A triangular prism and its net are shown below. Please answer the questions EASY 20 points

The two points of tangency are (-1,3) and (1,-3).

What is the equation of a tangent to the circle?

The equation of a tangent to a circle is a linear equation that describes a line that touches the circle at exactly one point, without crossing it. A tangent line is perpendicular to the radius of the circle at the point of contact.

Since the line T is tangent to the circle, the radius of the circle drawn to the point of tangency (-1,3) is perpendicular to the line T. Therefore, the center of the circle must lie on the line perpendicular to T at (-1,3).

The equation of the tangent line T can be found by taking the derivative of the equation of the circle and evaluating it at the point of tangency (-1,3):

2x + 2y(dy/dx) = 0

dy/dx = -x/y

At the point (-1,3), dy/dx = -(-1)/3 = 1/3. Therefore, the equation of the tangent line T is:

y - 3 = (1/3)(x + 1)

y = (1/3)x + 10/3

The slope of any line perpendicular to T is -3 (the negative reciprocal of 1/3). The point-slope form of the equation of a line with slope -3 passing through (-1,3) is:

y - 3 = -3(x + 1)

y = -3x

To find the points of tangency, we need to solve the system of equations consisting of the equation of the circle and the equation of the tangent line:

x² + y² = 10

y = -3x

Substituting y = -3x into the first equation, we get:

x² + (9x²) = 10

10x² = 10

x² = 1

x = ±1

Substituting these values of x into y = -3x, we get:

(-1,3) and (1,-3)

Therefore, the two points of tangency are (-1,3) and (1,-3).

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Shape P could have been transformed using a translation, rotation, reflection or a combination of these transformations.

Transformation in maths is a way of changing the position, size or shape of a given object. It involves moving the object from one position to another. This can be done using a combination of translation, rotation, reflection and enlargement.

A translation is when a shape is moved in a straight line and all points are moved the same distance in the same direction. A rotation is when a shape is rotated around a fixed point and all points are moved the same angle. A reflection is when a shape is flipped over a line and all points are reversed on the other side of the line.

In the case of Shape P, since one point was invariant, the transformation must have been either a translation, rotation or a combination of both. A translation would have been impossible as all points are moved the same amount and direction, hence, the invariant point would have been moved. A rotation is possible as all points are moved the same angle, and the angle of rotation could be adjusted to keep the invariant point in the same place. A combination of both of these transformations could also have been used to keep one point invariant.

Overall, Shape P could have been transformed using a translation, rotation, reflection or a combination of these transformations. In this case, the transformation must have been either rotation or a combination of both translation and rotation. The angle of rotation or the combination of translation and rotation would have been adjusted to keep the invariant point in the same place.

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The measure of angle x to the nearest tenth of a degree is 51.8°

The figure in the image is a right triangle.

From the image;

To solve for the measure of angle x, we use one of the six (6) trigonometric ratio.

Sine = Opposite / Hypotenuse.

Plug in the given values and solve for angle x.

sin( x ) = 11 units / 14 units.

Take the sine inverse.

x = sin⁻¹( 11/14 )

x = 51.7867

x = 51.8 degrees.

Therefore, the value of x is 51.8 degrees.

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Answer: they small angel is 12

Step-by-step explanation:because the third angle is 36 and 12 times three is 36  

When x = 5, y =  9 / 11

When x = 0, y = -1 / 6

when x = -6, y = -13

When x = 5

we would have

[tex]y = \frac{2(5) - 1}{5 + 6}[/tex]

y = 10 - 1 / 11

y = 9 / 11

when the value of x = 0

[tex]y = \frac{2(0) - 1}{0 + 6}[/tex]

y = -1 / 6

When the value of x = -6

[tex]y = \frac{2(-6) - 1}{-6 + 6}[/tex]

y = -12 - 1 / 0

y = -13 / 0

y = -13

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The average rate of change of a function f(x) over the interval [a, b] is given by the formula:

average rate of change = (f(b) - f(a)) / (b - a)

In this case, the function is f(x) = 2x^3 - x and the interval is [4, 6]. So we have:

f(4) = 2(4)^3 - 4 = 124

f(6) = 2(6)^3 - 6 = 330

Therefore, the average rate of change of f(x) over [4, 6] is:

(330 - 124) / (6 - 4) = 103

So the average rate of change of the function f(x) over the interval [4, 6] is 103.

Answer:

151

Step-by-step explanation:

Average Rate of Change Formula

[tex]\frac{f(b)-f(a)}{b-a}\\\frac{f(6)-f(4)}{6-4} \\\frac{((2*6^3)-6)-((2*4^3)-4)}{2} \\\frac{(432-6)-(128-4)}{2} \\\frac{426-124}{2}\\\\ \frac{302}{2} = 151[/tex]

If you have trouble remembering the rate of change formula, it's the same as the slope formula.

[tex]f(b) = y_2\\f(a) = y_1\\b = x_2\\b = x_1\\slope = \frac{y_2-y_1}{x_2-x_1} \\[/tex]

Similarly to the slope formula, it doesn't matter which point you set up to be the second coordinate, as long as it is consistent across the numerator and denominator.

The linear regression equation for the data-set in this problem is given as follows:

y = -1.04x + 9.57.

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are usually given in a scatter plot or in a table.

The seven points that represent the data-set for this problem are given as follows:

(1, 10), (2,6), (3, 3), (4,10), (5, 4), (6, 3), (7, 2).

Inserting these points into the linear regression calculator, the linear regression equation for the data-set in this problem is given as follows:

y = -1.04x + 9.57.

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Answer:

Leaving equation Q the same, multiply both sides of equation P by -5.

(y + z = 6) × -5

The greatest integer value for x​ is -8

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

|x| - 5|x + 6 = 0

Express properly

So, we have

|x| - 5|x + 6| = 0

This gives

|x| = 5|x + 6|

When both sides of the equation are compared, we have

x = 5x + 30

So, we have

4x = -30

Divide by 4

x = -7.5

Approximate to an integer

x = -8

Hence, the value of x is -8

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Answer:

A. x < 0

Step-by-step explanation:

function y is increasing from -8 to 0 as x is increasing from -4 to 0. Therefore the answer is A

Answer:

P(5) ≈ 0.0537.

Step-by-step explanation:

La fórmula para la distribución binomial es:

P(K) = (n choose k) * p^k * (1-p)^(n-k)

donde "n" es el número de ensayos, "p" es la probabilidad de éxito en cada ensayo, "k" es el número de éxitos y "n choose k" representa el número de formas de obtener k éxitos en n ensayos.

(a) Para n = 5, p = 1/4 y k = 2:

P(2) = (5 choose 2) * (1/4)^2 * (3/4)^3

= 10 * 1/16 * 27/64

= 0.2637

Por lo tanto, P(2) ≈ 0.2637.

(b) Para n = 10, p = 1/2 y k = 7:

P(7) = (10 choose 7) * (1/2)^7 * (1/2)^3

= 120 * 1/128 * 1/8

= 0.0820

Por lo tanto, P(7) ≈ 0.0820.

(c) Para n = 8, p = 2/3 y k = 5:

P(5) = (8 choose 5) * (2/3)^5 * (1/3)^3

= 56 * 32/243 * 1/27

= 0.0537

Por lo tanto, P(5) ≈ 0.0537.

In summary, to find m z1, we need to know the relationship between the rail lines and the angles formed by their intersection.

An equation is a mathematical statement that shows the equality of two expressions. It is composed of two sides, separated by an equals sign (=), indicating that the two sides are equivalent in value. An equation may contain variables, which are unknown values represented by letters, as well as constants, which are known values. Equations are used in many areas of mathematics and science to model and solve problems. For example, the equation y = mx + b is a linear equation that describes the relationship between the variables x and y in a straight line, where m is the slope of the line and b is the y-intercept. Equations can be solved by manipulating the variables and using mathematical operations to isolate the unknown value.

Here,

In order to help Carmen find m z1, we need some additional information about the rail lines and the angles involved.

Assuming that z1 is an angle formed by the intersection of two rail lines, we can use the following steps to find its measure:

Identify the other angles formed by the two rail lines. If the rail lines are perpendicular, then z1 is a right angle and has a measure of 90 degrees. If the rail lines are not perpendicular, then they form two pairs of opposite angles, each with a measure of x degrees.

Use the fact that the sum of the measures of all angles formed by the intersection of two rail lines is 360 degrees. This means that the sum of the measures of the two pairs of opposite angles is 360 degrees.

Solve for x by setting the sum of the measures of the two pairs of opposite angles equal to 360 degrees and then solving for x. Once you have x, you can find the measure of any of the angles formed by the intersection of the rail lines, including z1.

For example, let's say that the two rail lines form two pairs of opposite angles, each with a measure of x degrees. Then, we have:

2x + 2z1 = 360 (since the sum of the measures of all angles formed by the intersection of two rail lines is 360 degrees)

Simplifying this equation, we get:

2z1 = 360 - 2x

z1 = (360 - 2x)/2

Now we need more information to find x, such as the measure of one of the opposite angles or the relationship between x and another angle in the figure. Once we know x, we can substitute it into the equation for z1 to find its measure.

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Answer:

the area of the shaded region is 0.9525 (rounded to four decimal places).

Step-by-step explanation:

Since IQ scores above 75 are shaded, we need to find the area to the right of 75 on the normal distribution curve with mean 100 and standard deviation 15.

Using a standard normal table or calculator, we can find the z-score corresponding to 75 as follows:

z-score = (75 - 100) / 15 = -1.67

The area to the right of this z-score is the probability that an IQ score is above 75, which is the shaded area in the graph.

Using a standard normal table or calculator, we find that the area to the right of a z-score of -1.67 is 0.9525 (rounded to four decimal places).

Therefore, the area of the shaded region is 0.9525 (rounded to four decimal places).

Answer:

To find out how many patients smoke, you can multiply the total number of patients by the percentage of smokers:

8500 x 25% = 2125

Therefore, there were 2125 patients who smoke last month in the trust.

Step-by-step explanation:

2125 of the patients are smoker.

Percentages are fractions with 100 as the denominator. It is the relation between part and whole where the value of whole is always taken as 100.

Given that, there were 8500 patients in total last month in the trust. 25% of these are smokers.

We need to find the number of the patients who smoke.

So,

25% of 8500

= 0.25 × 8500

= 25 × 85

= 2125

Hence, 2125 of the patients are smoker.

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Therefore , the solution of the given problem of function comes out to be f(x) = 3x + 1 is the linear function with the specified properties.

Numerous subjects, including mathematics, numbers, and their subsets, as well as building, construction, and both real and fictitious geographic locations, are covered in the mathematics programme. The relationships between various variable elements that all cooperate to create the same outcome are covered in a work. A utility is composed of several unique parts that, when combined, give particular outcomes for each input.

Here,

The slope-intercept form of the linear function f(x) is written as

=>  f(x) = mx + b,

where m is the slope and b is the y-intercept.

We can infer from the listed characteristics that f(0) = 1 and f's slope is 3.

We have the following equation for a line in the point-slope form:

=>  f - 1 = 3(x - 0) (x - 0)

When we simplify this solution, we obtain:

=> f = 3x + 1

Consequently, f(x) = 3x + 1 is the linear function with the specified properties.

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Answer: B and C

Step-by-step explanation:

The answer is [tex]\sqrt{58} = 7.62[/tex]

So, if you draw this down, you will see that the direct distance is hypotenuse c of a right triangle which sides are 3 blocks (1 south and 2 north) and 7 blocks (4 west and 3 east).

Use the Pythagorean theorem:

[tex]c^2 = a^2 + b^2[/tex]

[tex]a = 3[/tex]

[tex]b = 7[/tex]

[tex]c^2 = 3^2 + 7^2[/tex]

[tex]c^2 = 9 + 49[/tex]

[tex]c^2 = 58[/tex]

[tex]c = \sqrt{58}[/tex]

[tex]c = 7.62[/tex]

The 5 foot 5 tall lady will cast a shadow of approximately 4.4 ft.

Given that, a 6 foot 2 man casts a shadow of 5 feet. Also, a lady is 5 foot 5 and we find the shadow she casted.

We can solve this problem by setting up a proportion:

The height and shadow length are proportional, so we can write:

6 feet 2 inches : 5 feet = 5 feet 5 inches : x

where x is the length of the shadow cast by the lady.

To solve for x, we can cross-multiply:

(6 feet 2 inches) × x = (5 feet) × (5 feet 5 inches)

To simplify the calculation, we can convert all the lengths from feets to inches:

Note: 1 ft = 12 in

(74 inches) × x = (60 inches) × (65 inches)

Now we can solve for x:

x = (60 inches)  × (65 inches) / (74 inches)

x = 3900/74

x = 52.70 inches

Convert back to ft

x = 4.4 ft

Therefore, the lady will cast a shadow of approximately 4.4 ft.

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Answer:

Step-by-step explanation:

a. To find the rate at which the x-coordinate of the bug is increasing when the bug is at the point (4, 16), we need to differentiate the equation y=x with respect to time t:

dy/dt = dx/dt

Since the bug is moving along the right side of the parabola y=x, the bug's position can be described by the equation y=x^2. Taking the derivative of both sides with respect to time t, we get:

2y(dy/dt) = 2x(dx/dt)

Simplifying and plugging in the given values for y and dy/dt:

2(16)(9) = 2(4)(dx/dt)

dx/dt = 36 cm/min

Therefore, the x-coordinate of the bug is increasing at a rate of 36 cm/min when the bug is at the point (4, 16).

b. The equation y=x^2 can be rewritten as x=sqrt(y). Differentiating both sides with respect to time t, we get:

dx/dt = 1/(2sqrt(y)) * dy/dt

Substituting y=16 and dy/dt=9, we get:

dx/dt = 1/(2sqrt(16)) * 9

dx/dt = 9/8 cm/min

c. We can use the same equation from part (a) to find the rate at which the y-coordinate of the bug is increasing when the bug is at the point (4, 16):

2y(dy/dt) = 2x(dx/dt)

Substituting y=16, x=4, and dx/dt=36, we get:

2(16)(dy/dt) = 2(4)(36)

Solving for dy/dt:

dy/dt = 18 cm/min

Therefore, the y-coordinate of the bug is increasing at a rate of 18 cm/min when the bug is at the point (4, 16).

d. Let D be the distance the bug is from the origin. We can use the Pythagorean theorem to relate D to x and y:

D^2 = x^2 + y^2

Substituting y=x^2, we get:

D^2 = x^2 + x^4

Taking the derivative of both sides with respect to time t, we get:

2D(dD/dt) = 2x(dx/dt) + 4x^3(dx/dt)

Simplifying and substituting x=4, dx/dt=36, and y=16:

2sqrt(16+16^2)(dD/dt) = 2(4)(36) + 4(4^3)(36)

Solving for dD/dt:

dD/dt = (836 + 44^3*36) / (2sqrt(16+16^2))

dD/dt = 72/(sqrt(17))

Therefore, the distance between the bug and the origin is increasing at a rate of 72/(sqrt(17)) cm/min when the bug is at the point (4, 16).

The rate of change is $1.25 per premium movie watched.

A. $1.25 / 1 premium movie

The rate of change in this scenario is the increase in cost for each additional premium movie watched.

In this case, the rate of change is constant, since the cost per premium movie remains the same regardless of the number of premium movies watched.

Therefore, the rate of change is simply the additional cost per premium movie, which is $1.25.

So, for example, if you watched 10 premium movies, the total cost would be:

$35 + (10 * $1.25) = $47.50

And if you watched 20 premium movies, the total cost would be:

$35 + (20 * $1.25) = $60.00

rate of change = (60 - 47.5) / (20 - 10) = 1.25

In both cases, the rate of change is still $1.25 per premium movie watched.

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Answer:

The first step is to determine the amount of interest charged for the month of December based on the average daily balance:

Average Daily Balance = $5600

Monthly Interest Rate = 2.5%

Interest Charged for December = Average Daily Balance * Monthly Interest Rate * Number of Days in December

Number of days in December is 31.

Interest Charged for December = $5600 * 0.025 * 31 = $4340.00

The total balance on the credit card on January 1 will be the sum of the unpaid balance at the end of December and the interest charged for December:

Total Balance on January 1 = Unpaid Balance at End of December + Interest Charged for December

Total Balance on January 1 = $6900 + $4340.00

Total Balance on January 1 = $11240.00

Rounded to the nearest cent, the total balance on the next billing date January 1 is $11,240.00.

The nearest cent, the total balance on the next billing date, January 1, is $12640.00.

To calculate the total balance on the next billing date, we need to consider the average daily balance for December, the unpaid balance at the end of December, and the monthly interest rate.

The monthly interest rate is 2.5% of the average daily balance. Let's calculate the interest charged for the month of December:

Interest charged = (2.5/100) * Average daily balance

= (2.5/100) * $5600

= $140

Next, let's calculate the total balance on the next billing date, January 1:

Total balance = Average daily balance + Interest charged + Unpaid balance

= $5600 + $140 + $6900

= $12640

Rounded to the nearest cent, the total balance on the next billing date, January 1, is $12640.00.

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Answer:104

Step-by-step explanation:

Answer:

I think the answer is 63%

Step-by-step explanation:

9/10 * 7/10 = 63/100 = 63%

(I am not fully sure.)

In response to the given question, we can state that As a result, the square answer is (D) 1 square yard.

In Euclidean geometry, a square is an equilateral quadrilateral having four equal sides and four equal angles. It is also known as a rectangle with two adjoining sides that have the same length. A square is an equilateral quadrilateral because it has all four equal sides and all four equal angles. Square angles are 90 degree or straight angles. Moreover, the square's diagonals are evenly spaced and divide at a 90-degree angle. an adjacent rectangle with two equal sides. A quadrilateral with four equal-length sides and four right angles. A parallelogram with two adjacent, equal sides that create a right angle. Rhombus with straight sides.

Then, calculate the length of each side of the square enclosure.

Vanessa utilised the garage's outer wall for one of the sides, so she only needed to create three more sides. She utilised three yards of fence for these three sides, therefore each must be three-thirds of a yard long.

As a result, the area of the enclosure is equal to the length of one side squared:

Area = side length + 1 yard + 1 yard = 1 square yard

As a result, the answer is (D) 1 square yard.

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The exact values of α and β as follows: α = 2π/3 and β = 7π/6. To find the exact value of the given trigonometric expressions, we need to use the Laws of Sines and Cosines.

The Law of Sines is a mathematical equation used to calculate the angles or sides of a triangle when two angles and one side are known. It states that the ratio of the sine of an angle to the length of the opposite side is constant.

The Law of Sines states that the ratio of a side to the sine of its opposite angle is equal for all sides and angles of a triangle. The Law of Cosines states that the square of a side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of those sides multiplied by the cosine of the included angle.

We begin by finding the exact value of tan α. Using the Law of Sines, we can find the measure of α by solving the equation: tan α = 3/4 = sin α/cos α. This can be rearranged to find cos α = 4/3, and then we can use the inverse of cosine to find the exact value of α.

Using the Law of Cosines, we can find the exact value of β by solving the equation: -15/17 = (cos β)2 = (1 - sin2 β). This can be rearranged to find sin β = -4/5, and then we can use the inverse of sine to find the exact value of β.

Finally, using the given conditions, we can find the exact values of α and β as follows: α = 2π/3 and β = 7π/6.

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-15x and 15x is the answer

Answer:

-12y and 12y

Step-by-step explanation:

lets do the multiplication to each equation

[tex]\left \{ {{(6x+3y)(-4)=9(-4)} \atop {(5x+4y)3=10(3)}} \right.[/tex]
this is
[tex]\left \{ {{-24x-12y=-36} \atop {15x+12y=30}} \right.[/tex]
if we add the systems notice the values that do cancel are -12y and 12y
and the results of the adition is
[tex]-9x=-6[/tex]
from this
[tex]x=\frac{-6}{-9} =\frac{2}{3}[/tex]
and you can find y from any of the first equation.

[tex]y=3-2x=3-\frac{4}{3} =\frac{5}3}[/tex]

Answer:

d = kw²

Step-by-step explanation:

The equation that expresses the relationship "d varies directly with the square of w" is:

d = kw² (or kw^2 if you prefer to write it that way!)

where k is the constant of proportionality.

Hope this helps! I'm sorry if it's wrong. If you need more help, ask me! :]

The equation which can be use to find the number of fish f in the bucket before Brooke feeds the dolphins is [tex]4 * 3 = f[/tex].

An equation refers to a mathematical statement that is made up of two expressions connected by an equal sign.

Let f be the number of fish in the bucket before Brooke feeds the dolphins. The equation that can be used to find the value of f is: [tex]4 * 3 = f[/tex]

This equation represents the fact that there are 4 dolphins and each dolphin receives 3 fish, so the total number of fish in the bucket must be equal to 4 times 3. Solving this equation, we get:

f = 12

Therefore, there were 12 fish in the bucket before Brooke fed the dolphins.

Full question "Brooke won the raffle at the zoo and gets to feed the dolphins! The dolphin trainer gives Brooke a bucket of fish to divide evenly among 4 dolphins. Each dolphin gets 3 fish. Which equation can you use to find the number of fish f in the bucket before Brooke feeds the dolphins"

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