When you look at a pencil in water, it looks bent. This illusion is due to refraction, or the bending of light when it moves from one substance to the next.

a. What is m∠1 ? Classify this angle as acute, right, or obtuse.

The proportional relationships for these problems are given as follows:

18. y = 0.5x, with constant k = 0.5.

22. y = -0.4x, with constant k = -0.4.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

In item 18, we have that when x = 2, y = 1, hence the constant is:

k = y/x = 1/2 = 0.5.

Hence the equation is:

y = 0.5x.

In item 22, we have that when x = -5, y = 2, hence the constant is:

k = y/x = -2/5 = -0.4.

Hence the equation is:

y = -0.4x.

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Answer: A=30 degrees, B=60 degrees, C=90 degrees

Step-by-step explanation:

B=2A

C=3A

A+B+C=180

A+2A+3A=180

6A=180

A=30 degrees

B=2A

B=2(30)

B=60 degrees

C=3(30)

C=90 degrees

Answer:

Angle A = 30°

Angle B = 60°

Angle C = 90°

Step-by-step explanation:

Let x represent the measure of A. Using this information, we can figure out the measure of B and C in terms of x.

Since B is twice the measure of A, then it would be 2x. Similarly, C is three times the measure of A, thus it would b 3x.

We also know that the sum of the angles is 180 degrees. We can use this information to set up an equation.

We know that:

Angle A + Angle B + Angle C = 180

Substituting the values we gave for A, B, and C, we find:

x + 2x + 3x = 180

Now, we solve the equation for x.

Start by combining like terms:

6x = 180

Now, divide both sides by 6:

x = 30

Since we know the value of x, we can find the values of the angles.

A = x = 30°

B = 2x = 60°

C = 3x = 90°

According to the question, the line is through the points [tex](0,5)[/tex] and [tex](-2,11)[/tex]

To calculate the slope using standard formula that is :

[tex]m = \frac{(y(2)-y(1))}{(x(2)-x(1))} = \frac{(11-5)}{(-2-0)} =\frac{6}{-2} = -3[/tex]

Now the slope equation will be: [tex]m(x(2)-x(1)) = (y(2)-y(1))[/tex]

[tex]y-5 =(-3)(x-0) = y = -3(x)+5[/tex]

The slope-intercept form is:[tex]y = -3x+5[/tex]

What is the equation of the line?

To represent the set of points in an algebraic form is known as the equation of line. The set of points represent lines in the coordinate system. The parameters can be calculated and those parameters are slope and y-intercept.

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Answer:

v= 0

6(2-0)+2(4)=20 is the simplified version of the equation.

The area that occupies on a plan drawn to the given scale is 0.024 m²

Given,

The area of the playing surface at the Olympics stadium in Beijing = 3/5 hectare

The scale factor on a plan drawn = 1:500

We have to find the area that occupies on a plan drawn to the given scale:

Applied to the area we consider k² as the area is the product of two dimensions.

So, k = 1/500

Now the area on plan:

a : k² = actual area

a : (1/500)² = (3/5) × 10000

a : (1/250000) = 3 × 2000

a × 250000 = 6000

a = 6000 / 250000

a = 0.024 m²

That is, the area that occupies on a plan drawn to the given scale is 0.024 m²

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Answer:

21

Step-by-step explanation:

.75 x 28 = 21

Answer:

find the value of x file attached x9

In some base [tex]B[/tex], we have

[tex]abab_B \equiv 555_{10}[/tex]

so that

[tex]aB^3 + bB^2 + aB + b = 555[/tex]

Factorize the left side.

[tex]aB (B^2 + 1) + b (B^2 + 1) = 555[/tex]

[tex](aB + b) (B^2 + 1) = 555[/tex]

Now, [tex]B[/tex] is a positive integer greater than 1, and [tex]a,b[/tex] are positive integers taken from [tex]\{0,1,2,\ldots,B-1\}[/tex]. So consider the prime factorization of 555 on the right side.

[tex](aB + b) (B^2 + 1) = 3\times5\times37[/tex]

which we can write as

[tex](aB + b) (B^2 + 1) = 15\times(6^2 + 1) = (2\times6 + 3) \times (6^2+1)[/tex]

and so the base is 6, and the number in question is 2323₆.

The missing step in the rational number proof is; Reason 2; Multiply to get a common denominator

Let  a/b and c/d be two rational numbers, where b and d are not zero and a, b, c and d are integers.

Step 1; a/b + c/d

Reason 1; Given

Step 2; a/b + c/d = ad/bd + cb/bd

Reason 2; Multiply to get a common denominator

Step 3; a/b + c/d = ad/bd + cb/bd = (ad + cb)/bd

Reason 3; Simplify

Since b and d cannot be zero, then bd cannot be zero. Also, since a, b, c, and d are integers, then bd, ad, bc and ad + bc are integers too. Thus, the fraction(ad + cb)/bd is a rational number.

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Answer:

An absolute number is a number that is represents a distance from 0. An absolute number is always positive since the distance between two number is always positive.

Step-by-step explanation:

Answer:

140.4 inches

Step-by-step explanation:

there are 36 inches in a yard

3.9 times 36 is 140.4

Hope It Helps

Sorry If I'm Wrong

3.9 yards is equal to 140.4 inches.

We have,

The concept used to convert 3.9 yards to inches is the conversion factor between yards and inches. The conversion factor states that 1 yard is equal to 36 inches.

By multiplying the given value in yards (3.9 yards) by the conversion factor (36 inches/yard), we can convert the measurement from yards to inches.

This concept of using a conversion factor allows us to convert between different units of measurement.

To convert 3.9 yards to inches, we can use the fact that 1 yard is equal to 36 inches.

So, to convert 3.9 yards to inches, we multiply 3.9 by 36:

3.9 yards * 36 inches/yard = 140.4 inches

Therefore,

3.9 yards is equal to 140.4 inches.

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Answer:

Step-by-step explanation:

The inequalities are matched with their correct graph respectively as follows:

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments:

In Geometry, if the leading coefficient of a quadratic equation is greater than (>) zero, the parabolic curve would open upward while the parabolic curve would open downward when the leading coefficient of a quadratic equation is less than (<) zero.

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Complete Question:

Match the questions with the graphs that are labeled A-H. (keep in mind that some questions might have the same answer)

1. A = {(x, y): y > x^2}

2. B = {(x, y): y ≥ x^2+ 3}

3. C = {(x, y): y ≤ 3x^2 + 2}

4. D = {(x, y): y ≥ 2x^2- 5x + 1}

6. x^2- 3x ≥ 0

7. x^2- 3x + 2 ≤ 0

8. {(x, y): y ≤ 1 - x^2}

9. {(x, y): y ≥ -1}

Answer: 8 runners

Step-by-step explanation:

If you mean that " if each person runs one more mile than the previous runner" then:

First person = 1

Second person = 1+1

.....

(1)+(1+1)+(1+1+1)+(1+1+1+1)+(1+1+1+1+1)+(1+1+1+1+1+1)+(1+1+1+1+1+1+1)+(1+1+1)

1  +   2 +    3    +     4      +       5       +         6        +            7         +    3  =31

(the last runner runs less miles then needed)

Answer:

360 - 6r

Step-by-step explanation:

just simplify the expression

The variable that would be the best choice when Pearce needs to choose a variable to represent the number of wallabies in an exhibit will be D. let w= the number of wallabies on the exhibit.

It should be noted that a variable simply means a symbol that's used to represent a situation in mathematics.

In this case, the variable that would be the best choice when Pearce needs to choose a variable to represent the number of wallabies in an exhibit so be let w= the number of wallabies on the exhibit.

This is because of the first alphabet used which is w.

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After estimating 48 ÷ 7, we get the result as 7.

We are given an expression

48 ÷ 7

We need to estimate the result.

First, we will divide 48 by 7

So, we get that:

48 ÷ 7 = 6.857

Now we will estimate it.

We will round of the result.

as 6 > 5, we will get it as:

48 ÷ 7 ≈ 7

Therefore, after estimating 48 ÷ 7, we get the result as 7.

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Answer:

See below

Step-by-step explanation:

The most important info is the rate ft^2 / min and how many minutes it took to mow.

From this, we need to know how much total area there is. We do this by multiplying the rate by the time.

[tex] \frac{ 4{ft}^{2} }{minute} \times 29minutes = 116 {ft}^{2} [/tex]

Then we need to write out the sum of the whole area in terms of length times width

[tex]6ft \times 14 ft + x \times 4ft = 116 {ft}^{2} [/tex]

Notice how we put x for the unknown variable, this turns it into an easy peasy algebra problem. I leave that to you, solve for x

The value of k  such that a is singular is ±√(5/2).

If a singular matrix's determinant is 0, it is a square matrix. Specifically, if and only if det A = 0, a square matrix A is unique. We are aware that the formula A-1 = (adj A) / can be used to get the inverse of a matrix A. Here, the denominator contains det A, which is the determinant of A. We are aware that a fraction with a denominator of 0 is not defined. Since det A = 0, A-1 is not defined. In other words, a single matrix's inverse is not defined. That is to say, there isn't a matrix B such that AB = BA = I.

A singular matrix means that the detA should be 0.

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The value of the given quadratic equation are = x = -(6/5) , x = 2

Quadratics are polynomial equations of the second degree, which means they have at least one squared term. It is also known as quadratic equations. The quadratic equation has the general form: ax2 + bx + c = 0.

Quadratic functions occupy a distinctive place in the school curriculum. They are functions whose values are easily estimated from input values, therefore they are a modest improvement over linear functions and provide a major shift away from attachment to straight lines.

Given (5x + 6)(3x - 6) = 0

Using the zero factor principle: if ab = 0 then a = 0 and b = 0

So,

(5x + 6) = 0 or (3x - 6) = 0

for the (5x + 6):

(5x + 6) = 0 (subtracting both side by 6)

5x + 6 - 6 = 0- 6

so, x = -(6/5)

Same calculation for (3x - 6) = 0 we get x = 2

The value of the given quadratic equation are = x = -(6/5) , x = 2

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Answer:

h(3) = 1

Step-by-step explanation:

[tex]h\left(3\right)=\left(3\right)\cdot \:2-3\\h\left(3\right)=3\cdot \:2-3\\h\left(3\right)=6-3\\h\left(3\right)=3[/tex]

Divide

[tex]\frac{h\cdot \:3}{3}=\frac{3}{3}\\h=1[/tex]

If a researcher wishes to conclude something about a population from a sample, it is best that the sample be taken randomly.

Sampling is the process by which a representative number is taken from a population for the purpose of study. The sample must be taken in such a way that it reflects the properties of the whole.

Thus, if a researcher wishes to conclude something about a population from a sample, it is best that the sample be taken randomly.

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Answer:

-8

Step-by-step explanation:

Any number raised to the power 1 is that number itself

So (-8)⁻¹ = -8

The Option A best explains the dual experiments: "In the experimental group, a chosen variable is altered in a known way. In the control group, that chosen variable is not altered so a comparison can be made."

Now,

Hence, amongst all the given options, The Option A best explains the dual experiments: "In the experimental group, a chosen variable is altered in a known way. In the control group, that chosen variable is not altered so a comparison can be made."

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Step-by-step explanation:

no lo se,no hablo ingles..........

If Point B [tex](3,1)[/tex] has translated 2 units to the right and 1 unit up, new coordinates of point B' are [tex](5,2)[/tex]

As per the question statement, Point B [tex](3,1)[/tex] is there on a cartesian plane. Point B is translated 2 units to the right and 1 unit up.

Before solving this question, we need to know about cartesian plane system in which, there are four quadrants which are made using positive and negative axes known as positive X and negative X (same for Y axis).

Now point B[tex](3,1)[/tex] lies in the first quadrant and value "3" describes the location of point on X axis and value "1" describes the location of point on Y axis.

If point B [tex](3,1)[/tex] is translated 2 units to the right and 1 unit up, the locations of X and Y axes will change to value "5" on X axis and value "2" on Y axis.

Hence the coordinates of point B' are [tex](5,2)[/tex]

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