What is (2x−6)+4(x−3)

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

Find a rational number halfway in between the two numbers. three sevenths and one tenth

strojnjashka [21]

Answer:
The rational number is : 37/140

Explanation:
The first number given is three sevenths which can be written as 3/7
The second number given is one tenth which can be written as 1/10

Now, we want to get the midpoint between these two numbers. The midpoint can be calculated as follows:
midpoint = (first number + second number) / 2
midpoint = [(3/7) + (1/10)] / 2
midpoint = 37/140

Hope this helps :)

4 0

3 years ago

Read 2 more answers

Which expression is equivalent to 16x16x16

DENIUS [597]

Answer:

16^3

Step-by-step explanation:

16 x 16 x 16 is the same thing as 16 to the 3rd power. The power is how many times you multiply the number by itself.

6 0

2 years ago

Read 2 more answers

PLSSS HELP IF YOU TURLY KNOW THISS

grigory [225]

<h2>Answer:</h2>

The answer is x = 2.

<h2>Step-by-step explanation:</h2>

* Scroll to the bottom for an explanation in list format :)

In this problem, our goal is to solve for x in order to identify said variable's value. To do this, we must isolate the variable x on one side, whilst the other side contains solely the value of x. The rules that we will be using for this problem are 'Line of Equality' and 'PEMDAS.' Line of Equality is a rule that states that what you do to one side of an inequality/equation, you must to do the other as well. PEMDAS is a mathematical acronym used as a tell-tale of sorts for order of operations - often OoO for inequalities such as this one. In PEMDAS, P stands for Parenthesis, E stands for Exponents, M stands for Multiplication, D stands for Division, A stands for Addition, and S stands for Subtraction. You use each letter in order of the spelling, with the exception that you do Multiplication and Division by whichever comes first in the equation; the same goes for Addition and Subtraction. However, when solving this inequality, we won't have to focus on the complications of P, E, or M at all.

The (original) inequality this problem gives us is 14 + 3x = 2 + 9x. Our first step is to choose which side we will isolate x to, leaving the other one to be its value. I would personally recommend isolate whichever x value is greater, but either way works. This time around, I chose to isolate 9x.

Since I've decided to isolate x on the right side (2 + 9x), that means I have to eliminate any other x values on either side of the inequality. The only other x value is 3x. Due to + 3x being adding a positive 3x, we have to counteract it by eliminating it and changing its value to 0. In this case, we can counteract + 3x by subtracting 3x (aka - 3x). Remember, the Line of Equality rule means we have to do the same to either side; if we subtract 3x on one side, we also have to do so on the other. 14 + 3x - 3x = 2 + 9x - 3x. +3x - 3x = 0, or 0x. 9x - 3x = 6x. After combining like terms, the new inequality is 14 = 2 + 6x.

Now, I have to eliminate any numerical values, or regular numbers (which, in this case, would be numbers without a variable attached to them), on the right side, since that is the side I want to isolate x on. The only numerical value on the right side of my inequality is 2. This 2, or + 2, can be counteracted by subtracting 2, or - 2. Our rule causes us to subtract 2 from both sides. 14 - 2 = 2 - 2 + 6x. 14 - 2 = 12. 2 - 2 = 0. After combining like terms, the new inequality is 12 = 6x.

Now, I have to simplify x and make it singular. 1x and x are the same thing, so I must make 6x into x. 6x is the same thing as 6 * x. Therefore, since 6 * x is multiplication, I have to do the opposite to get the desired result. I should divide 6x by 6 to get 6. Due to the Line of Equality, I also have to divide 12 by 6. 12 ÷ 6 = 6x ÷ 6. 12 ÷ 6 = 2. 6x ÷ 6 = x. After combining like terms, the new inequality is 2 = x.

Lastly, mainly for a bonus step, we should flip the places of 2 and x. This is because, similarly to most problems, this question places x on the left side of the inequality. The 2 and x in 2 = x must switch places in order to properly finish this problem. Since this inequality uses an equal sign, the symbol will remain as an = when the inequality is flipped. However, it should be noted that when using symbols such as greater than (>) or less than (<), the sign will flip with the rest of the inequality. = is a symmetrical sign, which is why it will remain the same; it is the same equivalent symbol even when flipped. After we flip the inequality, the new equation becomes x = 2. Therefore, our answer is x = 2.

<h3>For those that want a list format of the procedure for this inequality's solving - here you go: </h3>

* Remember the 'Line of Equality' Rule: What you do on one side, on the other do the same.

14 + 3x = 2 + 9x

Subtract 3x from both sides.

14 + 3x - 3x = 2 + 9x - 3x

14 = 2 + 6x

Subtract 2 from both sides.

14 - 2 = (+)2 - 2 + 6x

12 = 6x

Divide both sides by 6.

12 ÷ 6 = 6x ÷ 6

2 = x

Flip the inequality. (The sign remains the same since it's the equal sign.)

x = 2

Therefore, our answer is x = 2.

7 0

3 years ago

HELP ASAP PLZ PLZ PLZ I GIVE BRAINLIEST

Yuki888 [10]

Answer:

12

Step-by-step explanation:

We can see that the base TA is 4, and the second base RS is 2. We can see that the height is 4. The area of a trapezoid is:

$A=\frac{h(b_1+b_2)}{2}$

Using this, we can substitute, and get:

$A=\frac{4\cdot(2+4)}{2} = \frac{24}{2} = 12$

Hope it helps!!

5 0

3 years ago