ANSWER:
C)
[tex]35+0.12x=44.36[/tex]STEP-BY-STEP EXPLANATION:
With the help of the statement, we can conclude that the equation is the following because the value of 0.12 must go together with the x, and that the total value must be 44.36
[tex]\begin{gathered} 35+0.12x=44.36 \\ \text{where x is the number of miles the familly drove} \end{gathered}[/tex]Ahmed takes out a loan charging 6.7% simple interest for 10 years.
At the end of 10 years Ahmed pays back $1278 in just interest. Round your answer
to the nearest penny. The original amount of the loan (principal) was
A/
Round your answer to the nearest penny..
Answer:
$1907.46
Step-by-step explanation:
You want the principal amount of a 10-year loan that earns $1278 in simple interest at the annual rate of 6.7%.
Simple InterestThe interest is given by the formula ...
I = Prt
Solving for P gives ...
P = I/(rt)
P = $1278/(0.067·10) ≈ $1907.46
The amount of the loan was $1907.46.
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Which ratio of cups of banana to cups of apple juice is also equivalent to ¼:⅓?• 4/4 : 3/3• 3/3 : 3/4• 3/4 : 4/3• 3/4 : 3/3
ANSWER
3/4 : 3/3
EXPLANATION
We have the ratio of cups of banana to cups of apple juice to be 1/4 : 1/3
Equivalent ratios can be gotten by multiplying the ratio with a common integer.
This means we can multiply bot sides of the ratio with the same integer e.g. 2, 4, 7...
Since from the diagram, the next equivalent ratio is given (2/4 : 2/3), we can obtain the next equivalent ratio by multiplying the ratio by 3. That is:
3/4 : 3/3
Therefore, the correct option is 3/4 : 3/3
PLEASE HELP!!!!! I really really really really really need help with this math problem can someome help me please its has to be done in 20 mins!!!!!!!! PLEASE HELP!!!
A) To do that we will draw a line inside the triangle that is perpendicular to the base as I have don above.
B) We will also do the same for B
Find the slope of each line and then determine if the lines are parallel, perpendicular or neither. If a value is not an integer type it as a decimal rounded to the nearest hundredth.Line 1: passes through (-8,-55) and (10,89) the slope of this line is Answer.Line 2: passes through (9,-44) and (4,-14) the slope of this line is Answer.The lines are Answer
For line 1 =
The coordinates given are (-8,-55) , (10,89)
The slope of the line is
[tex]m=\frac{89+55}{10+8}=\frac{144}{18}=8[/tex]For line 2 =
The coordinates given are (9,-44) , (4,-14)
The slope of the line is
[tex]m=\frac{-14+44}{4-9}=\frac{30}{-5}=-6[/tex]
The lines are not perpendicular or parallel because the slope of the lines does not satisfy the condition of perpendicular or parallel slopes.
Hence the answer is neither.
a) How many hand-held color televisions can be sold at $ 400 per television?b) How many televisions will be sold when supply and demand are equal?c) Find the price at which supply and demand are equal.
a) Since we are interested in the number of TVs that can be sold at $400, we need to use the Demand model equation and set p=400; thus,
[tex]\begin{gathered} p=400 \\ \Rightarrow N=-7\cdot400+2820=20 \\ \Rightarrow N=20 \end{gathered}[/tex]The answer to part a) is 20 TVs per week.
b) Set N=N, then
[tex]\begin{gathered} N=N \\ \Rightarrow-7p+2820=2.4p \\ \Rightarrow9.4p=2820 \\ \Rightarrow p=\frac{2820}{9.4}=300 \\ \Rightarrow p=300 \end{gathered}[/tex]Therefore, using p=300 and solving for N,
[tex]\begin{gathered} \Rightarrow N=2.4\cdot300=720 \\ \Rightarrow N=720 \end{gathered}[/tex]The answer to part b) is 720 TVs per week.
c) In part b), we found that when supply and demand are equal, p=300. Thus, the answer to part c) is $300
9 x+3=9 3x=9 3+x=9 x=9-3 x=9=3 < those are the answers
Based on the diagram of the figure, the equation is:
x + 3 = 9
how do I solve them to know what is the correct answer
For:
[tex]8x^3+16x^2[/tex]Factor 8x² out of the expression:
[tex]8x^2(x+2)[/tex]-------------------------------------------------------------------
For:
[tex]\begin{gathered} 2x^2-x+8x-4 \\ \end{gathered}[/tex]Add like terms:
[tex]2x^2+7x-4[/tex]The coefficient of x² is 2 and the constant term is -4. The product of 2 and -4 is -8. The factors of -8 which sum to 7 are -1 and 8, thus:
[tex]\begin{gathered} 2x^2+7x-4=4(2x-1)+x(2x-1) \\ so\colon \\ 4(2x-1)+x(2x-1)=(2x-1)(x+4) \end{gathered}[/tex]Show that if the diagonals of a quadrilateral bisect each other at right angles then it is a rhombus.
To Show that if the diagonals of a quadrilateral bisect each other at right angles then it is a rhombus.
Proof:
Let ABCD be a quadrilateral such that the diagonals bisect each other,
Therefore,
[tex]\begin{gathered} OA=OC\ldots(1) \\ OB=OD\ldots(2) \end{gathered}[/tex]the diagonal bisect at right angle.
Hence,
[tex]\begin{gathered} \angle AOB=90^{\circ} \\ \angle BOC=90^{\circ} \\ \angle COD=90^{\circ} \\ \angle AOD=90^{\circ}\ldots(3) \end{gathered}[/tex]to prove: ABCD is rombus,
Rombus: its is a parallelogram, with all the sides equal.
so, to prove ABCD a parallelogram.
consider the triangle,
[tex]\begin{gathered} triangleAOD\text{ and triangle }COB, \\ OA=OC \\ \angle AOD=\angle COB \\ OD=OB \\ \end{gathered}[/tex]thus, traingle
[tex]\text{AOD}\cong COB[/tex]consider the sides, AD and BC
with the transversal ac,
The angles,
[tex]\angle OAD\text{ AND }\angle OCB[/tex]are alterntaive angles. they are equal.
this implies, AD is parallel BC.
similarly, AB is parallel to DC.
Hence, AD II BC and AB II DC.
In ABCD the opposite sides are parallel,
This implies, ABCD is parallelogram.
Now, to prove that ABCD is a rombus.
for that all the sides of ABCD should be equal.
now, consider the triangle AOD and COD.
[tex]\begin{gathered} OA=OC \\ \angle AOD=\angle COD \\ OD=OD\text{ common side} \end{gathered}[/tex]By SAS congruent rule,
Traingles,
[tex]AOD\cong COD[/tex]Thus, by CPCT Corresponding parts of congruent triangles ,
AD= CD
we know that,
AD=CB and CD=AB
Thus, AD=CD=CB=AB.
hence, all the sides are eqaul and ABCD is parallelogram.
So, ABCD is a rhombus.
Select ALL the expressions that have the same value as 9s
1. 9+s
2. 9*s
3. 3s + 6s
4. 3(3s)
5. s(5+4)
6. 3s * 3s
7. s+s+s+s+s+s+s+s+s2. 3s+2t=-4-6s-10t=-7What’s the value of s ?
ANSWER
2, 3, 4, 5, and 7 are the correct expressions that have the same values as 9s
STEP-BY-STEP EXPLANATION
Using Simultaneous equation
3s + 2t = -4 .............................................(1)
-6s - 10t = -7 .............................................(2)
multiply equation 1 by 2 and multiply equation 2 by 1:
equ 1 x 2: 6s + 4t = -8 ...............................(3)
equ 2 x 1: -6s -10t = -7 ................................(4)
Add equation 3 and 4 together
0s -6t = - 15
Divide through by -6:
[tex]\begin{gathered} t\text{ = }\frac{-15}{-6} \\ t\text{ = }\frac{5}{2} \end{gathered}[/tex]substitute the value of t into equation 1:
[tex]\begin{gathered} 3s\text{ + 2t = -4} \\ 3s\text{ + 2(}\frac{5}{2})\text{ = -4} \\ 3s\text{ + 5 = -4} \\ 3s\text{ = -4 -5} \\ 3s\text{ = -9 } \\ s\text{ = }\frac{-9}{3} \\ s\text{ = -3} \\ \end{gathered}[/tex]Now solving for the expression that has the same value as 9s:
Note: 9s = 9(-3) = -27
1. 9 + s = 9 - 3 = 6
2. 9 * s = 9 * -3 = -27
3. 3s + 6s = 3(-3) + 6(-3) = -9 -18 = -27
4. 3(3s) = 9s = 9(-3) = -27
5. s(5 + 4) = s(9) = -3(9) = -27
6. 3s * 3s = 3(-3) * 3(-3) = -9 * -9 = 81
7. s+s+s+s+s+s+s+s+s = -3-3-3-3-3-3-3-3-3 = -27
Hence, 2, 3, 4, 5, and 7 are the correct expressions that have the same values as 9s.
Jan Sara and maya ran a total of 64 miles last week. Jan and maya ran the same amount and Sarah 8 miles less then maya. how many miles did Sarah run
Let:
x = Distance traveled by Jan
y = Distance traveled by Sara
z = Distance traveled by maya
Jan Sara and maya ran a total of 64 miles last week, so:
[tex]x+y+z=64_{\text{ }}(1)[/tex]Jan and maya ran the same amount and Sarah 8 miles less then maya. therefore:
[tex]\begin{gathered} x=z_{\text{ }}(2) \\ y=z-8_{\text{ }}(3) \end{gathered}[/tex]Replace (2) and (3) into (1):
[tex]\begin{gathered} z+z-8+z=64 \\ 3z=64+8 \\ 3z=72 \\ z=24mi \end{gathered}[/tex]Replace z into (2):
[tex]\begin{gathered} y=24-8 \\ y=16mi \end{gathered}[/tex]Sara ran 16 mi
Simplify using the distributive property.8(y + 12)8 y + 9620 + y8 y + 1220 y
Solution:
Concept:
The distributive property of multiplication states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately, then adding the two products together for the same result as multiplying the first number by the sum.
The expression is given below as
[tex]\begin{gathered} 8(y+12) \\ =8\times y+8\times12 \\ =8y+96 \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow8y+96[/tex]You TryWrite an equation for each of the following,then solve for the variable.20 is the same as the sum of 4 and g.
Given statement:
20 is the same as the sum of 4 and g
Let us break down the statement into parts and then write the equation
the sum of 4 and g:
[tex]\text{= 4 + g}[/tex]This sum is equal to 20:
[tex]4\text{ + g = 20}[/tex]Hence, the equation is:
[tex]4\text{ + g = 20}[/tex]Solving for the variable:
[tex]\begin{gathered} \text{Collect like terms} \\ g\text{ = 20 -4} \\ g\text{ = 16} \end{gathered}[/tex]Answer Summary
[tex]\begin{gathered} \text{equation: 4 + g = 20} \\ g\text{ = 16} \end{gathered}[/tex]40% of the students on the field trip love the museum. If there are 20 students on the field trip, how many love the museum?
well, what's 40% of 20?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{40\% of 20}}{\left( \cfrac{40}{100} \right)20}\implies 8[/tex]
How much would $200 interest compounded monthly be worth after 30 years
Given:
Principal (P)=$200
Rate of interest (r) =4%
time (t)=30 years
Number of times compounded per year(n) = 12
Required- the amount.
Explanation:
First, we change the rate of interest in decimal by removing the "%" sign and dividing by 100 as:
[tex]\begin{gathered} r=4\% \\ \\ =\frac{4}{100} \\ \\ =0.04 \end{gathered}[/tex]Now, the formula for finding the amount is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Put the given values in the formula, we get:
[tex]A=200(1+\frac{0.04}{12})^{12\times30}[/tex]Solving further, we get:
[tex]undefined[/tex]If you apply the changes below to the absolute value parent function, f(x) = [X,which of these is the equation of the new function?• Shift 2 units to the left.• Shift 3 units down.O A. g(x) = 5x + 21 - 3O B. g(x) = (x - 21 - 3O c. g(x) = 5x + 31 - 2O D. g(x) = \x - 31 - 2
h is the translation left or right
h > 0 the function shifts to the right h units
h < 0 the function shifts to the left h units
k is the translation up or down
k > 0 the function shifts up k units
k < 0 the function shifts down k units
For the given transformations:
Shift 2 units to the left. h: -3
Shift 3 units down. k: -3
Then, the function g(x) is:
[tex]\begin{gathered} g(x)=\lvert x-(-2)\rvert-3 \\ \\ g(x)=\lvert x+2\rvert-3 \end{gathered}[/tex]Solve F=mv^2/R for V
SOLUTION
We want to solve for v in
[tex]F=\frac{mv^2}{R}[/tex]This means we should make v the subject, that is make it stand alone. This becomes
[tex]\begin{gathered} F=\frac{mv^2}{R} \\ m\text{ultiply both sides by }R,\text{ we have } \\ F\times R=\frac{mv^2}{R}\times R \\ R\text{ cancels R in the right hand side of the equation we have } \\ FR=mv^2 \end{gathered}[/tex]Next, we divide both sides by m, we have
[tex]\begin{gathered} FR=mv^2 \\ \frac{FR}{m}=\frac{mv^2}{m} \\ m\text{ cancels m, we have } \\ \frac{FR}{m}=v^2 \\ v^2=\frac{FR}{m} \end{gathered}[/tex]Lastly, we square root both sides we have
[tex]\begin{gathered} v^2=\frac{FR}{m} \\ \sqrt[]{v^2}=\sqrt[]{\frac{FR}{m}} \\ \text{square cancels square root, we have } \\ v=\sqrt[]{\frac{FR}{m}} \end{gathered}[/tex]Hence the answer is
[tex]v=\sqrt[]{\frac{FR}{m}}[/tex]For the polyhedron, use eular's foemula to find the missing number
Given:
Edges of the polyhedron, E = 10
Vertices, V = 5
A polyhedron is a three-dimensional figure.
Let's find the number of faces using Euler's formula.
To find the number of faces of the polyhedron, we have the Euler's formula:
V + F - E = 2
Substitute values into the formula:
5 + F - 10 = 2
Combine like terms:
F + 5 - 10 = 2
F - 5 = 2
Add 5 to both sides:
F - 5 + 5 = 2 + 5
F = 7
Therefore, the number of faces of the polyhedron is 7
ANSWER:
7 faces
What is the mean before the rent ? What is the mean after the change ?
Given:
The data set of the monthly rent paid by 7 tenants
990, 879, 940, 1010, 950, 920, 1430
We will find the mean of the data:
Mean = Sum/n
n = 7
Sum = 990+879+940+1010+950+920+1430 = 7119
Mean = 7119/7 = $1017
One of the tenants change from 1430 to 1115
The mean after the change will be as follows:
Sum = 990+879+940+1010+950+920+1115 = 6804
n = 7
Mean = 6804/7 = 972
So, the answer will be:
Mean before the change = 1017
Mean after the change = 972
Find the augmented matrix for the systemIt gives us 3 numbers already
It is required that we find an augmented matrix for the system.
Recall that a matrix that contains the coefficients and constant terms of a system of equations, each written in the standard form with the constant terms to the right of the equals is called an augmented matrix.
The given system of equations is:
[tex]\begin{cases}x+5y+8z=-9 \\ 3x+z=-4 \\ 7x+5y+7z=3\end{cases}[/tex]The first, second, and third equations can be rewritten to get:
[tex]\begin{cases}1x+5y+8z=-9 \\ 3x+0y+1z=-4 \\ 7x+5y+7z=3\end{cases}[/tex]Hence, the augmented matrix using the system is:
[tex]\begin{bmatrix}{1} & 5 & 8{|} & {-9} \\ {3} & {0} & {1|} & {-4} \\ {7} & {5} & {7|} & {3} \\ & {} & {} & {}\end{bmatrix}[/tex]What is the domain of the function shown in the graph below? y 10 9 8 7 6 5. 4 3 2 -10 -9 -8 -7 -6 in -4 3 -2 1 6 2 8 9 10 -2 -3 -4 -5 -6 -8 9 10 W Type here to search Et TH-WL-57336
1) As the Domain is the set of inputs (x) for that function, as we can see in the graph.
There's one point in the graph x =8, where should be an asymptote i.e. a vertical or horizontal line that prevents both graphs do not trespass.
So we can write the Domain as
D =(-∞, 8) U (8, ∞)
Because in this function, the point x=8 is not included, and from point 8 on the function continues.
The equation 8x+8y=16 in slope-intercept form
Help me with number 4 please Identify the 17th term of a geometric sequence where a1 = 16 and a5 = 150.06 Round the common ratio and 17th term to the nearest hundredth.
Common ratio = 1.75
17th term = 123,802.31
Explanations:Given the following parameters:
[tex]\begin{gathered} a_1=16 \\ a_5=150.06 \end{gathered}[/tex]Since the sequence is geometric, the nth term of the sequence is given as;
[tex]a_n_{}=a_{}r^{n-1}[/tex]a is the first term
r is the common ratio
n is the number of terms
If the first term a1 = 16, then;
[tex]\begin{gathered} a_1=ar^{1-1}_{} \\ 16=ar^0 \\ a=16 \end{gathered}[/tex]Similarly, if the fifth term a5 = 150.06, then;
[tex]\begin{gathered} a_5=ar^{5-1} \\ a_5=ar^4 \\ 150.06=16r^4 \\ r^4=\frac{150.06}{16} \\ r^4=9.37875 \\ r=1.74999271132 \\ r\approx1.75 \end{gathered}[/tex]Hence the common ratio to the nearest hundredth is 1.75
Next is to get the 17th term as shown;
[tex]\begin{gathered} a_{17}=ar^{16} \\ a_{17}=16(1.75)^{16} \\ a_{17}=16(7,737.6446) \\ a_{17}\approx123,802.31 \end{gathered}[/tex]Hence the 17th term of the sequence to the nearest hundredth is 123,802.31
Write an equation and solve.The supplement of an angle is 63º more than twicethe measure of its complement. Find the measure ofthe angle.
The measure of the angle is 63 degrees
Explanation:Let the angle in question be x degrees.
The supplement is (180 - x) degrees, and the complement is (90 - x) degrees.
Given that the supplement is 63 degrees more than twice the measure of its complement, we have the equation:
180 - x = 2(90 - x) + 63
Solving for x in the above:
180 - x = 180 - 2x + 63
2x - x = 180 - 180 + 63
x = 63
Last week, Shelly rode her bike a total of 30 miles over a three-day period. On the second day, she rode LaTeX: \frac{4}{5}45 the distance she rode on the first day. On the third day, she rode LaTeX: \frac{3}{2}32 the distance she rode on the second day
We make expressions for each afirmation
Where X is the first day, Y second day and Z the third
1. the sum of the 3 days gives us 30
[tex]X+Y+Z=30[/tex]2. Second day is 4/5 of the first day
[tex]Y=\frac{4}{5}X[/tex]3.Third day is 3/2 of the second day
[tex]Z=\frac{3}{2}Y[/tex]Whit the expressions I try to represent everything as a function of X
I must represent Z in function of X, for this I can replace Y of the second expression in the third expression
[tex]\begin{gathered} Z=\frac{3}{2}(\frac{4}{5}X) \\ Z=\frac{12}{10}X \\ Z=\frac{6}{5}X \end{gathered}[/tex]So I have:
[tex]\begin{gathered} Y=\frac{4}{5}X \\ Z=\frac{6}{5}X \\ \end{gathered}[/tex]And I can replace on the first expression
[tex]\begin{gathered} X+Y+Z=30 \\ X+(\frac{4}{5}X)+(\frac{6}{5}X)=30 \end{gathered}[/tex]I must find X
[tex]\begin{gathered} (1+\frac{4}{5}+\frac{6}{5})X=30 \\ 3X=30 \\ X=\frac{30}{3} \\ X=10 \end{gathered}[/tex]So, if I have X I can replace on this expressions to find de value:
[tex]\begin{gathered} Y=\frac{4}{5}X \\ Z=\frac{6}{5}X \end{gathered}[/tex]Where X is 10
[tex]\begin{gathered} Y=\frac{4}{5}\times10 \\ Y=\frac{40}{5}=8 \\ \\ Z=\frac{6}{5}\times10 \\ Z=\frac{60}{5}=12 \end{gathered}[/tex]To check:
[tex]\begin{gathered} X+Y+Z=30 \\ (10)+(8)+(12)=30 \\ 30=30 \\ \end{gathered}[/tex]The result is correct, therefore:
[tex]\begin{gathered} X=10 \\ Y=8 \\ Z=12 \end{gathered}[/tex]Create a "rollercoaster using the graphs of polynomials with real and rational coefficients.
The coaster ride must have at least 3 relative maxima and/or minima.
The coaster ride starts at 250 feet (let this be your y-intercept).
The ride dives below the ground into a tunnel (under the x-axis) at least once.
The graph must have at least one even multiplicity, two real solutions, and two imaginary solutions.
The polynomial that represents the rollercoaster, using the Factor Theorem, is given as follows:
y = 400(x - 1)²(x + 1)(x² + 0.1)(x + 5).
What is stated by the Factor Theorem?The Factor Theorem states that a polynomial function with zeros [tex]x_1, x_2, \codts, x_n[/tex], also represented by factors [tex]x - x_1, x - x_2, \cdots x - x_n[/tex] is given by the rule presented as follows:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient of the polynomial function with the given roots.
For this problem, the requirements are as follows:
At least 3 relative maxima and/or minima -> derivative of 3rd order -> 4 unique rootsy-intercept of 250 feet -> controlled by the leading coefficient.The roots will be given as follows:
Root at x = 1 with even multiplicity -> (x - 1)².Real solution at x = -1 -> (x + 1).Two imaginary solutions -> (x² + 0.1).Unique root at x = -5 -> (x + 5).Hence the function is:
y = a(x - 1)²(x + 1)(x² + 0.1)(x + 5).
At x = 0, the function assumes a value of 250, hence the leading coefficient is obtained as follows:
0.5a = 200.
a = 400.
Thus the function is:
y = 400(x - 1)²(x + 1)(x² + 0.1)(x + 5).
Which has the desired features, as shown by the image at the end of the answer.
More can be learned about the Factor Theorem at https://brainly.com/question/11813480
#SPJ1
Simplify (a + 15) •2
(a + 15) •2
Multiply each term in the parentheses by 2
a*2 + 15*2
2a + 30
If: x+y+z=2-x+3y+2z=84x+y=4Find the value of x, y and z
We have
[tex]\begin{gathered} x+y+z=2 \\ -x+3y+2z=8 \\ 4x+y=4 \end{gathered}[/tex]We have with the third equation
[tex]y=4-4x[/tex]We substitute in the first and second equation
[tex]\begin{gathered} x+4-4x+z=2 \\ -3x+z=-2 \end{gathered}[/tex][tex]\begin{gathered} -x+3(4-4x)+2z=8 \\ -x+12-12x+2z=8 \\ -13x+2z=8-12 \\ -13x+2z=-4 \end{gathered}[/tex]Then we have
[tex]z=-2+3x[/tex]We substitute
[tex]\begin{gathered} -13x+2(-2+3x)=-4 \\ -13x-4-6x=-4 \\ -19x=0 \\ x=0 \end{gathered}[/tex]if x=0
[tex]z=-2[/tex]and if x=0
[tex]y=4[/tex]ANSWER
x=0
y=4
z=-2
select the graph represented by the exponential function y = 4(1/2)×
SOLUTION
We want to tell the graph that represents the function
[tex]y=4(\frac{1}{2})^x[/tex]The graph of this function is shown below
Comparing this to what we have in the options,
we can see that the correct answer is option D
Drag each label to the correct location on the table. Each label can be used more than once, but not all labels will be used. Simplify the given polynomials. Then, classify each polynomial by its degree and number of terms.polynormial 1:[tex](x - \frac{1}{2})(6x + 2)[/tex]polynormial 2:[tex](7 {x}^{2} + 3x) - \frac{1}{3} (21 { x}^{2} - 12)[/tex]polynormial 3:[tex]4(5 {x}^{2} - 9x + 7) + 2( - 10 {x}^{2} + 18x - 03) [/tex]
Given the polynomials, let's simplify the polynomials and label them.
Polynomial 1:
[tex]\begin{gathered} (x-\frac{1}{2})(6x+2) \\ \text{Simplify:} \\ 6x(x)+2x+6x(-\frac{1}{2})+2(-\frac{1}{2}) \\ \\ =6x^2+2x-3x-1 \\ \\ =6x^2-x-1 \end{gathered}[/tex]After simplifying, we have the simplified form:
[tex]6x^2-x-1[/tex]Since the highest degree is 2, this is a quadratic polynomial.
It has 3 terms, therefore by number of terms it is a trinomial.
Polynomial 2:
[tex]\begin{gathered} (7x^2+3x)-\frac{1}{3}(21x^2-12) \\ \\ \text{Simplify:} \\ (7x^2+3x)-7x^2+4 \\ \\ =7x^2+3x-7x^2+4 \\ \\ \text{Combine like terms:} \\ 7x^2-7x^2+3x+4 \\ \\ 3x+4 \end{gathered}[/tex]Simplified form:
[tex]3x+4[/tex]The highest degree is 1, therefore it is linear
It has 2 terms, therefore by number of terms it is a binomial
Polynomial 3:
[tex]\begin{gathered} 4(5x^2-9x+7)+2(-10x^2+18x-13) \\ \\ \text{Simplify:} \\ 20x^2-36x+28-20x^2+36x-26 \\ \\ \text{Combine like terms:} \\ 20x^2-20x^2-36x+36x+28-26 \\ \\ =2 \end{gathered}[/tex]Simplified form:
[tex]2[/tex]The highest degree is 0 since it has no variable, therefore it is a constant.
It has 1 term, by number of terms it is a monomial.
ANSWER:
Polynomial Simplified form Name by degree Name by nos. of ter
1 6x²-x-1 quadratic Trinomial
2 3x + 4 Linear Binomial
3 2 Constant Monomial
use the invert-and-multiply rule to divide. Reduce your answer to lowest terms.4 divide (- 2/5)
ANSWER:
- 10
STEP-BY-STEP EXPLANATION:
We have the following expression
[tex]4\div\mleft(-\frac{2}{5}\mright)[/tex]We know that when dividing from, the nvert-and-multiply rule must be applied, as follows
[tex]\begin{gathered} 4\div\mleft(-\frac{2}{5}\mright)\rightarrow4\times\mleft(-\frac{5}{2}\mright)=\frac{4\cdot-5}{2}=\frac{-20}{2}=-10 \\ \end{gathered}[/tex]Therefore the result of the operation is -10