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2 years ago

Which of the options is a solution for the following system of inequalities

Mathematics

1 answer:

oksian1 [2.3K]2 years ago

8 0

Answer:

(5, - 2)

Step-by-step explanation:

2x+y>3

x-y>1

2x + y > 3 - - - - (1)

x - y > 1 - - - (2)

Using trial and error method :

Using :

(5,-2)

2x + y > 3

2(5) + (-2) > 3

10 - 2 > 3

8 > 3 (true)

x - y > 1

5 - (-2) >1

5 + 2 > 1

7 > 1 (True)

For 0,5

2x + y > 3

2(0) + (5) > 3

0 + 5 > 3

5 > 3 (true)

x - y > 1

0 - (5) >1

-5 > 1

--5 > 1 (false)

Also, all other options do not hold true for bitb inequality statements, hence answer is (5, - 2)

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Kyle wants to compare 0.02 to 1/4 using fractions. Which fraction can you use for 0.02?

Crazy boy [7]

Answer:

$\frac{1}{50}$

Step-by-step explanation:

$\text{Kyle wants to compare 0.02 to }\frac{1}{4} \text{ using fractions}\\\\\text{we need to convert 0.02 into fractional form.}\\\\\text{to convert a decimal into fractional form we divide by }10^n,\\\text{where n is the number of digits after decimal, and remove decimals}\\\text{from the number.}\\$

$\text{here in 0.02, we can see that the number of digits ater decimal is 2,}\\\text{so to convert it into fractional form, we get}\\\\0.02=\frac{2}{10^2}\\\\=\frac{2}{100}\\\\=\frac{1}{50}\\\\\text{so in decimal form, we can write 0.02 as }\frac{1}{50}\\$

3 0

3 years ago

Help me solve this please

damaskus [11]

1) A quadratic will have no real roots when its discriminant is negative

$0 = ax^2 + bx + c = x^2 + 2k x + (4k-3)$

$d = b^2 - 4ac = (2k)^2 - 4(1)(4k-3) = 4k^2 - 16k + 12 < 0$

Dividing by 4,

$k^2 - 4 k + 3 < 0 \quad\checkmark$

We have a positive coefficient on k^2 so this parabola is a CUP (concave up positive) so has a minimum at the vertex. If the vertex y value is less than zero, the inequality will be true in the range between the zeros.

$(k-3)(k-1)$

That's true for

$1 < k < 3$

2) We look for the meet of the line and the parabola:

$2x + k + 2 = 2x^2 + (k+2)x + 8$

$0 = 2x^2 + kx + (6-k)$

For two intersections we need a positive discriminant:

$k^2 - 4(6-k)(2) > 0$

$k^2 + 8k - 48 > 0$

$(k+12)(k-4) > 0$

That's means two negative or two positive, so

$k < 12$ or $k > 4$

6 0

3 years ago

The sum of a number and -15 is equal to the product of that number and 1/4.what is the number

Zolol [24]

Answer:

Step-by-step explanation:

(x−a)(x−b)=x2−(a+b)x+ab

Hope this was helpful----

3 0

2 years ago

100 POINTS!!!

Brums [2.3K]

Answer: x = 4

Step-by-step explanation:

2(x+1)=10

Distributive properties

a*(b+c)=(a*b)+(a*c)

Using distributive properties

Then

2*(x+1)=(2*x)+(2*1)

2*(x+1)=2x+2

Now, commutative properties

a*b=b*a

Addition is cumulative

a+(-b)=(-b)+a

Therefore applying to 2x+2

2x+2+(-2)=2x+(-2)+2

Then, applying to the equation

2x+2+(-2)=10+(-2), +×-=-

2x+2 -2=10-2

2x=8

Using division properties

ax=b

If a is none zero

Then ax/a=b/a

Therefore x=b/a

Applying that to 2x=8

2x=8. Divide both side by 2 which is none zero

2x/2= 8/2

x=4

Option B

Subtraction Property of equality

please click thanks and mark brainliest if you like :)

7 0

2 years ago

Ln (3x+1)-ln (5+x) = ln 2

RideAnS [48]

First you would simplify the left side to get,

ln( ( 3x+1 ) / ( 5+x ) ) = ln 2

Then raise both sides as the power of e, so it would basically cancel out the ln's.

3x+1 / 5+x = 2

3x+1 = 2( 5+x )

3x+1 = 10+2x

x = 9

3 0

3 years ago