Answers
The value of the composition (g ° f) (x) between the linear equation g(x) and the quadratic equation f(x) evaluated at x = 5 is equal to 6.
How to find and evaluate a composition between two functions
In this problem we find a quadratic equation f(x) and a linear equation g(x), of which we must derive a composition consisting in substituting the input variable of the linear equation with the quadratic equation. Later, we evaluate the resulting expression at x = 5.
Now we present the complete procedure:
(g ° f) (x) = - 2 · (x² - 6 · x + 2)
(g ° f) (x) = - 2 · x² + 12 · x - 4
(g ° f) (5) = - 2 · 5² + 12 · 5 - 4
(g ° f) (5) = - 50 + 60 - 4
(g ° f) (5) = 6
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Related Questions
in the diagram of BED below, FC||ED,BF=6,FE=18, and BC=22. What is the length of BD
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we know that
The side splitter theorem states that if a line is parallel to a side of a triangle and the line intersects the other two sides, then this line divides those two sides proportionally
so
18/6=DC/11
solve for DC
DC=3*11
DC=33
Find the length of BD
BD=BC+DC
BD=11+33=44 units
therefore
the answer is 44 units
Aldo gets paid biweekly. His gross pay for each pay period is $850.He has 16% withheld for taxes and 7% withheld for personal deductionsWhat is the amount of his annual net pay?a. $8,160b. $17,340c. $17,017d. $17,680
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First, we compute the 16% of $850 and the 7% of $850:
[tex]\begin{gathered} 850(0.16)=136 \\ 850(0.07)=59.5 \end{gathered}[/tex]Then, after deductions, Aldo gets paid $850-$136-$59.5=$654.5 biweekly. Therefore, since he gets paid biweekly we multiply $654.5 per 26 and get that Aldo earns $17017 per year.
Answer: Option C.
-87, -70, -27, -36,...a(n)= 17n - 10432nd term
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We have the arithmetic progression given by
[tex]a_n=17n-104[/tex]if n = 1 we have the first term, n = 2 the second one and, so on, to find the 32nd term we just do n = 32, therefore
[tex]\begin{gathered} a_{32}=17\cdot32-104 \\ \\ a_{32}=544-104 \\ \\ a_{32}=440 \end{gathered}[/tex]The 32nd term is 440.
solve for r 2r + 7 = 4r - 13
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2r + 7 = 4r - 13
subtract 4 from both-side of the equation
2r - 4r + 7 = 4r - 4r - 13
-2r + 7 = -13
subtract 7 from both-side of the equation
-2r + 7 = -13 - 7
-2r = -20
divide both-side of the equation by -2
r = 10
8ftÜ4ft7ft5ftA right angle is removed from a rectangle to create the shaded region shown below find the area of the shaded region be sure to include the correct unit in your answer
Answers
First, we need to find the sides of the triangle.
The base of the triangles is 8ft - 5ft = 3ft.
The height for the triangle is 7ft - 4ft = 3ft
Now, we need to find the area of the triangle:
[tex]A_t=\frac{base\cdot height}{2}[/tex]Replacing the values:
[tex]A_t=\frac{3ft\cdot3ft}{2}[/tex]Then
[tex]A_t=4.5ft^2^{}[/tex]Now, we need to find the area for the rectangle:
Area for a rectangle = Length * Width
In this case:
Length = 8ft
Width = 7ft
Therefore:
[tex]A_r=8ft\cdot7ft[/tex]Then
[tex]A_r=56[/tex]Finally, to find the area of the shaded region we need to subtract the triangle area from the rectangle area:
[tex]A=A_r-A_t[/tex]Therefore:
[tex]A=56ft^2-4.5ft^2[/tex][tex]A=51.5ft^2[/tex]Hence, the area for the shaded region is 51.5 ft².
the endpoints of line segment DEF are D(1,4) and and F(16,14). Determine and state the coordinates of E, if DE:EF = 2:3.
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The coordinates can be obtained using section formula
[tex]\begin{gathered} \text{Let the coordinates of D be (x}_{1_,}y_1)andFbe(x_2,y_2) \\ \text{The point E divides the line in m:n ratio.} \\ U\sin g\text{ section formula, coordinates of E is} \\ \frac{mx_2+nx_1}{m+n},\text{ }\frac{my_2+ny_1}{m+n} \\ \end{gathered}[/tex][tex]\begin{gathered} (x_1,y_1)=(1,4),(x_2,y_2)=(16,14),\text{ m:n=2:3} \\ \text{Substitute the values in section formula} \\ \frac{2\ast16+3\ast1}{2+3},\text{ }\frac{2\ast14+3\ast4}{2+3} \\ \frac{32+3}{5},\text{ }\frac{28+12}{5} \\ \frac{35}{5},\text{ }\frac{40}{5} \\ 7,\text{ 8} \end{gathered}[/tex]The x coordinate of E is 7 and y coordinate is 8.
Find the common ratio of the geometric sequence 19, -76,304, ...
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(X-3) times (4x+2) yawing distributive property
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For two binomials, the distributive property is:
[tex](a+b)\cdot(c+d)=a\cdot c+a\cdot d+b\cdot c+b\cdot d[/tex]So, let's solve this problem.
Step 01: Multiply the first term of the binomial (x - 3) by both terms of the binominal (4x + 2).
[tex](x-3)\cdot(4x+2)=x\cdot4x+x\cdot2+\cdots_{}[/tex]Step 02: Multiply the second term of the binomial (x - 3) by both terms of the binominal (4x + 2).
[tex](x-3)\cdot(4x+2)=x\cdot4x+x\cdot2+(-3)\cdot4x+(-3)\cdot2[/tex]Step 03: Multiply the terms.
[tex]=4x^2+2x-12x-6[/tex]Step 04: Add like terms.
[tex]=4x^2-10x-6[/tex]Answer:
[tex]4x^2-10x-6[/tex]In the diagram below of rhombus ABCD,angle C is 100,what is angle DBC
Answers
Okay, here we have this:
Considering the provided information, that in a rhombus opposite angles are equal, and that the sum of the angles of a triangle is 360 °, we obtain:
360°=100°+100°+4(m∠DBC)
Now, let's clear "m∠DBC":
360°=200°+4(m∠DBC)
4(m∠DBC)=360°-200°
4(m∠DBC)=160°
m∠DBC=160°/4
m∠DBC=40°
Finally we obtain that the correct answer is the option A.
dog brought a new jet ski for $299 down in 14 monthly payments are $57 how much did Doug pay for the jet ski total
Answers
If he paid $57 monthly for 14 months, the total amount paid is:
[tex]57\times14=798[/tex]He paid $798 in total
2. A grocery store is tracking how many people buy barbeque chips and jalapeno chips. The table shows how the number of barbeque chips and jalapeno chips are related. Ax + By = C y = mx + b Barbeque Jalapeno Write the standard form and slope intercept form equations for the scenario given. Chips (x) Chips (y) 200 100 160 140 120 180 80 220 Hint: use your calculator (STAT: Edit)
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step 1
Find the slope m
we need two points
so
(200,100) and (80,220)
m=(220-100)/(80-200)
m=120/-20
m=-6
step 2
Find the equation of the line in point slope form
y-y1=m(x-x1)
we have
m=-6
(x1,y1)=(200,100)
substitute
y-100=-6(x-200)
Convert to slope intercept form
y-100=-6x+1200
y=-6x+1300step 3
Find the equation in standard form
Ax+By=C
where
A is a positive integer
B and C are integers
so
y=-6x+1300
6x+y=1300i need help with this pls
Answers
Mathematically speaking, the linear pair postulate and linear pair theorem both express the same thing.
A linear pair is made up of two angles, and the sum of their measures is 180°.What is the formula for linear pairs?A two-variable linear equation of the form axe + by + c, with a, b, and c all being real numbers and not equal to zero.The Transitive Property states that if all real numbers x, y, and z are equal, then x=z. Substituting characteristics. If x=y, then x can be swapped to y in any equation or formula.Mathematically speaking, the linear pair postulate and linear pair theorem both express the same thing. A linear pair is made up of two angles, and the sum of their measures is 180°.Line pairs can be congruent. Adjacent angles are joined by a vertex. Angles that are similar cross across. A linear pairing is unnecessary.
Therefore, mathematically speaking, the linear pair postulate and linear pair theorem both express the same thing.
A linear pair is made up of two angles, and the sum of their measures is 180°.To learn more about the Linear pair theorem refer to:
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The percentage of students in the school that attended the talent show for the years 2008 to 2013 are shown.This Year, the school had a total of 360 students. How many students do you expect to attend the talent show this year? Explain.
Answers
Considering this year as the last year in the table which is 2013
[tex]\text{the total number of students in 2013=360}[/tex][tex]\text{The percentage of students attendance in 2013=95\%}[/tex]Therefore,
The number of students to attend this year's talent show will be calculated by
[tex]A\text{ttendance}=\text{percentage of students}\times total\text{ number of students}[/tex][tex]\begin{gathered} \text{Attendance}=95\text{ \%}\times360 \\ \text{Attendance}=\frac{95}{100}\times360 \\ \text{Attendance}=\frac{34200}{100} \\ \text{Attendance}=342\text{ students} \end{gathered}[/tex]Hence.
The attendance for this year is 342 students
Betsy has $400 in a personal bank account, and then withdraws $14 perweek. Carlos has $25 in a personal bank account, and then deposits $61earned from babysitting each week. After how many weeks will they have thesame amount of money in the bank?
Answers
Given:
Betsy has $400 in a personal bank account, and then withdraws $14 per
week.
Carlos has $25 in a personal bank account, and then deposits $61
earned from babysitting each week.
Required:
The same amount will they have in the bank after how many week.
Explanation:
After 5 weeks Betsy will have $330 in her account.
Since
[tex]\begin{gathered} 14\times5=70 \\ \Rightarrow400-70=330 \end{gathered}[/tex]After 5 weeks Carlos will have $330 in her account.
Since
[tex]\begin{gathered} 61\times5=305 \\ \Rightarrow305+25=330 \end{gathered}[/tex]Hence, after 5 weeks they will have the same amount of money $330 in the bank.
Final Answer:
After 5 weeks they will have the same amount of money $330 in the bank.
A) how many of these voters plan to vote for the library? B) how many voters are not planning to vote for the library?
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Answer:
Explanation:
From the information given, 3
Find the surface area of the cone. Use 3.14 for pi.The surface area is about __in.2.(I need just the answer, I don't need explanation)
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
s = 50in
d = 20in
surface area of a cone = ?
Step 02:
surface area of a cone
SA = πr² + πrs
r = d/2 = 20in / 2 = 10in
SA = 3.14*(10in)² + 3.14*50in*10in
SA = 314in² + 1570in²
SA = 1884in²
The answer is:
SA = 1884in²
help i’ll greatly appreciate it :)
Answers
Answer: i think B
Step-by-step explanation:
im not that sure tho
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!
Answers
Answer:
To find the perimeter of the triangle, you would add p + m + n. To find the area of the triangle you would use (p x m) /2. To find a missing side of the triangle, given that it is a right triangle, you would use p^2 + m^2 = n^2
The elevation of a mountain is 6510 feet above sea level.
Write a signed number to represent this elevation.
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Pic attached of problem. Answer must be with proper number of significant figures
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Answer:
1310 cubic feet per minute
Explanation:
Let x represent the value in cubic feet per minute
Note that;
1 cubic meter per second = 2118.87997 cubic feet per minute
Given 0.618 cubic meter per second, to be able to solve for x, we'll go ahead and set the proportions as seen below;
[tex]\frac{1\text{ cubic meter per second}}{0.618\text{ cubic meter per second}}=\frac{2118.87997\text{ cubic f}eet\text{ per minute}}{x\text{ cubic f}eet\text{ per minute}}[/tex]Let's go ahead and cross-multiply;
[tex]\begin{gathered} x=2118.87997\times0.618 \\ x=1309.46782146cfm \\ x=1310\text{cfm (to 3 significant figures)} \end{gathered}[/tex]What is the product of 8i and 4i
Answers
The product of given complex number that is 8i and 4i will be -32 by the properties of complex number that states i*i will be -1 and 8*4 will be 32.
What is complex number?Every complex number can be expressed in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element denoted I also known as the imaginary unit, and satisfying the equation i²=-1.
What are the property of complex number?Commutative, Associative, Distributive Properties: All complex numbers are commutative and associative under addition and multiplication, and multiplication distributes over addition.
Here,
The product of 8i*4i=-32
as 8*4=32
and i²=-1
32*-1=-32
Due to the properties of complex numbers, which state that i*i will be -1 and 8*4 will be 32, the product of the given complex number, which is 8i and 4i, will be -32.
To know more about complex numbers,
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Leeds Company produced the following number of maps during the first five weeks of last year. Prepare a bar graph. Week Maps 1 800 2 600 3 400 4 700 5 300
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The bar graph is attached below.
The heights of the rectangular bars in a bar graph, which displays complete data, are proportionate to the values they indicate. The graph's bars can be displayed either vertically or horizontally. Bar graphs, commonly referred to as bar charts, are a visual depiction of groups of data. It is one method of processing data. A bar graph is a great tool for representing data that are unrelated to one another and do not need to be displayed in any particular sequence. The bars provide a visual representation for comparing amounts in several categories. The x and y axes, commonly known as the horizontal and vertical axes, the title, labels, and a bar graph are all included.
Hence we frame the desired bar graph.
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Mai works as a tutor for $12 an hour and as a waitress for $7 an hour. This month,she worked a combined total of 85 hours at her two jobs. Let t be the number of hours Mai worked as a tutor this month. Write an expression for the combined total dollar amount she earned this month.total earned (in dollars) = ?
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Solution:
Let t be the number of hours Mai works as a tutor.
Given that She earns $12 a hour as a tutor, this implies that for t number of hours, she will earn
[tex]\begin{gathered} \$12\times t \\ =\$\text{ 12t} \end{gathered}[/tex]For the month, she worked a combined total of 85 hours. This implies that
[tex]\begin{gathered} 85=t\text{ + (number of hours worked as a waitress) } \\ \Rightarrow nu\text{mber of hours worked as a waitress = (85-t) hours} \end{gathered}[/tex]Her total eranings for the month is expressed as
[tex]\text{Total earnings = 12(number of hours worked as a tutor)+7(number of hours worked as a waitress)}[/tex]Recall that she earnes $7 an hour while working as a waitress.
Thus, we have her combined total amount in dollars expressed as
[tex]\text{Total earned (in dollars)=12t+7(85-t)}[/tex]Hence, the expression is
[tex]\begin{gathered} \text{12t+7(85-t) } \\ \text{open parentheses} \\ \Rightarrow12t+595-7t \\ \text{collect like terms.} \\ \text{thus, the expression is simplied to be} \\ 5t+595 \end{gathered}[/tex]what is[tex](6 {x}^{2} - 13x + 5) [/tex]divided by[tex](2x - 1)[/tex]
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1. Divide the first term of the dividend into the first term of the divisor:
[tex]\frac{6x^2}{2x}=3x[/tex]2. Multiply the result above by the divisor:
[tex]3x(2x+1)=6x^2+3x[/tex]3. Subtract the result above from the divident to get a new polynomial:
4. Repeat the process with the new polynomial:
[tex]\begin{gathered} -\frac{16x}{2x}=-8 \\ \\ -8(2x+1)=-16x-8 \end{gathered}[/tex]Then, the result of the division is:[tex]\frac{6x^2-13x+5}{2x+1}=3x-8+\frac{13}{2x+1}[/tex]Evaluate the following expression.
1-4x (-3) +8 x (-3)
Answers
Answer:
-11
Step-by-step explanation:
1-4x(-3)+8x(-3)=
first you multiple
-4x(-3)=12
8x(-3)= -24
bring down the 1
1+12-24=
now we add
13-24=
then subtract and we get
-11
the smallest four digit number that can be formed using 5, 6, 3, 0 is
Answers
Answer:
3056 can be be formed as the smallest four digit number
In one us city the taxi cost is 2$ plus .50c per mile . If you are traveling from the airport there is an additional charge of 3.50$ for tolls how far can i travel for 33$
Answers
Let the number of miles I can travel for $33 be x;
The total cost of taxi ride from the airport is;
Flat fee + Tolls fee + Charge/Mile = Total cost
Flat fee = $2.00
Toll fee = $3.50
Charge per mile = 0.50x
Total cost = $33.00
Thus, we have;
[tex]\begin{gathered} 2.00+3.50+0.50x=33.00 \\ 0.50x=33.00-5.50 \\ 0.50x=27.50 \\ x=\frac{27.50}{0.50} \\ x=55 \end{gathered}[/tex]Thus, the number of miles
B. Are the graphs of y = a|x| and y = |ax| the same when a is negative? Why?
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The absolute value gives always a positive number.
If a is negative, then a|x| is negative and |ax| is positive.
Therefore, the graph of y=a|x| won't be the same as the graph of y=|ax|.
Another way to see it, is by using the property:
[tex]\mleft|ax\mright|=\mleft|a\mright|\cdot\mleft|x\mright|[/tex]Since a is negative, then |a| = -a. So, |ax| = -a|x|, which is clearly different from a|x|.
I need help with this problem. Quick answer is fine
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[tex]a^{\frac{-m}{n}}=\frac{1}{a\frac{m}{n}}=\frac{1}{\sqrt[n]{a^m}}[/tex]
What is the measure of the unknown angle? (2 points)120°2100009240
Answers
To find the angle measure "n", we proceed as follows:
Step 1: Recall that the sum of angles at a point is 360 degrees, as below:
[tex]\begin{gathered} the\text{ sum of angles at a point = 360 degrees} \\ n+120\text{ = 360} \\ n=360\text{ - 120} \\ n=240^o \\ \end{gathered}[/tex]Therefore, the meas