1. An angle in a right triangle is identified as θ. If the tangent of θ equals one, what must be true about the triangle side lengths?

A. The side adjacent to theta is half the length of the hypotenuse.
B. The side opposite to theta is longer than the adjacent side.
C. The sides opposite and adjacent to theta are the same length.
D. The side adjacent to theta is longer than the adjacent side.

The description of the motion of the ball, which is a projectile are as follows;

(a) The window coordinates are; (0, 138.49)

(b) The x–component is 7.22 m)s

The y–component is -3.22 m/s

(c) The equations for displacement are;

(d) 16.07 m from the base

(e) Height of the ball location before it was thrown is 138.49 meters

(f) Time to reach 10.0 m. is 1.14 s

Projectile motion is the motion of an object that is thrown or thrusted into the air such that the major force acting on an object is the force of gravity

(a) The parameters of the motion of the ball are;

Initial velocity of the ball = 7.8 m/s

Direction to which the ball is tossed = 24° below the horizontal

Time it takes the ball to strike the ground = 5.00 s

Location of the origin of the coordinates = The base of the building

[tex]h = v_{iy} \cdot t + 0.5 \cdot g \cdot t²[/tex]

Where;

h = The height of the window

[tex]u_{y}[/tex]

The initial vertical velocity = 7.8×sin(24°) ≈ 3.173 m/s

g = The acceleration due to gravity ≈ 9.81 m/s²

t = The time duration of the motion = 5.00 s

Therefore;

h = 3.173×5 + 0.5×9.81×5²≈ 138.49

The height of the window, h ≈ 138.49 meters

Given that the window shares the same x–coordinates with the base, which is 0, we have;

(b) The x and y–component of the initial velocity are therefore;

v = 7.9 m/s × (cos(24°)•i - sin(24°)•j)

v = 7.22•i - 3.21•j

The x and y component of the velocity are therefore

x–component [tex] v_{ix} [/tex] = 7.22•i

y–component, [tex] v_{y} [/tex] = -3.21•j

Therefore;

(c) The equation of the x–component of the position is found as follows;

x = 7.9×cos(24°) × t = 7.22 •t

y = 7.9×sin(24°) × t+ 0.5× 9.81×t²

(d) The distance from the base of the building where the ball lands is given by the equation

d ≈ 3.21 × 5 ≈ 16.07

(e) The height from which the ball was thrown, h, is given by the y–coordinate in option (a) therefore;

(f) When the distance traveled = 10 meters, we have;

[tex]h = v_{iy} \cdot t + 0.5 \cdot g \cdot t²[/tex]

Which gives;

10 = 3.21•t + 0.5×9.81×t²

Solving with a graphing calculator, gives;

t ≈ -1.79 or t = 1.14

The possible value for the time it takes to reach the point 10 meters is therefore;

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The perimeter is the sum of all the sides of a geometric figure, so

To resolve this inequality you can first subtract 8 from both sides

Then you divide by 4 on both sides of the inequality

Therefore, for the perimeter of the rectangle to be less than 120, its shortest side must measure less than 28.

Answer: 25 ft

Step-by-step explanation:

Let the shortest side be s. Then, the other two sides are 2s and s+21.

[tex]s+2s+s+21=121\\\\4s+21=121\\\\4s=100\\\\s=25[/tex]

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

frequency histogram

Step 02:

discrete math:

sum of two dice:

we must analyze the graph to find the solution.

most frequent outcome:

value of dice = 8

frequency = 20

least frequent outcome:

value of dice = 2

frequency ≅ 2

how many times (7):

15 times (frequency)

percentage of times (7):

percentage (7) = (15 / 100) * 100%

percentage (7) = 15%

shape of distribution:

non-symmetric, bimodal

That is the full solution.

For given details the function is f(t) = 2400 - 48t

a) the amount of air in the tank is a function of the number of minutes it contain the air.

b) Domain of the function: [0, 50] and  the domain is continuous one.

c) Graph of the function is attached below.

Function:

The function also know as expression, rule, or law that defines a relationship between one variable and another variable.

Given,

The amount of air in a scuba diving tank with a capacity of 2400 liters is decreasing at a constant rate of 48 liters per minute.

Here we need to find the following:

a) Whether the amount of air in the tank a function of the number of minutes?

b) Domain of the function

c) Graph of the function

Through the given question we know that,

The total amount of air in the tank = 2400 liters

Discharge unit per minute = 48 liters

Let us consider f(t) be the amount of air in a scuba diving tank.

where t represents the time in minutes.

Through the given information we get a function,

f(t) = 2400 - 48t

While using the given function, we can observe that the amount of air in the tank a function of the number of minutes.

Now, we need to find the domain of the function f(t)

Let us consider f(t) = 0

2400 - 48t = 0

2400 = 48t

t = 2400 / 48

t = 50

Therefore, t takes values in from the interval [0, 50]

We know that time is continuous to the function.

so, the domain is also continuous.

Now we have to plot the graph of the function..

Therefore, for given situation the function is f(t) = 2400 - 48t is attached below.

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Answer:

Step-by-step explanation:

Given,

The ratio of boys to girls in Fiona's class is 1:3

The total student in the class is 24

To find,

how many students are girls

Solution,

It is clear that the total number of boys and girls is 24

i.e., boys + girls=24 ------ (equation 1)

Let the ratio be in the terms of x

Consider boys ratio as x

And the girl's ratio as 3x

Now as per the equation 1,

x + 3x= 24

4x= 24

x= 6

Hence, Boys (x)= 6

And Girls (3x)= 3× (6)= 18

You can verify it by adding 6+18= 24

By using a trigonometric identity, we will see that the value of sin(x/2) is:sin(x/2) =  ±√39/√56 = ± 0.834

Here we need to use the identity: (sin(x/2))^2 = (1 - cos(x))/2

So, we know that:

cos(x) = -11/28

Then:

(1 - cos(x)) = 1 + 11/28 = 28/28 + 11/28 = 39/28

Replacing the identity that we get:

(sin(x/2))^2 = (1 - cos(x))/2 ]= (39/28)/2 = (39/56)

Now we can apply the square root in both sides, so we will get:

sin(x/2) = ±√(39/56)=  ±√39/√56 = ± 0.834

So, the value of sin(x/2) can be either 0.834 or -0.834.

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Population of Planet Eenie is  1.4 × [tex]10^{3}[/tex] times greater than the population of Planet Meenie.

Two planets named Eenie and Meenie.

Population of  Planet Eenie = 72,980,001

Population of  Planet Meenie =  54,908

We need to find how many times greater is the population of Planet

Eenie than the population of Planet Meenie. So, we need to follow the steps written below:

( Population of  Planet Eenie / Population of  Planet Meenie )

= ( 72,980,001 / 54,908 )

= 1329.1323

= 1.33 × [tex]10^{3}[/tex]

This calculated value is near option 2 i.e., 1.4 × [tex]10^{3}[/tex]. So,  1.4 × [tex]10^{3}[/tex] is the correct option.

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Answer:

P(B) = 0,35

Step-by-step explanation:

P(B) = P(A and B) divided by P(A)

The number which is decreased by 20% and result is 336 then number is 420

According to the question, given that

when a number is decreased by 20 % of itself, it became 336

then, the number is :

x - (x ×[tex]\frac{20}{100}[/tex] )= 336

x - [tex]\frac{x}{5}[/tex] = 336

[tex]\frac{5x - x}{5}[/tex] = 336

[tex]\frac{4x}{5}[/tex] = 336

x = [tex]\frac{336 *5}{4}[/tex]

x = 84 * 5

x = 420

Therefore, we get the number is 420

PERCENT INCREASE =(new amount−original amount)/original amount

Some people append 100% at the end of this calculation to stress that it should be stated as a percent since it represents an increase in percentage.

So, as an alternative, here is the formula:

PERCENT INCREASE = (new amount−original amount)/original amount*100%

PERCENT DECREASE=(original amount−new amount)original amount

OR

PERCENT DECREASE=(original amount−new amount)original amount*100%

Both formulas have the following pattern:

PERCENT INCREASE/DECREASE=change in amount /original amount

OR

PERCENT INCREASE/DECREASE=change in amount/ original amount*100%

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Answer:

0.0475

Step-by-step explanation:

Answer:

multiply length times width.

Step-by-step explanation:

Answer:

B. Diagonals that are congruent

The given expression is :

To simplify the expression for x :

Add 5 on both side :

Divide the expression by 4 on both side :

Thus : x ≥ 3

The graph is :

Since x is greater than or equal to 3

So, it is closed on 3

Answer :

The graph has a closed circle on 3 and is shaded to the right of the origin

After evaluting the  expression 8+ 9/4 (-2) we get 8 1/4.and result in decimals: 8.25

Given expression -

8+ 9/4 (-2) = ?

Combine the whole numbers and fractions together:

(8 – 2) + (9/4 - 0)

The whole numbers part is:

8 – 2 = 6

For the fractions part:

(9/4 - 0)

The Least Common Multiple (LCM) of 4 and 1 is 4. Multiply the numerator and denominator of each fraction by whatever value will result in the denominator of each fraction being equal to the LCM:

9/4 - 0 = 9/4 - 0/4

Now that the fractions have like denominators, subtract the numerators:

9 - 0/4 = 9/4

9 ÷ 4 = 2R1, therefore

9/4 = 2 1/4

Put the whole number and fraction together:

6 +2(1/4) 1

8 1/4.

Hence , the result of the expression 8+ 9/4 (-2) = 8 1/4.

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The savings plan balance (future value) after 3 years with a 7% APR and monthly payments of $100 is $3,993.01.

The future value is the present value or cash flows compounded at an interest rate for a period.

The future value can be computed using an online finance calculator.

N (# of periods) = 36 months

I/Y (Interest per year) = 7%

PV (Present Value) = $0

PMT (Periodic Payment) = $100

Results:

FV = $3,993.01

Sum of all periodic payments = $3,600 ($100 x 36)

Total Interest = $393.01

Thus, at the end of 3 years, the saving plan balance grew to a future value of $3,993.01.

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The function exists a Power function. The power of function is 3 and the constant variation is - 1/3

Any function where y = x n, where n is any real constant integer, is referred to be a power function. In reality, many of our parent functions, including linear and quadratic functions, are power functions. A few other power functions are y = x³, y = 1/x, and y = x squared.

A parameter function used in statistical testing that represents the likelihood of rejecting the null hypothesis for a given value of the parameter, assuming that value is true.

Therefore, the power of function is 3 and the constant variation is - 1/3.

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The tangent relation is given by the length of the opposite side to the angle over the length of the adjacent side to the angle.

So we have:

Therefore the correct option is C.

The given expression xy = yx represents the cumulative property of multiplication.

If altering the operands' order has no effect on the outcome, the binary operation is commutative in mathematics. Numerous binary operations share this essential characteristic, and numerous mathematical arguments rely on it.

The given expression is xy = yx.

The expression xy = yx is representing the cumulative property of multiplication. According to this property, the value of the expression will remain the same after the order is changed.

Let x = 5 and y = 10. Now verify the cumulative property of multiplication.

xy = yx

5 x 10 = 10 x 5

50 = 50

Therefore, the given expression xy = yx represents the cumulative property of multiplication.

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Airthemetic Sequence : arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

It express as :

In the given question the 88 term is ( 25)

Substitute the value in the expression of n terms

In the given Airthmetic sequence the constant difference, d = 4

Now for the position of term 8

for n= 5 terms is 8

Now for the term of position 8:

So, the term with position 8 is 20

Now for the position of term 36 :

Thus, for n = 10, an = 36

Now, for the term of position 19

Thus at n = 19 the term i 64

The formula that most accurately captures the dilatation that Triangle ABC underwent to produce A'B'C will be:

(x, y) → (1/2x, 1/2y)

Detailed explanation?

A triangle's vertices are given.

A(-2, -4) (-2, -4)

B(2, -4) (2, -4)

C(-8, -4) (-8, -4)

The vertices of an image triangle should be after the dilatation

A' (-1, -2) (-1, -2)

B '(1, -2) (1, -2)

C' (-4, -2) (-4, -2)

If we look attentively, we can see that the vertices of the image triangle, A'B'C', make up half of the original triangle ABC.

For example, (x, y) (1/2x, 1/2y)

verification

A(-2, -4) → A'(-2/2, -4/2) = A'(-1, -2) (-1, -2)

B(2, -4) → B'(2/2, -4/2) = B'(1, -2) (1, -2)

C(-8, -4) → C'(-8/2, -4/2) = C'(-4, -2) (-4, -2)

As a result, it is confirmed, and we come to the conclusion that the rule that best captures the dilatation that Triangle ABC underwent to form A'B'C' will be:

(x, y) → (1/2x, 1/2y)

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4/15 = 3.75

10/13 = 1.3    

you have to divide it from its higher number or you'll get something like this: 0.7692307692307692 but if it helps it = 0.00205128205

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Answer:

para hacer la repuesta xd

The side length of the triangle Elizabeth drew cannot form a right triangle.

A right triangle is a triangle that has one of its angle as 90 degrees.

The sides of a right triangles are hypotenuse side, adjacent side and the opposite side. This is base on the angle position.

Right triangle obeys Pythagoras's theorem.

a² + b² = c²

where

Therefore, let's test if the labelled side of the triangle Elizabeth drew is a right triangle.  We will use Pythagoras theorem to confirm it

5² + 8² = 14²

25 + 64 = 196

Therefore,

89 ≠ 196

Therefore, the side length cannot form a right triangle

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Given:

Let's solve using law of indices below:

Using the same method, we have:

ANSWER:

Using the arithmetic progression, If a theatre has 30 rows of seats there are 22 seats in the first row,26 in the second row, 30 in the third row, then the total number of people that the theatre hold is 2400

The total number of rows = 30

Number of seats in the first row = 22

Number of seats in the second row = 26

Number of seats in the third row = 30

Common difference= Second term - first term

= 26-22

= 4

The given sequence is in arithmetic progression

Sum of n terms = [tex]\frac{n}{2}[2a+(n-1)d][/tex]

Substitute the values in the equation

= [tex]\frac{30}{2}[2(22)+(30-1)4][/tex]

= 15[44+29×4]

= 15[44+116]

= 15×160

= 2400

Hence, using the arithmetic progression, if a theatre has 30 rows of seats  and there are 22 seats in the first row,26 in the second row, 30 in the third row, then the total number of people that the theatre hold is 2400

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The perimeter of the hexagon ABCDEF is 36.01.

Given,

The hexagon ABCDEF

We have given the points:

A(-6, 2), B(1, 5), C(6, 5), D(6, -1), E(1, -3), F(-6, -3)

We have to find the perimeter of hexagon.

Perimeter of hexagon = AB + BC + CD + DE + EF + FA

Now,

Distance formula is as [tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

So,

A(-6, 2), B(1, 5) : x₁ = 1, x₂ = -6, y₁ = 2, y₂ = 5

[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

= [tex]\sqrt{(1-(-6))^{2} +(5-2)^{2} }[/tex]

=[tex]\sqrt{7^{2} +3^{2} }[/tex]

= [tex]\sqrt{49+9}[/tex]

= √58

= 7.62

B(1, 5), C(6, 5) : x₁ = 1, x₂ = 6, y₁ = 5, y₂ = 5

[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

= [tex]\sqrt{(6-1)^{2}+(5-5)^{2} }[/tex]

= √5²

= 5

C(6, 5), D(6, -1) : x₁ = 6, x₂ = 6, y₁ = 5, y₂ = -1

[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

= [tex]\sqrt{(6-6)^{2}+(-1-5)^{2} }[/tex]

= √-6²

= 6

D(6, -1), E(1, -3) : x₁ = 6, x₂ = 1, y₁ = -1, y₂ = -3

[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

= [tex]\sqrt{(1-6)^{2}+(-3-(- 1))^{2} }[/tex]

= [tex]\sqrt{(-5)^{2} +(-3+1)^{2} }[/tex]

= [tex]\sqrt{25 + 4}[/tex]

= √29

= 5.39

E(1, -3), F(-6, -3)  : x₁ = 1, x₂ = -6, y₁ = -3, y₂ = -3

[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

= [tex]\sqrt{(-6-1)^{2}+(-3-(-3))^{2} }[/tex]

= √-7²

= 7

F(-6, -3), A(-6, 2)  : x₁ = -6, x₂ = -6, y₁ = -3, y₂ = 2

[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

= [tex]\sqrt{(-6-(-6))^{2} +(-3-(2))^{2} }[/tex]

= √-5²

= 5

So, we have

AB = 7.62

BC = 5

CD = 6

DE = 5.39

EF = 7

FA = 5

Now,

Perimeter of hexagon = AB + BC + CD + DE + EF + FA

Perimeter of hexagon= 7.62 + 5 + 6 + 5.39 + 7 + 5

Perimeter of hexagon = 36.01

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Conclusions that can be made about the line in the table include:

The slope of a line is found by the formula:

= Change in y / Change in x

Two points from the table:

(-6, -7) (2, -3)

Slope is:
= (-3 - (-7)) / 2 - (-6))

= 4 / 8

= 1/2

The y-intercept is:

y = Slope (x) + y-intercept

-3 = 2(1/2) + y-intercept

y-intercept  = -3 - 1

y-intercept  = -4

Points on the line as shown on the table:

(-2, -5) and (8,0)

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