what is the formula for the nth term of the sequence (1x3),(2x4),(3x5)

Based on the table, the rate of change of the weight of the rabbit in pounds per week will be 1.75 pounds.

In the first week, there's 9.5 pounds. This can be illustrated using the arithmetic progression. The formula will be:

= a + (n - 1)d

where,

a = first term

d = common difference

3rd term = a + 2d

13 = 9.5 + 2d

2d = 13 - 9.5

2d = 3.5

d = 3.5/2

d = 1.75

Therefore, the rate of change of the weight of the rabbit in pounds per week will be 1.75 pounds.

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To find differences in the angles of the intersections we must know how many degrees each angle corresponds to. We must also take into account that the sum of the internal angles must equal 180°.

A triangle is a polygon that is characterized by having three sides, three vertices, and three angles. An indispensable rule of the interior angles of the triangles is that they must add up to 180º.

Triangles are classified according to their characteristics as shown below:

According to the above, depending on the measurements of the length of the sides and the angles of a triangle, its characteristics and classification change.

Note: This question is incomplete because the image is missing. However I can answer it based on my general prior knowledge.

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The equation we can use to find the value of x in the diagram given is: B. (5x + 30) + 5x = 90.

Angles that give a sum of 90 degrees when added are referred to as complementary angles.

The angles, (5x + 30) and 5x are complementary angles, since the sum of both gives a right angle (90 degrees).

Therefore, the equation that we can use to find x in the diagram is: B. (5x + 30) + 5x = 90.

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Answer:

this is your answer

hope it will help you

Using the Empirical Rule, it is found that about 143 trees fall within two standard deviations of the mean.

It states that, for a normally distributed random variable:

95% of the measures are within 2 standard deviations of the mean, hence, out of 150 trees, the amount is:

A = 0.95 x 150 = 142.5, rounded to 143.

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A circle can be characterized by its center's location and its radius' length. The correct option is A.

A circle can be characterized by its center's location and its radius' length. Let the center of the considered circle be at (h,k) coordinate and the radius of the circle be 'r' units. Then, the equation of that circle would be:

(x-h)² + (y-k)² = r²

The given graph is the graph of a circle that has its origin at (0,0) and has a radius of 4 units, therefore, the equation will be,

(x-0)² + (y-0)² = 4²

x² + y² = 16

Multiply both the sides of the equation by 2,

2x² + 2y² = 32

Hence, the correct option is A.

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If the volume of the aluminum brick will be 2218.5 cubic cm. Then the approximate density of the aluminum will be 8.9 grams per cubic cm.

Density is defined as the mass per unit volume. It is an important parameter in order to understand the fluid and its properties. Its unit is kg/m³.

The mass and density relation is given as

Density = mass/volume

A brick of aluminum weighs 19,745 grams and has the following dimensions: length 29 cm, height 15 cm, and width 51 mm.

Then the approximate density of the aluminum will be

The volume of the aluminum brick will be

V = 29 x 15 x 5.1

V = 2218.5 cubic cm

Then the density will be

D = 19,745 / 2218.5

D = 8.900 gram per cubic cm

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Answer:

141/1.95 km/hr, or 72.308 km/hr

Step-by-step explanation:

To find the average speed, we need to know the total distance traveled / time (hours).
The total distance is 72 km + 69 km =  141 km.
The total time is 48 minutes / 60 (because we want this in hours, not minutes) + 69/60 = 1.95 hours
141/1.95 =  72.3 km/hr

Answer:

x=24

Step-by-step explanation:

6×(5/6)x +6(10)=6(30)

5x +60=180

5x +60-60=180 - 60

5x=180 -60

5x=120

5x/5 =120/5

x=24

Answer:

5x²+12x+4

Step-by-step explanation:

5x²+10x+2x+4

5x²+12x+4

Answer:

[tex]5x^{2}+12x+4[/tex]

Step-by-step explanation:

Use the FOIL method to expand.

5x*x+

2*x+

5x*2+

2*2

which is

5x^2+2x+10x+2

combining the two x s we get

5x^2+12x+4

Answer:

y=1

Step-by-step explanation:

In order to solve this problem, you have to substitute 3 in for x. Then you would multiply 3 by 3, which equals 9. Subtract 9 from 10, equals 1.

I included a picture so you can see the work.

Hope this helped!

Answer:

V = 324 cm³

Step-by-step explanation:

the volume (V) of the pyramid is calculated as

V = [tex]\frac{1}{3}[/tex] Ah ( A is the area of the base and h the height )

here A = 9² = 81 cm² and h = 12 , then

V = [tex]\frac{1}{3}[/tex] × 81 × 12 = 27 × 12 = 324 cm³

Answer:

x = ± 2

Step-by-step explanation:

10 - 3x² = - 2 ( subtract 10 from both sides )

- 3x² = - 12 ( divide both sides by - 3 )

x² = 4 ( take square root of both sides )

x = ± [tex]\sqrt{4}[/tex] = ± 2

then x = - 2, x = 2

Answer:

x=2,-2

Step-by-step explanation:

10-3[tex]x^2\\[/tex]=-2

Can also be written as 12=3[tex]x^2[/tex]

[tex](12=3x^2)/3[/tex]

[tex]4=x^2\\\sqrt{4} =+-\sqrt{x^2} \\[/tex]

2=+-x or x=2,-2

x=2,-2

Answer:

QR = 3

Step-by-step explanation:

given that Q is on the segment PR , then

PQ + QR = PR ( substitute values )

16 + QR = 19 ( subtract 16 from both sides )

QR = 3

The calculated length of the segment QR is 3 units

From the question, we have the following parameters that can be used in our computation:

Point Q is on line segment PR

PQ = 16 and PR = 19

using the above as a guide, we have the following:

PQ + QR = PR

substitute the known values in the above equation, so, we have the following representation

16 + QR = 19

So, we have

QR = 19 - 16

Evaluate

QR = 3

Hence. the length of the segment QR is 3

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The distance of the robot from the charging base is gotten as; 62 cm

From the image attached showing the movement of Kapil's robot, we can use cosine rule to find the value of h which is the distance of the robot from the charging base.

The distance of the robot from the charging base is gotten by;

h = x² + b² - 2xb cos 60

h = 50² + 70² - 2*50*70 * 0.5

h = 62 cm

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It looks like you might have intended to say the roots are 7 + i and 5 - i, judging by the extra space between 7 and i.

The simplest polynomial with these characteristics would be

[tex]f(x) = (x - (7 + i)) (x - (5 - i))[/tex]

but seeing as each of the options appears to be a quartic polynomial, I suspect f(x) is also supposed to have only real coefficients. In that case, we need to pair up any complex root with its conjugate to "complete" f(x). We end up with

[tex]f(x) = (x - (7 + i)) (x - (7 - i)) (x - (5 - i)) (x - (5 + i))[/tex]

which appears to most closely resemble the third option. Upon expanding, we see f(x) does indeed have real coefficients:

[tex]f(x) = (x^2 - (7^2 - i^2)) (x^2 - (5^2 - i^2)) = (x^2 - 8) (x^2 - 6) = x^4 - 14x^2 + 48[/tex]

Answer:

C on edge 23

Step-by-step explanation:

because i said so

Answer: 18 kilograms

Step-by-step explanation:

If each pumpkin weighs 3 kilograms and the farmer has 6 pumpkins the equation would be 6x3=18 in order to find the mass of the farmer's pumpkins.

Step-by-step explanation:

3x and 2x are like terms so,

3x + 5 - 2x

3x - 2x + 5 = x + 5

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to simplify the expression

[tex]\star~~\large\pmb{3x+5-2x}[/tex].

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

The like terms here are: 3x-2x; let's combine them:

[tex]\star~\large\pmb{x+5}[/tex]

We can't simplify this any further, because x and 5 are not like terms.

[tex]\ddot\bigstar[/tex] Remember this...

[tex]\fbox{Variables\:and\;numbers\;are\;not\;like\;terms}[/tex]

Hope it helps you out! :D

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~Just a smiley person helping fellow students :)

Answer:

hope you can understand

Using proportions, it is found that he can be expected to hit 36 home runs during the 162 game season.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, the player hits 10 home runs in 45 games, hence the proportion is:

p = 10/45.

Then, in 162 games, the amount is:

HR = 10/45 x 162 = 36.

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The graphs with no solutions are the ones with no intercepts between the curves. These are the first one and the last one.

If we have an equation like:

f(x) = g(x).

One way of finding the solutions is to graph:

y = f(x) and y = g(x) and see where the two curves intercept.

From that, the graphs where the curves do not intercept are the graphs that indicate that the equations have no solutions.

The two graphs with no intercepts are the first one (top left) and the last one (bottom right), so these are the correct options.

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Answer:

kid named finger

Step-by-step explanation:

I simply just used a form of alien math solving and I got my answers but I'm not willing to share

Answer:

y=586.4

Step-by-step explanation:

64^2= 64x64 = 4096

4096-7y+9=0

4105-7y=0    1. +7y on both sides

4105=7y       2. /7 on both sides

y=586.4

[tex]~~~~~~\dfrac{2x-3}{4} = 3x\\\\\implies 2x-3 = (3x)(4)\\\\\implies 2x -3 = 12x \\\\\implies 12x -2x = -3\\\\\implies 10x = -3\\\\\implies x = -\dfrac{3}{10}[/tex]

Answer:

x = -3/10

Step-by-step explanation:

Given :

[tex]\frac{2x-3}{4} = 3x[/tex]

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

Multiply both sides with 4 :

⇒ [tex]4 \times \frac{2x-3}{4} = 4 \times 3x[/tex]

⇒ 2x - 3 = 12x

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

Subtract 2x from both sides :

⇒ 2x - 3 - 2x = 12x - 2x

⇒ -3 = 10x

⇒ x = -3/10

Answer:

[tex]d = \sqrt{109}[/tex]

Step-by-step explanation:

Use the distance formula.

[tex]\text{The distance between two points } (x_1, y_1) \text{ and } (x_2, y_2) \text{ is given by the formula:}\\d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Your points are (-4, 11) and (6, 8).

[tex]d = \sqrt{(-4 - 6)^2 + (11 - 8)^2}\\\\d = \sqrt{(-10)^2 + (3)^2}\\\\d = \sqrt{100 + 9}\\\\d = \sqrt{109}[/tex]

This is not an identity.

[tex]\dfrac{2(\cos(x)\sin(x) - \sin(x)\cos(2x))}{\sin(2x)} \neq \sec(x)[/tex]

Check x = π/4, for which we have cos(π/4) = sin(π/4) = 1/√2. Together with sin(2•π/4) = sin(π/2) = 1 and cos(2•π/4) = cos(π/2) = 0, the left side becomes 1, while sec(π/4) = 1/cos(π/4) = √2.

Keeping the left side unchanged, the correct identity would be

[tex]\dfrac{2(\cos(x)\sin(x) - \sin(x)\cos(2x))}{\sin(2x)} = -2\cos(x) + 1 + \sec(x)[/tex]

To show this, recall

• sin(2x) = 2 sin(x) cos(x)

• cos(2x) = cos²(x) - sin²(x)

• cos²(x) + sin²(x) = 1

Then we have

[tex]\dfrac{2(\cos(x)\sin(x) - \sin(x)\cos(2x))}{\sin(2x)} = \dfrac{2\cos(x)\sin(x) - 2\sin(x)\cos(2x)}{\sin(2x)} \\\\ = \dfrac{\sin(2x) - 2\sin(x)\cos(2x)}{\sin(2x)} \\\\ = 1 - \dfrac{2\sin(x)\cos(2x)}{\sin(2x)} \\\\ = 1 - \dfrac{2\sin(x)(\cos^2(x) - \sin^2(x))}{2 \sin(x)\cos(x)} \\\\ = 1 - \dfrac{\cos^2(x) - \sin^2(x)}{\cos(x)} \\\\ = 1 - \cos(x) + \dfrac{\sin^2(x)}{\cos(x)} \\\\ = 1 - \cos(x) + \dfrac{1 - \cos^2(x)}{\cos(x)} \\\\ = 1 - \cos(x) + \sec(x) - \cos(x) \\\\ = -2\cos(x) + 1 + \sec(x)[/tex]

Answer:, Volume of triangular prism = (1/2) bh × L.

[tex] \sqrt{8 \: + \: 2 \sqrt{15} } [/tex]

[tex] \sqrt{( \sqrt{3 } \: + \: \sqrt{5} ) ^{2} } [/tex]

[tex] \boxed{ \bold{\sqrt{3} \: + \: \sqrt{5} }}[/tex]