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Kryger [21]
3 years ago
15

How many solutions exist for the given equation?

Mathematics
2 answers:
faust18 [17]3 years ago
8 0

Answer:

\Huge \boxed{\mathrm{infinite \ solutions}}

Step-by-step explanation:

\sf 12x + 1 = 3(4x + 1) - 2

Using distributive property.

\sf 12x + 1 = 12x+3 - 2

\sf 12x + 1 = 12x+1

Subtracting 1 from both sides.

\sf 12x=12x

Dividing both sides by 12.

\sf x=x

All real numbers are solutions.

There are infinite solutions.

Tpy6a [65]3 years ago
4 0

Answer:

infinitely many

Step-by-step explanation:

12x + 1 = 3(4x + 1) - 2

Distribute

12x + 1 = 12x + 3 - 2

Combine like terms

12x+1 = 12x +1

Subtract 12x from each side

1 =1

Since this is always true, we have infinite solutions

You might be interested in
Please help with these math questions
anastassius [24]
4) x=16
Vertical angles have equal angles when two lines intersect, which they do in this case. 
3x-3=2x+13
Solve for x:
x=16

5) 34 degrees
Lines AK and MJ bisect each other perpendicually, so <ADJ is 90 degrees. 
4x+3x-8=90
7x-8=90
7x=98
x=14
<CDJ=3x-8
=3(14)-8
=34 degrees

Hope this helps :)

6 0
4 years ago
A train goes twice as fast downhill as it can go uphill, and 2/3 feet as fast uphill as it can go on level ground. If it goes 12
Yuri [45]

Answer:

0.5hrs

Step-by-step explanation:

Let the speed downhill be x,

Speed uphill is 0.5x. We are told than speed uphill is \frac{2}{3} the speed on flat ground. Therefore the speed on level ground will be \frac{0.5x}{2/3}=0.75x.

From this info, we can obtain the actual speed,v_g on level ground as:

x=120m/h\\0.75x=v_g\\\\\therefore v_g=\frac{0.75x \times 120m/h}{x}\\v_g=90m/h

speed, distance and time have the relation s=d/t so to obtain time to cover 45miles:

t=d/s\\=45/90\\=0.5h

Hence it takes 0.5hrs to cover 45miles on flat ground.

4 0
3 years ago
The following scatter plot shows the number of page views for a popular website and how many people signed up to receive emails
My name is Ann [436]

Answer:

See Explanation.

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtract Property of Equality

<u>Algebra I</u>

Slope Formula: \displaystyle m=\frac{y_2-y_1}{x_2-x_1}

Slope-Intercept Form: y = mx + b

  • m - slope
  • b - y-intercept

Linear Regression

Step-by-step explanation:

We can draw any best line of fit, as long as it is <em>reasonable</em> around the points that are given.

We can just take 2 points and use slope formula and Slope-Intercept Form to find the equation for the best line of fit.

Using Linear Regression, we can determine the <em>true</em> best line of fit using graphing utilities.

<u>Finding the best line of fit</u>

<em>Define 2 points</em>

Point (21600, 205)

Point (27000, 290)

<em>Find slope m</em>

  1. Substitute in point [SF]:                    \displaystyle m=\frac{290-205}{27000-21600}
  2. [Fraction] Subtract:                           \displaystyle m=\frac{85}{5400}
  3. [Fraction] Simplify:                            \displaystyle m=\frac{17}{1080}

<em>Find equation</em>

  1. Define equation [SIF]:                        \displaystyle y = \frac{17}{1080}x + b
  2. Substitute in point:                            \displaystyle 290 = \frac{17}{1080}(27000) + b
  3. Multiply:                                             \displaystyle 290 = 425 + b
  4. Isolate y-intercept <em>b</em>:                         \displaystyle -135 = b
  5. Rewrite:                                             \displaystyle b = -135
  6. Redefine equation:                           \displaystyle y = \frac{17}{1080}x - 135

Slope-Intercept Form tells us that our slope <em>m</em> = \displaystyle \frac{17}{1080} and our y-intercept \displaystyle b = -135.

Setting this as function f(x), we can see from the graph that it is extremely accurate (Blue line).

<u>Using Linear Regression</u>

Depending on the graphing calc you have, the steps may be different.

Using a graphing calc, we can use statistics and determine the <em>best</em> best line of fit.

When we determine the values, we should see that our equation would be g(x) (Green Line).

<em>Credit to Lauren for collabing w/ me in graphing.</em>

6 0
3 years ago
Max went to the store and bought 22 apples. He bought twice as many red apples as he did green, and he bought one-third many yel
katrin [286]

Let the number of green apples bought be x


Green apples = x

Red apples = 2x

Yellow apples = 1/3 (2x) = 2/3 x


Total = 22 apples

x + 2x + 2/3 x = 22

11/3 x = 22

11x = 66

x = 6


Green apples = x = 6

Red apples = 2x = 2(6) = 12

Yellow apples = 2/3 (2x) = 2/3 (6) = 4


Answer: Green = 6, Red = 12, Yellow = 4

7 0
3 years ago
Tara wants to weigh her three stuffed animals. They will only fit on the scale two at a time. Together Addie and Missy weight 18
Pepsi [2]

Answer: Addie weighs 4 ounces

Missy weighs 14 ounces

Corky weighs 8 ounces

Step-by-step explanation:

Let a represent the weight of Addie.

Let m represent the weight of Missy.

Let c represent the weight of Corky.

Together Addie and Missy weigh 18 ounces. This means that

a + m = 18 - - - - - - - - - 1

Missy and Corky weigh 22 ounces. This means that

m + c = 22

m = 22 - c - - - - - - - - - - 2

Addie and Corky weigh 12 ounces. This means that

a + c = 12

a = 12 - c - - - - - - - - - - - 3

Substituting equation 2 and equation 3 into equation 1, it becomes

22 - c + 12 - c = 18

34 - 2c = 18

- 2c = 18 - 34 = - 16

c = - 16/ - 2 = 8

Substituting c = 8 into equation 2, it becomes

m = 22 - 8

m = 14

Substituting c = 8 into equation 3, it becomes

a = 12 - 8

a = 4

3 0
3 years ago
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