Expand: (2a - 3b +5c) square
2) if asquare + bsquare + csquare = 74 and ab + bc + ca = 61, find the value of a + b+ c.
Answers
An expression is defined as a set of numbers, variables, and mathematical operations. The value of (a + b+ c) is 14.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
1.) The expansion of (x+y+z)² can be done as shown below,
(x + y + z)² = x² + y² + z² + 2(xy + yz + xz)
If you substitute the value of x as 2a, y as -3b, and z as 5c, then,
(2a - 3b +5c)² = 4a² + 9b² + 25c² - 12ab - 30bc + 20ac
2.) if a² + b² + c² = 74 and ab + bc + ca = 61, find the value of a + b+ c.
Since (x + y + z)² = x² + y² + z² + 2(xy + yz + xz) therefore,
(a + b + c)² = 74 + 2(61)
(a + b + c) = √196
(a + b + c) = 14
Hence, the value of (a + b+ c) is 14.
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Related Questions
Choose the solution to this inequality. 43< − 8/3 y
Answers
Since there is a negative on the y term, we need to get rid of that and thus flip the sign at the same time. Getting.
-43>8/3y
Now we just need to divide 8/3 on both sides dividing 8/3 on left can also be written as *3/8
-43*3/8>y
Now flip this entire equation
y<-43*3/8
y<-129/8
If your teacher want you to calculate just divide the fraction, but I recommend not to if your teacher don't ask for it and just leave it this way.
Hope it helps! :D
Pls help this assignment is due today! I will give brainliest!
Answers
Answer:
Step-by-step explanation:
The slope is defined as the ratio of the “rise” divided by the “run” between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line.
The inclination of a straight line is the angle that the line makes with the positive direction of the x-axis. The tangent of the angle that a line makes with the positive direction of the x-axis is called the slope or gradient of the line. The slope of a line is generally denoted by m.
Given two points (x1, y1) and (x2, y2) on a line, the slope m of the line is y = (y2 – y1)/(x2 – x1)
The slope-intercept form of a line is given by y = mx + b gives the slope of line m and the y-intercept of line b. The inclination of the line with the horizontal axis is called the slope of the line. The point at which the curve cuts or crosses the y – axis is called the y-intercept.
Is △XYZ equilateral, isosceles, or neither? Explain your reasoning. (Make sure to include how/why you know which of these categories the triangle falls into!)
Answers
Answer:
equilateral
Step-by-step explanation:
You want to know if the given triangle with angles marked (2x)°, (2x)°, and (3x-30)° is equilateral, isosceles, or neither.
AnglesOn the face of it, the triangle is at least isosceles, as two angles are marked identically as (2x)°.
When we apply the angle sum theorem, we find ...
(2x)° +(2x)° +(3x -30)° = 180°
7x -30 = 180
7x = 210
x = 30
2x = 2(30) = 60
3x -30 = 3(30) -30 = 60
All of the angles have the same measure, 60°, so the triangle is equilateral.
Answer:
3 equal angles = equilateral triangle
Step-by-step explanation:
the sum of the interior angles in a triangle is 180°
2x + 2x + 3x - 30 = 180
7x = 210
x = 210 : 7
x = 30
find angle Y & Z2 x 30 = 60°
find angle x3 x 30 - 30 = 60
3 equal angles = equilateral triangle
At the clothing store, you purchase a shirt for $29.85. pants for $32.15, and jewelry for $15.45. The total bill comes tobefore tax
Answers
The total bill is the sum of all the items purchased.
The items purchased includes;
A shirt for $29.85
Pants for $32.15
Jewelry for $15.45
The sum of this items is;
\(\begin{gathered} T=29.85+32.15+15.45 \\ T=\text{ \$}77.45 \end{gathered}\)Therefore, the total bill comes to $77.45 before tax.
Solve the system of equations.
y equals x plus 8
y equals 3 x plus 2
Answers
Answer:
The answer is (3,11) or x = 3, y = 11
Step-by-step explanation:
:)
Answer:
(3, 11 )
Step-by-step explanation:
y = x + 8 → (1)
y = 3x + 2 → (2)
substitute y = 3x + 2 into (1)
3x + 2 = x + 8 ( subtract x from both sides )
2x + 2 = 8 ( subtract 2 from both sides )
2x = 6 ( divide both sides by 2 )
x = 3
substitute x = 3 into either of the 2 equations and solve for y
substituting into (1)
y = 3 + 8 = 11
solution is (3, 11 )
One morning, Muhammad's deli shop sells 15 sandwiches in 10 minutes. If the shop continues to sell sandwiches at the same rate, about how many sandwiches will the shop sell in 3/4 of an hour?
Answers
Answer:
68 sandwiches
Step-by-step explanation:
Given that,
A shop sells 15 sandwiches in 10 minutes.
10 minutes = (10/60) hour = (1/6) hour
In (1/6) hour shop sells 15 sandwiches
In 1 hour = 90 sandwiches
To find, no of sandwiches in 3/4 hours, multiply 3/4 by 90. So,
In 3/4 hour = \(90\times \dfrac{3}{4}=67.5\) sandwiches
or
≅ 68 sandwiches
So, 68 sandwiches can be made in 3/4 hour.
A ___________ is used to visualize sample data graphically and to draw preliminary conclusions about the possible relationship between the variables.
Answers
A scatter plot is used to visualize sample data graphically and to draw preliminary conclusions about the possible relationship between the variables.
A scatter plot is used to visualize sample data graphically and to draw preliminary conclusions about the possible relationship between the variables. It is a type of mathematical diagram that utilizes Cartesian coordinates to display values for typically two variables for a set of data.
The data is displayed as a collection of points, each with the value of one variable determining the position on the horizontal axis and the value of the other variable determining the position on the vertical axis. Scatter plots are extremely useful when there are a large number of data points.
Summery:A scatter plot is used to visualize sample data graphically and to draw preliminary conclusions about the possible relationship between the variables.
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There are 39 chocolates in a box, all identically shaped. There 16 are filled with nuts, 13 with caramel, and 10 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting a nut chocolate followed by a caramel chocolate.
Answers
Answer:
16/117Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probability = expected outcome of event/total outcome of event
Given the total amount of chocolate in a box = 39chocolates
Amount of nuts = 16
Mount of caramel = 13
Amount of solid chocolate = 10
If he randomly selects a nut chocolate and eat, the probability of selecting a nut chocolate = Amount of nuts/total chocolate in the box = 16/39
IF he selects a seconnd piece (caramel chocolate) and eat, the probability of selecting a caramel chocolate = Amount of caramel/total chocolate in the box = 13/39 = 1/3
The probability of selecting a nut chocolate followed by a caramel chocolate will be 16/39*1/3 = 16/117
6(2 + 4) -1 divided by 2.3+1
Answers
Answer:
when 6(2+4) -1 divided by 2.3 + 1 the answer is 36.5652174
Which two expressions are equivalent to
2
−
6
?
−
2
6
− − 2 6
−
64
− − 64
1
2
6
1 2 6
2
−
2
⋅
2
4
⋅
2
−
8
2 − − 2 ⋅ ⋅ 2 4 ⋅ ⋅ 2 − − 8
2
3
⋅
2
−
2
2 3 ⋅ ⋅ 2 − − 2
Answers
Equivalent expressions are expressions with equal values
How to determine equivalent expressionsFor two different expressions to be equivalent, then the expressions must have equal values when compared and/or simplified.
The parameters in the question are unclear. So, I will make use of the following expressions to answer the question.
1/3 and 2/6 are equivalent.
This is so because 2/6 can be reduced to 1/3
1/3 and 2/7 are not equivalent
This is so because none of the expressions can be reduced to the other.
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i need help with ratios of special triangles i was able to teach myself how to do the short leg and hyp but i cant figure out how to do the long leg on a 60 30 90
Answers
the hypotenuse is equal to twice the length of the shorter leg, which is the side across from the 30 degree angle. the longer leg, which is across from the 60 degree angle, is equal to multiplying the shorter leg by the square root of 3. so quite basically, hypotenuse = short leg square root, long leg = short leg squared :3 ( ex: short leg is 2 , 2^2 = 4, 2^3= 6 )
4×5+-8÷(7×9) what is the answer?
Answers
Answer:
19.87301587
Step-by-step explanation:
Answer:
Step-by-step explanation:
Ok, so you would use PEMDAS, which is the correct order in which you would need to solve an equation. The idea is that the operations that come first would have to be solved first.
If you don't know it, PEMDAS is:
Parentheses
Exponents
Multiplication/division
Addition/subtraction
In this case, you would need to solve the parentheses. (7x9) is 63.
It would be rewritten as 4x5-8/63
There are no exponents, so you can skip the next operation.
Then you would do multiplication next, which would be 4x5 = 20
The equation would be rewritten as 20-8/63
-0.126984127 is -8/63
Lastly, 19.8730159 is the result of 20-0.126984127
Hope this helps!
Evaluate 7y - 5x^2 when x =2 and y=3
Answers
Answer:
1
Step-by-step explanation:
7x3=21
2x2=4
4x5=20
21-20=1
A space shuttle can orbit the earth at 330 mi above sea level. The average commercial airplane can fly at 5.7 mi above sea level. What is the distance between the two aircraft?
Answers
Answer:
324.3mi
Step-by-step explanation:
Given Space Shuttle height above ground = 330mi
Airplane height above ground = 5.7mi
Difference between two aircrafts = Space Shuttle height - airplane height above ground
= 330 - 5.7
= 324.3mi
Maryland transportation authority decided to setup toll booths on either side of the Fort McHenry tunnel due to increased traffic. After studying the traffic patterns, MTA found that peak traffic occurs in the evenings on Friday and Saturday. On average, 4796 vehicles per hour pass through the tunnel each way during peak times. The vehicles need to go through the toll booths. MTA would like to keep the average time spent at each toll booth to less than 2 minutes. How many lanes should MTA open if they do not want to have more than 10 vehicles waiting in line (on average)? Hint: Start by calculating the number of cars waiting as if there is only one toll booth (i.e., calculate L using the information). Then calculate the number of toll booths needed if each booth is limited to 10 vehicles. NOTE: Round up your answer. For example, if you get an answer of 8.86 then round up the answer to 9.
Answers
Problem: Maryland transportation authority decided to setup toll booths on either side of the Fort McHenry tunnel due to increased traffic. After studying the traffic patterns, MTA found that peak traffic occurs in the evenings on Friday and Saturday.
On average, 4796 vehicles per hour pass through the tunnel each way during peak times. The vehicles need to go through the toll booths. MTA would like to keep the average time spent at each toll booth to less than 2 minutes. How many lanes should MTA open if they do not want to have more than 10 vehicles waiting in line (on average)?Solution:We are given that:- Average number of vehicles that passes through the tunnel each way during peak time = 4796 per hour- Vehicles need to go through the toll booth.- Maximum allowable average time at each toll booth is 2 minutes.- MTA does not want more than 10 vehicles waiting in line at a time.We need to find out how many lanes MTA should open in order to fulfill the above criteria.
We can calculate the number of cars waiting in the line, using the formula:- L = Wq / λ - µWhere,- L is the number of cars in the system (waiting in line or being serviced),- Wq is the average waiting time in the queue,- λ is the arrival rate of the vehicles (i.e., the number of vehicles arriving per minute),- µ is the service rate (i.e., the number of vehicles that can be served per minute).So, first let’s calculate the number of vehicles arriving per minute.- λ = (4796 vehicles / hour) / (60 minutes / hour) = 79.9333 vehicles / minuteNow let’s calculate the number of lanes (number of toll booths) we need, assuming that we have only one toll booth and the average waiting time is less than 2 minutes.
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3. (6 pts) consider three branch prediction scheme: predict not taken, predict taken, and dynamic prediction. assume that they all have zero penalty when they predict correctly and two cycles when they are wrong. assume that the average predict accuracy of the dynamic predictor is 90%. which predictor is the best choice for each of the following branches? justify your answers. a. a branch that is take with 5% frequency. b. a branch that is taken with 95% frequency. c. a branch that is taken with 70% frequency.
Answers
There are three branch prediction scheme: predict not taken, predict taken, and dynamic prediction. assume that they all have zero penalty when they predict correctly and two cycles when they are wrong.
In computer architecture, a branch predictor is a digital circuit that attempts to guess which direction a branch (e.g. an if-then-else construct) is going finally announced. The purpose of the branch predictor is to improve the flow of the instruction pipeline. Branch predictors play a key role in achieving high performance in many modern pipeline microprocessor architectures.
1. If the branch is taken 5% of the time, the branch prediction scheme is ``predicted-taken'' because the process must start fetching and then executing at the target address.
2. If a branch is taken 95% of the time, the branch outcome is known with certainty, so the branch prediction scheme is "unpredictable".
3. If the branch is taken 70% of the time, then the prediction scheme is "dynamic prediction" and the branch prediction can change dynamically during program execution.
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find the point at which the line intersects the given plane. x = 3 − t, y = 2 t, z = 2t; x − y 5z = 9 (x, y, z) = incorrect: your answer is incorrect.
Answers
To find the point at which the line intersects the given plane, we will first substitute the parametric equations of the line into the equation of the plane and then solve for the parameter 't'.
The parametric equations of the line are:
x = 3 - t
y = 2t
z = 2t
The equation of the plane is:
x - y + 5z = 9
Step 1: Substitute the parametric equations of the line into the plane equation:
(3 - t) - (2t) + 5(2t) = 9
Step 2: Simplify the equation and solve for 't':
3 - t - 2t + 10t = 9
7t - t = 6
6t = 6
t = 1
Step 3: Substitute the value of 't' back into the parametric equations of the line to find the intersection point (x, y, z):
x = 3 - t = 3 - 1 = 2
y = 2t = 2(1) = 2
z = 2t = 2(1) = 2
Therefore, the point at which the line intersects the given plane is (2, 2, 2).
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Which one is the simplest fraction, 6/20, 15/35, 8/14, or 9/16?
Answers
Answer:
9/16
Step-by-step explanation:
Answer:
9/16
Step-by-step explanation:
20 POINTS What are the lengths of the major and minor axes of the ellipse?
(x−3)212+(y+4)224=1
Drag a value to the boxes to correctly complete the table.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Length of major axis Length of minor axis
Answers
The lengths of the axes in the elipse are given as follows:
Major axes: \(8\sqrt{14}\).Minor axes: \(4\sqrt{53}\).Equation of an elipseThe equation of an elipse of center (x*, y*) is given according to the following rule:
(x - x*)²/a² + (y - y*)²/b² = 1.
The lengths of the axes are given as follows:
Major axes: 2 x greater of a or b.Minor axes: 2 x lesser of a or b.In this problem, the equation of the elipse is given as follows:
(x - 3)²/212 + (y + 4)²/224 = 1.
Hence the measures of a and b are calculated as follows:
Measure of a: a² = 212 -> a = sqrt(212) -> a = 2sqrt(53).Measure of a: b² = 224 -> b = sqrt(224) -> b = 4sqrt(14).Hence the lengths of the axes have numeric values given by:
Major axes: 2 x 4sqrt(14) = 8sqrt(14) = \(8\sqrt{14}\).Minor axes: 2 x 2sqrt(53) = 4sqrt(53) = \(4\sqrt{53}\).The difference in the measures is because I suppose there was a typo in the equation of the ellipse, but the procedure is as presented in this problem.
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Subtract 1/8 minus 3/4
Answers
Answer: 5/8
Step-by-step explanation:
Which ensation strates the Sum Version
12-8-15-12-15-3
1218115-12-13-15)
o 12-8-15-18.15
12-8-15-12-31 15
Answers
Answer:
desculpa mas não sei essa
an agency for the us government spends millions of dollars funding research on cancer. in particular, 20 research projects are funded to test a drug used to reduce pancreatic tumors. in one of these projects (project number 11) researchers find that the drug significantly reduces the size of tumors with a p-value of 0.027. there are no significant effects found in the other 19 projects (p-values all greater than 0.05) for the drug. given the entirety of this information, would it be proper to conclude that the drug is effective in reducing the size of pancreatic tumors?
Answers
The result from project number 11 suggests that the drug may be effective in reducing the size of pancreatic tumors, but it is not sufficient to conclude definitively that the drug is effective using hypothesis.
The p-value of 0.027 indicates that if there were truly no effect of the drug, the probability of observing a result as extreme as or more extreme than what was observed in project number 11 would be 0.027. This suggests that the result is unlikely to have occurred by chance alone. However, it is possible that the result is a false positive or due to chance variation, especially given that 20 research projects were conducted. It would be important to replicate the result in additional studies and consider the overall body of evidence before concluding definitively that the drug is effective.
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At an ice cream shop, 2 of the last 16 cones sold had chocolate ice cream. What is the experimental probability that the next cone sold will have chocolate ice cream? Write your answer as a fraction or whole number. P(chocolate)=
Answers
Answer:
i think its 1/8
Answer:
1/8
Step-by-step explanation:
GEOMETRY PLS HELP!! AB=2x+2 and AC=4x-14
Answers
Answer:
x = 8
AB = 18
Step-by-step explanation:
Equilateral triangle:
In an equilateral triangle, all three sides are equal, all three angles are equal, and each angle is 60°.
AC = AB
4x - 14 = 2x + 2
Add 14 to both sides
4x - 14 +14 = 2x + 2 + 14
4x = 2x + 16
Subtract '2x' from both sides,
4x - 2x = 2x - 2x + 16
2x = 16
Divide both sides by 2
\(\sf \dfrac{2x}{2}=\dfrac{16}{2}\)
\(\sf \boxed{\bf x = 8}\)
AB = 2x + 2
= 2*8 + 2
= 16 + 2
AB = 18
Step-by-step explanation:
ATTACHED IS YOUR SOLUTION!
suppose that five microchips in a production run of fifty are defective. a sample of seven is to be selected to be checked for defects. (a) how many different samples of seven can be chosen from the production run of fifty? (b) how many samples will contain at least one defective chip? the set of samples that do not contain any defective chips and the set of samples that contain at least one defective chip are ---select--- sets. so, the number of samples with at least one defective chip is . (c) what is the probability (as a percent) that a randomly chosen sample of seven contains at least one defective chip? (round your answer to one decimal place.) %
Answers
The answer to following parts are and this can be solved by using probability.
a) 15,890,700 different samples can be chosen
b) 6,523,881 will contain at least one defective chip
c) 41.1%
What is probability?
A probability is the number of desired outcomes divided by the number of total outcomes.
Main body:
The order in which the microchips are chosen is not important. So we use the combinations formula to solve this question.
Combinations formula:
Cₙ,ₓ is the number of different combinations of x objects from a set of n elements, given by the following formula.
Cₙ,ₓ =\(\frac{ n!}{x!(n-x)!}\)
(a) How many different samples can be chosen?
Samples of 6 from a set of 50.
Then
C₅₀,₆ = \(\frac{50!}{6!(50-6)!}\) =15,890,700
15,890,700 different samples can be chosen
(b) How many samples will contain at least one defective chip?
Either a sample contains no defective chip, or it contains at least one. From a), the sum of them is 15890700.
Then
No defective chips:
Four are defective.
So 50-4 = 46 are not.
This is samples of 6 from a set of 46.
C₄₆,₆ = 46!/6!*40!
9,366,819 samples contain no defective chips.
At least one:
9366819 + n = 15890700
n = 6523881
6,523,881 will contain at least one defective chip
(c) What is the probability (as a percent) that a randomly chosen sample of six contains at least one defective chip
6,523,881 out of 15,890,700
6,523,881/15,890,700 = 0.411
As a percent
41.1%
Hence the answer are as follows.
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WILL GIVE BRAINLIEST 100 POINTS PLEASE HELP DON't BE WRONG
If triangle ABC undergoes a dilation of scale factor 3 centered at the origin, what will be the coordinate of the image of point B?
A. (6,3)
B. (2,9)
C. (5,6)
D. (6,9)
If triangle ABC undergoes a dilation of scale factor 3 centered at the origin, what will be the coordinate of the image of point B?
A. (6,3)
B. (2,9)
C. (5,6)
D. (6,9)
Will love you forever if right ;D
Answers
Answer:
D
Step-by-step explanation:
Answer:
D. (6, 9)
Step-by-step explanation:
B(2, 3) → B'(6, 9)
multiply by 3
Slope = -1, through point (-3,5)
Answers
The equation of the line having slope = -1 and passing through a point (-3, 5) is y = -x + 2 and graph is given below.
The general equation of a line is y = m × x + c, where m is the slope and c is the y-intercept of the line.
Given slope is equal to -1.
Therefore the equation of the required line is y = (-1) × x + c.
Given that this line passes through the point (-3, 5).
Therefore we have 5 = (-1) × (-3) + c
⇒ 5 = 3 + c
⇒ 5 - 3 = c
⇒ 2 = c
⇒ c = 2
Therefore the y-intercept of the required line in cartesian coordinate form is (0, 2).
Therefore the required equation of the line is y = (-1) × x + 2
⇒ y = -x + 2.
Refer to the attached image for the graph of this line.
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Disclaimer: The question is not incomplete.
Assuming the following as the complete question.
Find the equation of the line having slope = -1, through point (-3,5) and also draw the graph of the line.
Which two equation could you ue a a ytem to find the cot of the entry fee and the cot of each ticket? Why?
Answers
On solving the provided question, we can say that - the entrance cost is $10, Each ticket will cost $2.
What is linear equation?A linear equation has the algebraic form y=mx+b, where m denotes the slope and b the y-intercept. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Ax+By=C is the typical form for linear equations with two variables. A linear equation in standard form is, for instance, 2x+3y=5. Finding both intercepts (x and y) for an equation of this type is not too difficult.
Let x be a symbol for the admission costs.
y denote the price of each ticket.
provided equation
\(x + 10y = 30 ... (i)\)
equation of Tristan
\(x + 15y = 40 ...... (ii)\)
equation of Keith
\(x + 10y = 30 .......... (iii)\\x = 10\\y = 2\)
the entrance cost is $10.
Each ticket will cost $2.
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A bag contains 10 marbles. Four of them are red, three blue, two white, and one yellow. A marble is drawn at random. What is the probability that it is yellow?
Answers
Simplify to a single power of 6:
Answers
Answer:
6^2
Step-by-step explanation:
it is a division between two power with the same base, so we have to subtract the exponents
6^(6-4) = 6^2
Answer:
36
Step-by-step explanation:
6^6/ 6^4
46656/1296
36