The zeros of the polynomial x⁴ - 6x³ - 21x² - 150x - 100 are 0.6511 and 8.262 respectively
Zeros of a PolynomialZeros of polynomial are the points where the polynomial equals zero on the whole. In simple words, we can say that zeros of polynomial are values of the variable such that the polynomial equals 0 at that point. Zeros of a polynomial are also referred to as the roots of the equation and are often designated as α, β, γ respectively.
The zeros of a polynomial f(x) are the values of x which satisfy the equation f(x) = 0. Here f(x) is a function of x, and the zeros of the polynomial are the values of x for which the f(x) value is equal to zero. The number of zeros of a polynomial depends on the degree of the equation f(x) = 0. All such domain values of the function, for which the range is equal to zero, are called the zeros of the polynomial.
To find the zeros of this polynomial function, we have to write the function appropriately.
x⁴ - 6x³ - 21x² = 150x - 100
x⁴ - 6x³ - 21x² - 150x - 100 = 0
The roots of this function is 0.6511 and 8.262 respectively
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2x-2y =-7 use elimination
Using elimination method in the equation 2x+y=7 and 2x*3y=3, x is 3 and y is 1.
Two equations are given solving it by using rule of elimination,
2x+y=7....(1) and 2x*3y=3. (2)
Multiply equation (1) by three to get 6x+3y=21. (3)
Add equations (2) and (3) together to get
8x=24
x=24/8
x= 3
Replace this number in equation (1):
2(3)+y=7
6+y=7
y=7-6
y= 1
Consequently, the answer is x=3,y=1.
To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.
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What is/are the effects when you perform the following transformations on your figure?
a. Reflections –
b. Translations –
c. Rotations –
d. Dilations –
Answer:
A. REFLECTION
Please guys do some research i know you're not that stu p id-_-
7. At time t seconds, the height, h, of a ball thrown vertically upward is modeled by the equation h = -5t² +33t+ 4. About how long will it take for the ball to hit the ground?
The ball thrown vertically upward, the ball hits the ground after 6.719 seconds.
Quadratic equation :
An algebraic equation of the second degree in x is a quadratic equation.its standard form is ax2 + bx + c = 0where a and b are the coefficients, x is the variable, and c is the constant term.To solve the quadratic equation:
h(t) = 0 = -5t² +33t+ 4
[tex]t = \frac{-b \pm\sqrt{(b)^2 - 4ac}}{2a}[/tex]
[tex]t = \frac{-33 \pm\sqrt{(33)^2 - 4(-5)(4)}}{2(-5)}[/tex]
t = {(-33) ±√(1169)}/(-10)
t = -0.1190
t = 6.719
neglecting the negative term we get :
t = 6.719 seconds
This represents that the ball hits the ground after 6.719 seconds.
The ball thrown vertically upward, the ball hits the ground after 6.719 seconds.
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A piece of land was purchased for $65,000. The value of the land has slowly been decreasing by 1% annually. What will the land be worth in 20 years?
The required value of the land after 20 years is $53,163.95.
Given that,
A piece of land was purchased for $65,000. The value of the land has slowly been decreasing by 1% annually, the land worth in 20 years is to be determined.
Here,
As the function decreases by 1% annually,
The expression for the decrease,
y = 65000(1-0.01)ˣ
y = 65000(0.99)ˣ
Put x = 20
y = 65000(0.99)²⁰
y = $53,163
Thus, the required value of the land after 20 years is $53,163.95.
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Shelp Corporation has provided the following information
If the total amount of period costs incurred to sell 9,000 units is closest to: D) $49,500.
How to determine the period costs?First step is to find the variable selling and administrative expense per unit
Sales commissions $ 0.50
Add variable administrative expense 0.50
Variable selling and administrative expense per unit $ 1.00
Now let find the total amount of period costs
Total variable selling and administrative expense $9,000
($1.00 per unit × 9,000 unit)
Add total fixed selling and administrative expense 40,500
Total period cost $ 49,500
Therefore the correct option is D.
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The complete question is:
Shelp Corporation has provided the following information:
Cost per Unit Cost per Period
Direct materials $ 7.15
Direct labor $ 3.35
Variable manufacturing overhead $ 1.40
Fixed manufacturing overhead $ 81,000
Sales commissions $ 0.50
Variable administrative expense $ 0.50
Fixed selling and administrative expense $ 40,500
For financial reporting purposes, the total amount of period costs incurred to sell 9,000 units is closest to:
A) $33,000
B) $9,000
C) $40,500
D) $49,500
How will this pie graph change if
temperatures on Earth continue to increase?
If the temperatures on Earth continue to increase, the change in the pie graph would be C. Less than 2% of the Earth's water will be in polar ice caps.
How are polar ice caps affected by Earth's temperature?The temperature of Earth has risen significantly in the last century as a result of human activity. This had led to the loss of polar ice caps due to them having melted into the oceans from the high temperatures.
This means that if the temperature of the planet should continue to increase, the polar ice caps we have will further be depleted. This would lead to less than 2% of the Earth comprising polar ice caps as is the case now.
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Complete: (Round your answers to the nearest cent.) picture Method Purchased Cost Recovery Class Recovery Year Cost Recovery MACRS July 20 $ 5,000 7 6 A MACRS Nov. 5 $ 11,000 20 13 B
The completion of the MACRS annual cost recovery on a straight-line basis is as follows:
Method Purchased Cost Recovery Recovery Cost
Class Year Recovery
MACRS July 20 $ 5,000 7 6 A = $833.33
MACRS Nov. 5 $ 11,000 20 13 B = $846.15
What is the MACRS straight-line method?Ordinarily, the MACRS (modified accelerated cost recovery system) depreciation method is the tax-allowed method that ensures that larger deductions for depreciation expense or cost recovery are made in the beginning years and lower deductions for later years.
However, the same deductions are made each year when the straight-line method is used.
The depreciation expense using the MACRS straight-line method is computed by dividing the asset's cost by the recovery year.
Method Purchased Cost Recovery Recovery Cost
Class Year Recovery
MACRS July 20 $ 5,000 7 6 A = $833.33 ($5,000/6)
MACRS Nov. 5 $ 11,000 20 13 B = $846.15 ($11,000/13)
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52 is 0.4% of what number? Use pencil and paper. Would you expect the answer to be a lot less than 52, slightly less than
52, slightly greater than 52, or a lot greater than 52? Explain.
Answer:
a lot less because 0.4 is not fully of 100%
Step-by-step explanation:
Answer:
52 is 0.4% of 130. You would expect the number to be a lot greater than 52
Step-by-step explanation:
If the number we are trying to find is x, we have to use the equation x*0.4=52 which can be rewritten as 52/0.4=x
If you solve that, you get 130.
The number is expected to be a lot greater than 52 because 0.4 is almost 0.5 and that would mean doubling 52 so the number would be almost double 52. That means it would be a lot greater.
Add the 2 polynomials:
(-77x²¹ +
2
·x² + x
3
+[52*+
1
-
Answer:
Step-by-step explanation:
Select answers from the drop-down menus to correctly complete the statements. A scale factor of Choose... was applied to the first triangle to the get the resulting image. This scale factor is Choose... .
((Image: An isosceles triangle with a side length of 3.4. An arrow points to a smaller isosceles triangle with a side length of 1.7)
Answer: A scale factor of 1/2 was applied to the first triangle to get the resulting image.
Step-by-step explanation: The initial side length of 3.4 is twice as long as 1.7, the initial triangle was reduced to half of the initial size.
Answer:
The triangle is still an equilateral triangle as before, and the only difference is that the side length is halved from 3.4 to 1.7 (3.4/2=1.7). Therefore, the scale factor is 1.7/3.4=0.5. A scale factor <1 means that the original shape is reduced. The scale factor would be a reduction.
Step-by-step explanation:
The image would be of a triangle.
Hope this helps! :))
Using the declining-balance method, complete the table as shown (twice the straight-line rate): (Enter your answers as a whole dollar amount.) Auto: $30,000 Estimated life: 5 years Residual value: $800 Year Cost Accumulated Depreciation B.O.Y Book Value B.O.Y Depreciation Expense Accumulated Depreciation E.O.Y Book Value E.O.Y 1 $30,000 A B C D E 2 $30,000 F G H I J 3 $30,000 K L M N O
Using the double-declining-balance method of depreciation, the completion of the table as shown is as follows:
Year Cost Accumulated Book Value Depreciation Accumulated Book
Depreciation B.O.Y Expense Depreciation Value
B.O.Y E.O.Y E.O.Y
1 $30,000 $0 $30,000 $12,000 $12,000 $18,000
2 $30,000 $12,000 $18,000 $7,200 $19,200 $10,800
3 $30,000 $19,200 $10,800 $4,320 $23,520 $6,480
What is the double-declining-balance method?The double-declining-balance method is a depreciation method that allocates more cost to the earlier years of the asset's life.
The double-declining-balance method uses twice the straight-line rate and is computed as the product of 100/estimated useful life multiplied by 2.
The double rate is applied at the end of the year's balance for each year's depreciation expense.
The difference between the previous year's ending balance and the residual value is taken as the depreciation expense for the last year.
Auto = $30,000
Estimated life = 5 years
Residual value = $800
Depreciable amount = $29,200 ($30,000 - $800)
Straight-line depreciation rate = 20% (100/5)
Double-declining depreciation rate = 40% (20% x 2)
Depreciation Expense:1st year = $12,000 ($30,000 x 40%)
2nd year = $7,200 ($18,000 x 40%)
3rd year = $4,320 ($10,800 x 40%)
4th year = $2,592 ($6,480 x 40%)
5th year = $3,088 ($3,888 - $800)
Year Cost Accumulated Book Value Depreciation Accumulated Book
Depreciation B.O.Y Expense Depreciation Value
B.O.Y E.O.Y E.O.Y
1 $30,000 $0 $30,000 $12,000 $12,000 $18,000
2 $30,000 $12,000 $18,000 $7,200 $19,200 $10,800
3 $30,000 $19,200 $10,800 $4,320 $23,520 $6,480
4 $30,000 $23,520 $6,480 $2,592 $26,112 $3,888
5 $30,000 $26,112 $3,888 $3,088 $29,200 $800
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PLEASE HELP Use the substitution method to solve the sysytem of linear equations. Enter your answer as an ordered pair. There are four different question with these equations
1. Y=2x+5 X=1
2. Y=2x+1 Y=6x-1
3. Y=2(x-7) X+y=4
4. 3x-y=6 X+3y=12
The solutions to these system of equations are given as follows:
1. x = 1, y = 7.
2. x = 0.5, y = 2.
3. x = 6, y = -2.
4. x = 3, y = 3.
What is a system of equations?A system of equations is a set of equations involving multiple variables that are related, and then operations are made to solve these equations and identify the numeric value of each variable in the context of a problem.
For item 1, it is already stated that the solution for x is x = 1, hence the solution for y is obtained as follows:
y = 2(1) + 5 = 7.
For item 2, we are given two equations for y, hence the solution for x is obtained as follows:
2x + 1 = 6x - 1
4x = 2
x = 2/4
x = 0.5.
Hence the solution for y is:
y = 2(0.5) + 1 = 1 + 1 = 2.
For item 3, from the second equation, we have that:
y = 4 - x.
Then the solution for x will be of:
2(x - 7) = 4 - x
2x - 14 = 4 - x
3x = 18
x = 18/3
x = 6.
The solution for y is:
y = 4 - 6 = -2.
For item 4, from the first equation, we have that:
y = 3x - 6.
Then, replacing on the second equation, the solution for x is obtained as follows:
x + 3(3x - 6) = 12
x + 9x - 18 = 12
10x = 30
x = 3.
Then the solution for y is:
y = 3x - 6 = 3(3) - 6 = 9 - 6 = 3.
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Please help
A T-shirt company can produce and sell x T-shirts per day. The total cost C (in dollars) for producing x T-shirts is
C = 1,780 + 7x,
and the total revenue R (in dollars) is
R = 14x.
Find the profit (in dollars) obtained by selling 275 T-shirts per day.
Answer:
$145
Step-by-step explanation:
The revenue - the cost is the profit.
14x - (1708 + 7x) Distribute what is in the parentheses by -1
14x -1(1780) -1(7x) Simplify
14x - 1780 -7x Combine like tersm
7x - 1780 Plug in 275 for x
7(275) - 1780
1925 - 1780
145
Calculating Loan Risk
Cass is reviewing historical data about loans the financial institution gave out to see how credit score was linked to defaulting. In the past, the financial institution gave loans only to those with a credit score of 501 or above.
Answer:
Loan analysis is an evaluation method that determines if loans are made on feasible terms and if potential borrowers can and are willing to pay back the loan. It checks the eligibility of the potential borrower against the criteria set forth for lending. Loan analysis helps in assessing the skills and financial knowledge of the borrower to ...
6(x-6)+2=8x-12 what does x=??
Answer:
-11
Step-by-step explanation:
6(x-6)+2=8x-12
6x-36+2=8x-12 First take care of the parenthesis
6x-34=8x-12 then combine numbers
-2x-34=-12 Subtract 8 from both sides
-2x=22 Add 34 to both sides
x= -11 Divide by -2 on both sides
Answer:
Step-by-step explanation:
Solution
Steps
6(x−6) +2 = 8x−12
Expand by applying the distributive law: a(b−c)=ab−ac
6(x−6)=6x-36
6x−36+2 = 8x−12
6x−34 = 8x−12
Add 34 to both sides
6x−34+34=8x−12+34
Simplify
6x=8x+22
Subtract 8x from both sides
6x−8x=8x+22−8x
Simplify
−2x=22
Divide both sides by −2
x=−11
Which equation is equivalent to the given equation x=x^2-20
x = [tex]x^{2}[/tex] - 20 is equivalent to [tex]x^{2}[/tex] - x - 20 = 0 .
What do you mean by algebraic expression?
Algebraic expressions are mathematical expressions that result when you perform operations such as addition, subtraction, multiplication, and division on variables and constants. Algebraic expressions have different components. Variables, constants, terms, and coefficients in algebraic expressions. A symbol that does not have a fixed value is called a variable.
Given equation:
x = [tex]x^{2}[/tex] - 20
⇒ [tex]x^{2}[/tex] - 20 - x = 0
⇒ [tex]x^{2}[/tex] - x - 20 = 0
Therefore, x = [tex]x^{2}[/tex] - 20 is equivalent to [tex]x^{2}[/tex] - x - 20 = 0 .
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Micheal wants to buy an efficient smart car that according to the latest EPA standards gets 33 mpg in the city and 40 mpg on the highway. The car that Micheal picked out costs $16,100. His dad agreed to purchase the car if Michael would pay it off in equal monthly payments for the next 70 months. The equation y= -230x+16,100 represents the amount, Y (in dollars), that Michael owes his father after X months.
A) How much does Michael owe his dad after six months?
B) determine the slope of the line and interpret its meaning in the context of this problem.
1) Micheal owes his father $[ ] after 6 months.
2) The slope is [ ]
3) The amount Michael owes his father [choose one] by $[ ] per month.
The intercept reveals that the first loan amount was $1,560.00.
Every month, Michael's debt to his father drops by 290.
What is an intercept?The term "intercept" refers to the x- and y-intercepts of of a given equation. The x-intercept is the point at which a line crosses the x-axis and the y-intercept is the point at which a line crosses the y-axis.acc to our question-
The amount Michael owes is given by :
y = - 290x +18,560
x = number of months ; y = amount owed
Amount owed after 3 months :
Put x = 3 in the equation :
y= - 290(3) +18,560
y = - 870 + 18560
y = 17690
According to the general form of a linear equation :
y = mx + c
Where, m = slope ; c = intercept
The slope = - 290 ; Intercept = 18560
Slope is the change in y per unit change in x ; The slope means that amount owed, y decreases by 290 per month
The intercept shows that the original amount borrowed is 18560.
Hence,The intercept reveals that the first loan amount was $1,560.00.
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Help!
WILL MARK BRAINLYIST!
Graph the function f(x) = [x + 3]
over the interval -2 ≤ x ≤ 2
Answer:
The graph of a function f is the set of points which satisfy the equation y = f(x). ... However, of these two answers, only x = −2 fits in the domain.
Step-by-step explanation:
Question 14 (2 points)
Complete the general form of the equation of a sinusoidal function having an
amplitude of 8, a period of 27, and a phase shift to the left 4 units.
The complete general form of the equation of the given sinusoidal function is y = 8sin[(27/2π)*(x - 4)] + c.
The general form of an equation for a sinusoidal function is presented below.
y = a×sin[b*(x - h)] + c
The variable "a" denotes the amplitude of the equation. The variable "T" represents the time period of the equation, and T = 2π/b. The variable "h" denotes the phase shift of the equation. The variable "c" denotes the vertical shift of the equation. The amplitude, period, and phase shift are 8, 27, and 4 units to the left, respectively. The general form of the equation of a sinusoidal function can be written as given below.
y = a×sin[b*(x - h)] + c
y = 8sin[(27/2π)*(x - 4)] + c
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A quadratic function y = f(x) is plotted on a graph and the vertex of the resulting
parabola is (-5, 3). What is the vertex of the function defined as g(x) = f(x) + 2?
Answer:
Submit Answer
Vertex of g(x) is: (-2, -4)
What is vertex?An element of a line is a line segment. A line segment that can be extended endlessly is known as a ray.An angle is created when two line segments or rays cross one another. A vertex is created by definition whenever two lines come together to produce an angle. Thus, we can state that a vertex is formed when two line segments or rays intersect.acc to our question:
Vertex form of a quadratic function:
f(x) = (x - h)² + k
We have (h, k) = (3, -4)
The function f(x) is:
f(x) = (x - 3)² - 4
The function g(x) is: g(x) = f(x + 5) =
(x + 5 - 3)² - 4 = (x + 2)² - 4Vertex of g(x) is:(-2, -4)
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An amusement park has two types of season passes. Plan 1 charges a one-time fee of $145.00 for admission
plus $5.00 every trip for parking. Plan 2 charges a one-time fee of $40.00 for parking plus $12.00 every trip for
admission. For what number of trips is the cost of these plans the same?
The number of trips after the cost of the plan A and plan B is 16.
According to the question,
We have the following information:
Plan 1 charges a one-time fee of $145.00 for admission plus $5.00 every trip for parking. Plan 2 charges a one-time fee of $40.00 for parking plus $12.00 every trip for admission.
So, this will make an arithmetic progression.
The formula to find nth term of an A.P:
an = a+(n-1)d where a is the first term
Now, on left hand side, we have nth term for plan A and on the right hand side, we have the nth term for plan B because their nth term will be equal.
145+(n-1)5 = 40+(n-1)12
145+5n-5 = 40+12n-12
5n+140 = 12n+28
140-28 = 12n-5n
7n = 112
n = 112/7
n = 16
Hence, the number of trips after the cost of the plan A and plan B is 16.
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What is the sum of −12, 5, and −10?
(A) −27
(B) −17
(C) 17
(D) 27
Which symbol replaces the box to make the statement true? 18÷6+3□6+12÷3 Responses > greater than < less than =
The correct expression of the inequality expression is 18 ÷ 6 + 3 □ 6 + 12 ÷ 3
How to complete the inequality expression?From the question, the expression is given as
18 ÷ 6 + 3 □ 6 + 12 ÷ 3
We start by converting the above expression to the same form
So, we start by solving the quotients
This gives
3 + 3 □ 6 + 4
Next, we evaluate the sum
So, we have
6 □ 10
In the above expression, we have
6 and 10
By convention, the number 6 is less than the number 10
This is so because 6 has a smaller value and 10 has a higher value
When the above numbers are compared, we have
6 is less than 10
This means that we make use of the inequality symbol <
So, we have
18 ÷ 6 + 3 < 6 + 12 ÷ 3
Hence, the complete inequality is 18 ÷ 6 + 3 □ 6 + 12 ÷ 3
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If 3 workers complete a certain task in 12 days, how many workers are needed to finish the same task in 4 days?
A total of 9 workers are needed to finish the same task in 4 days
How to determine the number of workers?From the question, we understand that:
3 workers can complete a certain task in 12 days
This means that
3 workers = 12 days
The proportionality constant is then calculated as
Proportionality constant = Number of workers x Number of days
Substitute the known values in the above equation So, we have the following equation
Proportionality constant = 3 * 12
Evaluate
Proportionality constant = 36
When the number of days is 4, we have
Days = 4
So, we have
Proportionality constant = Number of workers x Number of days
This gives
36 = Number of workers x 4
Divide both sides by 4
Number of workers = 9
Hence, the number of workers is 9
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(7x-7)
63°
(3x +45)
(9-4)
Find x and y
The value of x is 33 and y is 39.
What is parallel line?The fundamental characteristics listed below make it simple to recognise parallel lines.
Straight lines that are always the same distance apart from one another are called parallel lines.No matter how far apart they are from one another, parallel lines can never intersect.As, (7x- 7) = 3x+ 45 (corresponding angles)
4x = 52
x= 13
Now, 7x- 7 + w + 63 = 180 (linear pair)
w= 180- 147
w= 33 degree.
y-6 = 33 (Alternate interior angle)
y= 39
Hence, the value of x is 33 and y is 39.
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4. The distance needed to stop a car varies directly as the square of its speed. It
requires 120 m to stop a car at 70 km/h. What distance is required to stop a car
at 80 km/h?
Answer:
156.7 m (nearest tenth)
Step-by-step explanation:
Define the variables:
Let d = distance in meters.Let v = speed in kilometers per hour.If the distance needed to stop a car varies directly as the square of its speed:
[tex]\boxed{d \propto v^2 \implies d=kv^2}[/tex]
where k is the constant of proportionality.
Given:
d = 120 mv = 70 km/hTo find the constant of proportionality, k, substitute the given values into the equation:
[tex]\begin{aligned}\implies 120&=k(70)^2\\k&=\dfrac{120}{70^2}\\k&=\dfrac{6}{245}\end{aligned}[/tex]
Substitute the found value of k back into the formula to create an equation for the given relationship:
[tex]\implies d=\dfrac{6v^2}{245}[/tex]
To find the distance (in meters) required to stop a car at 80 km/h, substitute v = 80 into the equation:
[tex]\implies d=\dfrac{6(80)^2}{245}[/tex]
[tex]\implies d=\dfrac{6\cdot 6400}{245}[/tex]
[tex]\implies d=\dfrac{7680}{49}[/tex]
[tex]\implies d=156.73469...\; \sf m[/tex]
[tex]\implies d=156.7\; \sf m\; (nearest \;tenth)[/tex]
Therefore, the distance required to stop a car at 80 km/h is:
156.7 m (2 d.p.).find the Doubling time for a city who is population is growing by 17% per year
The doubling time will be 4.4 years for a city is population is growing by 17% per year.
What is the doubling time?It's time to double down on the time-doubling equation (pun intended). On the assumption that the growth in amount remains constant from one period to the next, the equation is as follows:
Doubling time = log 2 / log (1 + increase)
It has given that the population of the city is growing back 17% per year.
Doubling time = log 2 / log (1 + increase)
Doubling time = log 2 / log (1 + 17/100)
[tex]\mathrm{Apply\:log\:rule}:\quad \frac{\log _c\left(b\right)}{\log _c\left(a\right)}=\log _a\left(b\right)[/tex]
[tex]=\log _{1+\frac{17}{100}}\left(2\right)[/tex]
Doubling time = 4.41484
Round to the nearest tenth decimal.
Doubling time = 4.4
Thus, the doubling time will be 4.4 years for a city is population is growing by 17% per year.
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Determine the value of x below. (only type the numerical value, do not include the degree sign)
By using the fact that the angles are supplementary, we can write and solve a linear equation to find that x = 62.
How to find the value of x?
In the image, we can see two supplementary angles, where by definition, two angles are supplementary if their addition is equal to a plane angle (an angle of 180°).
With that in mind, we can write the linear equation:
x + 118 = 180
So we just need to isolate x in that simple linear equation.
If we subtract 118 in both sides, we will get:
x + 118 - 118 = 180 - 118
x = 62
So the unknown angle has a measure of 62°.
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Please help me w this hehehehehh
Answer:
-25x-45y, because if we have got + and -, so we will write minus.
75% of what amount is $337.50?
Answer:
450
Step-by-step explanation:
You can easily calculate 337.5 is 75 percent of what number by using any regular calculator, simply enter 337.5 × 100 ÷ 75 and you will get your answer which is 450