Answer:
Step-by-step explanation:
To find the zeros of the function f(x) = -3x² + 75, we need to solve the equation -3x² + 75 = 0 for x. We can start by factoring out a common factor of -3:
-3x² + 75 = 0
-3(x² - 25) = 0
Now we can use the difference of squares formula to factor the expression inside the parentheses:
-3(x - 5)(x + 5) = 0
This equation is satisfied when one of the factors is equal to zero, so we can set each factor equal to zero and solve for x:
x - 5 = 0 --> x = 5
x + 5 = 0 --> x = -5
Therefore, the zeros of the function are x = -5 and x = 5, and we can write them in order from least to greatest as:
lesser x = -5
greater x = 5
Calculator solution:
To verify these results using a calculator, you can graph the function y = -3x² + 75 and look for where the graph intersects the x-axis. Here's how you can do that on a TI-84 calculator:
1) Press the "Y=" button to enter the function.
2) Enter "-3x^2 + 75" after "Y1=".
3) Press the "GRAPH" button to see the graph.
4) Press the "2nd" button followed by the "CALC" button (which is the "TRACE" button).
5) Select option 2: "zero" by pressing the number 2 on the calculator or using the arrow keys to highlight it and pressing "ENTER".
6) Move the cursor to the left of the zero on the left side of the graph and press "ENTER".
7) Move the cursor to the right of the zero on the right side of the graph and press "ENTER".
8) The calculator will display the zeros and ask if you want to store them to a variable. You can simply write down the values and press "ENTER" twice to exit the calculator's calculation.
The calculator will confirm that the zeros are x = -5 and x = 5, as we found above.
3.75 +9.25-(-4.75*0.5-0.2*2-3)
Answer:
-7.225 according to a calculator.
9. Find BD if AABC~AXYZ
A
BD and
and
B
12
A
D
C X
YW
are medians.
We have found that: AB = (BD/2) * (XZ/AY) and we can solve for BD:
BD = 2 * AB * AY / XZ
What is triangle?
A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.
Since BD is a median of triangle ABC, it divides side AC into two equal parts. Let's label the midpoint of AC as M. Similarly, YW is a median of triangle XYZ and it divides side XZ into two equal parts, with the midpoint labeled as N.
Since AABC~AXYZ, we know that the corresponding sides are proportional. Thus,
AB/AX = AC/AY = BC/BZ
Since AB = BC (given that B is a vertex of both triangles), we have:
AB/AX = AC/AY
We can rewrite this equation as:
AB/AC = AX/AY ----(1)
Since BD is a median of triangle ABC, we have:
BD = 1/2 AC ----(2)
Similarly, since YW is a median of triangle XYZ, we have:
YW = 1/2 XZ ----(3)
From equation (1), we have:
AB/AC = AX/AY
Multiplying both sides by AC, we get:
AB = AX * (AC/AY)
Now, using equation (2), we can substitute AC/2 for BD:
AB = AX * BD/AY
Finally, using equation (3), we can substitute XZ/2 for YW:
AB = (BD/2) * (XZ/AY)
Therefore, we have found that:
AB = (BD/2) * (XZ/AY)
Hence, we can solve for BD:
BD = 2 * AB * AY / XZ
Note that we need to know the actual values of AB, AY, and XZ to find BD.
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If y varies inversely as X and y=16 when X=4,find y when X=32
[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" varies inversely with "x"}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=4\\ y=16 \end{cases} \\\\\\ 16=\cfrac{k}{4}\implies 64 = k\hspace{9em}\boxed{y=\cfrac{64}{x}} \\\\\\ \textit{when x = 32, what's "y"?}\qquad y=\cfrac{64}{32}\implies y=2[/tex]
The following figure is made of 1 triangle and 1 rectangle 5,6,9
The area of the triangle is 12 square units. The area of the rectangle is 30 square units. The area of the whole figure is 42 square units,
What is area?A two-dimensional surface's area, such as the surface of a shape or item, can be measured. Typically, it is expressed in terms of square measurements, such as square metres (m2) or square feet (ft2). The length and width of a rectangle can be multiplied to determine the area of a shape, or alternative formulas, like base times height divided by two for a triangle, can be used for other shapes.
The area of triangle is:
A = 1/2*b*h
A= 1/2*4*6=12 square units
A = 12 square units
The area of rectangle is:
B = 6(5) = 30 sq. units,
The area of the whole figure is:
A + B = 12 + 30 = 42 square units.
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The complete question is:
You have just been approved for a 30 year 6.0% fixed home mortgage. The monthly payment that you qualify for is $1112.10. Use the table provided to determine the price of a home that can be purchased. Round your answer to the nearest cent. A 5-column table with 4 rows titled Monthly Payments per 1000 dollars of mortgage. Column 1 is labeled Interest Rate (percent) with entries 5, 5.5, 6, 6.5. Column 2 is labeled 10 Years with entries 10.61, 10.86, 11.11, 11.36. Column 3 is labeled 20 years with entries 6.60, 6.88, 7.17, 7.46. Column 4 is labeled 30 years with entries 5.37, 5.68, 6.00, 6.33. Column 5 is labeled 40 years with entries 4.83, 5.16, 5.51, 5.86. a. $183,147 c. $185,350 b. $184,789 d. $186,523
The price of a home that can be purchased is $185,350.
What is interest rate?The supply and demand for credit, the rate of inflation, and the state of the economy as a whole all influence interest rates.
To determine the price of a home that can be purchased, we need to use the given monthly payment of $1112.10 and the interest rate of 6.0% for a 30-year fixed mortgage.
From the table, we can see that the monthly payment per $1000 of mortgage for a 30-year fixed mortgage with a 6% interest rate is $6.00.
So, the mortgage amount can be calculated as:
Mortgage amount = Monthly payment / Monthly payment per $1000 of mortgage
Mortgage amount = $1112.10 / $6.00 = $185,350 (rounded to the nearest cent)
Therefore, the price of a home that can be purchased is $185,350.
Therefore, the answer is (c) $185,350.
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I really really really need someone help
Answer:
[tex]m = \frac{13.0 - 11.2}{14 - 4} = \frac{1.8}{10} = \frac{9}{50} [/tex]
[tex]13 = \frac{9}{50} (14) + b[/tex]
[tex] \frac{650}{50} = \frac{126}{50} + b[/tex]
[tex]b = \frac{524}{50} [/tex]
[tex]y = \frac{9}{50} x + \frac{524}{50} [/tex]
In the past few years, many small businesses have been faced with difficulty keeping their doors open, and in many cases large corporations with cash on hand have come in to take over the companies and their real estate. In such case, a large restaurant chain purchased a small corner tavern with plans to use the name to build a local franchise. The cost of buying the franchise naming rights was four times the cost of buying the physical property. If the total purchase price was $1,250,000, how much did the restaurant chain pay for each individual element of the sale ( naming rights and physical property)?
The restaurant chain paid $625,000 for the physical property and $2,500,000 for the franchise naming rights, for a total purchase price of $1,250,000.
What is sale?Sale refers to the transfer of ownership of goods or services from one person to another in exchange for money or other consideration.
The total purchase price of the franchise naming rights and physical property was $1,250,000.
To calculate the amount paid for each individual element of the sale, the total purchase price must be divided by the two elements.
The total purchase price of $1,250,000 divided by two elements equals $625,000.
This means that the restaurant chain paid $625,000 for the franchise naming rights and $625,000 for the physical property.
The amount of money paid for the franchise naming rights (four times the cost of buying the physical property) can be calculated by multiplying the cost of the physical property, which is
$625,000/4 .
When the cost of the physical property is multiplied by four, the result is $2,500,000.
This means that the restaurant chain paid $2,500,000 for the franchise naming rights.
In summary, the restaurant chain paid $625,000 for the physical property and $2,500,000 for the franchise naming rights, for a total purchase price of $1,250,000.
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Calculate the perimeter of this shape.
Answer: 52.8 m
Step-by-step explanation:
What you want to try to do when you come across these shapes is to think about it as two different shapes instead of one. The bigger rectangle should have a perimeter of 31 (12.3+12.3+3.2+3.2). Now for the bottom rectangle, you have to solve for one of the side lengths. Subtract 3.2 from 8.6 (as 3.2 is already being used by the top rectangle's perimeter) to get 5.4. The perimeter of the smaller rectangle should be 21.8 (5.5+5.5+5.4+5.4). Now add 31+21.8 to get 52.8 and that should be the total perimeter of your shape. :)
The function f(x)= -3|x-4.7|+2 represents to the temperatures of the solo in degrees Fahrenheit, x minute into an experiment on what interval is temperature positive?
To find on what interval the temperature is positive, we need to find the values of x for which f(x) is greater than zero.
The function f(x) is defined as:
f(x) = -3|x - 4.7| + 2
Since the absolute value of any real number is always non-negative, we can see that f(x) will be positive only if the expression inside the absolute value bars is less than 2/3. So, we can set:
-3|x - 4.7| + 2 > 0
Solving for |x - 4.7|, we get:
|x - 4.7| < 2/3
This means that x must be within 2/3 units of 4.7. So, the interval on which the temperature is positive is:
4.7 - 2/3 < x < 4.7 + 2/3
Simplifying, we get:
4.0333 < x < 5.3667
Therefore, the temperature is positive on the interval (4.0333, 5.3667).
can someone pls help me with this and explain thanks!
Check the picture below.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{37}\\ a=\stackrel{adjacent}{35}\\ o=\stackrel{opposite}{BD} \end{cases} \\\\\\ BD=\sqrt{ 37^2 - 35^2} \implies BD=\sqrt{ 144 }\implies BD=12 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{13}\\ a=\stackrel{adjacent}{AD}\\ o=\stackrel{opposite}{12} \end{cases} \\\\\\ AD=\sqrt{ 13^2 - 12^2}\implies AD=\sqrt{ 169 - 144 } \implies AD=\sqrt{ 25 }\implies \boxed{AD=5}[/tex]
1.- Un activo tiene un valor de contado de $5.000.000 fue adquirido a crédito
mediante las siguientes condiciones:
• Cuota inicial $500.000
El saldo debe ser cancelado mediante dos (2) cuotas, la primera cuota
en el mes 3 por $1.000.000 y segunda cuota en el mes nueve (9)
• Financiación 26% capitalizable trimestralmente
Hallar el valor cancelado en la segunda cuota
The value canceled in the second installment is $4,279,322.14.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To find the value canceled in the second installment, we need to determine the total amount owed at the beginning of the ninth month, and then subtract the first installment paid in the third month.
Let's start by finding the total amount owed at the beginning of the ninth month, using the given financing conditions.
The initial fee of $500,000 is not subject to financing, so we can exclude it from our calculations.
The amount financed is the remaining balance, which is:
$5,000,000 - $500,000 = $4,500,000
The financing rate is 26% capitalizable quarterly, which means that each quarter, the amount owed increases by 26% of the previous balance.
Since there are two quarters between month 3 and month 9, the amount owed at the beginning of month 9 is:
$4,500,000 × (1 + 0.26/4)^2 = $5,279,322.14
Next, we subtract the first installment of $1,000,000 paid in the third month:
$5,279,322.14 - $1,000,000 = $4,279,322.14
Therefore,
The value canceled in the second installment is $4,279,322.14.
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The complete question.
An asset with a cash value of $5,000,000 was purchased on credit.
through the following conditions:
• Initial fee $500,000
The balance must be paid in two (2) installments, the first installment
in month 3 for $1,000,000 and second installment in month nine (9)
• Financing 26% capitalizable quarterly
Find the value canceled in the second installment
From a point 340 feet away from the base of the Peachtree Center Plaza in Atlanta, Georgia, the angle of elevation to the top of the building is 65°. Find the height of
the building. (Hint: The angle of elevation is from the ground up to the top of the
building!)
Solution:
Given data:
Distance from a point to the Peachtree Center Plaza in Atlanta, Georgia (base) = 340 feet
The angle of elevation to the top of the building = 65°
To find height of the building (perpendicular- p):
tan thetha = p/b
Tan 65°= h/340
tan 65°=2.144507
Now,
h= tan 65° * 340
= 2.144507 * 340
= 729.132 feet
So, the height of the building is 729.132 feet
Enrollment in French class at a high school is 0.72 of enrollment in Spanish class. What is enrollment in French class compared to Spanish class as a fraction and as a percent?
Question content area bottom
Part 1
What is the equivalent fraction?
What is the equivalent percent?
Using fractions, we can determine that the enrolment percentage in relation to the Spanish class is 72%.
What are fractions?A fraction is a component of a whole.
Mathematically, the number is expressed as a quotient, where the numerator and denominator are divided.
In a simple fraction, both are integers.
In a complex fraction, a fraction can be found in either the numerator or the denominator.
A suitable fraction has a numerator that is less than its denominator.
So, let's say that x students are enrolled in the Spanish class.
The enrolment in the French class is 0.72 times as large as the attendance in the Spanish class, or 0.72, according to the figures provided.
The enrollment as a percentage of Spanish classes is:
0.72x / x = 0.72
The enrolment percentage in relation to the Spanish class is:
0.72 x 100% = 72%
Therefore, sing fractions, we can determine that the enrolment percentage in relation to the Spanish class is 72%.
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Correct question:
Enrollment in French class at a high school is 0.72 of enrollment in Spanish class. What is enrollment in French class compared to Spanish class as a fraction and as a percent?
it is known that the average IQ of the population of adults is 100. A sample of 50 college students has an average IQ of 108. The probability of this difference being caused by random chance is 1/1000. Are these results statistically significant?
Options:
no, because the results are likely to occur by chance
no, because the results are unlikely to occur by chance
yes, because the results are likely to occur by chance
yes, because the results are unlikely to occur by chance.
Answer:
yes, because the results are unlikely to occur by chance
Step-by-step explanation:
1/1000 is converted to 10% as a decimal. That's like saying for everyone 1000 people, at least one of the can be this "random chance". The smaller the general population is, the higher the affect this percentage has on that group. If the population is lower, than there might be more of a chance that it'll occur but also because there's a smaller population, there's less variety.
Terrence had some problems to complete for math homework. He completed six problem as shown in the diagram which represented 40% of the problem he had to do in all.How many problems does he have altogether for homework?
After answering the presented questiοn, we can cοnclude that equatiοn Therefοre, Terrence had 150 prοblems altοgether fοr his math hοmewοrk.
What is equatiοn?A mathematical equatiοn is a fοrmula that cοnnects twο statements and denοtes equivalence with the equals symbοl (=). An equatiοn is a mathematical statement that shοws the equality οf twο mathematical expressiοns in algebra. In the equatiοn 3x + 5 = 14, fοr example, the equal sign separates the variables 3x + 5 and 14.
A mathematical fοrmula describes the cοnnectiοn between the twο sentences that οccur οn οppοsite sides οf a letter. The symbοl and the single variable are frequently the same. As in 2x - 4 Equals 2, fοr instance.
6 is tο 40% as X is tο 100%
Therefοre, Terrence had 150 prοblems altοgether fοr his math hοmewοrk.
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Solve and explain the following: if F(x) = -5 - 7x, find F(-2).
The value of the function as f(-2) is 9
What are functions?Functions are simply described as those equations, expressions, or laws that explains or shows the relationship between two variables.
These two variables are namely;
The dependent variableThe independent variableFrom the information given, we have that;
f(x) = -5 - 7(x)
substitute the values of x as -2
Then, we have;
f(-2) = -5 - 7(-2)
expand the bracket
f(-2) = -5 + 14
Add the values, we have;
f(-2) = 9
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you are running in the 100 meter dash. from the starting line, you sprint up to 42m/sec at the accelertion rate of 2 m/s/s/ down the track to win the race How long did it take you to win the race.
it took the runner 21 seconds to win the race
What are Distance and velocity ?
velocity is a unit of measurement for the Distance an object travels in a
the predetermined period of time. Here is a word equation that illustrates the connection between space, speed, and time: velocity is calculated by
dividing the total Distance traveled by the journey time.
We want to find t, so we can rearrange the equation to isolate t:
t = (v - u) / a
Substituting the values we have:
t = (42 m/s - 0 m/s) / (-2 m/s^2)
t = -21 s
Wait a minute, why is the time negative? That's because we chose a coordinate system where positive is in the direction of motion, and negative is opposite to it. In other words, the runner is going in the negative direction of the x-axis, so the displacement (100 meters) is negative. Therefore, the time is negative as well. However, we can take the absolute value of time to get the magnitude:
|t| = |-21 s| = 21 s
So it took the runner 21 seconds to win the race (assuming constant acceleration, which may not be realistic for human sprinters).
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I forgot my angles. I’ll please help.
The name of types of angles shown in the diagram is straight angles, right angle, and supplementary angles.
What are supplementary angles?Supplementary angles are two angles that add up to 180 degrees. In other words, if you have two angles, and the sum of those angles is 180 degrees, then those two angles are supplementary. For example, if one angle is 60 degrees, then the other angle would be 120 degrees in order for them to be supplementary. Supplementary angles can be adjacent (share a common vertex and side) or non-adjacent (do not share a common vertex or side).
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put equation in conic form
Answer:
I'm happy to help you put an equation in conic form, but you haven't provided an equation to work with. Please provide the equation and I'll do my best to assist you.
help plsss
rotate tuv 90 degrees clockwise around the origin
Answer: T'=(-1,-1), U'=(-3,-1), V'=(-1,-4)
Step-by-step explanation:
Sofia has 3 candy bars. She gives of each candy bar to her friends. Which expression represents the
amount of candy that is left?
A. 4 x 3/4
B. 3 x 4/3
C. 4 x 4/3
D. 3 x 3/4
12-2=11-1 true or false
Answer: True
Step-by-step explanation:
12-2=10
11-1=10
Answer:
True
Step-by-step explanation:
12-2 equals to 10
11-1 also equals to 10
Therefore, 12-2=11-1 is true
Blanche has recently inherited $8100
, which she wants to deposit into a savings account. She has determined that her two best bets are an account that compounds daily at an annual rate of 4.7%
(Account 1) and an account that compounds annually at an annual rate of 3%
(Account 2).
Step 2 of 2 : How much would Blanche's balance be from Account 1 over 4.8
years? Round to two decimal places.
Therefore, Blanche's balance from Account 1 over 4.8 years would be approximately $10,081.25.
How to find annual amount?To find the annual amount, you first need to know the frequency of the payment. If the payment is made monthly, you need to multiply the monthly payment by 12 to get the annual amount. If the payment is made weekly, you need to multiply the weekly payment by 52 (the number of weeks in a year) to get the annual amount.
If the payment is irregular or occurs at different intervals, you can add up the total amount received over the course of the year and use that as the annual amount.
by the question.
To calculate the balance of Account 1 after 4.8 years, we can use the formula for compound interest:
[tex]A = P(1 + r/n)^{(nt)}[/tex]
where:
A = the final amount
P = the principal (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time period (in years)
Plugging in the values given in the problem, we have:
[tex]A = 8100(1 + 0.047/365)^{(365*4.8)}[/tex]
[tex]A=8100(1+0.00128)\\A=8100(1.00128)\\A=8,110.43[/tex]
[tex]A \approx8,110.43[/tex]
Therefore, Blanche's balance from Account 1 over 4.8 years would be approximately $10,081.25.
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Above are two different models of the same rectangular patio. If the area of the model on the left is 4 sq cm, what is the area of the model on the right? A. 29 sq cm B. 100 sq cm C. 20 sq cm D. 40 sq cm
the area of the model on the right is 100 sq cm.So, the answer is (B) 100 sq cm.in order to solve this use area of rectangle formula
what is area of rectangle ?
The area of a rectangle is the amount of space that is enclosed within its boundaries. It is the product of the length and width of the rectangle. The formula for the area of a rectangle is:
Area = length x width
In the given question,
Since the two models are of the same rectangular patio, they have the same length and width. Let the length of the rectangle be L and the width be W.
The area of a rectangle is given by the formula A = L x W.
For the model on the left, we are given that the area is 4 sq cm.
A = L x W = 4
For the model on the right, the length and width are both increased by a factor of 5. Therefore, the new length is 5L and the new width is 5W.
The area of the new rectangle is:
A = (5L) x (5W) = 25LW
We know that LW = 4 from the model on the left. Therefore:
A = 25LW = 25(4) = 100
Therefore, the area of the model on the right is 100 sq cm.
So, the answer is (B) 100 sq cm.
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The circle below is centered at the origin, and the length of its radius is 3. Write the equation for the circle.
Answer: $x^2+y^2=9$
Step-by-step explanation:
A circle is the locus of points such that its distance from its center is constant. In our case, we have that the center of the circle is the origin, while the radius is 3. Thus, by the Pythagorean Theorem, the equation of the circle is $x^2+y^2=3^2=9$.
A 2-column table with 6 rows. The first column is labeled x with entries negative 1, 0, 1, 2, 3, 4. The second column is labeled f of x with entries negative 9, negative 8, negative 7, 0, 19, 56.
What is the x-intercept of the continuous function shown in the table?
(0, –8)
(0, 2)
(–8, 0)
(2, 0)
Which interval contains a local minimum for this function?
In the given situation the required x-intercept is (2,0).
What is the x-intercept?The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.
Alternatively, we may state that the x-intercept is the value of the x coordinate of a position where the value of the y coordinate equals zero.
It is the value of the x-coordinate of the point where the graph intersects the x-axis.
So, the software displays a table of values for x and their corresponding values for the function f(x):
x f(x)
1 -9
0 -8
1 -7
2 0
3 19
4 56
The term "x-intercept" in the question refers to the value of x when f(x)=0.
When f(x) = 0, x equals 2 when analyzing the table.
To sum up, the x-intercept is (2,0)
Therefore, in the given situation the required x-intercept is (2,0).
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Correct question:
A 2-column table with 6 rows. The first column is labeled x with entries negative 1, 0, 1, 2, 3, 4. The second column is labeled f of x with entries negative 9, negative 8, negative 7, 0, 19, 56. What is the x-intercept of the continuous function shown in the table?
a. (0, –8)
b. (0, 2)
c. (–8, 0)
d. (2, 0)
A bond currently has a price of $1,050. The yield on the bond is 7%. If the yield increases 20 basis points, the price of the bond will go down to $1,040. The duration of this bond is __________ years.
The duration of the bond is approximately 0.0045 years or 1.64 days.
HOW TO CALCULATE DURATION OF BOND?We can use the formula for bond price sensitivity to changes in yield to find the duration of the bond:
D = - (1/P) * (dP/dy)
where D is the duration, P is the price of the bond, y is the yield, and dP/dy is the derivative of the bond price with respect to yield.
We are given that the bond price is currently $1,050 and the yield is 7%, so we can plug these values into the formula:
P = $1,050
y = 7% or 0.07
Next, we need to find the derivative of the bond price with respect to yield, which is the percentage change in bond price divided by the percentage change in yield.
We know that if the yield increases by 20 basis points (0.20%), the price of the bond will decrease to $1,040. Using this information, we can calculate the percentage change in bond price and yield:
Percentage change in bond price = (new price - old price) / old price = ($1,040 - $1,050) / $1,050 = -0.0095 or -0.95%
Percentage change in yield = 0.20%
Using these values, we can calculate the derivative of the bond price with respect to yield:
dP/dy = (percentage change in bond price) / (percentage change in yield) = -0.0095 / 0.002 = -4.75
We can now enter each value into the duration formula as follows:
D = - (1/P) * (dP/dy) = - (1/$1,050) * (-4.75) = 0.0045 years or 1.64 days
Therefore, the duration of the bond is approximately 0.0045 years or 1.64 days.
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I need a quick answer!!
The transformed function that is shown in the graph is:
g(x) = e^x + 3
Which equation represents the transformed function?We know that the graph is a transformation of the parent exponential function.
Notice that for the parent function:
f(x) = e^x
The horizontal asymptote (left side of the graph) is to y = 0
While on the graph, the horizontal asymptote is at y = 3.
So we just had a translation of 3 units upwards, then the function in the graph is:
g(x) = f(x) + 3
g(x) = e^x + 3
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NEED help on 20-25 please and thank you
The sum of the measures of the interior angles of a nonagon is 1260 degrees
The measure of each interior angle of a regular octagon is 135 degrees
How to calculate the anglesA nonagon is a polygon with nine sides, and the formula to calculate the sum of the measures of the interior angles of a polygon with n sides is:
Sum of interior angles = (n-2) x 180 degrees
Therefore, the sum of the measures of the interior angles of a nonagon is:
Sum of interior angles = (9-2) x 180 degrees = 1260 degrees
An octagon is a polygon with eight sides, and the formula to calculate the measure of each interior angle of a regular polygon with n sides is:
Measure of each interior angle = (n-2) x 180 degrees / n
Therefore, the measure of each interior angle of a regular octagon is:
Measure of each interior angle = (8-2) x 180 degrees / 8 = 135 degrees
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Find area of the shaded region.
The area of the shaded region of the composite figure is 389 square units.
What is area of composite figure?A geometric shape made up of two or more simpler shapes is known as a composite figure. You must divide a composite figure into simpler shapes and then add up each shape's unique regions to determine the composite figure's area.
The methods you can take to determine a composite figure's area are as follows: Slice up the composite figure into more basic forms. You can separate the composite figure into its component parts, for instance, if it is made up of a rectangle and a triangle.
Calculate the area of each shape separately.
The total area of the composite figure can be calculated by adding the areas of all the simpler shapes.
The shaded region can be divided into a rectangle and a triangle.
The area of the rectangle with l = 19 and w = 17 is:
Area = length x width = 17 x 19 = 323 square units
Now, the dimensions of the triangle are:
base = 17 - 6 = 11
height = 31 - 19 = 12
Thus,
Area = (base x height) / 2 = (11 x 12) / 2 = 66 square units
Now, the total area of the shaded portion is:
Area = 323 + 66 = 389 square units.
Hence, the area of the shaded region of the composite figure is 389 square units.
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