-3+8n=-5 for 7th grade math equation algebra

The direction and speed the plane traveling is at About 84.3° west of north at approximately 502.5 mph. Option C

We need to first  find the distance between points A and C using the distance formula; Distance AC = √((x2 - x1)² + (y2 - y1)²)

If we input the figures as seen in the diagram, it becomes

Distance AC = √((-30 - 20)² + (520 - 20)²)

which is 502.49. if we round it off, it becomes 502.5

We have to find find the angle θ that the plane is traveling using the law of cosines

cos(θ) = (AB² + BC² - AC²) / (2 x AB x BC)

cos(θ) = (500² + 50² - 502.5²) / (2 x 500 x 50)

which is -0.000125

θ = arccos( -0.000125)

θ = 90.0071621563 (in degrees)

Give than the wind is blowing west, the angle should be measured west of north.

180° - 90.01° = 90°

It only mean that the plane is travelling at approximately 84.3° west of north  

The answer is based on the question below;

A plane is set to fly due north, but it is pushes off course by crosswind blowing west. At 1 pm, the plane is located at point A and at 2pm, the plane is located at point C, as shown in the diagram. In what direction and at what speed is the plane traveling?

A. About 5.7° west of north at approximately 500.1 mph.

B. About 5.7° west of north at approximately 502.5 mph

C. About 84.3° west of north at approximately 500.1 mph.

D. About 84.3° west of north at approximately 502.5 mph

Point C coordinates (-30, 520)

Point A (20, 20)

Distance from A to B on a straight course is 500

B to C is 50

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The square root can be simplified as 7√2

Irrational numbers are numbers in the form of square roots, which when evaluated cannot be expressed in the form a/b e.g. √7, π, 2/√5, 3√11, etc. They are also called surd.

The opposite of an irrational number is called rational number. A rational number is a number that can be written in the form of a/b, where a and b are integers, and b is not equal to 0. e.g. 1/3, 2/3, √4 = 4/1, etc.

The square root can be simplified as follow:

√98 = √(49 * 2)

        = √49 * √2

        = 7 * √2

        = 7√2

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Answer:

The resulting linear equation is 3d = 12, so d = 4 and e = 0.

The total number of zero pairs in the expression (-5) + (-8) is 2.

We must pair the negative numbers so that their sum is equal to zero in order to determine the number of zero pairs in this expression. To put it another way, we need to find pairs of numbers whose sum is the same as their additive inverse.

We are combining two negative numbers in the expression (-5) + (-8).

In this case, we can pair the (-5) with a (+5), since (-5) + (+5) = 0, and we can also pair the (-8) with a (+8), since (-8) + (+8) = 0.

As a result, the expression (-5) + (-8) contains two zero pairs: one for (-5) and (+5) and one for (-8) and (+8).

Therefore, there are a total of 2 zero-pairs in the expression (-5) + (-8).

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A way to find 2/7 of a number is by Multiply by 7/2. The correct answer is D).

To find 2/7 of a number, we need to multiply the number by the fraction 2/7. Therefore, the correct answer is to multiply the number by 2/7, which is equivalent to option D: Multiply by 7/2.

Dividing by 2 and 7 or multiplying by 7 and dividing by 2 will not give us the correct answer because 2/7 is not equal to either 1/2 or 7/2. Therefore, we need to use the fraction 2/7 to calculate the desired amount.

To find 2/7 of a number, we can multiply the number by 2/7.

For example, let's say we want to find 2/7 of 42. We can multiply 42 by 2/7

2/7 x 42 = (2 x 42)/7 = 84/7 = 12

Therefore, 2/7 of 42 is 12.

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The entries in both columns when matched are

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

The graph

When the line of best fit is drawn, we have

(8, 0) and (0, 8)

The equation is calculated as

y = mx + c

So, we have

8 = 0 * m + c

0 = 8 * m + c

This gives

c = 8

0 = 8 * m + 8

So, we have

m = -1

This means that the equation is

y = -x + 8

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

Equation of line of best fit: y = -x + 8

Slope = -1

y-intercept = 8

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Answer:

7034529

Step-by-step explanation:

Assuming you mean to multiply 0.75 by 9379372, the result would be:

0.75 x 9379372 = 7034529

Answer:

  (-4, 2)∪(8, ∞)

Step-by-step explanation:

Given a particle's position is described by x(t) = t³ -6t² -96t, you want the intervals where speed is increasing.

The speed of the particle is the magnitude of its rate of change of position.

The rate of change of position is ...

  x'(t) = 3t² -12t -96 = 3(t² -4t) -96

  x'(t) = 3(t -2)² -108

This describes a parabola that opens upward, with a vertex at (2, -108). It has zeros at x = 2 ± 6 = {-4, 8}.

The magnitude of the speed is shown by the blue curve in the attachment. Between t=-4 and t=8, it is the opposite of the parabola described by the above equation.

The rate of change of speed is the derivative of speed with respect to time. The green curve in the attachment shows the particle's rate of change of speed. Speed is increasing when the green curve is above the x-axis.

Between the point when speed is 0, at t=-4, and when it reaches a local maximum, at t=2, it is increasing. Speed is increasing again after it becomes 0 at t=8.

The intervals of increasing speed are (-4, 2) ∪ (8, ∞).

__

Additional comment

We have made the distinction between speed and velocity. Velocity is the signed rate of change of position. If position is plotted on a number line increasing to the right, then velocity is positive anytime the particle is moving to the right. Velocity is increasing if acceleration is to the right (positive).

Velocity of this particle is increasing on the interval (2, ∞).

The intervals in which the function is decreasing. [tex][-\pi , -\frac{\pi }{3} ], [\frac{\pi }{3}, \pi ][/tex]. Option 3

We're given a function f(x) = 2 sin x - x, which describes a curve on a graph. We want to find the intervals where this curve is decreasing (going down) within the range of -π to π.

To find when the function is decreasing, we look at its slope. The slope tells us if the curve is going up or down. We find the slope by taking the first derivative of the function: f'(x) = 2 cos x - 1.

We now have an equation for the slope, f'(x) = 2 cos x - 1. A negative slope means the function is decreasing. So, we want to find where f'(x) is less than 0 (negative).

We set up the inequality: 2 cos x - 1 < 0. We solve it to find the x-values where the slope is negative. The solution is cos x < 1/2.

From the inequality cos x < 1/2, we find the intervals within the range of -π to π where the function is decreasing. These intervals are [-π, -π/3] and [π/3, π].

The above answer is in response to the question below as seen in the picture.

Determine the interval(s) in [tex][-\pi, \pi ][/tex] on

which f(x) =  2 sin x - x

is decreasing.

1. [tex][-\frac{\pi }{3}, \frac{\pi }{3} ][/tex]

2. [tex][-\frac{\pi }{6}, \frac{\pi }{6} ][/tex]

3. [tex][-\pi , -\frac{\pi }{3} ], [\frac{\pi }{3}, \pi ][/tex]

4. [tex][-\pi , -\frac{-2\pi }{3} ], [\frac{2\pi }{3}, \pi ][/tex]

5. [tex][-\pi , - \frac{5x}{6} ], [\frac{\pi }{6}, \pi ][/tex]

6. [tex][-\frac{\pi }{6}, \frac{5\pi }{6} ][/tex]

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For statement 5/3 = slope, the reason is Definition of slope and for statement 5/3 = 15/9 , the reason is Triangle A is similar to triangle B.

If slope of triangles are equal than Triangle A is similar to triangle Therefore, in statement 5/3 = 15/9 when we simplify

we get 5/3 = 5/3.

Then the reason for this statement is "If slope of triangles are equal" and the definition of slope in general is m = y/x.

Therefore, for the statement 5/3 = slope, the reason is Definition of slope.

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The machine's book value at the end of year three is $164,000.

The total amount of hours used by the machine in the first three years is: 2,000 + 4,000 + 8,000 = 14,000 hours

To calculate the annual depreciation expense, we must first establish the depreciation rate per machine hour. The following is how the depreciation rate per machine hour is calculated:

Depreciation rate per machine hour = (machine cost - estimated residual value) / total number of machine hours estimated

Rate of depreciation per machine hour = ($500,000 - $20,000) / 20,000 machine hours

Depreciation per machine hour = $480,000 divided by 20,000 machine hours

Rate of depreciation per machine hour = $24 per machine hour

We may compute the depreciation expense for each year by using the depreciation rate per machine hour:

Depreciation expense in year one = depreciation rate per machine hour x hours used in the first year

Depreciation expense in year one = $24 x 2,000 hours

Depreciation expense for the first year = $48,000

Year 2 depreciation expense = Depreciation rate per machine hour multiplied by the number of hours consumed in year 2.

Depreciation expense for year 2 = $24 x 4,000 hours

Depreciation expense for year two = $96,000

Depreciation expense in year three = depreciation rate per machine hour x hours used in year three

Depreciation expense in year three = $24 x 8,000 hours

Depreciation expense during the third year = $192,000

The accumulated depreciation for the first three years is the sum of the following depreciation expenses:

Accumulated depreciation equals the sum of year one depreciation expense, year two depreciation expense, and year three depreciation expense.

Depreciation accumulated = $48,000 + $96,000 + $192,000

Depreciation accumulated = $336,000

To compute the machine's book value at the end of the year 3. We deduct the accumulated depreciation from the machine's cost:

Machine book value = machine cost minus accumulated depreciation

The machine's book value is $500,000 minus $336,000

The machine's book value is $164,000

As a result, the machine's book value at the end of year three is $164,000.

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Answer:

-tan(x)/sin^2(x).

Step-by-step explanation:

To simplify the expression:

sec(x)sin(-x) + tan(-x)

1 + sec(-x)

We can use the fact that sin(-x) = -sin(x), cos(-x) = cos(x), and tan(-x) = -tan(x) to rewrite the expression as:

-sec(x)sin(x) - tan(x)

1 + sec(x)

Next, we can multiply both the numerator and denominator by the conjugate of the denominator, 1 - sec(x), to eliminate the square root in the denominator. This gives:

(-sec(x)sin(x) - tan(x))(1 - sec(x))

(1 + sec(x))(1 - sec(x))

Simplifying the numerator by distributing and combining like terms, we get:

-sec(x)sin(x) + sec(x)tan(x) + tan(x) - sec(x)tan(x)

1 - sec^2(x)

Simplifying further by canceling out the sec(x)tan(x) terms in the numerator, we get:

-tan(x)

1 - sec^2(x)

Finally, we can use the identity 1 - sec^2(x) = sin^2(x) to rewrite the denominator and simplify further:

-tan(x)

sin^2(x)

Therefore, the simplified expression is -tan(x)/sin^2(x).

The distance that the ball has traveled when the height of the ball is 80 feet is either about 9.86 feet or about 3.64 feet.

We are given that;

Velocity= 140feet

Inclination= 45degrees

Function  ​h(x)=(-32x^2/140^2)+x

Now,

To find the distance that the ball has traveled when the height of the ball is 80 feet, we need to solve the equation:

h(x) = 80

Substituting h(x) with the given function, we get:

(-32x2/1402) + x = 80

Multiplying both sides by 140^2 and simplifying, we get:

-32x^2 + 140x - 11200 = 0

Dividing both sides by -32 and simplifying, we get:

x^2 - (35/4)x + 350 = 0

Using the quadratic formula, we get:

x = [ (35/4) ± √( (35/4)^2 - 4(350) ) ] / 2 x ≈ 9.86 or x ≈ 3.64

Using a graphing utility, we can confirm that these are the approximate x-intercepts of the function h(x) - 80.

Therefore, by graphing the answer will be about 9.86 feet or about 3.64 feet.

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Solution:

Notice that for each function, they are simply in the form [tex]f(k(x))[/tex], where [tex]k(x)[/tex] is some function of [tex]x.[/tex] More specifically,[tex]g(x)=f(x-2), h(x)=f(2x), \text{ and } j(x) = f(x^2).[/tex]

Thus, because the Interval of Convergence of [tex]f(x)[/tex] is [tex]-3 < x < 3,[/tex] the Interval of Convergence of [tex]g(x)[/tex] should be [tex]-3 < x-2 < 3 \implies -1 < x < 5.[/tex]

Similarly, the Interval of Convergence of [tex]h(x)[/tex] is [tex]-3 < 2x < 3 \implies -\frac32 < x < \frac32.[/tex]

Finally, the Interval of Convergence of [tex]j(x)[/tex] should be [tex]-3 < x^2 < 3 \implies 0 < x < \sqrt{3}.[/tex]

Answer:  2/4 or 1/2

Step-by-step explanation: Based on the spinner shown, there are 5 equal sections, 1 of which is yellow and 2 of which are blue. If the spinner does not land on yellow, it will land on one of the 4 other sections, 2 of which are blue.

Therefore, the probability of landing on blue given that it does not land on yellow is 2/4 or 1/2.

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The lengths of the corresponding segments are given as follows:

Hence the scale factor is given as follows:

k = 4/2

k = 2.

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The dimensions of cone B is radius, 6.8 units and height 7 units.

The possible dimensions of cone B is calculated as follows;

Volume of cone = ¹/₃πr²h

Volume of cone A = ¹/₃π(6²)(4) = 150.8 units³

Volume of cone B = 487 units³ - 150.8 units³ = 336.2 units³

The dimensions of cone B is calculated as;

¹/₃πr²h = 336.2 units³

r²h = 321

Let the height of cone B = 7, then the radius of the cone is calculated as;

7r² = 321

r² = 321/7

r² = 45.86

r = √45.86

r = 6.8 units

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Answer: D

Step-by-step explanation:

It's not A because the 4 is a constant, not a factor.

It's not B because the 11 is not constant because its a negative, therefore being subtracted.

It's not C because 3 is not an exponent, it is simply a term.

The answer is D because 2 is a coefficient, because it is a number infront of a variable.

The rating of chips whose cost is $1.10 is obtained replacing the value of x on whichever's equation is correct by 1.10.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The problem is incomplete, hence the procedure to estimate the rating of chips whose cost is $1.10 is presented.

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Answer:

1 Mexican Peso = 0.0552 US Dollar Hope this helped! Have a great day! :)

Step-by-step explanation:

Answer:

1 United States Dollar is equivalent or equal to 18.24 (Mexican peso)

The equation of the tangent line to the graph of y = g(x) at x = 2 is y = 6x - 17.

The point-slope form of the equation of a line can be used to find the equation of the tangent line to the graph of y = g(x) at x = 2.

y - y1 = m(x - x1)

where m is the tangent line's slope and (x1, y1) is the point on the g(x) graph at x = 2.

Given that g(2) = -5, the point on the g(x) graph at x = 2 is (2, -5).

We are told that g'(2) = 6, which is the slope of the tangent line at x = 2.

As a result, the tangent line equation is: y - (-5) = 6(x - 2)

We get the following after simplifying and rearranging:

y + 5 = 6x - 12 y = 6x - 17

Hence, the equation of the tangent line to the graph of y = g(x) at x = 2 is y = 6x - 17.

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Yes, The statement given in the problem is correct.As, <a> satisfies all three conditions- identify, Closure and inverse, it is a subgroup of G.

A subgroup in mathematics is a subset of a group that, with regard to the same operation, is also a group. To put it another way, a subgroup is a smaller group that is a part of a bigger group.

Technically, let H be a subset of G and let G be a group that is subject to some operation (such as addition, multiplication, or composition). H is referred to be a subgroup of G if it forms a group on its own with regard to the same operation.

For given statement,

Let G is a group, and let a is the element of G. The set of all powers of a, denoted as<a>, is a subgroup of G, and it is the subgroup generated by a.

To show that <a> is a subgroup of G, we need to verify that it satisfies three conditions:

As, All the three conditions were satisfied by <a> , it is a subgroup of G

Moreover, it is the subgroup generated by a , as it is the smallest subgroup of G that contains a. This means that < a > includes all the powers of a, as well as their products and inverses, and nothing more.

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The solutions to the equations are marked and matched

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

4 + x = -8x - 5

Adding 8x on both sides , we get

9x + 4 = -5

Subtracting 4 on both sides , we get

9x = -9

Divide by 9 on both sides , we get

x = -1

b)

2 ( 5x + 2 ) = 10x - 4

On simplifying the equation , we get

10x + 4 = 10x - 4

Subtracting 10x on both sides , we get

4 ≠ 4

So , it has no solution

c)

7 + 2x = 2x - 7

Subtracting 2x on both sides , we get

7 ≠ -7

So , it has no solution

d)

-3x + 3 = 3 ( 1 - x )

-3x + 3 = 3 - 3x

x = all real numbers

Hence , the equations are solved

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Answer:

The correct answer is B.

Approximately 200 students received a test score between 70.5 and 80.