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3 years ago

Evaluate lal - Ibl, given a = 5, b = -3, and c = -2.a. 2 b. 3 c. 7 d. 8

Mathematics

1 answer:

Natali [406]3 years ago

3 0

Answer:

A. 2

Step-by-step explanation:

Absolute Valie: how many units a number is from zero. (ex: |5|=5, |-7|=7, |-126|=126)

|a| = the absolute value of a (a=5) so the absolute value of a is 5

|b| = the absolute value of b (b=-3) so the absolute value of b is 3.

|a| - |b| = answer : the absolute value of a subtracting/minus the absolute value of b is the answer. So...

|a| = 5

|b| = 3

(|a|=5) - (|b|=3) = (5) - (3) = 2

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A reflecting pool is shaped like a right triangle with one leg along the wall of a building. the hypotenuse is 9 feet longer tha

morpeh [17]

Answer:

Leg side along the wall = x ft = 8 ft

The other leg side = 7+x ft = 7+8=15 ft

The Hypotenuse =9+x ft = 9+8 = 17 ft

Step-by-step explanation:

In the question, the shape of the pool is right triangle.

Let the leg side along the wall to be the x ft

Let the other leg side to be 7+x ft

Let the longest side/hypotenuse to be x+9 ft

Apply the Pythagorean relationship where the sum of squares of the legs equals the square of the hypotenuse

This means;

$x^2 +(x+7)^2=(x+9)^2\\\\$

Expand the terms in brackets

$x^2+(x+7)^2=(x+9)^2\\\\\\x^2+x^2+14x+49=x^2+18x+81$

collect like terms

$x^2+x^2-x^2=18x-14x+81-49\\\\\\x^2=4x+32\\\\\\x^2-4x-32=0$

solve for x in the quadratic equation by factorization

$x^2-4x-32=0\\\\\\x^2-8x+4x-32=0\\\\\\x(x-8)+4(x-8)=0\\\\\\(x+4)(x-8)=0\\\\\\x+4=0,x=-4\\\\x-8=0,x=8$

Taking the positive value of x;

x=8ft

Finding the lengths

Leg side along the wall = x ft = 8 ft

The other leg side = 7+x ft = 7+8=15 ft

The Hypotenuse =9+x ft = 9+8 = 17 ft

6 0

3 years ago

Find the erea of the trapezoid.<br> show work for brainliest

Alexandra [31]

Answer:

the area of the trapezoid is 32

Step-by-step explanation:

a (base)2

b (Base)6

h (height)8

6 0

3 years ago

Major help and if you can, please explain how you got your answer

hjlf

The correct answer is: [A]: " 384 in² " .
_______________________________________________________

Explanation:
______________________________________________________
The formula for the surface area of a cube is:
______________________________________________________

→ A = 6a² ;
______________________________________________________ → in which:
______________________________________________________
  A = surface area of the cube— for which we shall solve ;
(in "square units" ; or, " in² " ; in our case) ;

a = side length = " 8 in " (given);

→ Note: A cube has all equal side lengths.

→ The "6" in the formula accounts for "6 sides" of a cube.

_______________________________________________________

→ To solve for the surface area of the cube; plug in our known value(s);
& solve; as follows:
_______________________________________________________
  → A = 6 a² ;

= 6 * (8 in)² ;

= 6 * 8² * in² ;

= 6 * 8 * 8 * in² ;

= 48 * 8 * in² ;

= 384 in² ;
_______________________________________________________
The answer is: " 384 in² " ;

→ which is: Answer choice: [A]: " 384 in² " .
_______________________________________________________

8 0

3 years ago

Prove the polynomial identity.

aleksandr82 [10.1K]

Explanation:

Since we have given that

$(2x+1)^2-2(2x+1)$