Given RP = 22, RA = 6, and PQ is tangent to .R at Q, find PQ.

Answer:

x=1, x=15

Step-by-step explanation:

[tex]x^2+16x=-15\\x^2+16x+(8)^2=-15+8^2\\x^2+16x+64=-15+64\\(x+8)^2=49\\\sqrt{(x+8)^2=49} \\x+8=+-7\\x=8-7 = 1\\x=8+7=15[/tex]

Step-by-step explanation:

csc(x) = 1/sin(x)

We know that sin(-x) = -sin(x), so we can rewrite csc(-176°) as:

csc(-176°) = 1/sin(-176°) = -1/sin(176°)

Now, we need to find sin(176°) without a calculator. We can use the fact that the sine function has period 360°:

sin(x) = sin(x - 360°)

Therefore, we can subtract 360° from 176° until we get an angle between 0° and 360°:

176° - 360° = -184° + 360° = 176° - 360° = -184° + 360° = ...

We can continue this process until we get an angle between 0° and 360°. Notice that after each subtraction of 360°, the sine function is negated:

sin(176°) = -sin(-184°) = sin(176° - 360°) = -sin(-184° + 360°) = ...

We can continue this process until we get an angle between 0° and 360°:

sin(176°) = -sin(-184°) = sin(176° - 360°) = -sin(-184° + 360°) = sin(176° - 720°) = -sin(-544°) = sin(544°)

Now, we need to find the sine of 544°, which is equivalent to the sine of 544° - 360° - 360° = -176°. We know that sin(-x) = -sin(x), so:

sin(544°) = -sin(-176°) = sin(176°)

Therefore:

csc(-176°) = -1/sin(176°)

Now, we can use the fact that sin^2(x) + cos^2(x) = 1 to find cos(176°):

sin^2(176°) + cos^2(176°) = 1

cos^2(176°) = 1 - sin^2(176°)

cos(176°) = ±sqrt(1 - sin^2(176°))

Since 0° ≤ 176° ≤ 180°, the cosine function is negative:

cos(176°) = -sqrt(1 - sin^2(176°))

Substituting this into the formula for csc(-176°), we get:

csc(-176°) = -1/sin(176°) = -1/(-sqrt(1 - cos^2(176°))) ≈ -17.204

Therefore, the value of csc(-176°) to the nearest thousandth is -17.204.

Answer:

(18, -14), 7

Step-by-step explanation:

y - (y-intercept) = slope (x - (x-intercept))

James should run along the shore for approximately 16.667 meters before jumping into the water to reach the child in the shortest possible time.

Let's call the distance James should run along the shore "x". Then, using the Pythagorean theorem, we can set up the following equation to represent the total distance James will travel to reach the child:

Simplifying and solving for x, we get:

Therefore, James should run along the shore for approximately 16.667 meters before jumping into the water to reach the child in the shortest possible time.

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Answer: 2.43082 & 20.56918

Step-by-step explanation: The two numbers with the product of -50 and the sum of 23 are the numbers in the answer box.

Step-by-step explanation:

1.

a. ∠ADC = 40° + 30° = 70°

b. ∠DBC = 45° (given)

c. ∠AEB (reflex) = 80° + 100° + 80° = 260° (a reflex angle has to be less than 360° and greater than 180°)

d. ∠BCD = 50° + 50° = 100°

.

2.

a. I added 2 photos of my drawings

b. 47° - acute (less than 90°)

147° - obtuse (greater than 90°, less than 180°)

247° - reflex (greater than 180°, less than 360°)

347° - reflex (greater than 180°, less than 360°)

.

3.

a.The sum of the triangle's angles is equal to 180°

i. 180° - 45° - 75° = 60°

ii. 180° - 8° - 11° = 161°

iii. 180° - 54° - 54° = 72°

iv. 180° - 138° - 21° = 21°

b. The third and the fourth, because they have two identical angles

.

4.

Quadrilateral's sum of angles is equal to 360°

a. 360° - 72° - 97° - 113° = 78°

b. 360° - 55° - 55° - 155° = 95°

c. 360° - 77° - 77° - 77° = 129°

.

5. a. No, because then they won't form a total of 360°, since each of them is greater than 90°

b. Yes, because then they would form a total of 360° (the fourth angle must be acute)

c. Yes, because it would still be possible for the sum of quadrilateral's angles to be 360° (the remaining 3 angles must be acute)

d. No, because 2 reflex angles would already form a minimum of 360° (or even more), that has to be the sum of 4 angles, so it wouldn't be possible for a quadrilateral to have only 2 angles

The angle of 2 = (7x+13) is  ∠1 = 146°,  ∠2= 34°, ∠3 =34° ∠4= 146°

and angle 8 = (10x-44) is  ∠5 =146°, ∠6= 34°, ∠7 = 34°, ∠8= 146°

An angle is a figure obtained from two lines or rays that have the same termination in plane geometry. The common terminal of the two rays is known as the vertex.

In the given question, ∠8= ∠5 = 10x-44

∠1=7x+13

As the corresponding angles on the same side of transversal are equal,

10x-44 = 7x+13

3x = 57

x = 19

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Answer:

Step-by-step explanation:

about 61

Answer:

To find the average (also known as the arithmetic mean) of the data values, we need to divide the sum of the values by the number of values. We are given the sum of 12 data values, which is 942. So:

Average = Sum of values / Number of values

Average = 942 / 12

We can simplify this by dividing both the numerator and denominator by their greatest common factor, which is 6:

Average = (942 ÷ 6) / (12 ÷ 6)

Average = 157 / 2

Average = 78.5

Therefore, the average of the 12 data values is 78.5.

Step-by-step explanation:

The equation we can use to find d, the total length of Alicia's trip in miles, is: 260 = (4/5)d

Let d be the total length of Alicia's trip in miles. According to the problem, the distance she drove to visit her grandparents is 4/5 of the total distance, so we can write:

260 = (4/5)d

To find the total distance d, we can solve this equation for d. First, we can multiply both sides by 5/4 to isolate d:

260 x 5/4 = (4/5)d x 5/4

325 = d

Therefore, the equation we can use to find d, the total length of Alicia's trip in miles, is: 260 = (4/5)d and the distance is d = 325

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Answer:

Using the Pythagorean theorem, we know that in a right-angle triangle, we have:

a^2 + b^2 = c^2

where c is the hypotenuse.

From the given information, we have:

ab = 11 - x

a = x

b = 11

c = 11 (given)

We can use the given values to eliminate a or b from the Pythagorean theorem:

a^2 + (11 - x)^2 = 11^2

Expanding and simplifying, we get:

a^2 + 121 - 22x + x^2 = 121

a^2 + x^2 - 22x = 0

Substituting a = x into the above equation, we get:

x^2 + x^2 - 22x = 0

2x^2 - 22x = 0

2x(x - 11) = 0

So, either x = 0 or x - 11 = 0.

Since x cannot be zero (as it represents a length), we have x - 11 = 0.

Therefore, x = 11.

Hence, the value of x in its simplest form with a rational denominator is 11/1 or just 11.

Answer:

[tex]x=11\sqrt{2}[/tex]

Step-by-step explanation:

The given right triangle is an isosceles right triangle since its legs are equal in length (denoted by the tick marks).

Side x is the hypotenuse of the isosceles right triangle.

Given both legs are 11 units in length, we can use Pythagoras Theorem to calculate the length of the hypotenuse.

[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]

As a and b are the legs, and c is the hypotenuse, substitute the following values into the formula and solve for x:

Therefore:

[tex]\implies 11^2+11^2=x^2[/tex]

[tex]\implies 121+121=x^2[/tex]

[tex]\implies 242=x^2[/tex]

[tex]\implies x^2=242[/tex]

[tex]\implies \sqrt{x^2}=\sqrt{242}[/tex]

[tex]\implies x=\sqrt{242}[/tex]

To simplify the radical, rewrite it as a product of prime numbers:

[tex]\implies x=\sqrt{11^2 \cdot 2}[/tex]

[tex]\textsf{Apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}[/tex]

[tex]\implies x=\sqrt{11^2}{\sqrt{2}[/tex]

[tex]\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]

[tex]\implies x=11\sqrt{2}[/tex]

Therefore, the length of side x in simplest radical form is 11√2.

Answer:

it's the 4th graph and for the second one it's vertical shrink by 1/4

Probability that fewer than 129 people in a random sample of 300 did not use the top web browser is approximately 0.0564 for z value.

We must use the normal approximation to the binomial distribution to determine the likelihood that less than 129 individuals in a random sample of 300 persons did not use the most popular web browser. The number of successes in a fixed number of independent trials with the same chance of success in each trial is modelled using the binomial distribution.

Secondly, based on the market share of 51.85%, we must determine the anticipated proportion of 300 participants who did not use the leading web browser:

Estimated percentage of users not using the most popular web browser: 300 * (1 - 0.5185) = 143.55

The standard deviation of the number of participants in a sample of 300 who didn't use the most popular web browser needs to be calculated next:

Standard deviation =[tex]\sqrt{(300 * 0.5185 * 0.4815)}[/tex] = 9.16

We must compute the z value for this value in order to determine the likelihood that fewer than 129 persons did not use the most popular web browser:

z = (129 - 143.55) / 9.16 = -1.59

The probability of a z-score smaller than -1.59 is 0.0564, according to a basic normal distribution table or calculator.

Hence, there is a 0.0564 percent chance that less than 129 out of 300 randomly selected participants did not utilize the most popular web browser.

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a.  the transition matrix P from {u, u2} to {e1, e2} is

P = [u u2]e = | 3 3 |

| 1 -1 |

b.)

the matrix representation of L with respect to {u, u2} is

[L]u = | 0 -3 |

|-4 -3 |

We must determine the coordinates of the basis vectors u and u2 with regard to the standard basis in order to determine the transition matrix from the basis u, u2 to the standard basis e1, e2.

Since u = (3,1) and u2 = (3,-1), we have

[u]e = | 3 | [u2]e = | 3 |

| 1 | |-1|

Hence, the transition matrix P from {u, u2} to {e1, e2} is

P = [u u2]e = | 3 3 |

| 1 -1 |

(b) To find the matrix representation of L with respect to {u, u2}, we need to find the coordinates of L(u) and L(u2) with respect to the basis {u, u2}. We have

L(u) = (-2)(3,1) + (2)(3,-1) = (0,-4)

L(u2) = (-6)(3,1) + (5)(3,-1) = (-3,-3)

Therefore, the matrix representation of L with respect to {u, u2} is

[L]u = | 0 -3 |

|-4 -3 |

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Justification for equation 23x−13=2(x+2) with Distributive Property, Addition or Subtraction Property of Equality, and Division Property of Equality. We also combined and isolated variable. The final solution is x = -1.1905.

Here is a step-by-step justification for each step in the solution of the equation 23x−13=2(x+2):

Step 1: Given

The equation 23x−13=2(x+2) is given as part of the problem statement.

Step 2: Distributive Property

We distribute the 2 on the right side of the equation by multiplying it by both terms inside the parentheses to get 2x + 4. This results in the equation 23x − 13 = 2x + 4.

Step 3: Combine like terms

We combine the like terms on the right side of the equation to get 6x + 12. This results in the equation 23x − 13 = 6x + 12.

Step 4: Distributive Property

We subtract 2x from both sides of the equation to isolate the variable on one side. This results in the equation 21x - 13 = 12.

Step 5: Addition or Subtraction Property of Equality

We add 13 to both sides of the equation to isolate the variable. This results in the equation 21x = 25.

Step 6: Division Property of Equality

We divide both sides of the equation by 21 to solve for x. This results in the solution x = 25/21 or x = -1.1905.

In conclusion, the Distributive Property, Addition or Subtraction Property of Equality, and Division Property of Equality were used to support each step in the solution of the problem 23x13=2(x+2). In order to make the equation simpler and isolate the variable on one side, we additionally combined like terms. x = -1.1905 is the solution's final form.

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The solution to the interest rate problems from part I to part VI can be found below.

Part I:

Part II:

Part III:

Interest = P * ((1 + r/n)^(n*t) - 1)

where P is the principal (in this case, $2500), r is the interest rate per year (0.1799), n is the number of times the interest is compounded per year (365), and t is the time in years (1).

Interest = 2500 * ((1 + 0.1799/365)^(365*1) - 1) = $449.23

Part IV:

If the APR had been 17.99%, compounded daily, for the whole year, the effective interest rate would be the same as the APR, since there is no introductory 0% period.

Effective annual interest rate = 17.99%

Part V:

Part VI:

As calculated in Part I, the interest Oliver would accrue during the first 90 days with the 17.99% APR is $33.53. Since the 0% APR for the first 90 days means he will not accrue any interest during that time, the 0% APR will save him $33.53 in interest.

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Answer:

(H) 5

Step-by-step explanation:

[tex](6)(3)(2y-9)=18 \\ \\ 2y-9=1 \\ \\ 2y=10 \\ \\ y=5[/tex)

General rules or principles that are stated mathematically are known as mathematical theorems.

A theorem is a statement or proposition in mathematics that can be proved using logic and previously established facts or principles. It is a statement that has been shown to be true through a logical and rigorous argument. A theorem is considered to be an important and fundamental concept in mathematics and plays a key role in the development and advancement of the subject. Many famous theorems, such as the Pythagorean Theorem and the Fundamental Theorem of Calculus, have had a profound impact on mathematics and other fields of science.

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Answer:

120ft²

Step-by-step explanation:

SA = 6(8) + (6+8+10) 3

= 48 + (24)(3)

= 48 + 72

= 120ft²

Answer:

572600

Step-by-step explanation:

572.6×1,000= 572600

And 572600 is already expressed as a decimal. Hope it helps.

Answer:

C

Step-by-step explanation:

It can't be A since you can't have a negative inside a square root

It can't be B [tex]-\sqrt{x+2}[/tex] since it would always be negative and the graph starts positive then turns negative at x=4

C makes since since the graph looks sort of like an upside down [tex]\sqrt{x}[/tex] and has an intercept at y=2

It can't be D since after x=2 the inside of the square root would become negative and you can't have a negative inside of a square root

Final outcome is: 1 quart, 2 cups. 2 quarts, 1 pint, and 2 cups are the outcome of removing 1 quart, 2 pints, and 1 cup from 3 quarts and 1 pint.

We must convert all the units to the same level of measurement in order to remove these two mixed volume units. We are aware that 2 pints and 2 cups equal 1 quart. In order to subtract the volumes, we can convert the pint and cup units to quarts.

We begin by converting 1 pint to quarts:

Pints equal half quarts.

The next step is to convert 1 cup to quarts:

1/4 pint is equal to one cup.

Hence, the second mixed unit is:

1.75 quarts are equal to 1 quart, 2 pints, and 1 cup (1 + 2(1/2) + 1/4).

We may now take the volumes away:

3 quarts and a pint minus a pint, a cup, and a quart equals 3 + 1/2 minus 1.75 to 2.75 quarts.

This result can be written as a whole number of quarts plus any leftover pints and cups to return it to mixed units. Since a quart is equal to two pints, we can write:

2.75 quarts equal 2 quarts plus a half-quart.

We may convert the remaining 1/2 quart to pints because 2 cups equal 1 pint:

2 pints from a half-quart

The end result is as a result:

1 quart, 2 cups

Therefore, 2 quarts, 1 pint, and 2 cups are the outcome of removing 1 quart, 2 pints, and 1 cup from 3 quarts and 1 pint.

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Answer:

The ratio of the number of votes in favor of the law to the total number of votes is:

14 (votes in favor of the law) : 50 (total number of votes)

This ratio can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 2:

7 (votes in favor of the law) : 25 (total number of votes)

So the ratio of votes in favor of the law to the total number of votes is 7:25.

Answer: We can use the fact that the sine function is an odd function, which means that:

sin(-x) = -sin(x)

So, we have:

sin(-15 degrees) = -sin(15 degrees)

We can use the sum and difference identity for sine, which states that:

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

Letting a = 45 degrees and b = 30 degrees, we get:

sin(45 degrees - 30 degrees) = sin(45 degrees)cos(30 degrees) - cos(45 degrees)sin(30 degrees)

We can use the fact that cos(45 degrees) = sin(45 degrees) = √2 / 2 and cos(30 degrees) = √3 / 2 and sin(30 degrees) = 1 / 2 to simplify:

sin(15 degrees) = (√2 / 2)(√3 / 2) - (√2 / 2)(1 / 2)

sin(15 degrees) = (√6 - √2) / 4

Therefore, we have:

sin(-15 degrees) = -sin(15 degrees) = -[(√6 - √2) / 4] = (-√6 + √2) / 4

So the exact value of sin(-15 degrees) is (-√6 + √2) / 4.

Step-by-step explanation:

The functions h(x) and g(x) are h(x) = -2x³ - 4 and  g(x) = √x - 4

Let's work backwards from the given function f(x) to find g(x) and h(x).

f(x) = √(-2x³ - 4) - 4

We can start by letting h(x) = -2x³ - 4.

This means that g(x) must take the square root of its input and then subtract 4 from the result.

In other words:

g(x) = √x - 4

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The function model and the population of water buffalo is

[tex]P_{current} = P_{estimated} \left(1-\frac{R}{100} \right)^t[/tex]

How to find the population function of decreasing at a certain rate?

Let assume some variable of population and rate change,

 [tex]P_{estimated} = Estimated\ population\ of\ water\ buffalo\\R = Rate\ of\ decreasing\ population\ of\ water\ buffalo\\t = time\ taken\ for\ decrease\\[/tex]

Therefore, the function for population of water buffalo decreasing, using compound interest is

[tex]P_{current} = P_{estimated} \left(1-\frac{R}{100} \right)^t[/tex]

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Hello, I was happy to solve the problem. If you find a bug, post in the comments or click on the report, I will see it and try to fix it as soon as possible.

The answer to this problem: 2

The area of the shaded region is evaluated to be equal to the expression 24z² - 22z + 3

To get the area of the shaded region, we subtract the area of the small square from the area of the bigger square as follows:

area of bigger square = (5z - 2)(5z - 2)

area of bigger square = 25z² - 20z + 4

area of small square = (z + 1)(z + 1)

area of bigger square = z² + 2z + 1

area of the shaded region = 25z² - 20z + 4 - (z² + 2z + 1)

area of the shaded region = 25z² - 20z + 4 - z² - 2z - 1

area of the shaded region = 24z² - 22z + 3

Therefore, the area of the shaded region is evaluated to be equal to the expression 24z² - 22z + 3

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Find the difference between year 4 and year 5 salary.

[tex]32,625 - 31,900 = 725[/tex] (rate of change)

Multiply [tex]4 \times 725[/tex] then subtract that number from 31,900 to find out base salary

[tex]4\times 724 = 2,900[/tex]

[tex]31,900 - 2,900 = 29,000[/tex]

That's the constant.

So,

[tex]f(n) = 725n + 29,000[/tex]