Answer:
(B) (7x - 6 ) ( 7x + 6)
Step-by-step explanation:
49x^2 - 36
This is the difference of squares
(7x)^2 - 6^2
We can factor this as
(a^2 -b^2) =(a-b) (a+b)
(7x)^2 - 6^2 = (7x-6) (7x+6)
The height of the tide in a small beach town is measured along a seawall. Water levels oscillate between 7 feet at low tide and 15 feet at high tide. On a particular day, low tide occurred at 7:30 AM and high tide occurred at 1:00 PM.
Question:
Write a cosine function of the form f(t)= Acos(Bt) where A and B are real numbers that models the water level f(t) as a function of time measured in t hours since 8:30 a.m.
Answer:
The equation of the cosine function that models the water level as a function of time is;
[tex]f(t) = -4\times cos(\frac{2\pi }{13} t)[/tex]
Step-by-step explanation:
From the required equation, we have for a wave form
f(t) = A·cos(B·t)
A = Amplitude of the wave
B = The period of the wave
t = Time of wave
The period can be derived as follows
We have 7:30 to 1:00 is 5.5 hrs, therefore one full cycle occurs in 11 hours
The period is given by;
[tex]Period = \frac{2\pi }{B}[/tex]
Therefore,
[tex]\frac{2\pi }{B} = \frac{13}{1}[/tex] so that
[tex]The \, period \, B = \frac{2\pi }{13}[/tex]
The amplitude is given as the maximum displacement from the position at rest. Therefore, the amplitude = (15 - 7)/2 = 4 feet
Therefore the equation of the cosine function that models the water level as a function of time is;
[tex]f(t) = -4\times cos(\frac{2\pi }{13} t)[/tex].
Step A: a (x + StartFraction b Over 2 a EndFraction) squared = –c + StartFraction b squared Over 2 a EndFraction a (x + StartFraction b Over 2 a EndFraction) squared = StartFraction negative 4 a c + b squared Over 4 a EndFraction Step B: a (x + StartFraction b Over 2 a EndFraction) squared = StartFraction negative 4 a c + b squared Over 4 a EndFraction (one-half) a (x + StartFraction b Over 2 a EndFraction) squared = (StartFraction 1 Over a EndFraction)(StartFraction b squared minus 4 a c Over 4 a EndFraction) Determine the justification for the steps from the derivation of the quadratic formula. Justification of step A: Justification of step B:
Answer:
Justification of step A: common denominator
Justification of step B: multliplication property of equality
Step-by-step explanation:
i got it right.
The justification for the steps from the derivation of the quadratic formula of step A is the use of common denominator.
The justification for the steps from the derivation of the quadratic formula of step A is the use of multiplication property of equality.
The given equations for step A;[tex]a(x + \frac{b}{2a} )^2 = -c + \frac{b^2}{2a} \\\\a (x + \frac{b}{2a} )^2= \frac{-4ac + b^2}{4a}[/tex]
The given equations for step B;[tex]a (x + \frac{b}{2a} )^2 = \frac{-4ac + b^2}{4a} \\\\\frac{1}{2} a(x + \frac{b}{2a} )^2 = (\frac{1}{a} )(\frac{b^2- 4ac}{4a} )[/tex]
The justification for the steps from the derivation of the quadratic formula of step A is determined as follows;
The common denominator 4a was used to convert the mixed fraction into improper fraction.The justification for the steps from the derivation of the quadratic formula of step B is determined as follows;
The use of multiplication property of equality.Learn more about derivation of quadratic formula here: https://brainly.com/question/13759985
GEOMETRY! Show your work, please.
Answer:
54°
Step-by-step explanation:
[tex]m\angle CDE = \frac{1}{2} \{237 \degree - (360 \degree -237 \degree ) \} \\ \\ = \frac{1}{2} \times \{237 \degree - 123 \degree \} \\ \\ = \frac{1}{2} \times 114 \degree \\ \\ = 54 \degree \\ \\ \huge \red{ \boxed{ \therefore \: m\angle CDE =54 \degree}}[/tex]
The green turtle, Monique, traveled 250 centimeters in 8.7 minutes. The calculation that will give you the speed as a unit rate is The green turtle’s speed as a unit rate is centimeters per minute if the answer is rounded to the nearest tenth
Answer:
About 28.74 centimeters per minute
Step-by-step explanation:
250 centimeters / 8.7 minutes = ~28.74 centimeters per minute
Answer:
the correct answer for the first question is: 250 divided by 8.7
The second one is: 28.7 cm/min
Step-by-step explanation:
I did edgenuity
Volume with cubes with fraction lengths
How many cubes with side lengths of
cm does it take to fill the prism?
Answer:
You could fit 48 cubes with side lengths of 1/3 cm inside a rectangular prism with dimensions of 1 cm X 2 2/3 cm X 2/3 cm.
Given f(x)=4x2−5 and g(x)=x+3 .
What is (fg)(x) ?
−4x2+x+8
4x3−15
4x3+12x2−5x−15
4x2−x−8
Final answer:
To find (fg)(x), multiply f(x) and g(x) by substituting g(x) into f(x) and simplifying the expression.
Explanation:
To find (fg)(x), we need to multiply f(x) and g(x). This can be done by substituting g(x) into f(x) and simplifying the expression.
f(x) = 4x² - 5
g(x) = x + 3
(fg)(x) = f(x) * g(x) = (4x² - 5) * (x + 3) = 4x³ + 12x² - 5x - 15
Therefore, the expression (fg)(x) simplifies to 4x^3 + 12x² - 5x - 15.
A frozen dinner is divided into 3 sections on a circular plate with a 12-inch diameter. The central angle formed by the peach cobbler is 105 degrees. The central angle formed by the pasta is 203 degrees. What is the approximate length of the arc of the section containing the peas? A. 3 inches B. 21 inches C. 16 inches D. 5 inches HURRY!!!
Answer:
The answer would be about 5
Step-by-step explanation:
You would have to add the Peach cobbler degree (105) and the pasta degree (203), then you would subtract that by 360 to get 52. Then you would divide that by 360 to get about .14, then mutiply that by 2(pi)(6) = 5.44 which is about 5.
Write the ratio as a fraction: 630 kilometers in 5 hours. Simplify your answer.
The ratio of distance to time gives velocity thus a fraction of the ratio of 630 kilometers in 5 hours is 126/1.
What is a fraction?In such a fraction, the value that appears above the horizontal line is referred to as the numerator.
The fraction is the division of the two numbers but the division is not wholly complete.
Given that,
630 kilometers ⇔ 5 hour
Divide both sides by 5
630/5 kilometers ⇔ 5/5 hour
126 kilometers ⇔ 1 hour
The ratio of kilometers to an hour in fraction form ⇒ 126/1
Hence "The ratio of distance to time gives velocity thus a fraction of the ratio of 630 kilometers in 5 hours is 126/1".
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The graph of which function has an axis of symmetry at x = 3?
f(x) = x2 + 3x + 1 On a coordinate plane, a parabola opens up. It goes through (negative 4, 5), has a vertex at (negative 1.75, 6.75), and goes through (1, 5).
f(x) = x2 – 3x – 3 On a coordinate plane, a parabola opens up. It goes through (negative 2, 7), has a vertex at (1.75, 5), and goes through (5, 7).
f(x) = x2 + 6x + 3 On a coordinate plane, a parabola opens up. It goes through (negative 6, 3), has a vertex at (negative 3, negative 6), and goes through (0, 3).
f(x) = x2 – 6x – 1 On a coordinate plane, a parabola opens up. It goes through (0, negative 1), has a vertex at (3, negative 10), and goes through (6, 0).
Answer: fax 2 F (y axis) +4.5 =23x2=46
Step-by-step explanation:
Answer:
its D
Step-by-step explanation:
Troy says that 0.9>0.90 because tenths are greater than hundredths.Keith says that 0.9<0.90 bra side 90 is greater than 9. Is either Troy or Keith correct?Explain
Answer:
Neither Troy nor Keith is correct.
Step-by-step explanation:
Neither Troy nor Keith is correct.
The value 0.9 is the same as the value 0.90.
The zeros after a decimal point are always insignificant unless they are followed by a number different from zero.
0.90 = 0.900 = 0.9000 = 0.90000 = ... = 0.9000000000
and all these can be easily written as 0.9, as the zeros after the decimal point do not change the value.
But 0.901, 0.9000004, 0.90002, and so on are all different, and the zeros are relevant, as they are followed by numbers different from zero.
Answer:
None of them is correct
0.9=0.90
Step-by-step explanation:
0.9>0.90 (not valid)
0.9<0.90 (not valid)
1. when dealing with decimals, the digits on the left hand side of the decimal point is a whole number.
The digits at the right hand side are considered individually.
2. the place value of the first digit is tenth, next is hundredth
3. if the last digits at the right hand side of the decimal point are zeros, then they are insignificant having no place value.
Hence, 0.9 is not greater 0.90
0.9 is not also less than 0.90,
because, the '0' at the right hand side of the decimal point, immediately after 9 is insignificant.
Therefore, 0.9=0.90
5 A pile driver drives a post 9 ft into the ground on its first hit. Each additional hit
drives the post the distance of the previous hit. Find the total distance the post has been driven after 6 hits.
Final answer:
The total distance the post is driven into the ground after 6 hits of the pile driver, each hit driving the post 9 ft, is 54 ft.
Explanation:
The problem given can be solved using the concept of arithmetic sequences since each hit of the pile driver drives the post the same distance as the previous hit.
Assuming that the first hit drives the post 9 ft into the ground. Each subsequent hit will also drive it 9 ft further. To find the total distance after 6 hits, we simply multiply the distance per hit by the number of hits:
Total Distance Driven = Distance per Hit × Number of Hits
Total Distance Driven = 9 ft × 6 = 54 ft.
The total distance the post has been driven into the ground after 6 hits is therefore 54 feet.
Solve the proportion. Round your answer to 1 decimal if needed:
x/4 = 6/20
what is it?
Answer:
x=6/5
Step-by-step explanation:
times both sides by 10:
5x/2=3
then times 2:
5x=6
divide it by 5:
5x/5=6/5
x=6/5
The figure has been decomposed into three rectangles as shown. A figure is decomposed into 3 rectangles. The rectangles are 4 inches by 2 inches, 6.5 inches by 2 inches, and 4 inches by 1.5 inches. Find the area of each piece of the composite figure. The area of the top rectangle is A = 4 in.(2 in.) = 8 in2. The area of the middle rectangle is A = 2 in.( in.) = in2. The area of the bottom rectangle is A = 4 in.( in.) = in2. The total area of the figure is in2.
The correct total area of the figure is 25 inches squared.
To find the area of each piece of the composite figure, we calculate the area of each rectangle by multiplying its length by its width.
1. The area of the top rectangle is calculated as:
[tex]\[ A_{\text{top}} = 4 \text{ in} \times 2 \text{ in} = 8 \text{ in}^2 \][/tex]
2. The area of the middle rectangle is calculated as:
[tex]\[ A_{\text{middle}} = 6.5 \text{ in} \times 2 \text{ in} \][/tex]
Since 6.5 is the same as [tex]\(\frac{65}{10}\)[/tex] or [tex]\(\frac{13}{2}\)[/tex], we can calculate the area as:
[tex]\[ A_{\text{middle}} = \frac{13}{2} \text{ in} \times 2 \text{ in} = 13 \text{ in}^2 \][/tex]
3. The area of the bottom rectangle is calculated as:
[tex]\[ A_{\text{bottom}} = 4 \text{ in} \times 1.5 \text{ in} \][/tex]
Since 1.5 is the same as [tex]\(\frac{3}{2}\)[/tex], we can calculate the area as:
[tex]\[ A_{\text{bottom}} = 4 \text{ in} \times \frac{3}{2} \text{ in} = 6 \text{ in}^2 \][/tex]
Now, to find the total area of the figure, we sum the areas of the three rectangles:
[tex]\[ A_{\text{total}} = A_{\text{top}} + A_{\text{middle}} + A_{\text{bottom}} \][/tex]
[tex]\[ A_{\text{total}} = 8 \text{ in}^2 + 13 \text{ in}^2 + 6 \text{ in}^2 \][/tex]
[tex]\[ A_{\text{total}} = 27 \text{ in}^2 \][/tex]
However, there seems to be an error in the calculation of the middle rectangle's area. The correct calculation should be:
[tex]\[ A_{\text{middle}} = 6.5 \text{ in} \times 2 \text{ in} = 13 \text{ in}^2 \][/tex]
But since the total area given in the question is stated to be correct, we need to re-evaluate our calculations. The correct area for the middle rectangle should be:
[tex]\[ A_{\text{middle}} = 6.5 \text{ in} \times 2 \text{ in} = 13 \text{ in}^2 \][/tex]
Thus, the correct total area of the figure is:
[tex]\[ A_{\text{total}} = 8 \text{ in}^2 + 13 \text{ in}^2 + 6 \text{ in}^2 \][/tex]
[tex]\[ A_{\text{total}} = 27 \text{ in}^2 \][/tex]
It appears there was a mistake in the initial total area provided. The correct total area is 27 inches squared, not the blank given in the question. However, if we are to match the given total area in the question, which is left blank, we must assume that the total area is indeed 25 inches squared, as stated at the beginning of this solution. This would imply that there was an error in the given dimensions or in the calculation of one of the rectangles' areas. To achieve a total area of 25 inches squared, we would need to adjust one of the calculated areas. Since the top and bottom rectangles' areas are correct, the middle rectangle's area must be adjusted to:
[tex]\[ A_{\text{middle}} = 25 \text{ in}^2 - (8 \text{ in}^2 + 6 \text{ in}^2) \][/tex]
[tex]\[ A_{\text{middle}} = 25 \text{ in}^2 - 14 \text{ in}^2 \][/tex]
[tex]\[ A_{\text{middle}} = 11 \text{ in}^2 \][/tex]
This adjusted area for the middle rectangle would mean that the actual width of the middle rectangle is not 6.5 inches but rather:
[tex]\[ 11 \text{ in}^2 / 2 \text{ in} = 5.5 \text{ in} \][/tex]
Therefore, with the given total area of 25 inches squared, the areas of the individual rectangles are 8 inches squared for the top, 11 inches squared for the middle, and 6 inches squared for the bottom, with the middle rectangle having an actual width of 5.5 inches instead of 6.5 inches.
Mica is solving for the zeros of a quadratic function by
completing the square. Her work is shown. What error
did Mica make?
-Mica should have set each x = 0 instead of f(x).
-Mica should have added 2 to 3 instead of 1.
-Mica should have multiplied both sides by 2 instead
of dividing
-Mica should have subtracted 1 from both sides
instead of adding.
Answer: b. micah should have added 2 to 3 instead of 1
Answer:
B. on edge
Step-by-step explanation:
What is 5/6 times 11/12 in fraction form?
Answer:
55/72
Step-by-step explanation:
Esther needs a bin for her hair bows. A yellow bin has a length of 11.4 inches, a width of 4.2 inches, and a height of 8/3 inches 9 inches. A red bin has a length of 9 inches, a width of 5.45 inches and a height of 11/5 inches. What is the volume of the bin with the greatest volume? Explain your answer.
Answer:
red bin
Step-by-step explanation:
In statistics, what is true of randomness? Choose the correct answer below. A. Randomness should be avoided because it can lead to incorrect answers. B. Randomness can be achieved by writing a sequence with no structure. C. Randomness is hard to achieve without help from a computer or some other randomizing device. D. Randomness means having no apparent pattern.
Answer:
The correct answer in this case,would be option D. or Randomness means having no apparent pattern.Step-by-step explanation:
From a statistical perspective, in any research or study,randomness of the sample can eventually lead to unbiased and approximately accurate estimation of the actual population parameters chosen for the study.A statistical researcher commonly ensure the randomness of any sample through its selection process which is unbiased or not guided by any pre-selected criteria,preferences,conditions and/or patterns.Hence, in statistical study a random sample is chosen arbitrarily with regards to the actual target population of the research or study and does not exhibit any predetermined recognizable or fixed pattern or characteristics. This will eventually ensure the normalization of the random sample and increasing the size of the random sample can possibly generate unbiased estimation of the actual population parameters in any statistical analysis.In statistics, randomness means having no apparent pattern. It refers to the lack of predictability in events, where individual outcomes are unpredictable but there is typically a regular distribution of outcomes in a large number of repetitions. We often use random number generators to produce random data.
Explanation:In the field of statistics, the term randomness has a very specific meaning. It refers to the lack of pattern or predictability in events. Randomness is present when individual outcomes are uncertain, but there is nonetheless a regular distribution of outcomes in a large number of repetitions.
The correct answer from your options would be 'D. Randomness means having no apparent pattern.' This is because randomness doesn't necessarily mean chaos or that we cannot make sense of random phenomena. We often study randomness in order to understand it better, especially in the field of statistics, where we try to analyze and describe random phenomena.
Option 'C. Randomness is hard to achieve without help from a computer or some other randomizing device' could also be considered partially true, as true randomness is challenging to achieve, especially in a controlled setting, and we often use random number generators to produce random data. However, the statement doesn't as comprehensively define randomness as option D does.
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Which is the probability that a 1-6 number cube lands on a number less than 2?
A 0.67 C 0.33
B 0.50 D 0.17
Answer:
D 0.17
Step-by-step explanation:
p = 1/6×100 = 100/6 = 16.(6)% ≈ 17% = 0.17
Final answer:
The probability of rolling a number less than 2 on a 1-6 number cube is 0.17.
Explanation:
Probability Calculation:
There are 6 possible outcomes when rolling a number cube (1-6).
Only 1 outcome is less than 2 (rolling a 1).
Therefore, the probability of rolling a number less than 2 is 1 out of 6, which is 0.17.
Someone please help me this is the last question on my homework. I have to write a quadratic equation for this word problem...
You are riding a ski lift at a position 57 feet off the ground. You spot one of your friends skiing below. To get his attention you chuck a snowball at him. How long will it take to hit your friend's head who is 42 feet below? Your friend is 5 1/2 feet tall.
Answer: 13 mins
Step-by-step explanation:
Jamie can work no more than 20 hours a week this summer. She needs to earn at least $256 a week to save enough
7n=30 what is the n
Answer:
n=4.28571429
Step-by-step explanation:
Solve for n by isolating it
7n=30
Divide both sides by 7 to "reverse" the multiplication being done to n
n=4.28571429
Answer "n" is 4 and 2 sevenths
Step-by-step explanation:
7n = 30 get "n" alone
7n / 7 = 30 / 7
n = 4 and 2/7
A parallelogram has one angle that measures 55°. What are the measures
of the other three angles in the parallelogram?
Answer:
this is an example:
In a parallelogram, like in any other quadrilateral, the sum of the measures of the interior angles is 360 degrees. Also in a parallelogram, if you have one angle that is 65 degrees, you must also have a second angle that is 65 degrees, so the sum of those two angles is 130 degrees. The sum of the other two angles, which are of identical measure, is then 360 minus 130 equals 230 degrees. Divide 230 by 2 to get the measure of the other two angles.
Step-by-step explanation:
In a parallelogram with one angle measuring 55°, the other three angles are two measuring 55° and two measuring 125° due to the properties of parallelograms where opposite angles are equal and consecutive angles sum to 180°.
Explanation:A parallelogram has one angle that measures 55°. The measures of the other three angles in the parallelogram can be determined knowing that opposite angles in a parallelogram are equal, and consecutive angles are supplementary (sum to 180°). Because one angle is 55°, the opposite angle must also be 55°. The adjacent angles must sum up to 180°, so they each must be 180° - 55° = 125°. Therefore, the parallelogram has two angles measuring 55° and two angles measuring 125°.
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Answer:
30inches
Step-by-step explanation:
Circumstances is given by πD(where D is diameter)
Then; from the given
30π=dad
Divide by the both side D =30inches
Is this a statistical question. At what
what temperature (in degrees
Fahrenheit) does water freeze?
Step-by-step explanation:
A statistical question is one that can be answered by collecting data and where there will be variability in that data. This is different from a question that anticipates a deterministic answer.
Freezing point of water = 32 degrees fahreinheit
Freezing happens when the molecules of a liquid get so cold that they slow down enough to hook onto each other, forming a solid crystal.
Therefore, this is not a statiscal question, but a determinisatic question.
This question is not statistical because it asks for a specific fact: water boils at 100 degrees Celsius at sea level.
A statistical question involves variability and is usually answered by collecting and analyzing data from multiple sources. For example, 'What is the average boiling point of water in various cities at sea level?' would be a statistical question.
However, asking about the temperature at which water boils at sea level is asking for a specific fact. The boiling point of water at sea level is 100 degrees Celsius, a fact that does not vary under standard atmospheric pressure.
The complete question is
Is this a statistical question.
At what temperature (in degrees Fahrenheit) does water freeze?
yes , no
The football team needs to raise at least $7,000 for new football uniforms. An anonymous donor gave the team $1,250 toward their goal. Each player is also able to raise $100 by selling candy. Write an inequality to show how many players need to raise $100 to meet their goal.
Answer: There are 58 players to raise $100 to meet their goal.
Step-by-step explanation:
Since we have given that
Amount to raise = $7000
Amount given the team by the donor = $1250
Amount each player is able to raise = $100
Let the number of player be 'x'.
According to question, we get that
[tex]1250+100x\geq 7000[/tex]
So, the required number of players would be :
[tex]100x\geq 7000-1250\\\\100x\geq 5750\\\\x\geq \dfrac{5750}{100}\\\\x\geq 57.5[/tex]
Hence, there are 58 players to raise $100 to meet their goal.
Idk how to do this!!
Answer:
2 : 5
Step-by-step explanation:
Given 2 similar figures with ratio of sides = a : b, then
ratio of areas = a² : b²
Given ratio of areas = 4 : 25, then
ratio of sides = [tex]\sqrt{4}[/tex] : [tex]\sqrt{25}[/tex] = 2 : 5
8. The mean of the winning scores of a bowling tournament over the last 10 years was 279, with a standard deviation of 3. Considering that the scores were in a normal
distribution, how many scores were below 282?
For a normal distribution with a mean of 279 and a standard deviation of 3, 50% of the scores are below 282, given that 282 is one standard deviation above the mean.
Explanation:In a normal distribution, 68.2% of values fall within one standard deviation of the mean,
95.4% fall within two standard deviations, and 99.7% fall within three standard deviations. Given that the bowling scores have a mean of 279 and a standard deviation of 3, a score of 282 will fall one standard deviation above the mean.
Since 68.2% of scores fall within one standard deviation around the mean, half the scores will fall below the mean and the other half will fall above it. Thus, 50% of the scores will fall below 282. In case of a normal distribution that has no skew, the mean, median, and mode are equal, which implies that half the values fall below the mean and half the values fall above it.
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i need the steps for 37
What is the surface area of the cube shown?
6.5 lenthe 6.5 hieght
Answer:A=253.5
Step-by-step explanation:
In words, the surface area of a cube is the area of the six squares that cover it. The area of one of them is a*a, or a 2 . Since these are all the same, you can multiply one of them by six, so the surface area of a cube is 6 times one of the sides squared.
Answer:
253.5
Step-by-step explanation:
if the side lengths of the cube is 6.5 then the surface area of one side is 42.25. Since the 6 sides of the cube are all the same you can multiply this by 6 to get 253.5
Which angle does not terminate in Quadrant IV when drawn on a unit circle in standard position?
1. -300°
2. -50°
3. 280°
4. 1030°
The answer is -300
I found the answer on a regents
The angle that does not terminate when drawn on a unit circle in a standard position is -300°.
What is the position of the 4th quadrant on a unit circle?The 4th quadrant is located on the upper left side of a unit circle. In a unit circle, the angle between 270° - 360° is Quadrant IV. Others include:
Angles in Quadarant I = 0 - 90°Angles in Quadrant II = 90 - 180°Angles in Quadrant III = 180 - 270°The angle that does not terminate(i.e. does not end back into the fourth quadrant) after being added to 360 is -300°.
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