For each function choose whether it’s graph opens upward or downward.Choose the equation with the widest graph.Choose the equation with the narrowest graph.
Answers
a) if a > 0 the graph opens upward and if a < 0 it opens downward, hence:
up, up, up, down
b) widest: y = 2/3|x|
c) narrowest: y = 4|x|
Related Questions
SHORT ANSWERWhy is 3Vx + 4x2not a polynomial?Answer in complete sentences.Н.BI U SX2 x?E= = =ATXVXEnter your answer here
Answers
is not a polynomial because the power of the unknown for polynomials are always positive integers.
In this case, the power of x has 0.5
the diagonals of a square measure 20. what is the length of a side of the squareleave anwer in simplest radical form
Answers
The square is formed by 2 right triangles, where 20 is the hypotenuse.
We can apply the Pythagorean theorem:
c^2 = a^2 + b^2
Where:
c = hypotenuse = 20
a & b = the other 2 legs of the triangle = s
Since a square has 4 equal sides s, both legs of the triangle are the same (s)
Replacing:
20^2 = s^2+s^2
Solve for s
20^2 = 2 s^2
20^2 = 2 s^2
400 = 2 s^2
400/2 = s^2
200 = s^2
√200 = s
√(2 x 100 ) = s
√2 √100 = s
10 √2 = s
Describe how the graph of the function is a transformation of the original function f.y=f(x-49)This results in a Answer shift to the graph Answer units Answer.
Answers
Given an original function
[tex]f(x)[/tex]Its graph is plotted as
When the function is transformed to the function
[tex]y=f(x-49)[/tex]Its plot becomes
The above plot shows that the graph moves horizontally to the right by 49 units
Thus, this results in a right shift to the graph
49 units
Find a formula for P = f(t), the size of the population that begins in year t = 0 with 2070 members and decreases at a 3.9% annual rate. Assume that time is measured in years. P = f(t) =
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Explanation
Step 1
let
[tex]P=f(t)[/tex]where P represent the population, and t represents the time in years
so,
when t=0, P=2070
[tex]\begin{gathered} P=f(t) \\ 2070=f(0) \end{gathered}[/tex]Step 2
if the population decrease 3.9% every year,in decimal form
[tex]\begin{gathered} \text{3}.9\text{ =3.9/100= 0.039} \\ \end{gathered}[/tex]so,after 1 year the population is
[tex]\begin{gathered} P_1=P(1-0.039)\rightarrow Eq1 \\ P_1=P(0.961) \\ P_1=2070(0.961) \\ P_1=1989.27 \end{gathered}[/tex]now, after the 2 years
[tex]\begin{gathered} P_2=P_1(1-0.039)=P(1-0.039)(1-0.039)=P(1-0.039)^2 \\ \end{gathered}[/tex]now, after 3 years
[tex]P_3=P_2(1-0.039)=P(1-0.039)(1-0.039)(1-0.39==P(1-0.039)^3[/tex]now, we can see the function
[tex]\begin{gathered} P(1-0.039)^t\rightarrow P_f=P(1-0.039)^t \\ f(t)=P(1-0.039)^t \end{gathered}[/tex]I hope this helps you
Which is more, 10 tons or 20,004 pounds?
Answers
A ton is equivalent to 2000 pounds. Then, 10 tons are 20,000 pounds.
Therefore, 20,004 pounds is more.
The topic is solving radical equations, but im just confused on whether to squafe it or not[tex]2 \sqrt{n} = n - 3[/tex]
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a We are given the following radical equation
[tex]2\sqrt[]{n}=n-3[/tex]To solve this equation we need to square both sides of the equation
[tex]\begin{gathered} (2\sqrt[]{n})^2=(n-3)^2 \\ 4n=(n-3)^2 \end{gathered}[/tex]Apply the squares formula on right-hand side of the equation
[tex](a-b)^2=a^2+b^2-2ab[/tex]So the equation will become
[tex]\begin{gathered} 4n=n^2+3^2-2(n)(3) \\ 4n=n^2+9-6n \\ 0=n^2+9-6n-4n \\ 0=n^2+9-10n \\ n^2-10n+9=0 \end{gathered}[/tex]So we are left with a quadratic equation.
The standard form of a quadratic equation is given by
[tex]ax^2+bx+c=0[/tex]Comparing the standard equation with our equation we get the following coefficients
a = 1
b = -10
c = 9
Now recall that quadratic formula is given by
what are the ordered pairs of the solutions for this system of equations?f (x)=x^2-2x+3;f (x)=-5x+1
Answers
we get:
[tex]\begin{gathered} x^2-2x+3=-5x+1\rightarrow \\ x^2+3x-2=0\rightarrow x=\frac{-3+\sqrt[]{17}}{2},x=\frac{-3-\sqrt[]{17}}{2} \end{gathered}[/tex]so the pairs are,
[tex](\frac{-3+\sqrt[]{17}}{2},\frac{15-5\sqrt[]{17}}{2}+1),(\frac{-3-\sqrt[]{17}}{2},\frac{15+5\sqrt[]{17}}{2}+1)[/tex]Instructions: Solve the triangle, find m
Answers
step 1
Find out the measure of angle A
we have that
In the given right triangle
[tex]\begin{gathered} cosA=\frac{17}{38}\text{ ----> by CAH} \\ \\ A=cos^{-1}(\frac{17}{38}) \\ A=63^o \end{gathered}[/tex]step 2
Find out the measure of angle C
Remember that
In the right triangle
A+C=90 degrees -----------> by complementary angles
[tex]\begin{gathered} 63^o+C=90^o \\ C=90^o-63^o \\ C=27^o \end{gathered}[/tex]Please help me I'm struggling very muchx^3+14x^2+48x=0
Answers
ANSWER
The solutions are:
• x = 0
,• x = -6
,• x = -8
EXPLANATION
First we can see that there's and x in every term of the polynomial, so one of the solutions to the equation is when x = 0, because x is a common factor:
[tex]\begin{gathered} x^3+14x^2+48x=0 \\ x(x^2+14x+48)=0 \end{gathered}[/tex]The other two solutions - we know that there are three because the degree of the polynomial is 3 - are the zeros of the polynomial in parenthesis. We can solve it with the formula:
[tex]\begin{gathered} ax^2+bx+c=0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]In our polynomial, a = 1, b = 14 and c = 48:
[tex]\begin{gathered} x=\frac{-14\pm\sqrt[]{14^2-4\cdot48}}{2} \\ x=\frac{-14\pm\sqrt[]{196-192}}{2} \\ x=\frac{-14\pm\sqrt[]{4}}{2} \\ x=\frac{-14\pm2}{2} \\ x_1=\frac{-14-2}{2}=\frac{-16}{2}=-8 \\ x_2=\frac{-14+2}{2}=\frac{-12}{2}=-6 \end{gathered}[/tex]Therefore the solutions to the equation are x = 0, x = -8 and x = -6
Answer:
x = - 8, x = - 6, x = 0
Step-by-step explanation:
x³ + 14x² + 48x = 0 ← factor out x from each term
x(x² + 14x + 48) = 0 ← factor the quadratic
consider the factors of the constant term (+ 48) which sum to give the coefficient of the x- term (+ 14)
the factors are + 8 and + 6 , then
x(x + 8)(x + 6) = 0
equate each factor to zero and solve for x
x = 0
x + 8 = 0 ⇒ x = - 8
x + 6 = 0 ⇒ x = - 6
Ben and Jerry’s sells 3 times more ice cream cones ($2) than shakes ($9). If last month’s sales totaled $9,600, how many of each were sold?
Answers
It is given that the sales of ice cream is three times as shakes.
Let x be the number of ice creams and y be the number of shakes,
So x=3y.
Also the total sales if ice cream is $2 and shake is $9 is $9600 so it follows:
[tex]\begin{gathered} 2x+9y=9600 \\ 2\times3y+9y=9600 \\ 15y=9600 \\ y=640 \end{gathered}[/tex]Since x=3y so it follows that x=1920.
So Number of shakes sold is 640 and number of ice cream cones sold is 1920.
Hannah bought an emerald pendant online. It cost $751 plus 19% shipping and handling. What was the total cost? Round your answer to the nearest dollar: $
Answers
To find the shipping cost we can use the rule of three:
[tex]\begin{gathered} 751\rightarrow100 \\ x\rightarrow19 \end{gathered}[/tex]Then:
[tex]x=\frac{19\cdot751}{100}=\frac{14269}{100}=142.69[/tex]Therefore the total cost is $893.69
Evaluate the expression when X = 2X to the second power -8x -3
Answers
Evaluate for x = 2:
[tex](2)^2-8(2)-3=4-16-3=4-19=-15[/tex]What is the remainder when x^2 + 5x - 24 is divided by x - 6?
Answers
Given:
The dividend is,
[tex]x^2+5x-24[/tex]The divisor is,
[tex]x-6[/tex]To find: The remainder
Explanation:
Let us take,
[tex]p(x)=x^2+5x-24[/tex]Using the remainder theorem,
Let p(x) be any polynomial of degree greater than or equal to one and let a be any real number.
If p(x) is divided by the linear polynomial x - a, then the remainder is p(a).
Here,
[tex]a=6[/tex]Substitute the value of a in the above polynomial.
[tex]\begin{gathered} p(6)=6^2+5(6)-24_{} \\ =36+30-24 \\ =42 \end{gathered}[/tex]Hence, the remainder is 42.
Final answer: The remainder is 42.
so I have to make a table for the following equations and then graph them y= 2x+7
Answers
we have
y= 2x+7
this is the equation of the line
Make the table
For different values of x, calculate the values of y
so
For x=-1
y=2*(-1)+7
y=5
For x=0
y=2*(0)+7
y=7
For x=1
y=2*(1)+7
y=9
For x=2
y=2*(2)+7
y=11
therefore
we have the points
(-1,5) (0,7) (1,9) (2,11)
Plot the points and join them to graph the line
using a graphing tool
see the attached figure
please wait a minute
In Livingston, the use of landlines has been declining at a rate of 20% every year. of there are 23,000 landlines this year, many will there be in 6 years?? if necessary, round your answer to the nearest whole number
Answers
In 6 years there are
Apply N1= 230000
N = N1 - N1•20/100 - N1• (20/100)^2 - N1•(20/100/^3 - N1•(20/100)^4 - N1(20/100)^5 - N1•(20/100) ^6
Then replace 20/100= 1/5
N= 23000 - 23000 • ( 1/5 + 1/25 + 1/125/ + 1/625 + 1/3125 + 1/15625 )
N= 23000 - 5750 = 17250
Then answer is
In 6 years there will be 17250 landlines
2. Rewrite by factoring the GCF from each expression.a) 8r + 12O 8 (r + 3)O 4 (2r + 3)O 4 (2r + 12)O 8 (r + 12)
Answers
We are asked to rewrite the given expression by factoring the GCF from the expression.
[tex]8r+12[/tex]GCF is the greatest common factor.
Factors of 8 = 1, 2, 4, 8
Factors of 12 = 1, 2, 3, 4, 6, 12
Notice that the greatest common factor is 4
So, take out 4 from the expression
[tex]8r+12=4(2r+3)[/tex]Therefore, the correct answer is
[tex]4(2r+3)_{}[/tex]Does the graph show an increasing or decreasing linear function?A) IncreasingB) Decreasing
Answers
The values of the y-variable decrease as the values of the x-variable increase, then the graph shows a decreasing liner function
How many time would Tamir have to swims to make the season pass less expensive than paying for each visit individual
Answers
Let x be the number of times Tamir swims
Season pass :
C = 185 where c is the total cost
Pay per day:
C = 5x
We want
185 < 5x so the season pass costs less than the pay per day
Divide each side by 5
185/5 < 5x/5
37 < x
He needs to swim more than 37 days so
38 or more days
Answer 38 or more days
Convert 10,000 feet to meters and kilometers
Answers
Answer:
10000 feet = 3048 meters = 3.048 kilometers
Explanation:
Recall,
1 foot = 0.3048 meters
10000 feet = 10000 x 0.3048
10000 feet = 3048 meters
Also,
1 meter = 0.001 kilometers
3048 meters = 3048 x 0.001
= 3.048 kilometers
What is the domain and range of the function? 15c
Answers
The first thing we have to know is that the Domain are all the values that x can take in the function and that the Range are all the values that the function takes in y
Taking this into account, the best way to see the domain and range is by graphing the function
[tex]\begin{gathered} f^{-1}(x)=3+\log _4(\frac{1-x}{3}) \\ f^{-1}(x)=3+\log _4(1-x)-\log _4(3) \end{gathered}[/tex]If you want to find the Domain we have to guarantee that what is inside the logarithm and have a x is greater than zero:
[tex]\begin{gathered} 1-x>0 \\ 1>x \end{gathered}[/tex]This means that the domain will only be those values less than 1
standing 200ft from the base of an antenna, Maria measures the angle of elevation to the top of the antenna to be 38 degrees. If her eye level is 5ft above the ground, what is the height of the antenna to the nearest foot?
Answers
Given: The bearing and distance of Maria and an antenna
To Determine: The height of the antenna from the given information
Solution
From the given information, the diagram below can be deduced
From the diagram above, the height of the antenna is TB
Using SOH CAH TOA
[tex]\begin{gathered} tan38^0=\frac{TC}{EC} \\ EC=BG=200ft \\ SO, \\ tan38^0=\frac{TC}{200} \\ TC=200\times tan38^0 \end{gathered}[/tex][tex]\begin{gathered} TC=156.257ft \\ TB=TC+CB \\ EG=CB=5ft \\ TB=156.257+5 \\ TB=161.257ft \\ TB\approx161ft \end{gathered}[/tex]Hence, the height of the antenna is 161ft
Given parallelogram ABCD; ED=7x and BD=16x-38. Find BD. * B C E А D
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f(x)=4x^2+7x-18 find f(-9)
Answers
To find f(-9) you have to replace x = -9 into f(x) as follows:
f(x)=4x²+7x-18
f(-9) = 4(-9)² + 7(-9) - 18
f(-9) = 4(81) - 63 - 18
f(-9) = 324 - 63 - 18
f(-9) = 243
X - y = 0X + y = - 4
Answers
We are given the following system of equations:
[tex]\begin{gathered} x-y=0,(1) \\ x+y=-4,(2) \end{gathered}[/tex]We are asked to determine the solution by graphing the system.
To do that we will graph each of the equations. We will solve for "y" in equation (1), to do that we will add "y" to both sides:
[tex]\begin{gathered} x-y+y=y \\ x=y \end{gathered}[/tex]Switching the direction of the equation we get:
[tex]y=x[/tex]Now, we graph the equation. We notice that this is the equation of a line since it has the form:
[tex]y=mx+b[/tex]In this case, m = 1 and b = 0.
To graph a line we need to know two points in the line. We will determine those points by giving values to "x". We will substitute the value x = 0, we get:
[tex]y=0[/tex]Substituting "x = 1" we get:
[tex]y=1[/tex]Therefore, the two points are:
[tex]\begin{gathered} (x_1,y_1)=(0,0) \\ (x_2,y_2)=(1,1) \end{gathered}[/tex]Now we plot both points and join them with a line. The graph is the following:
Now we solve for "y" in equation (2). To do that we will subtract "x" from both sides:
[tex]y=4-x[/tex]Now, we graph using the same procedure as before. We will graph both lines in the same coordinate system and we will determine their interception point, like this:
The interception point is the solution of the system. Therefore, the solution is:
[tex](x,y)=(-2,-2)[/tex]Can this relation also be represented as {(-1, 1), (0, -2), (3, 1), (4, -1)}.?
Answers
In general, a relation can be represented by a set of ordered pairs (x,y), where x is a value in the domain of the relation and y is its corresponding value in the codomain.
Therefore, in our case, the relation is
[tex]\lbrace(0,-2),(3,1),(4,-1),(-1,-1)\rbrace[/tex]On the other hand, notice that (-1,1) is in the given set; that implies that the corresponding value of -1 in the codomain is 1 which is not true.
Thus, the answer is NO. It must be (-1,-1), not (-1, 1)Find the perimeter and area of a rectangle of cardboard measuring 18.2 cm by 5.6 cm Perimeter: I cm Enter an integer or decimal number (more
Answers
The perimeter of a rectangle is given by the following formula:
P = 2w+ 2l
Where w is the width and l is the length of the figure.
The area of a rectangle is given by the following formula:
A = w×l
By replacing 18.2 for l and 5.6 for w, we get:
P = 2×5.6 + 2×18.2 = 47.6
A = 5.6×18.2 = 101.92
Then, the perimeter of the rectangle equals
How do I do this math problem I’m kinda lazy
Answers
17x-12<90
+12 +12
—————
17x<102
Divide by 17 on both sides
17x
— 17 cancels out leaving you with just x.
17
102 divided by 17 is 6.
X<6
Graph 6 on the number line like this:
6(open circle) with arrow like this:
<————-
<————-6
Find the values of each variable using sin, cos or sine
Answers
To obtain the value of x, substitute the values of the following.
[tex]\begin{gathered} \theta=70\degree \\ \text{opposite side}=x \\ \text{hypothenuse}=30 \end{gathered}[/tex]Thus, we obtain the following
[tex]\begin{gathered} \sin \theta=\frac{opposite\text{ side}}{hypothenuse} \\ \sin 70\degree=\frac{x}{30} \end{gathered}[/tex]Multiply both sides of the equation by 30 and then simplify.
[tex]\begin{gathered} 30\sin 70\degree=x \\ x\approx28.19 \\ x\approx28 \end{gathered}[/tex]Since the two sides are equal, the base angles must be equal. Thus, we obtain the following.
[tex]\begin{gathered} \theta=70\degree \\ \text{adjacent side}=y \\ \text{hypothenuse}=30 \end{gathered}[/tex]Substitute the values using the following equation.
[tex]\begin{gathered} \cos \theta=\frac{adjacent\text{ side}}{hypothenuse} \\ \cos 70\degree=\frac{y}{30} \end{gathered}[/tex]Multiply both sides of the equation by 30 and then simplify.
[tex]\begin{gathered} 30\cos 70\degree=y \\ y\approx10.26 \\ y\approx10 \end{gathered}[/tex]Therefore, the value of x is approximately 28.19 and the value of y is approximately 10.26.
Choose the equation of the horizontal line that passes through the point (-5,9)
Answers
We are asked to find the equation of the horizontal line that passes through the point (-5, 9)
Recall that point-slope is given by
[tex]y-y_1=m(x_{}-x_1)[/tex]Where m is the slope of the line and x1 and y1 are the coordinates of the given point.
We know that the slope of a horizontal line is 0.
So let us substitute m = 0 and the given point into the above formula
[tex]\begin{gathered} y-9_{}=0\cdot(x_{}-(-5)_{}) \\ y-9=0 \\ y=9 \end{gathered}[/tex]Therefore, the equation of the line is y = 9
The angle of depression from d measures 25 if EF= 10 find De.
Answers
Step 1: You draw the diagram
The term angle of depression denotes the angle from the horizontal downward to an object. An observer's line of sight would be below the horizontal.
The angle of depression is equal to angle
Step 2: Apply trigonometric ratio to find the side DE.
[tex]\begin{gathered} \tan \theta\text{ = }\frac{Opposite}{\text{Adjacent}} \\ \theta\text{ = 25} \\ \text{Opposite DE = ?} \\ \text{Adjacent EF = 10 yd} \end{gathered}[/tex]Step 3: Substitute the values in the tangent equation to find side DE.
[tex]\begin{gathered} \tan 25\text{ = }\frac{DE}{10} \\ 0.4663\text{ = }\frac{DE}{10} \\ \text{Cross multiply} \\ DE\text{ = 10 x 0.4663} \\ DE\text{ = 4.663} \end{gathered}[/tex]Final answer
DE = 4.7 yard