The farthest gold dust strike is 76 miles away from the gold vein.
The formula of the distance between two points is P(x₁, y₁) and Q(x₂, y₂) is given by:
d (P, Q) = √ (x₂ – x₁)² + (y₂ – y₁) ²
As per the question, we have to find the distance between the gold vein at (-2, 7) and the farthest gold dust strike at (74, 7).
Substituting the values into the distance formula, we have:
d = √((74 - (-2))² + (7 - 7)²)
d = √(76²)
d = 76
Therefore, the farthest gold dust strike is 76 miles away from the gold vein.
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when the function f(x) = 2x^n + ax² - 6 is divided by (x+3), the remainder is 129.
calculate the value of "a" and "n" and hence write the complete polynomial function.
The complete polynomial is f(x) = 2x³ + 15x² - 6 if n = 3 and a = 15
Given is polynomial f(x) = 2xⁿ + ax² - 6, when divided by (x+3), the remainder is 129,
Calculating the values of a and n :-
From the question, we have the following parameters that can be used in our computation:
f(x) = 2xⁿ + ax² - 6 is divided by (x+3), the remainder is 129
This means that,
f(-3) = 129
So, we have
f(-3) = 2(-3)ⁿ + a(-3)² - 6
f(-3) = 2(-3)ⁿ + 9a - 6
2(-3)ⁿ + 9a - 6 = 129
2(-3)ⁿ + 9a = 135
Assume n = 3
So, we have
2(-3)³ + 9a = 135
2/27 + 9a = 135
9a = 135 - 2/27
9a = 3643/27
a = 3643/243
a = 15
Therefore,
n = 3 and a = 15
So, the complete polynomial is f(x) = 2x³ + 15x² - 6
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I need to know surface area
Answer: 165 ft squared
Step-by-step explanation:
1. First find the area of the bottom face (you don’t need to divide by two because the other triangle makes the one on the bottom a full rectangle.)
10x4.5=45
2. Find area of face facing you. (The lateral one, rectangle face)
10x5=50
3. Find area of left and right lateral faces (its at the back)
6x5=30
8x5=40
4. Add all answers to get total surface area
40+30+50+45=165
5.Add unit and then celebrate because you did it!
165 ft squared
Hope this helps!
Please help and explain, I'm not getting this at all
The quotient function for this problem is given as follows:
(f/g)(x) = (x + 2)/(2x² + 4x - 5)
How to obtain the quotient function?The functions f(x) and g(x) have the definitions presented as follows:
f(x) = x + 2.g(x) = 2x² + 4x - 5.To obtain the quotient of the two functions, we simply divided the definition of the function f(x) by the definition of the function g(x).
Both functions are defined on the bullet point, hence the quotient function for this problem is given as follows:
(f/g)(x) = (x + 2)/(2x² + 4x - 5)
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Compare the functions shown below: f(x) = (x + 3)2 − 2 g(x) linear graph with y intercept of negative 3 over 2 and x intercept of 3 h(x) x y −3 2 −2 7 −1 14 0 23 1 34 2 47 3 62 What is the correct order of the functions from least to greatest according to the average rate of change on the interval from x = −1 to x = 3? Group of answer choices f(x), g(x), h(x) g(x), f(x), h(x) h(x), g(x), f(x) g(x), h(x), f(x)
The correct order of the functions from least to greatest is g(x), f(x) and h(x).
The given function is f(x)=(x+3)²-2.
g(x) linear graph with y-intercept = c = -3/2 and x-intercept = 3
f (x) = (x + 3)² - 2
For x = -1
f (-1) = (-1 + 3)² - 2
f (-1) = (2)² - 2
f (-1) = 4 - 2
f (-1) = 2
For x = 3
f(3) = (3 + 3)² - 2
f(3) = (6)² - 2
f(3) = 36 - 2
f(3) = 34
AVR = ((34) - (2))/((3) - (- 1))
AVR = 8
For g(x):
linear graph with and intercept of negative 3 over 2 and x intercept of 3
y = mx + b
b = -3/2
For me we have:
0 = m (3) - 3/2
3m = 3/2
m = 1/2
The function g(x) is:
g (x) = (1/2) x - 3/2
For x = -1
g (-1) = (1/2) (- 1) - 3/2
g (-1) = -1/2 - 3/2
g (-1) = -4/2
g (-1) = -2
For x = 3
g (3) = (1/2) (3) - 3/2
g (3) = 3/2 - 3/2
g (3) = 0
AVR = ((0) - (- 2)) / ((3) - (- 1))
AVR = 1/2
For h(x):
Using the table we have:
AVR = ((62) - (14)) / ((3) - (- 1))
AVR = 12
From least to greatest g(x), f(x), h(x)
Therefore, the correct order of the functions from least to greatest is g(x), f(x) and h(x).
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Find f(-3) for the piecewise function:
We need to use the first part of the function, we can see that:
f(-3) = 0
The correct option is the third one.
How to find the value of f(-3)?Here we have a piecewise function. It means that the function behaves differently on different parts of its domain.
Here we want to evalaute the function in x = -3, so we need to find which of the parts of the function we need to use.
We can see that:
f(x) =x + 3 if x ≤ 0
and -3 is smaller than zer, so we need to use this one.
Then:
f(-3) = -3 + 3 = 0
The correct option is the third one.
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Maricopa's Success scholarship fund receives a gift of $ 195000. The money is invested in stocks, bonds, and CDs. Stocks pay 10.1 % interest, bonds pay 4.8 % interest, and CDs pay 4.75 % interest. Maricopa Success invests $ 35000 more in bonds than in CDs. If the annual income from the investments is $ 13580 , how much was invested in each account?
Maricopa Success invested $ in stocks.
Maricopa Success invested $ in bonds.
Maricopa Success invested $ in CDs.
Using a system of equations, the investments in each account are as follows:
Maricopa Success invested $80,000 in stocks.
Maricopa Success invested $75,000 in bonds.
Maricopa Success invested $40,000 in CDs.
What is a system of equations?A system of equations is two or more equations solved simultaneously, concurrently, or at the same time.
The total scholarship fund received = $195,000
The earnings from the investments:
Stocks = 10.1% = 0.101
Bonds = 4.8% = 0.048
CDs = 4.75% = 0.0475
Let the amount invested in CDs = x
Let the amount invested in Bonds = x + 35,000
Let the amount invested in stocks = y
The annual income from the investments = $13,580
Forming Equations:x + x + 35,000 + y = 195,000
2x + 35,000 + y = 195,000
2x + y = 160,000 ... Equation 1
0.101y + 0.048x + 1,680 + 0.0475x = 13,580
0.0955x + 0.101y = 11,900 ... Equation 2
Multiply Equation 1 by 0.101:
0.202x + 0.101y = 16,160 ... Equation 3
Subtract Equation 2 from Equation 3:
0.202x + 0.101y = 16,160
-
0.0955x + 0.101y = 11,900
0.1065x = 4,260
x = 40,000
Substitute x = 40,000 in Equation 1:
2x + y = 160,000
2(40,000) + y = 160,000
80,000 + y = 160,000
y = 80,000
Investment in CDs = $40,000
Investment in Bonds = $75,000 ($40,000 + $35,000)
Investment in Stocks = $80,000
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On a test, the highest grade was 40.5 points higher then the lowest grade. The sum of the two grades was 138. Find the lowest grade.
Answer:
48.75
Step-by-step explanation:
call highest H and lowest L
H = L + 40.5
sum of them = 138
H + L = 138
(L + 40.5) + L = 138
2L + 40.5 = 138
2L = 138 - 40.5 = 97.5
L = 48.75
A student is creating a graph to represent the equation y=2/3x-5. Which point is not on the line represented by the students graph? A. (9,1) B. (12,7) C. (15,5) D. (21,9)
Answer: B. (12, 7)
Step-by-step explanation: If we substitute the x values in the equation the answer has to equal the y value of the coordinate. If we substitute 12 for the x we get y = 3. So answer B is the coordinate not represented by the student's graph.
In the football game, a penalty of -15 yards was applied to a gain of 43 yards. What was the net gain?
A = 58 yards
B = 32 yards
C = 28 yards
D = 18 yards
find the coordinates
Answer:
2?
Step-by-step explanation:
