Which function has a period of л?
A. y = cos x
B. y = csc x
C. y = cot x
D. y = sin x​

Answer:

Step-by-step explanation:

3

Answer:

x=6

Step-by-step explanation:

4(x+5) =9x+4x-34

1. we can simplifying the right hand side by adding 9x+4x

this gives us

           4(x+5)=13x-34

2. we expand the brackets to get

           4x+20=13x-34

3. we take the x on one side in this case we will subtract 4x from each side and add 34 on each side to get

          54=9x

4. we divide each side by 9 because we want to find the value of x this gives us

         6=x

The area of land inside the fence is 7600 square feet.

What is the area of the triangle?

If the height of the triangle is 'h' and the base is 'b', then the area of the triangle can be computed by using the formula,

           Area = 1/2 * base * height

To find the area of the land inside the fence, we can use the formula for the area of a right triangle:

Area = (1/2) * a * b

where a is the length of one of the legs of the triangle and b is the length of the hypotenuse.

We are given that the length of fence b is 130 feet and that the measure of angle A is 42°. Since the triangle is right, angle A is complementary to angle 90°, so the measure of angle A is 90° - 42° = 48°. Since the measure of angle A is 48°, the other leg of the triangle (which we will call "a") is the side opposite angle A.

We can use the sine function to find the length of side a:

a = b * sin A

= 130 * sin 48°

= approximately 117.3 feet

Substituting these values into the formula for the area of a right triangle gives:

Area = (1/2) * 117.3 feet * 130 feet

= approximately 7600.5 square feet

Rounded to the nearest square foot, the area of land inside the fence is 7600 square feet.

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From Properties of Triangles , both figures are connected and angle ∠B or ∠2 is 65°

Basic properties of triangles are:

1)A triangle's (of all varieties) total sum of angles is 180°.

2)The length of a triangle's two longest sides added together is longer than the third side.

3)Similar to this, the length of the third side of a triangle's third side is shorter than the difference between its two sides.

4)The longest of a triangle's three sides is the side that faces the larger angle.

5)A triangle's exterior angle is always equal to the product of its inner and exterior opposite angles. The outer angle attribute of a triangle refers to this characteristic.

As sum of angles in a triangle is 180° and sum of angles on a line is also 180°, both the figures are related.

Sum of angles=180°;

[tex]50+B+65=180;\\B=65[/tex]

∠B=65°

Similarly angle 2 is also 65°

From Properties of Triangles , both figures are connected and angle ∠B or ∠2 is 65°

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Answer:

W = width

L = length = 2W + 3

P = 36 = 2W + 2L = 2W + 2(2W + 3) =

6W + 6 = 36

6W = 30

W = 5

L = 13

The Formula for h(x) is 7.5cos(51.4x - 154.3)-1.5.

What is trigonometric function ?

Trigonometric functions are referred to as Circular Functions will be merely outlined because the functions of associate degree angle of a triangle.

The difference in y values from max to min = 15. 15/2 = a
max cosine = 1, min cosine =-1
7.5 x 1 - 1.5 = 6
7.5x -1 -1.5 = -7.5-1.5= -9
h(x) = 7.5cos(bx+c) -1.5
now just get a period or frequency that matches the x coordinates 3 and 6.5 to get b and c
at (3,6) cosine = 1 to get a maximum value. cosine is at a max when cos(bx+c) = 1 and bx+c=0, 360, 720...
if x=3, then 3b +c=0 and c=-3b
for (6.5,-9) to be a minimum h value, then cos(6.5b+c) =-1 that happens when the angle = 180. +n360 for any integer n. 6.5b+c = 180
c= 180-6.5b
c=-3b
180-6.5b =-3b
add 6.5b to both sides to get
180= 3.5b
b = 180/3.5 = 51 1/7
c=-3b = -153 3/7
h(x) = 7.5cos(51.4x - 154.3)-1.5
hence , Formula for h(x) is 7.5cos(51.4x - 154.3)-1.5

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Answer:

12 notches from both left and right of 0

you want the absolute value of (-12). all that means is how far is the number away from 0. in this case it's just 12

Answer:

B) 18 ft

Step-by-step explanation:

The scale is 1 in. model : 6 ft real.

6/1 = 6

To go from model size to real size, multiply the model size by 6 and change from inches to feet.

3 in. model = 3 × 6 ft = 18 ft

Length of AB in the cuboid is 20.784cm.

There are 6 faces, 12 edges, and 8 vertices on a cuboid.

All of the cuboid's faces have rectangular shapes.

The cuboid's opposing edges are parallel to one another.

The three dimensions of a cube are length, width, and height.

All of the angles created at the cuboid's vertices are 90 degree angles.

Length of Diagonal of cuboid is [tex]\sqrt{a^2+b^2+c^2}[/tex], where a,b,c are side lengths of cuboid,

Given:

AG=24cm;

AB=2BC;

CG=6m;

We know that diagonal of cuboid length is [tex]\sqrt{a^2+b^2+c^2}[/tex]

Here

Let AB=a, BC=b, CG=c;

So a=2b;

Now  

[tex]AG=\sqrt{a^2+b^2+c^2}=\sqrt{(2b)^2+b^2+6^2}=\sqrt{ 5b^2+36 }=24\\5b^2+36=576\\5b^2=540\\b=10.392cm\\AB=a=2b=20.784cm[/tex]

Length of AB in the cuboid is 20.784cm.

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The total number of pairs sold by SoccerWorld is 57

How to determine the total number of pairs sold by SoccerWorld?

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

SoccerWorld sold 3 as many boots as JP Sports

DirectSportz sold 5 more boots than JP Sports.

Cost of each pair = £70

Amount in sales = £7000

The above parameters means that

s = 3j

d = 5 + j

70(s + d + j) = 7000

Where

j = JP Sports

s = SoccerWorld

d = DirectSportz

Divide both sides of 70(s + d + j) = 7000 by 70

s + d + j = 100

Substitute s = 3j and d = 5 + j

3j + 5 + j + j = 100

Evaluate the like terms

5j = 95

Divide by 5

j = 19

Substitute j = 19 in s = 3j

s = 3 * 19

So, we have

s = 57

Hence, the number of pairs is 57

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Answer: A 2/1

Step-by-step explanation:

Determine the slope of the line by finding 2 points

(2,-1),(4,3)

use slope formula

y2-y1/x2-x1

plug in and solve

3+1/4-2

4/2

2

the slope is 2 or 2/1

The value of y is 54 when x = -2

The value of y is 18 when x = -1.

The value of y is 6 when x = 0.

The value of y is 2 when x = 1.

The value of y is 2/3 when x = 2.

What is a function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Given function is

y = 6(⅓)^x

To find the value at x = -2, -1, 0, 1, 2, put the value of x in the given equation.

Putting x = -2 in the equation y = 6(⅓)^x

y = 6(⅓)⁻²

Applying index formula (1/a)^(-m) = a^m

y = 6(3)²

y = 6 × 9

y = 54

Putting x = -1 in the equation y = 6(⅓)^x

y = 6(⅓)⁻¹

Applying index formula (1/a)^(-m) = a^m

y = 6(3)¹

y = 6 × 3

y = 18

Putting x = -1 in the equation y = 6(⅓)^x

y = 6(⅓)⁰

Applying a⁰ = 1

y = 6 × 1

y = 6

Putting x = 1 in the equation y = 6(⅓)^x

y = 6(⅓)¹

y = 6 × 1 /3

y = 2

Putting x = 2 in the equation y = 6(⅓)^x

y = 6(⅓)²

y = 6 × (1/9)

y = 6/9

Divide the denominator and numerator by 3:

y = 2/3

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Answer:

Step-by-step explanation:

The unit rate is 400 square feet per gallon.

What is unitary method ?

Unitary method is a mathematical way of deriving a single unit and then finding the required unit by multiplying.

A graph is shown in the diagram and two points are given x co-ordinate represents paint used per gallon and y co-ordinate represents wall painted in square feet.

Given (1/4,100) implies 1/4th of a gallon paint is needed to pain 100 square feet of wall.

∴ In 1 gallon (100)÷1/4 square feet of wall can be painted which is 400 square feet.

And the unit rate is 400 square feet per gallon.

L= 97

Step-by-step explanation:

The perimeter is all of the sides of the rectangular pool added up. We know the both widths are gonna be 54m. So to find both widths together you need to multiply 54 by 2 to give us 108. The we need to find both lengths together, so subtracting 302-108 will get us 194. Both lengths together, 194,  divided by 2 is 97, which is our length.  

No, The given table is not in proportional.

What is Proportional?

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

The table is,

 Width of photo                              Height of photo

      2                                                     3

      4                                                     6

      5                                                     7

      8                                                     10

Now,

Since, The table is,

 Width of photo                              Height of photo

      2                                                     3

      4                                                     6

      5                                                     7

      8                                                     10

So, By definition of proportional, we get;

⇒ Width /Height = 2 / 3

⇒ Width /Height = 4 / 6 = 2 / 3

⇒ Width /Height = 5 / 7

⇒ Width /Height = 8 / 10 = 4 / 5

Clearly, All the proportion are not in same ratio.

Thus, The given table is not in proportional.

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According to the exchange rates £1 = €1. 18, £1 = $1. 72 the job in New York will pay Salma the higher salary.

In mathematics, the term "more than" refers to an inequality between two values, quantities, or numbers, where one is greater than the other. In other terms, we say that A is more than B when A is greater in contrast to B.

A job in Milan offer €70,000 per year;

And exchange rate are:

£1 = €1. 18

so she will get

£=70,000x1. 18

£=82600

on other hand job in New York offer $102,900 per year. The exchange rate are:

£1 = $1. 72

so she will get

£= 102,900x1. 72

£=176988

So the job in New York will pay her higher salary.

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Answer:

Step-by-step explanation:

The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is:((x1 + x2)/2, (y1 + y2)/2)Substituting the coordinates of points P and Q into the formula, we get:((2 + (-7))/2, (4 + (-2))/2) = (-2.5, 1)The coordinates of the midpoint of segment PQ are (-2.5, 1).To verify that this point is on the line through P and Q, we can find the slope of the line using the coordinates of points P and Q:slope = (y2 - y1)/(x2 - x1) = (-2 - 4)/(-7 - 2) = -6/-9 = 2/3We can then use the point-slope form of a linear equation to write the equation of the line through points P and Q:y - y1 = m(x - x1)

y - 4 = (2/3)(x - 2)We can substitute the coordinates of the midpoint (-2.5, 1) into this equation to see if it is a solution:1 - 4 = (2/3)(-2.5 - 2)

-3 = -10/3The equation is true, so the midpoint (-2.5, 1) is on the line through points P and Q.To show that this point is just as far from P as it is from Q, we can use the distance formula to find the distance from the midpoint to points P and Q:distance = √((x2 - x1)^2 + (y2 - y1)^2)distance from (-2.5, 1) to (2, 4) = √((2 - (-2.5))^2 + (4 - 1)^2) = √(4.5^2 + 3^2) = √(20.25 + 9) = √(29.25) = 5.4distance from (-2.5, 1) to (-7, -2) = √((-7 - (-2.5))^2 + (-2 - 1)^2) = √(4.5^2 + 3^2) = √(20.25 + 9) = √(29.25) = 5.4. Since the distance from the midpoint to points P and Q is the same, the midpoint is just as far from P as it is from Q.

Answer:

x = 2

Step-by-step explanation:

-2x - 48 ≥ 10x - 24

-48 + 24 ≥ 10x + 2x

24 = 12x

x = 2

The correct matrix representation is [tex]\left[\begin{array}{ccc}2&3\\3&-1\\\end{array}\right][/tex]

We can represent a vector pointing at a point by its x coordinate, and y coordinate, and Let us say there are two points represented by their x-, y coordinates as P₁(x₁,y₁) P₂(x₂,y₂)

Given here the points are P₁(2,3) and P₂(3,-1)

Thus by the coordinates of the two vectors, we can represent  the matrix  

[tex]\left[\begin{array}{ccc}2&3\\3&-1\\\end{array}\right][/tex]

Hence, Option D) is the correct answer.

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The triangle congruency theorem which can be used to prove

â–³ ≅ â–³onp is  ASA (angle  side angle)

Let the triangles be ONP and GHL

The congruence theorem, which will demonstrate that "GHL" and "ONP ," are congruent is to be discovered.

As can be seen, side lengths GH of GHL and ON of ONP are equal.

Furthermore, we are informed that mONP = mHKJ.

Since line segments GK and JL connect to produce them, we can see that GHL is the vertical opposite angle of ONP . Therefore, using the vertical angles theorem, mONP  congruence mKHJ.

We can see that both triangles contain two congruent angles and one congruent included side; as a result,

GHL ONP by ASA congruence.

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flips a fair coin five times, 5/16 is the probability that there are 3 heads in a row somewhere in the sequence of five flips.

The number of positive outcomes to all possible outcomes of an event is the ratio, which is known as probability.

The number of positive outcomes may be expressed by x for an experiment with n number of outcomes.

The following equation can be used to determine an event's probability:

Probability(Event) = Favorable outcomes / Total Outcomes = x/n

Considering a fair coin, after 5 flips, there are [tex]2^5[/tex] = 32 different arrangements of heads and tails.

To get exactly 3 heads,

[tex]^5C_3[/tex] = 5! / (5 - 3)! 3!

     = 5!/ 3! 2!

     = 10 ways

P(exactly 3 heads) = 10/32 = 5/16

Therefore, the probability of exactly 3 heads is 5/16.

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From the sampling distribution we know:

a. will become more variable as the sample size increases.

A sampling distribution is the probability distribution of a statistic that was acquired from more samples taken from a certain population. The distribution of frequencies for a variety of potential outcomes that could happen for a population statistic makes up the sampling distribution of a specific population.

When it comes to the spread of all sample proportions, theory predicts behaviour far more accurately than just stating that larger samples have a smaller spread. In actuality, the sample size, n, and the standard deviation of each sample proportion.

Thus, option (a) correctly describe about sampling distribution of the sample proportion.

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The measure of ∠XYZ is 112° if WXYZ is a rhombus.

A quadrilateral with four equal-length sides is known as a rhombus in plane Euclidean geometry (plural rhombi or rhombuses). Another term for this shape is an equilateral quadrilateral since all of its sides are equal in length. The rhombus is frequently referred to as a "diamond" after the diamonds suit in playing cards, which resembles the projection of an octahedral diamond.

Every rhombus is straightforward (does not self-intersect), and it is a particular instance of a parallelogram and a kite. Right-angled rhombuses are called square.

A rhombus's diagonals cut through two opposing angles:

∠YWZ=∠WYZ

Now, we have to substitute ∠YWZ=56° into ∠YWZ=∠WYX: 56°=∠WYX

We have to calculate 56°=∠WYX:∠WYX=56°

The angle addition postulate is, ∠XYZ=∠WYX+∠WYZ

Now, substitute ∠WYZ=56°, ∠WYX=56° into ∠XYZ=∠WYX+∠WYZ

∠XYZ=56°+56°

∠XYZ=112°

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One tablet weighs will be 1.93 pounds.​

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The combined weight of 4 identical tablet computers and a 4 3-pound laptop is 10.7 pounds.

Now,

Let the weight of 1 tablet = x

So, We can formulate;

⇒ 4x + 3 = 10.7

Solve for x as;

⇒ 4x = 10.7 - 3

⇒ 4x = 7.7

⇒ x = 7.7 / 4

⇒ x = 1.93 pounds

Thus, One tablet weighs = 1.93 pounds.​

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Answer:

The amount of water at the Georgia Aquarium is 20 times greater than the aquarium of the Americas hold.

Step-by-step explanation:

What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the tanks at the Georgia Aquarium hold approximately 8.4 × 10⁶ gallons of water. The tanks at the Audubon Aquarium of the Americas hold about 400,000 gallons of water.The number of the time will be calculated as below:-= 8.4 × 10⁶ / 400,000= 20.1

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In order to increase the likelihood that a blue marble would be drawn at random to 3/4, we must thus add 32 more blue marbles.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to express probabilities.

Here,

Let the number of blue marbles added be x,

Probability=3/4

Total marbles=20

Number of blue marbles=7

(7+x)/(20+x)=3/4

4(7+x)=3(20+x)

28+4x=60+3x

x=60-28

x=32

So, we need to add 32 more blue marbles to make the probability of randomly drawing a blue marble be 3/4.

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Answer:

x=125,2x=250

Step-by-step explanation:

A hexagon sum of angles is 720 degrees.

The sum of the hexagon's angles is 345+3x

345+3x=720

3x=375

x=125

2x=250

The difference in the areas of the signals based on the information given is 549.5km².

The formula to calculate the area of a circle will be:

= πr²

where r = radius

Mast 1 broadcast radio signals that can be heard within a radius of 15km. The area will be:

= πr²

= 3.14 × 15²

= 706.5km²

Mast 2 broadcast radio signals that can be hear within a radius of 20km. The area will be:

= πr²

= 3.14 × 20²

= 1256km²

The difference in the areas will be:

= 1256km² - 706.5km²

= 549.5km²

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Complete question

Mast 1 broadcast radio signals that can be heard within a radius of 15km.

Mast 2 broadcast radio signals that can be hear within a radius of 20km.

Calculate the difference in the areas of the signals.

The values needed for the box plot that Adams wants to display are:

Lower quartile = 6.8

Median = 8.4

Upper quartile = 9.5

Given the following data that represents the records of the increase in the height of a plant for 10 weeks, 4.5, 3.2, 8.0, 9.1, 10.2, 6.8, 7.2, 9.5, 10.0, 8.8, in order to draft a box plot, the following steps are what Adams should take to find each of the values needed.

Step 1: Order the data set from least to the greatest.

3.2, 4.5, 6.8, 7.2, 8.0, 8.8, 9.1, 9.5, 10.0, 10.2

Step 2: Find the median.

The median is the middle of the data set = (8.0 + 8.8)/2 = 16.8/2 = 8.4

Step 3: Find the lower quartile which is the center of the first part of the data that is divided by the median.

Lower quartile = 6.8

Step 4: Find the upper quartile which is the center of the second part of the data that is divided by the median.

Upper quartile = 9.5

Therefore, the values that Adam needs for his box plot are:

Lower quartile = 6.8

Median = 8.4

Upper quartile = 9.5

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The sum of the fractions (- 3/5 + 1/5) in simplest form is - 11/20.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, Are two proper fractions - 3/4 and - 1/5, and we are required to take the difference which is,

= - 3/4 - (- 1/5).

Now the negative signs will distribute to positive which is,

= - 3/4 + 1/5.

Now, the LCM of 4 and 5 is 20.

= {(-3×5) + (1×4)}/20.

= (- 15 + 4)/20.

= - 11/20.

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