Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles

Among all the statements the correct statement is cosec B=4/3 which is last statement.

Given a triangle in which angles are different.

We are required to find the correct statement among the given statements.

We have to take statements one by one and find the trigonometric ratios.

Trigonometric ratios are the ratios which expresses the ratios of the sides of a right angled triangle.

Sin Θ=P/H    

Cos Θ=B/H

Tan Θ=P/B

Cosec Θ=H/P

Sec Θ=H/B

Cot Θ=B/P

When we take angle B then we can find that cot B=5/6.

So the first statement is wrong.

When we take angle C then we can find that cosec C=8/5.

So the second statement is also wrong.

When we take angle C then we can find that cot C=6/5.

So the third statement is also wrong.

When we take angle B then we can find that Cosec B=8/6=4/3

So the fourth statement is correct.

Hence among all the statements the correct statement is cosec B=4/3 which is last statement.

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Based on the scatterplot, the equation that BEST represents the relationship between velocity and time is y = 2.2x + 6

The line of best fit is the line that best represents the relationship between 2 variables. The equation of a line in slope-intercept form is expressed as:

y = mx + b

where

m is the slope

b is the intercept

Using the coordinate points on the plane (0, 6) and (10, 28)

Determine the slope

Slope = 28-6/10-0
Slope = 22/10
Slope = 2.2

Determine the y-intercept

6 = 2.2(0) + b

b = 6

Determine the equation of aline of best fit.

y = 2.2x + 6

Hence based on the scatterplot, the equation that BEST represents the relationship between velocity and time is y = 2.2x + 6

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If the equation is 19-5=3z-11 then the value of z is 15/3.

Given an equation in terms of z is 19-5=3z-11.

We are required to find the value of variable z which exist in equation.

Equation is like a  relationship between two or more variables expressed in equal to form. Equations of two or more variables look like ax+by=c. It may be linear equation, quadratic equation,cubic equation,or many more depending on power of the variable.

The value of z can be find as under:

19-5=3z-11

4=3z-11

3z=4+11

3z=15

z=15/3

Hence if the equation is 19-5=3z-11 then the value of variable z is 15/3.

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The average rate of change of the given function is 10π.

Given function

a = πx^2

Where a is the area of a circle with radius x

The radius changes from x = 4 to x = 6.

Calculating the average rate of change of function:

The method of finding the average rate between the function value over a certain interval is called the average rate of change.

The formula is given by :

Average = [tex]\frac{f(b)-f(a)}{b-a}[/tex]

Where f(a) and f(b) are the function value over the limit a and b.

Average = [tex]\frac{f(6)-f(4)}{6-4}[/tex]

= [tex]\frac{\pi (6)^{2} -\pi (4)^{2} }{6-4}[/tex]

= [tex]\frac{\pi (36-16)}{2}[/tex]

= [tex]\frac{20\pi }{2}[/tex]

= 10π

The average rate of change of the given function is 10π.

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Answer:

[tex]\huge\boxed{\sf a_{400}=1276}[/tex]

Step-by-step explanation:

79, 82, 85, 88, ....

[tex]a_n=a_1+(n-1)d[/tex]

Where,

Put the givens in the above formula

[tex]a_{400}=79 +(400-1)3\\\\a_{400}=79 + 399\times3\\\\a_{400}=79+ 1197\\\\a_{400}=1276\\\\\rule[225]{225}{2}[/tex]

By applying Pythagoras theorem, the missing segment lengths of this triangles include:

Since triangle ACD is a right-angle triangle, we would use Pythagoras theorem to find the missing segment lengths of this triangles as follows:

c² = a² + b² ≡ AD² = CD² + AC²

Next, we would use cos trigonometric ratio to find side CD,

cos45 = adjacent/hypotenuse

cos 45 = CD/20

1/√2 = CD/20

CD = 1/√2 × 20

CD = (20√2)/2

CD = 10√2

For side AC, we have:

AD² = CD² + AC²

AC² = AD² - CD²

AC² = 20² - (10√2)²

AC² = 400 - 100(2)

AC = √200

AC = 10√2

From triangle ABC, we have:

cos45 = BC/10√2

BC = 10√2 × cos45

BC = 10√2 × 1/√2

BC = (10√2)/√2

BC = 10

For side AB, we have:

AB² = (10√2)² - 10²

AB² = 200 - 100

AB² = 100

AB = 10.

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Answer:

the money should be split as per each girl sold. total boxes sold is 100.

Step-by-step explanation:

total boxes sold is 100. Mia sold 57/100 keela 28/100 and Michelle 15/100.

mia=456$

keela=224$

michelle=120$

calculated as boxes sold/100 x 800$

The price of the product before promotional sales was 500,000.

To find what the previous price of the product was, we must take into account that we know that 87% of the value is equal to 435,000. So to find out how much the 13% (discount) that the product had is equivalent to, we do the following operation:

435,000 × 100 ÷ 87 = 500,000

So we know that the 13% discount was 65,000

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Answer:

2: choice b

Step-by-step explanation:

a: $1.66 / 10 oz = $0.166/oz

b: $3.22 / 20 oz = $0.161/oz

Answer: 2: choice b

For a triangle with base of 10 inches and altitude of 16 inches, its area will be 80 in² (third option).

Calculation For the Area of the Triangle:

It is given that,

The base of the triangle, B = 10 inches

The altitude from the base of the triangle or height, H = 16 inches

Now, the formula used for finding the area of a triangle is given as follows,

Area, A = (1/2) × B × H

Substituting the given values of B and H in the above formula for area, we get,

A = (1/2) × (10 inches) × (16 inches)

A = 5 × 16 inches²

A = 80 inches²

Thus, the area of the triangle have base 10 inches and altitude 16 inches is 80 square inches.

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Step-by-step explanation:

I understand this that we need to find a point B for each of a) to f).

remember, the slope is the (y coordinate difference / x coordinate difference) when going from one point on the line to the other.

a)

the slope 2/3 means that when going to B x has to increase by 3, and y has to increase by 2.

so, B = (-2 + 3, 5 + 2) = (1, 7)

b)

-2/3 means that either x or y have to decrease and the other to increase.

e.g. x increases by 3, y decreases by 2.

so, B = (-2 + 3, 5 - 2) = (1, 3)

c)

4 stands for 4/1.

so, x increases by 1, y increases by 4.

B = (-2 + 1, 5 + 4) = (-1, 9)

d)

similar to c) -3 stands for -3/1.

and similar to b) either x or y has to decrease and the other to increase.

e.g. x increases by 1, y decreases by 3.

B = (-2 + 1, 5 - 3) = (-1, 2)

e)

that means the y difference is 0. B has the same y coordinate.

e.g. B = (3, 5)

x can be any value.

the line is a horizontal line going through y = 5 or (0, 5) on the y-axis.

f)

that means the x difference is 0. B has the same x coordinate.

e.g. B = (-2, 9)

y can be any value.

the line is a vertical line going through x = -2 or (-2, 0) on the x-axis.

Answer: 4.5

Step-by-step explanation:

2 + 0.5x

x = 5

2 + 0.5 ( 5 )

2 + 2.5

2 + 2.5 = 4.5

Hope this helps!

The average number of miles he will ride each day to meet his goal is 6.6 miles

He wants to ride his bicycle 30.4 miles this week.

He has already ridden 4 miles.

He rides 4 more days.

Therefore, the average number of miles he would have to ride each day to meet his goal can be calculated as follows:

let

x = number of miles driven

Hence, the equation can be represented as follows;

4x + 4 = 30.4

Therefore,

4x + 4 = 30.4

4x + 4 - 4 = 30.4 - 4

4x = 26.4

x = 26.4 / 4

x = 6.6

Therefore, the average number of miles he will ride each day to meet his goal is 6.6 miles

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the order from smallest to largest is:

41, 56, 83.

Here we have 3 values, that are:

{83, 56, 41}

To list it from smallest to largest, we first need to write the smallest number, which we can identify is 41.

Then the middle number. Which is 56, that is larger than 41 and smaller than 83.

Finally, the largest number, which is 83.

Then the order is:

41, 56, 83.

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The length of the wall of the tank in feet is 62.8 feet.

Circumference is the perimeter of a circular object. Therefore,

circumference = 2πr

where

The fountains pool is enclosed by a circular plastic tank.

The distance from the centre of the pool to the wall of the tank is 10 feet. This is the radius of the circle

Hence,

length of the tank = 2πr

length of the tank = 2 × 3.14 × 10

length of the tank = 20 × 3.14

length of the tank = 62.8 feet.

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Answer:

[tex] \frac{1 \\ }{3125} [/tex]

Answer:

x = 9

Step-by-step explanation:

        [tex]\sf \dfrac{a^m}{a^n}=a^{m-n}\\\\\\ \dfrac{1}{a^m}=a^{-m}[/tex]

[tex]\sf \dfrac{5^x}{5^{14}}=\dfrac{1}{5^5}\\\\5^{x -14} = 5^{-5}[/tex]

Base are same. Compare the exponents.

 x - 14 = -5

        x = -5 + 14    {Addition property of equality}

        x = 9

Answer:

length = 24 meters
breadth = 16 meters

Step-by-step explanation:

Let L be length and B be breadth

From the first fact we get the equation
L = B + 8         (1)

We know that perimeter = 2(L+B) and this is given as 80

So 2(L+B) = 80

L + B = 80/2 = 40
or
L = 40 - B              (2)

If we add equations (1) and (2) we can eliminate B

We get 2L = B + 8 + 40 - B =48

L = 48/2 = 24

Substituting for L in equation (1) we get

24 = B + 8  ==>

B = 24-8 =16

Cross-check

Perimeter = 2 (L+B) = 2(24 + 16) = 2(40) = 80

Hence check OK

Answer:

Ben was standing in the

Step-by-step explanation:

84 000 000

+ 00 530 000

+ 00 000 216

_________________

84 530 216

From this u can see that the 3 is in the ten thousands place

Answer:

x>-3

Step-by-step explanation:

7x+18>-3

transpose 18 to the other side to group the like terms

7x>-3-18

7x>-21

You divide bother sides by a 7 to get the value of x

7x/7>-21/7

therefore x>-3

The Five number summary for the given data:

Minimum: 24

Lower quartile: Q1 = 29

Median: 43

Upper quartile: Q3 = 50

Maximum: 56

Interquartile range: IQR = 21

The interquartile range is calculated by

IQR = Q3 - Q1

Where Q3 - upper quartile and Q1 - lower quartile

Q3 = 3/4(n + 1) th term

Q1 = 1/4(n + 1) th term

The given data points are

24, 27, 29, 29, 35, 39, 43, 45, 46, 49, 51, 51, 56

where n = 13

Maximum data value = 56

Minimum data value = 24

Calculating Median:

Median = (n+1)/2 th term

⇒ Median = (13 + 1)/2 = 7th term

∴ Median = 43

Calculating the quartiles:

Upper quartile Q3 = 3/4(n + 1)th term

⇒ Q3 = 3/4(13 + 1) = 10.5

⇒ Q3 = 10th term + 1/2(11th term - 10th term)

⇒ Q3 = 49 + 1/2(51 - 49)

⇒ Q3 = 49 + 1

∴ Q = 50

Lower quartile Q1 = 1/4(n + 1)th term

⇒ Q1 = 1/4(13 + 1) = 3.5

⇒ Q1 = 3rd term + 1/2(4th term - 3rd term)

⇒ Q1 = 29 + 1/2(29 - 29)

∴ Q1 = 29

Calculating the IQR:

IQR = Q3 - Q1

      = 50 - 29

      = 21

Thus, the interquartile range is 21.

Therefore, the five-number summary for the given data:

Minimum: 24

Lower quartile: Q1 = 29

Median: 43

Upper quartile: Q3 = 50

Maximum: 56

Interquartile range: IQR = 21

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The sum of the squares of the root is 4113

In a quadratic equation ax² + bx + c , the sum of the roots is -b/a and the product of the roots is c/a

Let m, n be roots of the given equation.

So,

m - n = 75                            -1)

m + n = 51  (as sum of roots of a quadratic equation is -b/a)                          -2)

adding both equations 1) and 2)

2m = 75 + 51

2m = 126

m = 63

substituting value of m in equation 1 we get

63 - n = 75

n = -12

So the sum of squares of the roots of the equation is = 63² + -12²

= 3969 + 144

= 4113

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There are 30240 ways in which we can select five people from a group of ten if the order of selection is important.

Given that there are 10 total number of people.

We are required to find the number of ways in which 5 people can be selected from 10 people.

Permutations is basically the number of arrangements that can be possible with the number of things , people, etc. It is denoted as [tex]nP_{r}[/tex]=n!/(n-r)!.

We have 10 people and we have to select 5 people from them then the number of ways can be find out by [tex]10P_{5}[/tex].

We have to expand this permutation.

=10!/(10-5)!

=10!/5!

=10*9*8*7*6*5!/5!

=10*9*8*7*6

=30240 ways

Hence there are 30240 ways in which we can select five people from a group of ten if the order of selection is important.

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Answer:

a.9

b.36

Step-by-step explanation:

Blue beans + orange beans + red beans = 54

6x + 2x-3 + 15-x = 54

6x+2x-x=54+3-15

7x=42

divide both sides by 7

x=6

a. orange beans = 2x-3

but x=6

2(6)-3

12-3

=9

b.blue beans =6x

6(6)

=36

Answer:

C) (6 x 3) - 18 ÷ 9

Step-by-step explanation:

I'll solve this question by writing down every step and doing it one by one.

1. Multiply 6 by 3

--> This will be represented as 6 x 3.

2. Subtract the quotient of 18 and 9

--> The quotient is a number resulting in a division of another number. In this case, 18 is bigger than 9, so the quotient will be: 18 ÷ 9.

--> Since we are subtracting this from the equation we got earlier, it can be expressed as (6 x 3) - (18 ÷ 9)

This equation is the same as C) (6 x 3) - 18 ÷ 9, so C is our final answer.

If joseph sells his home,  profit will he make = (a)  $79720

What is profit and its example?

Profit earned on the house if he sells = $79720

Amount paid by Joseph for his home = $105000

His house has increased its property value by 2.0% every year

So, Property cost after 20 years :

[tex]Cost = 105000 * (1.02)^{20}[/tex]

Cost = 105000 × 1.4859

Cost = 156020

Also, Due to renovations and improvements to the house, the property cost is increased by $28700

So, Total cost of the house after 20 years = 156020 + 28700

                                                                     = $184720

So, Profit earned on the house if he sells = 184720 - 105000

                                                                      = $79720

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Answer:a)  $79720

Step-by-step explanation:edge

Answer:

169.74+26.80

= 196.54

the correct decimal answer is 196.54

The order of the stages of recession will be 4, 2, 3, 1, 3.

What happens in a recession?

Who benefits in a recession?

Rental agents, landlords, and property management companies can thrive during a recession when renting is likely to become a more appealing option, if not the only one available.

So, these stages are occur -

4. peak production

2. falling production

3. falling demand (occurs twice)

1. job loss

3. falling demand (occurs twice)

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The complete question is-

There are five stages in a recession.

1. job loss

2. falling production

3. falling demand (occurs twice)

4. peak production

In which order do these stages occur?

4, 3, 2, 1, 3

3, 2, 1, 3, 4

4, 3, 2, 3, 1

4, 2, 3, 1, 3

4, 2, 3, 1, 3.Answer:4, 2, 3, 1, 3.

4, 2, 3, 1, 3.Step-by-step explanation:4, 2, 3, 1, 3.

The feet of cloth that she should buy for the capes is 4 feet.

The mathematical operations that would be used to determine the answer are addition and multiplication.

Addition is the process of summing two or more numbers together. Multiplication is the process of determining the product of two or more numbers.

The first step is to convert yard to feet

According to the unit of conversion : 1 yard = 3 feet

1 x 3 = 3 feet

The second step is to add the feet needed for Akira's cape with the foot needed for the puppy's cape

Total feet needed = 3 + 1 = 4 feet

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Based on the calculations, the measure of m∠BDA and m∠BCA are 55° and 70° respectively.

In geometry, a tangent is also referred to as a tangent line and it can be defined as a straight line that touches a plane curve at a specific point.

A circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Also, a circle simply refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).

First of all, we would determine angle BOA:

∠BOA + ∠BOA = 360° (Angles at a point)

∠BOA + 250° = 360°

∠BOA = 360° - 250°

∠BOA = 110°

Next, we would determine angle BDA:

2 × m∠BDA = ∠BOA (Angle inscribed at the center is twice the angle at the circumference)

2 × m∠BDA = 110°

m∠BDA = 110°/2

m∠BDA = 55°.

The theorem of intersecting secants states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.

By applying the theorem of intersecting secants, angle BCA will be given by this formula:

m∠BCA = ½ × (m<AO - m<BO)

Substituting the given parameters into the formula, we have;

m∠BCA = ½ × (250 - 110)

m∠BCA = ½ × 140

m∠BCA = 70°.

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Answer:

70

Step-by-step explanation: