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3 years ago

S2 Summer Holiday Homework

Mathematics

1 answer:

Juli2301 [7.4K]3 years ago

6 0

I. xy + 2y=3 Not linear equation because is grade 2 equation (xy).

II. x-2y = y Are linear equations in two unknowns (x and y).

III. 3x + 2y = 5 Are linear equations in two unknowns (x and y).

<h2>Corect ansver: C) II and III only</h2><h2></h2>

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Question 1)<br>Solve 8x + 3 = 3x + 18

Dafna1 [17]

Step-by-step explanation:

8x-3x = 18-3(like terms)

or,5x = 15

or,x=15/5

or,x=3

8 0

3 years ago

Read 2 more answers

For positive acute angles A and B, it is known that tan A = 35/12 and sin B = 20/29. Find the value of sin(A - B ) in the simple

almond37 [142]

Answer:

$\displaystyle \sin(A-B)=\frac{495}{1073}$

Step-by-step explanation:

We are given that:

$\displaystyle \tan(A)=\frac{35}{12}\text{ and } \sin(B)=\frac{20}{29}$

Where both A and B are positive acute angles.

And we want to find he value of sin(A-B).

Using the first ratio, we can conclude that the opposite side is 35 and the adjacent side is 12.

Then by the Pythagorean Theorem, the hypotenuse is:

$h = \sqrt{35^2 + 12^2} =37$

Using the second ratio, we can likewise conclude that the opposite side is 20 and the hypotenuse is 29.

Then by the Pythagorean Theorem, the adjacent is:

$a=\sqrt{29^2-20^2}=21$

Therefore, we can conclude that:

So, for A, the adjacent is 12, opposite is 35, and the hypotenuse is 37.

For B, the adjacent is 21, opposite is 20, and the hypotenuse is 29.

We can rewrite sin(A-B) as:

$\sin(A-B)=\sin(A)\cos(B)-\cos(A)\sin(B)$

Using the above conclusions, this yields: (Note that since A and B are positive acute angles, all resulting ratios will be positive.)

$\displaystyle \sin(A-B)=\Big(\frac{35}{37}\Big)\Big(\frac{21}{29}\Big)-\Big(\frac{12}{37}\Big)\Big(\frac{20}{29}\Big)$

Evaluate:

$\displaystyle \sin(A-B)=\frac{735-240}{1073}=\frac{495}{1073}$

6 0

3 years ago

UPPER AND LOWER BOUNDS - PLEASE HELP!

Marianna [84]

Qn. 1
Lower bound for Zoe's weight = 62 - (1/2) = 62 - 0.5 = 61.5 kg

Qn. 2
Upper bound for length AB = 8.3+ (0.1/2) = 8.3+0.05 = 8.35 cm

Qn. 3
Upper bound for Anu's wight = 83+(0.5/2) = 83+0.25 = 83.25 kg

Qn. 4
Lower bound for length CD = 27-(0.5/2) = 27-0.25 = 26.75 cm

Qn. 5
Upper bound for sides of the hexagon = 3.6+(0.1/2) = 3.6+0.05 = 3.65 cm
Upper bound for the perimeter = upper bound for the sides*6 = 3.65*6 = 21.9 cm

Qn. 6
Perimeter = 4*length => side = Perimeter/4 = 24/4 = 6
Bound = 0.5/4 = 0.125
Lower bound of the length = 6-0.125 = 5.875 cm

Qn. 7
For the area,
Upper bound = 80+(10/2) 80+5 = 85 cm^2
For the length
Upper bound = 12+(1/2) = 12+0.5 = 12.5

Then, upper bound for the width = Upper bound for the area/upper bound for the length = 85/12.5 = 6.8 cm

Qn. 8
Lower bound for the area = 230-(1/2) = 230-0.5 = 229.5 cm^2
Lower bound for the sides of the square = Sqrt(Lower bound of the area) = Sqrt (229.5) = 15.15
Then,
Lower bound of perimeter = 4(Length) = 4*15.15 = 60.6 cm

8 0

3 years ago

Can someone help me with this???

Varvara68 [4.7K]

Answer:

?????????????????????????

4 0

2 years ago

Broccoli costs $1.50 PER POUND at a grocery store. How much money does 64 OUNCES of broccoli cost?

Gnoma [55]

$6.00
Show your work in the attachment. Down below

5 0

3 years ago