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3 years ago

LU 1- 2x + 3 < 5 and - 4x – 3 > 9

Mathematics

2 answers:

Lynna [10]3 years ago

5 0

Answer: x>-1

x<-3

Step-by-step explanation:

$-2x+3$

subtract 3 on both sides

$-2x$

divide -2 on both sides

$x>-1$

The sign changed because I divided by a negative.

$-4x-3>9$

add 3 on both sides

$-4x>12$

multiply -1 on both sides

$4x$

divide 4 on both sides

$x$

Brainlist please

choli [55]3 years ago

3 0

Answer:

x > -1

x < -3

Step-by-step explanation:

-2x + 3 < 5

Subtract 3 on both sides.

-2x < 5 - 3

-2x < 2

Divide -2 into both sides.

x < 2/-2

x > -1

-4x - 3 > 9

Add 3 on both sides.

-4x > 9+3

-4x > 12

Divide -4 into both sides.

x > 12/-4

x < -3

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1/be + 1/bi +1/e=1/12
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3 years ago

Plz help I have no idea how to answer it

saveliy_v [14]

5. Answer: see explanation

Step-by-step explanation:

If the roots are m and 3m, then x = m and x = 3m

⇒ x - m = 0 and x - 3m = 0

⇒ (x - m)(x - 3m) = 0

⇒ x² - 4mx + 3m² = 0

Since x² + px + q = 0 then p = -4m and q = 3m²

3p² = 3(-4m)² 16q = 16(3m²)

= 3(16m²) = 48m²

= 48m²

3p² = 48m² = 16q ⇒ 3p² = 16q

**********************************************************************************************

6. Answer: 8 or 18

Step-by-step explanation:

The Area of the entire rectangle (A = L × w) is 12 × 10 = 120

The Area of the shaded region is 72, so the Area of the non-shaded region is 120 - 72 = 48.

There are two non-shaded triangles.

Bigger non-shaded Δ: L = 12-x, w = 10 ⇒ $A = \dfrac{10(12-x)}{2}$
Smaller non-shaded Δ: L = x, w = x ⇒ $A=\dfrac{x(x)}{2}$

Combine the Areas of both triangles and set it equal to the Area of the non-shaded region:

$\dfrac{x(x)}{2}+\dfrac{10(12-x)}{2}=48\\\\\\\dfrac{x^2}{2}+\dfrac{120-10x}{2}=48\\\\\\\dfrac{x^2-10x+120}{2}=48\\\\\\x^2-10x+120=96\\\\x^2-10x+24=0\\\\(x-4)(x-6)=0\\\\x - 4 = 0\quad or\quad x-6=0\\x=4\qquad or\qquad x=6\\\\\text{Based on the image provided, it appears that the x-value will be the}\\\text{smallest of the two possible solutions (4), but both solutions are valid.}$

Area of ΔBEF:

$\text{when x = 4, A =}\ \dfrac{4(4)}{2}=\dfrac{16}{2}=8\\\\\\\text{when x = 6, A =}\ \dfrac{6(6)}{2}=\dfrac{36}{2}=18$

5 0

3 years ago

san4es73 [151]

8+6+4+2+2=22

22-8-6-4=4

4+2+4+6+8+44-8=58

4 0

3 years ago

Use a linear approximation (or differentials) to estimate the given number. (Round your answer to five decimal places.)

Salsk061 [2.6K]

Answer:

Mix fraction: 3 1/27

Improper fraction: 82/27

Decimal approximation: 3.037

Step-by-step explanation:

What value is close to 28 that is a perfect cube...27 which equals 3^3.

So let's find the tangent line to the curve y=cubert(x) at x=27.

We will use this equation to approximate what happens at x=28.

First let's rewrite the radical in our equation;

y=x^(1/3)

Now differentiate

y'=(1/3) x^(1/3-1) by power rule

Simplify

y'=(1/3) x^(-2/3) or (1)/(3x^[2/3])

So the slope of our tangent line at x=27 is (1)/(3(27)^[2/3])=1/(3(3)^2)=1/(3×9)=1/27.

We will also need a point on this tangent line....We know we have the point at x=27 because that is what our tangent line to curve is being found at.

So at x=27, we have y=cubert(27)=3. We used our equation y=cubert(x) here.

So we want to find the equation of the line that contains point (27,3) and has slope 1/27.

Point-slope form is

y-y1=m(x-x1)

Plug in our values

y-3=(1/27)(x-27)

Add 3 on both sides

y=3+(1/27)(x-27)

We will use this linear equation to approximate cubert(28) by replacing x with 28.

y=3+(1/27)(28-27)

y=3+(1/27)(1)

y=3+1/27

You can write that as a mix fraction if you want.

This value is than 3 but super close to 3 since 1/27 is close to 0.

Mix fraction: 3 1/27

Improper fraction: 82/27

Decimal approximation: 3.037

Cubert of 28 when smashed into calculator as is gives approximately 3.0366 which is pretty close to our approximation.

4 0

2 years ago

Read 2 more answers

What is the value of x in the equation 3x – y = 18, when y = 27?

atroni [7]

3x – y = 18

We start by plugging in 27 for y. The goal is to isolate x by itself to solve for x.

3x - 27 = 18

Then we add 27 to both sides of the equation

3x = 45

Lastly, we divide both sides by 3 to finally isolate x by itself and solve.

x = 15

3 0

3 years ago

Read 2 more answers

LU 1- 2x + 3 < 5 and - 4x – 3 > 9​

LU 1- 2x + 3 < 5 and - 4x – 3 > 9