Given
\(\begin{gathered} y=\frac{7}{5}x-\frac{3}{5}....Equation\text{ i} \\ \\ 7x-5y=8...Equation\text{ ii} \end{gathered}\)Solution
multiply all through by 5 equation
We have
\(5y=7x-3\text{ ...equation iii}\)\(\begin{gathered} Rearrange\text{ equation iii} \\ -7x+5y=-3 \\ \end{gathered}\)We have
\(\begin{gathered} -7x+5y=-3...Equation\text{ iii} \\ \end{gathered}\)Add equation ii and Equation iii
\(\begin{gathered} 7x-5y=8\text{ ....Equation ii} \\ -7x+5y=-3\text{ ....Equation iii} \end{gathered}\)We now have
\(0=5\)This means NO SOLUTION
thrill drop to nearest food. Number of minutes
What number should you multiply this equation by to eliminate the decimals?
5x + 0.1x − 0.3 = 0.2x
Answer:
by 10
Step-by-step explanation:
What is the constant of proportionality for the relationship shown in the table? x 2 4 6 8 y 1 2 3 4
1/2
2
4
8
Answer:
\(k = \frac{1}{2}\)
Step-by-step explanation:
Given
x 2 4 6 8
y 1 2 3 4
Required
Determine the constant of proportionality (k)
The relationship between x and y is:
\(y = kx\)
When y = 1, x = 2;
So, we have:
\(1 = k * 2\)
\(2 * k = 1\)
Make k the subject
\(k = \frac{1}{2}\)
Hence, the constant of proportionality is 1/2
What is the next pattern ?
What is the constant rate of change for the relationship shown in the table?
Answer:
\(\frac{1}{3}\)
Step-by-step explanation:
The rate of change is the change in y over the change in x. In this table, the change in y is +1, and the change in x is +3, so we get \(\frac{1}{3}\)
Show that equation (5.3) is true by considering an investment in the asset combined with a short position in a futures contract. Assume that all income from the asset is reinvested in the asset. Use an argument similar to that in footnotes 2 and 4 of this chapter and explain in detail what an arbitrageur would do if equation (5.3) did not hold.
5.3 equation:
F0= S0e(r-q)T
Footnote 2:
For another way of seeing that equation (5.1) is correct, consider the following strategy: buy one unit of the asset and enter into a short forward contract to sell it for F0 at time T. This costs S0 and is certain to lead to a cash inflow of F0 at time T. Therefore S0 must equal the present value of F0; that is, S0= F0erT, or equivalently F0= S0erT
Equation 5.1 F0= S0erT.
Footnote 4:
For another way of seeing that equation (5.2) is correct, consider the following strategy: buy one unit of the asset and enter into a short forward contract to sell it for F0 at time T. This costs S0 and is certain to lead to a cash inflow of F0 at time T and an income with a present value of I. The initial outflow is S0. The present value of the inflows is I+ F0e-rT. Hence, S0=I + F0e-rT, or equivalently F0= (S0 – I)erT
Equation 5.2 F0= (S0 – I)erT
The futures price F0 must be equal to the present value of the expected future spot price, which is \(S0e^{(r-q)} T\). Hence, equation (5.3) is true.
We can use a similar strategy to Footnote 2 to show that equation (5.3) is correct.
Consider an investor who wants to invest in an asset with spot price S0, which pays a continuous dividend yield of q, and simultaneously take a short position in a futures contract with maturity T, which has a futures price of F0. The investor buys one unit of the asset for S0 and sells a futures contract for F0.
At maturity T, the futures contract will be settled at the spot price of the asset, ST. If ST > F0, the investor makes a profit of ST - F0 on the asset, but incurs a loss of F0 - ST on the futures contract. If ST < F0, the investor incurs a loss of F0 - ST on the asset, but makes a profit of ST - F0 on the futures contract.
Now, suppose that equation (5.3) does not hold, i.e., \(F0 \neq S0e^{(r-q)} T\). If \(F0 > S0e^{(r-q)} T\), then the investor can buy the asset for S0, sell a futures contract for F0, and invest the difference \((F0 - S0e^{(r-q)} T)\) at the risk-free rate r. At maturity T, the investor will receive ST from the asset, F0 from the futures contract, and \((F0 - S0e^{(r-q)} T)e^r(T-t)\) from the investment. The total cash inflow will be \(ST + F0 + (F0 - S0e^{(r-q)} T)e^r(T-t).\) But this is greater than the initial outflow of S0, which means that the investor can make a riskless profit, violating the no-arbitrage principle.
Similarly, if\(F0 < S0e^{(r-q)} T\), then the investor can short-sell the asset for S0, buy a futures contract for F0, and borrow the difference \((S0e^{(r-q)} T - F0)\) at the risk-free rate r. At maturity T, the investor will receive ST from the short sale, F0 from the futures contract, and \((S0e^{(r-q)} T - F0)e^r(T-t)\)from the borrowing. The total cash inflow will be \(ST + F0 + (S0e^{(r-q)} T - F0)e^r(T-t)\). But this is greater than the initial outflow of S0, which means that the investor can make a riskless profit, violating the no-arbitrage principle.
Therefore, to avoid arbitrage opportunities, The futures price F0 must be equal to the present value of the expected future spot price, which is \(S0e^{(r-q)} T\). Hence, equation (5.3) is true.
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The table contains the lengths of the sides of different triangles. Do the given side lengths form a right triangle?
Drag and drop Yes or No into the box next to the side lengths.
5 cm, 12 cm, 13 cm
8 cm, 9 cm, 10 cm
3 cm, 4 cm, 4 cm
7 cm, 24 cm, 25 cm
1 cm, 4 cm, 9 cm
Answer:
ans: it's order wise
a) yes
b) no
c) no
d) no
Step-by-step explanation:
use pythagoras theorem
h² = p² + b²
data given satisfying the theorem form right angled triangle
shirts are 30% off. The original price of one shirt is$20. What is the total cost,in dollars, of three shirts, at the sale price, including a 15% sales tax
Answer:
$48.30
Step-by-step explanation:
the other answer's start is correct.
30% discount of $20 is 30/100*20 = $6
so, a shirt costs now only $14.
but sales tax is always calculated from the actual sales price. not from the original list price.
so, we need to calculate 15% of $14 (and not $20) as sales tax.
=> 15/100*14 = $2.10
a shirt now costs incl. sales tax $14 + $2.10 = $16.10
three shirts cost 3 * $16.10 = $48.30
Enter the unknown value that makes this statement true:
20% of _ is 40.
Answer:
50
Step-by-step explanation:
0.8 * x = 40
40/0.8=50
Three biscuits in a packet of 28 are cracked.what fraction is cracked?
3/28 it should be because I c can't reduce it any lower.
Please solve using dimensional analysis
Answer:
34^23 (that is 34 to the 23 power)
Step-by-step explanation:
Do 3.4x10^23=34^23
Which of the following symbols would replace the O and create an inequality with no solutions?
x 3 and x <3
>
VI
IV
<
The symbol which would replace the O and create an in equality with no solution is; > (greater than)
InequalitiesThe two inequalities given according to the attached image are;
x O 3 and x<= 3.We are required to identify which symbol would replace the O and create an inequality with no solutions.
In essence, since the other inequality is; x<= 3.
We can conclude that a contradictory inequality would be; x > 0.Therefore, the required replacement is; >Read more on inequalities;
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What is (2x + 3)??
(2x + 3)?
1x2 +
Answer:
4x^2+12x+9
Step-by-step explanation:
(2x+3)(2x+3)
Multiply 2x by 2x first.
then 2x by 3
and then repeat that step and you add like terms
then recieve your answer.
Answer:
4x^2 + 12x + 9
Step-by-step explanation:
Actually, you are to find (2x + 3)^2, which is "the square of 2x + 3."
2x + 3 is a binomial. There is a formula for the square of a binomial:
(a + b)^2 = a^2 + 2ab + b^2
Following this pattern,
(2x + 3)^2 becomes:
[2x]^2 + 2[2x][3] + [3^2], or
4x^2 + 12x + 9
Definition: In x3, x is called the
is 10.
Example: When using scientific notation the
es )
Term: Type term here
Answer:
it is exponent less than 1
Determine whether Rolle's Theorem applies to the following function on the given interval. If so, find the point(s) that are guaranteed to exist by Rolle's Theorem.
g(x) = x3 + x2-x-1:(-1,1)
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. Rolle's Theorem applies and the point(s) guaranteed to exist is/are x =
(Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)
B. Rolle's Theorem does not apply.
Answer:
I have attached the answers
matthew has 219 pens to put in the packages. Each package must hold 8 pens
How many packages of pens can matthew make? how many pens would be left over?
Help will give thanks to the first to answer
Answer:
x-4
Step-by-step explanation:
because a number could be x and all you have to do is subtract 4 from a number making it x-4
Answer:
4-x
Step-by-step explanation:
Because it says that x is subtracted from 4 which would make it understood that 4 is the first term and then x.
how to find n if sn=969 of A.p,a1=9 and d=6
need help asap. pls somebody help.
Answer:
D
Step-by-step explanation:
why the panic ? you only need to compare the tiles with the actual terms in the equations and add them up.
x²
-x²
-x -x
x x x x (clearly that means 4x)
-1 -1 -1
1 1
so, we see it is D.
If f(x)=x^3 −17x^2 +76x−60, which of the following is a factor of f(x)?
Answer:
(x - 1)
(x - 6)
(x - 10)
Step-by-step explanation:
f(x)=x^3 −17x^2 +76x−60=(x - 1) (x - 6) (x - 10)
(x - 1)
(x - 6)
(x - 10)
are the factor
check by factor theorem:
f(1)=f(6)=f(10)=0
can somebody plllllzzzzzzzzzzz help me with this-2 (x + 4 + 5y)
Answer:
-2x -8-10y
Step-by-step explanation:
-2 (x + 4 + 5y)
distribute
-2x -8-10y
help very urgent if i figure it out i will award brainlyness (or whatever its called lol) thank you !
Answer:
Step-by-step explanation:
I tried to draw as best i could.
g(x) is a function with 3 different parts
First, from when x= -3 is from -8 to -2, it is a line that goes across -3, also because there is this symbol with the line under ≤ , it means the dot is closed and filled in becuase the function includes 8. at -2 there is < with no line so the circle is open and unfilled because it is not included
2nd, There is a line at y=1, from -2 to 4, Same rules apply for open or closed circles. -2 is closed and 4 is open
3rd, There is another line at y=5 from 4 to 10 where 4 is closed and 10 is open
Is this correct??????? Someone plz help
Solve by elimination:
3x + 4y = 0
5x-3y = -58
(6, -8)
B (-6, -8)
C (-8, 6)
Answer:
The answer is (-8, 6)
if you click the image it will show you how to solve the equation. I hope this helps you.
b) The completed construction of a regular hexagon is shown below. Explain why AACF is a 30°-
60°-90° triangle. (10 points)
ACF is a 30º-60º-90º triangle because of the following:
1) Based on a theorem, in a 30°-60°-90° triangle the sides are in the ratio 1 : 2 : \(\sqrt{3}\)
1 → short leg
2 → hypotenuse
\(\sqrt{3}\) → long leg
Side length of the hexagon is the short leg of the triangle. It is 1.
r1 is the radius of the incircle in a regular hexagon. 2(r1) is the diameter of the incircle. It is also the hypotenuse of the right triangle. It is 2.
Using Pythagorean theorem.
\(a^2 + b^2 = c^2\)
\(1^2 + b^2 = 2^2\)
\(b^2 = 2^2 - 1^2\)
\(b^2 = 4 - 1\)
\(b^2 = 3\)
\(\sqrt{b^2} = \sqrt{3}\)
\(b = \sqrt{3}\)
Ralph is 3 times as old as Sara. In 4 years, Ralph will be only tice as old as Sara will be then.
If x represents Sara's age now, which of the following expressions represents Ralph's age in four years?
A. 3x
B. 2x+4
C. 3x+4
Answer:
In 6 years, Ralph will be only twice as old as Sara
Step-by-step explanation:
Answer:
The answer is C, 3x+4
Step-by-step explanation:
The “in four years” part translates to +4. The 3x translates to 3 times his current age. Hope this helped :)
The American Population is living longer. Along with the longevity of life comes additional challenges with both medical and Psychiatric problems. Your patient is about to be discharged from a short-tern rehab center. You overhear the daughter confiding in the nursing student that she cannot handle her mother and will be looking for a Memory care unit to put her mother in. You also hear the student nurse who was raised in a foreign country state, " I would NEVER put my mother in a home. I would take care of her woth my two sisters junti she dies.
what considerations might you make withthis students. Address the cultural differneces in elder care and adress the conself od "Role Strain" in caring for special populations.
Cultural sensitivity is crucial in elder care. Cultural beliefs impact elderly care. A foreign-raised nursing student desires to care for her mother and sisters until her mother's passing.
What is the cultural Strain?Consider cultural values: Students from certain backgrounds may see caring for their elderly parents as a moral duty. Respecting elder beliefs is critical in discussing care options. Have open, non-judgmental communication with the nursing student. Show empathy and listen to her perspective.
Educate the nursing student about caring for a loved one with medical and psychiatric problems. Explain physical, emotional, and financial consequences, including effects on relationships and responsibilities.
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Consider the following figure.
(Note that the figure is not drawn to scale.)
20°
L
47°
89°
Order the side lengths IK, KL, IJ, IL, and LJ from least to greatest.
The side lengths from least to greatest as follows:
IK < KL < IJ < IL < LJ
To order the side lengths IK, KL, IJ, IL, and LJ from least to greatest, we can analyze the given figure.
Since the figure is not drawn to scale, we cannot determine the exact lengths of the sides. However, we can make some observations based on the given angles.
Let's analyze the angles:
Angle L: Since angle L is marked as 47°, we know that side KL is the shortest side, as it is opposite to the smallest angle in a triangle.
Angle I: Since angle I is marked as 20°, we can infer that side IJ is longer than side IK, as it is opposite to a larger angle.
Angle LJ: Since angle LJ is marked as 89°, we can conclude that side LJ is the longest side, as it is opposite to the largest angle in the triangle.
Based on these observations, we can order the side lengths from least to greatest as follows:
IK < KL < IJ < IL < LJ
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Question
From a point P on a level ground and directly west of a pole, the angle of elevation of the top of the pole is 45° and from point Q east of the pole, the angle of elevation of the top of the pole is 58°. If |PQ|= 10m, calculate, correct to 2 significant figures, the:
a) distance from P to the pole;
b) height of the pole.
a) The distance from point P to the pole is: 6.2 m
b) The height of the Pole is: 6.2 m
How to find the distance and height from angle of elevation?The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.
Now, we are given that:
The angle of elevation of the top of the pole = 45°
Angle of elevation of the top of the pole = 58°.
|PQ|= 10m
a) PR is distance from point P to the pole and using trigonometric ratios, gives us:
PR/sin 58 = 10/sin(180 - 58 - 45)
PR/sin 58 = 10/sin 77
PR = (10 * sin 58)/sin 77
PR = 8.7 m
b) P O can be calculated with trigonometric ratios as:
P O = PR * cos 45
P O = 8.7 * 0.7071
P O = 6.2 m
Now, the two sides of the isosceles triangle formed are equal and as such:
R O = P O
Thus, height of pole R O = 6.2 m
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How do you turn 8 1/3% into a proper fraction?
Answer:
multiply 3 with 8 and then add 1
25/3
Step-by-step explanation: