MATHEMATICS HIGH SCHOOL

Solve the following system of equations using substitution. What is the value of y?2x+3y=105
x+2y=65
I somehow got -1(4/6)x=-5. Can someone provide a clear explanation on how to do this?

Answers

Answer 1
Answer: I have no idea how did you get this result but I can show you the method of elimination. I think that it is the easiest way to solve the system of equations.
2 x + 3 y =105
x + 2 y = 6  /*(-2)      // We will multiply 2nd equation by -2. That is because                                         we want to cancel out the x`s//
2 x + 3 y = 105
-2 x - 4 y = -12        // Then we will add down these equations/ and x`s will                                          cancel out//
3 y - 4 y = 105 - 12
- y = 93
y = -93
We can also solve x:
x + 2 * (-93)=6
x - 186 = 6
x = 6 + 186
x = 192 

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4. Find the length of side EG.

Answers

Answer:

42 cm

Step-by-step explanation:

the first triangle is 7 times bigger than the second triangle. ( 4 x 7 = 28)

so to find out line EG, you times 6 cm by 7. which is 42

Find nth term of 14,23,32,41

Answers

Answer:

The nth term of the series is 5-9n.

Step-by-step explanation:

Given : Series 14, 23, 32, 41,..

To find : The nth term of the series ?

Solution :

The given series 14, 23, 32, 41,.. is an arithmetic series as the difference between term is common.

Where, first term is a=14 and common difference d=23-14=9

The nth term of the arithmetic series isa_n=a+(n-1)d

a_n=a+(n-1)d

a_n=14+(n-1)9

a_n=14+9n-9

a_n=5-9n

Therefore, The nth term of the series is 5-9n.
1.14
2.23
3.32
4.41
5.50
6.59
7.68
8.77
9.86

Each face of cabinet 413s is in the shape of a rectangle. What is the volume of model 413s in cubic feet

Answers

Hopefully this is the question you are talking about!
They want us to find the volume of model 413S in ft³
This isnt tough!
change the side measurements from Inches to Feet
12 in = 1 ft

so therefore:
24 in = 2 ft
72 in = 6 ft
18 in = 1.5 ft

Volume of a cuboid is:
Area of base × height of cuboid
V = 2 ft × 6 ft ×1.5 ft
   = 18 ft³
Volume of the cabinet (Model 413S) is 18 ft³ 
Each side of the model of 413s is rectangular shaped.
So, by this statement we got to know that the model is in cuboid shape.
Hence, its volume will be (length×width×height) cubic feet.

Which sequence is geometric and has 1/4 as its fifth term and 1/2 as the common ratio?…, 1, 1/2, 1/4, 1/8, …

…, 1/4, 1/2, 1, 2,…

…, 1/72, 1/36,1/18, 1/9, …

…, 8, 4, 2, 1, …

Answers

the answer is 0.5. Because you have to half 1

Ruth, Daisy, and Martin share £750 in the ratio of 3:5:7. Determine how much money Ruth receives.

Answers

Answer:

Ruth receives £150

Step-by-step explanation:

sum the parts of the ratio, 3 + 5 + 7 = 15 parts

divide the total £750 by 15 to find the value of one part of the ratio

£750 ÷ 15 = £50 ← value of 1 part of the ratio

Then

3 parts = 3 × £50 = £150 ← amount Ruth receives

Can you solve this?
1+cot^2θ=csc^2θ

Answers

the equation above is a "pythagorean identity", and therefore, the left-side is indeed equal to the right-side.

what are the values of θ that make the equation true?  well, all possible angles.
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