Given: x + y = 15.Which of the following are ordered pairs of this equation?

a.{(-3, 14),(0, 15),(3, 16)}
b.{(-3, 16),(0, 15),(3, 14)}
c.{(16, -3),(15, 0),(14, 3)}
help

Answers

Answer 1

Answer:

Final answer:

Upon testing all the given sets of ordered pairs, none of the sets satisfy the equation x + y = 15 as when the x and y values are substituted into the equation, they don't sum up to 15.

Explanation:

The task is to determine which of the given sets of ordered pairs satisfies the given equation, x + y = 15. In order to solve this, we can plug in the x and y values from each ordered pair into the equation to see if the equation holds true.

For the set (-3, 14), (0, 15), (3, 16):
-3 + 14 = 11, which is not equal to 15.
0 + 15 = 15, which is equal to 15.
3 + 16 = 19, which is not equal to 15. So this set is incorrect.
For the set (-3, 16), (0, 15), (3, 14):
-3 + 16 = 13, which is not equal to 15.
0 + 15 = 15, which is equal to 15.
3 + 14 = 17, which is not equal to 15. So this set is also incorrect.
For the set (16, -3), (15, 0), (14, 3):
16 - 3 = 13, which is not equal to 15.
15 + 0 = 15, which is equal to 15.
14 + 3 = 17, which is not equal to 15. So this set is also incorrect.

Therefore, none of the options given are ordered pairs of the equation x + y = 15.

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Answer 2

Answer:

Final answer:

The correct set of ordered pairs which satisfy the equation x + y = 15 are {(16, -3),(15, 0),(14, 3)}. The other options contain pairs that do not add up to 15.

Explanation:

The question is about identifying the correct ordered pairs from the given equation x + y = 15. An ordered pair is a pair of elements with a particular order, typically used to describe coordinates on a graph. In this case, we need to find the pairs of numbers that, when added together, equal 15.

Looking at the options:

Option a: {(-3, 14),(0, 15),(3, 16)} - These pairs do not add up to 15.
Option b: {(-3, 16),(0, 15),(3, 14)} - Only the pairs (0, 15) and (3, 14) add up to 15. The pair (-3, 16) does not.
Option c: {(16, -3),(15, 0),(14, 3)} - All these pairs add up to 15.

Hence, the correct option is

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Factorise fully the following
A) 2x+10
B) 5x-15
C) 8x+6
D) 12x-8

Answers

Factorization of an algebraic expression means to write the given expression as a product of its factors.

The factorized form are:

A) 2x+10 = 2 ( x + 5 )

B) 5x-15 = 5 ( x - 3 )

C) 8x+6 = 2 ( 4x + 3 )

D) 12x-8 = 4 ( 3x - 2 )

What is factorization?

Factorization of an algebraic expression means to write the given expression as a product of its factors.

These factors can be numbers, variables, or algebraic expressions.

We have,

A) 2x + 10

we have a common factor of 2.

= 2x + 10

= 2 ( x + 5 )

B) 5x - 15

We have a common factor of 5.

= 5x - 15

= 5 ( x - 3 )

C) 8x + 6

We have a common factor of 2.

= 8x + 6

= 2 ( 4x + 3 )

D) 12x - 8

We have a common factor of 4.

= 12x - 8

= 4 ( 3x - 2 )

Thus the factorized form are:

A) 2x+10 = 2 ( x + 5 )

B) 5x-15 = 5 ( x - 3 )

C) 8x+6 = 2 ( 4x + 3 )

D) 12x-8 = 4 ( 3x - 2 )

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Step-by-step explanation:

A .2x+10

2(x+5)

B. 5x-15

5(x-3)

C. 8x+6

2(4x+3)

D. 12x-8

4(3x-2)

The height of water shooting from a fountain is modeled by the function f(x) = -4x2 + 24x - 29 where x is the distance from the spout in feet. Complete the square to determine the maximum height of the path of the water. -4(x - 3)2 - 29; The maximum height of the water is 3 feet.
-4(x - 3)2 - 29; The maximum height of the water is 29feet.
-4(x - 3)2 + 7; The maximum height of the water is 7 feet.
-4(x - 3)2 + 7; The maximum height of the water is 3 feet.

Answers

yo don't need max height
yo use 'find vertex' equestion

since leading term is negative, this equation has a max

the vertex is the max
in the form
y=ax^2+bx+c
vertex=-b/2a

-4x^2+24x-29
a=-4
b=24

vertex=-24/(2*-4)=-24/-8=3

max height is 3 feet
dunno wat the compete square is

I can do that fo ou though
move -29 off to side and undistriute -4
-4(x^2-6x)-29
complete the square, take 1/2 of -6 an square it andadd 0
-4(x^2-6x+9-9)-29
complete square
-4((x-3)^2-9)-29
move the 9 out by distributing the -9 to the -4
36
-4(x-3)^2+36-29
-4(x-3)^2+7

answer is 3rd option

Answer: The correct answer for this question is option...

(C) −4(x − 3)2 + 7; The maximum height of the water is 7 feet.

Hope this helps :)

Have a great day!!

What is the value of m2-2mn+n2 for m=-2 and n=4

Answers

Answer: The required value is 36.

Step-by-step explanation: We are to find the value of the following expression for m = -2 and n = 4 :

$m^2-2mn+n^2.$

Substituting the values m = -2 and n = 4 in the given expression, we get

$m^2-2mn+n^2\n\n=(-2)^2-2* (-2)* 4+4^2\n\n=4+16+16\n\n=36.$

Thus, the required value is 36.

m2 -2mn + n2 =4 - (-16) + 16 =20 + 16 = 36Have a nice days.......

A hot air balloon can hold 90,000 cubic feet of air. It is being inflated at a rate of 6,000 cubic feet per minute. The total cubic feet of air a(t) is a function of the in minutes t. a. Identify the independent and dependent variables. b. What values of the domain and range make sense for this situation? Explain. c. Write a function to represent the total amount of air. Then determine the total amount of air in 6 minutes.

Answers

a. The independent variable is the variable whose variation does not depend on that of another, it is often denoted by x.
In our case independent variable is time in minutes
The dependent variable is the volume of air in the balloon.

b] The domain of the of this situation is:
[0≤t≤15]
this is because t will take 15 minutes for the balloon to get filled.

The range of the situation will be:
[0≤a(t)≤90000]

c]The function that represents this situation is a linear function given by:
y=ax+b
where:
a=rate/slope
b= initial amount of air in the balloon=0
Thus our function will be:
a(t)=6000t

d]
The total amount of air in the balloon after 6 minutes will be given by:
from
a(t)=6000t
a(6)=6000(6)
a(6)=36000 cubic feet

Given: 3x - 2 ≤ 2x + 1. Choose the solution set.

{x | x R, x ≤ -3}
{x | x R, x ≤ -1}
{x | x R, x ≤ 1}
{x | x R, x ≤ 3}

Answers

The solution set is Option D.

{x | x R, x ≤ 3}

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality relation be A

And the equation is 3x - 2 ≤ 2x + 1.

So , on simplifying the equation , we get

3x - 2 ≤ 2x + 1.

Subtracting 2x on both sides of the inequality equation , we get

x - 2 ≤ 1

Adding 2 on both sides of the inequality equation , we get

x ≤ 3

Therefore , the value of x satisfies all the numbers that are less than or equal to 3

Hence , The solution set is {x | x R, x ≤ 3}

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Answer: D

Step-by-step explanation:

If (cos)x= 1/2 what is sin(x) and tan(x)? Explain your steps in complete sentences.

Answers

The correct answers are:
1) sin(x) = $( √(3) )/(2)$
2) tan(x) = $√(3)$

Explanation:
Given:
$cos(x) = (1)/(2)$

Step 1:
Since, according to the Trigonometric identity:
$sin^2(x) + cos^2(x) = 1$ -- (1)

Step 2:
Plug in the value of cos(x) in equation (1):
$sin^2(x) + ( (1)/(2) )^2 = 1 \n sin^2(x) + (1)/(4) = 1 \n sin^2(x) = (3)/(4)$

Step 3:
Take square-root on both sides:
$√(sin^2(x)) = \sqrt{(3)/(4)}$

sin(x) = $( √(3) )/(2)$

Now to find the tan(x), we would use the following formula:

tan(x) = $(sin(x))/(cos(x))$ --- (2)

Plug in the values of sin(x) and cos(x) in equation (2):
tan(x) = $( ( √(3) )/(2) )/( (1)/(2) )$

Hence tan(x) = $√(3)$

Answer:

The value of $\sin x=(√(3))/(2)$