MATHEMATICS HIGH SCHOOL

How do you solve this using additional method elimination
3x + y = 17
4x - y = 18

Answers

Answer 1
Answer:

// Solve equation [1] for the variable  y 
 

[1] y = -3x + 17

// Plug this in for variable  y  in equation [2]

  [2] 4x - (-3x+17) = 18  [2] 7x = 35

// Solve equation [2] for the variable  x 

  [2] 7x = 35   [2] x = 5 

// By now we know this much :

  x = 5  y = -3x+17

// Use the  x  value to solve for  y 

  y = -3(5)+17 = 2 Solution : {x,y} = {5,2}  
Is the answer

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Compare the numbers √11 and 3.7. Use the symbols <,>,or=.

Answers

Answer: Hi! here we want to compare the numbers √(11) and 3.7

and we need to use <,> or =

So the first thing i would look is the square root.

we know that 3^(2) = 9, 4^(2)  = 16

so 3< √(11) <4

now we can see 3.7^(2)  = (3 + 0.7)*(3 + 0.7) = (3*3 + 2*0.7*3 + 0.7*0.7) =(9 + 6*0.7 + 0.7*0.7)

is easy to see that 0.7*6 \geq 0.5*6=3

then 3.7^(2)  = (9 + 0.7*6 + 0.7*0.7)  > (9 + 3 + 0.7*0.7) > 9 +3 = 12

so 3.7^2 > 12, and 12>11

then:  3.7 > √(11)

You also can use a calculator, but i think this is not the idea of the problem.
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Put the equation y=x²−14x+40 into the form y=(x-h)²+k y= ____

Answers

Answer:

y = (x - 7)² - 9

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

(h, k ) are the coordinates of the vertex and a is a multiplier

given

y = x² - 14x + 40

to obtain vertex form use the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² - 14x

y = x² + 2(- 7)x + 49 - 49 + 40

 = (x - 7)² - 49 + 40

 = (x - 7)² - 9 ← in vertex form

Find the equation of the line through the given point and perpendicular to the given line(0,0);-2x+4y=12

Answers

-2x+4y=12 <=> y = (-1/2)x + 3 => the slope of given line is -1/2;

the new line and the given line are perpendicular =>( the slope of new line )*(-1/2) = -1 =>

the slope of new line is 2;

the equation of the new line is y -0  =2( x -0) <=> y = 2x.
-2x+0 is perpendicular to -2x+4y=12, and go through (0,0).
So the answer is -2x+0

Skye's two new aquariums each hold exactly 200 gallons of water. One aquarium will hold small fish and the other will hold large fish. Now hew needs new fish for his aquariums. She will buy 5 small fish for every 10 gallons of water in the aquarium. She will buy 8 large fish for every 40 gallons of water in the aquarium. What is the total number of fish Skye will have?

Answers

Answer=140 fish

200 gallons of water in the first aquarium.

200 gallons of water in the second aquarium.

The first will be for the small fishes.

   5 small fish            x fish
_____________=__________
     10 gallons        200 gallons

cross multiply
10x=1000
divide both sides by 10
x=100 small fish

The first aquarium has 100 small fish.

The second aquarium holds large fish.

   8 large fish            x fish
____________=___________
    40 gallons        200 gallons

cross multiply
40x=1600
divide both sides by 40
x=40 large fish

The second aquarium has 40 large fish.

100small fish+40 large fish=140 total fish
In terms of the first aquarium, the number of small fish Skye will have is:
200 gallons of water* (5 small fish/ 10 gallons of water)= 100 small fish.

In terms of the second aquarium, the number of large fish Skye will have is:
200 gallons of water* (8 large fish/ 40 gallons of water)= 40 large fish.

The total number of fish Skye will have is:
100 fish+ 40 fish= 140 fish.

Final answer: 140 fish.

Hope this would help~

Find the GCF of each expression. Then factor the expression. 25b^2 - 20b

Answers

Hello!

The prime factors of these two numbres are :

25b^2 = 5^2* b^2\n 20b = 5* 2^2 * b

The GCF can be calculated by multiplying common primes factors :
5* b = 5b

So the GCF is 5b and the expression can be factored this way :
25b^2 - 20b = 5b* 5b - 4* 5b = 5b\left(5b-4\right)

PLEASE HELP ME!! BEST ANSWER GETS BRAINLIEST

Which of the following could represent a diver’s position in relation to the surface of the water after diving into a pool? Select all that apply.
3 meters
-2 meters
-3.1 meters
1 and StartFraction 7 over 8 EndFractionmeters
Negative 2 and one-halfmeters

Answers

The numbers to represents a diver’s position in relation to the surface of the water after diving into a pool is;

-2 meter

-3.1 meter

Negative 2 and one-half meters

Given that;

A diver’s position is in the surface of the water diving into a pool.

We have to find number to represents a diver’s position in relation to the surface of the water after diving into a pool.

What is Negative number?

A number less than zero is called the negative number.

A diver’s position is in the surface of the water diving into a pool.

Since, Diving into a pool is represents negative number.

Hence, The number to represents a diver's position is in negative sign.

So, The numbers are;

⇒ -2 meter

⇒ -3.1 meter

⇒ Negative 2 and one-half meters.

Learn more about the negative number visit:

brainly.com/question/28014674

#SPJ2

Answer:

-2, -3.1, -2.5

Step-by-step explanation:

Since the diver dived into the pool, they are below the surface (assuming it is an inground pool). So the correct answers will be the negative answers.
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