Which of these could be the value of x in
the triangle below?
42°
C
A 5
B 6
38
53
A
85
© 8
10
26
B

Step-by-step explanation:

To determine whether a triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Let's denote the three sides of the given triangle as a = 23, b = 30, and c = 19. We can check if these side lengths satisfy the Pythagorean theorem as follows:

c^2 = a^2 + b^2

19^2 = 23^2 + 30^2

361 = 529 + 900

Since 361 is not equal to 529 + 900, we can see that the given triangle is not a right triangle.

There is no stationary point at x = 2. The nature of the curve at x = 2 cannot be determined since there is no stationary point.

To verify that the curve has a stationary point at x = 2, we need to find the derivative of the equation and set it equal to zero.

Given the equation:

y = 2x + 1/(x-1)²

Let's find the derivative dy/dx:

dy/dx = d/dx [2x + 1/(x-1)²]

To find the derivative, we can use the power rule and the chain rule. Let's differentiate each term separately:

For the first term, 2x, the derivative is 2.

For the second term, 1/(x-1)², we can rewrite it as (x-1)^(-2) to apply the power rule. The derivative is then:

d/dx [(x-1)^(-2)] = -2(x-1)^(-3) * d/dx (x-1)

Using the chain rule, d/dx (x-1) = 1, so the derivative becomes:

-2(x-1)^(-3) * 1 = -2/(x-1)^3

Now, let's set dy/dx equal to zero and solve for x:

-2/(x-1)^3 = 0

This equation is satisfied when the numerator is equal to zero:

-2 = 0

However, -2 is not equal to zero, which means there is no x value that makes dy/dx equal to zero.

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Answer:

Step-by-step explanation:

sin 325=sin (360-35)=-sin 35=-t

cos 325=cos (360-35)=cos  35=√(1-sin²35)=√(1-t²)

tan 215=tan (180+35)=tan 35

[tex]=\frac{sin~35}{cos~35} \\=\frac{-t}{\sqrt{1-t^2} }[/tex]

The proposition X^2 > 0 for every real number x is true.

We are given that;

The equation x^2 > 0

Now,

The square of any real number is always greater than or equal to zero.

An example of a mathematical proposition is “For all real numbers x, x + 1 = 2.” This is a proposition because it makes a claim about all real numbers x.

Therefore, by the given function X^2 > 0 the answer will be true.

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Using cosine addition formula, the value of cos(a + b) is -16/25

Using cosine addition formula, the exact value of cos (a + b) is calculated as;

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

Our given data;

cos a = 4/5,  0 < a < π/2

cos b = 5/13, -π/2 < b < 0

Using Pythagorean identity;

sin a and sin b;

sin² x + cos² x = 1

To solve for a;

sin a = √(1 - cos² a) = √(1 - (4/5)²) = √(1 - 16/25) = √(9/25) = 3/5

Solving for b;

sin b = √(1 - cos² b) = √(1 - (5/13)²) = √(1 - 25/169) = √(144/169) = 12/13

Substituting the values into cosine addition formula

cos(a + b) = (4/5) * (5/13) - (3/5) * (12/13)

cos(a + b) = (20/65) - (36/65)

cos(a + b) = -16/65

Therefore, the exact value of cos(a + b) is -16/65.

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its:

[tex]\pi \times {r}^{2} \times h[/tex]

The passing grade should be set to 10 out of 15, which means a student needs to get at least 10 correct answers to pass the quiz.

Let X be the number of correct answers a student gets by guessing on each question. Since each question is true/false, the probability of guessing correctly is 0.5. Then, X follows a binomial distribution with parameters n = 15 and p = 0.5.

To find the passing grade, we need to find the minimum number of correct answers a student needs to pass the quiz. Let k be the passing grade. Then, the probability of passing by guessing is:

P(X ≥ k) = 1 - P(X < k)

Using the binomial probability formula, we can calculate:

P(X < k) = Σi=0k-1 (15 choose i) 0.5^15

We want to find the value of k such that P(X < k) is less than 0.1, or equivalently, P(X ≥ k) is greater than or equal to 0.9. We can use a calculator or a table to find that the smallest k that satisfies this condition is k = 10.

Therefore, the passing grade should be set to 10 out of 15, which means a student needs to get at least 10 correct answers to pass the quiz.

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Answer:

average=9 hours

Step-by-step explanation:

10hours on Friday

12 hours on Saturday

300 mins to hours= 300÷60=5

5 hours on Sunday

average=10+12+5

average=27

average=27÷3

average=9 hours

Answer:

Step-by-step explanation:

You want to identify the graphs that go with each of these functions, along with a particular point on the curve.

The equations are written here in standard form, factored form, and vertex form. (The "factored form" is sometimes called "intercept form.") Each of these forms can be analyzed for characteristics relevant to identifying the corresponding graph.

In general, we can readily identify the opening direction, based on the sign of the leading coefficient. Depending on the form, we can also identify zeros, the vertex, and the y-intercept.

The line of symmetry (x-coordinate of the vertex) of the equation in the form ax² +bx +c is x = -b/(2a). That is, it will be left of the y-axis when the coefficients 'a' and 'b' have the same sign.

The graph of equation A will be graph 4, the only one with its vertex left of the y-axis. The y-intercept is the constant: point S = (0, 9).

Equation B has a positive leading coefficient, so opens upward. The zeros of the factors are -3 and +9, so identify the places where the graph crosses the x-axis. Graph 3 is the only one that opens upward and has x-intercepts. Point R is (9, 0).

The vertex form of a quadratic is ...

  y = a(x -h)² +k . . . . . . . vertex (h, k); leading coefficient 'a'

Equation C has its vertex at (h, k) = (3, 9) and opens upward (a>0). Graph 1 is the only one matching those characteristics. Point P is the vertex, so point P is (3, 9).

Equation D is the same as equation B, but with a negative leading coefficient. That is, it opens downward and crosses the x-axis in two places, at x = -3 and x = 9. Graph 2 is matches this description. The left zero is point Q, (-3, 0).

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Answer:

36 hours

Step-by-step explanation:

1 person will be larger than 12 hours certainly

therefore 12*3 = 36

Answer:

36 hours

Step-by-step explanation:

P. : h

3. : 12

1. : ?

3÷1=3

12×3=36 times by 3 because if there are less people painting the room it's going to take more time

so it's takes 1 person 36 hours to paint the room

Hello !

2(5 - 2 * 3 - 4)​

= 2(5 - 6 - 4)

= 2 * (-5)

= -10

Answer: 8.5

Step-by-step explanation: 45-45-90 triangle will always have the same length of legs. The hypotenuse will be the leg length times √2

a^2+b^2=c^2

A and B are the same.

6^2+6^2=6√2✅

6√2=8.5✅

Answer:

Step-by-step explanation:

The Axiom of Pairing in mathematics states that for any two sets, there exists a set that contains exactly those two sets as its only elements. In other words, given sets A and B, there exists a set {A, B} whose only elements are A and B.

For example, consider the sets A = {1, 2} and B = {3, 4}. According to the Axiom of Pairing, there exists a set that contains exactly these two sets as its only elements. We can form such a set as {A, B} = {{1, 2}, {3, 4}}, where A and B are the elements of the set. Thus, {A, B} is a set that satisfies the Axiom of Pairing.

The meaning of the number 30,500 is given as follows:

The maximum altitude of the airplane.

The coordinates of the vertex are (h,k), meaning that:

Considering a leading coefficient a, the quadratic function is given as follows:

y = a(x - h)² + k.

In which a is the leading coefficient.

The function for this problem is given as follows:

y = -16(t - 12)² + 30500.

The coordinates of the vertex are given as follows:

(12, 30500).

The leading coefficient is negative, hence the meaning of the vertex is given as follows:

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Answer:

12% more than 72 is

80.64

Step-by-step explanation:

It will cost approximately $16 per person if 95 people rent the bus.

The price per person of renting a bus varies inversely with the number of people renting the bus. This means that as the number of people increases, the price per person decreases, and vice versa.

Given that it costs $20 per person when 76 people rent the bus, we can use this information to find the constant of variation (k) in the inverse variation equation. Let's denote the number of people as "n" and the cost per person as "c":

c = k/n

We can substitute the values into the equation to solve for k:

20 = k/76

Multiplying both sides by 76 gives:

k = 20 × 76 = 1520

Now, we can determine the cost per person when 95 people rent the bus by plugging the values into the equation:

c = 1520/95 ≈ 16.00

Therefore, it will cost approximately $16 per person if 95 people rent the bus.

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so we have a point at -2-i or -2 - 1i, that means that both "x" and "y" are negative, the only occurs in the III Quadrant, so hmmm let's find the modulus and angle θ

[tex]\stackrel{a}{-2}\stackrel{b}{-1i}\hspace{5em} \begin{cases} r=\sqrt{(-2)^2 + (-1)^2}\\ \qquad \sqrt{5}\\ \theta =tan^{-1}\left( \frac{-1}{-2} \right)\\[1em] \qquad \approx 206.57^o \end{cases} \\\\\\ \stackrel{\textit{let's keep in mind that}}{\sqrt[3]{\sqrt{5}}\implies \left( 5^{\frac{1}{2}} \right)^{\frac{1}{3}}}\implies 5^{\frac{1}{6}}\implies \sqrt[6]{5} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\sqrt[n]{z}=\sqrt[n]{r}\left[ \cos\left( \cfrac{\theta+2\pi k}{n} \right) +i\sin\left( \cfrac{\theta+2\pi k}{n} \right)\right]\quad \begin{array}{llll} k\ roots\\ 0,1,2,3,... \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\boxed{k=0}\hspace{5em} \sqrt[ 3 ]{\sqrt{5}} \left[ \cos\left( \cfrac{ 206.57^o + 360^o( 0 )}{3} \right) +i \sin\left( \cfrac{ 206.57^o + 360^o( 0 )}{3} \right)\right] \\\\\\ \sqrt[ 6 ]{5} \left[ \cos\left( \cfrac{ 206.57^o }{3} \right) +i \sin\left( \cfrac{ 206.57^o }{3} \right)\right] \\\\\\ \sqrt[6]{5}\left[ \cos(68.86^o) +i \sin(68.86^o)\right] ~~ \approx ~~ 0.47~~ + ~~1.22i \\\\[-0.35em] ~\dotfill[/tex]

[tex]\boxed{k=1}\hspace{5em} \sqrt[ 6 ]{5} \left[ \cos\left( \cfrac{ 206.57^o + 360^o( 1 )}{3} \right) +i \sin\left( \cfrac{ 206.57^o + 360^o( 1 )}{3} \right)\right] \\\\\\ \sqrt[ 6 ]{5} \left[ \cos\left( \cfrac{ 566.57^o }{3} \right) +i \sin\left( \cfrac{ 566.57^o }{3} \right)\right] \\\\\\ \sqrt[ 6 ]{5} \left[ \cos(188.86^o) +i \sin(188.86^o)\right] ~~ \approx ~~ -1.29~~ - ~~0.20i \\\\[-0.35em] ~\dotfill[/tex]

[tex]\boxed{k=2}\hspace{5em} \sqrt[ 6 ]{5} \left[ \cos\left( \cfrac{ 206.57^o + 360^o( 2 )}{3} \right) +i \sin\left( \cfrac{ 206.57^o + 360^o( 2 )}{3} \right)\right] \\\\\\ \sqrt[ 6 ]{5} \left[ \cos\left( \cfrac{ 926.57^o }{3} \right) +i \sin\left( \cfrac{ 926.57^o }{3} \right)\right] \\\\\\ \sqrt[ 6 ]{5} \left[ \cos(308.86^o) +i \sin(308.86^o)\right] ~~ \approx ~~ 0.82~~ - ~~1.02i[/tex]

just a quick clarification, notice that if we get the inverse tangent of (-1 / -2) the angle we get will be in the range of ±π/2, that's because that is the range inverse tangent is restricted to, however, our terminal point on the complex plane is on the III Quadrant, not the 1st one, so we use the reference angle on the III Quadrant, and that is about 206.57°.

Answer:

The total number of marbles is 10, the number of blue marbles is 3, and the red marbles are 4.

Step-by-step explanation:

have a nice day.

Answer:

To calculate the percent increase in the amount of interest paid between a household with a 740 credit score and one with a 730 credit score , we need to find the total amount paid for each score and then calculate the percent increase.

From the given table , we can see that the simple interest rate for a credit score of 740-799 is 15%, and the total number of payments is 33 . So, the total amount paid for a principal balance of $18,000 with a credit score of 740 is:

Principal + Total Interest = Total Amount Paid

$18,000 + ($18,000 * 15% * 33/12) = $20,700

Similarly, for a credit score of 730, we need to use the simple interest rate for a credit score of 670-739 , which is 18%, and the total number of payments is 38. So, the total amount paid for a principal balance of $18,000 with a credit score of 730 is:

Principal + Total Interest = Total Amount Paid

$18,000 + ($18,000 * 18% * 38/12) = $21,240

Now, to calculate the percent increase in the amount of interest paid , we can use the following formula:

Percent increase = |(New value - Old value) / Old value| * 100%

Plugging in the values, we get:

Percent increase = |($21,240 - $20,700) / $20,700| * 100%

Percent increase = 2.6%

Rounding to the nearest tenth, we get the final answer as:

Percent increase = 2.6% ≈ 2.5%   (rounded to the nearest tenth)

Therefore, the answer is O 2.5%.

Step-by-step explanation:

The acceleration of the runner is 0.2 m/s².

We can use the following equation to get the runner's acceleration:

Acceleration (a) = (Final Velocity - Initial Velocity) / Time

In this case, the initial velocity (u) is 0 m/s, the final velocity (v) can be calculated using the formula:

v = s / t

where t is the amount of time spent and s is the distance travelled.

The time taken (t) and the distance travelled (s) are both provided as 500 m.

Calculate the b (v):

v = 500 m / 50 s

v = 10 m/s

Plug into the formula for acceleration:

a = (10 m/s - 0 m/s) / 50 s

a = 10 m/s / 50 s

a = 0.2 m/s²

Therefore, the acceleration of the runner is 0.2 m/s².

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Answer:

Shorter leg is 6

Step-by-step explanation:

In a 30°-60°-90° triangle, the hypotenuse is twice the length of the shorter leg. Therefore, if the hypotenuse is 12, then the shorter leg is 6.

The standard deviation is around 1.06, and there are on average 2 frogs having the feature.

Given that the trait is usually found in 1 out of every 8 frogs, the probability of a frog having the trait is p = 1/8. Therefore, the probability of a frog not having the trait is q = 1 - p = 7/8.

(a) To find the probability of not finding any frogs with the trait, we calculate the probability of a frog not having the trait and raise it to the power of the number of trials:

P(X = 0) = (7/8)¹⁶ ≈ 0.0747

(b) To find the probability of finding at least 1 frog with the trait, we subtract the probability of finding none from 1:

P(X ≥ 1) = 1 - P(X = 0) ≈ 1 - 0.0747 ≈ 0.9253

(c) The mean (μ) and standard deviation (σ) of the number of frogs with the trait can be calculated using the formulas:

μ = np

σ = √(npq)

For this case, n = 16, p = 1/8, and q = 7/8:

μ = 16 * (1/8) = 2

σ = √(16 * (1/8) * (7/8)) ≈ 1.06

Therefore, the mean number of frogs with the trait is 2, and the standard deviation is approximately 1.06.

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The polar form of the rectangular coordinates (4√3, -4) is (8, -π/6).

To convert rectangular coordinates (x, y) to polar form (r, θ), we can use the following formulas:

r = √(x² + y²)

θ = arctan(y/x)

Given (4√3, -4) as the rectangular coordinates

we can substitute the values into the formulas:

r = √((4√3)² + (-4)²) = √(48 + 16) = √64 = 8

θ = arctan((-4)/(4√3))

= arctan(-1/√3)

= -π/6 (since -π/6 is in the range 0 ≤ θ < 2π)

Therefore, the polar form of the rectangular coordinates (4√3, -4) is (8, -π/6).

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Step-by-step explanation:

14 out of 20 were full in the experiment   14/20 = 7/10 chance that the next one will be full too.

The cosine of the angle θ in the circle s -12/13

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

The unit circle

Where we have

(x, y) = (-12/13, -5/13)

In a unit circle, we have

(cos θ, sin θ) = (x, y)

Using the above as a guide, we have the following:

cos θ = -12/13

Hence, the cosine of the angle θ is -12/13

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Answer:

The given function f(x) = alxl is not a valid absolute value function because the absolute value symbol is represented by two vertical bars (|) and not the letter "l". Additionally, the point (3,-4) cannot be on the graph of an absolute value function because the output of an absolute value function is always non-negative.

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Answer:

  x = 1, 12

Step-by-step explanation:

You want the solutions to y = x² -13x +12 when y = 0, using the quadratic formula.

The quadratic formula gives the solutions to ...

  ax² +bx +c = 0

as ...

  [tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Your equation has a = 1, b = -13, c = 12, so the solutions are ...

  [tex]x = \dfrac{-(-13)\pm\sqrt{(-13)^2-4(1)(12)}}{2(1)}=\dfrac{13\pm\sqrt{169-48}}{2}\\\\\\x=\dfrac{13\pm11}{2}\\\\\boxed{x=\{12,1\}}[/tex]

This answer is correct because we used and evaluated the formula correctly. There are several ways to check the answer is correct.

A graph of the equation is attached. It shows the x-intercepts (zeros) to be x = 1 and x = 12.

When the equation is factored, it looks like ...

  y = (x -12)(x -1)

The zeros are the values of x that make the factors zero: 12 and 1.

The equation can be rewritten to simplify evaluating it:

  y = (x -13)x +12

For x = 1, y = (1 -13)(1) +12 = -12 +12 = 0.

For x = 12, y = (12 -13)(12) +12 = -12 +12 = 0.

The values x = 1 and x = 12 are zeros of the function.

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