All categories

3 years ago

4(2x + 2) + 12 > 100

Mathematics

1 answer:

Komok [63]3 years ago

3 0

Answer:

x > 10

Step-by-step explanation:

4(2x + 2) + 12 > 100

4(2x + 2) > 100 -12

4(2x + 2) > 88

2x + 2 > 22

2x> 22-2

2x > 20

x > 10

You might be interested in

The coordinates of A, B, and C in the diagram are A (p, 4), B (6, 1 ), and C (9, q). Which equation correctly relates p and q? ↔

aivan3 [116]

Answer:

D. p + q = 7

Step-by-step explanation:

The slope of AB is ...

mAB = (y2 -y1)/(x2 -x1) = (1 -4)/(6 -p) = -3/(6 -p)

The slope of BC is ...

mBC = (q -1)/(9 -6) = (q -1)/3

We want the product of these slopes to be -1:

mAB·mBC = -1 = (-3/(6 -p))·((q -1)/3)

-(q-1)/(6 -p) = -1 . . . . cancel factors of 3

q -1 = 6 -p . . . . . multiply by -(6 -p)

q + p = 7 . . . . . matches choice D

8 0

3 years ago

Help friends please :(

olga nikolaevna [1]

The correct answer is: [B]: " 2⁶ * 2^(3/10) * 2^(8/100) " .
________________________________________________________

7 0

3 years ago

Standard form for 78 hundreds 58 tens 19 ones

Nastasia [14]

Answer:

8399

Step-by-step explanation:

78*100=7800

58*10=580

7800+580+19=8399

4 0

3 years ago

Find the distance between points A = (2, 0) and

allochka39001 [22]

Answer:

9.2

Step-by-step explanation:

You want the distance between A(2, 0) and B(0, 9).

<h3>Distance</h3>

The distance formula is based on the Pythagorean theorem. It tells you the distance between (x1, y1) and (x2, y2) is ...

d = √((x2 -x1)² +(y2 -y1)²)

For the given points, this becomes ...

d = √((0 -2)² +(9 -0)²) = √(4+81) = √85

d ≈ 9.2

The distance between A and B is about 9.2 units.

3 0

2 years ago

The difference between the two roots of the equation 3x^2+10x+c=0 is 4 2/3 . Find the solutions for the equation.

andrezito [222]

Answer:

Given the equation: $3x^2+10x+c =0$

A quadratic equation is in the form: $ax^2+bx+c = 0$ where a, b ,c are the coefficient and a≠0 then the solution is given by :

$x_{1,2} = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$ ......[1]

On comparing with given equation we get;

a =3 , b = 10

then, substitute these in equation [1] to solve for c;

$x_{1,2} = \frac{-10\pm \sqrt{10^2-4\cdot 3 \cdot c}}{2 \cdot 3}$

Simplify:

$x_{1,2} = \frac{-10\pm \sqrt{100- 12c}}{6}$

Also, it is given that the difference of two roots of the given equation is $4\frac{2}{3} = \frac{14}{3}$

i.e,

$x_1 -x_2 = \frac{14}{3}$

Here,

$x_1 = \frac{-10 + \sqrt{100- 12c}}{6}$ , ......[2]

$x_2= \frac{-10 - \sqrt{100- 12c}}{6}$ .....[3]

then;

$\frac{-10 + \sqrt{100- 12c}}{6} - (\frac{-10 + \sqrt{100- 12c}}{6}) = \frac{14}{3}$

simplify:

$\frac{2 \sqrt{100- 12c} }{6} = \frac{14}{3}$

$\sqrt{100- 12c} = 14$

Squaring both sides we get;

$100-12c = 196$

Subtract 100 from both sides, we get

$100-12c -100= 196-100$

Simplify:

-12c = -96

Divide both sides by -12 we get;

c = 8

Substitute the value of c in equation [2] and [3]; to solve $x_1 , x_2$

$x_1 = \frac{-10 + \sqrt{100- 12\cdot 8}}{6}$

$x_1 = \frac{-10 + \sqrt{100- 96}}{6}$ or

$x_1 = \frac{-10 + \sqrt{4}}{6}$

Simplify:

$x_1 = \frac{-4}{3}$

Now, to solve for $x_2$ ;

$x_2 = \frac{-10 - \sqrt{100- 12\cdot 8}}{6}$

$x_2 = \frac{-10 - \sqrt{100- 96}}{6}$ or

$x_2 = \frac{-10 - \sqrt{4}}{6}$

Simplify:

$x_2 = -2$

therefore, the solution for the given equation is: $-\frac{4}{3}$ and -2.

3 0

3 years ago