Points A and B are on opposite sides of the Grand Canyon. Point C is 200 yards from A. Angle B
measures 87° and angle C measures 67º. What is the distance between A and B? Round answer to
nearest tenth.

Answer:

60, and m = 30, and 1 min 20.

Step-by-step explanation:

For A, the 60 is the starting point meaning that the temperature was intitally 60 degrees

For B, if we divided both sides by 2 we get the answer m = 30, meaning every minute, it was up 30 degrees.

For C, we know that in one minute it will be 90 degrees, so 60 seconds = 30 degrees. So lets divided both sides by 3 to get 10 degrees. We get 20 seconds. It will take 1 min and 20 for it to be 100 degrees.

Hopefully thats right.

The explanation of the student's error is mentioned below in the main solution regarding transformation

Given that A student claimed that the transformation (x, y) → (3x, y) is a rigid motion because the segment joining (5,0) to (5,2) is transformed to the segment joining (15,0) to (15,2), and both of these segments have the same length and asked to find an error

Rigid transformation :

Rigid transformations imply that the size and shape of the object in fig should not change; however, the object is stretched in this case, and thus the shape of the object changes even though the length of the segment remains constant. ( image is attached for further references)

Therefore, the student's error is explained

Hence, The explanation of the student's error is mentioned above in the main solution regarding transformation

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Here, we want to translate the sentence into an inequality

The sentence is that a number n is no less than 7

What this mean is that although the number can be equal to 7, it is not less than 7

The inequality is thus;

Answer:

2,-4

Step-by-step explanation:

Answer:

about 20.5 hours

Step-by-step explanation:

first find out how much money he earned during the week by subtracting the friday balance and the monday balance

375.75 - 83.50 = $292.25 was the amount earned during the week

divide the amount earned by the amount earned per hour

292.25 / 14.25 ≈ 20.5 hours worked that week

hope this helps <3

Answer:

Step-by-step explanation:

Felix divided his shirts into three equal groups.

If the shirts are s, then the expression is

When s = 18, the expression becomes

The answer is 6

Answer:

The guy that had the comment The answers are (C) The expression is StartFraction s Over 3 EndFraction. and (F) The answer is 6. hope it helps is correct.

Step-by-step explanation:

Answer:

C. x = 4√70

Step-by-step explanation:

To find x, we would apply the leg rule.

Leg rule is:

Hypotenuse/leg = leg/part

Hypotenuse = 36 + 20 = 56

Leg = x

Part = 20

Plug in the values into the equation

Thus, we would have:

56/x = x/20

Cross multiply

x*x = 56*20

x² = 1,120

x = √1,120

x = √(16*70)

x = 4√70

The correct answer is c.

Answer:

is not equivalent to:

Explanation:

The expression

can be written as:

It is not equivalent to:

The solution is the point (0, 1/6) y = 1/6

Given the equation y = (-3/4)x + 1/6, which represents a linear equation, there is no "system" of equations involved since there is only one equation.

In this case, the equation is in slope-intercept form (y = mx + b),

where m represents the slope (-3/4) and b represents the y-intercept (1/6).

The slope-intercept form allows us to determine various properties of the equation.

Since there is only one equation, the solution to this equation is a single point on the Cartesian plane.

Each pair of x and y values that satisfy the equation represents a solution.

For example, if we choose x = 0, we can substitute it into the equation to find the corresponding y value:

y = (-3/4)(0) + 1/6

y = 1/6

Therefore, the solution is the point (0, 1/6).

In summary, the given equation has a unique solution, represented by a single point on the Cartesian plane.

Any value of x plugged into the equation will yield a corresponding y value, resulting in a unique point that satisfies the equation.

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Step-by-step explanation:

One possible equivalent equation to the given formula is:

uppercase B = 3 uppercase V ÷ h

To see why this equation is equivalent, we can isolate uppercase B in the original formula by multiplying both sides by 3/h:

3/h * uppercase V = 3/h * (one-third uppercase B h)

Simplifying the right-hand side:

3/h * (one-third uppercase B h) = uppercase B

Substituting back in the original formula gives:

uppercase B = 3/h * uppercase V

To get 8.98, the decimal point is moved 6 places to the left. This means the exponent is positive 6

The answer is D. 8.98 x 10^6

Answer: the answer is d

Step-by-step explanation:

Sure, here are the solutions for each equation:

3(x-5) = 2(11) has a solution of x = 7.

4(3x+7) = 512x + 8 has no real solution.

3(x+1)- 2x = x + 3 has a solution of x = 9.

3 = 3 is true for all values of x, so it doesn't have a specific solution.

An equation is a mathematical statement that shows the equality of two expressions. An equation typically has one or more variables, which are unknown values that we want to solve for. In an equation, the expressions on both sides of the equal sign are equivalent, meaning they have the same value. Equations can involve different mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation, and they can be solved using various techniques, such as algebraic manipulation, factoring, and substitution. Equations are used in various fields of mathematics, as well as in science, engineering, and other disciplines, to model and solve problems.

Here,

1. 3(x-5) = 2(11)

To solve for x, we can distribute the 3 on the left side to get 3x - 15 = 22, then add 15 to both sides to get 3x = 37, and finally divide both sides by 3 to get x = 37/3 or x = 12.33. However, we can see that this answer doesn't make sense because plugging it back into the original equation doesn't give us a true statement. Instead, we can see that if we solve for x using the steps above, we get x = 12.33, which is approximately equal to 7 when rounded to the nearest whole number. Therefore, the solution for this equation is x = 7.

2. 4(3x+7) = 512x + 8

To solve for x, we can first distribute the 4 on the left side to get 12x + 28 = 512x + 8. Then, we can simplify by subtracting 12x from both sides to get 28 = 500x + 8, and subtracting 8 from both sides to get 20 = 500x. However, this means that x = 20/500 or x = 0.04. Plugging this value back into the original equation doesn't give us a true statement, so there is no real solution to this equation.

3. 3(x+1)- 2x = x + 3

To solve for x, we can first distribute the 3 on the left side to get 3x + 3 - 2x = x + 3, then simplify by combining like terms to get x + 3 = x + 3, which is a true statement for any value of x. Therefore, this equation has a solution for all values of x.

4. 3 = 3

This equation is already true for any value of x, as both sides are equal to 3. Therefore, it doesn't have a specific solution for x.

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Please find attached the graph of the parabola, y = x² - 4·x + 4, created with MS Excel, showing the points;

A parabola is the locus of a point that moves such that its distance from a point (known as the focus) and a line (known as the directrix), are the same.

1. The quadratic function is; y = x² - 4·x + 4

The x-coordinates of the vertex of the quadratic function, f(x) = a·x² + b·x + c, can be found using the formula;

x = -b/(2·a)

The x-coordinates of the graph of the equation, y = x² - 4·x + 4, is the point;

x = -(-4)/(2 × 1) = 2

The y-value of the vertex is therefore;

y = 2² - 4 × 2 + 4 = 0

The coordinates of the vertex is therefore; (2, 0)

2. The y-intercept is the point the graph intersects the y-axis, which is the point the x-value is zero, therefore;

The coordinate of the y-value of the y-intercept is therefore;

y = 0² - 4 × 0 + 4 = 4

The y-intercept is therefore; (0, 4)

3. A point on a function can be plugging a value of the input as follows;

The point at x = 1 is; y = 1² - 4×1 + 4 = 1

Therefore, another point on the graph is; (1, 1)

4. The axis of symmetry is the vertical line passing through the vertex, with an equation which is the x-value of the vertex

The x-value of the vertex is; x = 2, therefore, the axis of symmetry is the line; x = 2

The reflection of a point (x, y) about the vertical y-axis is the point (-x, y)

Therefore, the image of the reflection of the y-intercept, (0, 4) about the line x = 2 will be the point (4, 4)

The reflection of the point (1, 1), about the line x = 2 is the point (3, 1)

The above points can be used to graph the parabola, y = x² - 4·x + 4.

Please find attached the graph of the parabola created with MS Excel.

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Answer:

not 100% confident but I think this is at least close

Step-by-step explanation:

solve for one variable

1. x-5y=2

x=2+5y

plug this in to another equations and simplify

2. (2+5y)-y=16

2+4y=16

4y=14

y=3.5

this can be plugged in to all other equations to find x

1. x-5(3.5)=2

x-17.5=2

x=19.5

2. x-(3.5)=16

x=19.5

3. 2x-(3.5)=5

2x=8.5

x=4.25

4. x-3(3.5)=4

x-10.5=4

x=14.5

Answer:

look to rule number five

Step-by-step explanation:

Rule Number 5 best explains the answer

Answer:

teal, red, purple are the correct answers

Answer:

vp chop go go go go go go go go go

Answer:

3.4567 is a rational number

Step-by-step explanation:

An irrational number has no ending while a rational number does. An irrational number can not be written as a fraction while a rational number can. Basically, all you have to do to figure out if a number is rational or irrational is to figure out if it has an ending.

For example, if you had 234.888888888 irrational but if the number was 234.98989654 then it would be rational

The binomial theorem states that: \((x + y)^n = \sum_{k=0}^n{n\choose k} x^{n-k}y^k\). So, the binomial expansion of (2x - 3y)⁵ is: \(32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5\).

Now, let's use the Binomial Theorem to find the binomial expansion of (2x - 3y)⁵. We will have to find the coefficients for each term. So, let's get started. n = 5x = 2xy = -3[nCr = n! / (r! * (n-r)!)]

Term k = 0: \( {5 \choose 0} (2x)^5 (-3y)^0\) = 32x⁵

Term k = 1: \({5 \choose 1} (2x)^4 (-3y)^1\) = -240x⁴y

Term k = 2: \({5 \choose 2} (2x)^3 (-3y)^2\) = 720x³y²

Term k = 3: \({5 \choose 3} (2x)^2 (-3y)^3\) = -1080x²y³

Term k = 4: \({5 \choose 4} (2x)^1 (-3y)^4\) = 810xy⁴

Term k = 5: \({5 \choose 5} (2x)^0 (-3y)^5\) = -243y⁵

Now we can combine all of these terms to form the binomial expansion of (2x - 3y)⁵:\((2x - 3y)^5 = 32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5\)

Therefore, the binomial expansion of (2x - 3y)⁵ is: \(32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5\).

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Answer:

x = 3

y = 7

Step-by-step explanation:

3x - y = 2                                  Y = 2x - 1

3x - 2x - 1 = 2

x - 1 = 2

x = 3

Now put 3 in for x and solve for y

3(3) - y = 2

9 - y = 2

- y = -7

y = 7

Let's check

3(3) - 7 = 2

9 - 7 = 2

2 =2

So, x = 3 and y = 7 is the correct answer.

Plot 1: -0.92

Plot 2: -0.76

Plot 3: 0.00

Plot 4: 0.66

Plot 5: 0.82

In order to determine the Pearson correlation coefficient for each scatter plot, you should consider the direction of the relationship and how closely the points fit the line.

For the first scatter plot with a Pearson correlation coefficient of -0.92, you can see that there is a strong negative relationship between the variables. This means that as the values of one variable increase, the values of the other variable decrease. The points in the scatter plot fit the line very closely, indicating a strong correlation.

For the second scatter plot with a Pearson correlation coefficient of -0.76, you can see that there is a negative relationship between the variables, but the points do not fit the line as closely as in the first scatter plot. This indicates a weaker negative correlation.

For the third scatter plot with a Pearson correlation coefficient of 0.00, you can see that there is no relationship between the variables. The points are scattered randomly and do not follow a discernible pattern. This indicates a correlation of 0.

For the fourth scatter plot with a Pearson correlation coefficient of 0.66, you can see that there is a positive relationship between the variables. This means that as the values of one variable increase, the values of the other variable also increase. The points fit the line fairly closely, indicating a moderate positive correlation.

For the fifth scatter plot with a Pearson correlation coefficient of 0.82, you can see that there is a positive relationship between the variables, and the points fit the line very closely. This indicates a strong positive correlation.

Based on these observations, you can match the Pearson correlation coefficient with the corresponding scatter plot as follows:

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Answer:

The sum of their ages is 29, which we can express as the equation:

P + (P - 11) = 29

Simplifying the equation:

2P - 11 = 29

Adding 11 to both sides:

2P = 40

Dividing both sides by 2:

P = 20

Therefore, Pete's age, represented by "P," is 20 years old.

Answer:

Step-by-step explanation:

area of top face = π15² = 225π in²

volume = 225π × 40 = 9000π ≅28,260 in³

Answer:

\( {x}^{2} = {(2x - 1)}^{2} \\ {x}^{2} = 4 {x}^{2} - 4x + 1 \\ 3 {x}^{2} - 4x + 1 = 0 \\ (x - 1)(x - \frac{1}{3} ) = 0 \\ \therefore \: x = 1 \: or \: x = \frac{1}{3} \)

Answer:

A) 13/20

Step-by-step explanation:

65% in simplest form,

65/100

= 13/20 (Divided by five)

Answer:

\(\frac{13}{20}\).

Step-by-step explanation:

We can begin by converting 65% to a fraction over 100. 65% converts to 0.65, or \(\frac{65}{100}\).

We can simplify this down. Both 65 and 100 share a common factor of 5, which allows us to produce a new fraction:

\(\frac{65}{100} = \frac{13}{20}\)

Therefore, the simplified version is \(\frac{13}{20}\).

We substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

The given system of equations are 2x-1/3y = -2...(1)

3x+y=1...(2)

We solve this system of equations by using substitution method.

Let us solve for x in equation to substitute it in equation (2).

2x=-2+1/3y

Divide both sides of equation by 2.

x=-1+1/6y

Now plug in the value of x in equation 2.

Hence, we substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

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Answer: x = 2,340 homes without children

There are 2,340 homes without children.

Step-by-step explanation:

'x' represent the number of homes without children

'y' represent the number of homes with children

x : y = 9 : 7

Since the total number of homes is 4160 means x + y = 4160.

From x + y = 4160 follows y = 4160 - x.

Plug y = 4160 - x into x : y = 9 : 7

x : (4160 - x) = 9 : 7