Question 2
In the diagram, BCD is a straight line. AD = 2V3 cm
Work out the exact length of CD. Give your answer in the form
a + bv3 where a and b are integers
Not drawn
accurately
2V3 cm​

Explanation:

The formula for law of cosines is:

[tex]a^{2} = b^{2} + c^{2} - 2bc(cosA)[/tex]

This is written at the top of your paper.

The angle is substituted where the capital A is. The side opposite to the angle is the angle name's lowercase. The two other sides are b and c.

Substitute all the information you know, then isolate the variable that you do not know.

When your formula is rearranged to look like this:

[tex]\frac{a^{2} - b^{2} - c^{2}}{- 2bc} = (cosA)[/tex]

Solve the left side and punch into your calculator:

cos⁻¹(left side) to find the angle A.

Answer:

The least number of days that will pass before Andy will have to do both chores together on the same days are 5 days.

Step-by-step explanation:

Let us start from the initial day.

Every 2 days Andy takes out the trash.

So, the days he takes out trash are second day, fourth day, sixth day , eighth day , tenth day and so on..          (1)

Every 3 days Andy sweeps the kitchen.

So, the days he sweeps the kitchen are third day,  sixth day , ninth day , twelfth day and so on..          (2)

Now, on comparing both equations (1) and (2) we see the first common day to both the chores is SIXTH DAY.

Hence, the least number of days that will pass before Andy will have to do both chores together on the same days are 5 days.

Answer:

[tex]\theta=54.25\°[/tex]

Step-by-step explanation:

we know that

When the sine of angle X is equal to the cosine of angle Y, then angle X and angle Y are complementary angles

so

[tex]X+Y=90\°[/tex]----> equation A

In this problem

[tex]X=\theta[/tex]

[tex]Y=(\theta-18.5)[/tex]

substitute in the equation A

[tex]\theta\°+(\theta-18.5)\°=90\°[/tex]

[tex]2\theta=90+18.5[/tex]

[tex]2\theta=108.5[/tex]

[tex]\theta=54.25\°[/tex]

Answer:

t = 3c - 5

Step-by-step explanation:

The relation between c and t is linear as the increase of the value of t is uniform for each unit increase in the value of c.

Now, any two points on the graph of the t = f(c) equation are sufficient to determine the equation.

Let the points are (2,1) and (3,4).

So, using two points formula of straight line we get the equation is  

[tex]\frac{t - 4}{4 - 1} = \frac{c - 3}{3 - 2}[/tex]

⇒ t - 4 = 3(c - 3)

⇒ t - 4 = 3c - 9

⇒ t = 3c - 5 (Answer)

Answer:

Cut it in half so that the two pieces are each 7 in by 4 in.

Answer:

x=36/11

Step-by-step explanation:

4(2x-1)=-3x+32

8x-4=-3x+32

8x-(-3x)-4=32

8x+3x-4=32

11x-4=32

11x=32+4

11x=36

x=36/11

Answer:

-20/21

Step-by-step explanation:

Answer:

IT IS ETHER A OR B BROBABLY

Step-by-step explanation:

Given:

LM = LN, KM = KN, KO bisects angle MKN

What we want to prove:

LO bisects angle MLN

=====================================

Proof:

Statement 1: KM = KN

Reason 1: Given

---------------------

Statement 2: KO bisects angle MKN

Reason 2: Given

---------------------

Statement 3: Angle MKO = Angle NKO

Reason: Definition of angle bisection

---------------------

Statement 4: KO = KO

Reason 4: Reflexive property of congruence

---------------------

Statement 5: Triangle MKO = Triangle NKO

Reason 5: SAS postulate

note: this combines statements 1, 3, and 4 (for the "S", "A", and "S" in that order)

---------------------

Statement 6: MO = ON

Reason 6: CPCTC

note: CPCTC stands for "corresponding parts of congruent triangles are congruent"

---------------------

Statement 7: Angle KOM = Angle KON

Reason: CPCTC

---------------------

Statement 8: OL = OL

Reason 8: Reflexive property of congruence

---------------------

Statement 9: Triangle MOL = Triangle NOL

Reason 9: SAS postulate

note: used statements 6, 7, 8 for the "S", "A", "S" in that order

---------------------

Statement 10: Angle MLO = Angle NLO

Reason 10: CPCTC

---------------------

Statement 11: LO bisects angle MLN

Reason 11: Definition of angle bisection

---------------------

That concludes the proof. We did not use the statement "LM = LN", so it is unnecessary.

To prove that LO bisects angle MLN, we can use the Angle Bisector Theorem. According to this theorem, if a line bisects an angle, it divides the opposite side into two segments that are proportional to the adjacent sides of the angle. We can prove this by using the given information and applying the theorem.

To prove that LO bisects angle MLN, we can use the Angle Bisector Theorem. According to this theorem, if a line bisects an angle, it divides the opposite side into two segments that are proportional to the adjacent sides of the angle. In this case, LO is the angle bisector of angle MLN if and only if (MN/NO) = (ML/LO). We can prove this by using the given information and applying the theorem.

Given:

To prove:

Proof:

So, we have proven that LO bisects angle MLN.

The given statement that is unnecessary for this proof is 'TLX TL' because it does not provide any additional information or requirement for proving that LO bisects angle MLN.

Answer:

a(1) = 8, a(n + 1) = a(n) + 5

Checking this:

a(2) = a(1) + 5 = 8 + 5 = 13

a(3) = a(2) + 5 = 13 + 5 = 18

a(4) = a(3) + 5 = 18 + 5 = 23

a(5) = a(4) + 5 = 23 + 5 = 28

Answer:

b=43/3

Step-by-step explanation:

2/3+5=20-b

2/3+15/3=20-b

17/3=20-b

b=20-17/3

b=60/3-17/3

b=43/3

[tex]7\frac{13}{21}[/tex] km thread will be needed for 8 boxes of shirts

Step-by-step explanation:

The proportion will be used to find the measurement of thread

Given

It takes 3 1/3 kilometers of thread to make 3 1/2 boxes of shirts.

Now,

As there are more boxes, more thread will be needed. So it is a direct proportion

So,

[tex]Km:box::Km:box\\3\frac{1}{3}: 3\frac{1}{2}::x:8\\\frac{10}{3}:\frac{7}{2}::x:8\\\frac{\frac{10}{3}}{\frac{7}{2}} = \frac{x}{8}\\\frac{10}{3} * \frac{2}{7} = \frac{x}{8}\\\frac{20}{21} = \frac{x}{8}\\x = \frac{20}{21} * 8\\x = \frac{160}{21}\\x = 7\frac{13}{21}[/tex]

Hence,

[tex]7\frac{13}{21}[/tex] km thread will be needed for 8 boxes of shirts

Keywords: Unit rate, conversion

Learn more about conversion at:

#LearnwithBrainly

Answer:

Step-by-step explanation:

It's perfectly logical that as the number of hours spent watching TV increases, the grades received on the quizzes drop.  There's a negative correlation between the two variables.

Answer:

the answer is A

Step-by-step explanation:

1.35 divided by 3 = 0.45

0.45 multiplyed by 8 = $3.60

Answer:

[tex]y = \frac{1}{3}x + 3[/tex]

Step-by-step explanation:

The slope of two parallel straight lines are the same.

Now, the slope of the line [tex]y = \frac{1}{2} x + 8[/tex] is [tex]\frac{1}{2}[/tex] as the straight line equation is in slope-intercept form.

Now, the equation of the straight line in slope-intercept form which is parallel to the above line is [tex]y = \frac{1}{2} x + c[/tex] ............. (1) , where c is any constant.

Now, point (-2,2) is on the line (1) {Given}

So, this point will satisfy the equation.

Hence, [tex]2 = \frac{1}{2} (- 2) + c[/tex]

⇒ c = 3.

Therefore, the equation of the required straight line is [tex]y = \frac{1}{3}x + 3[/tex] (Answer)

Answer:

30%

Step-by-step explanation:

120/400= 0.3

0.3x100=30

Answer:

A. (2 × 6) + (3 × 8) + 6²

72 sq. inches.

B. 9 in. by 8 in.

Step-by-step explanation:

The white shape has dimensions of 2 in. by 6 in. and the green shape is a square.

So, the dimension of the green shape is 6 in. by 6 in.

Therefore, the length of the blue shape is (6 + 2) = 8 in.

Now, given that the area of the blue shape is 24 sq. in.

So, the width of the blue shape is [tex]\frac{24}{8} = 3[/tex] in.

Now, if we consider the total figure, then area of the entire figure = area of the  white shape + area of the green shape + area of the blue shape.

= (2 × 6) + (3 × 8) + 6² (Answer)

= 12 + 24 + 36  

= 72 sq, inches. (Answer)

Now, the length of the entire figure is (6 + 3) = 9 in. and width of the entire figure is (2 + 6) = 8 in.

Therefore, the dimensions of the entire figure will be 9 in. by 8 in. (Answer)

Answer: 71 hours

Step-by-step explanation:

Answer:

$15

Step-by-step explanation:

Answer:

X=16

Step-by-step explanation:

Line QT is congruent with line RS, while line RQ is also congruent with line TS. All in all, each line is congruent to the other. Meaning all sides equal the same amount. We know that angle measure must equal 180, so you must take 3x+5+9x-17=180. Then you will get the variable X to equal 16.

Answer:

Prime number

Step-by-step explanation:

41 is a prime number.

How to test:

Divide 41 by every whole number from 1 until about it's square root.

√41 is about 6.4, round up to 7.

If any quotient is not a decimal number, 41 is not prime.

41/2 = 20.5

41/3 = 13.7

41/4 = 10.25

41/5 = 8.2

41/6 = 6.8

41/7 = 5.9

These are all decimal numbers.

Step-by-step explanation:

The answer would be A

To find 1/2% as a decimal we can divide this by 100. (This is shown in the question)

1/2 = 0.5

0.5 / 100 = 0.005 (0.5% divided by 100 = 0.005)

_______

Best Regards,

Wolfyy :)

Answer:

C

Step-by-step explanation:

Answer:

Equation: 3x + 2 = 50

# of friends: 16

Step-by-step explanation:

3 chocolates each or 3x because what "each" means is not known yet-

3x

Note: Always use x for an unknown value

2 remaining chocolates-

3x + 2

50 total chocolates-

3x + 2 = 50

Remove two to keep the x alone-

3x = 48

Remove the 3 or the "Coefficient" by dividing-

48/3 = 16

x = 16

Equation: 3x + 2 = 50

# of friends: 16

Answer:

25 + 2n

Step-by-step explanation:

25 increased by twice the number n.

25 increased by 2 x n

25 + 2n

Answer:

Ariel

Step-by-step explanation:

Ariel is diving which is below the surface of the water

Answer:

ariel

Step-by-step explanation:

Step-by-step explanation:

A line and a quadratic (parabola) can have either 0, 1, or 2 solutions.

It is impossible for a linear-quadratic system to have more than 2 solutions.

Answer:

Elga's age is 5.

Step-by-step explanation:

3x=y

x+y=20

-------------

x+3x=20

4x=20

x=20/4

x=5

3(5)=15

y=15

x=5, y=15

Answer:

  (x - 56) / 9

Step-by-step

We represent the original number of cans of soup by the variable x. After 56 cans of soup were sold, the remaining number of cans of soup is x - 56. Since we have shelves that can hold 9 cans, the number of shelves needed to fit all the remaining cans is