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Given the function:
[tex]h(x)=-3x^3-2x^2-8x-2[/tex]Let's use the rational zeros theorem to list all possible rational zeros of the given polynomial.
To use the rational roots theorem we have:
[tex]\pm\frac{p}{q}[/tex]Where p is a factor of the constaant (last term).
q is a factor of the leading coefficient,
Thus, we have:
p: Factors of -2 = ±1, ±2
q: Factors of -3 = ±1, ±3
The rational zero will be every combination of ±p/q.
Thus, we have:
[tex]\begin{gathered} \pm\frac{p}{q}=\pm\frac{1}{1},\pm\frac{1}{3},\pm\frac{2}{1},\pm\frac{2}{3} \\ \end{gathered}[/tex]Simplify:
[tex]\pm\frac{p}{q}=\pm1,\pm\frac{1}{3},\pm2,\pm\frac{2}{3}[/tex]Therefore, the list of all possible rational zeros are:
[tex]\pm1,\pm\frac{1}{3},\pm2,\pm\frac{2}{3}[/tex]ANSWER:
[tex]\pm1,\pm\frac{1}{3},\pm2,\pm\frac{2}{3}[/tex]Related Questions
in the number 75,462.24 the digit in the tenths place is the value of the digit in the ones place.
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the digit in the tenths place is ten times the value of the digit in the ones place.
the answer is A) 10 times
Determine two co-terminal angles (one positive and one negative) for [tex]0 = 5\pi \div 6[/tex]0 is fada
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The co-terminal angles are 510 and -210 degrees
Here, we want to get the co-terminal angle of the given angle
Co-terminal angles can be obtained by subtracting or adding 2pi to the given angle
So firstly, we have to write the given angle in degrees
Mathematically;
[tex]\begin{gathered} \frac{5\pi}{6}\text{ = 150} \\ \text{add 360 = 150 + 360 = 510} \\ \text{subtract 360 = 150-360 = -210} \\ \end{gathered}[/tex]The graph above shows a plot a data set. We know that the slope of the line of best fit is - 1/5. What vertical changeneeds to be applied to the function y = 1/5x to make the linear function best model the data set?A) a vertical change of down 5 unitsB) a vertical change of up 6 unitsC) a vertical change of up 5 unitsD) a vertical change of down 1/5 units
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C) y=-1/5x +5
1)Since the function y=-1/5x is a decreasing line, that crosses the origin.
Then the needed transformation the best fits the data set would be a vertical change up of 5 units.
2) Above the parent function y=-1/5x and y=-1/5x +5
Two sides of a triangle have the following measures. Find the range of possible measures for the third side. 8, 11
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Evaluate #2-7 given the functions f(x), g(x) and h(x) below. Show all work! x² - 1 –5 if if XS-1 xs-3 h(x) = 4 if '-13549(4) = {-x-4)-1 if x 4 x² – 5 if x 5 |x - 51 - 2 if x > 4 2. **g(4) 3. *f(-3) 4. 4. ** (-5) 5. ** h(6) 6. g(6) 7. f(-
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ANSWER:
Given following piecewise functions (Defined on more than one intervals).
[tex]h(x)\text{ =}\begin{cases}x^2-1\text{ , x }\leq-1\text{ } \\ 4,\text{ -1 }We will evaluate these functions in order as f(x) , g(x) and finally h(x).Next these functions will be evaluated.
[tex]\begin{gathered} f(-\frac{7}{2})=-5 \\ g(4)=-3 \\ h(-\frac{1}{2})=-\frac{1}{2} \end{gathered}[/tex]NOTE! To evaluate h(x) at given x, we were required to evaluate g(x) at the same x value.
This is the result of evaluating three piecewise functions at specified x values, as it was asked in the question.!
If the spinner in the photo is spun once, what is P(multiple of 3 and even)? *5/61/610/122/12the spinner is numbered 1-12
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The spiner in the photo is divided into 12 segments all numbered fro 1 to 12. That means there are a total of 12 possible outcomes for every spin. If the spinner is spun once, we want to find the probability that the outcome would be a multiple of 3. All the multiples of 3 are the expected outcomes or results of this experiment. The expected results are 3, 6, 9, and 12, which is four possible outcomes. Hence the probability of of obtaining a multiple of 3 is calculated as
P [multiple of 3] = No of expected outcomes/No of total possibilities
P [multiple of 3] = 4/12
P [multiple of 3] = 1/3
Next we note that the spinner has 6 even numbers, that is 2, 4, 6, 8, 10 and 12. The probability that the experiment yields an even number is calculated as follows;
P [even number] = No of expected outcomes/No of total possibilities
P [even number] = 6/12
p [even number] = 1/2
Therefore the probability that the spinner when spun once would result in a probability of a multiple of 3 and an even number is calculated as follows;
P [multiple of 3 and even] = P[multiple of 3] * P[even number]
P[multiple of 3 and even] = 1/3 * 1/2
P[multiple of 3 and even] = 1/6
The correct answer is Option B
Solving for x3x+2y=8 showing the steps
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The given equation is
[tex]3x+2y=8[/tex]To solve for x, first, we subtract 2y from each side.
[tex]\begin{gathered} 3x+2y-2y=8-2y \\ 3x=8-2y \end{gathered}[/tex]Then, we divide the equation by 3.
[tex]x=\frac{8-2y}{3}[/tex]Hence, the answer is [tex]x=\frac{8-2y}{3}[/tex]Really need help answering this, having trouble solvingIt’s from my ACT prep guide online
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When an angle is drawn in standard position its vertex is located at the point (0,0) in the grid and its initial side has to be located along the positive x-axis. So basically the initial side of angle A is any segment along the positive x-axis and its terminal side is the segment between (0,0) and (10,-4). Here is important to recall an important property of angles in standard position.
If its terminal side of angle A has a length of 1 unit then its extreme is given by the point (cosA,sinA). So if we find a 1 unit segment that is part of the old terminal side of A we can brand it as the new terminal side (the measure of the angle doesn't change, only the length of the side) and use its end to find the cosine of A. With the cosine of A we can find sec(A).
So first of all let's find our new terminal side. This has to be a segment inside the original terminal side that starts at point (0,0) so in order to find its end we just need to multiply (10,-4) by a positive number:
[tex]a\cdot(10,-4)=(10a,-4a)[/tex]The length of this side is given by the square root of the sum of the squares of its coordinates and it has to be equal to 1:
[tex]\begin{gathered} \sqrt[]{(10a)^2+(-4a)^2}=1 \\ \sqrt[]{100a^2+16a^2}=\sqrt[]{116a^2}=1 \end{gathered}[/tex]If we square both sides of this equation we get:
[tex]\begin{gathered} (\sqrt[]{116a^2})^2=1^2 \\ 116a^2=1 \end{gathered}[/tex]Then we divide both sides by 116 and then we apply a square root:
[tex]\begin{gathered} 116a^2=\frac{1}{116} \\ a^2=\frac{1}{116} \\ \sqrt{a^2}=\sqrt{\frac{1}{116}} \\ a=\frac{1}{\sqrt[]{116}} \end{gathered}[/tex]So the new terminal side is the segment between (0,0) and:
[tex](\frac{10}{\sqrt[]{116}},-\frac{4}{\sqrt[]{116}})[/tex]Which means that the cosine of A is:
[tex]\cos A=\frac{10}{\sqrt[]{116}}[/tex]And the secant is defined as 1 divided by the cosine so we have:
[tex]\sec A=\frac{1}{\cos A}=\frac{1}{\frac{10}{\sqrt[]{116}}}=\frac{\sqrt[]{116}}{10}[/tex]Then the answer is:
[tex]\sec A=\frac{\sqrt[]{116}}{10}[/tex]What is the rectangular form of the parametric equations?What interval does x fall under?
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Given:
[tex]\begin{gathered} x\left(t\right)=t+6 \\ y(t)=4t^2-10 \end{gathered}[/tex]Required:
To find the rectangular form of the parametric equations.
Explanation:
x(t) = t+6
t = x(t) -6
Substitute this value of x in the equation
[tex]\begin{gathered} y(t)\text{ =4t}^2-10 \\ y(t)=4(x(t)-6)^2-10 \\ y(t)\text{ = 4\lparen x\lparen t\rparen}^2-12x(t)+36)-10 \\ y(t)\text{ =4x\lparen t\rparen}^2-48x(t)+144-10 \\ y(t)\text{ = 4x\lparen t\rparen}^2-48x(t)+134 \end{gathered}[/tex]Ms. Jenkins Has two daughters. The sum of their ages is twenty-four. The product of their ages is one hundred forty. How old is Ms. Jenkins’ oldest daughter?A) 10B) 12 C) 14 D) 16
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Ms. Jenkins Has two daughters. The sum of their ages is twenty-four. The product of their ages is one hundred forty. How old is Ms. Jenkins’ oldest daughter?
Let the youngest daughter's age be y and the oldest be x.
x + y = 24
x*y = 140
Let's solve the system of equations using the substitution method:
x + y = 24
x*y = 140
x = 24-y
(24-y)*y = 140
24y-y²-140 = 0
-y²+24y -140 = 0
Now we're going to use the quadratic formula to solve the equation:
[tex]\begin{gathered} y=\frac{-b\pm\sqrt[]{b^{2}-4ac}_{}}{2a} \\ y=\frac{-24\pm\sqrt[]{576-4\cdot-1\cdot-140}}{-2} \\ y=\frac{-24\pm\sqrt[]{16}}{-2} \\ y=\frac{-20}{-2} \\ y=10 \end{gathered}[/tex]So, the daughters' ages are 10 and 14 years old.
Answer: Letter C
Do you think a rotated image would ever coincide with the original figure
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Answer:
Yes, the rotated image coincide with the original figure when the angle of translation is 360 degrees or a multiple of 360 degrees because 360 degrees is the measure of a complete rotation.
A hotel in Las Vegas is famous for its large-scale model of the Eiffel Tower. The model, built to scale, is 128 meters tall and 41 meters wide at its base. Ifthe real tower is 324 meters tall, how wide is the base of the real Eiffel Tower?
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The model of the Eiffel Tower are: tall: 128 wide 41 and the real one is 324 so we can find the constant of proporcionality with the hight of the towers so:
[tex]\begin{gathered} k=\frac{324}{128} \\ k=2.5 \end{gathered}[/tex]so the wide of the original Eiffel Tower will be:
[tex]\begin{gathered} W=41\cdot2.5 \\ W=102.5 \end{gathered}[/tex]So it has a wide of 102.5 meters
if p || , m<7 = 131°, and m<16 = 88°, find the measure of the missing angle m<3=?
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According to the property, the alternate interior angles, formed by a transversal on two parallel sides, are always equal.
Consider that in the given diagram, the lines 'p' and 'q' are parallel, and line 'r' acts as the transversal on the lines 'p' and 'q'.
And the angles 3 and 7 constitute a pair of alternate interior angles, formed by the transversal 'r' on the parallel sides 'p' and 'q'. So they must be equal,
[tex]\begin{gathered} \angle7=\angle3 \\ \angle3=131^{\circ} \end{gathered}[/tex]Thus, the angle 3 measures 131 degrees.
Calculate the final price. Round all answers to the hundredths place and make sure to write your answer in the form of $12.34. Dinner: $32.50. Discount: 20%
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If the dinner has the 20% of discount. We only need to pay the 80% of the total price, so we get:
[tex]32.5\cdot\frac{80}{100}=26.00[/tex]so the answer is
$26.00
what equation describe amonth pf money for taco truck 2, where A is the amonth of money and T is the number of tacos sold.?
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Okay, here we have this:
Considering that Truck 2 started $2 and sold 2 the tacos for $1. This mean that each taco cost $0.5, so we obtain the following:
Total amounth of money (A)=Initial Money+$0.5*Number of tacos sold (T)
Finally we obtain the following equation A=$2+$0.5(T)
Set up an equation to solve the given word problem
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Let a and b be two numbers. The first equation described in the sentence is
[tex]a=22+b[/tex]And the second equation is
[tex]ab=-121[/tex]Notice that the first equation implies that b>a, so we can rename b as x, obtaining the next two equations
[tex]\begin{gathered} a=22+x \\ ax=-121 \end{gathered}[/tex]Then,
[tex]\begin{gathered} \Rightarrow ax=(22+x)x \\ \Rightarrow x(22+x)=-121 \\ \Rightarrow x(x+22)=-121 \end{gathered}[/tex]The answer is option c.
Finally, solve the equation above for x, as shown below
[tex]\begin{gathered} x(x+22)=x^2+22x \\ \Rightarrow x^2+22x=-121 \\ \Rightarrow x^2+22x+121=0 \\ \Rightarrow(x+11)^2=0 \\ \Rightarrow x+11=0 \\ \Rightarrow x=-11 \end{gathered}[/tex]The answer is x= -11
And number a is x+22=-11+22, a=11
Find the x-intercept and y-intercept of the line.6x+3y=-6x intercept-y intercept-
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To find the x-intercept of any equation, substitute y by 0 in it
To find the y-intercept of any equation substitute x by 0 in it
The given equation is
[tex]6x+3y=6[/tex]Substitute y by 0 to find the x-intercept
[tex]\begin{gathered} y=0 \\ \\ 6x+3(0)=6 \\ \\ 6x+0=6 \\ \\ 6x=6 \end{gathered}[/tex]Divide both sides by 6
[tex]\begin{gathered} \frac{6x}{6}=\frac{6}{6} \\ \\ x=1 \end{gathered}[/tex]The x-intercept is (1, 0)
Substitute x by 0 to find the y-intercept
[tex]\begin{gathered} x=0 \\ \\ 6(0)+3y=6 \\ \\ 0+3y=6 \\ \\ 3y=6 \end{gathered}[/tex]Divide both sides by 3
[tex]\begin{gathered} \frac{3y}{3}=\frac{6}{3} \\ \\ y=2 \end{gathered}[/tex]The y-intercept is (0, 2)
x-intercept = (1, 0)
y-interscept = (0, 2)
Can someone please help me with this? I am trying but cannot figure it out.
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Remember that
Vertical intercept is the same that y-intercept (value of y when the value of x is zero)
Horizontal intercept is the same that x-intercept (value of x when the value of y is zero)
so
Graph N 1
we have the horizontal line
y=-80
Vertical intercept is the point (0,-80)
Horizontal intercept -----> Don't have
Graph N 2
we have
Vertical intercept -----> (0,-50)
Horizontal intercept -----> (40,0)
1) Complete the table with any 5 solutions for the equation. y = 4x + 1
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Using the given equation, we can find y-values for x = 0, 1, 2, 3, 4.
Let's evaluate the equation for all those values.
x = 0.
[tex]\begin{gathered} y=4x+1 \\ y=4(0)+1=1 \end{gathered}[/tex]x = 1.
[tex]y=4(1)+1=4+1=5[/tex]x = 2.
[tex]y=4(2)+1=8+1=9[/tex]x = 3.
[tex]y=4(3)+1=12+1=13[/tex]x = 4.
[tex]y=4(4)+1=16+1=17[/tex]Using these values, we complete the table.x y
0 1
1 5
2 9
3 13
4 17
Multiplication and the distributive property of 85 divided by 5
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17
Explanation
The distributive property of multiplication states that when a number is multiplied by the sum of two numbers
[tex]a\cdot(b+c)=ab+ac[/tex]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
so, 85 can be written as
[tex]\begin{gathered} \frac{85}{5} \\ (5\cdot10)+(5\cdot7)=85 \\ 5\cdot17=85 \end{gathered}[/tex]hence
I hope this helps you
Use the metric table to help complete the statement.To convert 67.9 decimeters to millimeters
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Let's make a conversion:
[tex]67.9dm\times\frac{100ml}{1dm}=6790\operatorname{mm}[/tex]Answer:
Multiply 67.9 by 10²
I need help explaining this problem or something similar to it!!
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Given:
The area of the triangle is 14 square inches.
The perpendicular (horizontal) height of the triangle is 7 inches.
To find:
The length of the shortest side.
Explanation:
Using the formula of the area of the triangle is,
[tex]A=\frac{1}{2}\times b\times h[/tex]Substituting the values we get,
[tex]\begin{gathered} 14=\frac{1}{2}\times b\times7 \\ b=\frac{14\times2}{7} \\ b=4inches \end{gathered}[/tex]Final answer:
The area of the triangle is 4 inches.
Question is stated in picture. DONT FIRGET TO ROUND TO NEAREST HUNDRETH!!!!
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In order to find the missing angle y we need to use a trigonometric function in this case the cosine because is the one that relates the adjacent side and the hypotenuse
[tex]\cos (\theta)=\frac{AS}{H}[/tex]where
θ=y
AS=8
H=13
then we substitute the values
[tex]\cos (y)=\frac{8}{13}[/tex]then we isolate the y
[tex]y=\cos ^{-1}(\frac{8}{13})[/tex][tex]y=52.02\text{\degree}[/tex]Slank 1:Question 2 (4 points)Given y = 6.510.85 identify the followingis the function a growth or decay? DecayWhat is the growth or decay factor? 235What is the growth or decay rate? 15What is the initial value?MathMLXBank 1: DecBlank 2Blank 3Blank 4
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EXPLANATION
The function y = 6.5(0.85)^x
1) It's a decay function
2) The decay factor is 0.85
3) The decay rate is 15
4) The initial value is 6.5
The number of cakes needed for party, C, is dependent upon the number of guest at the party, G. Which equation shows the number of cakes as a function of the number of guests?
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In this problem we have that
the variable independent is g
the variable dependent is c
so
f(c)=g/12
answer is the first option
I need help h(8)-2•f(3)
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Please upload the definition of the functions h(x) and f(x) so we can use them to answer the question.
We are asked to evaluate the expression
h(8) - 2 * f(3)'so we first evaluate f(3) and h(8) given the functional expressions of f an h:
f(x) = - x^2 + 8x - 11
f(3) = - 3^2 + 8 (3) - 11 = 4
h(x) = - x - 7
h(8) = - 8 - 7 = -15
Now we use these values in the requested expression:
h(8) - 2 * f(3) = - 15 - 2 * (4) = -15 - 8 = - 23
In the xy-plane, the line determined by the points (2,k) and (k, 32) passes through the origin. Which of the following could be the value of k ? A) 0 B) 4 C) 8 D) 16
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1) Considering that those points (2,k) and (k,32) determines one same line, within the plane. Therefore we can say that
2) Considering that since they pass through the origin then their x -coordinate is equal to zero, and their y coordinate as well so
3) We can state that as a matter of fact (2, k) and (K, 32) can be rewritten as (2,0) and (0,32)
k=0
hi I cricled the correct answer but I just need to solve how to get it.
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In order to solve this problem we are gonna use a trick that consist in expressing 64 and 16 as powers of 2.
We can write 64 and 16 in the following way:
[tex]\begin{gathered} 64=2^6 \\ 16=2^4 \end{gathered}[/tex]Now, we replace the equations of above in the equation of the statement:
[tex]\begin{gathered} (2^6)^{2x}=2^4 \\ 2^{6\cdot2x}=2^4 \\ 2^{12x}=2^4 \end{gathered}[/tex]In the intermediate steps we have aplied the rule that the powers multiply.
Now, in the last equation, the exponents must be equal if want to have both sides of the equation equal. So:
[tex]\begin{gathered} 12x=4 \\ x=\frac{4}{12}=\frac{1}{3} \end{gathered}[/tex]The correct answer is B
Boyle's Law states that the pressure exerted by a gas held at a constant temperature varies inversely with the volume of the gas. At a volume of 2 L the pressure of a gas is 150 kPa. If the volume of the gas is 6 L, what would be the pressure of the gas in kPa?
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Here, we want to use the proportionality to get the value of the pressure of the gas
From the question, we have it that the pressure and the volume are inversely related at constant temperature
Let us have the pressure as P, volume as V and temperature as T
Thus, we have the relationship as follows;
[tex]\begin{gathered} P\text{ }\propto\text{ }\frac{1}{V} \\ PV\text{ = T} \\ \\ At\text{ V = 2 and P = 150} \\ T\text{ = 150}\times2\text{ = 300} \\ \end{gathered}[/tex]When V = 6, we have P as follows;
[tex]\begin{gathered} 6\times P\text{ = 300} \\ P\text{ = }\frac{300}{6} \\ P\text{ = 50 KPa} \end{gathered}[/tex]Determine if the side lengths could form a triangle. Use an inequality to justify your answer.34 km, 27 km, 58 km
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At first we should know that:
The sum of two sides of the triangle must be greater than the third side
So, we will chick the given side lengths 34 km, 27 km, 58 km
So,
34 + 27 = 61 > 58
34 + 58 = 92 > 27
27 + 58 = 85 > 34
So, the side lengths could form a triangle.