Two strait lengths of wire are placed on the ground forming vertical angles. if the mesure of one of the angles formed is 72 what are the other three angles

Answer:

6+5]4

Step-by-step explanation:

Angle A is located in the third quadrant and solved to be a value of  255.522 degrees.

A quadrant refers to fourth division. In a circle, a quadrant represents a quarter of a circle.

In angle calculations, there are 4 quadrants. The first quadrant is between angles 0 to 90 degrees. The second quadrant is between angles 90 to 180 degrees. The third quadrant is between angles 180 to 270 degrees. The fourth quadrant is between 270 to 360 degrees.

The each quadrant is at 90 degrees interval. and the in angle calculations, the rotation is in anticlockwise direction

cos A = 1/4

where 270°

270 degrees represent the third quadrant. Hence angle A is in the third quadrant

solving for angle A

let cos a = 1/4

a = arc cos ( 1/4 )

a = 75.522 degrees ( in first quadrant )

A = a + 180 degrees

A = 75.522 degrees + 180 degrees

A = 255.522 degrees

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In the given angles X is 73 degrees, Y is 107 degrees, and Z will be 73 degrees respectively according to the given figure.

In plane geometry, an angle is a shape made up of two rays or lines with the same terminal.

The vertex, or identical termination of the two rays, is referred to as an angle's sides.

Since we lack a measurement for angular rotation, the angle is a valuable tool for measuring angular distance.

For instance, a meter or an inch is a unit of measurement for linear motion.

So, one is 107° given the four angles.

in the opposite vertical angle:

y = 107°

Since x and z are vertically opposing angles, both will have the same value.

So,

x = z = n

The total angle will now equal 360°.

107 + x + z + y = 360

107 + 2n + 107 = 360

2n = 146 ⇒ n = 73°

Therefore, In the given angles X is 73 degrees, Y is 107 degrees, and Z will be 73 degrees respectively according to the given figure.

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Answer:

Step-by-step explanation:

Trigonometric relations can be used to transform p to q.

To transform x into 1/x, you can press the following sequence of buttons:
1. Press the sin button.
2. Press the cos^-1 button.
3. Press the tan button.

To transform \(\sqrt[2]{x}\) to \(\sqrt[2]{x+1}\), you can press the following sequence of buttons:
1. Press the sin^-1 button.
2. Press the cos button.
3. Press the tan button.

To show that you can get any positive rational number, you can use the fact that any positive rational number can be expressed as a ratio of two positive integers, say p and q. Then, you can press the following sequence of buttons:
1. Press the sin button q times.
2. Press the cos button p times.
3. Press the tan button.

By pressing this sequence of buttons, the calculator will display the desired positive rational number q.

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Answer:

y^2 + x^2 = 8^2

Step-by-step explanation:

Mathematically the equation of a circle is written as;

(y-a)^2 + (x-b)^2 = r^2

Where (a, b) = (0,0)

r = 8

Substituting these values, we have ;

y^2 + x^2 = 8^2

x^2 + y^2 = 64

The maximum amount of fuel that an F1 car can burn during a race, given the specified regulations and a fuel specific gravity of 0.75, is 109.25 kg.

The maximum amount of fuel that an F1 car can burn during a race, we need to consider the fuel limits set by the regulations.

The FIA (Fédération International de automobile) specifies that F1 race cars are allowed a maximum of 110 kg of fuel to start the race. Additionally, they must have at least 1.0 liter of fuel left at the end of the race for fuel sample testing.

To calculate the maximum fuel burn, we need to find the difference between the initial fuel amount and the fuel left at the end. First, we convert the 1.0 liter of fuel to kilograms. The density of the fuel can be determined using its specific gravity.

Since specific gravity is the ratio of the density of a substance to the density of a reference substance, we can calculate the density of the fuel by multiplying the specific gravity by the density of the reference substance (water).

Given that the specific gravity of the fuel is 0.75, the density of the fuel is 0.75 times the density of water, which is 1000 kg/m³. Therefore, the density of the fuel is 0.75 * 1000 kg/m³ = 750 kg/m³.

To convert 1.0 liter of fuel to kilograms, we multiply the volume in liters by the density in kg/m³. Since 1 liter is equivalent to 0.001 cubic meters, the mass of the remaining fuel is 0.001 * 750 kg/m³ = 0.75 kg.

Now, to find the maximum amount of fuel burned during the race, we subtract the remaining fuel mass from the initial fuel mass: 110 kg - 0.75 kg = 109.25 kg.

Therefore, the maximum amount of fuel that an F1 car can burn during a race, given the specified regulations and a fuel specific gravity of 0.75, is 109.25 kg.

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Answer:

$1,699.29

Step-by-step explanation:

Step-by-step explanation:

p< 6b is for p less than 6 times b.

Answer:

6b > p

Step-by-step explanation:

The question is not clear, just in case you are asking the equation.

Answer:

5(-2m - 4) is equivalent to 10m + 20.

Answer:

D) 10m+20

Step-by-step explanation:

To solve for this, we have to solve -5(-2m-4).

To do this, distribute (multiply) -5 to both of the numbers in the parathesis:

-5x-2m

=10m

-5x-4

=20

10m+20

So, D is the correct answer.  Hope this helps :)

The probability of choosing sausage and onion by Rosa's mom from the given 8 different toppings as per given condition is equal to

(1/ ⁸C₂).

As given in the question,

Total number of different toppings = 8

Number of different toppings choose by Rosa's mom randomly = 2

Possibility of choosing sausage and onion (any one) = 1

Total number of outcomes = ⁸C₂

Number of favorable outcomes = 1

Probability of choosing sausage and onion ( exactly ) one topping

= ( Number of favorable outcomes ) / ( Total number of outcomes )

= ( 1/⁸C₂ )

Therefore, the probability when Rosa's mom chooses sausage and onion out of 8 toppings is equal to ( 1/⁸C₂ ).

The above question is incomplete, the complete question is:

A pizza restaurant is offering a special price on pizzas with 2 toppings. They offer the toppings

below:

Pepperoni ,Sausage, Chicken ,  Green pepper , Mushroom ,Pineapple, Ham, Onion

Suppose that Rosa's favorite is sausage and onion, but her mom can't remember that, and she is going to randomly choose 2 different toppings.

What is the probability that Rosa's mom chooses sausage and onion?

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Answer:

1/8c^2

Step-by-step explanation:

Khan Acadmey

Answer: -2, -4, -1

Step-by-step explanation:

\(17-7x > 3(10x-4)+61\\\\17-7x > 30x-12+61\\\\17-7x > 30x+49\\\\-32 > 37x\\\\x < -\frac{32}{37}\)

So, the values of x are -2, -4, -1.

A linear regression model of the form Y = β0 + β1X + ε can be written as:

Yi = β0 + β1Xi + ei .

A linear regression model of the form Y = β0 + β1X + ε can be written as:

Yi = β0 + β1Xi + ei

Where ei is the residual for observation i. The plot of ei against Xi is known as a residual plot. The purpose of a residual plot is to check for non-linearity, unequal error variances, and outliers.

In this case, it appears that there is non-linearity present in the data. There appears to be a curved pattern in the residuals, suggesting that a linear regression model may not be the best approach to analyzing the relationship between Y and X. A transformation of the data, such as taking a logarithm of the variables, could potentially alleviate the non-linearity in the data.  This could potentially improve the fit of the linear regression model.

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The next step to find the y intercepts is the substitute the value of m2 and coordinate of point P in the equation of the line intercepts from equation y= mx + b and then solve for b in each equation.

Bernie wants to write equations in the form of y=mx+b where m stands for slope. The line passing through the point P and that is perpendicular to the s and parallel to the line r.

we are aware that if two lines are parallel then the slopes are equal.

So, m1=m2

and if two lines are perpendicular then product of slopes equal to -1

m1×m2=-1

the y intercepts are the point of intersection between the straight line.

y = mx +b and the y axis. The y intercepts value of y when x=0.

The next step to find the y intercepts is the substitute the value of m2 and the coordinate of point P in the equation of the line intercept from equation y=mx +b and then solve for b in each equation.

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Answer:

x = 14.56

Step-by-step explanation:

angle opposite x is 29° ( 180 - 50 - 101 = 29 )

use the sine rule to determine x:

\( \frac{x}{ \sin(29) } = \frac{23}{ \sin(50) } \\ \frac{x}{ \sin(29) } \times \sin(29) = \frac{23}{ \sin(50) } \times \sin(29) \\ x = \frac{23}{ \sin(50) } \times \sin(29) \\ x = Rationalize(14.55610228078) \\ x = 14.56\)

x = lbs

y = total cost

ABC shipping: $7 + $1x = y

XYZ shipping: $10 + $0.75x = y

We set each equation equal to the other.

$7 + $1x = $10 + $0.75x. Subtract $7 from both sides and subtract $0.75x from both sides

$0.25x = $3. Divide each side by $0.25.

x = 12 lbs

When a package is 12lbs the cost is the same.

Answer:

(B) \(\frac{\sqrt{6} }{9}\)

Step-by-step explanation:

Greatest number that divides 300, 560 and 500 is 20 .

Given numbers : 300, 560 and 500

First let’s find prime factors of 300,560 and 500

300 = 2^2 *3^1 *5^2

560= 2^4 * 7^1 *5^1

500 = 2^2 * 5^3

So,

Here highest common power of 2 is 2

Here highest common power of 3 is 0

Here highest common power of 5 is 1

Here highest common power of 7 is 0

Thus HCF (300, 560 and 500) = 2^2 * 5^1 * 3 ^0 * 7 ^0

=4*5*1*1

= 20

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The value of the derivatives of f df(x, y, z)/dx + df(x, y, z)/dy is 20, when x = 1, y = 1, and z = 1.

To determine df/dt using the chain rule, we need to compute the partial derivatives of f with respect to x, y, and z, as the derivatives of x(t), y(t), and z(t) with respect to t.

We are given that the function as f (x, y, z)= 3x² + xyz + 4y³ z²

To Find df(x, y, z)/dx + df(x, y, z)/dy when x = 1, y = 1, and z = 1.

f (x, y, z)= 3x² + xyz + 4y³ z²

Therefore,

df(x, y, z)/dx = 6x + yz

df(x, y, z)/dy = xz + 12y² z²

Now we have;

df(x, y, z)/dx + df(x, y, z)/dy

6x + yz + xz + 12y² z²

When x = 1, y = 1, and z = 1 then we get;

6 + 1 + 1 + 12

= 20

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The number of buckets of fish that the sea otters fed each day is  7/6 buckets .

In the question ,

it is given that ,

the number of buckets of fish that the dolphin are fed at the Washington aquarium = 1/2 bucket

the sea otters are fed \(2\frac{1}{3}\) times as many as fish .

So , the number of buckets that are fed to otters is = (7/3) × (number of buckets eaten by fish)

Substituting the values of number of buckets eaten by fish ,

we get

= (7/3) × (1/2)

Simplifying further ,

we get ,

= 7/6 buckets .

Therefore , the sea otters are fed 7/6 buckets of fish each day .

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Considering the dimensions of the rectangular prism and it's volume, it is found that:

The volume of a rectangular prism is given by the multiplication of the dimensions of the prism, which are the width symbolized by w, the height symbolized by h and the length symbolized by l, that is:

V = l x w x h.

In the context of this problem, from the image, the dimensions are given as follows:

Then the polynomial expression regarding the volume of the prism is obtained as follows:

V(x) = 2x(x - 3)(2x - 5)

V(x)= 2x(2x² - 11x + 15)

V(x) = 4x³ - 22x² + 30x.

The features of the polynomial expression V(x) = 4x³ - 22x² + 30x is obtained as follows:

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Answer:

54°

Step-by-step explanation:

Here :-

Measure of 6 :-

Answer:

m<6 = m<2 = 54º

Step-by-step explanation:

13x + 9 + 5x + 9 = 180

18x + 18 = 180

18x = 180 - 18

18x = 162

x = 162 / 18

x = 9

13x + 9

13(9) + 9

126

180 - 126

54

m<6 = m<2 = 54º

     The surface area is found by finding the area of all shapes creating the surface, and then adding them together.

Example:

     If we have a 5 x 5 x 5 cube, we will find all six sides. Since 5 x 5 is 25, and 25 x 6 = 150, the surface area of this example cube will be 150 units².

     Why the x 6? Since it is a cube all the sides have the same area, and a cube has 6 sides.

(a) The equation is y ≈ 0.36x + 17.45 (m ≈ 0.36, b ≈ 17.45). (b) The temperature when the crickets chirp 144 times a minute is approximately 356.31 degrees Fahrenheit.

(a) To find the equation of the line that models the relationship between the number of cricket chirps (y) and temperature (x), we can use the given data points (128, 63) and (173, 79).

First, let's find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1)

m = (79 - 63) / (173 - 128) = 16 / 45 ≈ 0.3556 (rounded to 4 decimal places)

Next, let's substitute one of the data points into the equation y = mx + b to solve for the y-intercept (b). Using (128, 63):

63 = 0.3556 * 128 + b

63 = 45.5488 + b

b ≈ 63 - 45.5488 ≈ 17.45 (rounded to 2 decimal places)

Therefore, the equation for the line that models this situation is approximately y = 0.3556x + 17.45.

(b) To find the temperature when the crickets are chirping 144 times a minute, we can substitute 144 for y in the equation y = 0.3556x + 17.45 and solve for x.

144 = 0.3556x + 17.45

0.3556x = 144 - 17.45

0.3556x = 126.55

x ≈ 126.55 / 0.3556 ≈ 356.31 (rounded to 2 decimal places)

Therefore, when the crickets are chirping 144 times a minute, it is approximately 356.31 degrees Fahrenheit (rounded to 2 decimal places).

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Answer:

Value of x = 97 degrees

Step-by-step explanation:

In the given quadrilateral

One angle = 83

2 other angles = 90 degrees each

Sum of all the four angles in a quadrilateral = 360 (Angle Sum Property of     quadrilaterals)

=>90+90+x+83= 360

=>180+83+x = 360

=> 263+x= 360

=>x= 360-263

=>x=97

260 miles / 60 miles = 4 1/3

He would need 4 1/3 more gas:

11.86 x 4 1/3 = 51.39

he would need $51.39

Answer:

-9x-2

Step-by-step explanation:

-7-3x+5-6x

=(-3x-6x) + (-7+5)

=(-9x)+(-2)

= -9x - 2

First, use the associative property of addition to reorder the terms in parentheses. Then, combine like terms and you will get your simplified answer of -9x - 2. Hope this helps!

A large t-statistic indicates a greater difference between the sample means and provides stronger evidence for a significant difference between the populations.

The t-statistic is a measure of the difference between two sample means relative to the variability within the samples. When the population means are different, the difference between the sample means will tend to be larger, which will result in a larger numerator in the t-statistic formula. The larger the difference between the sample means, the greater the evidence for a difference between the populations. In contrast, if the population means are similar, the difference between the sample means will be smaller, resulting in a smaller numerator and a weaker test of significance.

The denominator of the t-statistic formula is the standard error of the mean, which measures the variability of sample means around the population mean. If the sample size is large enough, the standard error of the mean will be small, resulting in a smaller denominator and a larger t-statistic. Therefore, when the population means are different, a larger t-statistic would be expected due to a combination of a larger numerator and a smaller denominator.

In summary, If the population means are different, a large t-statistic would be expected.

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The maximum error we can tolerate for the basketball radius is approximately 3 times the maximum error in the volume divided by (4πr₀²).

To determine the maximum error we can tolerate for the basketball radius given a 5% error in the volume, we can use the formula for the volume of a sphere:

V = (4/3)πr³

Let's denote the original radius as r₀ and the maximum error in the volume as ΔV. The original volume can be expressed as:

V₀ = (4/3)πr₀³

Given that the volume can have a 5% error, we have:

ΔV = 0.05 * V₀

Substituting the expression for V₀, we get:

ΔV = 0.05 * (4/3)πr₀³

Now, we can solve for the maximum error in the radius (Δr) by rearranging the formula:

ΔV = (4/3)π(r₀ + Δr)³ - (4/3)πr₀³

Simplifying the equation, we have:

ΔV = (4/3)π(r₀³ + 3r₀²Δr + 3r₀(Δr)² + (Δr)³ - r₀³)

ΔV = (4/3)π(3r₀²Δr + 3r₀(Δr)² + (Δr)³)

Since we are interested in finding the maximum error, we can neglect the terms that are smaller and consider only the first-order term, which is proportional to Δr:

ΔV ≈ (4/3)π(3r₀²Δr)

Now, we can solve for Δr:

Δr ≈ ΔV / ((4/3)π(3r₀²))

Simplifying further:

Δr ≈ 3ΔV / (4πr₀²)

Therefore, the maximum error we can tolerate for the basketball radius is approximately 3 times the maximum error in the volume divided by (4πr₀²).

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