Given the rule, find the 8th term in the arithmetic
sequence.
an =3n + 4

Answer:

The answer is 600

Step-by-step explanation:

Because 60×10=600.

Answer:

600

Step-by-step explanation:

60*10=600

I might have misunderstood. If I have, please tell me

Answer:

Step-by-step explanation:

Because in your previous question the scale factor was 1:30 you would simply multiple 5 by 30 to get 150 inches

The required two pairs of polar coordinates for the point (0, -10) are:

(10, π/2) and (10, -π/2)

To convert from Cartesian coordinates (x, y) to polar coordinates (r, θ), we can use the following formulas:

\(r = \sqrt{(x^2 + y^2)}\\\theta = \tan^{-1}(y/x)\)

Since the x-coordinate of the point (0, -10) is 0, we can directly say that the angle θ is either π/2 or -π/2, depending on whether y is positive or negative.

For y = -10, we get:

\(r = \sqrt{(0^2 + (-10)^2)} = 10\)

Therefore, two pairs of polar coordinates for the point (0, -10) are:

(10, π/2) and (10, -π/2)

Both of these pairs have the same distance from the origin (r = 10) but different angles (π/2 and -π/2).

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Texas' location and climate led to the development of the aviation industry.

What is the significance of Texas in the development of the aviation industry?

The development of the aviation industry in Texas can be attributed to its favorable geographical location and climate. Texas is located in the southern part of the United States, making it a strategic location for air travel between the east and west coasts of the country. Additionally, its warm and dry climate provided ideal conditions for flight testing and training.

Reason what led to the development of the aviation industry :

Texas has a long history of aviation, with the Wright brothers conducting one of their earliest flight demonstrations in the state in 1910. The establishment of military bases during World War II and the subsequent development of aircraft training facilities in Texas further fueled the growth of the aviation industry in the state. Additionally, the placement of the Johnson Space Center in Houston helped to establish Texas as a hub for aerospace research and development. However, it is Texas' favorable location and climate that truly made it a prime location for the aviation industry. Its central location made it a strategic location for air travel and logistics, while its warm and dry climate provided ideal conditions for flight testing and training. Today, Texas remains one of the top states for aviation and aerospace industries, with major airports, aircraft manufacturers, and research institutions located throughout the state.

Therefore, option (d) is correct.

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\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ Q(\stackrel{x_1}{-7}~,~\stackrel{y_1}{-5})\qquad J(\stackrel{x_2}{1}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ QJ=\sqrt{(~~1 - (-7)~~)^2 + (~~3 - (-5)~~)^2} \implies QJ=\sqrt{(1 +7)^2 + (3 +5)^2} \\\\\\ QJ=\sqrt{( 8 )^2 + ( 8 )^2} \implies QJ=\sqrt{ 64 + 64 } \implies QJ=\sqrt{ 128 }\implies QJ\approx 11.31\)

The average rate of change of the function f(x) = √(x+4) over the interval 2 ≤ x ≤ 6 is approximately 0.29 to the nearest hundredth.

To find the average rate of change of the function f(x) = √(x+4) over the interval 2 ≤ x ≤ 6, we need to calculate the change in the function divided by the change in the input variable over that interval.

The change in the function between x = 2 and x = 6 is:

f(6) - f(2) = √(6+4) - √(2+4) = √10 - √6

The change in the input variable between x = 2 and x = 6 is:

6 - 2 = 4

So, the average rate of change of the function over the interval 2 ≤ x ≤ 6 is:

(√10 - √6) / 4

To approximate the answer to the nearest hundredth, we can use a calculator or perform long division to get:

(√10 - √6) / 4 ≈ 0.29

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Answer:

I think the answer is B

Step-by-step explanation:

1.2 * 10^6 is 1,200,000

1.38 * 10^7 is 13,800,000

you just have to divide 13,800,000 by the numbers until you get to 1,200,000. So, 13,800,000 / 11.5 is 1,200,000

Hope this helps! Have an amazing day :)

Answer:

11.5

Step-by-step explanation:

we will need to divide both of them

1.38 × 10^7 ÷ 1.2 × 10^6

1.38÷1.2 × 10^7-6

= 1.15 × 10¹

= 11.5

Answer:

y=2x

Step-by-step explanation:

The line passes through the origin, so the y-intercept = 0

the slope m can be found with

m = (y2-y1)/(x2-x1) = (8-2)/(2-1) = 2

Therefore the equation of the line is

y = 2x + 0 = 2x

Answer:

A) y = 2x

Step-by-step explanation:

We are given the points (4,8) and (1,2).

\(\frac{2-8}{1-4}=\frac{-6}{-3}=\frac{6}{3}=\boxed{2}\)

The line passes through the origin.

Option A should be correct.

Hope this helps.

Given:

Required:

To find the accumulated amount.

Explanation:

Consider the formual

Here

Final Answer:

Accumulated aount is $2,650.66

Answer:

it would be

18 x 5x = 915

solve the equation

18 x 5 = 90

90x = 915

divide by 90

x =10.1666

Step-by-step explanation:

The side length of the triangle Elizabeth drew cannot form a right triangle.

A right triangle is a triangle that has one of its angle as 90 degrees.

The sides of a right triangles are hypotenuse side, adjacent side and the opposite side. This is base on the angle position.

Right triangle obeys Pythagoras's theorem.

a² + b² = c²

where

Therefore, let's test if the labelled side of the triangle Elizabeth drew is a right triangle.  We will use Pythagoras theorem to confirm it

5² + 8² = 14²

25 + 64 = 196

Therefore,

89 ≠ 196

Therefore, the side length cannot form a right triangle

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Based on the given histogram, the data is skewed with a maximum range of 49.

This is because the frequency bars are not evenly distributed across the x-axis intervals, indicating that the data is not symmetric. The lack of a shaded bar for the 40 to 49 interval also suggests that there were fewer donations in that range compared to the other intervals.

One possible explanation for this skewness could be that the charity had suggested donation levels, with a minimum of $10, resulting in a large number of donations in the 10 to 19 interval. Additionally, the shaded bar stopping at 1 for the 30 to 39 and 50 to 59 intervals suggests that there were fewer donations in those ranges. This could be due to a variety of reasons, such as donors being more likely to give in the suggested $10 increments, or the charity's fundraising efforts being more effective at attracting donors in certain age or income brackets.

Overall, the histogram does not suggest a bimodal distribution, as there is not a clear separation between two distinct modes. The maximum range of 49 also indicates that there were no extreme outliers or large donations that would skew the data towards a higher range. Therefore, it is likely that the data represents a typical distribution of donations to a charity, with most donors giving smaller amounts and fewer donors giving larger amounts.

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The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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Answer:

Part A)

\(86=2(x+22)\)

Part B)

\(l=26\text{ cm}\)

Step-by-step explanation:

We know that the rectangle has a length of (x+5) and a width of 12 cm.

Part A)

Remember the formula for the perimeter of a rectangle:

\(P=2(l+w)\)

We know that the perimeter is 86. Substitute that for P:

\(86=2(l+w)\)

Substitute (x+5) for the length l and 17 for w. So:

\(86=2((x+5)+17)\)

We can simplify this to acquire our equation:

\(86=2(x+22)\)

Part B)

To find the length, let's find our x first. We have the equation:

\(86=2(x+22)\)

Divide both sides by 2:

\(43=x+22\)

Now, subtract 22 from both sides. Therefore, our x is:

\(x=21\)

To find the length, remember that the length is:

\(l=x+5\)

Since we now know the value of x, substitute 21 for x:

\(l=21+5\)

Add:

\(l=26\text{ cm}\)

So, the length is 26 centimeters.

And we're done!

The observation I can make of the pattern is that the sequence always increase by 10.

The sequence above shows an arithmetic pattern. Therefore, the arithmetic formula can be used to solve the next sequence.

7, 17, 27, 37, 47, 57..

Therefore,

aₙ = a + (n - 1)d

where

Therefore,

a = 7

d = 17 - 7 = 10

Hence, the arithmetic formula is as follows:

aₙ = 7 + (n - 1)10

aₙ = 7 + 10n - 10

aₙ = 10n - 3

The sequence always increase by 10.

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The number that satisfies the equation is x = -31/7. This means that if we increase two by the product of a number and 7, the result is at most -29 if the number is -31/7.

The expression we need to solve is "Two increased by the product of a number and 7 is at most -29". We can express this as 2 + x × 7 ≤ -29 where x is the number we need to find.In order to solve this equation, we need to start by isolating the variable x. We can subtract 2 from both sides of the equation to get x × 7 ≤ -31. Then, we divide both sides of the equation by 7 to get x ≤ -31/7.Therefore, the number that satisfies the equation is x = -31/7. This means that if we increase two by the product of a number and 7, the result is at most -29 if the number is -31/7.

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The number that satisfies the equation is x = -31/7. This means that if we increase two by the product of a number and 7, the result is at most -29 if the number is -31/7.

The expression we need to solve is "Two increased by the product of a number and 7 is at most -29". We can express this as 2 + x × 7 ≤ -29 where x is the number we need to find.In order to solve this equation, we need to start by isolating the variable x. We can subtract 2 from both sides of the equation to get x × 7 ≤ -31. Then, we divide both sides of the equation by 7 to get x ≤ -31/7.Therefore, the number that satisfies the equation is x = -31/7. This means that if we  two by the product of a number and 7, the result is at most -29 if the number is -31/7.

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Answer:

1, 120

Step-by-step explanation:

    3.2 x 107 = 342.4

+   7.2 x 108 = 777.6

_____________________

                       1, 120                          

Answer:

(3.2 × 107) + (7.2 × 108) =

342.4 + 777.6 =

1120

Step-by-step explanation:

Answer: j=8.4

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

Answer:

y - 7 = \(\frac{1}{2}\) (x + 5)

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

here m = \(\frac{1}{2}\) and (a, b ) = (- 5, 7 ) , then

y - 7 = \(\frac{1}{2}\) (x - (- 5) ) , that is

y - 7 = \(\frac{1}{2}\) (x + 5)

Using the inverse function, it is found that the equation is:

\(P(t) = \frac{e^{0.1t}}{50} + 20\)

It's initial value is 20.

---------------------------

We want to find the inverse of:

\(y = P^{-1}(t) = 10\ln{50t - 1000}\)

To do this, we exchange y and t, and isolate y.

Then:

\(10\ln{50y - 1000} = t\)

\(\ln{50y - 1000} = \frac{t}{10}\)

\(e^{\ln{50y - 1000}} = e^{0.1t}\)

\(50y - 1000 = e^{0.1t}\)

\(50y = e^{0.1t} + 1000\)

\(y = \frac{e^{0.1t} + 1000}{50}\)

\(y = \frac{e^{0.1t}}{50} + \frac{1000}{50}\)

\(P(t) = \frac{e^{0.1t}}{50} + 20\)

It's initial value is:

\(P(0) = \frac{e^{0.1(0)}}{50} + 20 = 0.02 + 20 = 20.02\)

Rounding, 20.

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Answer:

P = 1/50e^0.1t + 20

Step-by-step explanation:

multiplication of the gradients of the two diagonals is equals to -1 if they are perpendicular

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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The only solution to the equation is cos(x) = 5/7.

We have,

cos²(x) + sin²(x) = 1:

Substituting.

7cos²(x) - 26 = 7(1 - sin²(x)) - 26

= 7 - 7sin²(x) - 26

= -19 - 7sin²(x)

Now,

-19 - 7sin²(x) = -20sin(x) - 7

We can simplify this equation by moving all the terms to one side:

7sin^2(x) - 20sin(x) - 12 = 0

We can solve this quadratic equation using the quadratic formula:

sin(x) = [20 ± √(20² - 4(7)(-12))] / (2(7))

sin(x) = [20 ± √(784)] / 14

sin(x) = (10 ± 28) / 14

sin(x) = 2/7 or sin(x) = -2.

However, we should check whether each solution is valid by substituting it back into the original equation and ensuring that both sides are equal.

So,

If sin(x) = 2/7,

7cos²(x) - 26 = -20 (2/7) - 7

7cos²(x) = -10/7

But since cos²(x) is always non-negative, there is no real solution to this equation.

If sin(x) = -2,

7cos²(x) - 26 = -20 (-2) - 7

7cos²(x) = 25

Taking the square root of both sides, we get:

cos(x) = ±5/7

The two solutions to the original equation are:

sin(x) = -2 and cos(x) = 5/7

or

sin(x) = -2 and cos(x) = -5/7

However, we should note that there is no real number whose sine is equal to -2, so there is no real solution to the equation.

Therefore, the only solution is:

cos(x) = 5/7

Thus,

The only solution is cos(x) = 5/7.

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Answer:

x=-5

Step-by-step explanation:

-3x+25=40

      -25   -25

-3x=15

  /-3    /-3

x=-5

Hope I helped!

Answer:

x= -5

Step-by-step explanation:

1. Subtract both sides by 25.

2. Divide both sides by -3

\( - 3 x= 15\)

\( \frac{ - 3x}{ - 3} = \frac{15}{ - 3} \)

3. Simplify

\(x = - 5\)

The solution set of this inequality is {x| x > -6.1}

Here we have the inequality:

2x + 8 > -4.2

To find the solution set, we need to isolate the variable x in one of the sides of the inequality. Doing that we will get:

2x + 8 > -4.2

2x > -4.2 - 8

2x > -12.2

x > -12.2/2

x > -6.1

So the set of all numbers larger than -6.1, this in number form is:

{x| x > -6.1}

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Answer:

The value of the given equation is 3.

Step-by-step explanation:

If :

Find the value of 3(x - y) + xy

\( \longrightarrow{\sf{3(x - y) + xy}}\)

Substituting the given values in the equation :

\( \longrightarrow{\sf{3 \bigg(5 - (-6) \bigg) + 5 \times - 6}}\)

\( \longrightarrow{\sf{3 \bigg( 5 + 6 \bigg) - 30}}\)

\( \longrightarrow{\sf{3 \bigg( 11 \bigg) - 30}}\)

\( \longrightarrow{\sf{ 33 - 30}}\)

\(\longrightarrow{\sf{\underline{\underline{ 3}}}}\)

Hence, the value of the given equation is 3.

To find the slope of the curve, first differentiate the equation of the curve and substitute the value of x in the result

The slope of the curve is the change in y coordinates with respect to the change in x coordinates of the line

To find the slope of the curve at a given point

First differentiate the given equation of the curve with respect to x

That is dy / dx.

The derivative of the equation of the curve  is the slope of the curve.

In next step substitute the value of x in the slope of the curve

The result will be the slope of the curve at a given point

Therefore, these are the steps to find the slope of the curve

I have answered the question in general, as the given question is incomplete

The complete question is:

How to find the slope of a curve at a given point?

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The triangle must then be translated 5 units to the left and 1 unit to the up.

Four distinct approaches to modify the position and/or shape of a point, line, or geometric figure are collectively referred to as transformations. The Pre-Image of the object is its initial shape, while the Image, after transformation, is the final shape and location of the thing.

Change is referred to as transformation. In light of this, to convert a geometric shape means to alter it in some way.

The triangle DEF's side lengths are twice as long as triangle ABC's, as can be seen in the figure.

This implies that ABC needs to be scaled back by a factor of two.

Additionally, each triangle is located on an x-axis side.

As a result, ABC must be reflected along the x-axis.

The triangle must then be translated 5 units to the left and 1 unit to the up.

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