special right triangle

Answer:

Below

Step-by-step explanation:

Complementary angles sum to 90 °

x = angle 1

4x = other angle            they sum to 90°

x   +    4x   = 90 °

5x = 90°

x = 18°        then      4x = 72°

The Simplified values are

1. 7∛3 + 2∛192 = 15∛3.

2. 10√7 - √28- 6√180 = 8√7 - 36√5

3. 8[tex]\sqrt[4]{48}[/tex] - 5√90 + 9[tex]\sqrt[4]{3}[/tex] = 25[tex]\sqrt[4]{3}[/tex] - 15√10

4. 5∛32x³[tex]y^4[/tex] - 3xy∛4y = 7xy ∛4y

Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.

For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base. The whole expression 34 is said to be power.

Given:

1. 7∛3 + 2∛192

= 7∛3 + 2 ∛ 2 x 2 x 2 x 2 x 2 x 2 x 3

= 7∛3 + 2 x 2 x 2 ∛3

= 7∛3 + 8∛3

= 15∛3.

2. 10√7 - √28- 6√180

= 10√7 - √2 x 2 x 7 - 6√2 x 2 x 3 x 3 x 5

= 10√7 - 2√7 - 36√5

= 8√7 - 36√5

3. 8[tex]\sqrt[4]{48}[/tex] - 5√90 + 9[tex]\sqrt[4]{3}[/tex]

=  8 x 2 [tex]\sqrt[4]{3}[/tex] - 5 x 3 √10 + 9[tex]\sqrt[4]{3}[/tex]

= 25[tex]\sqrt[4]{3}[/tex] - 15√10

4. 5∛32x³[tex]y^4[/tex] - 3xy∛4y

= 10xy ∛4y - 3xy∛4y

= 7xy ∛4y

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An algebraic expression which is equivalent to the expression

csc[arccos(x -1)] is equal to 1 / √2x - x² .

Let us consider the expression arccos(x - 1 ) = y .

arccos(x - 1 ) = y

⇒ cos y = (x - 1 ) ___( 1 )

Now the required algebraic expression is equivalent to :

csc[arccos(x -1)]

= csc y

= ( 1 / sin y )

= 1 / √ 1 - cos²y   __(2)

Substitute the value of cosy from (1 ) in the expression ( 2 ) we get,

= 1 / √ 1 - ( x - 1 )²

= 1 / √ 1 -  ( x² -2x + 1 )

= 1 / √ 1 - x² + 2x - 1

= 1 / √ 2x - x²

Therefore, the expression csc[arccos(x -1)] is equivalent to an algebraic expression is  1 / √ 2x - x².

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The probability that one of the cards is an ace and another one is either a ten or a jack, and the other one is either a queen or a king is [tex]$\frac{4}{2197}[/tex]  (or) 0.00182

Let:

A: Drawing one ace card

B: Drawing either a ten or a jack card

C: Drawing either a queen or a king card

Probability of drawing one ace card

P(A) = [tex]$\frac{4}{52} \\[/tex]

Probability of drawing one ten-numbered card.

A number of ten cards 4.

= [tex]$\frac{4}{52}[/tex]

Probability of drawing one jack card.

A number of jack cards 4.

= [tex]$\frac{4}{52}[/tex]

[tex]$ P(B)=\frac{4}{52}+\frac{4}{52}=\frac{8}{52}[/tex]

Probability of drawing one queen card.

A number of queen cards 4.

= [tex]$\frac{4}{52}[/tex]

Probability of drawing one king card.

A number of king cards 4.

= [tex]$\frac{4}{52}[/tex]

[tex]$P(C)=\frac{4}{52}+\frac{4}{52}=\frac{8}{52}[/tex]

Now Probability (one of the cards is an ace and another one is either a ten or a jack and the other one is either a queen or a king

[tex]P(A \cap B \cap C)[/tex] = P(A) P(B) P(C)

[tex]$=\frac{4}{52} \times \frac{8}{52} \times \frac{8}{52}[/tex]

[tex]$=\frac{4}{2197}[/tex] (or)

= 0.00182

Therefore the probability is [tex]$\frac{4}{2197}[/tex]  (or) 0.00182

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(A) The point (2, 80) represents that at 2 hours there are 80 miles of water in a tank.

(B) Writing an equation for the relationship in the form of y = mx, we get y = 40x.

What is Proportionate Relationship?

It is given that there is a proportional relationship between hours, x, and number of miles, y, of water in a tank.

Also, the point (2, 80) is on a graph of this relationship.

(A) The point (2, 80) represents that at 2 hours there are 80 miles of water in a tank.

(B) We have the given point, (2, 80)

Writing the relationship in the form of equation, y = mx using the point (2, 80), we get

80 = m × 2

⇒ m = 80/2

⇒ m = 40

Thus, writing an equation for the relationship in the form of y = mx when m = 40, we get y = 40x.

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Answer:

Step-by-step explanation:

The sum of the first 20 terms of a linear sequence can be found using the formula for the sum of an arithmetic series:

S = n/2 * (a1 + a20)

where n = number of terms = 20, a1 = first term = 1, and a20 = 20th term = 1 + 4 * (20 - 1) = 77

Substituting these values, we have:

S = 20/2 * (1 + 77) = 20/2 * 78 = 20 * 39 = 780

So, the sum of the first 20 terms of the sequence 1, 5, 9, 13 is 780.

The velocity and acceleration vectors and the equation of the tangent line for the curve = 3i+4tj

What is Velocity?

When an item is moving, its velocity is the rate at which it is changing position as seen from a certain point of view and as measured by a specific unit of time.

What is Acceleartion?

Acceleration is the rate at which an object's velocity with respect to time changes. They are vector quantities, accelerations. The direction of the net force acting on an object determines the direction of its acceleration.

r(t) = 3cos(t)+sin4(t)j

velocity,V(t) = dr(t)/dt

=3sin(t)i + 4cos4(t)j

and acceleration a(t) = dv(t)/dt

= [tex]d^{2}r(t)/dt^{2}[/tex]

i.e a(t) = -3cos(t)i - 16sin(4t)j

v(0) = 0.i + 4j =4j

and a(0) = -3i -0j

=-3i

now we find the equation of the tangent line for the curve (t) at t=0

r(0) = 3i

r(t) = -3sin(t)i +4 cos 4(t)j

r (0) = 4j

equation target to the curve r(t) at t=0 is

1(t) = r (0) + (t)r(0)

= -3i+(t).4j

= -3i+4tj

The curve's tangent line equation, velocity and acceleration vectors, is -3i+4tj

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Answer:

1/4

Step-by-step explanation:

The probability of the spinner landing on any one number = 1/8 since there are 8 possible outcomes and we are looking for the probability of one outcome out of those

So P(2) = P(4) = 1/8

P(4) and P(2) is the sum of these two probabilities = 1/8 + 1/8 = 2/8 = 1/4

Answer:  A=4.5m²

Step-by-step explanation:  length: 1.5 Width: 300

Unit Conversion:l=1.5mw

A=wl=3·1.5=4.5m²

the area of the given kite will be 60 feet².

What is area of Kite?

A polygon with four vertices and four sides enclosing four angles is called a quadrilateral. A unique quadrilateral known as the kite has successive sides that are all congruent, but the opposite sides are not. A rhombus is a kite that has four congruent sides. A kite's diagonals are perpendicular. The area of a kite is calculated as half of the diagonal product, which is the same as the area of a rhombus. The formula: can be used to express the area of a kite.

Area of Kite = 1/2*D1 * D2

D1 = long diagonal of kite

D2 = short diagonal of kite

The diagonals intersect each other so that the shorter diagonal is split into parts that are 2 feet and 2 feet and the longer diagonal is split into parts that are 10 feet and 20 feet.

So Area = 1/2 * 4 * 30 = 60 feet²

Hence the area of the given kite will be 60 feet².

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Answer:

Step-by-step explanation:

Given that sin θ = -4/9 and 3π/2 ≤ θ ≤ 2π, we can use the trigonometric identities to find cot θ.

cot θ = 1/tan θ = 1/ (sin θ / cos θ) = cos θ / sin θ

As we know the sin θ = -4/9, we can find cos θ = √(1 - sin^2 θ) = √(1 - (-4/9)^2) = √(1 - 16/81) = √(65/81)

So cot θ = (√(65/81)) / (-4/9) = -9/4 * √(65/81) = -(9/2) √(65/81)

Note that, since 3π/2 ≤ θ ≤ 2π, the value of cot θ will be negative

Answer:

y=x+3

Step-by-step explanation:

The length of the rectangle is 23 km and the width of the rectangle is 15 km.

A rectangle is 8 km longer than it is wide.

Its area is 345 sq-km.

Let the width of the rectangle is x.

The length is 8 km longer than the width.

So the width of the rectangle is x + 8 km.

The formula of the area of rectangle is:

A = length × width

We know A = 345 sq-km.

Now putting the value

x × (x + 8) = 345

Now simplifying

x^2 + 8x = 345

Subtract 345 on both side, we get

x^2 + 8x - 345 = 0

Now factor the equation

x^2 + (23 - 15)x - 345 = 0

x^2 + 23x - 15x - 345 = 0

x(x + 23) - 15(x + 23) = 0

(x - 15)(x + 23) = 0

Now equation the factor equal to zero.

x - 15 = 0           or             x + 23 = 0

x = 15                or              x = -23

Since the dimension of the rectangle can't be negative. So

The width of the rectangle is 15 km.

Now we determine the value of length

x + 8 = 15 + 8 = 23

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The approximate value of the integral using the trapezoidal rule with ten equal subintervals is [tex]2 + |E_T| = 2 - 1/300 = 599/300[/tex].

To find the exact value of the definite integral of 4x over the interval [0,1] we can found using the antiderivative:

[tex]\int_0^1 4x dx = 2x^2 |_0^1 = 2(1)^2 - 2(0)^2 = 2.[/tex]

To approximate the value of the integral using the trapezoidal rule with ten equal subintervals, we can break the interval into ten equal subintervals of length 1/10 and approximate each subinterval using a trapezoid.

The error of the trapezoidal rule is given by:

[tex]|E_T| = -(b-a)^3/(12n^2) * f''(c)[/tex]

where a and b are the limits of the integration, n is the number of subintervals, and f''(c) is the second derivative of the integrand evaluated at some value c in the interval.

The error of this approximation will depend on the value of f''(c) for some value c in the interval [0,1]. The second derivative of 4x is constant and equal to 4, so the error will be a constant value:

[tex]|E_T| = -(1-0)^3/(12*10^2) * 4 = -1/300.[/tex]

Thus, the approximate value of the integral using the trapezoidal rule with ten equal subintervals is [tex]2 + |E_T| = 2 - 1/300 = 599/300[/tex].

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The  number should replace A to give the best scale for the vertical axis of this data is 15.75

From the given parameters and graphs, we notice that we should find the mean of the set of data.

The scale should be chose in a way that the center shows the the mean of the frequencies

Recall that mean is the average of all the frequencies, then we have to find the mean of the means of the two frequencies.

(30+12+10)/2  52/3 = 17.3

Also, (27+6+13)/3  = 14.2

Then we find the average of the two averages to have

(17.3+14.2)/2 = 31.5/215.75

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Total 13,608,000 has length of eight are there containing exactly six distinct characters.

Total number of string = 10

The length of the string should be = 8

The distinct characters = 6

So the same character should be = 2

There are total 10 numbers in which 6 are distinct, so

[tex]^{10}P_{6}=\frac{10!}{(10-6)!}[/tex]

[tex]^{10}P_{6}=\frac{10!}{4!}[/tex]

[tex]^{10}P_{6}[/tex] = 3,628,800/24

[tex]^{10}P_{6}[/tex] = 151,200

Hence, strings of length eight are there containing exactly six distinct characters = 151,200 × 10 × 9

Strings of length eight are there containing exactly six distinct characters = 13,608,000

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Answer:

5

Step-by-step explanation:

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the slope of the line, we can use the following formula:

m = (y2 - y1) / (x2 - x1)

Plugging in the coordinates (2,4) and (-2,-8) into the formula:

m = (-8 - 4) / (-2 - 2) = -12/ -4 = 3

We can use one of the coordinates to find the y-intercept.

Plugging in the point (2,4) and the slope 3 into the equation y = mx + b, we get:

4 = 3*2 + b

so b = -2

Therefore, the equation of the line is y = 3x - 2.

Answer: this is the answer it is a screenshot of the graph

Answer:-2.5

Step-by-step explanation:

1. Set up your problem it would be 5x+2y=-5

2. Then you would set your x to be 0 so you can solve for y

5(0)+2y=-5 aka 2y=-5

3. Divide each side by 2

2y (divided by 2) = -5 (divided by 2)

y=-2.5

I hope this helps!

Answer:

Step-by-step explanation:

As stated in the question that One vehicle transports 14 tourists and there are 34 tourists

Number of vehicles required = 34/14 = 2 vehicles + 6 people left

So, the remaining 6 people will be transported through 3rd vehicle.

So, there are 3 vehicles needed to transport 34 tourists.

a) The vectors a and b are collinear when compa b=compb a. This means that they have the same direction, so that they're pointing in the same direction or opposite directions. In other words, if the angle between them is 0° or 180°, then they are collinear.

b) The vectors a and b are orthogonal when proja b=proj b a. This means that they are perpendicular to each other, so that the angle between them is 90°. Furthermore, it means that the projection of one vector onto the other is equal to zero.

This is because the projection of a vector onto itself is equal to the magnitude of the vector, while the projection of a vector onto a vector orthogonal to it is equal to zero.

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The solution to the equation is x = 2

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

|x^3-1|-7=0

Add 7 to both sides

So, we have

|x^3-1| = 7

Remove the absolute bracket

x^3 - 1  = 7

So, we have

x^3 = 8

Take tge cube roots of both sides

x = 2

Hence, the solution is 2

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Answer:

3°

Step-by-step explanation:

33 +19x = 90     subtract 33 from both sides of the equation

19x = 57             divide both sides by 19

x = 3°

If Canister contained [tex]6\frac{1}{8}[/tex] cup of flour when Karina started making cookie and used [tex]2\frac{1}{2}[/tex] cup then number of cup left in Canister is 29/8 cups   .

the number of cups of floor in the canister initially is = [tex]6\frac{1}{8}[/tex] = 49/8 ;

the amount of floor that she used is =   [tex]2\frac{1}{2}[/tex] = 5/2 cups ,

To find out how much flour is left in the canister, we need to subtract the amount used from the total amount.

We can start by converting the mixed fractional cups to improper form ,

we get ;

number of cups left in the canister is = 49/8 - 5/2 = 49/8 - 20/8 = 29/8 .

Therefore , 29/8 cups were left in the canister .

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Answer:

110.0%

Step-by-step explanation:

25% of 88 is 22. 88+22=110 Fahrenheit

to get this you divide 88 by 100 which is 0.88, then multiply by 25 which gets you 22.

In the line of symetry for this parabola is x = -1.

The maxima or minima of the parabola is [tex]-\frac{21}{4}[/tex]

Estimate the gradient of the curve at x = 4 is 5.

The equation of the tangent of the point (4, 1) is 5x² - y² - 40x + 2y + 89 = 0.

The gradient of the curve at the point (-1, 1) is -1.

The steps are as follows:

The function of parabola y = x² - 3x - 3

(i) In the line of symetry for this parabola.

Symetry of the parabola:

x =  [tex]-\frac{b}{2a}[/tex]    → for y = ax² + bx + c

x =  [tex]-\frac{-3}{-3}[/tex]

x = -1

(ii) The maxima or minima of the parabola.

The maximum or minimum parabola can be found when the derivative is 0

y = x² - 3x - 3

y' = 2x - 3

0 = 2x - 3

2x = 3

x =  [tex]\frac{3}{2}[/tex]

The maxima or minima of the parabola

y = x² - 3x - 3

  = ( [tex]\frac{3}{2}[/tex] )² - 3 (  [tex]\frac{3}{2}[/tex] ) - 3

  =  [tex]\frac{9}{4}[/tex]  -   [tex]\frac{9}{2}[/tex]  - 3

  =   [tex]\frac{9}{4}[/tex]  -  [tex]\frac{18}{4}[/tex]  -  [tex]\frac{12}{4}[/tex]

  = [tex]-\frac{21}{4}[/tex]

(iii) Estimate the gradient of the curve at x = 4

y = x² - 3x - 3

y' = 2x - 3

y' = m = 2(4) - 3

          = 8 - 3

          = 5

y = x² - 3x - 3

y = 4² - 3(4) - 3

  = 16 - 12 - 3

  = 1

(iv) The equation of the tangent of the point (4, 1)

(y - b)² = m (x - a)²

(y - 1)² = 5 (x - 4)²

y² - 2y + 1 = 5 (x² - 8x + 16)

y² - 2y + 1 = 5x² - 40x + 90

5x² - y² - 40x + 2y + 90 - 1 = 0

5x² - y² - 40x + 2y + 89 = 0

(v) The gradient of the curve at the point (-1, 1)

y = x² - 3x - 3

y' = 2x - 3

y' = m = 2(1) - 3

          = 2 - 3

          = -1

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Answer:12.405 would be correct

Step-by-step explanation:

In probability theory and statistics, variance is the squared deviation from the mean of a random variable. The variance is also often defined as the square of the standard deviation. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value

The variance is a measure of variability

Therefore c is your answer!

The population of grasshoppers can be estimated by using a formula that takes into account the number of weeks that have passed since the start of the experiment (0 < t < 12).

The population of grasshoppers can be estimated with a formula that takes into account the amount of weeks that have passed since the start of the experiment (0 < t < 12). The first step in this process is to define the variables that will be used. The variable p will represent the population of grasshoppers after t weeks and t will represent the number of weeks that have passed. The next step is to use a formula to estimate the population of grasshoppers. This formula will take into account the amount of weeks that have passed and will likely result in an exponential increase in the population of grasshoppers as the weeks pass. After the formula is applied, the result will be the estimated population of grasshoppers after t weeks.

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