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likoan [24]
3 years ago
13

A gardener is planting two types of trees: Type A is 5 feet tall and grows at a rate of 19 inches per year. Type B is 7 feet tal

l and grows at a rate of 16 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.
Mathematics
1 answer:
iren [92.7K]3 years ago
7 0

it will take 8 months for these trees to be same height

Further explanation:

Let x be the number of years then,

Type A is 5 feet tall and grows at a rate of 19 inches per year

The expression for Type A is:

5+19x

Type B is 7 feet tall and grows at a rate of 16 inches per year

The expression for Type B is:

7+16x

Putting both of them equal will give us the time in which both to be same height

5+19x=7+16x\\Subtracting 16x from both sides\\5+19x-16x=7+16x-16x\\5+3x=7\\Subtracting 5 from both sides\\5+3x-5=7-5\\3x=2\\x=\frac{2}{3}\\Mutiplying\ numerator\ and\ denominator\ of\ fraction\ by\ 4\\x=\frac{8}{12}

Hence, it will take 8 months for these trees to be same height

Keywords: Rate of Change, Linear Equations

Learn more about linear equations at:

  • brainly.com/question/2116906
  • brainly.com/question/2131336

#LearnwithBrainly

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Please Helppppppppppp
sineoko [7]

Answer:

The width of the actual pool is 12 meters

Step-by-step explanation:

You can put Kiara's scale into a ratio or fraction to help visualize it better: 13/6. Now, let's put what we do know for the other ratio into a fraction. we know that the pool is 26 centimeters wide, and since the 26 matches with the 13, that goes in the numerater. since we don't know the denominator, we can just put 26/x (you can use whatever letter you like but I'll use x here)

So in order to get 13/6 to 26/x, we need to find how to figure out what we are doing to the original fraction. Since 13 x 2= 26, it looks like we are multiplying the ratios by 2. Now that we know that, we can multiply the denominator (6) by 2 to equal 12, our answer.

Hope this helps :)    

8 0
2 years ago
A triangular playground has angles with measures in the ratio 8 : 6 : 4. What is the measure of the smallest angle?
Airida [17]

Answer:

20°

Step-by-step explanation:

One way of doing this is to find the constant of proportionality, k:

8k + 6k + 4k = 90°    Then 18k = 90°, and k turns out to be 90/18, or 5.

Then the angles are 8(5), 6(5) and 4(5).  The smallest of these angles is thus 20°

8 0
3 years ago
Read 2 more answers
How do I solve this?
vampirchik [111]
4 , divide the x by the y to find a constant
4 0
2 years ago
How do you solve multi variable equations?​
Mekhanik [1.2K]
1. Understand what multi-variable equations are.

Two or more linear equations that are grouped together are called a system. That means that a system of linear equations is when two or more linear equations are being solved at the same time.
[1] For example:
• 8x - 3y = -3
• 5x - 2y = -1
These are two linear equations that you must solve at the same time, meaning you must use both equations to solve both equations.

2. Know that you are trying to figure out the values of the variables, or unknowns.

The answer to the linear equations problem is an ordered pair of numbers that make both of the equations true.
In the case of our example, you are trying to find out what numbers ‘x’ and ‘y’ represent that will make both of the equations true.

• In the case of this example, x = -3 and y = -7. Plug them in. 8(-3) - 3(-7) = -3. This is TRUE. 5(-3) -2(-7) = -1. This is also TRUE.

3. Know what a numerical coefficient is.

The numerical coefficient is simply the number that comes before a variable.[2] You will use these numerical coefficients when using the elimination method. In our example equations, the numerical coefficients are:

• 8 and 3 for the first equation; 5 and 2 for the second equation.


4. Understand the difference between solving with elimination and solving with substitution.

When you use elimination to solve a multivariable linear equation, you get rid of one of the variables you are working with (such as ‘x’) so that you can solve the other variable (‘y’). Once you find ‘y’, you can plug it into the equation and solve for ‘x’ (don’t worry, this will be covered in detail in Method 2).

• Substitution, on the other hand, is where you begin working with only one equation so that you can again solve for one variable. Once you solve one equation, you can plug in your findings to the other equation, effectively making one large equation out of your two smaller ones. Again, don’t worry—this will be covered in detail in Method 3.


5. Understand that there can be linear equations that have three or more variables.

Solving for three variables can actually be done in the same way that equations with two variables are solved. You can use elimination and substitution, they will just take a little longer than solving for two, but are the same process.
6 0
3 years ago
See attached photo below
Daniel [21]

Answer:

  • Library 2 charges more for each book loaned.
  • Library 1 has a cheaper subscription fee.

Step-by-step explanation:

Based on the table, we can write the equation for the cost of borrowing from Library 2 using the two-point form of the equation of a line:

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

for (x1, y1) = (2, 15.50) and (x2, y2) = (8, 26) this equation becomes ...

  y = (26 -15.50)/(8 -2)(x -2) +15.50 . . . . . fill in the values

  y = (10.50/6)(x -2) +15.50 . . . . . . . . . . . . simplify a bit

  y = 1.75x -3.50 +15.50 . . . . . . simplify more

In the above, we have x = number of books; y = cost. We can use "n" and "C" for those, respectively, as in the equation for Library 1. Then the monthly cost for Library 2 is ...

  C = 12 + 1.75n . . . . . . . arranged to the same form as for Library 1

_____

Now, we can answer the questions.

Library 2 charges more for each book loaned. (1.75 vs 1.50 for Library 1)

Library 1 has a cheaper subscription fee. (10 vs 12 for Library 2)

_____

The numbers in the cost equations are ...

  C = (subscription fee) + (cost per book loaned)·n

8 0
3 years ago
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