Light travels 9.45 \cdot 10^{15}9.45⋅10 ​15 ​​ 9, point, 45, dot, 10, start superscript, 15, end superscript meters in a year. there are about 3.15 \cdot 10^73.15⋅10 ​7 ​​ 3, point, 15, dot, 10, start superscript, 7, end superscript seconds in a year. how far does light travel per second?

The distance around the bases in yards is 30 yards.

In order to determine the distance between each base in yards the unit of conversion of feet to yards have to be first determined. 1 foot is equivalent to 0.333333 yards.

1 feet = 0.333333 yards

The second step is to multiply the distance between each base by the unit of conversion.

Distance between each base x unit of conversion

90 x 0.333333

= 30 yards

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Answer:

605 words per 11 minutes!

Step-by-step explanation:

60 / 55 = 1.0909

11 x 60 = 660

660 / 1.0909 = 605 + (6x - [tex]\int\limits^a_c {b} \, dx[/tex]) / 10

605 + (6x - [tex]\int\limits^a_c {b} \, dx[/tex]) / 10 rounded = 605

The equation which is equivalent to the given expression is 4x + y = 21.

Expression is a finite combination of symbols that is well-formed according to rules that depend on the context. An expression is a combination of numbers, variables, or a combination of numbers and variables, and symbols and it is connected by the sign of equal.

We have,

Expression [tex]\frac{12x^4(x-3)(x+5)}{30x(x+3)(x+5)}[/tex]

So,

Now,

To get the equivalent expression,

Cancel the common factor (x + 5) of the given expression,

On solving,

We get,

[tex]\frac{12x^4(x-3)}{30x(x+3)}[/tex],

Now,

On solving further,

We get,

[tex]=\frac{2x^3(x-3)}{5(x+3)}[/tex]

So, We can not solve it further,

So, This is the expression that is equivalent to the given expression.

Hence, we can say that the equation which is equal to the given expression is [tex]\frac{2x^3(x-3)}{5(x+3)}[/tex].

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The expression '3/3 - 12i' simplifies to '1 - 12i' which is already in the standard form for a complex number.

The expression you've mentioned is 3/3-12i. First, we need to simplify it. The term 3/3 equals to 1. So, the expression becomes 1 - 12i. This is already in a standard form for a complex number.Standard form for a complex number is represented as a + bi, where a and b are real numbers and i represents the imaginary unit. Therefore, our expression 1-12i is in standard form of complex numbers, where a=1 (real part) and b=-12 (imaginary part).

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Answer:

0.7 (85 + h) = 74.90

Step-by-step explanation:

Answer:

error in step 2. 20 is added on both sides instead of subtraction.

Step-by-step explanation:

Given: [tex]2(10-13)=-34+60[/tex]

Step 1: Distribute

[tex]20-26 = -34+60[/tex]

2 is distributed inside the parenthesis. 2 times 10 is 20

2 times -13 is -26

Step 2: Addition Property of Equality

[tex]-26 = -34+80[/tex]

To eliminate 20 we subtract 20 from both sides. Here 20 is added on both sides. To eliminate any number we do opposite operation. So there is an error in this step.

Step 3: Addition Property of Equality

8=80

Step 4: Division Property of Equality

=10

The types of 3D objects on which one face is triangular are triangular prism, triangular-based pyramid, and square-based pyramid so Matt's solid figure can be anyone among the three.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

As per the given,

Matt used a 3D block to draw a triangle on the paper.

Now in order to draw a triangle there are three types of 3D objects that can be used,

01) Triangular prism,

02) Triangular-based pyramid

03) Square-based pyramid

Hence "The types of 3D objects on which one face is triangular are triangular prism, triangular-based pyramid, and square-based pyramid so Matt's solid figure can be anyone among the three".

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A line with a positive slope generally moves upward from left to right, representing an increase in y-values as x-values rise.

If a line has a positive slope, its general direction is upward from left to right. This means that as the x-values increase, the y-values also increase. The slope of a line in mathematics represents the rate at which y changes with respect to x. A positive slope indicates a direct relationship between the two variables involved; as one increases, so does the other. In the context of a graph, this manifests as a line that rises as it moves along the x-axis.

The nature of the slope determines the line's direction. A higher positive slope indicates a steeper ascent, while a smaller positive slope results in a less steep, flatter incline. The concept of slope is crucial in economics as well, as it measures the relationship between two variables, such as price and quantity supplied, where a positive slope illustrates that firms supply more as the price goes higher.

We will use the slope formula and fill it in accordingly.

[tex] m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]

Our x2 is 5 and x1 is -2; our y2 is -3 and y1 is 6

[tex] m=\frac{-3-6}{5-(-2)}=\frac{-9}{7} [/tex].

The slope of your line is -9/7

Answer

Find out the slope of the points  G(–2, 6) and H(5, –3).

To prove

The equation for finding the slope of two points be

[tex]m = \frac{y_{2} -y_{1}}{x_{2} - x_{1}}[/tex]

where m represented the slope .

As given

points G(–2, 6) and H(5, –3).

[tex]m = \frac{-3-6}{5+2}[/tex]

solving the above terms

[tex]m = \frac{-9}{7}[/tex]

Therefore the slope of  points G(–2, 6) and H(5, –3) is

[tex]m = \frac{-9}{7}[/tex]

The centroid of the region bounded by [tex]\(y=x\), \(y=\frac{1}{x}\), \(y=0\),[/tex] and [tex]\(x=2\)[/tex] is at [tex]\((\frac{2}{3}, 0)\).[/tex]

To find the centroid of the region bounded by the curves[tex]\(y=x\), \(y=\frac{1}{x}\), \(y=0\), and \(x=2\),[/tex]we need to first find the area of the region and then compute the coordinates of the centroid using the following formulas:

The centroid of a region with area[tex]\(A\)[/tex]  is given by [tex]\((\bar{x}, \bar{y})\)[/tex]where

[tex]\[\bar{x} = \frac{1}{A} \int\int_R x \, dA\][/tex]

[tex]\[\bar{y} = \frac{1}{A} \int\int_R y \, dA\][/tex]

First, let's find the points of intersection for the curves:

1. [tex]\(y=x\) and \(y=1/x\):[/tex]

  [tex]\[ x = \frac{1}{x} \implies x^2 = 1 \implies x = 1 \][/tex]

  So, the intersection point is [tex]\((1,1)\).[/tex]

2. [tex]\(y=0\) and \(x=2\):[/tex]

  This intersection occurs at [tex]\((2,0)\).[/tex]

Now, we'll integrate to find the area and then the centroid:

1. Area:

[tex]\[ A = \int_{0}^{1} (x - \frac{1}{x}) \, dx + \int_{1}^{2} (\frac{1}{x}) \, dx \][/tex]

 [tex]\[ A = \left[\frac{x^2}{2} - \ln|x|\right]_{0}^{1} + \left[\ln|x|\right]_{1}^{2} \][/tex]

[tex]\[ A = \left(\frac{1}{2} - 0 - (0 - \infty)\right) + (\ln(2) - \ln(1)) \][/tex]

 [tex]\[ A = \frac{1}{2} + \ln(2) \][/tex]

2. Centroid[tex](\(\bar{x}\)):[/tex]

 [tex]\[ \bar{x} = \frac{1}{A} \left[\int_{0}^{1} x(x - \frac{1}{x}) \, dx + \int_{1}^{2} x(\frac{1}{x}) \, dx\right] \][/tex]

 [tex]\[ \bar{x} = \frac{1}{A} \left[\left[\frac{x^3}{3} - \frac{1}{2}\ln|x|\right]_{0}^{1} + \left[\ln|x|\right]_{1}^{2}\right] \][/tex]

 [tex]\[ \bar{x} = \frac{1}{A} \left(\frac{1}{3} - 0 - (0 - \infty) + (\ln(2) - \ln(1))\right) \][/tex]

 [tex]\[ \bar{x} = \frac{\frac{1}{3} + \ln(2)}{\frac{1}{2} + \ln(2)} \][/tex]

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

3. Centroid [tex](\(\bar{y}\)):[/tex]

[tex]\[ \bar{y} = \frac{1}{A} \left[\int_{0}^{1} (x - \frac{1}{x}) \cdot 0 \, dx + \int_{1}^{2} (\frac{1}{x}) \cdot 0 \, dx\right] \][/tex]

 [tex]\[ \bar{y} = 0 \][/tex]

Therefore, the centroid of the region is at the point [tex]\(\left(\frac{2}{3}, 0\right)\).[/tex]

Answer: 4.25

Step-by-step explanation:

Answer:-4 < x < 6

Step-by-step explanation:

The maximum number of students that will receive the paper and crayons are 30.

Ratio is a quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

Given is Mrs. Evans who has 120 crayons and 30 pieces of paper to give to her students.

We have 120 crayons and 30 pieces of paper.

Then for 1 paper, we will have (120/30) which is equivalent to 4 crayons.

So, every student will get 1 paper and 4 crayons.

Assume that the maximum number of students that will receive the paper and crayons are [x]. Then, we can write -

x + 4x = 120 + 30

5x = 150

5x = 150

x = 30

Therefore, the maximum number of students that will receive the paper and crayons are 30.

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True........................

Final answer:

To produce a positive product, the expression (12)(-6.3)(-0.2)(-15.9) should be used.

Explanation:

To determine which expression will produce a positive product, we need to consider the sign rules for multiplication.

If we have an even number of negative signs within a set of parentheses, the product will be positive. If we have an odd number of negative signs, the product will be negative.

Let's analyze the given expressions:

Therefore, the expression (12)(-6.3)(-0.2)(-15.9) will produce a positive product.

The expression that will produce a positive product is (12)(-6.3)(-0.2)(-15.9) because it contains an even number of negative signs, which results in a positive product according to the rules of multiplication regarding signs.

To find which expression will produce a positive product, we must recall the rules of multiplication regarding signs:

We can now evaluate the expressions given:

The correct expression that will produce a positive product is (12)(-6.3)(-0.2)(-15.9).