Instructions

Solve each given equation and show your work. Tell whether it has one solution, an infinite number of solutions, or no solutions

Bingel [31]

These are three equations and three answers.

Answers:

A) infinite solutions, identity
B) one solution, x = 27, neither contradiction nor identiy
C) x = no solutions, contradiction

Explanation:

Equation A: 20 - 4x = 12 - x + 8 - 3x

The objective is clearing the unknown, which is to isolate it in one side of the equation.

These are the steps and properties that you need to use:

1. Combine like terms on right side:

20 - 4x = 20 - 4x

2. Use addition property of equality (add 4x on each side).

20 = 20 ↔ identity

Conclusion: you have gotten a condition that is always true, no matter the value of x, which means that the equation has infinite solutions and it is an identity.

Equation B: 5x + 4x - 3 = 24 + 8x (note that I placed the equal sign as it was missing)

1. Combine like terms on each side:

9x - 3 = 24 + 8x

2. Subtraction property and addition propertiy of equality (subtract 8x and add + 3 on both sides)

x = 27 ↔ solution (neither contradiction nor identity)

Conclusion: the solution is x = 27.

Equation C: 5x + 6 = 2x + 6 + 3x - 15 (note that I placed the equal signs as it was missing)

1. Comitne like terms on the right side:

5x + 6 = 5x - 9

2. Subtraction property of equality (subtract 5x from each side)

6 = - 9 ↔ contradiction

Conclusion: the equation does not have a solution since the final equality is always false (a condradiction or absurd).

For your information, when the variable (x) dissapears and fhe final equality is always true (for example 0 = 0, or 20 = 20), the equation is an identity.

6 0

4 years ago

Read 2 more answers

Solve x^2 + 6x = 24.

Sunny_sXe [5.5K]

Hello DestinyKiara99 o/
We can solve this equation using the quadratic formula
Check it out...

x² + 6x - 24 = 0

Δ = 6² - 4.1.(-24)
Δ = 36 + 96
Δ = 132

x = -6 +/- √132 x' = -3 + √33
<span> -------------- /
2 \
x'' = - 3 - </span>√33
The correct answer is the letter D
I hope this help =)

8 0

4 years ago

Find the surface area of the cylinder to the nearest whole number. The figure is not drawn to

Anettt [7]

Answer:

correct option is 2187

Total surface area is 2,185.44 square inches.

lateral surface area is 640.56 square inches

Step-by-step explanation:

Given

radius of cylinder = 12 inches

height of cylinder = 17 inches

we will us value of pi as 3.14

surface area for cylinder consist of two part

1. lateral surface area which is gven by $2\pi rl$

where r is radius of cylinder and l is height of cylinder

Thus, lateral surface area for given cylinder is

$2\pi rl\\ =>2* 3.14*12*17\\=> 1281.12$

Thus, lateral surface area for given cylinder is 1281.12 square inches.

_________________________________

second part of surface area is area of two base (upper and lower) of cylinder.

area of base is given by area of circle $\pi r^2$

$area \ of \base = \pi r^2 = 3.14*12^2\\=>area \ of \base = 3.14*144 = 452.16$

This, area of base is for one base of cylinder

since there are 2 base

area of both base will be = 2* area of one base

= 2*452.16 = 904.32.

Thus, area of base is 904.32 sq. in.

_______________________________________

Total surface area of cylinder = area of two base+ lateral surface area of cylinder = 1281.12 square inches + 904.32 square inches

= 2,185.44 square inches.

Thus, total surface area is 2,185.44 square inches.

lateral surface area is 640.56 square inches

but option which is closest to calculated value is 2187.

Thus, correct option is 2187

___________________________________________

Note: this problem can be directly solved using formula

total surface area for cylinder = $2\pi r^2 + 2\pi rl$

5 0

3 years ago

Given congruent triangles name the corresponding sides and corresponding angles

Alborosie

Answer:

See explanation

Step-by-step explanation:

Given $\triangle ABC\cong \triangle ADC$

According to the order of the vertices,

side AB in triangle ABC (the first and the second vertices) is congruent to side AD in triangle ADC (the first and the second vertices);

side BC in triangle ABC (the second and the third vertices) is congruent to side DC in triangle ADC (the second and the third vertices);

side AC in triangle ABC (the first and the third vertices) is congruent to side AC in triangle ADC (the first and the third vertices);

angle BAC in triangle ABC is congruent to angle DAC in triangle ADC (the first vertex in each triangle is in the middle when naming the angles);

angle ABC in triangle ABC is congruent to angle ADC in triangle ADC (the second vertex in each triangle is in the middle when naming the angles);

angle BCA in triangle ABC is congruent to angle DCA in triangle ADC (the third vertex in each triangle is in the middle when naming the angles);

6 0

4 years ago

Equation:<br><img src="https://tex.z-dn.net/?f=5%20%2B%205%20%3D%205x%20%2B%205%20-%202" id="TexFormula1" title="5 + 5 = 5x + 5

dem82 [27]

Answer:

x = $\frac{7}{5}$

Step-by-step explanation:

To solve for x, we need to isolate it [get it alone on one side]

We should start by simplifying (combining the like-terms of our equation):

5 + 5 = 5x + 5 - 2

10 = 5x + 3

- 3 - 3 (subtract 3 from both sides to isolate x)

7 = 5x

÷5 ÷5 (divide both sides by 5 to find "1"x)

$\frac{7}{5}=x$

So, x = $\frac{7}{5}$

(x = 7/5)

hope this helps!!

7 0

2 years ago

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