Fundamental Theorem of Arithmetic is not a method for solving a system of equations.
What are system of equation?A system of equations is a collection of two or more equations with a same set of unknowns.
The system of equation can be solved using the following method.
Graphing methodSubstitution methodLinear combinationThe graphing involves using graph to find the intersection of the system of equation.
Substitution method involves substituting one variable to another.
Therefore, Fundamental Theorem of Arithmetic is not a method for solving a system of equations
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One of the tables below contains (x, y) values that were generated by a linear function.
Part I: Determine which table contains values associated with a constant slope. Find that slope value and show the work you used to come to your decision.
Part II: Using the slope you found in Part I and the values in the table, write the equation of the linear function represented by the table you selected.
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation for table 3 is y=(5/2)x-4.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is y-intercept.
The slope for the tables,
Table 1.
m₁ = (3-1)/(5-2) = 2/3
m₂ = (43-31)/(20-17) = 12/3 = 4
Since the slope is different the relationship is not linear.
Table 2.
m₁ = (13-10)/(2-1) = 3/1
m₂ = (34-29)/(7-6) = 5/1
Since the slope is different the relationship is not linear.
Table 2.
m₁ = (6-1)/(4-2) = 5/2
m₂ = (31-26)/(14-12) = 5/2
Since the slope is the same the relationship is linear.
The equation for table 3 will,
y = (5/2)x + c
1 = (5/2)2 + c
1 = 5 + c
c = -4
Hence, the equation for table 3 is y=(5/2)x-4.
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Sheridan Rental Company provided the following information to its auditors. For the year ended March 31, 2017, the company had revenues of $880,300, general and administrative expenses of $353,300, depreciation expenses of $131,455, leasing expenses of $108,195, and interest expenses equal to $78,122. If the company's average tax rate is 34 percent, what is its net income after taxes?
If the company's average tax rate is 34 percent, Its net income after taxes is: $138,090.48.
Net income after taxes
Revenues of $880,300
General and administrative expenses ($353,300)
Leasing expenses ($108,195)
Earning before interest, taxes, depreciation and amortization $418,805
Depreciation expenses ($131,455)
Earning before interest and taxes $287,350
Interest expenses ($78,122)
Earning before taxes $209,228
Taxes 34% $71,137.52
Net income/Loss $138,090.48
Therefore Its net income after taxes is: $138,090.48.
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Select all figures that can be proven to be parallelograms by the markings in the diagram. explain answer
All the figures can be proven to be parallelograms by the markings
How to determine the parallelogram?The properties of parallelogram are:
Parallel opposite sidesCongruent opposite sidesDiagonals may or may not be congruentCongruent opposite anglesBased on the above properties, all the figures can be proven to be parallelograms
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You start your working career when you are 24 years old. Each month, you deposit $144 into a pension plan. You continue making deposits into the plan you are 68 years old. What is the balance, in dollars, when the plan earns 6%, compounded monthlyRound your answer to the nearest cent
The balance, in dollars, (future value) when the pension plan earns 6% compounded monthly is $372,134.19.
What is future value?The future value refers to the compounded future value of an asset, for example, a pension plan, based on a growth rate of interest for a future period.
The future value can be determined with the FV formula, table, or using an online finance calculator as follows:
Data and Calculations:N (# of periods) = 528 months (68 - 24 x 12 months)
I/Y (Interest per year) = 6%
PV (Present Value) = $0
PMT (Periodic Payment) = $144
Results:
FV = $372,134.19
Sum of all periodic payments = $76,032 ($144 x 528)
Total Interest = $296,102.19
Thus, the balance, in dollars, (future value) when the pension plan earns 6% compounded monthly is $372,134.19.
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help me solve this please
If the number of types of massages is represented by 4x + 3 and the number of
types of manicures is represented by -6x + 5 and the number of types of pedicures
is represented by 8x - 7, what is the expression for the total number of services they
have to choose from?
The expression for the total number of services the have to choose from is 6x - 1
Simplifying an expressionFrom the question, we are to determine the expression for the total number of services
From the given information,
Number of types of massages = 4x + 3
Number of types of manicures = -6x + 5
Number of types of pedicures = 8x - 7
Then,
Total number of services = 4x + 3 + (-6x + 5) + 8x - 7
Total number of services = 4x + 3 - 6x + 5 + 8x - 7
Total number of services = 4x - 6x + 8x - 7 + 3 + 5
Total number of services = 6x - 1
Hence, the expression for the total number of services the have to choose from is 6x - 1
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Answer: the answer is actually 6x+1, not 6x-1
(a) (2x³+4x²y + 5xy²-3y²)-(x²-3x²y +5xy²-2y²)
Answer:
Your answer is 2x³ + 7x²y + y²- x²
Step-by-step explanation:
(a) ( 2x³ + 4x²y + 5xy² - 3y² ) - ( x² - 3x²y +5xy² - 2y² )
= 2x³ + 4x²y + 5xy² - 3y² - x² + 3x²y - 5xy² + 2y²
= 2x³ + 4x²y + 3x²y + 5xy² - 5xy² + 3y² + 2y² - x²
= 2x³ + 7x²y + y²- x² ans.
Hope its helpful!
Please mark me as brainlist.
Step-by-step explanation:
(a) ( 2x³ + 4x²y + 5xy² - 3y² ) - ( x² - 3x²y +5xy² - 2y² )
= 2x³ + 4x²y + 5xy² - 3y² - x² + 3x²y - 5xy² + 2y²
= 2x³ + 4x²y + 3x²y + 5xy² - 5xy² + 3y² + 2y² - x²
= 2x³ + 7x²y + y²- x² ans.
Question 15 (1 point)
The radioactive isotope of phosphorus P-32 is used as a tracer in the liver. If 3.5 mg
is left in a sample after 288 hrs then how much P-32 was administered initially? [The
half-life of P-32 is 14.3 days.]
6.26 mg
4.17 mg
1.96 mg
7 mg
The radioactive isotope of phosphorus P-32 is used as a tracer in the liver. If 3.5 mg is left in a sample after 288 hrs then the initial amount of P-32 administered was 7 mg.
What is radioactive isotope?A radioactive isotope is a form of an element that has an unstable nucleus and undergoes radioactive decay, emitting radiation in the form of particles and/or energy.
These isotopes can be used for various purposes in medicine, industry, and research.
We can use the radioactive decay formula to solve this problem:
N = N0 * (1/2)^(t/T)
where:
- N is the final amount of P-32 remaining after 288 hours (3.5 mg)
- N0 is the initial amount of P-32
- t is the time elapsed (288 hours)
- T is the half-life of P-32 (14.3 days converted to hours is approximately 343.2 hours)
Substituting the given values into the formula, we get:
3.5 mg = N0 * (1/2)^(288/343.2)
Simplifying and solving for N0:
N0 = 3.5 mg / (1/2)^(288/343.2) = 7 mg
Therefore, the initial amount of P-32 administered was 7 mg.
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Twice the sum of two consecutive integers is 22. What are the two integers?
consider the functions f(x) = -2(x-3)² + 2 which is represented by the graph
drag each interval to the correct location in the table to describe key features of f(x) and g(x)
The intervals of the function on the graph are:
Domain = (-∝, ∝)Range = (-∝, 2]Increases (-∝, 3]Decreases [3, ∝)The key features of the function?The function is given as:
f(x) = -2(x-3)² + 2
See attachment for the graph.
From the graph, we have;
Domain = (-∝, ∝)
Because it takes all real values as its input
Range = (-∝, 2]
Because it has a vertex of (3, 2) and the vertex is a maximum
Also, it increases on the interval (-∝, 3] and decreases on the interval [3, ∝)
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Spencer visits different states every summer. This summer, he started with 3 states already and visited and will visits 4 states per day.
Write an equation to model this situation (use d for days and s for states) which would represent the total number of states visit
Answer:
s = 3 + (4d)
Step-by-step explanation:
s is the number of states, so we put a s and an equal sign. Then 3 is the number of days he started with, so we add that, and 4d is 4 states times the number of days.
In a sale, the price of a TV is reduced from £250 to £180
What is the percentage decrease?
Answer:
28%
Step-by-step explanation:
250÷ .28 = 180
.28 = 28%
how to find the determinant of a 4×4 matrix
Answer:
Step-by-step explanation:
Solve for X show all work. Round to the nearest hundredth if necessary
The value of x, using the cosine ratio, is approximately: 11.47.
How to Apply the Cosine Ratio?The cosine ratio is:
Cos ∅ = adjacent length/hypotenuse length.
Given the parameters:
∅ = 55°
Adjacent length = x
Hypotenuse length = 20
Apply the cosine ratio:
cos 55 = x/20
x = (cos 55)(20)
x ≈ 11.47
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The graph of the function f(x)=log6(x) is stretched vertically by a factor of 7, reflected over the x-axis, reflected over the y-axis, and shifted up by 2 units.
The resulting function after all transformations have been carried out is; -7log6(-x) - 2.
Which function results from all the Transformations?The transformations which ensued on the function given are as follows;
Stretched vertically by a factor of 7; Hence, we have; 7f(x) = 7log6(x).Reflected over the x-axis; -7f(x) = -7log6(x).Reflected over the y-axis; -7f(x) = -7log6(-x).Shifted up by 2 units; -7f(x) -2 = -7log6(-x) - 2.On this note, it follows that the resulting function upon all the Transformations is; = -7log6(-x) - 2.
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HELP! ASAP!
Thank you in advance :)
By the corresponding angles theorem,
∠AFG, ∠BGD, and ∠CHD are congruent∠BAF, ∠CBG, and ∠DCH are congruentThus, triangles AFD, BGD, and CHD are similar by AA.
Answer:
If all of these are parralel and all touching a single line(FD), then they must be the same. Also, they are perpendicular. :/
Step-by-step explanation:
What’s the equation of the regression line you’d use to predict stopping distance based on speed?
Answer:
Interpret the slope of the regression line.
Answer:
Find a 95% confidence interval for the slope of the regression line.
Answer:
Test the hypothesis H0: β1 = 0 and Ha: β1 ≠ 0.
Answer:
Suppose, instead of testing H0: β1 = 0, you decided to test H0: β1 = 5 against Ha: β1 ≠ 5. What P-value would be associated with this test?
From the given output the regression equation is
StopDist = ₋89.99 ₊5.7053(speed)
The slope of the regression equation is 5.7053
from the Excel output the 95% confidence interval for the slope of the regression line is (5.0809, 6.3296)
By the rejection rule ,reject the null hypothesis.
Given,
from the given output the regression equation is
StopDist = ₋89.99 ₊ 5.7053(speed)
Interpreting the slope of the regression line.
from the given output the regression equation the slope is 5.7053.
To find a 95% confidence interval for the slope of the regression line follow the excel procedure:
click on the data>data analysis>Regression.In input Y range enter $B$2:$B$11In X range enter $A$2:$A$S11.Enter confidence level as 95.click on ok.From the excel output the 95% confidence interval for the slope of the regression line is (50809, 6.3296).
State the hypothesis
Null hypothesis:
H₀ : β₁ ≠ 0
Alternative hypothesis:
Hₓ : β₁ ≠ 0
Reject rule:
If p value≤ α(=0.05), then reject the null hypothesis.
By the rejection rule, reject the null hypothesis (H₀)
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Una empresa dedicada a la fabricación de ropa para niños ofrece 300 overoles a S/ 75 por unidad y a un precio de S/. 84 por overol. La misma empresa producirá 600 unidades al mes. Escriba, entonces, la ecuación y determine si es de oferta o demanda.
The supply equation of the company's total cost is 0.75x
How to determine the equation?The question implies that we determine the equation of the company production and categorize the equation as demand or supply
The given parameters are:
Overalls = 300Cost price = $0.75 per unitSelling price = $0.84 per unitProduction per month = 600The total cost of production is calculated as:
Total Cost = Overalls * Cost price
To determine the equation, we set the number of overalls to x.
So, we have:
Total Cost = x * 0.75
Evaluate
Total Cost = 0.75x
Hence, the equation of the company's total cost is 0.75x
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In investing $6,150 of a couple's money, a financial planner put some of it into a savings account paying 6% annual simple interest. The rest was invested in a riskier mini-mall development plan paying 9% annual simple interest. The combined interest earned for the first year was $477. How much money was invested at each rate?
Answer:
3200
Step-by-step explanation:
0.13x + 0.04*(6100-x) = 532 dollars.
0.13x + 0.04*6100 - 0.04x = 532
(0.13 - 0.04)x = 532 - 0.04*6100
x = 532 - 0.04 - 6100/0.13-0.04 = 3200
The couple invested:
$2550 in savings account at 6% simple interest annually, and$3600 in development plan at 9% simple interest annually,to earn $477 as the total interest for the first year.
What is interest over an investment?The interest over an investment is the additional amount that a person receives on investing his/her money in the cause.
How to solve the question?In the question, we are informed that in investing $6,150 of a couple's money, a financial planner put some of it into a savings account paying 6% annual simple interest. The rest was invested in a riskier mini-mall development plan paying 9% annual simple interest. The combined interest earned for the first year was $477.
We are asked to find the amount invested in each rate.
We assume the amount invested in savings account to be $x.
Therefore, the amount invested in development plan is $(6150 - x).
Simple interest on a sum of money (P), at a rate (r) over a time period (t), is given as S.I. = (Prt)/100.
We calculate the interest earned in both investments:-
Investment in savings account:
Amount invested (P) = $x.
Rate of interest (r) = 6%.
Time for investment (t) = 1 year.
Therefore, interest received = (Prt)/100 = $(x*6*1)/100 = $ (6x)/100
Investment in development plan:
Amount invested (P) = $(6150 - x).
Rate of interest (r) = 9%.
Time for investment (t) = 1 year.
Therefore, interest received = (Prt)/100 = $((6150 - x)*9*1)/100 = $ {9(6150 - x)}/100.
We know that the total interest received is $477.
Thus on adding Interests from both the investments, we can write an equation:
(6x)/100 + {9(6150 - x)}/100 = 477
or, 6x + 55350 - 9x = 47700,
or, 55350 - 47700 = 3x,
or, 3x = 7650,
or x = 7650/3 = 2550.
Thus, the investments in:
Savings account = $x = $2550.Development plan = $(6150 - x) = $(6150 - 2550) = $3600.Learn more about simple interests at
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Given the situation, which inequality models the number of additional weeks marie needs to continue saving to afford the home repairs? select the correct answer.
In the inequality models, the number of additional weeks is 1558+60x≥2158.
Given that the initial savings is $1558, the amount needed is $2158 and additional savings is $60 weekly.
Let the number of weeks be x.
So, she will save 60x in x weeks.
Total savings after x weeks is
Initial saving +60x .......(1)
According to the question, she needs $1258 for repair.
So, that means the minimum requirement is 2158.
≥2158 ........(2)
Combine equations (1) and (2) and get
Initial savings +60x≥2158
As given that the initial savings is 1558.
Substitute this in above inequality and get
1558+60x≥2158
To find the number of weeks find value of x.
Subtract 1558 from either sides of the inequality.
1558+60x-1558≥2158-1558
60x≥600
Divide both sides with 60 as
60x÷60≥600÷60
x≥10
Hence, the inequality that models the number of additional weeks marie needs to continue saving to afford the home repairs is 1558+60x≥2158 and she needs to save $60 for at least 10 weeks.
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3(5+7)-6(4-2x) what is equivalent to this equation
Answer:
[tex]12(1 + x)[/tex]
Step-by-step explanation:
We will use order of operations to simplify this expression.
We will evaluate the brackets first.
3(5+7)-6(4-2x) =
[tex]3(12) - 6(4 - 2x) \\ = 36 - 6(4 - 2x) \\ = 36 - 24 + 12x \\ = 12 + 12x[/tex]
You can further simplify it by factorising it:
[tex]12 + 12x \\ = 12(1 + x)[/tex]
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{3(5 + 7) - 6(4 - 2x)}[/tex]
[tex]\mathsf{= 3(5) + 3(7) - 6(4) - 6(-2x)}[/tex]
[tex]\mathsf{= 15 + 21 - 24 + 12x}[/tex]
[tex]\mathsf{= 36 - 24 + 12x}[/tex]
[tex]\mathsf{= 12 + 12x}[/tex]
[tex]\mathsf{= 12x + 12}[/tex]
[tex]\huge\text{Therefore, your answer should be:\boxed{\mathsf{12x + 12}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Choose the most convenient method to graph the line y=−13x+5
Select the correct answer below:
Recognize the equation as that of a vertical line passing through the x-axis at 5
Recognize the equation as that of a horizontal line passing through the y-axis at 5
Identify the slope and y-intercept and then graph
Find the x- and y-intercepts and then graph
Answer:
X and Y intercept
Step-by-step explanation:
X and Y intercept is much easier as the equation is linear it is easy to find the intercepts
The manufacturer is considering production quantities of 40,000 units or 80,000 units. For the 40,000 unit plan, assume 95% of product will be sold and 5% will be salvaged; for the 80,000 unit plan, assume 80% of product will be sold and 20% will be salvaged.
The production quantity of 40,000 units, it is estimated that 38,000 units will be sold and 2,000 units will be salvaged. For the production quantity of 80,000 units, it is estimated that 64,000 units will be sold and 16,000 units will be salvaged.
Based on the information provided, let's analyze the production quantities of 40,000 units and 80,000 units, considering the assumptions for product sales and salvage.
40,000 unit plan:
Sold: 95% of 40,000 units = 0.95 * 40,000 = 38,000 units
Salvaged: 5% of 40,000 units = 0.05 * 40,000 = 2,000 units
80,000 unit plan:
Sold: 80% of 80,000 units = 0.80 * 80,000 = 64,000 units
Salvaged: 20% of 80,000 units = 0.20 * 80,000 = 16,000 units
Therefore, for the production quantity of 40,000 units, it is estimated that 38,000 units will be sold and 2,000 units will be salvaged.
For the production quantity of 80,000 units, it is estimated that 64,000 units will be sold and 16,000 units will be salvaged.
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What is the area of a sector when r = 2 and 0 = 1.75 radians?
Step-by-step explanation:
Area of sector = (θ/2) × r2
= (1.75/2) × 2×2
= (0.875) ×4
= 3.5 In2
Use the number line below to help you compare the numbers 26.3 and 26.5.
26.0
26.5 < 26.3
26.5 = 26.3
O 26.3 > 26.5
26.3 < 26.5
Answer: 26.3 < 26.5
Step-by-step explanation:
On the number line, 26.3 lies to the left of 26.5, meaning that 26.3 is less than 26.5.
can someone help me pls :)
Answer:
Second one i believe
Step-by-step explanation:
Well u know the sides arent given
Given the graph of the function f(x) shown below, find the average rate of change of the function f(x) on the interval [5,15].
Step-by-step Expression;
- Given; The function f(x) on the interval [ 5,15]
- To find the average rate of change of the function f(x)=?
x = 5 , y = 15,
I can't solve it anymore,please can you solving?
5
0000
The value of x is:
3
m_ii હું
15
CN
y
X
Hello :
3/8 = x/(15 + x)
⇔ 3(15 + x)/8 = x
⇔ (45 + 3x)/8 = x
⇔ 45 + 3x = 8x
⇔ 8x - 3x = 45
⇔ 5x = 45
⇔ x = 45/5
⇔ x = 9
if f(x)=(x^m+9)^2, which statement about f(x) is true? a. f(x) is an even function for all vaues of m. b.f(x) is an even function for all even values of m. c.f(x) is an odd function for all values of m. d.f(x) is an odd function for all odd values of m.
Answer: b. f(x) is an even function for all even values of m.
Step-by-step explanation:
[tex]f(x)=(x^m +9)^2[/tex]
If m is even, then [tex](-x)^m=x^m[/tex].
This means that [tex]f(-x)=(x^m+9)^2 \implies f(-x)=f(x)[/tex]
Thus, b is the correct answer.
write an equations in slope-intercept form of the line that passes through the point(5,9) with slope 7
Answer:
[tex]y=7x-26[/tex]
Step-by-step explanation:
1) Write it in the slope-intercept form of [tex]y=mx+b[/tex], where m is the slope and b is the y-intercept.
[tex]y=7x +c[/tex]
2) Substitute the given coordinates into [tex]y=7x +b[/tex], and then solve for c.
[tex]9=7(5) +b\\9=35+b\\9-35=b\\b= -26[/tex]
3) Substitute c into [tex]y=7x +b[/tex]
[tex]y=7x-26[/tex]
Therefore, the answer is [tex]y=7x-26[/tex].