If BY = 4, YC = 7, XC = 10. Which of the following proportions could be used to solve for AC?

4/7 = 10/AC
7/4 = 10/AC
4/11 = 10/AC
7/11 = 10/AC

To calculate the arc length, multiply the angle in radians (7pi/3) by the radius (3 inches). After simplifying, the arc length for this circle is 21 inches.

To find the arc length for a central angle of 7pi/3 radians in a circle with a radius of 3 inches, we use the formula for arc length, which is the product of the central angle in radians and the radius of the circle.

The formula for the arc length (As) is given by:

As = r times theta

Where:

r is the radius of the circle.

theta is the central angle in radians.

Substituting the given values, we get:

As = 3 inches times 7pi/3 radians

The 7pi/3 terms cancel out the pi/3 from the angle and /3 from the radius, giving us:

As = 3 times 7 inches

The arc length is therefore 21 inches.

The new price of the item after 75% reduction is $11.25.

To find the price of the item after a 75% reduction:

Calculate the amount of the reduction: 75% of $45 is $33.75.

Subtract the reduction from the original price: $45 - $33.75 = $11.25.

The sum of the given geometric series (5 + 25 + 125 + 625 + 3,125 + 15,625) is -78120.

The question is asking for the sum of a geometric series. In a geometric series, each term is multiplied by a common ratio to get the next term. In this case, the first term (a) is 5 and the common ratio (r) is 5 (since we get each term by multiplying the previous one by 5).

The sum (S) of the first n terms of a geometric series can be calculated using the formula S = a * (1 - r^n) / (1 - r). In this case, there are n=6 terms in the series, so we will plug these values into the formula.

Therefore, S = 5 * (1 - 5^6) / (1 - 5). So, the sum of this geometric series is -78120.

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Answer:

5 quarts , 9 pints, 2 gallons

Step-by-step explanation:

Answer:

C. is the answer 1,4 or 5

Step-by-step explanation:

Answer:

1. The six-sided figure can have 4 sides congruent but is not a square.

Step-by-step explanation:

We are given the statement,

'A square is a figure with four congruent sides'.

It is required to find the statement which is the counter-example for the above statement.

For the counter-example, the statement should hold:

1. The figure has 4 congruent sides

2. The figure is not a square.

According to the options, we see that,

The six-sided figure can have 4 sides congruent but is not a square.

Thus, option 1 is true.

A counterexample to the faulty definition will be that A six-sided figure can have four sides congruent.

In conclusion, the correct option is A.

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The range of the function is the distance from the maximum of the function to the minimum of the function. The minimum amount of pairs of plates that you can add to the bar (x) is 0, meaning you add no plates. The maximum amount of plates that you can add to the bar is 6, because this is how many plates come in one weight set. The range of the function is y values, and 0 and 6 are x values, so we must plug these values into the function to find the range values.

f(x) = 20x + 4 = 20(0) + 4 = 0 + 4 = 4

f(x) = 20x + 4 = 20(6) + 4 = 120 + 4 = 124

Therefore, the range of the function is 120 pounds, or from [4, 124].

Hope this helps!

The range of a function is the possible output values of the function. The range of [tex]f(x) =20x + 4[/tex] is [4,124]

Given that:

[tex]f(x) =20x + 4[/tex]

To determine the range of the function, we simply determine the value of f(x) using the input values

When no pair is added (this means x = 0).

So, we have:

[tex]f(0) =20 \times 0 + 4[/tex]

[tex]f(0) = 0 + 4[/tex]

[tex]f(0) = 4[/tex]

When 4 pairs are added (this means x = 4).

So, we have:

[tex]f(4) = 20 \times 4 + 4[/tex]

[tex]f(4) = 84[/tex]

When 6 pairs are added (this means x = 6).

So, we have:

[tex]f(6) = 20 \times 6 + 4[/tex]

[tex]f(6) = 124[/tex]

f(6) is greater than f(4).

i.e. [tex]124 > 84[/tex]

So, the range of the function is: [0,124] or [tex]4 \le x \le 124[/tex]

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Answer:

b. - 0.6

Step-by-step explanation:

Since, the total coordinates from -2 to 10 = 10 - (-2) = 10 + 2 = 12,

Also, if it is divided into 10 congruent segments,

Then, the length of each segment = [tex]\frac{12}{10}[/tex] = 1.2,

That is, the difference between the marked point is 1.2,

So, the marked points from -2 to 10 are,

-2,   -0.8,   0.4,    1.6,   2.8,   4.0,   5.2,   6.4,    7.6,    8.8,    10,

Hence, except -0.6 all points are the marked points,

Option b is correct.

Answer:

Option B is correct

d = 13.8

Step-by-step explanation:

Definition:

If two secant segments are drawn to a circle from the same external point(P),

the product of the length of one secant segment and its external part is equal to product of the length of the other secant segment and its external part.

As per the statement:

Labelled the diagram:

then;

PA = 14 units , AB = 20 units, PC = 16 units and CD = d units

Find PB and PD:

PB = 14+20 = 34 units

PD = 16+d units

then by above definition we have;

[tex]PA \cdot PB = PC \cdot PD[/tex]

⇒[tex]14 \cdot 34 = 16 \cdot (16+d)[/tex]

⇒[tex]476=16 \cdot (16+d)[/tex]

Divide both sides by 16 we have;

[tex]29.75 = 16+d[/tex]

Subtract 16 from both sides we have;

13.75 = d

or

d = 13.75 units

Therefore, the value of d to the nearest tenth is, 13.8

Answer:

B. 24

Step-by-step explanation:

We have been given a data set that represents the math scores of five of Max's classmates. We are asked to find the range of the given data set.

Math score: 98, 76, 100, 88, 82.

Since we know range is the difference between the largest and smallest values of the data set.

[tex]\text{Range}=\text{The largest value of data set - The smallest value of data set}[/tex]

We can see that largest score is 100 and smallest score is 76.

[tex]\text{Range}=100-76[/tex]

[tex]\text{Range}=24[/tex]

Therefore, the range of the given test scores is 24 and option B is the correct choice.

Final answer:

To find the number of sides of a polygon, one can use the relations between interior or exterior angles and the number of sides. For an interior angle of 156 degrees, the polygon has 15 sides. For an exterior angle of 36 degrees, the polygon has 10 sides.

Explanation:

The question is about finding the number of sides of a polygon based on the interior and exterior angles. For part (a), where the measure of each interior angle of a regular polygon is 156 degrees, and for part (b), where the measure of each exterior angle is 36 degrees, we can use specific formulas to find the number of sides.

Part A: Interior Angle 156 Degrees

For a regular polygon, the formula connecting the number of sides (n) to an interior angle (A) is A = [(n-2) * 180] / n. Solving for n when A = 156 degrees gives us:

156 = [(n-2) * 180] / n
Solving this equation yields n = 15, meaning the polygon has 15 sides.

Part B: Exterior Angle 36 Degrees

The measure of each exterior angle of a polygon (E) is related to the number of sides (n) by the formula E = 360 / n. When E = 36 degrees:

36 = 360 / n
Solving for n gives us n = 10. Therefore, the polygon has 10 sides.

If each text message costs $.15, and you have $10, you can send a maximum of 66 text messages after rounding down.

To figure out how many text messages you can send with $10, given that each text message costs $.15, we need to divide the total amount of money ($10.00) by the cost of each text message ($.15).

It's a simple division problem: $10.00 ÷ $.15 = 66.67.

However, you can't send a fraction of a message, so we need to round down to the nearest whole number. So, you can send a total of 66 text messages for $10.

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Answer:

(C) 0.3(10 + 4h) = 0.25(6h)

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