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KiRa [710]
3 years ago
14

What is the value of y in the following system of equations? explain how you found your answer

Mathematics
2 answers:
AlekseyPX3 years ago
7 0

Step-by-step explanation:

I've used elimination method over here but it can also be done by using substitution.

Andreyy893 years ago
5 0
2x + 3y = 6
2x + y = -2

Solve the second equation for y and substitute into the first equation

2x + y = -2
y = -2x - 2

2x + 3y = 6
2x + 3(-2x - 2) = 6
2x - 6x - 6 = 6
-4x - 6 = 6
-4x = 12
x = -3

Plug back in to solve for y
2x + y = -2
2(-3) + y = -2
-6 + y = -2
y = 4

Plug into other equation to check
2x + 3y = 6
2(-3) + 3(4) = 6
-6 + 12 = 6
6 = 6 :)
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If a is half b , and b is twice c , then a:c=​
faust18 [17]

Answer: a/c = 1

a/b = 1/2 => a = 1/2 .b

b/c = 2 => c = 1/2 .b

=> a/c = (1/2.b)/(1/2.b) = 1

Step-by-step explanation:

4 0
3 years ago
Carl is standing at the top of 35 Ft cliff looking down at a rock for motion in the sea. He estimates the angle of depression is
Liula [17]

The horizontal distance between Carl and the rock at sea is approximately 60.62ft.

Data;

  • Angle = 30 degree
  • Opposite = 35
  • Adjacent = x

<h3>Trigonometric Ratio</h3>

Given the angle of depression from his point to the sea, we can use trigonometric ratio to calculate for the horizontal distance from his location to the bottom of the sea.

SOHCAHTOA

Since we have the value of angle and opposite and we need to calculate the adjacent side of the right-angle triangle, we can use the tangent of the angle to this effect.

Tan\theta = \frac{opposite}{adjacent} \\tan 30 = \frac{35}{x}\\ x = \frac{35}{tan30}\\ x = 60.62ft

The horizontal distance between Carl and the rock at sea is approximately 60.62ft.

Learn more on trigonometric ratio here;

brainly.com/question/12172664

7 0
2 years ago
Ann studied the effects of watching television on time spent exercising
34kurt

The response variable in the study that Ann has done here can be said to be Time spent exercising.

<h3>What is a response variable?</h3>

This is the name that is used to refer to the dependent variable. This is the variable that is of interest in the study. The goal is to see the changes that occurs in the particular variable based on the actions that another variable would have such as the independent variable.

From this we can see that The response variable in the study that Ann has done here can be said to be Time spent exercising.

Read more on response variable here:

brainly.com/question/22046153

#SPJ1

8 0
1 year ago
Cone W has a radius of 8 cm and a height of 5 cm. Square pyramid X has the same base area and height as cone W. Paul and Manuel
sergij07 [2.7K]

This question is incomplete because it lacks the appropriate attachment containing the argument of Paul and Manuel

Kindly find attached the appropriate attachment necessary to solve this question.

The attachment was sourced online

Answer:

a) Paul's argument is correct, Manuel used the wrong formula to find the volume of square pyramid X

Step-by-step explanation:

From the above question, we are given two shapes: Cone W and Square Pyramid

Cone W: Radius = 8cm, Height = 5cm

Volume of a Cone = 1/3 πr²h

Where π = 3.14

Volume of Cone X = 1/3 × 3.14 × 8² × 5

= 334.93cm³

For Square pyramid X

Volume = 1/3 × Base Area × Height

Base Area of Cone W = Base Area of square pyramid X = πr²

Where π = 3.14

Base area = 3.14 × 8² = 200.96cm²

Height of Square pyramid X = Height of Cone W = 5cm

Volume of Square pyramid = 1/3 ×200.96cm² × 5cm

= 334.93cm³

Therefore, from my above calculation and compared with the arguments of Paul and Manuel, Option a) "Paul's argument is correct, Manuel used the wrong formula to find the volume of square pyramid X" is the correct option.

The reason why is because the correct formula for the volume of a square pyramid = 1/3 × Base area × Height

This was the formula Paul used.

Manuel on the other hand used the formula: Base Area × Height to find the volume of cone W. This formula is wrong.

Option a, is the correct answer.

4 0
3 years ago
Find the domain for the function f(x)=sqrt x^2-x+6
dybincka [34]

Answer:

The domain is {x : x ∈ R} or (-∞ , ∞)

Step-by-step explanation:

* Lets explain how to find the domain

- The domain of the function is the values of x which make the

  function defined

- The quantity under the square root must be ≥ 0 because there is

  no square root for negative value

* Lets solve the problem

∵ f(x) = √(x² - x + 6)

∴ The value of (x² - x + 6) must be greater than or equal zero because  

   there is no square root for negative value

- Graph the function to know which values of x make the quantity

  under the root is negative that means the values of x which make

  the graph under the x-axis

∵ The graph doesn't intersect the x-axis at any point

∵ All the graph is above the x-axis

∴ There is no value of x make f(x) < 0

∴ x can be any real number

∴ The domain of f(x) is all real numbers

∴ The domain is {x : x ∈ R} or (-∞ , ∞)

6 0
3 years ago
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