i need help in geometry 1

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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The surface area and volume of the square pyramid is 96 squared centimeter and 48 cubic centimeters respectively.

The surface area of a square pyramid is expressed as:

SA = [tex]a^2 + 2a \sqrt{\frac{a^2}{4}+h^2 }[/tex]

The volume of a square pyramid is expressed as:

Volume = [tex]a^2*\frac{h}{3}[/tex]

Where a is the base edge and h is the height.

From the figure a = 6cm

First, we determine the h, using pythagorean theorem:

h² = 5² - (6/2)²

h² = 5² - 3²

h² = 25 - 9

h² = 16

h = √16

h = 4 cm

Solving for surface area:

SA = [tex]a^2 + 2a \sqrt{\frac{a^2}{4}+h^2 }[/tex]

[tex]= a^2 + 2a \sqrt{\frac{a^2}{4}+h^2 }\\\\= 6^2 + 2*6 \sqrt{\frac{6^2}{4}+4^2 }\\\\= 36 + 12 \sqrt{\frac{36}{4}+16 }\\\\= 36 + 12 (5)\\\\= 36 + 60\\\\= 96 cm^2[/tex]

Solving for the volume:

Volume = [tex]a^2*\frac{h}{3}[/tex]

[tex]= a^2*\frac{h}{3}\\\\= 6^2*\frac{4}{3}\\\\= 36*\frac{4}{3}\\\\=\frac{144}{3}\\\\= 48 cm^3[/tex]

Therefore, the volume is 48 cubic centimeters.

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Answer:

|5x - 1| < 1

-1 < 5x - 1 < 1

0 < 5x < 2

0 < x < 2/5

The shaded fraction of the shape is 2/3.

To determine the fraction of the shape that is shaded, we need to compare the shaded area to the total area of the shape.

1. Identify the shaded region in the shape. In this case, we have a shape with some part shaded.

2. Calculate the area of the shaded region. Given the dimensions provided, the area of the shaded region is determined by multiplying the length and width of the shaded part. In this case, the dimensions are 18 mm and 10 mm, so the area of the shaded region is (18 mm) × (10 mm) = 180 mm².

3. Calculate the total area of the shape. The total area of the shape is determined by multiplying the length and width of the entire shape. In this case, the dimensions are 18 mm and 12 mm, so the total area of the shape is (18 mm) × (12 mm) = 216 mm².

4. Determine the fraction. To find the fraction, divide the area of the shaded region by the total area of the shape: 180 mm² ÷ 216 mm². Simplifying this fraction gives us 5/6.

5. Convert the fraction to its simplest form. By dividing both the numerator and denominator by their greatest common divisor, we get the simplified fraction: 2/3.

Therefore, the fraction of the shape that is shaded is 2/3.

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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]

In triangle PAD, using the Pythagorean theorem, we find AD = 5√2. Given that ∠PAQ's opposite side is PQ, which equals 3, we have sin∠PAQ = PQ/AQ = √2/10.

In square ABCD, we are given that points P and Q are on lines BC and CD respectively such that BP=4 and PC=1, DQ=4 and QC=1. Considering triangle PAD, it is a right triangle in the given square, and, using the Pythagorean theorem, we can find the hypotenuse AD as AD = √(5² + 5²) = 5√2. The same reasoning, AD = AQ.

Because ∠PAQ is the angle we are interested in finding the sine of, we know that sin∠PAQ = opposite/hypotenuse. In this case, the opposite side is PQ which we determine is 3 using the given distances (PC+QC). So, sin∠PAQ = PQ/AQ = 3/(5√2) = √2/10. Thus, the sine of angle PAQ is √2/10.

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The equation of the function is y = 1/(x + 3) - 1

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

The reciprocal function shifted down one unit and left three units

The equation of the reciprocal function is represented as

y = 1/x

When shifted down one unit, we have

y = (1/x) - 1

When shifted left three units, we have

y = 1/(x + 3) - 1

Hence, the equation of the function is y = 1/(x + 3) - 1

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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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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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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.

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

Answer:

9.5 years

Step-by-step explanation:

P(t) = P(t)

106.67t+4763.67=308.8t+2844.18

Minus 106.67t on both sides

4763.67=202.13t+2844.18

Minus 2844.18 on both sides

1919.49=202.18t

Solve for t

t=9.4963...

t=9.5 years

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

Answer:

X=11 trust me on my mom

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

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.

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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The value of the expression (-2)(3)º(4) - 2 is -164.

Based on the answer choices provided, none of the options matc.

To solve the expression (-2)(3)º(4)-2, we need to follow the order of operations, which is parentheses, exponents, multiplication, and subtraction.

Let's break down the expression :

(-2)(3)º(4) -2

First, we calculate the exponent:

(-2)(81) - 2

Next, we perform the multiplication:

-162 - 2

Finally, we subtract:

-164

Therefore, the value of the expression (-2)(3)º(4) - 2 is -164.

Based on the answer choices provided, none of the options match the value of -164.

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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:

Step-by-step explanation:

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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The value of the algebric  expression [tex]2^{-3} \cdot 3^{-2}$ is $\frac{1}{72}[/tex].

To compute the expression [tex]2^{-3} \cdot 3^{-2}[/tex], we can simplify each term separately and then multiply the results.

First, let's simplify [tex]2^{-3}[/tex]. The exponent -3 indicates that we need to take the reciprocal of the base raised to the positive exponent 3. Therefore, [tex]2^{-3} = \frac{1}{2^3} = \frac{1}{8}[/tex].

Next, let's simplify 3^{-2}. Similar to before, the exponent -2 means we need to take the reciprocal of the base raised to the positive exponent 2. So, [tex]3^{-2} = \frac{1}{3^2} = \frac{1}{9}[/tex].

Now that we have simplified both terms, we can multiply them together: [tex]\frac{1}{8} \cdot \frac{1}{9}[/tex]. When multiplying fractions, we multiply the numerators together and the denominators together. So, [tex]\frac{1}{8} \cdot \frac{1}{9} = \frac{1 \cdot 1}{8 \cdot 9} = \frac{1}{72}[/tex].

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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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x² + 3x - 2

(5)² + 3 × 5- 2

25 + 15 - 2

40 - 2

38...

118 be the median of a positively skewed distribution with a mean of 122. Option D.

To determine which of the given values could be the median of a positively skewed distribution with a mean of 122, we need to consider the relationship between the mean, median, and skewness of a distribution.

In a positively skewed distribution, the tail of the distribution is stretched towards higher values, meaning that there are more extreme values on the right side. Consequently, the median, which represents the value that divides the distribution into two equal halves, will typically be less than the mean in a positively skewed distribution.

Let's examine the given values in relation to the mean:

A. 122: This value could be the median if the distribution is perfectly symmetrical, but since the distribution is positively skewed, the median is expected to be less than the mean. Thus, 122 is less likely to be the median.

B. 126: This value is higher than the mean, and since the distribution is positively skewed, it is unlikely to be the median. The median is expected to be lower than the mean.

C. 130: Similar to option B, this value is higher than the mean and is unlikely to be the median. The median is expected to be lower than the mean.

D. 118: This value is lower than the mean, which is consistent with a positively skewed distribution. In such a distribution, the median is expected to be less than the mean, so 118 is a plausible value for the median.

In summary, among the given options, (118) is the most likely value to be the median of a positively skewed distribution with a mean of 122. So Option D is correct.

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Note the complete question is

If the mean of a positively skewed distribution is 122, which of these values could be the median of the distribution?

A. 122

B. 126

C. 130

D. 118

Answer:

Step-by-step explanation:

add it then subtract the value

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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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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