Identify the number fo zeros for each function. Show your work.
1. P(x)=x³+2x²-12x+1
2.P(x)=2x⁵-5x+10
3.P(x)=3x⁴+2x
Answers
The number of zeros for each function is given as follows:
1. Three zeros.
2. One zero.
3. Two zeros.
How to obtain the number of zeros for each function?The number of zeros for each function is obtained looking at the graph of the function, counting the number of times that the function either touches or crosses the x-axis, which is the horizontal axis.
Thus the graph for each function is plotted, using a graphing calculator, as shown by the image at the end of the answer, and the number of zeros for each of the functions is given by the number of times that the function touches or crosses the x-axis.
The colors of each function are given as follows:
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Related Questions
If her garden is 2 square feet, she can grow 8 carrots at a time. Write the equation for the relationship between x and y
Answers
Let's assume that x represents the number of square feet in the garden, and y represents the number of carrots that can be grown at a time.
We are given that when the garden is 2 square feet, she can grow 8 carrots at a time. This suggests a linear relationship between x and y.
To find the equation, we can use the concept of proportionality. Since the number of carrots grown is directly proportional to the area of the garden, we can set up a proportion:
x/y = 2/8
Cross-multiplying, we have:
8x = 2y
Dividing both sides by 2, we get:
4x = y
So, the equation for the relationship between x and y is y = 4x.
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(ANSWER #17!)
PLEASE HELP!
Answers
The linear function y = -x + 2 is graphed at the end of the function.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, we have that:
The y-intercept is of 2, hence b = 2.The x-intercept of 2 means that when y = 0, x = 2.The limits mean that the function is decaying, that is, the slope is negative.Then:
y = mx + 2.
When y = 0, x = 2, hence:
0 = 2m + 2
2m = -2
m = -1.
Then the function is:
y = -x + 2.
The function is graphed at the end of the answer.
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write a compound inequality that represents each situation. graph your solution.
Answers
The answer is the first option -6
Because we are looking numbers that are stricly bigger than -6 and stricly smaller than 6, we need to use < or >, and not the ≤ or ≥.
Then we can rule aout t
if a person randomly draws two cards without replacement, find the probability of drawing a seven and then a four.
Answers
The probability of drawing a seven and then a four when randomly drawing two cards without replacement is 0.0045 or approximately 0.45%.
The probability of drawing a seven and then a four when randomly drawing two cards without replacement can be calculated using the following steps:
First, we need to determine the total number of possible outcomes when drawing two cards from a standard deck of 52 cards without replacement. This can be found using the combination formula:
C(52,2) = 52! / (2! * (52-2)!) = 1,326
Next, we need to determine the number of favorable outcomes where we draw a seven and then a four.
There are four sevens and four fours in a deck of 52 cards, so the probability of drawing a seven on the first draw is 4/52. Since we are not replacing the card, there are now 51 cards left in the deck, and three of them are fours. Therefore, the probability of drawing a four on the second draw is 3/51.
The probability of drawing a seven and then a four is the product of the probabilities of drawing a seven on the first draw and a four on the second draw:
P(seven and then four) = (4/52) * (3/51) = 0.0045 or approximately 0.45%.
Therefore, the probability of drawing a seven and then a four when without replacement is 0.0045 or approximately 0.45%.
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Consider the vector field \( \vec{F}=\langle 3 x+4 y, 4 x+6 y\rangle \) Is this vector field Conservative? If so: Find a function \( f \) so that \( \vec{F}=\nabla f \) \( f(x, y)= \) \( +\mathrm{K} \
Answers
The vector field is not conservative since its curl is non-zero. Therefore, there is no function \( f \) such that \( \vec{F} = \nabla f \).
To determine if the vector field \( \vec{F} = \langle 3x+4y, 4x+6y \rangle \) is conservative, we can check if its curl is zero. If the curl is zero, then the vector field is conservative. Let's calculate the curl of \( \vec{F} \):
The curl of \( \vec{F} \) is given by:
\( \nabla \times \vec{F} = \left( \frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z} \right) \times \langle 3x+4y, 4x+6y \rangle \)
Expanding the cross product, we get:
\( \nabla \times \vec{F} = \left( \frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z} \right) \times \langle 3x+4y, 4x+6y \rangle \)
\( = \left( \frac{\partial}{\partial y} (4x+6y) - \frac{\partial}{\partial z} (4x+6y), \frac{\partial}{\partial z} (3x+4y) - \frac{\partial}{\partial x} (4x+6y), \frac{\partial}{\partial x} (4x+6y) - \frac{\partial}{\partial y} (3x+4y) \right) \)
\( = \langle 6-6, 0-4, 4-3 \rangle \)
\( = \langle 0, -4, 1 \rangle \)
Since the curl of \( \vec{F} \) is not zero (it has non-zero components), the vector field \( \vec{F} \) is not conservative.
Therefore, the vector field is not conservative since its curl is non-zero. Therefore, there is no function \( f \) such that \( \vec{F} = \nabla f \).
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Find the volume of a pyramid whose height is 10.5 feet and whose base is a rectangle with dimensions of 7.2 feet by 6.9 feet.
Answers
A pyramid has a volume of 173.88 ft3, is 10.5 feet tall, and has a rectangle-shaped base that is 7.2 feet by 6.9 feet in size.
A rectangular pyramid has five faces altogether. Its rectangular base serves as one face, and the remaining four faces are all triangular in shape. All of the triangles in this are congruent with the triangle to the opposite. The formula for a pyramid's total surface area is 12 pl + B, where p is the base's perimeter, l is the pyramid's slant height, and B is the base's area.
The volume of a rectangular pyramid is found using the formula Volume = 1/3 × base area × height.
height is 10.5 feet
dimensions of 7.2 feet by 6.9 feet.
volume = L× B × H /3
volume = 7.2·6.9·10.5 /3
volume = 173.88ft³.
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2/3h-2/3h+11=8 solve this equation , check steps
Answers
Answer:
Step-by-step explanation:
There is no answer if the question is as written. If you subtract 2/3 h from 2/3 h you get 0.
That means that 11 = 8 which has no meaning.
chris has been given a list of bands and asked to place a vote. his vote must have the names of his favorite and second favorite bands from the list. how many different votes are possible?
Answers
There are nC2 different votes possible, where n is the number of bands on the list and nC2 represents the number of ways to choose 2 bands out of n.
To calculate nC2, we can use the formula for combinations, which is given by n! / (2! * (n-2)!), where ! represents factorial.
Let's say there are m bands on the list. The number of ways to choose 2 bands out of m can be calculated as m! / (2! * (m-2)!). Simplifying this expression further, we get m * (m-1) / 2.
Therefore, the number of different votes possible is m * (m-1) / 2.
In the given scenario, we don't have the specific number of bands on the list, so we cannot provide an exact number of different votes. However, you can calculate it by substituting the appropriate value of m into the formula m * (m-1) / 2.
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11634 Ibm/h of a 80 weight% H2SO4 solution in water at 120F is continuously diluted with chilled water at 40F to yield a stream
containing 50 weight % H2SO4 at 140F. What is the rate of heat transfer in Btu/h for the mixing process? Assume that the chilled
water is saturated liquid.
Answers
The rate of heat transfer in Btu/h for the mixing process is given by Q = -9.282mi + 15000. The heat transfer rate, we can use the formula Q = mcΔT, where Q is the heat transferred, m is the mass, c is the specific heat, and ΔT is the change in temperature.
First, we need to calculate the mass and specific heat of the solution by applying mass balance and energy balance equations.
Mass balance:
mi = mf (1)
where mi is the mass flow rate of the initial solution, and mf is the mass flow rate of the final stream.
From the mass balance equation, we have:
mi = mf + mw (2)
where mw is the mass flow rate of water.
The weight percent of the solution can be expressed in terms of specific gravity (SG) using the equation:
w = [(SG - 1)/(SG + 1)] × 100
The specific gravity of the solution can be calculated using the equation:
SG = 1.0054 + 0.0005 × °API + 0.0012 × % H2SO4
The specific heat of the solution (cp) can be calculated using the equation:
cp = 0.4479 + 0.000125 * t
The mass flow rate of water is:
m w = 150 - mi [lb/h]
We will use the energy balance equation to calculate the rate of heat transfer:
Q = mi × cp × ΔTi + mW × cW × ΔTw
where ΔTi = 120 - 140 = -20°F (temperature drop of H2SO4 solution)
cP = 0.4479 + 0.000125 × 120 = 0.4629 Btu/lbm °F
Tw = 40 - 140 = -100°F (temperature drop of water)
cW = 1 Btu/lbm °F (specific heat of water)
So,
Q = (mi × 0.4629 × -20) + (150 - mi) × 1 × -100
Q = -9.258mi + 15000
Since the stream contains 50 weight% of H2SO4, the mass flow rate of the final stream, mf = mi, and the mass flow rate of water, mw = 150 - mi.
From equation (2):
mi + mw = mf
The final stream contains 50 weight% of H2SO4, therefore:
0.5 = [(SG - 1)/(SG + 1)] × 100
=> SG = 1.2
From the equation:
SG = 1.0054 + 0.0005 * °API + 0.0012 * %H2SO4
=> 1.2 = 1.0054 + 0.0012 × %H2SO4
=> %H2SO4 = 165
Therefore, the specific gravity of the final solution is 1.2 at 140°F. The specific heat of the final solution (cp) can be calculated using the equation:
cp = 0.4479 + 0.000125 * 140 = 0.4641 Btu/lbm °F
We will apply the energy balance equation to calculate the heat transfer rate:
Q = mi × cp × ΔTi + mW × cW × ΔTw
Q = (mi × 0.4641 × -20) + (150 - mi) ×
1 × -100
Q = -9.282mi + 15000
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The circle below has a center D and its diameter is 10 feet. Given that m angle A D B equals 35 degree, find the length of major arc stack A C B with overparenthesis on top.
A circle with center D and points A B C on the circle. Angle A D B is 35 degrees formed by radius B D and A D.
Group of answer choices
35 over 36 straight pi feet
325 over 18 straight pi feet
325 over 36 straight pi feet
35 over 18 straight pi feet
Answers
The length of major arc ACB with angle measure of 325° and diameter of 10 feet is (325/36)π
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
angle of arc ACB = 360° - 35° = 325°
The length of major arc ACB = (325/360) * π * 10 = (325/36)π
The length of major arc ACB with angle measure of 325° and diameter of 10 feet is (325/36)π
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the melting point of each of 16 samples of a certain brand of hydrogenated vegetable oil was determined, resulting in a sample mean of 94.32. assume the distribution of melting point is normal with a population standard deviation of 1.20. does the true mean melting point differ from 95? use a significance level of 0.01
Answers
We do not have enough evidence to conclude that the true mean melting point differs from 95 at a significance level of 0.01.
To determine if the true mean melting point differs from 95, we can use a one-sample t-test with a significance level of 0.01.
The null hypothesis is that the true mean melting point is equal to 95, and the alternative hypothesis is that the true mean melting point is different from 95.
We can calculate the t-statistic using the formula:
t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))
where sample size is 16, sample mean is 94.32, hypothesized mean is 95, and sample standard deviation is the same as the population standard deviation of 1.20.
Plugging in these values, we get:
\(t = (94.32 - 95) / (1.20 / \sqrt{(16)} ) = -2.6667\)
Using a t-distribution table with 15 degrees of freedom (n-1=16-1), and a two-tailed test at a significance level of 0.01, the critical t-value is ±2.947.
Since our calculated t-value of -2.6667 falls within the acceptance region (-2.947 < -2.6667 < 2.947), we fail to reject the null hypothesis.
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For what value of x is the rational expression below undefined? 3x-12/9-x
A.9
B.-4
C.-9
D.4
Answers
Answer:
9 (A)
Step-by-step explanation:
9 makes the denominator 0, which cannot be possible in a fraction.
50 Points
Show your steps of the conversion of the decimal numbers write in your own steps.
1. 3
2. 8
3. 15
4. 18
5. 33
6. 49
7. 64
8. 108
9. 251
Answers
\(\\ \tt\longrightarrow 3=\dfrac{3}{10}=0.3\)
\(\\ \tt\longrightarrow 8=\dfrac{8}{10}=0.8\)
\(\\ \tt\longrightarrow 15=\dfrac{15}{100}=0.15\)
\(\\ \tt\longrightarrow \dfrac{18}{10}=1.8\)
\(\\ \tt\longrightarrow 33=\dfrac{33}{100}=0.33\)
\(\\ \tt\longrightarrow 49=\dfrac{49}{100}=0.49\)
\(\\ \tt\longrightarrow 64=\dfrac{64}{100}=0.64\)
\(\\ \tt\longrightarrow 108=\dfrac{108}{100}=1.08=1.1\)
\(\\ \tt\longrightarrow 251=\dfrac{251}{1000}=0.251\)
Which equation represents the relationship between the
number of pets Scott watches and his fees?
Answers
Given the points (1,8), (2,11), (3,14), (2,17) we can use the table to figure out what our equation will be
Notice on the table as you go on the y term from 8 to 11 to 14 to 17 you are having a constant rate of change of 3. So that’s your change in y
On the left side which is your x, you are going up by 1 every time because it’s {1,2,3,4} So your change in x is 1
Your slope or m in y=mx+b can be found by using the following formula
Change in y/change in x
So here our change in y is 3 and our change in x is 1. So that means our slope is
m=3/1 = 3
y=3x+b
To find b, you can plug in one of the points. Let’s use (1,8). So x=1 and y=8. Now we can plug these in and solve for b.
8=3(1)+b
8=3+b
Subtracting 3 on both sides we have
b=5
Therefore given y=3x+(b) we can plug b in to obtain the following equation
y=3x+5. So that’s your answer
I hope this helps!!! Mark for brainliest!!!
21. Select Yes or No to indicate whether each ordered pair is a point of intersection between the line y = 2x + 4 and the parabola y = x² + 4x + 1
Ordered Pairs
(-3,-2)
(1,6)
(0,4)
Answers
Yes (-3,-2) is true.
No (1,6) is false
No (0,4) is false
How to determine the ordered pairTo determine if an ordered pair is a point of intersection between the line and the parabola, we need to check if the coordinates satisfy both equations.
(-3, -2)
y = 2x + 4 => -2
= 2(-3) + 4 => -2 = -2 (True)
y = x² + 4x + 1 => -2
= (-3)² + 4(-3) + 1 => -2 = -2 (True)
Answer: Yes
(1, 6)
y = 2x + 4 => 6
= 2(1) + 4 => 6 = 6 (True)
y = x² + 4x + 1 => 6
= (1)² + 4(1) + 1 => 6 ≠ 6 (False)
Answer: No
(0, 4)
y = 2x + 4 => 4
= 2(0) + 4 => 4 = 4 (True)
y = x² + 4x + 1 => 4
= (0)² + 4(0) + 1 => 4 ≠ 1 (False)
Answer: No
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Given parallelogram A B C D below, DE = 31 If EB = x-7, solve for x.
Answers
The diagonals of the parallelogram intersect at the center. Then the value of the variable 'x' is 38.
What is a parallelogram?It is a polygon with four sides. The total interior angle is 360 degrees. A parallelogram's opposite sides are parallel and equal. Its diagonals intersect in the center.
Given parallelogram A B C D below, DE = 31 If EB = x - 7.
By the definition, then the equation is given as,
EB = DE
x - 7 = 31
Simplify the equation, then we have
x - 7 = 31
x = 31 + 7
x = 38
The value of the variable 'x' is 38.
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10 points Help Me Please I will give brainiest
Answers
Answer:
ITS C
Step-by-step explanation:
Because since it has a one time fee of 5, the graph has to start at 5, then you narrow it down to c or d, if you look at d then you can see that the graph isnt going up 2 dollars, so then the answer is c.
plz help me asnwer this
Answers
Answer:
x= 0
y= -3
Step-by-step explanation:
6x-5y=15
substitution...
6(y+3)-5y=15
6y+18-5y=15
y+18=15
-18 -18
y= -3
substitution again...
6x-5(-3)=15
6x+15=15
-15 -15
6x=0
/6 /6
x= 0
Answer:
(0, -3)
x = 0
y = -3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesAlgebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define systems
6x - 5y = 15
x = y + 3
Step 2: Solve for y
Substitution
Substitute in x: 6(y + 3) - 5y = 15Distribute 6: 6y + 18 - 5y = 15Combine like terms: y + 18 = 15Isolate y: y = -3Step 3: Solve for x
Define original equation: x = y + 3Substitute in y: x = -3 + 3Add: x = 04x - 5y - z= 18
-2x - 5y -2z= 12
-2x + 5y + z = 4
Answers
Answer:
x=-4, y=0, z=-2
Step-by-step explanation:
What is the probability that a random sample of 12 second grade students results in a mean reading rate of more than 95 words per minute?
Answers
The probability that a random sample of 12 second grade students results in a mean reading rate of more than 95 words per minute is 0.4582.
Given that the population mean, \(\mu\) = 90 wpm
The standard deviation of the population ,\(\sigma\) = 10
Sample size, n = 12
Sample mean, \(\bar x\) = 95
The reading rate of students follows the normal distribution.
Let z = \(\frac{\bar x - \mu}{\frac{\sigma}{\sqrt n} }\)
= \(\frac{95 - 90}{\frac{10}{\sqrt 12} }\)
= 1.732
Probability that the mean reading exceeds 95 wpm = P(\(\bar x\) >95)
= P(z>1.732)
= 1- P(z<1.732)
= 0.4582
[The value 0.4582 found from the area under the normal curve using tables].
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an urn contains 6 blue balls and 6 orange balls. in how many ways can we select 2 blue balls and 2 orange balls from the urn?
Answers
The no. of ways to select the 2 blue balls and 2 orange balls from the urn is 0.4545
No. of Blue balls in the urn = 6
No. of Orange balls in the urn = 6
Total no. of balls in the urn = No. of blue balls + No. of orange balls
= 6 + 6
= 12 balls
No. of blue balls to be selected = 2
No. of orange balls to be selected = 2
No. of balls to be selected = 4
The total. no of ways 4 balls can be selected =\(^{12}C_{4}\)
The No. of ways 2 blue balls can be selected = \(^{6}C_{2}\)
The No. of ways 2 orange balls can be selected = \(^{6}C_{2}\)
Therefore, No. of ways to select 2 blue balls and 2 orange balls from the urn
= \(^{6}C_{2} \times ^{6}C_{2} /^{12}C_{4}\)
Probability = No. of ways to select blue balls x No. of ways to select orange balls / Total no. of ways to select balls
P = (15×15)/495
= 225 / 495
P = 0.4545
Therefore, the no. of ways to select blue and orange balls is 0.4545
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and his friends decided to have a water fight on a hot summer day. They filled a bunch of water balloons and started the fight at 1:00 P.M. The water balloons lasted for 1 hour. When all the water balloons were gone, they sprayed water with hoses for 30 minutes, until Rudy's dad showed up with ice cream. What time was it when the water fight ended?
Answers
Answer:
the water fight ended at 2:30pm
Step-by-step explanation:
the balloons lasted an hour bringing it to 2pm then they used the hoses for 30 min bringing it to 2:30pm
Jayne has a home-based business putting on children’s parties. She charges $60 to design the party and then $10.00 per child. Write a function rule that relates the total cost of the party to the number of children n.
f(n) = 10n – 55
f(n) = 10 – 55n
f(n) = 10 + 60n
f(n) = 60 + 10n
Answers
Answer: D. f(n) = 60 + 10n.... algebra.com
f(n) = 10 + 60n
f(n) = 60 + 10n
f(n) = 10n � 55
f(n) = 10 � 55n
ANSWER: f(n)=$60+$10n
Step-by-step explanation: D. f(n) = 60 + 10n.... brainly.com
She charges $60 to design the party
So we know we need to add 60. So 60 +
then $10.00 per child
10 dollars per child mean 10 times # of children so we have:
10n
Put it all together:
60 + 10n
f(n) = 60 + 10n
Steps are on paper
Round 297,433 to the nearest hundred.
Answers
Hope this helps!
Answer:
297,433 rounded to the nearest hundred would be 297,400. You can see that 33 is less than 50, so it would be rounded down to 0.
Need help on this math equation 6c^2-5d+8 when c=5 and d=4
Answers
Answer:
138
Step-by-step explanation:
first you want to replace c and d with the numbers given,
6(5)^2-5(4)+8
and then solve!
2•(-x)
x=-0.75
plzzzz help
Answers
Answer:
The solution is 1.50 You can leave the zero off for this question.
Step-by-step explanation:
I'm not totally certain I'm reading this correctly.
2*(-x)
2*(- -0.75)
2*(0.75)
1.50
Help me with this please!!!
Answers
Answer: y = 80*
all circles have 360* so we can subtract what we have to get what we want
360 - 110 - 90 - 80 = 80*
Which situation could be represented by the equation
15.5 = ?
A. Julie drove 15.5 miles to the grocery store. Her mother drove from the grocery store back home. What is x, the amount
miles each person drove?
B. Julie drove 15.5 miles from her home to the grocery store. Julie drives the same path going back home. What is x, the total
amount of miles traveled to the grocery store and back home?
C. It is 15.5 miles to the grocery store from Julie's home. On the way to the store, she decided to take a detour which
shortened her distance by half a mile. What is x, the new distance to the grocery store including the detour?
D. Julie went to a grocery store 15.5 miles away. Amanda also went to a grocery store 15.5 miles away. The grocery store was
half way in between their houses. What is x, the distance from Julie's home to the grocery store?
ASAP 30 points and brainliest for best answer
Answers
Sam and Mary are picking a topping for the ice cream. Their choices are strawberries, chocolate chips, gummi bears, caramel sauce, and whip cream. What is the probability that they both pick gummi bears as their topping?
Answers
Answer:
2/5
Step-by-step explanation: Total outcomes=5
favourable outcomes=2
Therefore ,P(E)=2/5
Please help I’m tired and I need to go to bed! I’ll mark Brainly thingy.
