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3 years ago

(English to algebra) twice K is the same as three times k plus one

Mathematics

2 answers:

ryzh [129]3 years ago

7 0

2k = 3k + 1

BTW k = -1

In-s [12.5K]3 years ago

3 0

2k = 3k + 1

Subtract 3k from both sides

-k = -1

Divide by -1

k = 1

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Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 2x-y=

Bond [772]

Answer:

The system of linear equations has infinitely many solutions

Step-by-step explanation:

Let's modified the equations and find the answer.

Using the first equation:

$2x-y=5$ we can multiply by 2 in both sides, obtaining:

$2*(2x-y)=2*5$ which can by simplified as:

$4x-2y=10$ which is equal to:

$4x=2y+10$

Considering the second equation:

$=4x+ky=2$

Taking into account that from the first equation we know that: $4x=2y+10$ , we can express the second equation as:

$2y+10+ky=2$ , which can be simplified as:

$(2+k)y=2-10$

$(2+k)y=-8$

$y=-8/(2+k)$

Because (-8) is being divided by (2+k), then (2+k) can't be equal to 0, so:

$2+k=0$ if $k=-2$

This means that k can be any number different than -2, and for each of these solutions, there is a different solution for y, allowing also, different solutions for x.

For example, if k=0 then

$y=-8/(2+0)$ which give us y=-4, and, because:

$4x=2y+10$ if y=-4 then $x=(-8+10)/4=0.5$

Now let's try with k=-1, then:

$y=-8/(2-1)$ which give us y=-8, and, because:

$4x=2y+10$ if y=-8 then $x=(-16+10)/4=-1.5$ .

Then, the system of linear equations has infinitely many solutions

8 0

3 years ago

2. There are 42 persons in a mathematics class, and everyone of them drinks either coffee or grape milk at

Basile [38]

Answer:

1. 8

2. 24

Step-by-step explanation:

The number of persons that drink grape milk only :

18 - 10 = 8

The number of persons that drink coffee :

42 - 8 = 34

The number of persons that drink coffee only :

34 - 10 = 24

5 0

2 years ago

Factor Completely.3g^2-78g+75

Umnica [9.8K]

✧･ﾟ: *✧･ﾟ:* *:･ﾟ✧*:･ﾟ✧

Hello!

✧･ﾟ: *✧･ﾟ:* *:･ﾟ✧*:･ﾟ✧

❖ 3g^2 - 78g + 75 factored completely is $3(g-1) * (g-25)$

First, write the expression as a difference:

$3(g^{2} -26g +25)$

Then factor the expression:

$3(g^{2} - g - 25g + 25)$

Factor the expression again:

$3 (g*(g-1)-25(g-1))$

Your final answer should be:

$3(g-1)*(g-25)$

~ ʜᴏᴘᴇ ᴛʜɪꜱ ʜᴇʟᴘꜱ! :) ♡

~ ᴄʟᴏᴜᴛᴀɴꜱᴡᴇʀꜱ

3 0

3 years ago

Read 2 more answers

Given that xy=3/2 and both x and y are nonnegative real numbers, find the minimum value of 10x (3y/5)

Stells [14]

The munimum value is, at x = 3/10, y = 5 and 10x+3y/5 = 6.

<h3>What are nonnegative real numbers?</h3>

Non-negative real numbers are the set of positive real numbers that are bigger than 0 (zero).
That is, the true values are either positive or negative.
The collection will include numbers such as 0, 1, 2, 3, 4, 5, and so on.

To find the minimum value of 10x (3y/5):

Given - y = 3/(2x)

So, we want the bare minimum of,

= 10x + 3/5 × 3/(2x)
= 10x + 9/(10x)

Take the derivative to obtain:

= 10 - 9/(10x^2)

When you set it to zero, you get:

= 100x^2 - 9 = 0
= (10x-3)(10x+3) = 0
= x = ± 3/10

So, at x = 3/10, y = 5 and 10x + 3y/5 = 3 + 3 = 6.

Therefore, the munimum value is, at x = 3/10, y = 5 and 10x+3y/5 = 6.

Know more about nonnegative real numbers here:

brainly.com/question/26606859

#SPJ4

5 0

2 years ago

Cristian is building a rectangular garden in his backyard. The width of the garden is set at 29 inches. He wants the fence to be

Gekata [30.6K]

Answer:

The length of the garden should be $42\ in$

Step-by-step explanation:

Let

x------> the length side of the garden

we know that

The area enclosed by the fence is equal to

$2,028=(29+5+5)(x+5+5)\\2,208=(39)(x+10)\\39x+390=2,028\\39x=2,028-390\\39x=1,638\\x=42\ in$

3 0

3 years ago