Answer:x=(1-sqrt(33))/4=-1.186
x=(1+sqrt(33))/4=1.686
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
(22x2 - 2x) - 8 = 0
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
4x2 - 2x - 8 = 2 • (2x2 - x - 4)
Trying to factor by splitting the middle term
3.2 Factoring 2x2 - x - 4
The first term is, 2x2 its coefficient is 2 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -4
Step-1 : Multiply the coefficient of the first term by the constant 2 • -4 = -8
Step-2 : Find two factors of -8 whose sum equals the coefficient of the middle term, which is -1 .
-8 + 1 = -7
-4 + 2 = -2
-2 + 4 = 2
-1 + 8 = 7
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step
3
:
2 • (2x2 - x - 4) = 0
STEP
4
:
Equations which are never true:
4.1 Solve : 2 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Parabola, Finding the Vertex:
4.2 Find the Vertex of y = 2x2-x-4
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 2 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 0.2500
Plugging into the parabola formula 0.2500 for x we can calculate the y -coordinate :
y = 2.0 * 0.25 * 0.25 - 1.0 * 0.25 - 4.0
or y = -4.125
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = 2x2-x-4
Axis of Symmetry (dashed) {x}={ 0.25}
Vertex at {x,y} = { 0.25,-4.12}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-1.19, 0.00}
Root 2 at {x,y} = { 1.69, 0.00}
Solve Quadratic Equation by Completing The Square
4.3 Solving 2x2-x-4 = 0 by Completing The Square .
Divide both sides of the equation by 2 to have 1 as the coefficient of the first term :
x2-(1/2)x-2 = 0
Add 2 to both side of the equation :
x2-(1/2)x = 2
Now the clever bit: Take the coefficient of x , which is 1/2 , divide by two, giving 1/4 , and finally square it giving 1/16
Add 1/16 to both sides of the equation :
On the right hand side we have :
2 + 1/16 or, (2/1)+(1/16)
The common denominator of the two fractions is 16 Adding (32/16)+(1/16) gives 33/16
So adding to both sides we finally get :
x2-(1/2)x+(1/16) = 33/16
Adding 1/16 has completed the left hand side into a perfect square :
x2-(1/2)x+(1/16) =
(x-(1/4)) • (x-(1/4)) =
(x-(1/4))2
Things which are equal to the same thing are also equal to one another. Since
x2-(1/2)x+(1/16) = 33/16 and
x2-(1/2)x+(1/16) = (x-(1/4))2
then, according to the law of transitivity,
(x-(1/4))2 = 33/16
We'll refer to this Equation as Eq. #4.3.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-(1/4))2 is
(x-(1/4))2/2 =
(x-(1/4))1 =
x-(1/4)
Now, applying the Square Root Principle to Eq. #4.3.1 we get:
x-(1/4) = √ 33/16
Add 1/4 to both sides to obtain:
x = 1/4 + √ 33/16
Since a square root has two values, one positive and the other negative
x2 - (1/2)x - 2 = 0
has two solutions:
x = 1/4 + √ 33/16
or
x = 1/4 - √ 33/16
Note that √ 33/16 can be written as
√ 33 / √ 16 which is √ 33 / 4
Solve Quadratic Equation using the Quadratic Formula
4.4 Solving 2x2-x-4 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 2
B = -1
C = -4
Accordingly, B2 - 4AC =
1 - (-32) =
33
Applying the quadratic formula :
1 ± √ 33
x = —————
4
√ 33 , rounded to 4 decimal digits, is 5.7446
So now we are looking at:
x = ( 1 ± 5.745 ) / 4
Two real solutions:
x =(1+√33)/4= 1.686
or:
x =(1-√33)/4=-1.186
Two solutions were found :
x =(1-√33)/4=-1.186
x =(1+√33)/4= 1.686
Answer:
x = 1
Step-by-step explanation:
[tex] {4}^{x} + 2 \times {2}^{x} - 8 = 0 [/tex]
[tex] {2}^{2x} + 2 \times {2}^{x} - {2}^{3} = 0[/tex]
[tex]substitute \: {2}^{x} = a[/tex]
[tex]a > 0[/tex]
[tex] {a}^{2} + 2 \times a - 8 = 0[/tex]
According to the Wiet theorem:
[tex]a1 = 2[/tex]
[tex]a2 = - 4[/tex]
[tex]when \: a = 2 \: \: \: \: {2}^{x} = {2}^{1} [/tex]
[tex]x = 1[/tex]
[tex]when \: a = - 4 \: \: \: \: {2}^{x} = - 4 \: \: \\ \: \: \: \: \: \: - 4 < 0[/tex]
[tex]x∈∅[/tex]
Coach Miller is using all the ground beef to grill 17 burgers. What is the cost for each burger?
Answer: We can only determine the cost for each burger if we know the total cost of all the ground beef. Let's assume that the ground beef costs $C in total.
If Coach Miller is using all the ground beef to grill 17 burgers, then the cost of each burger is:
Cost per burger = Total cost of ground beef / Number of burgers
We know that the total cost of ground beef is $C, and we know that there are 17 burgers. Substituting these values into the formula gives:
Cost per burger = C / 17
Therefore, the cost for each burger is C/17. We cannot determine the numerical value of C or the cost per burger without additional information.
Step-by-step explanation:
John and Anvil share some money in the ratio 10: 6.
John gets $36 more than Anvil. How much do they get each?
Answer:
54 , 90
Step-by-step explanation:
Let John = 10x
Let Anvil = 6x
10x = 36 + 6x
10 - 6x = 36
4x = 36
x=9
Anvil = 6*9 = 54
John = 10*9 = 90
You are trying to hang a tire swing. To get the rope over a tree branch that is 15 feet high, you tie the rope to a weight and throw it over the branch. You release the weight at a height of 5.5 feet. What is the minimum upward velocity needed to reach the branch?
a) 7.5 feet per seconds
b) 19.7 feet per seconds
c) 20.5 feet per seconds
d) 24 feet per seconds
Since the minimum upward velοcity cannοt be negative, the answer is (A) 7.5 feet per secοnd. If we had taken the absοlute value οf the velοcity, the answer wοuld be (B) 19.7 feet per secοnd.
What is Velοcity?Velοcity is a physical quantity that describes the rate οf change οf an οbject's pοsitiοn with respect tο time. It is a vectοr quantity that has bοth magnitude and directiοn, with the magnitude representing the speed οf the οbject and the directiοn indicating its mοtiοn. In οther wοrds, velοcity tells us hοw fast an οbject is mοving and in which directiοn.
Tο find the minimum upward velοcity needed tο reach the branch, we can use the cοnservatiοn οf energy principle. At the height οf 5.5 feet, the weight has pοtential energy, which will be cοnverted tο kinetic energy as it falls. When the weight reaches the branch at a height οf 15 feet, all οf its initial pοtential energy will be cοnverted tο kinetic energy. Therefοre, we can equate the pοtential energy at the initial height with the kinetic energy at the final height:
[tex]mgh = (1/2)mv^2[/tex]
There m is the mass οf the weight (which cancels οut), g is the acceleratiοn due tο gravity (32 ft/s²), h is the initial height (5.5 ft), and v is the velοcity at the final height (15 ft).
Substituting the values, we get:
(32 ft/s²) * (15 ft - 5.5 ft) = (1/2) * v²
v² = 2 * (32 ft/s²) * (15 ft - 5.5 ft) = 800 ft²/s²
Taking the square rοοt οf bοth sides gives:
v = √(800) = 28.28 ft/s
Hοwever, we need the minimum upward velοcity, sο we must subtract the initial dοwnward velοcity (due tο gravity) οf 32 ft/s:
minimum upward velοcity = v - g = 28.28 ft/s - 32 ft/s = -3.72 ft/s
Since the minimum upward velοcity cannοt be negative, the answer is (A) 7.5 feet per secοnd, which is the magnitude οf the upward velοcity.
Nοte: If we had taken the absοlute value οf the velοcity, the answer wοuld be (B) 19.7 feet per secοnd. Hοwever, the minimum upward velοcity is the cοrrect answer in this cοntext.
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If 25 tapered pins can be machined from a steel rod 15 ft long, how many tapered pins can be made from a steel rod 9 ft long?
If 25 tapered pins are machined from a steel rod 15 ft long, then total 15 tapered pins can be made from a steel rod 9 ft long.
The unitary method is a method where you find the value of one unit and then find the value of the number of units you want. The formula for the units method is to find the value of a single unit and then multiply the value of the single unit by the number of units to get the desired value. We have specify that 25 tapered pins can be made up from a steel rod 15 ft long. Let 'x' represent the number of pins that can be made from 9 ft long steel rod. Now, using the unitary method,
number of pins machined from a 15 ft long steel rod = 25
number of pins machined from a 1 ft long steel rod = 25/15
So, number of pins machined from a 9 feet long steel rod, x = (25/15)×9
=> x = 3×5 = 15
Hence, required tapered pins made from a steel rod 9 ft long is equals to the 15 pins.
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simplify (1/2)³x(1/2)² and write in exponential form
Answer:
To simplify (1/2)³x(1/2)², we can multiply the coefficients and add the exponents with the same base:
(1/2)³x(1/2)² = (1/2)^(3+2) = (1/2)^5
Therefore, (1/2)³x(1/2)² simplified is equal to (1/2)^5, which can also be written as 1/32 in fraction form.
Step-by-step explanation:
In order to multiply we use the formula for indices' multiplication that is
[tex] {n}^{a} \times {n}^{b} = {n}^{a + b} [/tex]
Hence,
[tex]{( \frac{1}{2} )}^{3}( { \frac{1}{2}}^{2}) = {( \frac{1}{2} )}^{5} [/tex]
[tex] ( \frac{{1}^{5} }{{2}^{5} } ) = {2}^{ - 5} [/tex]
The Colossus Ferris wheel debuted at the 1984 New Orleans World’s Fair. The ride is 180 ft tall, and passengers board the ride at an initial height of 15 ft above the ground. The height above ground, h, of a passenger on the ride is a periodic function of time, t. The graph displays the height above ground of the last passenger to board over the course of the 15 min ride.
*REFERRING TO THE GRAPH*
Sine function model: where h is the height of the passenger above the ground measured in feet and t is the time of operation of the ride in minutes.
2) The duration of the ride is 15 min.
(a) How many times does the last passenger who boarded the ride make a complete loop on the Ferris wheel?
(b) What is the position of that passenger when the ride ends
3. A power outage occurs 6 min after the ride started. Passengers must wait for their cage to be manually cranked into the lowest position in order to exit the ride.
Sine function model: Where h is the height of the last passenger above the ground measured in feet and t is the time of operation of the ride in minutes.
(a) What is the height of the last passenger at the moment of the power outage? Verify your answer by evaluating the sine function model.
(b) Will the last passenger to board the ride need to wait in order to exit the ride? Explain.
The heights of the passenger as they move on the Colossus Ferris wheel described by the specified sine function are;
2. (a) 22 times
(b) 180 feet which is the highest point on the ride
3. (a) 15 feet
(b) The last passenger will not need to weight
What is a sine function?A sine function is a mathematical function that describes a smooth repetitive oscillation. The sine function is a periodic function which repeats itself after certain interval. The sine function is the ratio of the opposite side to the hypotenuse side of a right triangle.
2. (a) The period of the sine function model, for the height, h = -82.5×cos(3·π·t) + 97.5 is 2·π/3. Therefore, the last passenger who boarded the ride makes a completer loop on the Ferris wheel every **2/3 minutes**. Since the duration of the ride is 15 minutes, the number of complete loops the passenger makes = 15/(2/3) = 22.5
The passenger completes the 22 times (The passenger cannot make a partial loop)(b) When the ride ends, the height of the last passenger can be found by evaluating the specified sine function at t = 15 minutes (the ride lasts for 15 minutes).
Therefore; h = -82.5 × cos(3 × π × 15) + 97.5 = 180.
Hence the position of the passenger when the ride ends is 180 feet or the highest point of the ride.3. (a) The time of operation of the ride when the power outage occurs is t = 6 minutes. The height of the last passenger at the time of the power outage is; h = -82.5 × cos(3 × π × 6) + 97.5 = 15
The height of the last passenger at the moment of the power outage therefore is; 15 feet(b) The last passenger to board the ride will not need to weight in order to exit the ride. This is because the height of the last passenger at the moment of the power outage is 15 feet, which is the initial height of the passenger when they board the ride. Therefore, the last passenger will be at the same height as the ground, and can exit the ride without waiting.
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There is a light pole that casts a shadow that is 75 feet. At the same time, there is a stop sign that is 8 feet tall and casts a shadow that is 12 feet. How tall is the light pole? If necessary, round your answer to the nearest tenth.
Answer: Therefore, the height of the light pole is 50 feet.
Step-by-step explanation:
We can use proportions to solve the problem.
Let h be the height of the light pole.
Then, we have:
h / 75 = 8 / 12
To solve for h, we can cross-multiply:
12h = 75 * 8
h = (75 * 8) / 12
h = 50
Find the length of LM.
Write your answer as a whole number or a decimal
Answer:
LM = 5
Step-by-step explanation:
A secant is a straight line that intersects a circle at two points.
A segment is part of a line that connects two points.
Intersecting Secants TheoremThe product of the measures of one secant segment and its external part is equal to the product of the measures of the other secant segment and its external part.
The given diagram shows two secant segments LN and PN that intersect at exterior point N. Their external parts are MN and ON, respectively.
Therefore, according to the Intersecting Secants Theorem:
[tex]\implies \sf LN \cdot MN =PN \cdot ON[/tex]
Given values:
LN = 3 + x - 2 = x + 1MN = 3PN = 4 + x - 5 = x - 1ON = 4Substitute the values into the equation and solve for x:
[tex]\implies \sf LN \cdot MN =PN \cdot ON[/tex]
[tex]\implies (x+1)\cdot 3=(x-1)\cdot 4[/tex]
[tex]\implies 3x+3=4x-4[/tex]
[tex]\implies 4x-4=3x+3[/tex]
[tex]\implies 4x-4-3x=3x+3-3x[/tex]
[tex]\implies x-4=3[/tex]
[tex]\implies x-4+4=3+4[/tex]
[tex]\implies x=7[/tex]
To determine the length of LM, substitute the found value of x into the expression for the line segment:
[tex]\implies \overline{LM}=7-2=5[/tex]
Therefore, the length of LM is 5.
what proportion of crows in the sample had lead levels that are classified by the biologist as unhealthy? the mean lead level of the 23 crows in the sample was 4.90 ppm and the standard deviation was 1.12 ppm. construct and interpret a 95 percent confidence interval for the mean lead level of crows in the region.
The 95 percent confidence interval that the true mean lead level of crows in the region is between 4.4157 and 5.3843.
What is a confidence interval?
An estimated range for an unknown parameter is known as a confidence interval. The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.
Here, we have
Given: the mean lead level of the 23 crows in the sample was 4.90 ppm and the standard deviation was 1.12 ppm.
= x ± t×s/√n
= 4.90 ± (2.074)×1.12/√23
= (4.4157, 5.3843)
Hence, the 95 percent confidence interval that the true mean lead level of crows in the region is between 4.4157 and 5.3843.
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What is the average rate of change of [tex]f(x)=\frac{1}{2}x-7[/tex] from [tex]x=2[/tex] to [tex]x=10[/tex] ?
Answer:
1/2
Step-by-step explanation:
You want to know the average rate of change of f(x) = 1/2x -7 on the interval [2, 10].
Linear functionA linear function has the same rate of change everywhere. Its instantaneous rate of change, average rate of change, and slope are all the same constant.
The given function is written in slope-intercept form, so we can identify the slope as the coefficient of x: 1/2.
The average rate of change is 1/2.
__
Additional comment
If you feel the need to "show work", you can evaluate ...
AROC = (f(10) -f(2))/(10 -2) = (-2 -(-6))/8 = 4/8 = 1/2
Assume that all grade-point averages are to be standardized on a scale between 0 and 5. How many grade-point averages must be obtained so that the sample mean is within 0.01 of the population mean? Assume that a 99 % confidence level is desired. If using the range rule ofthumb,\sigma can be estimated as range over 4 End Fraction equals Start Fraction 5 minus 0 Over 4 end Fraction equals 1.25. does the sample size seem practical?
Collecting data on 83,359 grade-point averages would be a significant undertaking and a 99% confidence level, especially if the data had to be collected in a short amount of time or if there were limited resources available for data collection.
To determine the sample size needed to estimate the population mean within a certain margin of error, we can use the formula:
[tex]n = (Z^2 * sigma^2) / E^2[/tex]
where n is the sample size, Z is the Z-score for the desired confidence level (in this case, 2.576 for a 99% confidence level), sigma is the population standard deviation (in this case, estimated as 1.25 using the range rule of thumb), and E is the desired margin of error (in this case, 0.01).
Plugging in the values, we get:
[tex]n = (2.576^2 * 1.25^2) / 0.01^2 = 83,358.08[/tex]
So we would need a sample size of at least 83,359 to estimate the population mean with a margin of error of 0.01 and a 99% confidence level.
However, this sample size may not be practical depending on the resources available. Collecting data on 83,359 grade-point averages would be a significant undertaking, especially if the data had to be collected in a short amount of time or if there were limited resources available for data collection.
In practice, researchers often use statistical software to calculate sample sizes based on the desired margin of error, confidence level, and population standard deviation. This allows them to determine a more realistic sample size based on the specific context of their study.
In summary, while the formula for determining sample size can provide an estimate of the number of observations needed to estimate the population mean with a certain level of precision, other factors such as the availability of resources must also be considered when determining a practical sample size.
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The number of students in tumbling classes this week is represented in the list. 5, 8, 11, 13, 5, 9, 2, 4, 6 What is the value of the mode for this data set? 13 6 5 2
in this particular data set, there is only one value that appears most frequently, which is 5.
What are statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It provides a set of methods and tools for extracting meaningful insights and making decisions based on data.
In statistics, the mοde is the value that is repeatedly οccurring in a given set. We can alsο say that the value οr number in a data set, which has a high frequency οr appears mοre frequently, is called mοde οr mοdal value. It is οne οf the three measures οf central tendency, apart frοm mean and median. Fοr example, the mοde οf the set {3, 7, 8, 8, 9}, is 8.
Therefοre, fοr a finite number οf οbservatiοns, we can easily find the mοde. A set οf values may have οne mοde οr mοre than οne mοde οr nο mοde at all.
In the given data 5 has the maximum frequency so 5 is style mode of the given data
Mode=5
Therefore, in this particular data set, there is only one value that appears most frequently, which is 5.
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safety information about a ladder indicates that a ladder should not be set up at an angle less than 45 degrees or at an angle greater than 75 degrees. What range of height can a 20-foot ladder reach?
According to the question the height of the ladder is 34.641 feet, or approximately 19.98 feet.
What is height?Height is the measure of vertical distance, either how "tall" something or someone is, or the distance between the top and bottom of an object. It is measured in either centimeters, meters, or feet and inches, and can be used to describe the elevation of land or the altitude of an aircraft.
Let x be the height of the ladder.
For a 20-foot ladder at an angle of 45°, we have the following trigonometric equation:
tan(45°) = x/20
Solving for x we get:
x = 20tan(45°)
x = 20 × 1
x = 20
Therefore, the height of the ladder is 20 feet.
For a 20-foot ladder at an angle of 75°, we have the following trigonometric equation:
tan(75°) = x/20
Solving for x we get:
x = 20tan(75°)
x = 20 × 1.73205
x = 34.641
Therefore, the height of the ladder is 34.641 feet, or approximately 19.98 feet.
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The range of height can be determined by trigonometric ratios and the rage is 20ft to 74.6 ft(approximately).
What is Trigonometric Ratios?
Trigonometric Ratios are based on the value of the ratio of sides of a right-angled triangle where Hypotenuse is the longest side Perpendicular is opposite side to the angle and Base is the Adjacent side to the angle. The ratios of these three sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
Given that a ladder should not be set up at an angle less than 45 degrees or at an angle greater than 75 degrees.
The ladder is 20 foot.
here the trigonometric function tangent will be used.
By the formula, tan Ф = Perpendicular/ adjacent side [ where Ф is the acute angle]
Let, the height of the ladder is x foot.
Then by formula of trigonometric ratio,
tan 45° = x/20
⇒ x/20 =1 [ since tan 45° =1 ]
⇒ x= 20
Again,
tan 75° = x/ 20
⇒ x= 20× tan 75°
⇒ x= 74.6 [ since tan 75° = 3.732]
Hence, the range of height is 20 foot to 74.6 foot ( approx ).
The rough diagram is attached below.
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pQRs is Rhombous '0' is the bisect of diagonal Qs and pR if p0=x or y-1 0Q=2x+7 and 0s =4y-5 what is value of x and y
Answer:
Step-by-step explanation:
y= -6x - 43
y= -8x - 59
what is the answer to x and y. Please include step by step.
Step-by-step explanation:
Don't worry we will take care of everything. It's easy. listen carefully
first of all write your questions carefully.
i think it should be like this-
y= -6x +43 ------ (i)
y= -8x -59---------(ii)
1. We have two unknowns x and y. and two equations .
2. CONCEPT:- there are several ways to solve it like.
Elimination methodmultiplication methodsubstitution method ( we will go with this)ACCORDING TO SUBSTITUTION METHOD:-
Simply, write the equation in term of single variable(unknown). * [ which is already done for us]
second step, substitute the expression of obtained variable in any one equation.
example: substitute the value of y from equation (i) in (ii)
we will obtained equation -
=> y= -8x -59 [ put value of y from (i) ]
=> -6x +43 = -8x -59
(solve and find x)
=> -6x +8x = -59 - 43
=> 2x = -102
=> x = -51
Third step in substitute method is, now substitute this obtained value of x in any equation (i) or (ii) to get unknown y.
y will be = 349
* your questions was wrong so i have made it by myself. if this does not match your question sorry from my side. buti have shown you the concept to solve this type of questions. You will be able to solve this by your self now by applying concepts.
Zahra is 4/5 as tall as Zayden. Zayden is 3/5 as tall as Eric. Eric is how many times as tall as Zahra?
Answer:
1/5 is the right answer in my opinion but I'm not sure
PLEASE HELP ME ASAP THANK YOU
Assume that the area of the bean field is 440ft^2.
If Farmer Bob buys fertilizer for the bean field at $5.50 per bag and each bag covers 100 ft^2 then how many bags does he need? Then, how much money will Farmer Bob spend on fertilizer?
Step-by-step explanation:
If the area of the bean field is 440ft^2 and each bag of fertilizer covers 100 ft^2, then Farmer Bob will need:
440 ft^2 / 100 ft^2 per bag = 4.4 bags of fertilizer
Since Farmer Bob can't buy a fraction of a bag, he will need to round up to 5 bags of fertilizer.
The total cost of the fertilizer will be the number of bags multiplied by the cost per bag, which is $5.50. Therefore, the total cost of the fertilizer will be:
5 bags x $5.50 per bag = $27.50
Explain how to find the diameter of a circle if you know the circumference.
If the value of C, the circumference is known, then the diameter is:
D = C/pi
How to get the diameter of the circle if you know the circumference?For a circle whose radius is R, the formula for the circumference is:
C = 2*pi*R
Where pi = 3.14
Particularly, we know that the diameter of a circle is twice the radius, os:
D = 2*R
We can rewrite the circumference equation to get:
C = pi*(2*R) = pi*D
So, solving that equation for the diameter, we will get:
D = C/pi
That equation gives the diameter if we know the value of the circumference.
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Add the polynomials functions, as indicated below. (Q+R)(x)
Answer:
x^3 + 5x - 23
Step-by-step explanation:
(Q+R)(x) is the same as Q(x) + R(x).
you just add them like so:
(x^3 - 9x^2 - 14) + (9x^2 + 5x - 9)
= x^3 + 5x - 23
At a parade 1/4 of the people have red hair, 1/6 of them have brown hair the rest of the people have black hair. What fraction of the people have black hair
A procession typically has one-fourth of the participants with red hair, one-sixth with brown hair, and the remaining participants with black hair. 7/12 of the population has black hair.
We are given that 1/4 of the people have red hair and 1/6 of them have brown hair.
Let's add these fractions together to find the fraction of people who have either red or brown hair:
[tex]\\\frac{1}{4} + \frac{1}{6}\\ =\frac{3+2}{12} \\ =\frac{5}{12}[/tex]
This means that 5/12 of the people have either red or brown hair.
Since the remaining people must have black hair, we can subtract this fraction from 1 to find the fraction of people who have black hair:
1 - 5/12
=12-5/12
= 7/12
Therefore, the fraction of people who have black hair is 7/12.
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Explain what value or values of c make the equation x^2+12x+c=0
Answer:x^2+12x-28=01. 12/2=62. (x+6)^2=x^2+12x+363. If we subtract 64 from this expression it becomesx^2+12x+36-64=x^2+12x-28 and so equals 0We now have (x+6)^2-64=0This is our old friend a^2-b^2=(a+b)(a-b)(x+6)^2-8^2=(x+6+8)(x+6-8)=(x+14)(x-2)=0 and so x=-14 or x=2
Step-by-step explanation:
if z,z+3 are the roots of the equation x²-5x+k then; z= and k=
The roots of the equation x² - 5x + k are z = (5/a - 3)/2 and z+3 = (5/a + 3)/2, and the value of k is 9/4.
Define roots of the equationThe roots of an equation are the values of the variable that satisfy the equation and make it true. In the case of a quadratic equation of the form ax² + bx + c = 0, the roots are the values of x that satisfy the equation and make it equal to zero.
Given: z and z+3 are the roots of the equation x² - 5x + k
The sum of the roots z and z+3 is:
z + (z + 3) = 2z + 3
And the product of the roots z and z+3 is:
z (z + 3) = z² + 3z
By Vieta's formulas, we know that the sum of the roots of a quadratic equation ax² + bx + c = 0 is -b/a and the product of the roots is c/a. Therefore, we can equate these expressions to the sum and product of the roots of the given equation:
2z + 3 = 5/a (since b = -5 and a = 1)
z² + 3z = k/a (since c = k and a = 1)
Solving for z in the first equation, we get:
2z = 5/a - 3
z = (5/a - 3)/2
Substituting this value of z into the second equation, we get:
[(5/a - 3)/2]² + 3[(5/a - 3)/2] = k/a
Simplifying and solving for k, we get:
k = a[(5/a - 3)/2]² + 3a[(5/a - 3)/2]
= (5a - 9a + 18)/4
= 9/4
Therefore, the roots of the equation x² - 5x + k are z = (5/a - 3)/2 and z+3 = (5/a + 3)/2, and the value of k is 9/4.
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Look at the poster below showing the price of pencils in a stationery shop. Riley wants to buy exactly 65 pencils. What is the lowest amount he can pay? Give your answer in pounds (£)
Answer:
13
Step-by-step explanation:
0.3*65
=19.5 pounds
[tex]\frac{2}{10} =0.2\\0.2*65=13[/tex]
HELP PLEASE!! ALSO IF U CAN PLEASE ANSWER MY RECENT QUESTIONS OF TODAY IF UR GENEROUS THANKS BAES
Answer:b
Step-by-step explanation:
just took the quiz
Anna Has d dimes Brittany has 4 times as many dimes as Anna has write and expression for the total number of dimes Anna and Brittany have them simplify the expression
The expression represent total number dime both have is 5d.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.
Here Anna Has d dimes and Brittany has 4 times as many dimes as Anna.
Then,
Number of dime Anna has = d Number of dime Brittany has = 4d
Now the total number of dimes both have is:
Total dimes = d+4d
= 5d
Hence the expression represent total number dime both have is 5d.
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expand 3(x+6)
please help me on the eqation
Answer:
3x + 18
Step-by-step explanation:
3 ( x + 6 )
= 3*x + 3*6
= 3x + 18
Answer:
3x + 18
Step-by-step explanation:
expand 3(x+6)
3(x + 6) =
3 * x + 3 * 6
3x + 18
ricky has 23 word hours each week to dedicate to his classes.Homework takes 6.5 hours and each class (c) is 1.5 hours long.How many classes does ricky take?
Ricky has 23-word hours each week to dedicate to his classes. Homework takes 6.5 hours and each class (c) is 1.5 hours long. Thus, 05 classes Ricky takes every week.
There are 60 minutes in 1 hour. To convert from minutes to hours, divide the number of minutes by 60. For example, 120 minutes equals 2 hours because 120/60 = 2.
According to the Question:
Let us consider
a = hour she dedicates to his classes = 6.5 hours
and
b = hours spend on homework= 1.5 hours
Total hours in a week devoted to his classes = 23/7
Therefore, 23/7 ×1.5
= 5 classes.
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The measures of the angles of a triangle are shown in the figure below. Solve for x.
36°
(6x+3)°
87°
Answer:
Step-by-step explanation:The sum of the measures of the angles in a triangle is always 180 degrees. So, we can set up an equation and solve for x:
36 + (6x+3) + 87 = 180
Combine like terms:
126 + 6x = 180
Subtract 126 from both sides:
6x = 54
Divide both sides by 6:
x = 9
Therefore, the value of x is 9.
(a) Find the intervals on which f is increasing or decreasing. (b) Find the local maximum and minimum values of f. (c) Find the intervals of concavity and inflection points.
f(x)= x^4-2x^2+3
Part (c) is where I'm having issues on how to derive the second derivative f'(x)=4x(x-1)(x+1)
can you please show all steps.
The inflection points are at x = -[tex]\sqrt{(1/3)}[/tex] and x = sqrt(1/3), and f is concave up on (-[tex]\sqrt{1/3}[/tex]), [tex]\sqrt{(1/3)}[/tex]), and concave down elsewhere.
(a) To find the intervals on which f is increasing or decreasing, we need to find the first derivative of f and determine its sign.
[tex]f(x) = x^4 - 2x^2 + 3[/tex]
[tex]f'(x) = 4x^3 - 4x[/tex]
Setting f'(x) = 0, we get:
[tex]4x(x^2 - 1) = 0[/tex]
This equation has roots at x = 0, x = -1, and x = 1. We can use the first derivative test to determine the intervals of increasing and decreasing.
When x < -1, f'(x) is negative, so f is decreasing.
When -1 < x < 0, f'(x) is positive, so f is increasing.
When 0 < x < 1, f'(x) is negative, so f is decreasing.
When x > 1, f'(x) is positive, so f is increasing.
Therefore, f is decreasing on (-∞, -1) and (0, 1), and increasing on (-1, 0) and (1, ∞).
(b) To find the local maximum and minimum values of f, we need to look for critical points and evaluate the function at those points.
Critical points occur where f'(x) = 0 or is undefined. We have already found that f'(x) = 0 at x = 0, x = -1, and x = 1.
f(0) = 3, f(-1) = 6, f(1) = 2
Therefore, f has a local maximum at x = -1, with a value of 6, and local minimums at x = 0 and x = 1, with values of 3 and 2, respectively.
(c) To find the intervals of concavity and inflection points, we need to find the second derivative of f and determine its sign.
[tex]f(x) = x^4 - 2x^2 + 3[/tex]
[tex]f'(x) = 4x^3 - 4x[/tex]
[tex]f''(x) = 12x^2 - 4[/tex]
Setting f''(x) = 0, we get:
[tex]12x^2 - 4 = 0[/tex]
[tex]x^2 = 1/3[/tex]
x = ±sqrt(1/3)
We can use the second derivative test to determine the intervals of concavity.
When x < -sqrt(1/3), f''(x) is negative, so f is concave down.
When -sqrt(1/3) < x < sqrt(1/3), f''(x) is positive, so f is concave up.
When x > sqrt(1/3), f''(x) is negative, so f is concave down.
Therefore, the inflection points are at x = -sqrt(1/3) and x = sqrt(1/3), and f is concave up on (-sqrt(1/3), sqrt(1/3)), and concave down elsewhere.
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Four times the sum of 5 and some number is 20. What is the number?
Applying mathematical operations, "Four times the sum of 5 and some number is 20," the number is 0.
What are the mathematical operations?The mathematical operations include addition, subtraction, division, and multiplication.
Mathematical or algebraic operations use mathematical operands to manipulate values, variables, constants, and numbers to solve mathematical problems.
Is zero a number?Zero is considered to be a neutral number since it is neither positive nor positive.
Zero is important as a number placeholder.
4 (5 + x) = 20
20 + 4x = 20
4x = 20 - 20
4x = 0
x = 0
Thus, in the mathematical operations of multiplying the sum of 5 and some number by 4, the applicable number is zero.
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