X^2+8x+19+39/(x-2)
I cant show how to use synthetic unless I attach a file
This statment only works for linear systems because in non-linear systems it is okay to have more than one soultion
but if the system is linear than you can define it by it two soultions or in other words it takes two points to form a line and if two lines pass through the same points then you can define them by those point and they are the same line
Answer:
Number of Pennies = 30
Number of Dimes = 90
Step-by-step explanation:
Let the number of pennies be p and number of dimes be d
We can write 2 equations and use substitution method to solve.
<u>Total value of all the coins is 9.30:</u>
We can write:
0.01p + 0.1d = 9.30
Note: value of penny is 0.01 and dime is 0.1, in dollars
<u>Number of dimes is 3 times number of pennies:</u>
We can write:
d = 3p
Now putting 2nd equation in first and solving for p:
0.01p + 0.1(3p) = 9.30
0.01p + 0.3p = 9.30
0.31 p = 9.30
p = 9.30 /0.31
p = 30
Now we know d = 3p, so d = 3 (30) = 90
Hence
Number of Pennies = 30
Number of Dimes = 90
About 68% of the people will score between 85 and 115.
The values of 85 and 115 are exactly 15 points away, or 1 standard deviation, away from the mean.
According to the empirical rule, about 68% of the values in a normal distribution are within 1 standard deviation of the mean.
1/4x - 2 = 3/8
First, to start solving this, we can rearrange our fraction. Let's take 1/4x and change it to x/4. Why? Well, a variable can also be considered as the number 1.
![\frac{x}{4} - 2 = \frac{3}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7B4%7D%20-%202%20%3D%20%20%5Cfrac%7B3%7D%7B8%7D%20)
Second, now we can continue solving for our variable (x). Let's add 2 to each side.
![\frac{x}{4} = \frac{3}{8} + 2](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7B4%7D%20%3D%20%20%5Cfrac%7B3%7D%7B8%7D%20%2B%202)
Third, let's simplify 3/8 + 2. (3/8 + 2 = 2.375 =19/8)
![\frac{x}{4} = \frac{19}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7B4%7D%20%3D%20%20%5Cfrac%7B19%7D%7B8%7D%20)
Fourth, continue trying to get the variable by itself. Multiply each side by 4.
![x = \frac{19}{8} \times 4](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B19%7D%7B8%7D%20%5Ctimes%204)
Fifth, let's simplify 19/8 × 4. This is simple. Leave the denominator be and just do 19 × 4, which equals 76.
![x = \frac{76}{8}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B76%7D%7B8%7D%20)
Sixth, our final step is to simplify our fraction. To do so, we will need to list the factors of the numerator and denominator and find the greatest common factor (GCF).
Factors of 76: 1, 2, 4, 19, 38, 76
Factors of 8: 1, 2, 4, 8
Since 4 is our first common factor, it is considered our GCF.
Seventh, now let's divide. Divide both the numerator and denominator by the GCF (4) to create our new simplified fraction.
![76 \div 4 = 19 \\ 8 \div 4 = 2](https://tex.z-dn.net/?f=76%20%5Cdiv%204%20%3D%2019%20%5C%5C%208%20%5Cdiv%204%20%3D%202)
Answer in fraction form:
![\fbox {x = 19/2}](https://tex.z-dn.net/?f=%5Cfbox%20%7Bx%20%3D%2019%2F2%7D)
Answer in decimal form: