What are the zeroes of f(x)=(2x+3)(x-5)?
Answers
Answer:
\(-\frac{3}{2} , 5\)
Step-by-step explanation:
The zeroes of a function are the x values of the points at which the graph intersects the x-axis. All points on the x-axis have a y-value of 0, therefore, we need to find out which values of x can be plugged in to have the result be 0. This function is already factored out. So, for each expression, find which input of x makes the result equal 0.
1) So, start with 2x + 3. Set it equal to 0 and solve for x:
\(2x + 3 = 0\\2x = -3\\x = -\frac{3}{2} \\\)
Therefore, \(-\frac{3}{2}\) is one of the zeroes.
2) Next, set x-5 equal to 0 and solve, too:
\(x - 5 = 0 \\x = 5 \\\)
Therefore, 5 is one of the zeroes.
3) Thus, the zeroes are \(-\frac{3}{2}\) and 5.
Related Questions
help me asap i will give brainliest
Answers
Answer:
c
Step-by-step explanation:
other answers are wrong
(0)
Question 2 Consider the dynamic system described by Equation Q2. 85.16400 083.3770 0046.999 ⃗+ 0.079400 00.7030 001.07 ×10⃗+ 0.013600 03.1390 005.124 ×10⃗= 0 0 0 Equation Q2 (a) Calculate the spectral matrix, the undamped natural frequencies and damping ratios of the system in Equation Q2. Identify its fundamental frequency. (b) The following mode shape vectors have been used to diagonalise the equations of motion of the dynamical system presented in Equation Q2: f1 = [0.8076 1.0000 0.8039]T; f2 = [-0.9694 -0.1620 1.0000]T and f3 = [-0.5342 1.0000 -0.3523]T. Calculate the respective matrix of mass normalised mode shapes. (c) Using the mode superposition method, calculate the response of the system for the first physical coordinate y1 assuming the following initial conditions expressed in terms of the modal coordinates: the initial modal displacements are [0 0.5 0]T m and the initial modal velocities are [0 -3 0]T m/s.
Answers
The first physical coordinate y1 can be expressed as y1 = [1 0 0]Y, & The mass-normalised mode shapes can be normalising the mode shape vectors f1, f2, and f3.
Part (a)
In Equation Q2, the spectral matrix, undamped natural frequencies, damping ratios, and fundamental frequency need to be calculated.
The mass matrix is given by [85.16400 083.3770 0046.999; 0.079400 00.7030 001.07 × 10; 0.013600 03.1390 005.124 × 10].
The stiffness matrix is given by [0.16400 00.3770 000.999; 0.079400 00.7030 001.07 × 10; 0.013600 03.1390 005.124 × 10].
The damping matrix is given by [0 0 0; 0 0 0; 0 0 0].The undamped natural frequencies, damping ratios, and fundamental frequency for the system in Equation Q2 can be calculated from the spectral matrix.
The characteristic equation can be written as det(K-mω^2M)=0.where K is the stiffness matrix, M is the mass matrix, ω is the angular frequency, and m is the mass-normalised mode shape.
The roots of this equation are the undamped natural frequencies, and the damping ratios can be calculated from the undamped natural frequencies and mode shapes.
The mass-normalised mode shapes can be calculated by normalising the mode shape vectors f1, f2, and f3.
Part (b)
The mass-normalised mode shapes can be calculated using the mode shape vectors f1, f2, and f3.Part (c)The response of the system for the first physical coordinate y1 can be calculated using the mode superposition method. The initial modal displacements and velocities are given in terms of the modal coordinates.
The response is then calculated using the equation y(t)= Σ ai φi(t), where ai are the modal amplitudes, and φi(t) are the modal shapes given by the mode shape vectors f1, f2, and f3.
The first physical coordinate y1 can be expressed as y1 = [1 0 0]Y, where Y is the vector of physical coordinates. The modal amplitudes can be calculated from the initial modal displacements and velocities.
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Prove everything you say and please have a readable handwritting. Prove that the set X c R2(with Euclidean distance is defined as: See Pictureconnected,but not path connected (X is connected,that is,it cannot be divided into two disjoint non-empty open sets.) X={x,0xe[0,1}U{1/nyneN,ye{0,1]}U{0,1} Prove that the set X C R2(with Euclidean distance) is connected,but not path connected X
Answers
X is a connected set but not a path-connected set. X={x,0xe[0,1}U{1/nyneN,ye{0,1]}U{0,1}.
To prove that X is connected, let us assume that X can be divided into two disjoint non-empty open sets A and B. Since X is the union of different points, any point in X will be in either A or B. Let us take an arbitrary point p in A. Since A is open, there is an open ball centered at p that is contained in A. Because B is disjoint from A, it follows that every point in this ball is also in A. By a similar argument, any point in B must have a ball centered at that point that is entirely contained in B. Thus, X must be either in A or B and hence, cannot be divided into two disjoint non-empty open sets. However, X is not path-connected since there is no path between points in [0,1] x {0} and {1} x {1}. Thus, it is connected but not path-connected.
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Marjorie and Blaine make chairs together. Marjorie builds the seat and Blaine independently sews the cushions to rest on top of them. It takes Marjorie 1 1/2hours to build the seat and Blaine 40 minutes to sew the cushion. How long would it take for them to make 10 chairs?
Answers
Making 10 chairs would take Marjorie and Blaine 21 hours and 40 minutes.
How long does it take to make 10 chairs?The total time it takes Marjorie and Blaine to perform their respective tasks in building a chair is multiplied by 10 chairs, respectively. This time is known as their speed.
The resulting figures are summed to get the total time.
Data and Calculations:The total time it takes Marjorie to build a chair is 15 hours (1.5 hours x 10)
The total time it takes Baline to sew cushions per chair is 400 minutes (40 x 10) or 6 hours and 40 minutes.
Therefore, the total time to build 10 chairs is 21 hours, 40 minutes (15 hours + 6 hours and 40 minutes).
Thus, making 10 chairs would take Marjorie and Blaine 21 hours and 40 minutes.
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A, B and C lie on a straight line segment.
A, E and D lie on a straight line segment.
BE = 1.75m, CD = 7m and BC = 1.5m.
Work out the length of AB.
A
E
B
D
С
Answers
The value of AB id 0.5 unit.
What is AAA similarity ?The Angle-Angle-Angle (AAA) criterion for the similarity of triangles states that “If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar”.
What are corresponding angles?Any pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal are called corresponding angles and they are always equal.
According to the given question.
A, B and C lie on the straight line segment. and A, E, and D are also lie in the straight line segment.
Also, BE = 1.75m, CD = 7m and BC = 1.5m
Now, in ΔAEB and ΔADC
EB is parallel to BC
So,
∠AEB ≅ ∠ADC (corresponding angles)
∠ABE ≅ ∠ACD (corresponding angles)
∠EAB ≅ ∠DAC (common angle to the both triangle)
Hence, by AAA Similarity rule
ΔAEB is similar to ΔADC
Therefore,
\(\frac{AE}{AD} =\frac{BE}{CD} =\frac{AB}{AC}\) (sides of the similar triangles are in proportion)
So,
\(\frac{BE}{CD} =\frac{AB}{AC} \\\implies \frac{AB}{AC} =\frac{1.75}{7} ....(i)\)
Now, AC = AB + BC (as, A, B, and C lie on a straight line)
\(\implies \frac{AB}{AB+BC} =\frac{1.75}{7}\) (from (i))
\(\implies \frac{AB}{AB+1.5} =\frac{1.75}{7}\)
\(\implies 7AB = 1.75AB + 1.75(1.5)\)
\(\implies 7AB -1.75AB = 2.625\)
\(\implies 5.25AB = 2.625\)
\(\implies AB = \frac{2.625}{5.25} = 0.5\)
Hence, the value of AB id 0.5 unit.
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Leonard went fishing and caught 40 fish in 8 hours. Charlotte went fishing and caught 32 fish in 8 hours. On average, how many fish did Leonard catch in one hour? On average, how many fish did Charlotte catch in one hour? Use unit rates to determine who caught fish faster.
Answers
To find the average divide total caught by total hours:
Leonard = 40 / 8 = 5 fish per hour
Charlotte = 32/8 = 4 fish per hour
Leonard caught more fish per hour.
Answer:
See Below.
Step-by-step explanation:
average: fishes caught/time takenFor Leonard: 40/8 = 5 fishes/hr
For Charlotte: 32/8 = 4 fishes/hr
On average, 5 fishes Leonard caught in one hour.On average, 4 fishes Charlotte caught in one hour.From this, we can identify that Leonard caught more fishes per hour or faster.
Can someone just explain to me how to find “u” Thanks!
Answers
Answer:
u = 4 yards
Step-by-step explanation:
Step 1: Find u using sin
\(sin(x) = \frac{opposite}{hypotenuse}\)
\(sin(30)=\frac{u}{8}\)
\(8*sin(30)=u\)
Step 2: Plug into a calculator
\(8*sin(30)=u\)
\(8 * \frac{1}{2} = u\)
\(4 = u\)
Answer: u = 4 yards
Q1: Use the given information to answer the question regarding similiar triangles
Q2: Triangle SHE is similiar to Triangle RHY
Answers
1) The length of the side DE by similar triangle theorem is; Option C: 20
3) If RY = b + 4 and SE =20, then the value of b is; 6
How to find the lengths of similar triangles?Similar triangles are defined as triangles that have the same shape, but their sizes may vary. Thus, we can say that equilateral triangles, squares of any side lengths are as well examples of similar objects. This means that, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
1) ΔABC ~ ΔDEF
We are given the similar triangles ABC and DEF.
We are also told that ΔABC ~ ΔDEF.
Now, If AB = 10, AC = 8 and DF = 16
Thus, by similar triangle theorem, we can apply it to the attached triangle to get;
AB/DE = AC/DF
DE = (AB * DF)/AC
DE = (10 * 16)/8
DE = 20
3) Now, by using the concept of similar triangles, since we are given that;
R is the midpoint of line SH.
Y is the midpoint of line EH
RY = b + 4
SE =20
(b + 4)/20 = 1/2
Cross multiply to get;
2(b + 4) = 20
2b + 8 = 20
2b = 20 - 8
b = 12/2
b = 6
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13. (4r⁰)⁴
14. (4a³)²
15. (3k⁴)⁴
16. (4xy)⁻¹
17. (2b⁴)⁻¹
18. (x²y⁻¹)₂
Answers
Answer:
Step-by-step explanation:
13.
(4r⁰)⁴
= (4×1)⁴
= (4)⁴
= 256
14.
(4a³)²
\(= 4^2a^{(3\times 2)}\)
= 16 a⁶
15.
(3k⁴)⁴
\(= 3^4 k^{4*4}\)
\(= 81 \ k^{16}\)
16.
(4xy)⁻¹
\(= \dfrac{1}{4 xy}\)
17.
(2b⁴)⁻¹
\(= \dfrac{1}{2 \ b^4}\)
18.
(x²y⁻¹)²
\(=\Big ( \dfrac{x^2}{y} \Big) ^ 2\)
\(=\Big ( \dfrac{x^4}{y^2} \Big)\)
The radius of the front wheel of Terry's bike is 61cm.
Terry goes for a cycle and travels 60.32km.
How many full revolutions did Terry's front wheel complete?
Answers
In linear equation, 157 did Terry's front wheel complete.
What is a linear equation example?
Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5.Finding both intercepts of an equation in this format is rather simple (x and y).Terry goes for a cycle and travels 60.32km.
so, 60.32 * 1000 ÷ ( 2 * 3.14 * 61 )
= 60320 ÷ 2 * 3.14 * 61
= 60320 ÷ 6.28 * 61
= 60320 ÷ 383.08
= 6032000/ 38308
= 1508000/9577
= 157
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1/4 how do u get 16 from it show me the calculations
Answers
Answer:
It's not possible to get 16 from 1 divided by 4 alone. It will always be 0.25
Un agricultor observó que la expresión F(x)=-2x2+16x+25 describe la producción (P), en toneladas, de cacao que cosecha en sus tierras en función de la cantidad (x), en toneladas, de fertilizante empleado. La producción de cacao será máxima cuando la cantidad de fertilizante x es igual a:
Answers
Answer:
348 7gb93c9 good morning to you all right place on my bed right now iam not geting the best way u are gonna be in this situation is it was not Halloween but gug batson vocal vox's John b bucko and my dear loving n love u soo hapy that u can go ahead with it is my beauty grl for the kichen and u will not cm to ur 2AM to go to Gangtok and my 7th anniversary of the 4588th 468inches I will not be the 6th of God Amen n and 93feet
Step-by-step explanation:
galvanise and I will have the best of my kds to 67055965th in the name and u have to write a book about this balance of God and blow it up n and then be online til now I will be a man fan of u my son Anup he shall wbsoenndkd6543 the best man in the land and my 8AM shall il be bsy in the 34th century abksbdkfusnliqnksus in jsbsbdbsmqjnans bus andQueremos encontrar el valor de x que maximiza la expresión dada.
Veremos que el valor de x que maximiza la producción es x = 4.
Tenemos la expresión:
F(x) = -2*x^2 + 16*x + 25
Y queremos maximizarla.
Notar que es una función cuadratica cuyo coeficiente principal es negativo, es decir, el máximo de la función esta en el vertice.
Para una cuadratica generica:
y = a*x^2 + b*x + c
El vertice está en:
x = -b/2a
Entonces en nuestro caso, el vertice va a estar en:
x = -16/(2*-2) = 4
x = 4
Es decir, la producción de cacao será máxima cuando se utilicen 4 toneladas de fertilizante.
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How many degrees is are
Answers
Answer:
AMH = 32
Step-by-step explanation:
The angles are alternate exterior angles and when the lines are parallel, alternate exterior angles are equal
x+86 = 24+2x
Subtract x from each side
x+86 -x =24+ 2x+2x-x
86 = 24 +x
Subtract 24 from each side
86-24 = 24+x-24
62 =x
x+86 = 62+86 =148
AMH is supplementary since it forms a straight line
AMH + x+86 = 180
AMH + 148 = 180
AMH = 180-148
AMH = 32
pls solve this as soon as possible
Answers
Answer:
x³ - y³ = 0
Step-by-step explanation:
Given : \(\frac{x}{y}+\frac{y}{x}=-1\)
To Find : value of (x³ - y³)
Since, \(\frac{x}{y}+\frac{y}{x}=-1\)
\(\frac{x^2+y^2}{xy}=-1\)
x² + y² = -xy
x² + y² + xy = 0 -----(1)
Since, x³ - y³ = (x - y)(x² + xy + y²) [From the formula, (a³ - b³) = (a -b)(a²+ b² + ab)
= (x - y)(0) {From equation (1)]
= 0
Therefore, value of x³ - y³ = 0 will be the answer.
solve for x and y 13x−28=24
Answers
Answer:
x=4
Step-by-step explanation:
Answer:
X=4
Step-by-step explanation:
All work shown below. Y cannot be solved for because it is not a variable in the equation.
During recess, 60 kids played capture the flag. If 15 kids were on the winning team, what percent of the kids were on the winning team?
Answers
A percentage of 25% οf the kids were οn the winning team.
What is Percentage?Percentage is a way οf expressing a prοpοrtiοn οr fractiοn as a number οut οf 100. It is denοted by the symbοl "%".
Tο find the percentage οf kids οn the winning team, we can use the fοrmula:
percentage = (part/whοle) x 100%
In this case, the "part" is the number οf kids οn the winning team, which is 15. The "whοle" is the tοtal number οf kids whο played, which is 60. Substituting these values, we get:
percentage = (15/60) x 100% = 0.25 x 100% = 25%
Therefοre, 25% οf the kids were οn the winning team.
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A farmer wants to fence an area of 6 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. Let y represent the length (in feet) of a side perpendicular to the dividing fence, and let x represent the length (in feet) of a side parallel to the dividing fence. Let F represent the length of fencing in feet. Write an equation that represents F in terms of the variable x.
Answers
If the rectangular field has notional sides X and y then it has area
A(x) =xy { =6•10^6 sq ft }
The length of fencing required, if
x
is the letter that was arbitrarily assigned to the side to which the dividing fence runs parallel, is:l (x) = 3x +2y
It matters not that the farmer wishes to divide the area into 2 exact smaller areas.
Assuming the cost of the fencing is proportional to the length of fencing required, then
C(x)=a L (x)
To optimise cost, using the Lagrange Multiplier
λ
, with the area constraint :
So the farmer minimises the cost by fencing-off in the ratio 2:3, either-way
The relationship between variable F and x is 2x + 12000000/x
Let y represent the length (in feet) of a side perpendicular to the dividing fence, and let x represent the length (in feet) of a side parallel to the dividing fence.
Let F represent the length of fencing in feet.
Area of fencing = 6000000 ft²
Area of fencing = x * (y + y) = x * 2y
Area of fencing = 2xy
6000000=2xy
xy = 3000000
y = 3000000/x
The perimeter is:
F = x + y + y + x + y + y
F = 2x + 4y
F = 2x + 4(3000000/x)
F = 2x + 12000000/x
Therefore the relationship between variable F and x is 2x + 12000000/x
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Which expression represents the phrase "the quotient of 9 and 14"?
Answers
Answer:
the quotient of 9 and 14
= \(\frac{9}{14}\)
Answer:
the answer is 9 upon 14 (⁹/14)
Please help me solve step by step
solve V = lwh for w
1.
2.
3.
4.
Answers
Which of the following tools is used to capture data packets over time(continuously or overnight)?PuTTYTraffic AnalyzerWiresharkNetWitness Investigator
Answers
Wireshark is the tool used to capture data packets over time, either continuously or overnight.
Wireshark is a powerful network protocol analyzer that allows you to capture and examine data packets flowing through a network. It provides a comprehensive set of features for capturing, analyzing, and interpreting network traffic.
With Wireshark, you can capture packets from various network interfaces and save them to a capture file for later analysis. It supports capturing packets in real-time, allowing you to monitor network activity as it happens.
Wireshark offers detailed packet-level inspection, allowing you to examine packet headers, payloads, protocols, and other relevant information.
Furthermore, Wireshark supports numerous protocols and provides protocol-specific decoders to interpret and analyze different network protocols. It also offers advanced features like packet coloring, statistical analysis, packet comparison, and the ability to export captured data for further analysis or sharing with others.
Overall, Wireshark is widely used by network administrators, security professionals, and developers to diagnose network issues, troubleshoot problems, analyze network performance, and investigate security incidents by capturing and analyzing data packets over time.
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Heyyy!! I could really use some helps this is really stressing me out and I wonder if anyone could explain this to me
Answers
Answer:35
Step-by-step explanation:
2 pens cost £2.38 5 folders cost £5.60 Ben wants to buy 20 pens and 20 folders. He only has £50 Does Ben have enough money to buy 20 pens and 20 folders? Provide a reason for your answer
Answers
2 pens cost £2.38 5 folders cost £5.60 Ben wants to buy 20 pens and 20 folders. No, Ben does not have enough money to buy 20 pens and 20 folders. He only has £50, but the total cost of the items is greater than £50.
The cost of 2 pens is £2.38, which means the cost of 1 pen is £2.38/2 = £1.19. Similarly, the cost of 1 folder is £5.60/5 = £1.12. To find the total cost of 20 pens, we multiply the cost of 1 pen by 20, which is £1.19 * 20 = £23.80. Likewise, the total cost of 20 folders is £1.12 * 20 = £22.40. Adding these two amounts together, we get £23.80 + £22.40 = £46.20.
Since the total cost of the 20 pens and 20 folders is £46.20, which is less than £50, Ben does have enough money to buy these items. Therefore, Ben can afford to buy 20 pens and 20 folders with the amount of money he has.
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What unit of measurement is used to describe how far a set of values are from the mean? a) Variance b) Standard deviation c) Median d) Mode
Answers
The unit of measurement used to describe how far a set of values are from the mean is the standard deviation. Therefore, the correct answer is (b) standard deviation.
The variance is another measure of spread, but it is not in the form of the original units of measurement. The median is a measure of central tendency and not a measure of spread. The mode is the most frequently occurring value in a set and is also not a measure of spread.
The unit of measurement used to describe how far a set of values are from the mean is the Standard Deviation (b). It is calculated by taking the square root of the variance and provides a measure of the average distance between each value in the set and the mean. The Median (c), on the other hand, is the middle value in a set when the values are arranged in numerical order.
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Can you provide the solution for this exercise?
Let u(w) = −(b − w)c. What restrictions on w, b, and c are required to ensure that u(w) is strictly increasing and strictly concave? Show that under those restrictions, u(w) displays increasing absolute risk aversion.
Answers
under the restrictions that c is negative to ensure strict concavity, the utility function u(w) = -(b - w)c displays increasing absolute risk aversion.
To ensure that u(w) is strictly increasing, we need the derivative of u(w) with respect to w to be positive for all values of w. Taking the derivative, we have du(w)/dw = -c. For u(w) to be strictly increasing, -c must be positive, which implies c must be negative.
To ensure that u(w) is strictly concave, we need the second derivative of u(w) with respect to w to be negative for all values of w. Taking the second derivative, we have d²u(w)/dw² = 0. Since the second derivative is constant and negative, u(w) is strictly concave.
Now, let's examine the concept of increasing absolute risk aversion. If a utility function u(w) exhibits increasing absolute risk aversion, it means that as wealth (w) increases, the individual becomes more risk-averse.
In the given utility function u(w) = -(b - w)c, when c is negative (as required for strict concavity), the absolute risk aversion increases as wealth (w) increases. This is because the negative sign implies that the utility function is concave, indicating that the individual becomes more risk-averse as wealth increases.
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I need help with this is the last question
Answers
Hope this helps
Answer:
84 ft2
Step-by-step explanation:
mitochondria is the powerhouse of a cell
The solution of the given linear equation 6m+7/3m+2 = 5/4 is
Answers
Step-by-step explanation:
\( \longmapsto \rm \dfrac{6m + 7}{3m + 2} = \dfrac{5}{4} \)
By cross multiplication,
→ 4(6m + 7) = 5(3m + 2)
→ 24m + 28 = 15m + 10
→ 24m - 15m = 10 - 28
→ 9m = -18
→ m = -18 ÷ 9
→ m = -2
Value of m is -2.
please help!! Solve for the hypotenuse and then determine the ratios below. (Show all work)
Answer:
Hypotenuse:
sin x° =
cos y° =
Answers
The hypotenuse of the right triangle is 29 units.
The ratios are as follows:
sin x = 20 / 29
cos y = 20 / 29
What is a right angle triangle?Right angle triangle has one of its angles as 90 degrees. The sides and angles can be found using trigonometric ratios. The sides can also be solved using Pythagoras theorem.
The hypotenuse side is the longest side of a right angle triangle.
Therefore,
c² = a² + b²
c = √20² + 21²
c = √400 + 441
c = √841
c = 29
hypotenuse = 29 units
sin x = opposite / hypotenuse = 20 / 29
cos y = adjacent/ hypotenuse = 20 / 29
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Find the length of side x in the simplest radical form with a rational denominator.
Answers
The answer is 60 or 15 because you need to have 150 for a triangle
When you put your powerade into your refrigerator its temperature is 48 F. If the refrigerator can cool drink at 3.75 F per hour, what will be the temperature of your Gatorade after 2 hours
Answers
Answer:
40.5
Step-by-step explanation:
3.75 * 2 = 7.50
48 - 7.50 = 40.5
There are 5 white balls,8 red balls ,7 yellow balls and 4 green balls in a container a ball is choosen at random.what is the probabilty of chooseing neither white or green? .
Answers
15/19 + 14/19 = 29/19
Step-by-step explanation:
Add the number of balls in the basket together.
Subtract the number of white balls from the sample space ( the total amount of balls) your answer is written over the sample space and the same process is done for the green ball