In order to identify bounds on the real zeros of this polynomial, first we need to find tendencies about the signal of f(x)
We know that the two term with highest degree is being multiplied by a positive coefficient. Therefore, we can initially conclude the f(x) tends to positive infinite as x grows either positive or negative.
We can check that, for x = -2, the first term is 272, and the remaining thermis togheter are given by:
[tex]17\cdot(-2)^3-(-2)^2-68\cdot(-2)-68=-72[/tex]Then for x < -2, and for also for x > 2, we can state for sure that f(x) remains always positive.
Then, any possible roots must lies in the intervel (-2,2)
e can also chegck that, for x = 1, f(x) = -103, and, for x = -1, f(x) = -1.
Therefore, f(x) must have a root between
Write a recursive definition for the following function. 40, 120,360,1080,3240
The recursive definition of the given geometric series is [tex]40 \times (3)^n[/tex]
What is geometric series?
Geometric series are those series in which ratio between the consecutive terms of the series are same.
Here the series is in geometric progression with a common ratio of 3
and first term 40
So the recursive definition of the given geometric series is [tex]40 \times (3)^n[/tex]
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options 1. a (-3,50) b (-2,0) c (0,-4) d (1,-6) 2. a (-3,50) b (0,-4) c (-1,-6) d (2,0)3. a (-3,50) b (-2,0) c (0,-4) d (2,0)
Answer:
The x-intercepts shown in the table are (-2, 0) and (2, 0).
The y-intercept shown in the table is (0, -4)
Explanation:
The x-intercepts are the points where the value of f(x) is 0. Then, these points are (-2, 0) and (2, 0)
Additionally, the y-intercept is the point where the value of x is 0, so the y-intercept is (0, -4).
Then, the answers are:
The x-intercepts shown in the table are (-2, 0) and (2, 0).
The y-intercept shown in the table is (0, -4)
Fourteen more than 4 times a number is 42what is equation?what is solution?
We have to express this phrase in mathematical terms.
We call the number x.
Then, four times a number is "4x".
Fourtenn more than 4x is "4x+14", and this is equal to 42.
Then, we can write:
[tex]4x+14=42[/tex]And solve as:
[tex]\begin{gathered} 4x+14=42 \\ 4x=42-14 \\ 4x=28 \\ x=\frac{28}{4} \\ x=7 \end{gathered}[/tex]Answer: the equation is 4x+14=42 and the solution is x=7
Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $30 and same-day tickets cost $15. For one performance,there were 50 tickets sold in all, and the total amount paid for them was $1275. How many tickets of each type were sold?
Given:
there are two types of tickets to a show: advance and same-day
Let the number of tickets from the type of Advance = x
And the number of tickets from the type of Same-day = y
there were 50 tickets sold in all
So,
[tex]x+y=50\rightarrow(1)[/tex]Advance tickets cost $30 and same-day tickets cost $15.
the total amount paid for them was $1275
So,
[tex]30x+15y=1275\rightarrow(2)[/tex]Solve the equations (1) and (2) to find (x) and (y)
[tex]\begin{gathered} x+y=50\rightarrow(\times-15) \\ 30x+15y=1275 \\ ============= \\ -15x-15y=-750 \\ 30x+15y=1275 \\ ============= \\ 15x=525 \\ x=\frac{525}{15}=35 \\ y=50-x=50-35=15 \end{gathered}[/tex]So, The answer will be:
The number of tickets from the type of Advance = x = 35
And the number of tickets from the type of Same-day = y = 15
GIVEN: P(N) = 0.25 and P(R) = 0.6If the probability of P(N R) = 0.15, are N and Rindependent events?a) Yes, because P(N) + P(R) +0.15b) No, because P(N).P(R) +0.15c) Yes, because P(N) X P(R) = 0.15d) Not enough information
P(N∩R) represents the probability of A and B.
When two events are independent events, the joint probability is calculated by multiplying their individual probabilities.
P(N∩R) For independent events:
[tex]P\mleft(N\cap R\mright)=P(N)\times P(R)[/tex]Substituting the known values for P(N) and P(R):
[tex]\begin{gathered} P(N\cap R)=0.25\times0.6 \\ P(N\cap R)=0.15 \end{gathered}[/tex]0.15 is the value of P(N∩R) given by the problem, and since we get the same result using the formula for independent events, we can affirm that N and R independent events.
Answer:
c) Yes, because P(N) X P(R) = 0.15
y=x-8 how would I do it
to find two points that satisfy the function, you need to give one value and calculate the other one, for example.
I will use x=4 and x=8
when x=4
y=4-8=-4
so one point is (4,-4)
and when x=8
y=8-8=0
so the other point is (8,0)
so you need to graph these points and then plot the line, like this:
nine cubes are glued together to form the solid shown in the digram .
ANSWER
D. 272.25 mm²
EXPLANATION
First we have to find the area of one face of one cube:
[tex]A=2.75^2=7.5625\operatorname{mm}^2[/tex]Now we have to count how many faces of the squares are in the surface of the solid. Or a faster way is to multiply the total number of faces of the 9 cubes: 6*9=54 and subtract the number of faces that are not on the surface:
There are 18 faces of the cubes that are not on the surface of the solid. The number of faces from the 9 cubes that are on the surface of the solid is:
[tex]54-18=36[/tex]The surface area of the solid is the area of a face of one cube multiplied by the number of faces on the surface of the solid:
[tex]SA=36\cdot A=36\cdot7.5625=272.25\operatorname{mm}^2[/tex]Answer:
D. 272.25 mm²
Step-by-step explanation:
Find f in:f ÷ -2/3 = -1/3
ANSWER
[tex]f\text{ = }\frac{2}{9}[/tex]EXPLANATION
We want to find f in:
[tex]f\text{ }\div\text{ -}\frac{2}{3}\text{ = -}\frac{1}{3}[/tex]To do that, we multiply both sides by -2/3.
That way, it cancels out the -2/3 on the left hand side and isolates f.
So we have:
[tex]\begin{gathered} f\text{ }\div(-\frac{2}{3})\cdot\text{ (-}\frac{2}{3})\text{ = -}\frac{1}{3}\cdot\text{ -}\frac{2}{3} \\ f\text{ = }\frac{2}{9} \end{gathered}[/tex]That is the answer.
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The length of given sides BC = 38 and EF = 38.
Given:
ΔABC ≅ ΔDEF
BC = x + 30 , EF = 4x + 6
we know that
BC = EF
x + 30 = 4x + 6
30 - 6 = 4x - x
24 = 3x
divide by 3 on both sides
3x/3 = 24/3
x = 8
BC = x + 30
= 8 + 30
= 38
EF = 4x + 6
= 4*8 + 6
= 32+6
= 38
Therefore the length of given sides BC = 38 and EF = 38.
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Suppose that a regression line for some data transformed with logarithmspredicts that when y equals 8, log(%) will equal 1.603. What does theregression line predict y will equal when y equals 8? Round your answer to thenearest whole number.
Given the relationship between y and x to be
[tex]y=a^x\text{ ------ equation 1}[/tex]Take the logarithm of both sides,
[tex]\begin{gathered} \log y=\log ^{}_{}a^x \\ \Rightarrow\log \text{ y = x }\times\text{ log a ---- equation 2} \end{gathered}[/tex]But when x = 8, log y = 1.603.
Thus, substituting the above values into equation 2, we have
[tex]\begin{gathered} 1.603\text{ = 8 }\times\text{ log a} \\ \text{divide both sides by 8} \\ \log \text{ a= }\frac{1.603}{8} \\ \Rightarrow\log \text{ a =0.2}004 \\ \text{Thus, } \\ a=1.586 \end{gathered}[/tex]From equation 1,
[tex]\begin{gathered} y=a^x \\ \Rightarrow y=1.586^x\text{ ----- equation 3} \end{gathered}[/tex]Thus, when x = 8
[tex]\begin{gathered} y=1.586^x \\ y=1.586^8 \\ \Rightarrow y=40.03 \end{gathered}[/tex]Thus, the value of y will be 40 (to the nearest whole number)
The correct option is D
how many FULL cases of oil can you get from a 150-gallon oil tank?
Given
The job is to fill the quart size of bottles, from a full 150 gallon oil tank.
And, the oil is packed into 24 quart's of oil.
To find the number of full cases of oil.
Explanation:
It is given that,
The total amount of oil is 150 gallon.
The number of cases it has to be filled is, 24.
Then, the number of the full cases of oil is,
[tex]\begin{gathered} Number\text{ of full cases of oil}=\frac{150}{24} \\ =\frac{50}{8} \\ =\frac{25}{4} \\ =\frac{24}{4}+\frac{1}{4} \\ =6+\frac{1}{4} \\ =6\frac{1}{4} \end{gathered}[/tex]Hence, the number of full cases of oil is 6.
Find the length of x.43a. 2.5b. 3C. 4d. 5e. 656
the given triangle is a right angle triangle.
by Pythagoras theorem.
4^2 + 3^2 = x^2
16 + 9 = X^2
25 = x^2
[tex]\begin{gathered} x^2=25 \\ x=5 \end{gathered}[/tex]so, the answer is x = 5.
the sum of three consecutive integers is 267.what is that largest interger
The sum of three consecutive integers is 267. If the first one is a, then the second would be a + 1, while the third would be a + 2. Therefore, you would have;
[tex]\begin{gathered} a+(a+1)+(a+2)=267 \\ a+a+1+a+2=267 \\ 3a+3=267 \\ \text{Subtract 3 from both sides} \\ 3a=264 \\ \text{Divide both sides by 3} \\ a=88 \end{gathered}[/tex]The largest (third) integer is a + 2, therefore
[tex]\begin{gathered} a+2=88+2 \\ a+2=90 \end{gathered}[/tex]The largest integer therefore is 90.
Use the Law of Cosines to determine the indicated angle 0. (Assume a = 65.01, b = 36.38, and c = 42.05. Round your answer to two decimal places.)
a = 65.01, b = 36.38, and c = 42.05.
And it is required to find the measure of angle 0 which will be the angle B
Using the law of cosine
[tex]\begin{gathered} b^2=a^2+c^2-2\cdot a\cdot c\cdot\cos B \\ \cos B=\frac{a^2+c^2-b^2}{2\cdot a\cdot c}=\frac{65.01^2+42.05^2-36.38^2}{2\cdot65.01\cdot42.05}=0.854 \\ \end{gathered}[/tex][tex]\angle\emptyset=\angle B=\cos ^{-1}0.854=31.31[/tex]the answer is rounded to two decimals
Introduction to Chord LengthsINPlace the following expressions so that they can be used to solve for X11 781211 7.8 1211 INN111712
SOLUTION
We know that the diameter of the circle is 18.8.
Therefore the value of its radius will be.
[tex]\frac{18.8}{2}[/tex]And we also know that the radius from the diagram is:
[tex]x+4.2[/tex]So we can equate both equations together to have an idea of what will give us the value of x.
[tex]\begin{gathered} \frac{18.8}{2}=x+4.2 \\ \text{Collect like terms} \\ \frac{18.8}{2}-4.2=x \end{gathered}[/tex]So going by the above solutions, the answers we will drag into the two boxes will be the 4th expression and the 6th expression
THAT IS:
[tex]\begin{gathered} \frac{18.8}{2} \\ \text{and} \\ -4.2 \end{gathered}[/tex]the dealer in a card game draws three cards from a deck of 52 cards and places them face-up on the table select all the correct probabilities
Explanation:
nCx give us the number of ways in which we can select x cards from a group of n cards.
So, the number of ways in which we can select 3 cards from 52 is:
52C3.
On the other hand, the number of ways to select 3 cards but none of them are kings is 48C3 because there are 48 cards that aren't kings. So:
[tex]P(no\text{ Kings)=}\frac{_{48}C_3}{_{52}C_3}[/tex]The number of ways to draw 2 fives is: 4C2*48C1
Because the dealer needs to draw 2 cards from the 4 that are fives and 1 card from the other 48 cards. So, P(2 fives) is:
[tex]P(\text{ 2 fives)=}\frac{_4C_2\times_{48}C_1}{_{52}C_3}[/tex]The number of ways to draw 1 heart and 2 spades is: 13C1*13C2
Because there are 13 heart cards and 13 spades cards. So, P(1 heart and 2 spades) is:
[tex]P(1\text{ Heart and 2 spades) = }\frac{_{13}C_1\times_{13}C_2_{}}{_{52}C_3}[/tex]Finally, the number of ways to select 4 aces and 1 ten is
Jane has a pre-paid cell phone with A Fee and Fee. She can't remember the exact costs, but her plan has a monthly fee and a charge for each minute of calling time. In June she used 430 minutes and the cost was $227.50. In July she used 780 minutes and the cost was $385.00.
Given:
the plan of the pre-paid cell phone
The plan has a monthly fee and a charge for each minute
Let the monthly cost = C
and the number of minutes = x
the general equation will be:
C = ax + b
Where (b) is the monthly fee, and (a) is the charge per minute
We will find the values of (a) and (b) using the following:
1) 430 minutes cost $227.50
2) 780 minutes cost $385.00.
So, we have the following equations:
[tex]\begin{gathered} 430a+b=227.5\rightarrow(1) \\ 780a+b=385\rightarrow(2) \end{gathered}[/tex]Solve the equations, subtract equation (1) from (2) to eliminate (b), and solve for (a):
[tex]\begin{gathered} 780a-430a=385-227.5 \\ 350a=157.5 \\ a=\frac{157.5}{350}=0.45 \end{gathered}[/tex]Substitute with (a) into equation (1) to find the value of (b)
[tex]\begin{gathered} 430\cdot0.45+b=227.5 \\ 193.5+b=227.5 \\ b=227.5-193.5=34 \end{gathered}[/tex]So, the equation of the monthly cost will be:
[tex]C=0.45x+34[/tex]Part (b): When x = 484 minutes, we will find C
so, substitute with (x) into the equation of C
[tex]\begin{gathered} C=0.45\times484+34 \\ C=217.8+34 \\ C=251.8 \end{gathered}[/tex]So, the answer will be:
A) C = 0.45x + 34
B) $251.8
Carmelo puts $2,200.00 into savings bonds that pay a simple interest rate of 3.4%. How much money will the bonds be worth at the end of 5.5 years? (Find the total worth of the bonds in 5.5 years)
Let's begin by listing out the information given to us:
Principal (P) = $2,200, Interest rate (r) = 3.4% = 0.034, Time (t) = 5.5 years
[tex]\begin{gathered} I=P\cdot r\cdot t=2200\cdot0.034\cdot5.5 \\ I=\text{ \$414.40} \end{gathered}[/tex]The bond will be worth the sum of the Principal and the Interest:
[tex]\begin{gathered} P+I=2200+411.40 \\ \Rightarrow\text{ \$}2611.40 \end{gathered}[/tex]which line is steeper y=+2 or y= -7/3x -5
The inclination of the lines in the coordinate system is given by their slopes, so to determine which line is steeper you have to compare the absolute values of both slopes.
The first equation y=2 has no slope, if you draw it you will see that for any value of x, y doesn't change, it is always 2.
You can also say that the slope of this equation is equal to zero.
For the second equation y=-7/3x-5, the slope is equal to -7/3.
The second equation is steeper than the first one since the absolute value of its slope is greater.
Find the perimeter of each circle. Use 3 for pi.
Part 1
We need to find the perimeter of a circle with a diameter of 18 inches.
The relation between the perimeter P and the diameter d is given by:
[tex]P=\pi d[/tex]Since d = 18 inches and we need to use 3 for π, we obtain:
[tex]P=3\cdot18\text{ inches }=54\text{ inches}[/tex]Therefore, the ribbon needs to be 54 inches long.
Part 2
We need to find the perimeter of a semicircle with a radius of 8 in.
The perimeter of this semicircle is the sum of half the perimeter of the whole circle and the line segment formed by two radii.
The relation between the perimeter P and the radius r of a circle is:
[tex]P=2\pi r[/tex]Thus, half the perimeter is:
[tex]\frac{P}{2}=\pi r[/tex]Since we need to use 3 for π and r = 8 in, we obtain:
[tex]\frac{P}{2}=3\cdot8\text{ in }=24\text{ in}[/tex]And the line segment measures:
[tex]2\cdot8\text{ in }=16\text{ in}[/tex]Therefore, the perimeter of the calzone is:
[tex]24\text{ in }+16\text{ in }=40\text{ in}[/tex]Answer: 40 in.
Solve the equation involving absolute value. Type you answers from smallest to largest. If an answer is not an integer then type it as a decimal rounded to the nearest hundredth. |x^2+2x-36|=12 x=Answer, Answer, Answer and Answer
Given:
The euqation is,
[tex]|x^2+2x-36|=12[/tex]Explanation:
Simplify the equation.
[tex]\begin{gathered} |x^2+2x-36|=12 \\ x^2+2x-36=\pm12 \end{gathered}[/tex]Solve the x^2 + 2x - 36 = 12 for x.
[tex]\begin{gathered} x^2+2x-36=12 \\ x^2+2x-36-12=0 \\ x^2+8x-6x-48=0 \\ x(x+8)-6(x-8)=0 \\ (x+8)(x-6)=0 \\ x=-8,6 \end{gathered}[/tex]Solve the equation x^2 + 2x - 36 = -12 for x.
[tex]\begin{gathered} x^2+2x-36+12=0 \\ x^2+2x-24=0 \\ x^2+6x-4x-24=0 \\ x(x+6)-4(x+6)=0 \\ (x+6)(x-4)=0 \\ x=-6,4 \end{gathered}[/tex]Thus solution of the equation is x = -8, -6, 4, and 6
1 Write the missing power of ten.0.04 x 10 = 0.4
Notice that in the number 0.4, the decimal point appears shifted one place to the right with respect to the number 0.04. When we multiply a number by the power 10^n, the decimal point is shifted n places to the right. Therefore, the power of 10 needed to move the decimal point from 0.04 one place to the right to get 0.4 is 1.
Therefore, the missing power of the base 10 is:
[tex]1[/tex]So, we can write:
[tex]0.04\times10^1=0.4[/tex]I need help with my math
At an amusement park, the two most popular rollercoasters are the Python and the Vortex. The Python is 212 feet long and the Vortex is 210 feet long. How many times as long is the Python as the Vortex?
Answer:
About 1.01 times longer
Step-by-step explanation:
we have to divide 212 by 210 since these are the lengths to get about 1.01.
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Which is the best estimate of 162% of 79?
We have to multiply 79 by the percentage in decimal form ( divided by 100)
79 x (162/100) = 79 x 1.62 = 127.98
rounded: 128
The best estimate is 128
2cuestionAngelique is buying towels for her apartment. She finds some green towels, x, that cost $5 each and bluetowels, y, that cost $9 each. She wants to buy at least 4 towels, but does not want to spend more than$38. How many of each towel can she purchase?Enter the system of inequalities that represents the situation. Then select the graph of the system andselect one possible solution.The system of inequalities
x: green towels (each one cost $5)
y: blue towels (each one cost $9)
She wants to buy at least 4 towels:
[tex]x+y\ge4[/tex]She does not want to spend more than $38:
[tex]5x+9y\leq38[/tex]The sytem of inequalitites is:
[tex]\begin{gathered} x+y\ge4 \\ 5x+9y\leq38 \end{gathered}[/tex]Graph: First inequality in red, second inequality in blue
Solution: Area shaded of both colours
[tex]undefined[/tex]Can someone please help me solve this problem number 9
The perimeter of the room was calculated in question 6, and it is 54 feet.
Since the borders come in 5-yard rolls, let's first convert 54 feet to yards.
Each yard has 3 feet, so we can divide the amount of feet by 3 to get it converted to yards:
[tex]\frac{54}{3}=18[/tex]Thus, the perimeter of the room is 18 yards. Since each roll has 5 yards,we will need:
[tex]\frac{18}{5}=3.6[/tex]Abou 3.6 rolls, but since we can only have whole rolls, we will have to approximate it to 4 rolls.
A full one- gallon container can beused to fill the one-liter containers, as shownbelow. Write a unit rate that estimates thenumber of liters per gallons.
Explanation
Step 1
as we can see in the picture
[tex]1\text{ gallons}\rightarrow3\text{ liters}[/tex]so, to find the unit rate make
[tex]\begin{gathered} \text{unit rate=}\frac{Number\text{ of liters}}{Number\text{ of gallons}} \\ \text{replace} \\ \text{Unit rate=}\frac{3\text{ liters}}{1\text{ gallon}}=\text{ 3 liters per gallon} \end{gathered}[/tex]I hope this helps you
Identify the normal equations of an exponential curve.ΣxY = AΣx + BΣx2 and ΣY = nA + BΣxΣxY = AΣx + BΣx2 and ΣY = A + BΣxΣxY = AΣx - BΣx2 and ΣY = nA + BΣxΣxY = AΣx + BΣx2 and ΣY = nA - BΣx
Given
The normal equations of an exponential curve.
Solution
[tex]The\text{ exponential equation is y=ax}^b[/tex]taking logarithm on both sides, we get
[tex]\begin{gathered} log10y=log10a+blog10x \\ \\ Y=A+bXwhereY=log10y,A=log10a,X=log10x \end{gathered}[/tex]which linear in Y,X
So the corresponding normal equations are
[tex]\begin{gathered} ∑Y=nA+b∑X \\ \\ ∑XY=A∑X+b∑X2 \end{gathered}[/tex]The final answer
Option A
What is the the musical instrument that is a pair of clash cymbals, originating in the Indian subcontinent, which makes high- pitched percussion sounds?
SOLUTION:
Step 1:
In this question, we are asked to find the musical instrument that is a pair of clash cymbals, originating in the Indian subcontinent, which makes high- pitched percussion sounds.
Step 2:
The details of the solution are as follows:
The Taal is a pair of clash cymbals, originating in the Indian subcontinent, which makes high-pitched percussion sounds. In its simplest form, it consists of a pair of small hand cymbals.
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