Answer:
a. y = -2x + 7
Step-by-step explanation:
First, find the slope by plugging the points into the slope formula, , which equals -2. Then use the slope and the point (7,-7) to make an equation in slope-point form. y+7=-2(x-7), finally solve for y to get y=-2x+7.
<u>Answer:</u>
<em>Mathew invested</em><em> $600 and $2400</em><em> in each account.</em>
<u>Solution:</u>
From question, the total amount invested by Mathew is $3000. Let p = $3000.
Mathew has invested the total amount $3000 in two accounts. Let us consider the amount invested in first account as ‘P’
So, the amount invested in second account = 3000 – P
Step 1:
Given that Mathew has paid 3% interest in first account .Let us calculate the simple interest earned in first account for one year,
Where
p = amount invested in first account
n = number of years
r = rate of interest
hence, by using above equation we get as,
----- eqn 1
Step 2:
Mathew has paid 8% interest in second account. Let us calculate the simple interest earned in second account,
Step 3:
Mathew has earned 4% interest on total investment of $3000. Let us calculate the total simple interest (I)
Step 4:
Total simple interest = simple interest on first account + simple interest on second account.
Hence we get,
By substituting eqn 1 , 2, 3 in eqn 4
12000=3P + 24000 - 8P
5P = 12000
P = 2400
Thus, the value of the variable ‘P’ is 2400
Hence, the amount invested in first account = p = 2400
The amount invested in second account = 3000 – p = 3000 – 2400 = 600
Hence, Mathew invested $600 and $2400 in each account.
Answer: 142°15'
Explanation:
Supplementary angles are angles that add up to make a straight angle ().
Therefore, we must find the angle ∠B such that
∠A + ∠B = 180° (1)
We know that ∠A = 37°45', so we can re-arrange equation (1) to find the magnitude of ∠B:
∠B = 180° - ∠A = 180° - 37°45' = 142°15'
So, the correct answer is
142°15'
Graph of f(x-3) is compressed by a factor of horizontally of f(x).
<u>Step-by-step explanation:</u>
We have, the graph of f(x)= , on replacing f(x) by f(x-3) we get:
=
.Below shown are the images for graph of f(x) and f(x-3). Both are functions are exponential , and so having exponential graph but f(x-3) is compressed by a factor of
horizontally . Domain and range of both functions are same i.e. F(x) & f(x-3) domain & range are same , just difference in graph :
.
