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3 years ago

1. How many solitions does this equation have -4(5-3x)=12x+20

Mathematics

2 answers:

Rom4ik [11]3 years ago

6 0

Answer:

1. no solutions

2. one solution

Step-by-step explanation:

1. -4(5-3x)=12x+20

-20+12x=12x+20

-40+12x=12x

-40=0?????

So no solutions.

2. 3x+7(x+1)=2(6x+5)+2

3x+7x+7=12x+10+2

10x+7=12x+12

-2x+7=12

-2x=5

x=-5/2

So one solution.

den301095 [7]3 years ago

5 0

Answer:

The answers are:

1. No solution.

2. One solution: $x=-\frac{1}{2}$

Step-by-step explanation:

In order to determine the solutions for both equations, we have to solve every one. In any equation of one variable, we could get three types of solution:

One solution. The variable has a unique value.
No solution. The equality is not fulfilled.
Infinite solution. The variable is eliminated from the equation and the equality is fulfilled.

So, solving both equation:

1.-

$-4(5-3x)=12x+20\\-20+12x=12x+20\\12x-12x=20+20\\0=40\\$

The equality is not fulfilled. There is not solution.

2.-

$3x+7(x+1)=2(6x+5)-2\\3x+7x+7=12x+10-2\\10x-12x=8-7\\-2x=1\\x=-\frac{1}{2}$

There is one solution. $x=-\frac{1}{2}$

Finally, the answers for both questions are:

1. No solution.

2. One solution: $x=-\frac{1}{2}$

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Which of these is the absolute value parent function?

bija089 [108]

Answer:

D. f(x) = |x|

Step-by-step explanation:

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f(x) = |x|

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3 years ago

Given g(x)=|-3x+16|, if g(x)=18, find x.

LenaWriter [7]

Answer:

x = - $\frac{2}{3}$ , x = $\frac{34}{3}$

Step-by-step explanation:

The absolute value function always gives a positive value, however, the expression inside can be positive or negative, that is

- 3x + 16 = 18 or -(- 3x + 16) = 18

Solving

- 3x + 16 = 18 ( subtract 16 from both sides )

- 3x = 2 ( divide both sides by - 3 )

x = - $\frac{2}{3}$

-(- 3x + 16) = 18

3x - 16 = 18 ( add 16 to both sides )

3x = 34 ( divide both sides by 3 )

x = $\frac{34}{4}$

As a check

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

| - 3(- $\frac{2}{3}$ ) + 16 | = | 2 + 16 | = | 18 | = 18 ← True

| - 3( $\frac{34}{3}$ ) + 16 | = | - 34 + 16 | = | - 18 | = 18 ← True

Thus x = - $\frac{2}{3}$ and x = $\frac{34}{3}$ are the solutions

8 0

3 years ago

Read 2 more answers

The data represents the number of runs allowed by 8 college softball pitchers. {18, 49, 38, 41, 33, 44, 42, 22}

lawyer [7]

This Question is incomplete

Complete Question:

The data represents the number of runs allowed by 8 college softball pitchers. {18, 49, 38, 41, 33, 44, 42, 22}

What is the five number summary:

a) Minimum

b) Q₁

c) Median

d) Q₃

e) Maximum

Answer:

a) Minimum = 18

b) Q₁ = 27.5

c) Median = 39.5

d) Q₃ = 43

e) Maximum = 49

Step-by-step explanation:

From the above diagram, we were given the following set of data.

{18, 49, 38, 41, 33, 44, 42, 22}

Before answering any of the questions, we have to rearrange the data from the lowest to the highest (ascending order). Hence, we have:

{18, 22, 33, 38, 41, 42, 44, 49}

a) Minimum

{18, 22, 33, 38, 41, 42, 44, 49}

Looking at this set of arranged data, the minimum number is the least or lowest number.

This number is 18

b) Q₁

{18, 22, 33, 38, 41, 42, 44, 49}

Q₁ means First Quartile. The formula is = ¼(n + 1)th value

n = Number of terms in the data set = 8

= ¼(8 + 1)th value

= ¼(9)th value

= 2 1/4 value

= 2.25 value

In the above Question, the 2.25 value is the value between the second and third number.

Hence:

22+33/2 = 55/2 = 27.5

Therefore, Q₁ = 27.5

c) Median

{18, 22, 33, 38, 41, 42, 44, 49}

The median of the number is the number in the middle

For this data, we have 8 number, Hence the median is the sum of the 4th and 5th term divided by 2

4th term = 38

5th term = 41

= 38 + 41/ 2 = 79/2

= 39.5

Hence, the median = 39.5

d) Q₃

{18, 22, 33, 38, 41, 42, 44, 49}

Q₃ means Third Quartile. The formula is = ¾(n + 1)th value

n = Number of terms in the data set = 8

= ¾(8 + 1)th value

= ¾(9)th value

= 6 3/4 value

= 6.75 value

In the above Question, the 6.75 value is the value between the sixth and seventh number.

Hence:

42+44/2 = 86/2 = 43

Therefore, Q₃ = 43

e) Maximum

{18, 22, 33, 38, 41, 42, 44, 49}

Looking at this set of arranged data, the Maximum number is the highest number.

This number is 49

6 0

3 years ago

The length of one side of a triangle is 2 feet less than three times the length of its second side. The length of the third side

seropon [69]

Answer:

7 feet, 3 feet, 7.5 feet

Step-by-step explanation:

Let the sides be a, b and c.

<h3>Given</h3>

The length of one side of a triangle is 2 feet less than three times the length of its second side

a = 3b - 2

The length of the third side is 3/4 of the sum of the lengths of the first two sides:

c = (3/4)(a + b)

The perimeter of the triangle is 17.5 feet:

a + b + c = 17.5

<h3>Solution</h3>

Substitute a with b in the second equation:

c = (3/4)(3b - 2 + b) = (3/4)(4b - 2) = (3/4)(4b) - (3/4)(2) = 3b - 1.5

Now substitute a and c with b in the third equation and solve for b:

a + b + c = 17.5

3b - 2 + b + 3b - 1.5 = 17.5
7b - 3.5 = 17.5
7b = 17.5 + 3.5
7b = 21
b = 3

Find the value of a:

a = 3b - 2 = 3*3 - 2 = 9 - 2 = 7

Find the value of c:

c = 3b - 1.5 = 3*3 - 1.5 = 9 - 1.5 = 7.5

The sides of the triangle are:

a = 7 feet, b = 3 feet, c = 7.5 feet

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1 year ago

What is a discrete function?

IgorLugansk [536]

Answer:

A discrete function is a function with distinct and separate values. This means that the values of the functions are not connected with each other (this will be shown as a bunch of points that are not connected together).

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2 years ago