EXPLANATION
Given the polynomial f(x) = x^3 +3x^2 -11x -21
Separating the expression into groups as shown as follows:
Solve for x(2x+3)(3x-2)=(3x+3)(2x-2)
To solve for x, we need to apply distributive property as:
[tex]\begin{gathered} \left(2x+3\right)\left(3x-2\right)=\left(3x+3\right)\left(2x-2\right) \\ 2x\cdot3x+2x\cdot(-2)+3\cdot3x+3\cdot(-2)=3x\cdot2x+3x(-2)+3\cdot2x+3\cdot(-2) \\ 6x^2-4x+9x-6=6x^2-6x+6x-6 \\ 6x^2+5x-6=6x^2-6 \\ 6x^2+5x-6+6=6x^2-6+6 \\ 6x^2+5x=6x^2 \\ 6x^2+5x-6x^2=6x^2-6x^2 \\ 5x=0 \\ x=0 \end{gathered}[/tex]Answer: x = 0
Write an explicit formula that represents the sequence defined by the following recursive formula: a1=7 and an=2a_n-1
Answer:
[tex]a_n=7(2^{n-1})[/tex]Explanation:
Given the sequence with the recursive formula:
[tex]\begin{gathered} a_1=7 \\ a_n=2a_{n-1} \end{gathered}[/tex]First, we determine the first three terms in the sequence.
[tex]\begin{gathered} a_2=2a_{2-1}=2a_1=2\times7=14 \\ a_3=2a_{3-1}=2a_2=2\times14=28 \end{gathered}[/tex]Therefore, the first three terms of the sequence are: 7, 14 and 28.
This is a geometric sequence where:
• The first term, a=7
,• The common ratio, r =14/7 = 2
We use the formula for the nth term of a GP.
[tex]\begin{gathered} a_n=ar^{n-1} \\ a_n=7\times2^{n-1} \end{gathered}[/tex]The explicit formula for the sequence is:
[tex]a_n=7(2^{n-1})[/tex]sketch the graph of each equation y= -5x
Step 1
To graph the function y= -5x
we set x=1 and y=0 individually.
[tex]\begin{gathered} when\text{ x= 1} \\ y=-5x \\ y=-5(1) \\ y=-5 \\ \text{coordinate points are (1,-5)} \\ \end{gathered}[/tex][tex]undefined[/tex]For one of the meals eaten duringthe field trip to Williamsburg, VA,WHMS will be charged $115.50 foradults to eat and $712.50 forstudents to eat WHMS will leave a10% tip. How much money willWHMS leave for the tip
The total amount the WHMS would be charged for adults and students to eat is
115.5 + 712.5 = $828
We were told that WHMS will leave a 10% tip. Recall that percentage is expressed in terms of 100. This means that the amount of money that WHMS will leave for the tip is
10/100 * 828 = $82.8
WHMS would leave $82.8 for the tip
For which values of A, B, and C will Ax + By = C be a horizontal line through the point (−4, 2)?
The set of values {A = 0, B = 1, and C = 2} to have a completely horizontal line.
What is a horizontal line?A horizontal line is defined as a line with slope m = 0 that is parallel to the x-axis.
A horizontal line across (-4,2) informs us of two things.
A horizontal line with slope m = 0 is parallel to the x-axis.
The line crosses the point (-4,2).
Ax + By = C has m = B/A = 0 slope and intersects point (-4,2).
Then, B = A×0 indicates that any constant A will work, and the Ax term disappears.
Ax + By = C then becomes y = C. To find C, use the point (-4,2).
⇒ C = 2
This line's equation is y = 2, and any point (x,2) matches the equation.
Therefore, the set of values {A = 0, B = 1, and C = 2} to have a completely horizontal line.
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Answer:
Step-by-step explanation:
17
DataNot ReceivingReceivingFinancial AidFinancial AidUndergraduates422238988120Graduates18797312610Total6101462910730If a student is selected at random, what is theprobability that the student receives aid and is agraduate (rounded to the nearest percent)? [? ]%UniversityTotal
There are 10730 students total as shown in the bottom right hand corner. So, the probability that the student receives aid and is a graduate is given by:
[tex]P=\frac{1879}{10730}\times100=17.51[/tex]Round to the nearest percent is 17.5%
Answer: 17.5%
Answer:
There are a total of 10730 students and 1879 students who are graduates as well as receiving financial aid. So the probability would be
(1879/10730)*100 = 17.51%
how much ice pop mixture can each mold hold when full?
Explanation:
To know how much ice pop mixture can each mold hold, we need to calculate the volume of the mold.
The volume of a cone is equal to
[tex]V=\frac{1}{3}\pi r^2h[/tex]Where r is the radius and h is the height of the cone. Replacing r = 2 cm and h = 15 cm, we get:
[tex]\begin{gathered} V=\frac{1}{3}\pi(2cm)^2(15cm) \\ V=\frac{1}{3}\pi(4cm^2)(15cm) \\ V=20\pi cm^3 \end{gathered}[/tex]Therefore, the answer is
A. 20
A pizza is to be cut into halves. Each of these halves is to be cut into fourths. What fraction of the pizza is each of thefinal pieces?
Given:
Each of these halves is to be cut into fourths.
So:.
A pizza is to be cut into halves
since half is represented by 1/2.
So each piece is now
[tex]\frac{1}{2}\text{ of the original.}[/tex]If each of these halves is to be cut into fourths, then the fraction of final pieces is:
[tex]\begin{gathered} =\frac{1}{2}\times\frac{1}{4} \\ =\frac{1}{8} \end{gathered}[/tex]
Answer:
1/8
Step-by-step explanation:
Fractions
We have 1/2
!/2 is to be cut in 1/4
1/2 * 1/4 = 1/8
A rectangle is 2 4/5 meters wide and 3 1/2 meters
long. What is its area?
Answer: Area = l × w
= 3.5 × 2.8
= 9.8 meters2
Step-by-step explanation:
Rhombus EfGH is shown in the diagram the measure of angle HEF =64 degrees. What is the measure of angle EJF.
Diagonals of a rhombus bisect each other at right angles, This means that
[tex]m\measuredangle EJF=90\text{ degre}es[/tex]Can someone show me how to do this one correctly?
ANSWER:
Juwan has 19 dimes and 6 quarters in his pocket.
STEP-BY-STEP EXPLANATION:
From the statement we can establish the following system of equations:
Taking into account that one dime is 10 cents and a quarter is 25 cents.
Let x be the number of dimes
Let y be the number of quarters
[tex]\begin{gathered} x+y=25\rightarrow x=25-y\text{ (1)} \\ 10x+25y=340\text{ (2)} \end{gathered}[/tex]We solve the system of equations by means of the substitution method, we substitute equation (1) in (2):
[tex]\begin{gathered} 10\cdot(25-y)+25y=340 \\ 250-10y+25y=340 \\ 15y=340-250 \\ y=\frac{90}{15} \\ y=6 \\ \\ \text{therefore, for x:} \\ x=25-6 \\ x=19 \end{gathered}[/tex]Therefore they are 19 dimes and 6 quarters
Here is a right triangle with a missing side length what is the missing side length
Right Triangles
A right triangle is recognized because it has an interior angle of 90°.
In right triangles, the Pythagora's Theorem is satisfied.
Being a and b the shorter sides (also called legs) of the triangle, and c the longer side (called hypotenuse), then:
[tex]c^2=a^2+b^2[/tex]The triangle shown in the image has the two legs of values a=15 and b=8. The hypotenuse is c=x, thus:
[tex]x^2=15^2+8^2[/tex]Operating:
[tex]x^2=225+64=289[/tex]Solving for x:
[tex]x=\sqrt[]{289}=17[/tex]x = 17
Simplify the expression by combing like terms.21v + 8 - 12v - 7 + 3t - t
We need to simplify the like terms.
"The like terms are whose with the same variable and exponent"
Therefore, the like terms are:
21v - 12v = 9v
8 - 7 = 1
3t - t = 2t
Now, the result is :
9v + 2t + 1
Hence, the correct answer is option D.
Let be two sets E and F such that:E = {x € R: -4 ≤ x ≤ 4}F = {x € R: | x | = x}What is the Cartesian product of the complement of E × F =?
Given:
[tex]\begin{gathered} E=\mleft\lbrace x\in\mathfrak{\Re }\colon-4\leq x\leq4\mright\rbrace \\ F=\mleft\lbrace x\in\mathfrak{\Re }\colon\lvert x\rvert=x\mright\rbrace \end{gathered}[/tex]If |x|=x that mean here x is grater then zero.
E is move -4 to 4 and F is grater then zero that mean multiplication of the function is obtaine all real value:
[tex]E\times F=\mleft\lbrace x\in\mathfrak{\Re }\mright\rbrace[/tex]If A={a,c} and B={d,g,w} then complete the Following:a. Find AxBb. Find n(AxB)c. write a multiplication equation involving numerals related to the parts in (a) and (b)...a. AxB = {____} Type an ordered pair. Use commas to separate answers as needed
Given the two sets:
[tex]\begin{gathered} A=\mleft\lbrace a,c\mright\rbrace \\ B=\mleft\lbrace d,g,w\mright\rbrace \end{gathered}[/tex]we can write the product set of A and B in the following form:
[tex]AxB=\mleft\lbrace(a,d\mright),(a,g),(a,w),(c,d),(c,g),(c,w)\}[/tex]next, we have that the number of elements in A is 2 and the number of elements in B is 3, then, we have:
[tex]n(AxB)=2\cdot3=6[/tex]finally, the equation that involves the numerals of the previous parts is:
[tex]n(AxB)=n(A)\cdot n(B)[/tex]where n(A) and n(B) represents the number of elements in A and B respectively.
Irlene has just returned from a business trip in Britain with £200 of uncashed traveller's cheques. How much would she receive from the bank when she converts the currency back to Canadian dollars, assuming that the bank offers an exchange rate of C$1.00 = £0.5544 and charges a 0.65% fee to convert the traveller's cheques to Canadian funds? For full marks your answer(s) should be rounded to the nearest cent.
The converted money in Canadian dollars is $111.6.
Given that, Irlene has just returned from a business trip in Britain with £200 of uncashed traveler's cheques.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the converted Canadian dollars be x.
x = 200 × 0.5544 + 0.65% of 200 × 0.5544
= 110.88 + 0.0065 × 110.88
= 111.60072
≈ 111.6
Therefore, the converted money in Canadian dollars is $111.6.
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HELP ASAP!!!
Find the square of 1-4i.
ANSAWER:
−15+8i
Explanation:
First, you can expand the square of the bynomial:
4 groups of a number
Answer:
[tex]4x[/tex]Step-by-step explanation:
In math, a group is a set equipped with an operation that combines any two elements of the set to produce a third element of the set.
Therefore, for 4 groups of a number.
Let x be the missing number
So, 4 multiply x:
[tex]4x[/tex]the first yr a community college offered a Certificate in data management , 12 people earned the certificate. the next year 17 people earned the certificate. what was the percent increase in the # of people earning the certificate?
we make an expression
[tex]12\times x=17[/tex]we know that if we multiply to twelve by the ratio of increase we will obtain 17
now solve for x that is the ratio
[tex]x=\frac{17}{12}=1.42[/tex]multiply by 100 to obtain a percentage
[tex]1.42\times100=142[/tex]the percentage is 142%
How do I Graph the line with the given slope m and y-intercept b.
M=-4/3,b=2
What is the measure of a?
Answer:
Explanation:
Answer:
<A=32°
Explanation:
<BEC = 90° because it has the red half square and we know that <DCE = 42°. <ACB= 2x because <ACD and <DCB both =x. The equation we would set up is
90+(42+x) +2x=180
We get x=16.
Since <ACB = 2x we multiple 16 by 2
16*2=32
So <ACB =32°
If a and b are the measure of two first quadrant angles, find the exact value of the functioncsc a =5/3 and tan 5/12 find the cod (a+b)
Input data
[tex]\begin{gathered} \cos a=\frac{5}{3} \\ \tan b=\frac{5}{12} \end{gathered}[/tex]
Now for cos(a+b)
[tex]\begin{gathered} a=\csc ^{-1}(\frac{5}{3})^{} \\ a=36.87 \end{gathered}[/tex][tex]\begin{gathered} b=\tan ^{-1}(\frac{5}{12}) \\ b=22.62 \end{gathered}[/tex][tex]\begin{gathered} \cos (a+b) \\ \cos (36.87+22.62) \\ \cos 59.5 \\ \frac{33}{65}=0.507 \end{gathered}[/tex]Evaluate the function for the indicated values of x. (2x + 1, x 5 f(-10) = F(2) = f(-5) = f(-1) = f(8) =
Explanation
[tex]f(x)f(x)=\mleft\{\begin{aligned}2x+1\text{ if x}\leq-5\text{ } \\ x^2\text{ if -5}Step 1you need to select the correct function depending on the number
i)f(-10)
[tex]-10\leq-5,\text{ then you n}eed\text{ apply}\Rightarrow f(x)=2x+1[/tex]Let x= -10, replacing
[tex]\begin{gathered} f(x)=2x+1 \\ f(-10)=(2\cdot-10)+1 \\ f(-10)=-20+1 \\ f(-10)=-19 \end{gathered}[/tex]Step 2
Now
ii) f(2)
[tex]\begin{gathered} 2\text{ is in the interval} \\ -5Letx=2,replacing
[tex]\begin{gathered} f(x)=x^2 \\ f(2)=2^2=4 \\ f(2)=4 \end{gathered}[/tex]Step 3
iii) f(-5)
[tex]\begin{gathered} -5\text{ is smaller or equal than -5} \\ -5\leq5,\text{ then apply}\Rightarrow f(x)=2x+1 \end{gathered}[/tex]Let
x=-5,replace
[tex]\begin{gathered} f(x)=2x+1 \\ f(-5)=(2\cdot-5)+1=-10+1 \\ f(-5)=-9 \end{gathered}[/tex]Step 4
iv)f(-1)
[tex]\begin{gathered} -1\text{ is in the interval} \\ -5<-1<5 \\ \text{then apply}\Rightarrow f(x)=x^2 \end{gathered}[/tex]let
x=-1,replace
[tex]\begin{gathered} f(x)=x^2 \\ f(-1)=(-1)^2 \\ f(-1)=-1\cdot-1=1 \\ f(-1)=1 \end{gathered}[/tex]Step 5
Finally
F(8)
[tex]\begin{gathered} 8\text{ is greater or equal than 5, then apply} \\ 8\ge5\Rightarrow apply\text{ f(x)=3-x} \\ f(x)=3-x \end{gathered}[/tex]Let
x=8,replace
[tex]\begin{gathered} f(x)=3-x \\ f(8)=3-8 \\ f(8)=-5 \end{gathered}[/tex]I hope this helps you
Find a given that the line through M(-2, a) and N(0, -2) has gradient -4
a=6
1) Given that we have M (-2, a), N(0, -2), and the gradient -4. Let's start by applying the formula for the gradient.
G = (y_2 - y_1 ) / (x_2- x_1)
2) So "a", the second coordinate of point M is equal to 6, and as the gradient is a negative number indicates a "downhill" a decreasing direction of that line.
You and a friend are in school and are trying to figure out where to eat. You told her that you would like to go to your favorite pizza place that is 5 miles away from your home. Both of you know that your home is 10 miles away from school. Approximately how far is the pizza place from the school?The pizza place is between approximately 5 to 15 miles away from school.Not enough information to solve the problem.The pizza place is approximately less than 5 miles away from school.
Okay, here we have this:
Considering the provided information, we are going to identify approximately how far is the pizza place from the school, so we obtain the following:
Then from the given information we can identify that the pizzeria can be 5 miles in the same direction from the school or 5 miles in any other direction,
This means that in the best case the distance from the pizzeria to the school is 5 miles (if it is halfway), and in the worst case it is 15 miles (if it is in a completely opposite sense).
And in an average case it can be at an angle other than 180 degrees, with which the distance would be between 5 and 15 miles, therefore the correct answer is:
The pizza place is between approximately 5 to 15 miles away from school.
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
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.
A music club charges an initial joining fee of $24.00. The cost per CD is $8.50. The graph shows the cost of belonging to the club as a function of CDs purchased. How will the graph change if the cost per CD goes up by $1.00.? (The new function is shown by the dotted line.)
Given the function with a graph that shows the cost of belonging to the club as a function of CDs purchased
linear function with the form
[tex]y=x[/tex]since the new graph has a new cd cost up by $1.00
then the new line is
Correct answer
Option C
Triangle Inequality TheoremDetermine if a triangle can be formed with the given lengths. If so, classify the triangle by its angle.YESorNO
Given:-
[tex]7,20,12[/tex]To find:-
Wheather the given sides form a valid triangle.
So now let,
[tex]A=7,B=20,C=12[/tex]To check we use the condition,
[tex]A+B>C,B+C>A,C+A>B[/tex]Substituting the values we get,
[tex]7+20>12,20+12>7,12+7>20[/tex]In the above condition 12+7>20 is wrong.
So the condition fails and the given sides doesnt form a triangle.
The length of each side of a square is extended 5 in. The area of the resulting square is 64 in,2 Find the length of a side of the
original square.
Answer: i donno
Step-by-step explanation:
ask Professor Ahmad Shaoki
Find the missing number to make the fractions equivalent. 3/4 = 9/?
We have the following:
[tex]\frac{3}{4}=\frac{9}{x}[/tex]solving:
[tex]\begin{gathered} x=\frac{9\cdot4}{3} \\ x=12 \end{gathered}[/tex]Therefore, the answer is [B] 12
