Apa pemfaktoran dari x2-6x-16=0

The perimeter of a triangular field is 120m. Two of the sides are 21m and 40m.Calculate the largest angle of the field.

Mama L [17]

Answer:

the largest angle of the field is 149⁰

Step-by-step explanation:

Given;

perimeter of the triangular filed, P = 120 m

length of two known sides, a and b = 21 m and 40 m respectively

The length of the third side is calculated as follows;

a + b + c = P

21 m + 40 m + c = 120 m

61 m + c = 120 m

c = 120 m - 61 m

c = 59 m

B

↓ ↓

A → → → → → → → → → → → C

Consider ABC as the triangular field;

Angle A is calculated by applying cosine rule;

$a^2 = b^2 + c^2 - 2bc \ Cos A\\\\Cos \ A = \frac{b^2 + c^2 - a^2}{2bc} \\\\Cos \ A = \frac{40^2 + 59^2 - 21^2}{2 \times 40 \times 59} \\\\Cos \ A = 0.983\\\\A = Cos ^{-1} (0.983)\\\\A = 10.6 \ ^0$

Angle B is calculated as follows;

$Cos \ B = \frac{a^2 + c^2 - b^2}{2ac} \\\\Cos \ B = \frac{21^2 + 59^2 - 40^2}{2 \times 21 \times 59} \\\\Cos \ B = 0.937\\\\B= Cos ^{-1} (0.937)\\\\B = 20.5 \ ^0$

Angle C is calculated as follows;

$Cos \ C = \frac{a^2 + b^2 - c^2}{2ab} \\\\Cos \ C = \frac{21^2 + 40^2 - 59^2}{2 \times 21 \times 40} \\\\Cos \ C = -0.857\\\\C = Cos ^{-1} (-0.857)\\\\C = 149\ ^0$

Therefore, the largest angle of the field is 149⁰.

8 0

3 years ago

Teboho has to sell a certain number of cars each month. For every car he sells over and above this number he earns 17% commissio

Nastasia [14]

The commission earned are R41123.17, R47931.67 and R15024.09

<h3>The prices of the cars before VAT was added</h3>

The VAT included prices are given as:

R271 800,00; R316 800,00 and R99 300,00.

The VAT rate is 12.36%.

So, the price before VAT is calculated as:

VAT included = Price without VAT * (1 + 12.36%)

This gives

VAT included = Price without VAT * 1.1236

So, we have:

Price without VAT = VAT included/1.1236

For the three cars, we have:

Price without VAT = R271 800.00/1.1236 = R241901

Price without VAT = R316800.00 /1.1236 = R281951

Price without VAT = R99300.00/1.1236 = R88377

Hence, the prices of the cars before VAT was added are R241901, R281951 and R88377

<h3>The commission he earned on the cars.</h3>

This is calculated as:

Commission = Price * 17%

So, we have:

Commission = R241901 * 17% = R41123.17

Commission = R281951 * 17% = R47931.67

Commission = R88377 * 17% = R15024.09

Hence, the commission earned are R41123.17, R47931.67 and R15024.09

Read more commission at:

brainly.com/question/20987196

#SPJ1

3 0

1 year ago

Six less than a number is twenty

nignag [31]

Answer:

the start numbew woould be 26

Step-by-step explanation:

6 less than 26 is 20

6 0

2 years ago

Read 2 more answers

The number of fiction books in a libary is %150 of the number of non-fiction books. the libary has 4,000 books in total. how man

Nitella [24]

Answer:

The number of

Fiction books = x = 2400 fiction books

Non fiction books = y = non fiction books

Step-by-step explanation:

Let the number of

Fiction books = x

Non fiction books = y

The libary has 4,000 books in total.

Hence: x + y = 4000........ Equation 1

The number of fiction books in a libary is %150 of the number of non-fiction books.

x = 150% of y

x = 150/100 × y

x = 1.5y

We substitute 1.5y for x in Equation 1

x + y = 4000

1.5y + y = 4000

2.5y = 4000

y = 4000/2.5

y = 1600 non fiction books

Solving for x

x = 1.5y

x = 1.5 × 1600

x = 2400 fiction books.

Therefore,

The number of

Fiction books = x = 2400 fiction books

Non fiction books = y = non fiction books

5 0

2 years ago

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.<br> r = 9 sin 7θ

boyakko [2]

Answer:

The given function symmetric about the y-axis.

Step-by-step explanation:

The given function is

$r=9\sin 7\theta$ .... (1)

1. Symmetry about the x-axis: If the point (r, θ ) lies on the graph, then the point (r,-θ ) or (-r, π - θ ) also lies on the graph.

2. Symmetry about the y-axis: If the point (r, θ ) lies on the graph, then the point (r,π - θ ) or (-r, -θ ) also lies on the graph.

3. Symmetry about the origin: If the point (r, θ ) lies on the graph, then the point (-r, θ ) or (r, π + θ ) also lies on the graph.

Put (r, -θ ) in the given function.

$r=9\sin 7(-\theta)=-9\sin 7\theta=-r\neq r$

Therefore it is not symmetric about x-axis.

Put (-r, -θ ) in the given function.

$-r=9\sin 7(-\theta)=-9\sin 7\theta=-r$

Therefore it is symmetric about y-axis.

Put (-r,θ ) in the given function.

$-r=9\sin 7(\theta)=r\neq -r$

Therefore it is not symmetric about the origin.

3 0

2 years ago