Find the circumference and area of a circle with a diameter of 8 feet. Use 3.14 to approximate the value of
as needed. Include units of measure with proper exponents when applicable.

Answer:

  76 units

Step-by-step explanation:

You want the length of AC in the given triangular pyramid.

The Pythagorean theorem can be used to find the lengths of AD and CD.

  AD² + 40² = 41²

  AD² = 41² -40² = 81 . . . . . = 9²

and

  CD² +40² = 85²

  CD² = 85² -40² = 5625 . . . . . = 75²

It can also be used to find AC:

  AD² + CD² = AC²

  81 + 5625 = AC²

  AC = √5706 = 3√634 ≈ 76

The length of side AC is about 76 units.

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Additional comment

The Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the legs of a right triangle.

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The probability of randomly selecting either a diamond or a 3 from the bag is 100%.

Random selection refers to the process of selecting elements from a group with equal probability of selection.

Probability is a measure of the likelihood of an event occurring, which is usually expressed as a fraction or a decimal.

When it comes to random selection of a diamond or 3, we can use probability to determine the likelihood of either event occurring.

For instance, suppose we have a bag containing 10 numbered balls: 5 of them are diamonds and 5 are threes.

To find the probability of randomly selecting a diamond, we divide the number of diamonds by the total number of balls: P(Diamond) = Number of diamonds/ Total number of balls = 5/10 = 0.5 or 50%

This means that the probability of randomly selecting a diamond from the bag is 50%.

To find the probability of selecting either a diamond or a 3, we add the probability of selecting a diamond to the probability of selecting a 3, since the events are mutually exclusive: P(Diamond or 3) = P(Diamond) + P(3) = 5/10 + 5/10 = 1

This means that the probability of randomly selecting either a diamond or a 3 from the bag is 100%.

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Answer:

AB is not tangent to the circle.

Step-by-step explanation:

A tangent is a straight line that touches a circle at only one point.

The tangent of a circle is always perpendicular to the radius.

Therefore, if AB is tangent to the circle, it will form a right angle with the radius, CA.

To determine if AB is tangent, we can use Pythagoras Theorem.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

If AB is tangent, then angle CAB will be a right angle. So AC and AB would be the legs of the right triangle, and BC would be the hypotenuse.

Therefore:

[tex]AC^2+AB^2=BC^2[/tex]

Substitute the values into the equation:

[tex]7^2+12^2=15^2[/tex]

[tex]49+144=225[/tex]

[tex]193 = 225 \; \leftarrow\; \sf not\;true[/tex]

As 193 ≠ 225, the equation does not hold, hence proving that AB is not tangent to the circle.

So, 'f+t=70' represents the constraint that the total number of $5 bills and $10 bills is equal to 70. And '5f + 10t = 575' represents the condition that the total value of the $5 bills and $10 bills is equal to $575.

a) Quincy might have written a problem involving the number of $5 bills (represented by variable 'f') and the number of $10 bills (represented by variable 't'), with certain constraints and conditions.

Quincy might have written a problem related to a scenario where he needed to determine the number of $5 bills and $10 bills. The problem could involve a specific situation.

b) In this linear system:

'f' represents the number of $5 bills.

't' represents the number of $10 bills.

So, 'f+t=70' represents the constraint that the total number of $5 bills and $10 bills is equal to 70.

In the linear system, 'f' represents the number of $5 bills Quincy has, while 't' represents the number of $10 bills. The equation 'f+t=70' implies that the total number of bills. The second equation, '5f + 10t = 575', represents the condition that the total value of the $5 bills (5f) and the $10 bills (10t) together amounts to $575.

And '5f + 10t = 575' represents the condition that the total value of the $5 bills and $10 bills is equal to $575.

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Answer:the answer is 15 units

Step-by-step explanation:

just took the test

Answer:

(5, 3 )

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

D (5, - 3 ) → (5, - (- 3) ) → (5, 3 )

Answer:

(5,3)

Step-by-step explanation:

got it right on edg

The correct answer is: O How to produce? How much to produce?

The statement "A manufacturing firm employs workers to monitor and maintain specialized machines making small metal parts" answers the economic questions of "How to produce?" and "How much to produce?"

How to produce: The statement indicates that the manufacturing firm has chosen to employ workers to monitor and maintain specialized machines. This suggests that they have made a decision regarding the production process and how they will go about manufacturing the small metal parts.

How much to produce: The fact that the manufacturing firm has employed workers to monitor and maintain the machines implies that they have determined a level of production that is deemed appropriate or necessary. The number of workers and the capacity of the machines can influence the quantity of small metal parts produced.

Therefore, the correct answer is: O How to produce? How much to produce?

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Triangles ZWN and ZXY are similar by the SAS congruence theorem.

The Side-Angle-Side (SAS) congruence theorem states that if two sides of two similar triangles form a proportional relationship, and the angle measure between these two triangles is the same, then the two triangles are congruent.

In this problem, we have that the angle Z is equals for both triangles, and the two sides between the angle Z, which are ZW = ZY and ZV = ZX, form a proportional relationship.

Hence the SAS theorem holds true for the triangle in this problem.

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From the graph, we can see that the parabola intersects the x-axis at two points, which are approximately (-0.5, 0) and (1, 0).

Therefore, the correct answer is: a. (1, 0) and (-0.5, 0)

To sketch the graph of the quadratic function y = -2x² + x + 1 and determine the x-intercepts, we can use a graphing calculator or analyze the equation directly.

Here's the visualization and explanation of the graph:

The graph of a quadratic function is a parabola.

The general form of a quadratic equation is y = ax² + bx + c,

where a, b, and c are constants.

In this case, we have y = -2x² + x + 1.

The coefficient of x², which is -2, tells us that the parabola opens downward.

The vertex of the parabola can be found using the formula x = -b / (2a). Plugging in the values from our equation, we get x = -(1) / (2[tex]\times[/tex] (-2)) = 1/4.

So, the x-coordinate of the vertex is 1/4.

To find the y-coordinate of the vertex, we substitute the x-coordinate into the equation: y = -2(1/4)² + (1/4) + 1 = -1/8 + 1/4 + 1 = 1 + 1/4 - 1/8 = 1 + 2/8 - 1/8 = 1 + 1/8 = 9/8.

Now that we have the vertex of the parabola, which is (1/4, 9/8), we can sketch the graph.

-1/2  1/4    1/2

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