From least to greatest. -1.4-1.02 -1.20
Answers
We could put these values in the number line:
Therefore, the order of the numbers from least to greatest is:
-1.4 , -1.20 , -1.02
The least number between all the options given is -1.4 because if you see, all numbers are negative, so, when a negative number is greater, as the amount after the negative sign becomes greater, the number is going to be least. That's the reason of the order.
Related Questions
Given: Circle PB52°РMAD =mBD =mBAC =:: 52°.: 90°:: 128°:: 142°.: 232°:: 308°
Answers
From the circle given, it can be observed that AC is the diameter of the circle and it divides the circle into two equal parts. The total angle in a semi-circle is 180°. It then follows that
[tex]arcAD+arcDC=arcAC[/tex][tex]\begin{gathered} \text{note that} \\ arcAC=180^0(\text{angle of a semicircle)} \\ arcDC=90^0(\text{given)} \end{gathered}[/tex][tex]\begin{gathered} \text{Therefore,} \\ arcAD+arcDC=arcAC \\ arcAD+90^0=180^0 \\ arcAD=180^0-90^0 \\ arcAD=90^0 \end{gathered}[/tex][tex]\begin{gathered} \text{From the circle, it can be seen that:} \\ arcBD=arcBA+arcAD \\ \text{note that } \\ arcBA=52^0(\text{given)} \\ arcAD=90^0(\text{calculated earlier)} \end{gathered}[/tex][tex]\begin{gathered} \text{Therefore,} \\ arcBD=52^0+90^0 \\ arcBD=142^0 \end{gathered}[/tex][tex]\begin{gathered} \text{From the given circle, it can be seen that} \\ arcBA+arcAD+arcDC=arc\text{BAC} \end{gathered}[/tex][tex]\begin{gathered} \text{Therefore,} \\ 52^0+90^0+90^0=\text{arcBAC} \\ 232^0=\text{arcBAC} \end{gathered}[/tex]Hence, arcAD = 90°, arc BD = 142°, and arc BAC = 232°
The graphs depict IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler IQ test).
a.find the Z score. Write that answer to the 2nd decimal place.
b. solve for x
Answers
The required Z-score with a value of 120 would be 1.33.
What is Z -score?A Z-score is defined as the fractional representation of data point to the mean using standard deviations.
The given graph depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
As per the given information, the solution would be as
ц = 100
σ = 15
X = 120 (consider the value)
⇒ z-score = (X - ц )/σ₁
Substitute the values,
⇒ z-score = (120 - 100)/15
⇒ z-score = (20)/15
⇒ z-score = 1.33
Thus, the required Z-score with a value of 120 would be 1.33.
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if f(x)=-2x-3, find f(-1)
Answers
Solve;
[tex]\begin{gathered} f(x)=-2x-3 \\ f(-1)=-2(-1)-3 \\ f(-1)=2-3 \\ f(-1)=-1 \end{gathered}[/tex]The answer is -1
That is f(-1) = -1
Solve.(3.3 × 10³) (2 × 10²)
Answers
Here are the steps in multiplying scientific notations:
1. Multiply the coefficients first.
[tex]3.3\times2=6.6[/tex]2. Multiply the base 10 by adding their exponents.
[tex]10^3\times10^2=10^{3+2}=10^5[/tex]3. Connect the result in steps 1 and 2 by the symbol for multiplication.
[tex]6.6\times10^5[/tex]Hence, the result is 6.6 x 10⁵.
Write an addition equation and a subtraction equation
to represent the problem using? for the unknown.
Then solve.
There are 30 actors in a school play. There are
10 actors from second grade. The rest are from third
grade. How many actors are from third grade?
a. Equations:
b. Solve
Answers
The Equation is 10 + x= 30 and 20 actors are from third grade.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
There are 30 actors in a school play.
There are 10 actors from second grade.
The rest are from third grade.
let the actors in third grade is x.
Equation is:
Actors from second grade + Actors from third grade = Total actors
10 + x= 30
Now, solving
Subtract 10 from both side
10 +x - 10 = 30 - 10
x = 20
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I need help with this question please. Just do question 1 please. Also this is just apart of a homework practice
Answers
Answer:
P(x) = 1.3x² + 0.1x + 2.8
Explanation:
We need to find an equation that satisfies the relationship shown in the table. So, let's replace x by 2 and then compare whether the value of p(x) is 8.2 or not
P(x) = 1.3x³ + 0.1x² + 2.8x
P(2) = 1.3(2)³ + 0.1(2)² + 2.8(2)
P(2) = 16.4
Since P(2) is 16.4 instead of 8.2, this is not a correct option
P(x) = 1.3x² + 0.2x - 2.8
P(2) = 1.3(2)² + 0.2(2) - 2.8
P(2) = 2.8
Since 2.8 and 8.2 are distinct, this is not the correct option
P(x) = 2.3x² + 0.2x + 1.8
P(x) = 2.3(2)² + 0.2(2) + 1.8
P(x) = 11.4
Since 11.4 and 8.2 are distinct, this is not the correct option
P(x) = 1.3x² + 0.1x + 2.8
P(2) = 1.3(2)² + 0.1(2) + 2.8
P(2) = 8.2
Therefore, this is the polynomial function for the data in the table.
So, the answer is P(x) = 1.3x² + 0.1x + 2.8
When drawing a trendline, which statement is true?
A. All datasets have a trendline
B. All trendlines begin at the origin.
C. Trendlines can have a positive or negative association.
D. Trendlines have only positive associations.
Answers
Trendlines have only positive associations. Option D is correct.
Given that,
When drawing a trendline, which statement is true is to be determined.
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Here,
Trendlines are the line that explains the drastic positive change in the graph,
So Trendline has only a positive association according to the statement mentioned above.
Thus, trendlines have only positive associations. Option D is correct.
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Which comparison is NOT correct?2 > -3-7 < -5-9 < 10 < -4
Answers
0 > -4 is incorrect
as -4 is a negative number and it comes on the left of 0 on a number line
and we know number increase from left to right
so option D is the answer.
Kaitlin's family is planning a trip from WashingtonD.C., to New York City New York City is 227 miles from Washington, D.C.and the family can drive an average of 55mi / h . About how long will the trip take?
Answers
Kaitlin's family's trip from Washington D.C., to New York City of 227 miles at average rate of 55 miles per hour is 4 hours 8 minutes
How to determine the how long the trip will takeinformation gotten from the question include
Washington D.C., to New York City is 227 miles
Kaitlin's family can drive an average of 55mi / h
Average speed is a function of ratio distance covered with time. this is represented mathematically as
average speed = distance covered / time
55 miles / h = 227 miles / time
time = 227 / 55
time = 4.127 hours
The trip take 4.127 hours
0.127 * 60 = 7.62 ≅ 8 minutes
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A certain species of deer is to be introduced into a forest, and wildlife experts estimate the population will grow to P(t) = (944)3 t/3, where t represents the number ofyears from the time of introduction.What is the tripling-time for this population of deer?
Answers
Ok, so
Here we have the function:
[tex]P(t)=944(3)^{\frac{t}{3}}[/tex]Now we want to find the tripling-time for this population of deer.
If we make t=0, we will find the initial population of deer. This is:
[tex]P(0)=944(3)^{\frac{0}{3}}=944[/tex]Now, we want to find the time "t" such that this population is the triple.
This is:
[tex]\begin{gathered} 944(3)=944(3)^{\frac{t}{3}} \\ 2832=944(3)^{\frac{t}{3}} \\ \frac{2832}{944}=3^{\frac{t}{3}} \\ 3=3^{\frac{t}{3}} \end{gathered}[/tex]We got this exponential equation:
[tex]3=3^{\frac{t}{3}}[/tex]As the base is the same, we could equal the exponents:
[tex]\begin{gathered} 1=\frac{t}{3} \\ t=3 \end{gathered}[/tex]Therefore, tripling-time for this population of deer are 3 years.
provide evidence that this function is not one to one. explain how your evidence supports that g(x) is not one to one
Answers
we have the function
g(x)=(x/3)+2 ---------> interval (-infinite, 1)
g(x)=4x-2 ------> interval [1, infinite)
the given function is not one-to -one function, because don't pass the Horizontal Line Test.
Example
For the horizontal line
y=2
we have the values of
x=0 ---------> g(x)=(x/3)+2
and
x=1 -----------> g(x)=4x-2
that means
two elements in the domain of g(x) correspond to the same element in the range of g(x)
therefore
the function is not one to onelet f(x)=8x+5 and g(x)=9x-2. find the function.f - g(f - g) (x) =find the domain.
Answers
Answer:
(f - g)( x ) = -x + 7
Domain;
[tex](-\infty,\infty)[/tex]Explanation:
Given the below functions;
[tex]\begin{gathered} f(x)=8x+5 \\ g(x)=9x-2 \end{gathered}[/tex]To find (f - g)( x ), all we need to do is subtract g(x) from f(x) as shown below;
[tex]\begin{gathered} (f-g)\mleft(x\mright)=(8x+5)-(9x-2) \\ =8x+5-9x+2 \\ =8x-9x+5+2 \\ =-x+7 \end{gathered}[/tex]The domain of the function will be all values from negative infinity to positive infinty, written as;
[tex](-\infty,\infty)[/tex]What are all of the answers for these questions? Use 3 for pi. Please do not use a file to answer, I cannot read it.
Answers
The company's sign has two(2) congruent trapezoids and two(2) congruent right angled triangle.
The area of the figure is:
[tex]A_{\text{figure}}=2A_{\text{trapezoid}}+2A_{\text{triangle}}[/tex]The area of a trapezoid is given by the formula:
[tex]\begin{gathered} A_{\text{trapezoid}}=\frac{1}{2}(a+b)h \\ \text{where a and b are opposite sides of the trapezoid} \\ h\text{ is the height} \end{gathered}[/tex]Thus, we have:
[tex]\begin{gathered} A_{\text{trapezoid}}=\frac{1}{2}(1\frac{1}{2}+3)2 \\ A_{\text{trapezoid}}=\frac{1}{2}(1.5+3)2 \\ A_{\text{trapezoid}}=\frac{1}{2}\times4.5\times2=4.5m^2 \end{gathered}[/tex]Area of a triangle is given by the formula:
[tex]A_{\text{triangle}}=\frac{1}{2}\times base\times height[/tex]Thus, we have:
[tex]\begin{gathered} A_{\text{triangle}}=\frac{1}{2}\times2\times1\frac{1}{2} \\ A_{\text{triangle}}=\frac{1}{2}\times2\times1.5=1.5m^2 \end{gathered}[/tex]Hence, the area of the company's sign is:
[tex]\begin{gathered} A=(2\times4.5)+(2\times1.5) \\ A=9+3=12m^2 \end{gathered}[/tex]Find all values for which at least one denominator is equal to 0.
Answers
Given:
There are given the expression:
[tex]\frac{4}{x+2}-\frac{5}{x}=1[/tex]Explanation:
To find the value of x that is equal to 0, we need to perform LCM in the denominator and then find the value for x:
Then,
From the given expression:
[tex]\begin{gathered} \frac{4}{x+2}-\frac{5}{x}=1 \\ \frac{4x-5(x+2)}{x(x+2)}=1 \end{gathered}[/tex]Then,
According to the question, the values at least one denominator is equal to .
So,
[tex]\begin{gathered} x(x+2)=0 \\ x=0 \\ x+2=0 \\ x=-2 \end{gathered}[/tex]Final answer:
Hence, the value of x is shown below:
[tex]x\ne0,-2[/tex]
The slope and one point on the line are given. Find the equation of the line (in slope-intercept form).(1/4, -4) ; m = -3 y=
Answers
Answer
y = -3x - 13/4
Step-by-step explanation
Equation of a line in slope-intercept form
[tex]y=mx+b[/tex]where m is the slope and (0, b) is the y-intercept.
Substituting into the general equation with m = -3 and the point (1/4, -4), that is, x = 1/4 and y = -4, and solving for b:
[tex]\begin{gathered} -4=(-3)\cdot\frac{1}{4}+b \\ -4=-\frac{3}{4}+b \\ -4+\frac{3}{4}=-\frac{3}{4}+b+\frac{3}{4} \\ -\frac{13}{4}=b \end{gathered}[/tex]Substituting into the general equation with m = -3 and b = -13/4, we get:
[tex]\begin{gathered} y=(-3)x+(-\frac{13}{4}) \\ y=-3x-\frac{13}{4} \end{gathered}[/tex]A popcorn stand offers buttered or unbuttered popcorn in three sizes: small, medium, and large. What is the P(buttered)
Answers
The popcorn we can order is either buttered or unbuttered.
Therefore, the probability of choosing buttered popcorn is 1/2
This probability distribution shows thetypical grade distribution for a Geometrycourse with 35 students.GradeEnter a decimal rounded to the nearest hundredth.Enter
Answers
Explanation:
The total number of students is
[tex]n(S)=35[/tex]Concept:
To figure out the probability that a student earns grade A,B or C
Will be calculated below as
[tex]P(A,BorC)=P(A)+P(B)+P(C)[/tex]The Probability of A is
[tex]P(A)=\frac{n(A)}{n(S)}=\frac{5}{35}[/tex]The probabaility of B is
[tex]P(B)=\frac{n(B)}{n(S)}=\frac{10}{35}[/tex]The probabaility of C is
[tex]P(B)=\frac{n(B)}{n(S)}=\frac{15}{35}[/tex]Hence,
By substituting the values in the concept, we will have
[tex]\begin{gathered} P(A,BorC)=P(A)+P(B)+P(C) \\ P(A,BorC)=\frac{5}{35}+\frac{10}{35}+\frac{15}{35}=\frac{30}{35} \\ P(A,BorC)=0.857 \\ P(A,BorC)\approx0.86(nearest\text{ }hundredth) \end{gathered}[/tex]Hence,
The final answer is
[tex]0.86[/tex]O EQUATIONS AND INEQUALITIESSolving a word problem with three unknowns using a linear...
Answers
Given:
The sum of three numbers is 81, The third number is 2 times the second, The first number us 9 moe than the second.
Required:
We need to find all the numbers
Explanation:
Assume that a, b and c are the first, second and third numbers respectively.
By given ststement
[tex]\begin{gathered} a+b+c=81\text{ .....\lparen i\rparen} \\ c=2b\text{ .....\lparen ii\rparen} \\ a=b+9\text{ .....\lparen iii\rparen} \end{gathered}[/tex]substitute c and a in equation (i)
[tex]\begin{gathered} b+9+b+2b=81 \\ 4b=72 \\ b=18 \end{gathered}[/tex]now put value of b in equation (ii) and (iii)
[tex]c=2*18=36[/tex]and
[tex]a=18+9=27[/tex]FInal answer:
first number a = 27
second number b = 18
third number c = 36
One group (A) contains 155 people. One-fifth of the people in group A will be selected to win $20 fuel cards. There is another group (B) in a nearby town that will receivethe same number of fuel cards, but there are 686 people in that group. What will be the ratio of nonwinners in group A to nonwinners in group B after the selections aremade? Express your ratio as a fraction or with a colon.
Answers
According to the information given in the exercise:
- Group A contains a total of 155 people.
- One-fifth of that people will be selected to win $20 fuel cards.
- The total number of people in Group B is 686.
Then, you can determine that the number of people that will be selected to win $20 fuel cards is:
[tex]winners_A=\frac{1}{5}(155)=31[/tex]Therefore, the number of nonwinners in Group A is:
[tex]N.winners_A=155-31=124[/tex]You know that Group B will receive the same number of fuel cards. Therefore, its number of nonwinners is:
[tex]N.winners_B=686-31=655[/tex]Knowing all this information, you can set up the following ratio of nonwinners in Group A to nonwinners in Group B after the selections are made:
[tex]\frac{124}{655}[/tex]Hence, the answer is:
[tex]\frac{124}{655}[/tex]5. What is the area of triangle ABC? (lesson 10.2)AN10 ftD 6 ftСA 15 square feetB 16 square feet© 30 square feetD 32 square feet
Answers
The answer is C, 30 square feet
A typical soda can has a diameter of 5.3 centimeters and height of 12 centimeters. How many square centimeters of aluminum is needed to make the can? My answer is 244. I am confused how I got the answer.
Answers
The can is made up of aluminium.
So the area of the can must be equal to the area of the Aluminium sheet.
The can is in the form of a cylinder with diameter (d) 5.3 cm, and height (h) 12 cm.
Then its area is calculated as,
[tex]\begin{gathered} A=\pi d(\frac{d}{2}+h) \\ A=\pi(5.3)(\frac{5.3}{2}+12) \\ A=243.9289 \\ A\approx244 \end{gathered}[/tex]Thus, the area of the Aluminium sheet required is 244 square centimeters.
1.23 × 10 to the 5th power
=
Answers
Answer:
1.23 x 10 to the 5th power is 123,000.
Step-by-step explanation:
math.
Rewrite the equation to easily determine the velocity of an object. solve the Equation for v
Answers
In order to solve for v in the given equation, follow these steps:
1. Divide both sides of the equation by "m"
[tex]\begin{gathered} E=\frac{1}{2}mv^2 \\ \frac{E}{m}=\frac{1}{2}\frac{mv^2}{m} \\ \frac{E}{m}=\frac{1}{2}\frac{m}{m}v^2 \\ \frac{E}{m}=\frac{1}{2}v^2 \end{gathered}[/tex]2. Multiply both sides by 2
[tex]\begin{gathered} \frac{E}{m}\times2=\frac{1}{2}v^2\times2 \\ 2\frac{E}{m}=\frac{2}{2}v^2 \\ 2\frac{E}{m}=v^2 \end{gathered}[/tex]3. in order to get rid of the exponent of v, take the square root on both sides
[tex]\begin{gathered} \sqrt{2\frac{E}{m}}=\sqrt{v^2} \\ \sqrt[]{2\frac{E}{m}}=v \\ v=\sqrt[]{2\frac{E}{m}} \end{gathered}[/tex]Then, v = √(2E/m)
In the diagram below, if < ACD = 54 °, find the measure of < ABD
Answers
Opposite angles in a quadrilateral inscribed in a circle add up to 180, therefore:
[tex]\begin{gathered} m\angle ACD+m\angle ABD=180 \\ 54+m\angle ABD=180 \\ m\angle ABD=180-54 \\ m\angle ABD=126^{\circ} \end{gathered}[/tex]Answer:
b. 126
The instructions are: Write,evaluate,graph on a Number Line the following inequalities:Six increased by twice a number is no more than 20.
Answers
• Given the description "Six increased by twice a number is no more than 20", you need to know the following:
- In this case, the word "increased" indicates an Addition.
- The word "twice" indicates a Multiplication by 2.
- "No more than" indicates that six increased by twice a number must be less than or equal to 20.
- The inequality symbol whose meaning is "Less than or equal to" is:
[tex]\leq[/tex]Knowing the information shown before, you can write the following expression to represent "Six increased by twice a number" (Let be "x" the unknown number):
[tex]6+2x[/tex]Therefore, you can write the following inequality that models the description given in the exercise:
[tex]6+2x\leq20[/tex]• Now you need to solve it:
1. Apply the Subtraction Property of Inequality by subtracting 6 from both sides of the inequality:
[tex]\begin{gathered} 6+2x-(6)\leq20-(6) \\ \\ 2x\leq14 \end{gathered}[/tex]2. Apply the Division Property of Inequality by dividing both sides of the inequality by 2:
[tex]\begin{gathered} \frac{2x}{2}\leq\frac{14}{2} \\ \\ x\leq7 \end{gathered}[/tex]• In order to graph the solution on a Number Line, you can follow these steps:
- Since the inequality symbol indicates that "x" is less than 7, it indicates that 7 is included in the solution. Therefore, you must draw a closed circle over that value.
- Draw a line from the circle to the left.
Then, you get:
Hence, the answer is:
- Inequality:
[tex]6+2x\leq20[/tex]- Solution:
[tex]x\leq7[/tex]- Number Line:
Kindly help by providing answers to these questions.
Answers
Graph of proportional relationship is given y =kx , answer of the following questions are as follow:
1. Based on the information ,the constant of proportionality represents the multiplicative relationship between two quantities.
2. Variable represents the constant of proportionality is k.
As given in the question,
Graph represents proportional relationship is given by:
y = kx
⇒ k = y/x
Represents the multiplicative relationship between the variables y and x.
1. Based on the information , the constant of proportionality represents the multiplicative relationship between two quantities.
'k' is the scale factor represents the constant of proportionality.
2. Variable represents the constant of proportionality is k.
Therefore, graph of proportional relationship is given y =kx , answer of the following questions are as follow:
1. Based on the information , the constant of proportionality represents the multiplicative relationship between two quantities.
2. Variable represents the constant of proportionality is k.
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The maintenance department at the main campus of a large state university receives daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 37 and a standard deviation of 10. iS Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 37 and 67?
Answers
Answer: 49.85%
Explanation:
From the information given,
mean = 37
standard deviation = 10
The 68-95-99.7 rule states that 68% of the data fall within 1 standard deviation of the mean. 95% of the data fall within 2 standard deviations of the mean and 99.7% of the data fall within 3 standard deviations of the mean. Thus,
1 standard deviation to the left of the mean = 37 - 10 = 27
1 standard deviation to the right of the mean = 37 + 10 = 47
3 standard deviation to the left of the mean = 37 - 3(10) = 37 - 30 = 7
3 standard deviations to the right of the mean = 37 + 3(10) = 37 + 30 = 67
We can see that the percentage of lightbulb replacement requests numbering between 37 and 67 falls within 3 standard deviations to the right of the mean. This is just half of the area covered by 99.7%. Thus
The percentage of lightbulb replacement requests numbering between 37 and 67
= 99.7/2 = 49.85%
Show your work Round to the nearest whole number if needed
Answers
Given:
Radius, r = 6
Let's find the chance of hitting the shaded area by finding the ratio.
Since the radius of the cirlce is 6, the length of one side of the square is the diameter:
s = 6 x 2 = 12
To find the ratio divide the area of the circle by area of the square. The area of the circle is the shaded area while the area of the square is the total possible area.
Thus,we have:
[tex]\text{ Area of circle = }\pi r^2=3.1416\ast6^2=3.1416\ast36=113.0976\text{ square units}[/tex][tex]\text{ Area of square = }s^2=12^2=12\ast12=144\text{ square units}[/tex][tex]\text{ Ratio=}\frac{shaded\text{ area}}{total\text{ possible area}}=\frac{area\text{ of circle}}{area\text{ of square}}=\frac{113.0976}{144}=0.7854\approx0.79[/tex][tex]\text{ Percentage ratio = 0.7854 }\ast\text{ 100=}78.54\text{ \%}[/tex]Therefore, the chance of hitting the shaded region is 78.54%
ANSWER:
78.54%
Consider the following loan. Complete parts (a)-(c) below.An individual borrowed $67,000 at an APR of 3%, which will be paid off with monthly payments of 347$ for 22 years.a. Identify the amount borrowed, the annual interest rate, the number of payments per year, the loan term, and the payment amount.The amount borrowed is $____ the annual interest rate is ____, the number of payments per year is _____, the loan term is _____ years, and the payment amount is _____$ b. How many total payments does the loan require? What is the total amount paid over the full term of the loan?There are ____ payments toward the loan and the total amount paid is ____$ c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest?The percentage paid toward the principal is _____% and the percentage paid for interest is ____%.(Round to the nearest tenth as needed.)
Answers
b) There are 12 payments per year for 22 years; multiply 12 by 22 to get the total number of payments:
[tex]12\times22=264[/tex]To find the total amount paid, multiply the number of payments by the payment amount:
[tex]264\times347=91,608[/tex]There are 264 payments toward the loan and the total amount paid is $91,608c) Toward principal: $67,000
Toward interest: subtract the principal from the payment amount:
[tex]91,608-67,000=24,608[/tex]Let 91,608 be the 100%, use a rule of three to find the % corresponding to the principal and interest:
[tex]\begin{gathered} Principal: \\ x=\frac{67,000\times100}{91,608}=73.1 \\ \\ Interest: \\ x=\frac{24,608\times100}{91,608}=26.9 \end{gathered}[/tex]The percentage paid toward the principal is 73.1% and the percentage paid for interest is 26.9%Use the method of equating coefficients to find the values of a, b, and c: (x + 4) (ar²+bx+c) = 2x³ + 9x² + 3x - 4.A. a = -2; b= 1; c= -1OB. a=2; b= 1; c= 1OC. a=2; b= -1; c= -1OD. a=2; b= 1; c= -1
Answers
To find the coefficients we first need to make the multipliation on the left expression:
[tex]\begin{gathered} (x+4)(ax^2+bx+c)=ax^3+bx^2+cx+4ax^2+4bx+4c \\ =ax^3+(4a+b)x^2+(4b+c)x+4c \end{gathered}[/tex]Then we have:
[tex]ax^3+(4a+b)x^2+(4b+c)x+4c=2x^3+9x^2+3x-4[/tex]Two polynomials are equal if and only if their coefficients are equal, this leads to the following equations:
[tex]\begin{gathered} a=2 \\ 4a+b=9 \\ 4b+c=3 \\ 4c=-4 \end{gathered}[/tex]From the first one it is clear that the value of a is 2, from the last one we have:
[tex]\begin{gathered} 4c=-4 \\ c=-\frac{4}{4} \\ c=-1 \end{gathered}[/tex]Plugging the value of a in the second one we have:
[tex]\begin{gathered} 4(2)+b=9 \\ 8+b=9 \\ b=9-8 \\ b=1 \end{gathered}[/tex]Therefore, we conclude that a=2, b=1 and c=-1 and the correct choice is D.