 cm = 4.0 m

Option B. 400 cm = 0.40 m

From standard measurement,

100 cm = 1 m

Converting 400 cm to m, we have:

[tex]400 cm = 1 m\\400 cm = \frac{400 cm * 1 m }{100 cm}\\400 cm = 4 m[/tex]

Thus, option A gives the correct answer.

6. Option A. 1 dm = 10 m

Option B. 1 dm = 0.10 m

From standard measurement,

10 dm = 1 m

Thus,

[tex]1 dm = \frac{1 dm * 1 m}{10 dm}\\1 dm = 0.1 m[/tex]

Therefore, option B gives the correct answer.

7. Option A. 100°C = 373 K

Option B. 373 K = 10°C

Recall:

T (K) = T(°C) + 273

T (K) = Temperature in Kelvin

T(°C) = Temperature in decree celcius

Next, we shall convert 100°C to K

T(°C) = 100°C

T (K) = T(°C) + 273

T (K) = 100 + 273

T (K) = 373 K

Thus, 100°C is equivalent to 373 K

Next, we shall convert 373 K to °C

T(K) = 373

T (K) = T(°C) + 273

373 = T(°C) + 273

Collect like terms

373 – 273 = T(°C)

T(°C) = 100°C

Thus, 373 K is equivalent to 100°C

Therefore, option A gives the correct answer.

SUMMARY:

1. Option A. 1 L = 1 dm³

2. Option A. 1 mL = 1 cm³

3. Option B. 0 K = −273 °C

4. Option B. 1000 g = 1 kg

5. Option A. 400 cm = 4.0 m

6. Option B. 1 dm = 0.10 m

7. Option A. 100°C = 373 K

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Answer:

-6 and - 65

Step-by-step explanation:

X-12x-29, by completing the square we get (x-6)^2-65

Step-by-step explanation:

sin and tan are the only ones with p positive valued