A given city is at 35°S and 200°W. How far is it from this city to A. the North Pole and B. the Equator C. the south pole
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The side length that prove a right angle triangle is √2, √3 and √5.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, a right angle triangle can be proved by using the Pythagoras's theorem as follows:

Hence,

c² = a² + b²

where

Therefore,

(√2)² + (√3)² = (√5)²

Hence, the right angle triangle is the triangle with sides √2, √3 and √5.

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I can't really see the graph clearly but I think that the x-intercepts should be (-16/7, 0) and (32/7, 0).

Answer:

x-intercepts:  -2, 4

Step-by-step explanation:

The given graph shows a parabola that opens downwards.

The y-intercept is the point at which the curve crosses the y-axis, so when x = 0. From inspection of the given graph, we can see that the parabola crosses the y-axis when y = 8. Therefore, the y-intercept is (0, 8).

The x-intercepts are the points at which the curve crosses the x-axis, so when y = 0. From inspection of the given graph, we can see that the parabola crosses the x-axis when x = -2 and x = 4. Therefore, the x-intercepts are (-2, 0) and (4, 0).

Answer:

B , D , A

Step-by-step explanation:

(4x³ - 4 + 7x) - (2x³ - x - 8)

distribute the first parenthesis by 1 and the second by - 1

= 4x³ - 4 + 7x - 2x³ + x + 8 ← collect like terms

= 2x³ + 8x + 4 ← equivalent to expression B

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

(- 3x² + [tex]x^{4}[/tex] + x) + (2[tex]x^{4}[/tex] - 7 + 4x) ← remove parenthesis

= - 3x² + [tex]x^{4}[/tex] + x + 2[tex]x^{4}[/tex] - 7 + 4x ← collect like terms

= 3[tex]x^{4}[/tex] - 3x² + 5x - 7 ← equivalent to expression D

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

(x² - 2x)(2x + 3)

each term in the second factor is multiplied by each term in the first factor, that is

x²(2x + 3) - 2x(2x + 3) ← distribute parenthesis

= 2x³ + 3x² - 4x² - 6x ← collect like terms

= 2x³ - x² - 6x ← equivalent to expression A

The equation of a parabola with its vertex at the origin includes a negative coefficient 'a', the parabola opens downward. option B.

The equation y = ax² represents a parabola with its vertex at the origin. In this case, if the coefficient 'a' is negative, it determines the direction in which the parabola opens.

When 'a' is negative, the parabola opens downward. This means that the vertex, which is at the origin (0, 0), represents the highest point on the graph, and the parabola curves downward on both sides.

To understand this concept, let's consider the basic equation y = x², which represents a standard upward-opening parabola. As 'a' increases, the parabola becomes narrower. Conversely, when 'a' becomes negative, it flips the parabola upside down, resulting in a downward-opening parabola.

For example, if we have the equation y = -x², the negative coefficient causes the parabola to open downward. The vertex remains at the origin, but the shape of the parabola is now inverted.

In summary, when the equation of a parabola with its vertex at the origin includes a negative coefficient 'a', the parabola opens downward. This can be visually represented as a U-shape curving downward from the origin. So Optyion B is correct.

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Answer: y = 12.6

Step-by-step explanation:

Since x = 2 and y = 6.3 * x, y = 6.3 * 2.

6.3 * 2 is equal to 12.6, so y is 12.6.

Answer:

y = 12.6

Step-by-step explanation:

y = 6.3x                     x = 2

Solve for y.

y = 6.3(2)

y = 12.6

So, the answer is 12.6

a. Mean = 3

Standard deviation = 2

b. The z-scores for each score in the sample are: 1, -1.5, 0.5, 1, -1, -0.5, 0.5.

a. To compute the mean and standard deviation for the sample, we follow these steps:

Calculate the mean (average)

Mean = (sum of all scores) / (number of scores)

Mean = (5 + 0 + 4 + 5 + 1 + 2 + 4) / 7

Mean = 21 / 7

Mean = 3

The mean of the sample is 3.

Calculate the standard deviation

The formula for standard deviation for a sample is given by:

Standard deviation = sqrt((sum of squared differences from the mean) / (number of scores - 1))

First, calculate the squared differences from the mean for each score:

(5 - 3)^2 = 4

(0 - 3)^2 = 9

(4 - 3)^2 = 1

(5 - 3)^2 = 4

(1 - 3)^2 = 4

(2 - 3)^2 = 1

(4 - 3)^2 = 1

Next, sum up these squared differences:

4 + 9 + 1 + 4 + 4 + 1 + 1 = 24

Now, divide this sum by (number of scores - 1):

24 / (7 - 1) = 24 / 6 = 4

Finally, take the square root of this result:

Standard deviation = sqrt(4) = 2

The standard deviation of the sample is 2.

b. To find the z-score for each score in the sample, we use the formula:

z = (X - Mean) / Standard deviation

For each score, we substitute the values into the formula:

X = 5, z = (5 - 3) / 2 = 2 / 2 = 1

X = 0, z = (0 - 3) / 2 = -3 / 2 = -1.5

X = 4, z = (4 - 3) / 2 = 1 / 2 = 0.5

X = 5, z = (5 - 3) / 2 = 2 / 2 = 1

X = 1, z = (1 - 3) / 2 = -2 / 2 = -1

X = 2, z = (2 - 3) / 2 = -1 / 2 = -0.5

X = 4, z = (4 - 3) / 2 = 1 / 2 = 0.5

The z-scores for each score in the sample are:

z = 1, z = -1.5, z = 0.5, z = 1, z = -1, z = -0.5, z = 0.5

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Answer:

Step-by-step explanation:

Answer:

(x + 13)(x - 7) = 69

x² + 6x - 91 = 69

x² + 6x - 160 = 0

(x + 16)(x - 10) = 0

x = 10, so the area of the original square is 100 m².

Answer:

I pass my classes.

Step-by-step explanation:

I had to add this sentence or else it wouldnt allow me to send it.

Answer:

In math, the word "if" can be used for piecewise functions. In piecewise functions, you can see equations where f(x) = x+3 IF x>0 and f(x) = -x IF x<0.

Answer:

Step-by-step explanation:

add it then subtract the value

Answer:

The person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.

Step-by-step explanation:

What is defined as the normal distribution?

A normal distribution is a data set arrangement in which the majority of values cluster inside the center of the range and the remainder taper off symmetrically toward any extreme.

A histogram inside a normal distribution curve is sometimes used to design the curve.

The formula for the normal distribution is;

z = (x - μ)/σ

where,

z = z- score, taken fro table

Mean μ = 110

Standard deviation σ = 15

Sample mean x.

If we want to be in the top 5%, we must outperform 95% of the remaining scores. So we must investigate.

In with us standard normal probability table, look up 0.95 and get the Z score that corresponds to that.

z = 1.7

Put the value in formula ad find x.

1. 7 = (x - 110)/15

x = 25.5 + 110

x = 135.5

x = 136 (whole number)

Thus, the person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.

Answer:

B.     [tex] 9^{\frac{1}{8}x} [/tex]

Step-by-step explanation:

[tex] \sqrt[4]{9}^{\frac{1}{2}x} = [/tex]

[tex] = ({9}^{\frac{1}{4}})^{\frac{1}{2}x} [/tex]

[tex] = 9^{\frac{1}{4} \times \frac{1}{2}x} [/tex]

[tex] = 9^{\frac{1}{8}x} [/tex]

The correct graph of the linear inequality 1/2x - 2y > -6 is the one where a solid straight line has a positive slope and goes through (negative 4, 2) and (4, 4), and everything below and to the right of the line is shaded.

Given the following diagram: We need to find the coordinates of triangle ABC, translate the triangle (-2, 5) and draw the new image on the grid above, and determine the amount each coordinate will move on the x-axis and y-axis during translation.

1. Coordinates of triangle ABC:A = (2, 6)B = (5, 8)C = (6, 3)2. Translation of triangle (-2, 5)The translation of a triangle can be done by adding or subtracting a constant value from the x-coordinates and y-coordinates of each vertex of the original triangle.

For example, if we want to translate a triangle by 3 units to the right and 2 units up, we would add 3 to the x-coordinates and add 2 to the y-coordinates of each vertex of the original triangle. Using this method, we can translate the triangle (-2, 5) as follows:

New coordinates of A = (2 + (-2), 6 + 5) = (0, 11)New coordinates of B = (5 + (-2), 8 + 5) = (3, 13)New coordinates of C = (6 + (-2), 3 + 5) = (4, 8)3. New image of triangle (-2, 5)The new image of the triangle (-2, 5) is shown in the following diagram:4. Amount each coordinate moves on x-axis During translation, each coordinate moves 2 units to the right (from -2 to 0).5. Amount each coordinate moves on y-axis During translation, each coordinate moves 6 units up (from 5 to 11).

Therefore, the coordinates of the translated triangle image are (0, 11), (3, 13), and (4, 8).

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The correct answer is c) =, because the fraction four eighths is equal to the fraction two fourths.

To determine which symbol should go in the box to make the equation true, let's analyze the fractions given and compare their values.

The fraction "two fourths" can be simplified to "one-half" since both the numerator and denominator can be divided by 2. Therefore, "two fourths" is equal to "one-half."

Now, let's look at the fraction "four eighths." We can simplify this fraction by dividing both the numerator and denominator by 4, which gives us "one-half" as well. So, "four eighths" is also equal to "one-half."

Now, based on the given fractions, we have the equation:

(one-half) [BOX] (one-half)

We need to determine the correct symbol to fill in the box.

Looking at the values of the fractions, we see that both "two fourths" and "four eighths" are equivalent to "one-half." Therefore, the correct symbol to make the equation true is the equality symbol (=).

Hence, the correct answer is:

c) =, because the fraction four eighths is equal to the fraction two fourths.

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x² + 3x - 2

(5)² + 3 × 5- 2

25 + 15 - 2

40 - 2

38...

Answer:

a) 50

Step-by-step explanation:

The variance will not change as all the observations are increased uniformly.

Proof:

Variance formula:

[tex]s^{2} = \frac{\sum x_i^{2} }{n} -\frac{(\sum x_i)^{2} }{n^{2} }[/tex]

When the obervations are inc by 20,

[tex]s_1^{2} = \frac{\sum (x_i + 20)^{2} }{n} -\frac{(\sum (x_i + 20))^{2} }{n^{2} }\\\\=\frac{\sum(x_i^{2} + 2*20*x_i + 20^{2} )}{n} - \frac{(\sum x_i +20n)^{2} }{n^{2} } \\\\=\frac{\sum x_i^{2} + 40\sum x_i + 20^{2}n }{n} - \frac{(\sum x_i)^{2} +2*20n\sum x_i + 20^{2} n^{2} }{n^{2} } \\\\= \frac{\sum x_i^{2}}{n} - \frac{(\sum x_i)^{2}}{n^{2} } +\frac{40\sum x_i}{n} + 20^{2} - \frac{40\sum x_i}{n} - 20^{2}\\\\s_1^{2}= \frac{\sum x_i^{2}}{n} - \frac{(\sum x_i)^{2}}{n^{2} }\\\\=s^{2}[/tex]

Therefore variance doesn't change

The system has no solution. Option C is correct.

To solve the given system of equations using row operations, we can write the augmented matrix and perform Gaussian elimination. The augmented matrix for the system is:

1  1 -1 |  6

3 -1  1 |  2

1  4  2 | -34

We'll use row operations to transform the augmented matrix into row-echelon form or reduced row-echelon form. Let's proceed with the row operations:

R2 = R2 - 3R1:

1  1 -1 |  6

0 -4  4 | -16

1  4  2 | -34

R3 = R3 - R1:

1  1 -1 |  6

0 -4  4 | -16

0  3  3 | -40

R3 = R3 + (4/3)R2:

1  1 -1 |  6

0 -4  4 | -16

0  0  0 |  -4

Now, we can rewrite the augmented matrix in equation form:

x +  y -  z =  6

      -4y + 4z = -16

              0 = -4

From the last equation, we can see that it leads to a contradiction (0 = -4), which means the system is inconsistent. Therefore, the system has no solution.

The correct answer is (C) This system has no solution.

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Answer:

ok t means some thing but zero and seven should be solved

To solve for x in the equation v2 = v0^2 + 2ax, we can rearrange the equation to isolate x:

x = (v2 - v0^2) / (2a)

In this equation, v2 represents the final velocity, v0 is the initial velocity, a is the acceleration, and x is the displacement. By substituting the given values of v2, v0, and a into the equation, we can calculate the value of x.

The equation v2 = v0^2 + 2ax is derived from the kinematic equation that relates displacement, velocity, acceleration, and time. By isolating x, we can determine the displacement.

The equation represents the final velocity (v2) as the sum of the square of the initial velocity (v0^2) and the product of twice the acceleration (2a) and displacement (x).

To solve for x, we subtract v0^2 from v2 to obtain (v2 - v0^2), and then divide this difference by 2a. This yields the value of x, which represents the displacement.

By substituting the provided values of v2, v0, and a, we can evaluate the expression and calculate the value of x. This equation is commonly used in physics and mechanics to determine the displacement of an object given its initial and final velocities and acceleration.

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Answer:

y = x + 12

Step-by-step explanation:

y = -x² + x + 12

y intercept form is, y = mx + c

where m = -b / a

the general quadratic equation is,

y = ax² + bx + c

thus, according to the question

m = -1 / -1 = 1

constant, c = 12

thus, the intercept form of the equation would be,

y = x + 12

The person's expenditure is $1,755. (30 words)

To find the expenditure, we need to determine the person's income first. Since the income tax is 13% of the income and is given as $585, we can calculate the income. Dividing the income tax by the tax rate gives us the income. So, $585 divided by 0.13 equals $4,500, which is the person's income.

Now, we can calculate the expenditure. Given that the expenditure is 75% of the income, we can multiply the income by 0.75 to find the expenditure. So, $4,500 multiplied by 0.75 equals $3,375. Therefore, the person's expenditure is $3,375. (120 words)

In summary, the person's expenditure is $3,375. To find this, we first determined the person's income by dividing the given income tax of $585 by the tax rate of 13%, resulting in an income of $4,500.  

Then, we calculated the expenditure by multiplying the income by 0.75 since the expenditure is stated to be 75% of the income. Thus, the person's expenditure is $3,375.

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The cost of Donna's club membership exhibits a non-proportional relationship over time.

The cost of Donna's club membership can be analyzed to determine whether it exhibits a proportional or non-proportional relationship over time.

In this scenario, Donna pays a monthly fee of $80, along with a yearly membership fee of $60.50. To assess the proportionality, we can examine how the cost changes relative to time.

In a proportional relationship, the cost would increase or decrease at a constant rate. For example, if the monthly fee remained constant, the total cost would be directly proportional to the number of months of membership.

However, in this case, the presence of a yearly membership fee indicates a non-proportional relationship.

The yearly membership fee of $60.50 is a fixed cost that Donna incurs only once per year, regardless of the number of months she remains a member.

As a result, the cost is not directly proportional to time. Instead, it has a fixed component (the yearly fee) and a variable component (the monthly fee).

In summary, the cost of Donna's club membership exhibits a non-proportional relationship over time. While the monthly fee is a constant amount, the yearly membership fee introduces a fixed cost that is independent of the duration of her membership.

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Answer:

centre = (5, - 6 ) , radius = 7

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

given

x² + y² - 10x + 12y + 12 = 0 ( subtract 12 from both sides )

x² + y² - 10x + 12y = - 12 ( collect terms in x/ y )

x² - 10x + y² + 12y = - 12

using the method of completing the square

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(- 5)x + 25 + y² + 2(6)y + 36 = - 12 + 25 + 36

(x - 5)² + (y + 6)² = 49 = 7² ← in standard form

with centre (5, - 6 ) and radius = 7

Answer:

Center = (5, -6)

Radius = 7

Step-by-step explanation:

To find the center and the radius of the circle represented by the given equation, rewrite the equation in standard form by completing the square.

To complete the square, begin by moving the constant to the right side of the equation and collecting like terms on the left side of the equation:

[tex]x^2-10x+y^2+12y=-12[/tex]

Add the square of half the coefficient of the term in x and the term in y to both sides of the equation:

[tex]x^2-10x+\left(\dfrac{-10}{2}\right)^2+y^2+12y+\left(\dfrac{12}{2}\right)^2=-12+\left(\dfrac{-10}{2}\right)^2+\left(\dfrac{12}{2}\right)^2[/tex]

Simplify:

[tex]x^2-10x+(-5)^2+y^2+12y+(6)^2=-12+(-5)^2+(6)^2[/tex]

       [tex]x^2-10x+25+y^2+12y+36=-12+25+36[/tex]

       [tex]x^2-10x+25+y^2+12y+36=49[/tex]

Factor the perfect square trinomials on the left side:

[tex](x-5)^2+(y+6)^2=49[/tex]

The standard equation of a circle is:

[tex]\boxed{(x-h)^2+(y-k)^2=r^2}[/tex]

where:

Comparing this with the rewritten given equation, we get

Therefore, the center of the circle is (5, -6) and its radius is r = 7.

The correct statement regarding the translation in this problem is given as follows:

A. The graph of g(x) is the graph of f(x) shifted up 3 units.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

In this problem, we have an addition by 3, hence there is a translation up 3 units.

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The function that matches the graph is of the form:

4cos((pi x)/7) + 1

Graphs of trigonometric functions are graphs used in representing trigonometric functions.

From these graphs, some basic properties such as Amplitude, phase difference, period and vertical shift can be deduced.

From the given graph in the question, it can be seen that the graph crosses the y-axis at it's amplitude (highest point), so its easier to use the cosine relation.

To calculate the midline M:

Use the formula,

M = (maximum + minimum)/2

= (5 + -3)/2 = 2/2 = 1

Vertical shift: It can be seen from the graph that there is a vertical upward shift of 1 unit. C = 1

Amplitude: Maximum value - vertical shift is:

A = 5 - 1 = 4

Period = spacing between repeating patterns. There are 14 units between each peak (peak when x = -14, next peak when x = 0).

k = 2pi/Period;

So: k = 2pi/14 = pi/7

Therefore y = 4cos(pix/7) + 1 is the function that matches the given graph.

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Answer:

39°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

let the other angle be x , then

x + 54° + 87° = 180°

x + 141° = 180° ( subtract 141° from both sides )

x = 39°

that is the other angle is 39°

In a triangle, the sum of all angles is always 180°. To find the third angle in a scalene triangle where two angles are known, subtract the known angles from 180°. In this case, subtracting 54° and 87° from 180° gives a third angle of 39°.

The question refers to finding the third angle in a scalene triangle, where we know two of the angles. A scalene triangle is a triangle where all three sides are of a different length, and therefore all three angles are also different. The sum of the angles in any triangle is always 180°.

To find the third angle in the triangle, you can use the equation: Angle C = 180° - Angle A - Angle B.

So, we subtract the known angles from 180°: Angle C = 180° - 54° - 87° = 39°.

Therefore, the third angle in this scalene triangle is 39°.

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