The table of values represents a quadratic function.What is the average rate of change for f(x) from x=−10 to x = 0?Please help me with this problem so that my son can understand better. Enter your answer in the box.xf(x)−10184−5390−654910204
Answers
We are given a quadratic function and the rather than the equation for this function we already have the outputs at each given input as shown in the table provided. This means, for example, for the function given, when the input is -10, the output is 184. Thus the table includes among other values;
[tex]x=-10|f(x)=184[/tex]To calculate the average rate of change we shall apply the formula for the slope (which is also the average rate of change). This is given below;
[tex]\text{Aerage Rate of Change}=\frac{f(b)-f(a)}{b-a}[/tex]Note that the variables are;
[tex]\begin{gathered} f(a)=\text{first input value} \\ f(b)=\text{second input value} \end{gathered}[/tex]The first input value is -10 and the function at that value is 184
The second input value is 0 and the function at that value is -6
We now have;
[tex]\begin{gathered} a=-10,f(a)=184 \\ b=0,f(b)=-6 \end{gathered}[/tex]We can now substitute these into the formula shown nearlier and we'll have;
[tex]\begin{gathered} \text{Ave Rate Of Change}=\frac{f(b)-f(a)}{b-a} \\ =\frac{-6-184}{0-\lbrack-10\rbrack} \end{gathered}[/tex][tex]\begin{gathered} =\frac{-190}{0+10} \\ \end{gathered}[/tex][tex]=\frac{-190}{10}[/tex][tex]\text{Average Rate of Change}=-19[/tex]ANSWER:
The average rate of change over the given interval is -19
Related Questions
Please give steps and explanations to how you get the correct answer I am confused
Answers
To find the area under a function in a given interval you need to find the definite integral of the function in that interval.
For the given function:
[tex]\begin{gathered} P=100(0.4)^t \\ \\ \int_0^8Pdt=\int_0^8100(0.4)^tdt \end{gathered}[/tex]Use the next properties to find the integral:
[tex]\begin{gathered} \int a\times f(x)dx=a\int f(x)dx \\ \\ \int a^xdx=\frac{a^x}{\ln(a)} \end{gathered}[/tex][tex]\int_0^8100(0.4)^tdt=100\int_0^80.4^tdt=100\times\frac{0.4^t}{\ln(0.4)}\lvert^8_0[/tex]Evaluate the result for the given interval:
[tex]\begin{gathered} (100\times\frac{0.4^8}{\ln(0.4)})-(100\times\frac{0.4^0}{\ln(0.4)}) \\ \\ =-0.07152-(-109.13566) \\ \\ =109.06 \end{gathered}[/tex]Then, the area under the given function in the interval (0,8) is 109.06The table below shows the average price of a Miami Marlins baseball ticket between 2006 and 2021.
Answers
Ticket price as a function of time. If you write the number [tex]2040[/tex] where you see [tex]x[/tex] in this function and take the value where you see [tex]y[/tex], you will reach the correct answer.
[tex]y=1.83(2040)-2225.5[/tex][tex]y=1507.7[/tex]which answer is the right one according to the image below
Answers
To do that, we have to do the following:
[tex]\begin{gathered} t(s(x))=t(x\text{ -}7) \\ =4(x\text{ - }7)^2\text{ - }(x\text{ - }7)+3 \\ \\ \end{gathered}[/tex]So, that would be the equivalent expression, because x is s(x), which is x - 7, so you have to replace every x value with (x - 7)
what property justifies the statement? if a=b and b=5,then a=5. A. addition property of equality. B. reflexive property.C transitive property. D. symmetric property.
Answers
a=b
b=5
a=5
Symmetric propery of equality. (D)
It states that if quantity a equals quantity b, then a equals b.
The confidence interval on estimating the heights of students is given as (5.4, 6.8). Find the sample mean of the confidence interval. A.6.8B.6.1C. 5.4D. 0.7
Answers
Solution
- The formula for finding the sample mean from the confidence interval is given below
[tex]\begin{gathered} \text{Given the Confidence interval,} \\ (A_1,A_2) \\ \\ \therefore\operatorname{mean}=\frac{A_1+A_2}{2} \end{gathered}[/tex]- Thus, we can find the sample means as follows
[tex]\begin{gathered} A_1=5.4 \\ A_2=6.8 \\ \\ \therefore\operatorname{mean}=\frac{5.4+6.8}{2} \\ \\ \operatorname{mean}=\frac{12.2}{2} \\ \\ \operatorname{mean}=6.1 \end{gathered}[/tex]Final Answer
The sample mean is 6.1 (OPTION B)
0.0032% in fraction
Answers
Recall that the x% in fraction form is:
[tex]\frac{x}{100}\text{.}[/tex]Therefore 0.0032% as a fraction is:
[tex]\frac{0.0032}{100}=\frac{\frac{32}{10000}}{100}\text{.}[/tex]Simplifying the above result we get:
[tex]\frac{\frac{32}{10000}}{100}=\frac{32}{100\times10000}=\frac{1}{31250}\text{.}[/tex]Answer:
[tex]\frac{1}{31250}[/tex]Answer to the question
Answers
Answer: [tex]m=\frac{y_2 -y_1}{x_2 -x_1}[/tex]
Step-by-step explanation:
[tex]y_2 =m(x_2 -x_1)+y_1\\\\y_2 -y_1=m(x_2 -x_1)\\\\m=\frac{y_2 -y_1}{x_2 -x_1}[/tex]
Would be the last one
M=y2(x2-x1)-x1
A spinner has the sections A through F. The spinner is spun and a 6-sided die is rolled. What is the probability that the outcome will be D and 5?1/361/181/121/6
Answers
To find the probability of having a D and %, we would use the concept of mutually exclusive events here
But probability is given as
[tex]P=\frac{\text{ number of favourable outcomes}}{\text{total number of }possible\text{ outcomes}}[/tex]The probability of choosing a D is
A, B, C, D, E and F. This can be found as
[tex]P_a=\frac{1}{6}[/tex]The probabilty of choosing a 5 out of 6 possible outcomes is
[tex]P_n=\frac{1}{6}[/tex]The probability of having a D and 5 would be
[tex]\begin{gathered} P=P_a\times P_n \\ P=\frac{1}{6}\times\frac{1}{6} \\ P=\frac{1}{36} \end{gathered}[/tex]From the calculations above, the answer to this question is 1/36
Marshawn has batting average of 0.727272... write his batting average as fraction in simplest form
Answers
Marshawn batting average as fraction in simplest form is 90909/125000.
Given a number into decimal form i.e., 0.727272...
Marshawn has batting average of 0.727272....
And, Write his batting average as fraction in simplest form.
Based on the given conditions,
Formulate:
0.727272..
Simplify in simplest form:
0.727272/1
= 7.27272/10
=72.7272/100
= 727.272/1000
= 7272.72/10000
=72727.2/100000
=727272/1000000
It is divided by 2, we get
= 363636/ 500,000
= 181,818/ 250,000
= 90909/125000
Hence, Marshawn batting average as fraction in simplest form is 90909/125000.
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The boxplot shown below results from the heights (cm) of males listed in a data set. What do the numbers in that boxplot tell us?
Answers
Given:
The boxplot is given.
To fill in the blanks:
Explanation:
As we know,
The minimum value is represented by the line at the far left end of the diagram.
So, the minimum height is 153cm.
The first quartile on the left side is represented by the line between the minimum value ad the median.
So, the first quartile is 166.6cm.
The second quartile (or median) is represented by the line at the centre of the box.
So, the second quartile is 173.2cm.
The third quartile on the right side is represented by the line between the maximum value ad the median.
So, the third quartile is 180.1cm.
The maximum value is represented by the line at the far right end of the diagram.
So, the maximum height is 193cm.
Final answer:
The minimum height is 153cm, the first quartile is 166.6cm, the second quartile is 173.2cm, the third quartile is 180.1cm, and the maximum height is 193cm.
Number 14. Directions in pic. And also when you graph do the main function in red and the inverse in blue
Answers
Question 14.
Given the function:
[tex]f(x)=-\frac{2}{3}x-4[/tex]Let's find the inverse of the function.
To find the inverse, take the following steps.
Step 1.
Rewrite f(x) for y
[tex]y=-\frac{2}{3}x-4[/tex]Step 2.
Interchange the variables:
[tex]x=-\frac{2}{3}y-4[/tex]Step 3.
Solve for y
Add 4 to both sides:
[tex]\begin{gathered} x+4=-\frac{2}{3}y-4+4 \\ \\ x+4=-\frac{2}{3}y \end{gathered}[/tex]Multply all terms by 3:
[tex]\begin{gathered} 3x+3(4)=-\frac{2}{3}y\ast3 \\ \\ 3x+12=-2y \end{gathered}[/tex]Divide all terms by -2:
[tex]\begin{gathered} -\frac{3}{2}x+\frac{12}{-2}=\frac{-2y}{-2} \\ \\ -\frac{3}{2}x-6=y \\ \\ y=-\frac{3}{2}x-6 \end{gathered}[/tex]Therefore, the inverse of the function is:
[tex]f^{-1}(x)=-\frac{3}{2}x-6[/tex]Let's graph both functions.
To graph each function let's use two points for each.
• Main function:
Find two point usnig the function.
When x = 3:
[tex]\begin{gathered} f(3)=-\frac{2}{3}\ast3-4 \\ \\ f(3)=-2-4 \\ \\ f(3)=-6 \end{gathered}[/tex]When x = 0:
[tex]\begin{gathered} f(0)=-\frac{2}{3}\ast(0)-4 \\ \\ f(-3)=-4 \end{gathered}[/tex]For the main function, we have the points:
(3, -6) and (0, -4)
Inverse function:
When x = 2:
[tex]\begin{gathered} f^{-1}(2)=-\frac{3}{2}\ast(2)-6 \\ \\ f^{-1}(2)=-3-6 \\ \\ f^1(2)=-9 \end{gathered}[/tex]When x = -2:
[tex]\begin{gathered} f^{-1}(-2)=-\frac{3}{2}\ast(-2)-6 \\ \\ f^1(-2)=3-6 \\ \\ f^{-1}(2)=-3 \end{gathered}[/tex]For the inverse function, we have the points:
(2, -9) and (-2, -3)
To graph both functions, we have:
ANSWER:
[tex]\begin{gathered} \text{ Inverse function:} \\ f^{-1}(x)=-\frac{3}{2}x-6 \end{gathered}[/tex]Drag "Yes" if the lengths could create a triangle, or "No" if the lengths could not create a triangle.
Answers
How do I add the probabilities? And what is the solution after doing that?
Answers
In order to calculate the probability of P(Z<3), let's add all cases where Z<3:
[tex]P(Z<3)=P(Z=0)+P(Z=1)+P(Z=2)[/tex]The minimum value of Z is given when X = 0 and Y = 1, so Z = 1.
The maximum value of Z is given when X = 1 and Y = 2, so Z = 3.
Therefore P(Z = 0) is zero.
Z = 1 can only happen when X = 0 and Y = 1.
Z = 2 can happen when X = 1 and Y = 1 or when X = 0 and Y = 2.
So we can rewrite the expression as follows:
[tex]\begin{gathered} P(Z<3)=0+P(X=0)P(Y=1)+[P(X=1)P(Y=1)+P(X=0)P(Y=2)\rbrack\\ \\ =0+0.5\cdot0.4+0.5\cdot0.4+0.5\cdot0.6\\ \\ =0+0.2+0.2+0.3\\ \\ =0.7 \end{gathered}[/tex]Therefore the correct option is A.
the measure of angle is 15.1 what is measure of a supplementary angle
Answers
we get that measure of the supplemantary angle is:
[tex]180-15.1=164.9[/tex]What is 58 divided into 7275
Answers
Answer:125.431034
Step-by-step explanation:
Find the indicated function given f(x)=2x^2+1 and g(x)=3x-5. When typing your answer if you have an exponent then use the carrot key ^ by pressing SHIFT and 6. Type your simplified answers in descending powers of x an do not include any spaces between your characters.f(g(2))=Answerf(g(x))=Answerg(f(x))=Answer (g \circ g)(x) =Answer (f \circ f)(-2) =Answer
Answers
Given the functions
[tex]\begin{gathered} f(x)=2x^2+1 \\ g(x)=3x-5 \end{gathered}[/tex]1) To find f(g(2))
[tex]\begin{gathered} f(g(x))=2(3x-5)^2+1 \\ f(g(x))=2(9x^2-15x-15x+25)+1=2(9x^2-30x+25)+1 \\ f(g(x))=18x^2-60x+50+1=18x^2-60x+51 \\ f(g(2))=18(2)^2-60(2)+51=18(4)-120+51 \\ f(g(2))=72-120+51=3 \\ f(g(2))=3 \end{gathered}[/tex]Hence, f(g(2)) = 3
2) To find f(g(x))
[tex]\begin{gathered} f(g(x))=2(3x-5)^2+1 \\ f(g(x))=2(9x^2-15x-15x+25)+1=2(9x^2-30x+25)+1 \\ f(g(x))=18x^2-60x+50+1=18x^2-60x+51 \\ f(g(x))=18x^2-60x+51 \end{gathered}[/tex]Hence, f(g(x)) = 18x²-60x+51
3) To find g(f(x))
[tex]\begin{gathered} g(f(x))=3(2x^2+1)-5 \\ g(f(x))=6x^2+3-5=6x^2-2 \\ g(f(x))=6x^2-2 \end{gathered}[/tex]Hence, g(f(x)) = 6x²-2
4) To find (gog)(x)
[tex]\begin{gathered} (g\circ g)(x)=3(3x-5)-5=9x-15-5=9x-20 \\ (g\circ g)(x)=9x-20 \end{gathered}[/tex]Determine the height of the lift, in metres, above the gym floor. show all your work algebraically. round to the nearest cm, if necessary.
Answers
Height of lift = x + x = 2x
We can find x using triangle ABC by the cosine rule
[tex]\begin{gathered} x^2=5.6^2+5.6^2-2(5.6)(5.6)\cos40^0 \\ x^2=62.72-48.04352 \\ x^2=14.67648 \\ x=\sqrt{14.67648} \\ x=3.831m \end{gathered}[/tex]Height of lift = 2 X 3.831m = 7.662m
This will be converted to cm by multiplying by 100
Height of lift = 7.662 X 100 cm
= 766.2 cm
= 766cm ( nearest cm )
Hence the answer is 766cm
A graph the line that passes through the points (1,-5) and (5,7)and determine the equation of the line
Answers
Answer:
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Class 11
>>Applied Mathematics
>>Straight lines
>>Various forms of the equation of a line
>>Find the equation of the line that passe
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Find the equation of the line that passes through the points (7,5) and (−9,5)
Hard
Updated on : 2022-09-05
Solution
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Verified by Toppr
Correct option is A)
Since slope of line passing through two points (x
1
,y
1
) and (x
2
,y
2
) is m=
x
2
−x
1
y
2
−y
1
We now find the slope of the line passing through the points (7,5) and (−9,5) as shown below:
m=
−9−7
5−5
=
−16
0
=0
Therefore, the slope of the line is 0.
Now use the slope and either of the two points to find the y-intercept.
y=mx+b
5=(0)(7)+b
b=5
Write the equation in slope intercept form as:
y=mx+b
y=(0)x+5
y=5
Hence, the equation of the line is y=5.
The probability on any given night that it's Abe’s responsibility to cook dinner is 24%. If it’s Abe’s responsibility to cook dinner, the probability that his family goes out to a restaurant to eat is 65%. If it is not Abe’s responsibility to cook dinner, the family goes to a restaurant only 15% of the time. Create a tree diagram for this situation: What is the probability that Abe’s family eats out on a night that Abe was not responsible to cook dinner?On any given night, what is the probability Abe’s family eats at a restaurant?Abe’s family did not eat at a restaurant. Determine the probability that Abe was not responsible for cooking?
Answers
Let A be the event that "it's Abe's responsibility to cook dinneron any given night" and B be the event that "family goes out to a restauarnt to eat".
iven that:
[tex]\begin{gathered} P(A)=0.24 \\ P(B|A)=0.65 \\ P(B|A^C)=0.15 \end{gathered}[/tex]Draw the tree diagram.
Use Baye's theorem
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex][tex]\begin{gathered} \text{P(Abe's family eats out on a night and Abe was not responsible to cook) } \\ =P(B\cap A^C) \\ =P(B|A^C)\cdot P(A^C) \\ =0.15(0.76) \\ =0.114 \end{gathered}[/tex][tex]undefined[/tex]Which number sentence can be used to find the difference between five times three and two times six?
x= 5x3-2x6
x = 5x2+3x6
x = 5(3+2x6)
x = 5x3+2x6
Answers
Which number sentence can be used to find the difference between five times three and two times six?
x= 5x3-2x6
x = 5x2+3x6
x = 5(3+2x6)
x = 5x3+2x6
100 Points.
A rectangle has sides measuring (2x + 5) units and (3x + 7) units.
Part A: What is the expression that represents the area of the rectangle? Show your work.
Part B: What are the degrees and classifications of the expression obtained in Part A?
Part C: How does Part A demonstrate the closure property for the multiplication of polynomials?
Answers
The expression that represents the area of the rectangle is [tex]6x^{2}[/tex]+29x + 35 square units , the degree of the obtained expression is 2.
According to the question,
We have the following information:
A rectangle has sides measuring (2x + 5) units and (3x + 7) units.
A) We know that following formula is used to find the area of rectangle:
Area = length*breadth
Area = (3x+7)(2x+5)
Area = [tex]6x^{2}[/tex] + 15x +14x + 35
Area = [tex]6x^{2}[/tex] +29x + 35 square units
B) The degree of an expression is the highest power of the expression. In this case, the highest power is 2. Hence, the degree of the expression obtained is 2.The expression can be classifies as a quadratic polynomial.
C) Part A demonstrates the closure property for the multiplication of polynomials because the expression within the brackets are polynomials and the result obtained is also a polynomial.
Hence, the area of the rectangle is [tex]6x^{2}[/tex] +29x + 35 square units and the degree of the obtained expression is 2.
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Select the quadratic equation that has no real solution.9x2–25x-30 = 09x? – 25x +30 = 09x2-30x +25= 0o 9x2-30x – 25 = 0
Answers
SOLUTION:
We are to select the quadratic equation that has no real solution.
Facts about Quadratic equations;
When considering,
[tex]b^2\text{ - 4ac}[/tex]If you get a positive number, the quadratic will have two unique solutions. If you get 0, the quadratic will have exactly one solution, a double root. If you get a negative number, the quadratic will have no real solutions, just two imaginary ones.
Looking at all the four options, I have examined all and the only one found to be negative is the second option. Let's consider it together
a = 9, b = -25 and c = 30
(b x b ) - 4 x a x c
(-25 x -25) - 4 (9) (30)
625 - 1080
- 455
-455 < 0
Since the discriminant is less than this quadratic equation is expected to have no real solution.
You can as well try the other three options one is zero and the remaining two are greater than zero.
( x+y+z = -1), ( y-3z = 11), ( 2x+y+5z = -12)1. determine whether the system is inconsistent or dependent2. if your answer is dependent, find the complete solution. Write x and y as functions of zx=y=
Answers
Inconsistent
Explanation:a) Given:
x + y + z = -1 . . .(1)
y - 3z = 11 . . . (2)
2x + y + 5z = -12 . . .(3)
To find:
If the solution of the system of equations is either consistent dependent solution or an inconsistent one
We need to solve the system of equations. From equation (2), we will make y the subject of formula:
y = 11 + 3z (2*)
Substitute for y with 11 + 3z in both equation (1) and (2):
For equation 1: x + 11 + 3z + z = -1
x + 11 + 4z = -1
x + 4z = -1-11
x + 4z = -12 . . . (4)
For equation 3: 2x + 11 + 3z + 5z = -12
2x + 11 + 8z = -12
2x + 8z = -12-11
2x + 8z = -23 . . .(5)
We need to solve for x and z in equations (4) and (5)
Using elimination method:
To eliminate a variable, its coefficient needs to be the same in both equations
Let's eliminate x. We will multiply equation (4) by 2:
2x + 8z = -24 . . . (4*)
Now both equations have the same coefficient of x. Subtract equation (4) from (5):
2x - 2x + 8z - 8z = -23 - (-24)
0 + 0 = -23 + 24
0 = 1
Let hand side is not the same as right hand side.
When the left hand side is not equal to right hand side, the solution is said to be inconsistent or no sloution.
Your answer is inconsistent
ABCD is a rectangle. Find the coordinates of P, the midpoint of AC. [B is (18,12) ]
Answers
the coordinates of P is (9, 6)
Explanation:Coordinate of B = (18, 12)
In a rectangle, the opposite parallal sides are equal
AB = DC
AD = BC
We need to find the coordinates of A and C inoder to get P:
Since the x coordinate of B is 18, the x coordinate of C will also be 18
C is on the y axis, this means its y coordinate will be zero
Coordinate of C (x, y) becomes: (18, 0)
The y coordinate of B is 12, the y coordinate of A will also be 12
A is on the y axis. This means the x coordinate of A will be zero
Coordinate of A (x, y becomes): (0, 12)
To get P, we will apply the midpoint formula:
[tex]\text{Midpoint = }\frac{1}{2}(x_1+x_2),\text{ }\frac{1}{2}(y_1+y_2)[/tex]Using the points A (0, 12) and C (18, 0) to get coordinates of P:
[tex]\begin{gathered} x_1=0,y_1=12,x_2=18,y_2\text{ = 0} \\ \text{midpoint = }\frac{1}{2}(0+18),\text{ }\frac{1}{2}(12+0) \\ \text{midpoint = }\frac{1}{2}(18),\text{ }\frac{1}{2}(12) \\ \text{midpoint = (9, 6)} \end{gathered}[/tex]Hence, the coordinates of P is (9, 6)
Juan and María López wish to invest in a no-risk saving account. they currently hace $30,000 in an account bearing 5.25% annual interest, compounded continuously. the following choices are available to them.A. Keep the Money in The account they currently have B. invest the Money in an account earning 5.875% interest compounded annually c. invest the Money in an account earning 5.75% compounded semi annually d. invest Money in an account earning 5.5% annual interést compounded quarterly
Answers
The general formula for the amount in savings account compounded annually is given as;
[tex]\begin{gathered} A=P(1+\frac{r}{100n})^{nt} \\ \text{Where A=Amount} \\ P=\text{Initial deposit} \\ r=\text{rate} \\ n=n\text{ umber of times it is compounded annually} \\ t=\text{time} \end{gathered}[/tex]A. The equation for the value of the investment as a function of t in the current account they have is;
[tex]A(t)=\text{ \$30000(1+}\frac{5.25}{100})^t[/tex]B. The equation for the value of the investment in an account earning 5.875% interest compounded annually is;
[tex]A(t)=\text{ \$30000(1+}\frac{5.875}{100})^{t^{}}[/tex]C. The equation for the value of the investment in an account earning 5.75% compounded semi-annually; that is twice in a year is;
[tex]\begin{gathered} A(t)=\text{ \$30000(1+}\frac{5.75}{100(2)})^{2t} \\ A(t)=\text{ \$30000(1+}\frac{5.75}{200})^{2t} \end{gathered}[/tex]D. The solution for the value of the investment in an account earning 5.5% annual interest compounded quarterly; that is four times in a year;
[tex]\begin{gathered} A(t)=\text{ \$30000(1+}\frac{5.5}{100(4)})^{4t} \\ A(t)=\text{ \$30000(1+}\frac{5.5}{400})^{4t} \end{gathered}[/tex]Use the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. Hint solve this problem using P and Q's and synthetic division f(x) = x^3 + 2x^2 - 5x - 6A -3, -1, 2; f(x) = (x + 3)(x + 1)(x - 2)B-1; f(x) = (x + 1)(x2 + x - 6)C-3; f(x) = (x + 3)(x2 - x - 2)D-2, 1, 3; f(x) = (x + 2)(x - 1)(x - 3)
Answers
Since all coefficients are integers, we can apply the rational zeros theorem.
The trailing coefficient is -6 with the following factors (possible values for p):
[tex]p\colon\pm1,\pm2,\pm3,\pm6[/tex]The leading coefficient is 1, with factors:
[tex]q=\pm1[/tex]Therefore, all the possible values of p/q are:
[tex]\frac{p}{q}\colon\pm\frac{1}{1},\pm\frac{2}{1},\pm\frac{3}{1},\pm\frac{6}{1}[/tex]Simplifying, the possible rational roots are:
[tex]\pm1,\pm2,\pm3,\pm6[/tex]Next, we have to check if they are roots of the polynomials by synthetic division, in which the remainder should be equal to 0.
0. Dividing ,f (x), by ,x−1,. Remainder = ,-8, ,+1, is ,NOT ,a root.
,1. Dividing ,f (x), by x+,1,. Remainder = 0, ,-1, ,IS ,a root.
,2. Dividing ,f (x), by x-2. Remainder = 0, ,+2, ,IS ,a root.
,3. Dividing ,f (x), by ,x+2,. Remainder = ,4, ,-2, is ,NOT ,a root.
,4. Dividing ,f (x), by ,x−3,. Remainder = 24,, ,+3, is ,NOT ,a root.
,5. Dividing ,f (x), by ,x+3,. Remainder = 0,, ,-3, IS ,a root.
,6. Dividing ,f (x), by ,x−6,. Remainder = 252,, ,+6, is ,NOT ,a root.
,7. Dividing ,f (x), by ,x+6,. Remainder = -120,, ,-6, is ,NOT ,a root.
Actual rational roots: A. -3, -1, 2; f(x) = (x + 3)(x + 1)(x - 2)
(a) The perimeter of a rectangular garden is 312 m.If the length of the garden is 89 m, what is its width?Width of the garden: ]וח(b) The area of a rectangular window is 6205 cm?If the width of the window is 73 cm, what is its length?Length of the window: 7 cm
Answers
EXPLANATION
Let's see the facts:
Perimeter = P = 312 m
Length = l = 89m
Width = w = unknown
The perimeter of a rectangle is given by the following relationship:
[tex]P=2(w+l)[/tex]Replacing terms:
[tex]312=2(w+89)_{}[/tex]Applying the distributive property:
[tex]312=2w\text{ + 178}[/tex]Subtracting 178 to both sides:
[tex]312-178=2w[/tex][tex]134=2w[/tex]Dividing 2 to both sides:
[tex]\frac{134}{2}=w[/tex]Simplifying:
[tex]67=w[/tex]Switching sides:
[tex]w=67[/tex]The width of the garden is 67 meters.
A grocery store sales for $522,000 and a 25% down payment is made a 20 year mortgage at 7% is obtain compute and amortization schedule for the first three months round your answer to two Decimal place if necessary
Answers
The value of the mortgage (the real amount to be financed) is A = $391,500.
The annual interest rate is r = 7%. We must convert it to montly decimal rate:
r = 7 / 12 / 100 = 0.005833
Note: The decimals will be kept in our calculator. Only two decimal places will be shown in the results.
The monthly payment is R = $3,034.13 which includes interest and principal.
For the first month, the loan has not been paid upon, so the interest for this period is:
I = $391,500 * 0.005833 = $2,283.75
From the monthly payment, the portion that goes to pay the principal is:
$3,034.13 - $2,283.75 = $750.38
So the new balance of the loan is:
$391,500 - $750.38 = $390,749.62
Thus, for payment 1:
Interest - Payment on Principal - Balance of Loan
$2,283.75 - $750.38 - $390,749.62
Repeating the calcuations for the second payment:
The interest for this period is:
I = $390,749.62 * 0.005833 = $2,279.37
From the monthly payment, the portion that goes to pay the principal is:
$3,034.13 - $2,279.37 = $754.76
So the new balance of the loan is:
$390,749.62 - $754.76 = 389,994.86
The table is updated as follows:
Interest - Payment on Principal - Balance of Loan
$2,283.75 - $750.38 - $390,749.62
$2,279.37 - $754.76 - $389,994.86
For the third month:
The interest for this period is:
I = $389,994.86 * 0.005833 = $2,274.97
From the monthly payment, the portion that goes to pay the principal is:
$3,034.13 - $2,274.97 = $759.16
So the new balance of the loan is:
$389,994.86 - $759.16 = $389,235.70
The final updated table is:
Interest - Payment on Principal - Balance of Loan
$2,283.75 - $750.38 - $390,749.62
$2,279.37 - $754.76 - $389,994.86
$2,274.97 - $759.16 - $389,235.70
12"retest: CirclesOASelect the correct answerArc XY located on circle A has a length of 40 centimeters. The radius of the circle is 10 centimeters. What is the measure of the correspondingcentral angle for XY in radians?O B.OC.OD. 34TResetSubmit TestNextReader Tools
Answers
step 1
Find out the circumference
[tex]C=2\pi r[/tex]where
r=10 cm
substitute
[tex]\begin{gathered} C=2\pi(10) \\ C=20\pi\text{ cm} \end{gathered}[/tex]Remember that
The circumference subtends a central angle of 2pi radians
so
Applying proportion
Find out the central angle by an arc length of 40 cm
[tex]\begin{gathered} \frac{2\pi}{20\pi}=\frac{x}{40} \\ \\ x=4\text{ rad} \end{gathered}[/tex]therefore
The answer is 4 radians Option B37. The average height of American adult males is 177 cm, with a standard deviation of 7.4 cm. Meanwhile, the average height of Indian males is 165 cm, with a standard deviation of 6.7 cm. Which is taller relative to his nationality, a 173-cm American man or a 150-cm Indian man? The American man The Indian man
Answers
ANSWER
The American man
EXPLANATION
To find the man that is taller relative to his nationality, we have to find the z-score of both men. The z-score represents how far away from the mean that a data value is.
To find the z-score, apply the formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where x = data value; μ = mean; σ = standard deviation
For the American man, the z-score is:
[tex]\begin{gathered} z=\frac{173-177}{7.4} \\ z=\frac{-4}{7.4} \\ z=-0.541 \end{gathered}[/tex]For the Indian man, the z-score is:
[tex]\begin{gathered} z=\frac{150-165}{6.7} \\ z=\frac{-15}{6.7} \\ z=-2.239 \end{gathered}[/tex]We see that the American man has a height with a z-score higher than that of the Indian man.
This means that the American man is taller than the Indian man relative to their nationalities.
