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Hoochie [10]
2 years ago
11

Given an = 3n-5, what is the common difference?

Mathematics
1 answer:
belka [17]2 years ago
5 0

Answer:

3

Step-by-step explanation:

A common difference is found in arithmetic sequences. The simplified formula for arithmetic sequences, which is what is used here, is a_{n}=dn-a_{0}. Where d is the common difference and a_{0} is the zeroth term. So, in the given equation 3 must be the common difference.

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Math problem please help
PolarNik [594]

Step-by-step explanation:

Equations:

68.75 = 0.5c + 1.25m

c + m = 100

First, let's get rid of one of the variables. Let's start with the simplest equation first. Let's move a variable, so that only one variable is equal to the rest of the equation.

c + m = 100 to c = -m + 100

(it doesn't matter which variable)

Next, since we have what variable <em>c </em>is equal to, we will now incorporate it into our more complex equation.

68.75 = 0.5(-m + 100) + 1.25 m

Now, to get rid of the parentheses, and just have a regular addition equation with the only variable being <em>m.</em>

68.75 = -0.5m + 50 + 1.25m

Next, we need to make it so that there is only one version of the variables. Just combine the variables together so that the form one cohesive unit.

68.75 = 0.75m + 50

Now, we are going to do the same thing that we did in our first equation (with a mix of the last step we just did), but instead of variables, we are going to do it with the whole numbers instead, and converge them onto one side of the equal sign. Keep in mind that at this step in the process, the variable with it's cohesive unit should be isolated on one side of the equal sign and the other being taken up solely by whole numbers.

118.75 = 0.75m

Now, we just need to make the variable equal to 1 (or just <em>m</em>). So we must either multiply or divide. In this case we will be multiplying both sides by 0.75.

118.75 x 0.75 = 0.75m

So, after this step, you should have an answer of;

89.0625

However, you can't just sell a 0.0625% portion of something to somebody (especially muffins, like come on). Also, the amount of cookies and muffins must be equal to 100 and each variable is in whole numbers (usually).

*Always make sure that when you are done with a problem that you double check it. Usually, with equations like this, you just plug in the variables into the equations, and if they fit both equations, you've done well.

From this point forward, I'm leaving you to your own devices. It's 2:38 a.m. and I need to get up at 7:15. I hope this helps!

7 0
2 years ago
the area of a triangle is 124 square units. what would it's new area be if its base was half as long and its height was three ti
Montano1993 [528]
To solve this problem you must apply the proccedure shown below:

 1. You have that the formula for calculate the area of a triangle is:

 A=bh/2

 Where A is the area of the triangle, b is the base of the triangle and h is the height of the triangle.

 bh/2=124
 bh=124x2
 bh=248

 2. The problem asks for the new area of the triangle <span>if its base was half as long and its height was three times as long. Then, you have:

 Base=b/2
 Height=3h

 3. Therefore, when you substitute this into the formula for calculate the area of a triangle, you obtain:

 A'=bh/2

 (A' is the new area)

 A'=(b/2)(3)/2
 A'=3bh/4

 4. When you substitute bh=248 into </span>A'=3bh/4, you obtain:
<span>
 A'=186 units</span>²
<span>
 The answer is: </span>186 units²
3 0
3 years ago
A basket contains 20 green apples and 30 red apples. If a piece of fruit is selected at random from the basket, what is the prob
Dmitrij [34]

Answer:

40%

Step-by-step explanation:

20/50 is the amount of apples that are green/not red. 20÷50=0.4, which is equal to 40%

4 0
3 years ago
Find dy/dx by implicit differentiation.
kow [346]

dy/dx by implicit differentiation is cos(πx)/sin(πy)

<h3>How to find dy/dx by implicit differentiation?</h3>

Since we have the equation

(sin(πx) + cos(πy)⁸ = 17, to find dy/dx, we differentiate implicitly.

So, [(sin(πx) + cos(πy)⁸ = 17]

d[(sin(πx) + cos(πy)⁸]/dx = d17/dx

d[(sin(πx) + cos(πy)⁸]/dx = 0

Let sin(πx) + cos(πy) = u

So, du⁸/dx = 0

du⁸/du × du/dx = 0

Since,

  • du⁸/du = 8u⁷ and
  • du/dx = d[sin(πx) + cos(πy)]/dx

= dsin(πx)/dx + dcos(πy)/dx

= dsin(πx)/dx + (dcos(πy)/dy × dy/dx)

= πcos(πx) - πsin(πy) × dy/dx

So, du⁸/dx = 0

du⁸/du × du/dx = 0

8u⁷ × [ πcos(πx) - πsin(πy) × dy/dx] = 0

8[(sin(πx) + cos(πy)]⁷ ×  (πcos(πx) - πsin(πy) × dy/dx) = 0

Since 8[(sin(πx) + cos(πy)]⁷ ≠ 0

(πcos(πx) - πsin(πy) × dy/dx) = 0

πcos(πx) = πsin(πy) × dy/dx

dy/dx = πcos(πx)/πsin(πy)

dy/dx = cos(πx)/sin(πy)

So, dy/dx by implicit differentiation is cos(πx)/sin(πy)

Learn more about implicit differentiation here:

brainly.com/question/25081524

#SPJ1

6 0
1 year ago
Find the 2th term of the expansion of (a-b)^4.​
vladimir1956 [14]

The second term of the expansion is -4a^3b.

Solution:

Given expression:

(a-b)^4

To find the second term of the expansion.

(a-b)^4

Using Binomial theorem,

(a+b)^{n}=\sum_{i=0}^{n}\left(\begin{array}{l}n \\i\end{array}\right) a^{(n-i)} b^{i}

Here, a = a and b = –b

$(a-b)^4=\sum_{i=0}^{4}\left(\begin{array}{l}4 \\i\end{array}\right) a^{(4-i)}(-b)^{i}

Substitute i = 0, we get

$\frac{4 !}{0 !(4-0) !} a^{4}(-b)^{0}=1 \cdot \frac{4 !}{0 !(4-0) !} a^{4}=a^4

Substitute i = 1, we get

$\frac{4 !}{1 !(4-1) !} a^{3}(-b)^{1}=\frac{4 !}{3!} a^{3}(-b)=-4 a^{3} b

Substitute i = 2, we get

$\frac{4 !}{2 !(4-2) !} a^{2}(-b)^{2}=\frac{12}{2 !} a^{2}(-b)^{2}=6 a^{2} b^{2}

Substitute i = 3, we get

$\frac{4 !}{3 !(4-3) !} a^{1}(-b)^{3}=\frac{4}{1 !} a(-b)^{3}=-4 a b^{3}

Substitute i = 4, we get

$\frac{4 !}{4 !(4-4) !} a^{0}(-b)^{4}=1 \cdot \frac{(-b)^{4}}{(4-4) !}=b^{4}

Therefore,

$(a-b)^4=\sum_{i=0}^{4}\left(\begin{array}{l}4 \\i\end{array}\right) a^{(4-i)}(-b)^{i}

=\frac{4 !}{0 !(4-0) !} a^{4}(-b)^{0}+\frac{4 !}{1 !(4-1) !} a^{3}(-b)^{1}+\frac{4 !}{2 !(4-2) !} a^{2}(-b)^{2}+\frac{4 !}{3 !(4-3) !} a^{1}(-b)^{3}+\frac{4 !}{4 !(4-4) !} a^{0}(-b)^{4}=a^{4}-4 a^{3} b+6 a^{2} b^{2}-4 a b^{3}+b^{4}

Hence the second term of the expansion is -4a^3b.

3 0
3 years ago
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