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The bisector angle is angle PQT which is equal to angle RQT.

Angle bisector or a bisector angle is a type of angle obtained after dividing the initial angle into two equal parts.

The bisected angle can be obtained using a pair of compass and a pencil attached to it.

To bisect the given angle RQP; we will take the following steps;

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Answer:

sin(3pi/4 ) = -√2/2

So, B.

The height of a house that has a shadow projection of 2 meters is given as follows:

2.5 meters.

The height of a house that has a shadow projection of 2 meters is obtained applying the proportions in the context of the problem.

The proportional relationship between the height of the building and the height of the shadow is given as follows:

5/4 = x/2

Hence we apply cross multiplication to obtain the height of the house, as follows:

4x = 10

x = 10/4

x = 2.5.

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The solution to the integration of the function given, ∫√(5x - 1) dx, is:

[tex]\frac{2}{15}(5x-1)^{3/2} + C[/tex]

To solve the integral of:

√(5x - 1) dx

we can use a u-substitution.

Let u = 5x - 1, then:

du = 5 dx

dx = du/5

Now we can rewrite the integral in terms of u:

∫√(5x - 1) dx = ∫√u * (du/5)

Simplifying the integral:

(1/5) ∫√u du

Integrating √u:

(1/5) * (2/3) * u^(3/2) + C

Where C is the constant of integration

Substituting back u = 5x - 1:

(2/15) * (5x - 1)^(3/2) + C

Therefore, the solution to the integral of √(5x - 1) dx is:

[tex]\frac{2}{15}(5x-1)^{3/2} + C[/tex]

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Using the center and distance between co-vertex and center, the equation of the hyperbola is written below

[tex]\frac{(y + 3)^2}{49} - \frac{(x - 10)^2}{144} = 1[/tex]

A hyperbola, in analytic geometry, is a conic section that is formed when a plane intersects a double right circular cone at an angle such that both halves of the cone are intersected.

The equation of hyperbola is given as;

[tex]\frac{(y - k)^2}{a^2} - \frac{(x - h)^2}{b^2} = 1[/tex]

where (h,k) is the center of the hyperbola, a is the distance between a vertex and the center, and b is the distance between a co-vertex and the center.

In this case, the center is (10,−3), a=7, and b=12. Therefore, the equation of the hyperbola is

The equation of the hyperbola is;

[tex]\frac{(y + 3)^2}{49} - \frac{(x - 10)^2}{144} = 1[/tex]

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Answer:

n = 10

Step-by-step explanation:

Factorial is denoted by an exclamation mark "!" placed after the number. It means to multiply all whole numbers from the given number down to 1.

Therefore, n! represents the product of all positive integers from 1 to n.

[tex]\boxed{n!=n \times(n-1) \times(n-2) \times ... \times 1}[/tex]

Given expression:

[tex]n! = (2^8)(3^4)(5^2)(7)[/tex]

The expression for n! has been given as the product of prime factors.

As n! represents the product of all positive integers from 1 to n, begin by writing out the positive integers from 1 in ascending order as the product of primes (using exponents where possible):

[tex]\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}\cline{1-14}\vphantom{\dfrac12}n&1&2&3&4&5&6&7&8&9&10&11&12&13\\\cline{1-14}\vphantom{\dfrac12}\sf Product\;of\;primes&1&2&3&2^2&5&3\cdot 2&7&2^3&3^2&5 \cdot 2&11&2^2\cdot 3&13\\\cline{1-14}\end{aligned}\;\;\sf etc.[/tex]

If we examine the prime products of the given expression, we can see that largest prime number 7 appears only once. Therefore, n must be less than 14, since the next time 7 appears as a prime factor is when 2 · 7 = 14.

The prime number 5 appears twice in the given expression.

From the above table, we can see that the first two times the number 5 is present is (1) on its own, and (2) as a factor of 10. Therefore, n must be equal to or more than 10.

The prime number 3 appears four times in the given expression.

From the above table, we can see that the first four times the number 3 is present is (1) on its own, (2) as a factor of 6, (3) & (4) as both factors of 9.

The 5th time prime number 3 is present is as a prime factor of 12. Therefore, n must be less than 12, else 2⁵ would be a factor of n!.

Therefore, we have determined that 10 ≤ n < 12.

As 11 is a prime number and does not appear in the given expression for n!, we can conclude that n = 10.

We can check this by calculating the given expression and 10!:

[tex]\begin{aligned}n! &= (2^8)(3^4)(5^2)(7)\\&=256 \cdot 81\cdot25\cdot7\\&=20738\cdot25\cdot7\\&=518400\cdot7\\&=3628800\end{aligned}[/tex]

[tex]\begin{aligned}10!&=10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=90 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=720 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=5040 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=30240 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=151200 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=604800 \cdot 3 \cdot 2 \cdot 1\\&=1814400 \cdot 2 \cdot 1\\&=3628800 \cdot 1\\&=3628800\end{aligned}[/tex]

Therefore, this proves that n = 10.

Based on the information, it should be noted that the value of tan(A-B) is 234/583.

Given:

tanA = 60/11

sinB = 45/53

A and B are in Quadrant I

We can use the following identity to find tan(A-B):

tan(A-B) = (tanA - tanB)/(1 + tanA*tanB)

Substituting the given values, we get:

tan(A-B) = (60/11 - 45/53)/(1 + (60/11)*(45/53))

= (15/53)/(295/583)

= 234/583

Therefore, the value of tan(A-B) is 234/583.

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Answer:

hello

the answer is:

f = 180 - 42 - 90 = 48

Answer:

12 cm ^2

Step-by-step explanation:

Using the formula

V=ABh

Solving forAB

AB=V

h=204

17=12cm²

Answer: C: (-4,-3)

Step-by-step explanation:

You have the correct answer selected!

The solution of a system of equations is where the graphs of the two lines intersect. we can read that point to be (-4,-3), so thats the answer :)

Answer: if it's true that 10 > 7 (P), then it's also true that 10 > 5 (Q).

Step-by-step explanation: In the context of logic and truth tables, p → q can be read as "if p then q." You've provided the truth values for the combinations of p and q, which I'll summarize here:

If p and q are both False (F), then p → q is True (T).

If p is True (T) and q is False (F), then p → q is False (F).

If p is False (F) and q is True (T), then p → q is True (T).

If p and q are both True (T), then p → q is True (T).

Given your propositions:

P: 10 > 7

Q: 10 > 5

P is True because 10 is indeed greater than 7. Q is also True because 10 is greater than 5.

Therefore, we're in the fourth case of your truth table: both p and q are True, so p → q is also True.

Since AC is the angle bisector of ∠BAD, the flowchart proof should be completed as follows;

Statement                                 Reason

AC bisects ∠BAD                      Given

∠BAC ≅ ∠DAC                         Definition of an angle bisector.

∠BCA ≅ ∠DCA                         Congruent angles of a triangle (SAS).

AC ≅ AC                                   Reflexive property

ΔABC ≅ ΔADC                         AAS postulate

In Mathematics and Geometry, an angle bisector can be defined as a type of line, ray, or segment, that typically bisects or divides a line segment exactly into two (2) equal and congruent angles.

By applying the angle bisector theorem to the given triangle, we have the following statements and justifications:

AC bisects ∠BAD       Given

∠BAC ≅ ∠DAC           Definition of an angle bisector.

Based on side, angle, side (SA) and congruent angles of a triangle (SAS), we can reasonably infer and logically deduce that ∠BCA is congruent to ∠DCA i.e ∠BCA ≅ ∠DCA.

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Answer:

V = (4/3) × 3.14 × 14³ = 11,310.08 cubic feet

Work Shown:

d = diameter = 28

r = radius = d/2 = 28/2 = 14

V = volume of a sphere

V = (4/3)*pi*r^3

V = (4/3)*3.14*(14)^3

V = 11,488.2133 cubic feet approximately

The info "weighs almost 8 tons" is never used. It is likely an intended distraction. All we need is the radius of the sphere to get its volume.

Answer:

y=8

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\sf x = 5}[/tex]

Step-by-step explanation:

20x + 30 = 28x - 10 (Corresponding angles)

20x + 30 + 10 = 28x

20x + 40 = 28x

40 = 28x - 20x

40 = 8x

5 = x

OR

[tex]\rule[225]{225}{2}[/tex]

Answer:

  125/384 ≈ 0.32552

Step-by-step explanation:

You want the area between the curves y = 5x and y = 8x².

The difference between the curves is ...

  f(x) = 5x -8x² = x(5 -8x)

This difference is zero when ...

  x = 0

  5 -8x = 0   ⇒   x = 5/8

The area will be the integral of f(x) with the limits 0 and 5/8:

  [tex]\displaystyle \text{area}=\int_0^\frac{5}{8}{(5x-8x^2)}\,dx=\dfrac{5}{2}\cdot\left(\dfrac{5}{8}\right)^2-\dfrac{8}{3}\cdot\left(\dfrac{5}{8}\right)^3\\\\\\\text{area}=\left(\dfrac{5}{8}\right)^2\left(\dfrac{5}{2}-\dfrac{8}{3}\cdot\dfrac{5}{8}\right)=\dfrac{25}{64}\cdot\dfrac{5}{6}=\boxed{\dfrac{125}{384}}[/tex]

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The domain for the square root function is the set of all whole numbers

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

Function type = square root function

Equation: square root of x

This means that

f(x) = √x

The domain for x in the function is the set of input values the function can take

In this case, the square root function can take any whole number as its input

This means that the domain for f(x) is the set of all whole number

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2x² -2x+2 is the  polynomial we obtained after subtraction

The given polynomials are (3x²-2x+5)-(x²+3)

Three times of x square minus two times of x plus five minus x square plus three

We have to subtract the polynomials

3x²-2x+5 -x² - 3

Combine the like terms

2x² -2x+2

Hence, the polynomial we obtained after subtraction is 2x² -2x+2

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The width, w, of the opening between x and y, is 6.9 ft.

We have,

From the diagram,

We have the radius of the circle and the angle subtended by the chord at the center of the circle.

So,

We can also use the formula.

= 2 x radius x sin(angle/2)

This is the length of the chord.

Now,

radius = 4 ft

angle = 360/3 = 120

Substituting the values.

= 2 x radius x sin(angle/2)

= 2 x 4 x sin (120/2)

= 2 x 4 x sin 60

= 2 x 4 x √3/2

= 4 x √3

= 4 x 1.732

= 6.928

Rounding to the nearest tenth.

= 6.9 ft

Thus,

The width, w, of the opening between x and y, is 6.9 ft.

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a) The mean of the random variable is 2.610 (rounded to 2 decimal places).

b) The variance of the random variable is 1.880 (rounded to 3 decimal places).

c) The standard deviation of the random variable is 1.372 (rounded to 3 decimal places).

d) The probability that a randomly selected student has a parent involved in 4 activities is 0.260 (rounded to 3 decimal places).

To compute the variance of the random variable, we need to calculate the squared deviation of each value from the mean, weighted by their respective probabilities, and then sum them up.

b) Variance [tex](\sigma^2)[/tex] of the random variable:

Variance is given by the formula[tex]Var(X) = \sum [(X - \mu)^2 \times P(X)],[/tex] where X represents the values of the random variable, μ is the mean, and P(X) is the probability.

Using the given data:

X: 0 1 2 3 4

P(X): 0.053 0.117 0.258 0.312 0.26

μ (mean): 2.610

Calculating the squared deviations for each value:

[tex](0 - 2.610)^2 \times 0.053 = 14.152[/tex]

[tex](1 - 2.610)^2 \times 0.117 = 0.291[/tex]

[tex](2 - 2.610)^2 \times 0.258 = 0.148[/tex]

[tex](3 - 2.610)^2 \times 0.312 = 0.122[/tex]

[tex](4 - 2.610)^2 \times 0.26 = 1.429[/tex]

Summing up the squared deviations:

Var(X) = 14.152 + 0.291 + 0.148 + 0.122 + 1.429 = 16.142

Therefore, the variance of the random variable is 16.142.

c) Standard deviation (σ) of the random variable:

The standard deviation is the square root of the variance.

Taking the square root of the variance calculated above:

Standard deviation (σ) = √(16.142) ≈ 4.020 (rounded to 3 decimal places)

d) Probability of a randomly selected student having a parent involved in 4 activities:

The probability of a specific value occurring in a discrete probability distribution is given by the corresponding probability value.

From the given data:

P(X = 4) = 0.26

Therefore, the probability that a randomly selected student has a parent involved in 4 activities is 0.26 (rounded to 3 decimal places).

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Answer: 150 deg

Step-by-step explanation:

cosine is negative in quadrants 2 and 3. the current angle, 210, is in quad 3. It will have an equal cosine value in quad 2.

that angle will be -210 degrees. in positive terms that is 360-210 = 150 degrees.

thus the answer which shows 150 degrees is correct.

in general:

[tex]cos(x) = cos(-x)[/tex]

Answer:

d

Step-by-step explanation:

Answer:

y = 3x + 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line

m = [tex]\frac{3-0}{0-(-1)}[/tex] = [tex]\frac{3}{0+1}[/tex] = [tex]\frac{3}{1}[/tex] = 3

the line crosses the y- axis at (0, 3 ) ⇒ c = 3

y = 3x + 3 ← equation of line

Answer:

I love math

Step-by-step explanation:

The formula for simple interest is:

I = P * r * t

where:

I = interest earned

P = principal amount

r = interest rate (as a decimal)

t = time (in years)

In this case, we know that:

P = $1,264

r = 2.75% = 0.0275 (as a decimal)

t = 2.5 years

So, we can plug in these values and solve for I:

I = 1,264 * 0.0275 * 2.5 = $87.55

Therefore, the interest earned over 2.5 years is $87.55. To find the ending balance, we need to add the interest earned to the principal:

Ending balance = $1,264 + $87.55 = $1,351.55

So, Quentin's account balance will be $1,351.55 at the end of 2.5 years.

Answer:

Expected winnings = $1.33

Expected profit or loss = -$2.67

Step-by-step explanation:

Winning Probability Prize Value

Yes   1/150         $200

No         149/150         $0

Expected winnings of one raffle ticket:

Expected winnings = (Probability of winning x Prize value) + (Probability of losing x Prize value)

Expected winnings = (1/150 x $200) + (149/150 x $0)

Expected winnings = $1.33

If a raffle ticket costs $4, the expected profit or loss of one raffle ticket can be calculated as:

Expected profit or loss = Expected winnings - Cost of ticket

Expected profit or loss = $1.33 - $4

Expected profit or loss = -$2.67

The ratios that are equivalent to the ratio 12:3 are 4:1 and 120:30.

We have,

To determine the ratios that are equivalent to the ratio 12:3, we need to find ratios that have the same value when simplified.

The ratio 12:3 can be simplified by dividing both numbers by their greatest common divisor (GCD), which in this case is 3.

Dividing 12 by 3 gives us 4, and dividing 3 by 3 gives us 1. Therefore, the simplified ratio is 4:1.

Now let's check the given options:

6:1 - This ratio is not equivalent because it is different from the simplified ratio 4:1.

1:4 - This ratio is not equivalent because the order of the numbers is reversed, and it is different from the simplified ratio 4:1.

4:1 - This ratio is equivalent to the original ratio 12:3. When simplified, both ratios result in 4:1.

246 - This is not a ratio and cannot be compared to the original ratio 12:3.

15:6 - This ratio is not equivalent because it is different from the simplified ratio 4:1.

120:30 - This ratio can be simplified by dividing both numbers by their GCD, which is 30.

Dividing 120 by 30 gives us 4, and dividing 30 by 30 gives us 1.

Therefore, the simplified ratio is 4:1, which is equivalent to the original ratio 12:3.

Thus,

The ratios that are equivalent to the ratio 12:3 are 4:1 and 120:30.

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