Substitute the first equation into the second equation. You will get:
4x - (2x - 5) = 7
Distribute the negative sign into the parenthesis:
4x - 2x + 5 = 7
Simplify
2x + 5 = 7
Subtract 5 on both sides
2x = 2
x = 1
Now, substitute x = 1 into the first equation:
y = 2(1) - 5
y = 2 - 5
y = -3
The solution to the system of equations is (1, -3).
Answer:
$17,771.92
Step-by-step explanation:
A = P (1 + r/n)^nt
A = Future value (the answer you're trying to find)
P = Initial deposit ($1000)
R = Interest rate (8.25%; this will be represented as a decimal in the equation (.0825))
N = # of times interest is compounded per unit t (12)
T = Time (35)
35 * 12 = 420
1000 (1 + .0825/12)^420
1000(1.006875)^420
1000*17.77191635
A = $17,771.92 (rounded to the nearest hundredths)
Answer: Seventh power of 10
Step-by-step explanation:
X > 1 so exponent will be positive and decimal point moves left. At each point divide X by 10, add 1 to exponent of 10. Exponent starts at zero.
Each time you move the decimal point one to left, you have divided the number by 10, so you have to compensate by multiplying the 10^n factor by 10, say 10 × 10^3 = 10×10×10×10 = 10^4.
12345678 = 12345678 × 10^0
= 1234567.8 × 10^1
= 123456.78 × 10^2
= 12345.678 × 10^3
= 1234.5678 × 10^4
= 123.45678 × 10^5
= 12.345678 × 10^6
= 1.2345678 × 10^7
Each time you move decimal to right, you have multiplied the number by 10, so you have to compensate by dividing the 10^n by 10, subtracting one from exponent.
0.000123 × 10^0 = 0.00123 × 10^-1
= 0.0123 × 10^-2 = 0.123 × 10^-3 = 1.23 × 10^-4
10^-2 / 10 = (1/(10×10)) / 10 = 1/(10×10×10) = 10^-3
Given:
The statement is:
{5, 6, 7} = {5, 5, 6, 7, 7}
To find:
Whether the given statement is true or false.
Solution:
Two sets are equal if they have exactly the same elements.
The given set {5, 6, 7} has three elements and the set {5, 5, 6, 7, 7} has five elements but we known that all the elements of a set are distinct. It means, it has no repeated element.
Set {5, 5, 6, 7, 7} has three distinct elements 5, 6, 7. So,
{5, 5, 6, 7, 7} = {5, 6, 7}
Therefore, the given statement is true.
The graph and inverse of a function are reflections of each other along the line y = x.
A relation made up of ordered pairs (x, y) has as its inverse the set of all ordered pairs (y, x).
When a point is mirrored over the line y = x, the x- and y-coordinates swap places. Similarly, when a point is mirrored over the line y = -x, the x- and y-coordinates swap places and become negated.
Therefore,
The point (x, y)'s reflection over the line y = x is (y, x).
The point (x, y)'s reflection over the line y = - x is (-y, -x).
Thus, the graph and inverse of a function are reflections of each other along the line y = x.
Learn more about reflections for inverse of a function at
brainly.com/question/14544356
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