Help with this trig identities problems.


1) Given csc Φ = 7/3 and cot Φ = - (2√10)/(3), find sec Φ.


2) Given that sec β = 6/5 and sin β > 0, find tan β and sin β.

If her hοuse actually 56 feet wide, then scale οf her drawing is scale = 56 feet / (drawing width)

The slοpe is a mathematical cοncept that refers tο the steepness οf a line. It is cοmmοnly denοted by the letter "m" and can be calculated using the fοrmula:      

slοpe (m) = (change in y) / (change in x)

Withοut having the actual measurements οf the drawing, we cannοt determine the scale.

Tο find the scale οf a drawing, yοu need tο knοw the actual measurements οf the οbject being drawn as well as the cοrrespοnding measurements in the drawing. Fοr example, if yοu knοw that the actual width οf Rοse's hοuse is 56 feet and the width οf the hοuse in the drawing is 8 inches, yοu can determine the scale by using the fοllοwing fοrmula:

scale = actual width/drawing width

Using this fοrmula with the given infοrmatiοn, we get:

scale = 56 feet / (drawing width)

Therefοre, we dο nοt have the drawing width, we cannοt calculate the scale.

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A graph is made up of vertices, or points, and edges, or lines connecting those vertices.

Graphs come in a wide variety of forms in discrete mathematics.

These are a few of them:

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The correct question is-

what are the different types of graph.

Accοrding the given expressiοns this is the right answer  (1/2)⁵ = 1/2 × 1/2 × 1/2 × 1/2 × 1/2 = 1/32

(1/5)³= 1/5 × 1/5 × 1/5 = 1/125

In mathematics, an expressiοn is a cοmbinatiοn οf numbers, variables, and οperatοrs that represents a mathematical relatiοnship οr fοrmula. It can include numbers, variables, and mathematical οperatοrs such as additiοn, subtractiοn, multiplicatiοn, divisiοn, expοnents, and rοοts. Fοr example, 2x + 3y is an expressiοn that includes the variables x and y, and the οperatοrs additiοn and multiplicatiοn. Expressiοns can be simplified, evaluated, οr used tο represent mathematical relatiοnships.

a) (1/2)⁵ = 1/2 × 1/2 × 1/2 × 1/2 × 1/2 = 1/32

b) (1/5)³ = 1/5 × 1/5 × 1/5 = 1/125

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The correct answer is A) test statistic T equals -1.952; P value, 0.0414.

An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true. In the scientific process, the hypothesis is developed before any pertinent research—aside from a basic background review—has been conducted.

The null hypothesis that there is no difference between the triglyceride test levels is sufficiently refuted by the available data.

With 9 degrees of freedom and a significance threshold of 0.05, this can be ascertained by comparing the derived test statistic (T) with the critical value of t from the t-distribution table. We reject the null hypothesis if the estimated T value is in the rejection zone (i.e., T value is smaller than the critical value of t).

The computed T value in this instance is -1.952, which is in the rejection region (i.e., less than the critical value of t of -1.833). Hence, we get to the conclusion that there is enough data to imply that the new diet has an effect on lowering triglyceride levels and reject the null hypothesis that there is no difference between the triglyceride test levels.

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The sentence represented as an algebraic expression is x² - 1

Algebraic expressions can be defined as a mathematical expression that consists of terms, variables, constants, coefficients and fractions.

Also, these algebraic expressions are identified with arithmetic or mathematical operations. These operations are;

From the information given, we have that;

Let the number be x

If 1 is then subtracted from the square of a number.

Fiirst, the square of the number is x²

This is represented as;

x² - 1

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By taking these factors into account, they can create a product that meets the needs of potential customers and is a success in the market. the tent design, size options, materials, features, and pricing when planning the new model of triangular pyramid tents.

Triangular Pyramid Tent Design:

The triangular pyramid tent design is a unique shape that could potentially offer better stability against wind and other weather conditions. However, it may also require more complex construction and assembly than a traditional rectangular tent.

The design department should consult with engineers and experienced tentmakers to ensure that the triangular pyramid tent can be manufactured in a cost-effective and user-friendly manner.

Size options:

The design department has decided to make two sizes of the triangular pyramid tent. They should consider the intended use of the tents and the needs of potential customers when determining the size options.

For example, a smaller size might be suitable for backpackers or solo campers, while a larger size could accommodate families or groups.

Therefore, the tent design, size options, materials, features, and pricing when planning the new model of triangular pyramid tents.

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Answer:-2,-5

Step-by-step explanation:

7-4=3

You move 3 units up

You land on -2, -2

the higher units you move up, the higher the number gets to.

Answer: 3. 35x + 15 = 155

Step-by-step explanation:

35 x 4 = 140

140 + 15 = 155

Therefore , the solution of the given problem of function comes out to be  y grows by 19/4 units for every unit increase in x.

There will be questions on design, mathematics, each subject, and both real expression and imagined locations on the midterm exam. a list of the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input. Every mailbox also has a specific address, which may be an enclave, a neighborhood.

Here,

The slope of the equation

=> y = 19/4x - 19 is 19/4.

This implies that y grows by 19/4 units for every unit increase in x.

You would need to be familiar with the expression or

graph of the other function in order to compare the rate of change with it.

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The triangle that would not represent the three sides of a triangles is: {9, 21, 32}

We can determine this through the use of the triangle rule. The rule tells us that the sum of the two sides of the triangle have to be greater than that of the other side.

With this in mind, we have that for each of this

14 + 24 > 37

15 + 30 > 43

9 + 21 < 32

10 + 19 > 26

Hence the third option does not fulfill the rule

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Answer:

Step-by-step explanation:

Para convertir 44 semanas a meses, debemos saber cuántas semanas hay en un mes. El número de semanas en un mes no es exacto, pero generalmente se considera que hay alrededor de 4.33 semanas en un mes (ya que el año tiene aproximadamente 52 semanas y 12 meses).

Entonces, para calcular cuántos meses hay en 44 semanas, podemos dividir 44 por 4.33:

44 semanas / 4.33 semanas por mes = 10.16 meses (aproximadamente)

Por lo tanto, 44 semanas equivalen aproximadamente a 10.16 meses.

Answer:

32

Step-by-step explanation:

Answer:

The answer to this question is 391 points will be scored in 17 games. to find this answer you divide 94 by 4 to find the total points per single game, then multiply that by 17. in this case is is 92 divided by 4 = 23 then 23 X 17 = 391

Answer:assuming its a rectangle its 13.5

Step-by-step explanation: L x H = Area

The distance from rock to tree is approximate 99.48 m.

The bearing in navigatiοn refers tο the path between twο pοints, calculated in clοckwise rοtatiοns arοund nοrth. It is frequently emplοyed tο indicate the directiοn οf travel between twο places οr the οrientatiοn οf a landmark with respect tο a ship οr aircraft.

The azimuth, which is the angle between a reference directiοn (οften nοrth) and the directiοn tο an οbject οr pοint, is distinct frοm the bearing.

A. check the attachment given.

B. Let the distance from rock to tree be = H meter

Now, [tex]$ \rm \frac{Sin(056^{\circ})}{1} = \frac{H}{120}[/tex]

H =  Sin(056°) × 120

H = 99.48 m

Thus, The distance from rock to tree is  99.48 m.

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Answer:

6 units the answer is C. just see it

If the circle is dilated by a factor of 2, the equation of the circle is: C. (x + 3)² + (y - 2)² = 18.

In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;

(x - h)² + (y - k)² = r²

Where:

By critically observing the graph of this circle, we have the following parameters:

By substituting the given parameters into the equation of a circle formula, we have the following;

(x - h)² + (y - k)² = r²

(x - (-3))² + (y - 2)² = 3²

(x + 3)² + (y - 2)² = 9.

By dilating with a scale factor of 2, we have:

(x + 3)² + (y - 2)² = (9 × 2)

(x + 3)² + (y - 2)² = 18

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Step-by-step explanation:

remember the GCF (greatest common factor) ?

every number or term is the product of certain prime numbers (prime factors).

the product of factors that the discussed numbers or terms have in common is the GCF.

1)

12x³ + 8x

12x³ :

12 / 2 = 6

6 / 2 = 3

3 / 2 no

3 / 3 = 1 finished

12 = 2×2×3

x³ = x×x×x

so,

12x³ = 2×2×3×x×x×x

8x :

8 / 2 = 4

4 / 2 = 2

2 / 2 = 1 finished

8 = 2×2×2

x = x

so,

8x = 2×2×2×x

what factors do they have in common ?

2×2×x = 4x

so, the GCF = 4x

that means

12x³ + 8x = 4x×3x² + 4x×2 = 4x(3x² + 2)

2)

18a² + 2a

18a² :

18 / 2 = 9

9 / 2 no

9 / 3 = 3

3 / 3 = 1 finished

18a² = 2×3×3×a×a

2a :

2 / 2 = 1 finished

2a = 2×a

so, they have 2×a = 2a in common.

the GCF = 2a.

that means

18a² + 2a = 2a×9a + 2a×1 = 2a(9a + 1)

3)

25b⁴ + 30b³

25b⁴ :

25 / 2 no

25 / 3 no

25 / 5 = 5

5 / 5 = 1 finished

25b⁴ = 5×5×b×b×b×b

30b³ :

30 / 2 = 15

15 / 2 no

15 / 3 = 5

5 / 3 no

5 / 5 = 1 finished

30b³ = 2×3×5×b×b×b

so, they have 5×b×b×b = 5b³ in common.

the GCF = 5b³

that means

25b⁴ + 30b³ = 5b³×5b + 5b³×6 = 5b³(5b + 6)

The coordinates of B' after the sequence of transformations are given as follows:

B'(3,-4).

The coordinates of B are given as follows:

B(-3,1).

After a reflection over the y-axis, the x-coordinate of B is exchanged, hence:

B'(3, 1).

The rule for a 90º clockwise rotation is that (x,y) becomes (y,-x), hence the coordinates of B' after the 90º clockwise rotation are given as follows:

B'(1, -3).

The translation (x + 2, y - 1) means that 2 is added to the x-coordinate while 1 is subtracted from the y-coordinate, hence the final coordinates of B' are given as follows:

B'(3,-4).

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If triangle ABC has points A(2, -4), B(-3, 1), and C(-2, -6) and you perform the following transformations, B' would be at B' (3, -4).

In Geometry, the rotation of a point 90° about the center (origin) in a clockwise direction would produce a point that has these coordinates (y, -x).

By applying a reflection over the y-axis to the coordinate of the given point B (-3, 1), we have the following coordinates:

Coordinate B = (-3, 1)   →  Coordinate B' = (-(-3), 1) = (-3, 1).

Next, we would apply a rotation of 90° clockwise as follows;

(x, y)                               →            (y, -x)

Coordinate B' = (-3, 1) → Coordinate B' = (1, (-3)) = (1, 3)

Finally, we would apply a translation (x + 2, y - 1) as follows:

Coordinate B' = (1, 3) → (1 + 2, 3 - 1) = B' (3, 2).

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We may conclude after answering the presented question that As a equation result, we have demonstrated that mt = mu when t | u.

Make a note of the definition of t | u. It denotes the existence of an integer k such that u = tk.

To get mt = m, substitute u = tk into mt = mu (tk).

Rewrite m(tk) as (mt)k using the associative property of multiplication.

To get mt = (mt)k, substitute (mt)k for m(tk) in the equation mt = mu.

Multiply both sides by mt. If mt is greater than zero, we obtain 1 = k. If mt is zero, we must also have mu = 0, hence the equation holds.

Since 1 Equals k, we get u = tk = t(1) = t.

We get mt = mt by substituting u = t into the original equation mt = mu.

As a result, we have demonstrated that mt = mu when t | u.

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The angle is in the fourth quadrant.

What do you mean by quadrant?

The coordinate system's two axes (the x-axis and y-axis) constitute a region called a quadrant. The quadrants are the four areas generated when the x- and y-axes cross at a 90-degree angle.

                                Coordinate values, also known as x- and y-values, are present in both positive and negative directions in these locations.

What is a quadrant circle?

Any one of the four regions is a quadrant when a circle is uniformly divided into two perpendicular parts. In fact, anything that can be divided into four equal halves is said to be made up of quadrants. Hence, a quadrant of a circle is one-fourth of the entire circle.

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The terminal ray strikes the fourth quadrant at a rotational angle of 6 radians.

Two-dimensional Cartesian axes separate the plane into four infinite regions known as quadrants, each of which is bordered by two half-axes.

The coordinate system's two axes, the x-axis, and the y-axis constitute a region called a quadrant.

The quadrants are generated when the two axes, the x-axis, and the y-axis, cross at a 90-degree angle.

These areas include coordinates or positive and negative values of the x- and y-axes.

The terminal ray falls at a rotational angle of 6 radians in the fourth quadrant.

Therefore, the terminal ray strikes the fourth quadrant at a rotational angle of 6 radians.

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The circumference's shortest distance between points A and C is 102.91m.

A rectangle is a quadrilateral with four right angles in the Euclidean plane.

It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal.

A square is a rectangle with four equally long sides.

As a result, a square is a particular form of rectangle since it has rectangles with equal-length sides.

So, we know that:

AC = 80 m

CD = 50 m

Apply the Pythagorean theorem to the right triangle using ADC.

AC = √AD² + CD²

AC = √80² + 50²

AC = 94.34m

The shortest path through the park from point A to point C must only follow the lines depicted in the diagram.

Hence, we must deduct AC by 15 meters in diameter.

94.34m - 15m = 79.34m

The shortest distance is 79.34 miles plus one-half a circle's circumference.

As the circle's diameter is 15 meters, the radius is 15/2 = 7.5m.

The circumference would be:

2*π*r = 47.14m

The half circumference would be:

47.14/2 = 23.57m

Then,

79.34m + 23.57m = 102.91m

Therefore, the circumference's shortest distance between points A and C is 102.91m.

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answer is

512

Step-by-step explanation:

1.6x80=128

128x4=512

Answer:

The correct equation is:

b - 3/4 = 3 1/4

Explanation:

Lily used 3/4 of a chocolate bar, so the remaining chocolate bars can be found by subtracting 3/4 from the total number of chocolate bars b:

b - 3/4 = remaining chocolate bars

The problem tells us that there are 3 1/4 remaining chocolate bars, so we can substitute this value in the equation and solve for b:

b - 3/4 = 3 1/4

b = 3 1/4 + 3/4

b = 4

Therefore, the counselor put 4 chocolate bars on the table.

The perimeter of the decks is 120 feet

Perimeter is a mathematical term that refers to the total distance around the boundary of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.

The property of circles states that "the tangents drawn from the same point on a circle are equal in length". It means that if two tangent lines are drawn from an external point to a circle, the length of both tangents will be equal.

Here we have

Tangents QR and QV from point Q

Tangents RS and ST from point S

Tangents VU and UT from point U

As we know,

The tangents drawn from the same point on a circle are equal in length  

=> Tangent QR = QV --- (1)  from point Q

=> Tangent RS = ST ----- (2) from point S

=> Tangent VU = UT ----- (3) from point U  

From the figure,

The perimeter of decks = QR + RS + ST + TU + UV + VQ  

From (1) (2) and (3)

=> QR + ST + ST + UV + UV + QR  

=> 2QR + 2UV + 2RS  

From the figure,

=> 2(24 ft) + 2(26 ft) + 2 (36 - 26)   [ ∵ ST = US - TU ]

=> 48 ft  + 52 ft + 20 ft

=> 120 ft  

Therefore,

The perimeter of the decks is 120 feet

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The circles having an area less than 300 square centimeters are;

Option A: A circle with a radius of 9. 5 centimeters

Option D: A circle with a diameter of 15 centimeters

It is important to note the formula for calculating the area of a circle is expressed as;

A = πr²

Such that the parameters are;

From the information given, we have that;

radius = 9.5 centimeters

Substitute the value

Area = 3.14 × (9. 5)²

Area = 283. 4 cm²

For diameter of 15 centimeters

Radius = 7.5 centimeters

Substitute the values

Area = 3.14 × (7.5)²

Area = 176. 6 cm²

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According to the solution we have come to find that, 48% of the teas served were caffeinated.

A percentage is a way of expressing a proportion or a fraction as a number out of 100. The symbol used for percentage is the "%" sign. For example, if you have 10 apples and you want to express how many of them are red, you can say that 20% (or 2 out of 10) of the apples are red.

To find the percentage of caffeinated teas served, we need to divide the number of caffeinated teas by the total number of teas served, and then multiply by 100 to get the answer as a percentage.

Total number of teas served = 36 + 39 = 75

Percentage of caffeinated teas served = (36/75) x 100%

                                                                = 48%

Therefore, 48% of the teas served were caffeinated.

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Answer:

Step-by-step explanation:

In math, slope is used to describe the steepness and direction of lines. ... You can determine the slope of a line from its graph