Answers
The domain of a function or coordinates of a function are the input values of the function "x" for which the function exists.
For instance, given the coordinates of the function {(-7, 2), (0, -2), (2, 5), (8, 1)}, the corresponding value of the x-coordinates are the domain. Therefore the domain of the given coordinate points are given as;
[tex]\text{Domain}=\mleft\lbrace-7,0,2,8\mright\rbrace[/tex]Get the value of f(2).
To get the value of f(2), we will find the y-value of the coordinate with a domain of 2. From the given coordinates, we can see that the coordinate that has a domain of 2 is (2, 5) and the corresponding y-value of the coordinate is 5. Hence f(2) = 5
Related Questions
Hello! Is it possible to get help on this question?
Answers
To determine the graph that corresponds to the given inequality, first, let's write the inequality for y:
[tex]2x\le5y-3[/tex]Add 3 to both sides of the expression
[tex]\begin{gathered} 2x+3\le5y-3+3 \\ 2x+3\le5y \end{gathered}[/tex]Divide both sides by 5
[tex]\begin{gathered} \frac{2}{5}x+\frac{3}{5}\le\frac{5}{5}y \\ \frac{2}{5}x+\frac{3}{5}\le y \end{gathered}[/tex]The inequality is for the values of y greater than or equal to 2/5x+3/5, which means that in the graph the shaded area will be above the line determined by the equation.
Determine two points of the line to graph it:
-The y-intercept is (0,3/5)
- Use x=5 to determine a second point
[tex]\begin{gathered} \frac{2}{5}x+\frac{3}{5}\le y \\ \frac{2}{5}\cdot5+\frac{3}{5}\le y \\ 2+\frac{3}{5}\le y \\ \frac{13}{5}\le y \end{gathered}[/tex]The second point is (5,13/5)
Plot both points to graph the line. Then shade the area above the line.
The graph that corresponds to the given inequality is the second one.
Which of the following inequalities would have solutions of -1, 1, 3, 4?Mark all that apply.A e > -1Bf <6c d < 4Db> -1EC < 5Fa> 0
Answers
Notice that for option B
f< 6 means that all numbers less than 6 are solution to the inequality, also notice that -1,1,3 and 4 are less than 6.
An analogous reasoning apllies for option E, all numbers less than 5 are solution to the inequality c<5 then -1,1,3 and 4 are solution.
For the rest of the inequalities at least one of the provided numbers are no solution for the inequality.
The garden that Julian is enclosing with chicken wire is in the shape of a parallelogram, Plan The measure of angle A is two thirds less than twice the measure of angle L. Find the measure of each angle of the garden enclosure.
Answers
Solution
We can do the following:
1) The condition given is:
m L -2/3
2) We have the other properties in a parallelogram:
m
m
And we also know that:
3) m L + m
2 m 2(2m 4 m6 mm
m
m< P = 1078/9
m < N= 542/9
What is the slope of the line shown in the graph
Answers
Step by step
We have the coordinate pairs of
(0, 3) and (-3, 5) as shown on the attachment
Slope is found by
y2 - y1 over x2 - x1
5 - 3 over -3 - 0
2 over -3
Slope is -2/3
You can also count from point to point y over x
Here we have -2 down and +3 over for a slope of -2/3
Remember if your line going left to right goes at a downward angle, it is a negative slope.
For each set of three side lengths in the table, determine how many unique triangles can be formed. Select the appropriate circle in each row.
Answers
The first one the 3 sides are equal to 1, this mean that it is a equilater triangle, so it is possible to made exactly one unique triangle.
now for the other triangles we will add the two shortest sides of the triangle, and if they are more than the greater side of the triangle, then it will be a unique triangle, if not there will be more than one triangle
for the second one:
[tex]3+4=7>5[/tex]so the second one have exactly one unique triangle.
for the number 3:
[tex]5+10=15=15[/tex]So in this case there is none unique triangles.
for the number 4:
[tex]6+16=22<26[/tex]So in this case there is none unique triangles.
and for the number 5:
[tex]10+50=60>55[/tex]So we hace exactly one unique triangle.
A recent study conducted by a health statistics center found that 27% of households in a certain country had no landline service. This raised concerns about the accuracy of certain surveys, as they depend on random-digit dialing to households via landlines. Pick five households from this country at random. What is the probability that at least one of them does not have a landline _________
Answers
We are going to use Binomial Probability Distribution
Probability that they have no landline = q = 27/100 = 0.27
Probability that they have landline = p = 1 - 0.27 = 0.73
Now, to find the probability that at least one of them does not have a landline, we have to find the probability that all the five have a landline first.
So let's find the probability that all the five have a landline:
[tex]\begin{gathered} P(X=x)=^nC_xp^xq^{n-x} \\ ^5C_5(0.73)^5(0.27)^{5-5} \\ P(X\text{ = 5) = }0.2073 \end{gathered}[/tex]So the probability that all the five have a landline = 20.73%
Now is the time to find the probability that at least one of them does not have a landline:
P(at least one has no landline) = 1 - P(All have landline)
= 1 - 0.2073
= 0.7927
So the probability that at least one of them does not have a landline = 79.27%
That's all Please
Find the 1st term, last term and the sum for the finite arithmetic series.
Answers
Answer:
Given that,
[tex]\sum ^{30}_{n\mathop=2}(3n-1)[/tex]Simplifying we get,
[tex]\sum ^{30}_{n\mathop{=}2}(3n-1)=\sum ^{30}_{n\mathop{=}2}3n+\sum ^{30}_{n\mathop{=}2}1[/tex][tex]=3\sum ^{30}_{n\mathop{=}2}n+\sum ^{30}_{n\mathop{=}2}1[/tex]we have that,
[tex]\sum ^n_{n\mathop=1}1=n[/tex]If n is from 2 to n we get,
[tex]\sum ^n_{n\mathop{=}2}1=n-1[/tex]Also,
[tex]\sum ^k_{n\mathop=1}n=\frac{k(k+1)}{2}[/tex]If n is from 2 to n we get,
[tex]\sum ^k_{n\mathop=2}n=\frac{k(k+1)}{2}-1[/tex]Using this and substituting in the required expression we get,
[tex]=3\lbrack\frac{30\times31}{2}-1\rbrack+30-1[/tex][tex]=3(464)+29[/tex][tex]=1421[/tex]Answer is: 1421
h(x) = x2 + 1 k(x) = x-2 (h - k)(3) = DONE
Answers
We are given two functions:
h(x) = x^2 + 1
and k(x) = x - 2
We are asked to find the value of:
(h - k) (3) (the value of the difference of the two functions at the point x = 3
So we performe the difference of the two functions:
(h - k) (x) = x^2 + 1 - (x - 2) = x^2 + 1 - x + 2 = x^2 - x + 3
So, this expression evaluated at 3 gives:
(h-k)(3) = 3^2 - 3 + 3 = 9
One could also evaluate what was asked by evaluating each function independently and subtracting the results of such evaluation:
h(3) = 3^2 + 1 = 10
k(3) = 3 - 2 = 1
Then, the difference is : h(3) - k(3) = 10 - 1 = 9
So use whatever method feels more comfortable for you.
The table represents the amount of money in a bank account each month. Month Balance ($) 1 2,215.25 2 2,089.75 3 1,964.25 4 1,838.75 5 1,713.25 What type of function represents the bank account as a function of time? Justify your answer.
Answers
The form of function that represents the bank account as a function of time is a linear function.
How to determine the type of function?The table of values is given as illustrated:
Month Balance ($)
1 2,215.25
2 2,089.75
3 1,964.25
4 1,838.75
5 1,713.25
From the above table of values, we can see that the balance in the bank account reduces each month by $125.5
So, we have
Difference = 1,838.75 - 1713.25 =125.5
Difference = 1,964.25 - 1,838.75 =125.5
Difference = 2,089.75 - 1,964.25 =125.5
Difference = 2,215.25 - 2,089.75 =125.5
This shows a linear function.
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Suppose that the functions and g are defined for all real numbers x as follows. f(x) = x + 3; g(x) = 2x - 2 Write the expressions for (fg)(x) and (f - g)(x) and evaluate (f + g)(3)
Answers
Solution
Given
[tex]\begin{gathered} f(x)=x+3 \\ \\ g(x)=2x-2 \end{gathered}[/tex]Then
[tex](f\cdot g)(x)=f(x)\cdot g(x)=(x+3)(2x-2)=2x^2+4x-6[/tex][tex](f-g)(x)=f(x)-g(x)=(x+3)-(2x-2)=x-2x+3+2=5-x[/tex][tex](f+g)(3)=f(3)+g(3)=(3+3)+(2(3)-2)=6+4=10[/tex]a scientist need to 6000 calories per day. Based on the percentage of total daily calories and the number of calories needed, how many biscuits, packages of pemmican, butter and coco does a person need each day?
Answers
EXPLANATION:
Given;
We are told that a scientist needs 6000 calories per day.
We are also given a table showing the percentage of daily calories he can get from three types of food.
These are;
[tex]\begin{gathered} Biscuits---40\% \\ pemmican---45\% \\ Butter\text{ }and\text{ }cocoa---15\% \end{gathered}[/tex]Required;
We are required to calculate how many of each type of food he would need to eat each day.
Step-by-step solution;
We shall solve this by first determining how many calories can be gotten from each type of food based on the percentage given. This is calculated below;
[tex]\begin{gathered} Biscuits: \\ 6000\times\frac{40}{100}=2400 \end{gathered}[/tex]This means if he gets 75 calories from one biscuit, then to get 2,400 calories he would have to eat;
[tex]\begin{gathered} 75cal=1b \\ 2400cal=\frac{2400}{75} \\ 2400cal=32 \end{gathered}[/tex]The scientist would have to eat 32 biscuits to get 2400 calories.
[tex]\begin{gathered} Pemmican: \\ 6000\times\frac{45}{100}=2700 \end{gathered}[/tex]This means if he gets 135 calories from one pack of dried meat, then to get 2700 calories he would have to consume;
[tex]\begin{gathered} 135cal=1pack \\ 2700cal=\frac{2700}{135} \\ 2700cal=20 \end{gathered}[/tex]Therefore, the scientist would have to eat 20 packs of pemmican to get 2700 calories
[tex]\begin{gathered} Butter\text{ }and\text{ }Cocoa: \\ 6000\times\frac{15}{100}=900 \end{gathered}[/tex]This means if he eats 1 package of Butter and cocoa he gets 225 calories. To get 900 calories he would have to eat;
[tex]\begin{gathered} 225cal=1pack \\ 900cal=\frac{900}{225} \\ 900cal=4 \end{gathered}[/tex]Therefore, the scientist would have to eat 4 packs of Butter and cocoa.
We now have the summary as follows;
ANSWER:
[tex]\begin{gathered} Biscuits=32 \\ Pemmican=20\text{ }packs \\ Butter\text{ }and\text{ }cocoa=4\text{ }packs \end{gathered}[/tex]Write the equation of the circle centered at (−4,−2) that passes through (−15,19)
Answers
In this problem, we are going to find the formula for a circle from the center and a point on the circle. Let's begin by reviewing the standard form of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]The values of h and k give us the center of the circle, (h,k). The value r is the radius. We can begin by substituting the values of h and k into our formula.
Since the center is at (-4, -2), we have:
[tex]\begin{gathered} (x-(-4))^2+(y-(-2))^2=r^2 \\ (x+4)^2+(y+2)^2=r^2 \end{gathered}[/tex]Next, we can use the center and the given point on the circle to find the radius.
Recall that the radius is the distance from the center of a circle to a point on that circle. So, we can use the distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Let
[tex](x_1,y_1)=(-4,-2)[/tex]and let
[tex](x_2,y_2)=(-15,19)[/tex]Now we can substitute those values into the distance formula and simplify.
[tex]\begin{gathered} r=\sqrt{(-15-(-4))^2+(19-(-2))^2} \\ r=\sqrt{(-11)^2+(21)^2} \\ r=\sqrt{562} \end{gathered}[/tex]Adding that to our equation, we have:
[tex]\begin{gathered} (x+4)^2+(y+2)^2=(\sqrt{562})^2 \\ (x+4)^2+(y+2)^2=562 \end{gathered}[/tex]Please help with this practice question
Answers
Explanation below:
For the function f(x)=3x2−4x−4,a. Calculate the discriminant.b. Determine whether there are 0, 1, or 2 real solutions to f(x)=0.
Answers
Answer:
a) Using the formula for the discriminant we get:
[tex]\begin{gathered} \Delta=(-4)^2-4(3)(-4), \\ \Delta=16+48, \\ \Delta=64. \end{gathered}[/tex]The discriminant is 64.
b) Based on the above result we know that the f(x)=0 has 2 real solutions,
Find the surface area. Do not round please Formula: SA= p * h + 2 * b
Answers
The shape in the question has two hexagonal faces,
The Area of each of the heaxagonal faces is
[tex]=42\text{ square units}[/tex]The shape also has 6 rectangular faces with dimensions of
[tex]8.2\times4[/tex]The area of a rectangle is gotten with the formula below
[tex]\text{Area}=l\times b[/tex]By substituting the values, we will have
[tex]\begin{gathered} \text{Area}=l\times b \\ \text{Area}=8.2\times4 \\ \text{Area}=32.8\text{square units} \end{gathered}[/tex]To calculate The total surface area of the shape, we will add up the areas of the hexagonal faces and the rectangular faces
[tex]\text{Surface area=}2\times(area\text{ of hexagonal faces)+ 6(area of rectangular faces)}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \text{Surface area=}2\times(area\text{ of hexagonal faces)+ 6(area of rectangular faces)} \\ \text{Surface area}=(2\times42)+(6\times32.8) \\ \text{Surface area}=84+196.8 \\ \text{Surface area}=280.8\text{ square units} \end{gathered}[/tex]Hence,
The Surface Area is = 280.8 square units
A person investigating to employment opportunities. They both have a beginning salary of $42,000 per year. Company A offers an increase of $1000 per year. Company B offers 7% more than during the preceding year. Which company will pay more in the sixth year? what will company A pay? and what will company B pay?
Answers
qANSWER
Company B will pay more
Company A =
EXPLANATION
Both companies start by paying $42,000 per year.
Company A offers an increase of $1000 per year.
This means that after n years, he would have earned:
Earnings = 42000 + 1000n
where n = number of years after the first year
So, after 6 years, he would have worked 5 years after the first, so his earnings would be:
Earnings = 42000 + 1000(5) = 42000 + 5000
Earnings = $47000
Company B offers 7% more than the previous year. That means that his earnings are compounded.
His earnings can then be represented as:
[tex]\text{ Earnings = P(1 + }\frac{r}{100})^t[/tex]where P = initial salary = $42000
r = interest rate = 7%
t = number of years spent = 6 years
Therefore, his earnings after the 6th year will be:
[tex]\begin{gathered} \text{ Earnings = 42000(1 + }\frac{7}{100})^6 \\ \text{ Earnings = 42000(1 + 0.07)}^6=42000(1.07)^6 \\ \text{ Earnings = }42000\cdot\text{ 1.501} \\ \text{Earnings = \$63042} \end{gathered}[/tex]He would have earned $63042.
Therefore, Company B will pay more.
qANSWER
Company B will pay more
Company A =
EXPLANATION
Both companies start by paying $42,000 per year.
Company A offers an increase of $1000 per year.
This means that after n years, he would have earned:
Earnings = 42000 + 1000n
where n = number of years after the first year
So, after 6 years, he would have worked 5 years after the first, so his earnings would be:
Earnings = 42000 + 1000(5) = 42000 + 5000
Earnings = $47000
Company B offers 7% more than the previous year. That means that his earnings are compounded.
His earnings can then be represented as:
[tex]\text{ Earnings = P(1 + }\frac{r}{100})^t[/tex]where P = initial salary = $42000
r = interest rate = 7%
t = number of years spent = 6 years
Therefore, his earnings after the 6th year will be:
[tex]\begin{gathered} \text{ Earnings = 42000(1 + }\frac{7}{100})^6 \\ \text{ Earnings = 42000(1 + 0.07)}^6=42000(1.07)^6 \\ \text{ Earnings = }42000\cdot\text{ 1.501} \\ \text{Earnings = \$63042} \end{gathered}[/tex]He would have earned $63042.
Therefore, Company B will pay more.
Draw the graph of the line that is perpendicular to Y= 4X +1 and goes through the point (2, 3)
Answers
Given:
[tex]\begin{gathered} y=4x+1 \\ \text{ point }(2,3) \end{gathered}[/tex]To find:
Draw a graph of a line that is perpendicular to the given line and passing through a given point.
Explanation:
As we know that relation between two slopes of perpendicular slopes of lines:
[tex]m_1.m_2=-1[/tex]Slope of given line y = 4x + 1 is:
[tex]m_2=4[/tex]So, the slope of line perpendicular to given line is:
[tex]m_2=-\frac{1}{4}[/tex]Also, so line equation that is perpendicular to given line is:
[tex]y=-\frac{1}{4}x+c...........(i)[/tex]Also, the required line is passing thorugh given point (2, 3), i.e.,
[tex]\begin{gathered} 3=-\frac{1}{4}(2)+c \\ c=3+\frac{1}{2} \\ c=\frac{7}{2} \end{gathered}[/tex]So, line equation that is perpendicular to given line is:
[tex]y=-\frac{1}{4}x+\frac{7}{2}[/tex]The required graph of line is:
Angie added a stone border 2 feet in width on all sides of her garden making her harder 12 by 6 feet. What is the area, in square feet, of the portion of the garden that excludes the border?
A. 4
B. 16
C. 40
D. 56
E. 72
Answers
The area, in square feet, of the portion of the garden that excludes the border is 40.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
We have been given that Angie added a stone border of 2 feet in width on all sides of her garden making her harder 12 by 6 feet.
Length = 12 ft
Width = 6 ft
The dimension of the garden that excludes the border of 2 feet are;
Length = 12 ft- 2 = 10 ft
Width = 6 ft - 2= 4 ft
Thus, Area = length × Width
Area = 10 x 4
Area = 40 square feet
Hence, the area, in square feet, of the portion of the garden that excludes the border is 40.
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Two planes fly in opposite directions. One travels 450 mi/h and the other 550 mi/h. How long will it take before they are 4,000 mi apart? The planes must fly Answer hours before they will be 4,000 mi apart.
Answers
Given,
The speed of first plane is 450 miles per hour.
The speed of second plane is 550 miles per hour.
The total distance between plane required is 4000 miles.
As, the planes are moving in opposite direction, then distance cover by both is must be added.
Number of distance both plane becomes apart in one hour is,
[tex]\text{Number of distance = 450+550=1000 miles.}[/tex]The Number of hours required to complete 4000 miles is,
[tex]\text{Time=}\frac{4000}{\text{1}000}=4\text{ hours}[/tex]Hence, it will take 4 hours before they are 4,000 miles apart.
What are the domain and range of y = cot x? Select onechoice for domain and one for range.
Answers
ANSWER:
A. Domain: x ≠ n
D. Range: All real numbers
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]y=\cot\left(x\right)[/tex]The domain of a function is the interval of input values, that is, the interval of x while the range is the interval of output values, that is, the interval of y.
In the cotangent function, x cannot take the value of radians (nor its multiples), since it is not defined, while the range is continuous on all real numbers.
That means the correct options are:
A. Domain: x ≠ n
D. Range: All real numbers
find the equation of the axis of symmetry of the following parabola algebraically. y=x²-14x+45
Answers
Answer:
x = 7, y = -4
(7, -4)
Explanation:
Given the below quadratic equation;
[tex]y=x^2-14x+45[/tex]To find the equation of the axis of symmetry, we'll use the below formula;
[tex]x=\frac{-b}{2a}[/tex]If we compare the given equation with the standard form of a quadratic equation, y = ax^2 + bx + c, we can see that a = 1, b = -14, and c = 45.
So let's go ahead and substitute the above values into our equation of the axis of symmetry;
[tex]\begin{gathered} x=\frac{-(-14)}{2(1)} \\ =\frac{14}{2} \\ \therefore x=7 \end{gathered}[/tex]To find the y-coordinate, we have to substitute the value of x into our given equation;
[tex]\begin{gathered} y=7^2-14(7)+45 \\ =49-98+45 \\ \therefore y=-4 \end{gathered}[/tex]Each of John’s notebook is 3/4 inches wide. If he has 36 inches of space remaining on his bookshelf, how many notebooks will fit? Write your answer in simplest form.
Answers
Given that:
- The width of each of John’s notebooks is:
[tex]\frac{3}{4}in[/tex]- The space remaining on his bookshelf is:
[tex]36in[/tex]Let be "x" the number of notebooks that will fit in John's bookshelf.
Knowing that:
[tex]\frac{3}{4}in=0.75in[/tex]You can set up the following proportion:
[tex]\frac{1}{0.75}=\frac{x}{36}[/tex]Now you have to solve for "x":
[tex]\begin{gathered} (\frac{1}{0.75})(36)=\frac{x}{36} \\ \\ \frac{36}{0.75}=x \end{gathered}[/tex][tex]x=48[/tex]Hence, the answer is:
[tex]48\text{ }notebooks[/tex]The graphs of the functions g and h are shown below. For each graph, find the absolute maximum and absolute minimum. If no such value exists, click on "None".
Assume that the dashed line shown is a vertical asymptote that the graph does not cross.
Answers
For the graph g, the absolute maximum is 2 and the absolute minimum is -4.
Similarly, for graph h, the absolute maximum is 3 and the absolute minimum is -5.
Absolute Maximum of a Graph:
The absolute maximum of a graph is the point on the graph with the highest y-value. There can only be one absolute maximum of a graph.
Absolute Minimum of a Graph:
The absolute minimum of a graph is the point on the graph with the lowest y-value. There can only be one absolute minimum of a graph.
Given,
Here we have the two graph called g and h.
Now, we need to find the absolute maximum and minimum from it.
AS per the given definition, we know that,
For graph g,
The absolute maximum is 2 and the absolute minimum is -4.
Similarly, for graph h, the absolute maximum is 3 and the absolute minimum is -5.
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Which is the equation of the line that passes through the points (-4, 8) and (1, 3)?A. Y=x+4B. Y=-x+12C. Y=-x+4D. Y=x+12
Answers
In order to find the equation that passes through both points, we can use the slope-intercept form of the linear equation:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
Using the given points on this equation, we have:
[tex]\begin{gathered} (-4,8)\colon \\ 8=m\cdot(-4)+b \\ b=8+4m \\ \\ (1,3)\colon \\ 3=m+b \\ 3=m+8+4m \\ 5m=3-8 \\ 5m=-5 \\ m=-1 \\ b=8+4\cdot(-1)=8-4=4 \end{gathered}[/tex]Therefore the equation is y = -x + 4 (correct option: C)
Evaluate theexpression belowwhen x = = 3.<54 : 2.3 - 22Enter your answer inthe box below.
Answers
The given expression is
[tex]54\frac{.}{.}2\times3-x^2[/tex]where x=3
the dot in the expression means multiplication
substitute into the expression above we have
[tex]\begin{gathered} 54\frac{.}{.}2\times3-3^2 \\ \end{gathered}[/tex]Applying BODMAS
[tex]27\times3-3^2[/tex][tex]\begin{gathered} 81-3^2 \\ 81-9 \\ 72 \end{gathered}[/tex]Therefore the value of the expression is 72
True or false? Based only on the given information, it is guaranteed thatAD EBDADGiven: ADI ACDBICBAC = BCBCDO A. TrueB. FalseSUBMIT
Answers
According to the information given, we can assure:
For both triangles, two interior angles and the side between them have the same measure and length, respectively. This is consistent with the ALA triangle congruence criterion.
ANSWER:
True.
please help me I dont understand A number is less than or equal to - 7 or greater than 12.
Answers
To translate the sentence as an inequality, we have:
[tex]x\leq-7,x>12[/tex]Since the number is less or equal ( < = ) we use this symbol to represent it as inequality, and greater than using the symbol ( > ).
Then, we can answer the question as:
x < = -7 or x > 12.
A loan is paid off in 15 years with a total of $192,000. It had a 4% interest rate that compounded monthly.
What was the principal?
Round your answer to the nearest cent and do not include the dollar sign. Do not round at any other point in the solving process; only round your answer.
Answers
The principal amount with the given parameters if $165.
Given that, Amount = $192,000, Time period = 15 years and Rate of interest = 4%.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100} )^{nt}[/tex]
Now, [tex]192,000=P(1+\frac{4}{100} )^{15\times 12}[/tex]
⇒ [tex]P=\frac{192,000}{(1.04)^{180}}[/tex]
⇒ P = $164.93
≈ $165
Therefore, the principal amount with the given parameters if $165.
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Answer:
Step-by-step explanation:
Use the compound interest formula and substitute the values given: $192,000=P(1+.0412)12(15). Simplify using order of operations: $192,000=P(1+.0412)180
P=192,000(1+.0412)180
P≈$105477.02
Consider the two polynomials p(x), q(x) in Z[x] by p(x) = 1+2x+3x2, q(x) = 4+5x+7x3. Then p(x) + q(x) is
Answers
The solution for polynomials p(x) + q(x) is 7x³ + 3x² + 7x + 5
Given,
The polynomials
p(x) = 1 + 2x + 3x²
q(x) = 4 + 5x + 7x³
We have to find the solution for p(x) + q(x)
Then,
p(x) + q(x) = (1 + 2x + 3x²) + ( 4 + 5x + 7x³)
p(x) + q(x) = 7x³ + 3x² + 2x + 5x + 1 + 5
p(x) + q(x) = 7x³ + 3x² + 7x + 5
That is,
The solution for polynomials p(x) + q(x) is 7x³ + 3x² + 7x + 5
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Need help with 3,4,5,and 6 please. I don’t understand it
Answers
4. The triangle has 3 given sides but no angles but we can get the angles using cosine law
[tex]\begin{gathered} \cos R=\frac{t^2+s^2-r^2}{2ts} \\ \cos \text{ R=}\frac{23.7^2+48^2-35^2}{2\times23.7\times48} \\ \cos R=\frac{561.69+2304-1225}{2275.2} \\ \cos R=\frac{1640.69}{2275.2} \\ \cos R=0.7211190225 \\ R=\cos ^{-1}0.7211190225 \\ R=43.8530535482 \\ R=44^{\circ} \end{gathered}[/tex][tex]\begin{gathered} \cos T=\frac{r^2+s^2-t^2}{2rs} \\ \cos T=\frac{35^2+48^2-23.7^2}{2\times35\times48} \\ \cos T=\frac{1225+2304-561.69}{3360} \\ \cos T=\frac{3529-561.69}{3360} \\ \cos T=\frac{2967.31}{3360} \\ \cos T=0.88312797619 \\ T=\cos ^{-1}0.88312797619 \\ T=27.977977493 \\ T=28^{\circ} \end{gathered}[/tex][tex]\begin{gathered} S=180-28-44 \\ S=108^{\circ} \end{gathered}[/tex]From largest to smallest it will be
[tex]\angle S,\angle R\text{ and}\angle T[/tex]