Answer: A
Step-by-step explanation:
The slope of the line that passes through the given points is \(\frac{-4-2}{5-(-1)}=-1\). Since parallel lines have equivalent slopes, we are looking for a line that also has a slope of -1, which is option A
What is the length of of BC? with work pls help
Answer:
31
Step-by-step explanation:
Assuming the drawing is to scale
The triangle is equilateral according to measure, So the measure of angles A, B and C are the same and the lengths of sides AB, BC and BA are equalThere is very little information to go off, so the measurements are done with a ruler etc.With that in mind, this means AC=BC, ergo \(6x-5=4x+7\) So, \(6x-4x=7+5\) then \(x=6\) Plugging that back into BC, we have \(4(6)+7=24+7=31\)what is the greatest perfect square that is a factor of 192
Answer:
either 3 or 64
Step-by-step explanation:
unable to process what I already know. 3 or 64
If 3x + 10 = 10 + 2x, what is the value of x?
A) x = 4
B) x = -4
C) x = -1
D) x = 0
Answer:
x=0
Step-by-step explanation:
3x + 10 = 10 + 2x
Subtract 2x from each side
3x-2x + 10 = 10 + 2x-2x
x+10 = 10
Subtract 10 from each side
x+10-10 = 10-10
x=0
Answer:
x=0
Step-by-step explanation:
3x + 10 = 10 + 2x
Subtract 2x from each side
3x-2x + 10 = 10 + 2x-2x
x+10 = 10
Subtract 10 from each side
x+10-10 = 10-10
x=0
in a public opinion poll 624 people from a sample of 1100 indicated they would vote for specific candidate how many votes can the candidate expect to receive from a population of 40000
Hello!
In a sample of 1100 people, the specific candidate got 624 votes. So, we can write it as 624/1100.
And if the total of voters is 40,000, how many votes this specific candidate will receive? We can write it as x/40,000.
Now, let's equal both fractions look:
\(\begin{gathered} \frac{624}{1100}=\frac{x}{40000} \\ \\ 1100x=624\times40000 \\ 1100x=24960000 \\ x=\frac{24960000}{1100} \\ \\ x\cong22691 \end{gathered}\)Answer:Approximately 22691 votes.
2x + 8y = 22
8x - 8y = 8
Answer:
(3, 2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesAlgebra I
Solving systems of equations using substitution/eliminationSolving systems of equations by graphingStep-by-step explanation:
Step 1: Define systems
2x + 8y = 22
8x - 8y = 8
Step 2: Solve for x
Elimination
Add 2 equations together: 10x = 30Divide 10 on both sides: x = 3Step 3: Solve for y
Define original equation: 8x - 8y = 8Substitute in x: 8(3) - 8y = 8Multiply: 24 - 8y = 8Subtract 24 on both sides: -8y = -16Divide -8 on both sides: y = 2Step 4: Graph systems
Check the systems.
2. Maria is monitoring the temperature of
two substances in her science lab.
Substance A is currently 96.2° and rising
1.5° each minute. Substance B is
currently 98.5° and cooling 0.8° each minute.
After how many minutes will the two
substances be at the same temperature?
a. Equation:
b. Solution:
Here, we are required to determine after how many minutes will the two substances be at the same temperature.
The equation of when the two substances will be at the same temperature and the solution are as follows;
(a) The equation is 96.2 + 1.5(x) = 98.5 + 0.8(x).
(b) The solution is, x = 3.285minutes.
For substance A which is currently at 96.2° and rising at 1.5° each minute; It's temperature after x minutes is given as;
T(a) = 96.2 + 1.5(x)For substance B which is currently at 98.5° and rising at 0.8° each minute; It's temperature after x minutes is given as;
T(b) = 98.5 + 0.8(x)(a) For the two substances to be at the same temperature; T(a) must be equal to T(b).
T(a) = T(b)The equation is therefore;.
96.2 + 1.5(x) = 98.5 + 0.8(x)
(b) To determine the solution;
1.5x - 0.8x = 98.5 - 96.2
0.7x = 2.3
x = 2.3/0.7
x = 3.285minutes.
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Please find the Y for both of these equation
4x - y = 4
X-2y=-6
Answer:
1). y= -4+ 4x
2). y= 3+ x/2
Step-by-step explanation:
hope this helps !
I had to hire a plumber to come fix a leaky pipe. The first day he worked 3 hours and charged me $450. The next day he came back and finished the job working another 5 hours charging me $700. Find the equation that represents the cost, y, after x hours of working.
Answer:
143.75X = Y
Explanation:
Since I had to hire a plumber to come fix a leaky pipe, and the first day he worked 3 hours and charged me $ 450, while the next day he came back and finished the job working another 5 hours charging me $ 700, to find the equation that represents the cost, and, after x hours of working, the following calculation must be performed:
(450 + 700) / (3 + 5) = Y
1150/8 = Y
143.75 = Y
Thus, the hourly cost of the plumber's work was $ 143.75.
Francium is an element with a half-life of 22 minutes. 1000 grams of francium is placed into a bowl determine how much Francium (in grams) will be left after 2 hours
The amount of the element, Francium, that will remain after 2 hours is 31.25 grams.
Half-life problemTo determine how much francium will be left after 2 hours, we need to calculate the number of half-lives that occur within that time period.
Given that the half-life of francium is 22 minutes, we can calculate the number of half-lives in 2 hours (120 minutes):
Number of half-lives = (Total time elapsed) / (Half-life)
Number of half-lives = 120 minutes / 22 minutes ≈ 5.4545
Since we can't have a fraction of a half-life, we take the integer part, which is 5.
Each half-life represents a halving of the amount of francium. So, after 5 half-lives, the remaining amount of francium can be calculated using the formula:
Remaining amount = Initial amount * (1/2)^(Number of half-lives)
Given that the initial amount is 1000 grams, we can calculate the remaining amount after 2 hours:
Remaining amount = 1000 grams * \((1/2)^5\)
Remaining amount ≈ 1000 grams * 0.03125
Remaining amount ≈ 31.25 grams
Therefore, after 2 hours, approximately 31.25 grams of francium will be left.
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PLS HELP ME
The function f(x) = -3(2)²+¹ +90 represents the number of tokens a child has x hours after arriving at an arcade.
What is the practical domain and range of the function?
Enter your answer by filling in the boxes to correctly complete the statements. If necessary, round to the nearest hundrea
The practical domain of the situation is x
Basic
The practical range of the situation is 90
A
O
Answer:
Practical domain: 0 ≤ x ≤ 3.907Practical Range: 0 ≤ y ≤ 84 where y is an integer, so we have the set {0,1,2,...,83,84}The 3.907 is approximate.
====================================
Explanation:
x = number of hours that elapse
y = f(x) = number of tokens
If we use a graphing tool like a TI84 or GeoGebra, then the approximate solution to -3(2)^(x+1) + 90 = 0 is roughly x = 3.907
At around 3.907 hours is when the number of tokens is y = 0. Therefore, this is the approximate upper limit for the domain. The lower limit is x = 0.
The domain spans from x = 0 to roughly x = 3.907, and we shorten that down to 0 ≤ x ≤ 3.907
------------
Plug in x = 0 to find y = 84. This is the largest value in the range.
The smallest value is y = 0.
The range spans from y = 0 to y = 84, so we get 0 ≤ y ≤ 84
Keep in mind y is the number of tokens. A fractional amount of tokens does not make sense, so we must have y be a whole number 1,2,3,...,83,84.
The x value can be fractional because 3.907 hours for instance is valid.
------------
Extra info:
The function is decreasing. It goes downhill when moving to the right.The points (0,84) and (1,78) and (2,66) and (3,42) are on this exponential curve.A point like (2,66) means x = 2 and y = 66. It indicates: "after 2 hours, they will have 66 tokens remaining".[1 6 9 3]
[2 5 8 1]
[0 2 2 4]
what are the dimensions of the matrix
Answer:
4 by 3
Explanation:
Rows by columns
STEM The table shows the mass in grams of one atom of each of
several elements. List the elements in order from the least mass to
greatest mass per atom.
Answer: are you in 8th grade cuz i got that question on my math course 3 note book. And I need help for that one too lol
I found out the answer is hydrogen,carbon,oxygen, silver and gold
The mass from the least to the greatest is hydrogen, carbon, oxygen, silver and gold
What is the mass from least to the greatest?The mass is written in scientific notation. Scientific notation is used in expressing large numbers in smaller numbers.
For example:
• The number : 1 x \(10^{-2}\) is equivalent to 0.01
• The number 5 x \(10^{-3}\)is equivalent to 0.001
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Answer: Using the linear model, a puppy grows _____ pounds each month. Fill in the blank.
Using the linear model, a puppy grows 6 pounds each month.
What is the point-slope form?In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At data point (2, 20), an equation of this line in slope-intercept form can be calculated by using the point-slope form:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 20 = (80 - 20)/(12 - 2)(x - 2)
y = 60/10(x - 2) + 20
y = 6x - 12 + 20
y = 6x + 8
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Urgent please help thank you all
In the number 725.78, how does the value of the 7 in the tenths place compare to the value of the 7 in the hundreds place?
Answer:
C. 1/1,000
Step-by-step explanation:
yes or no ?
x+y+z=600
40x + 25y + 20z = 15850
35x + 50y + 35z = 13450
The solution for the equation for x, y,z are 318.3 , 503.33 , 785.
What is equation?
In arithmetic, AN equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =
Main body:
given equation are:
x+y+z=600 ----(1)
40x + 25y + 20z = 15850 ----(2)
35x + 50y + 35z = 13450 ---(3)
using equation 1,
x =600 - z -y
substituting value of x in eqn (3)
35(600 - y - z) +50y +35z = 13450
21000 - 35y - 35 z + 50y + 35z = 13450
15 y = -7550
y = -503.33
substituting the value of x and y in eqn (2)
40(600-y-z) +25 y +20z = 15850
24000 - 40y -40z +25 y+ 20z = 15850
24000 -15y -20z = 15850
3y +4x = 1630
3(-503.33) +4x = 1630
z = 785
Hence the value to these equation are as follows.
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I need the answers for the table below.
The values of f(x) for the given x - values rounded to 4 decimal places are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013 respectively
Given the function :
tan(πx)/7xSubstitute the given value of x to obtain the corresponding f(x) values :
x = -0.6
f(x) = (tanπ(-0.6))/7(-0.6) = 0.0078358
x = -0.51
f(x) = (tanπ(-0.51))/7(-0.51) = 0.0078350
x = -0.501
f(x) = (tanπ(-0.501))/7(-0.501) = 0.001967
x = -0.5
f(x) = (tanπ(-0.5))/7(-0.5) = 0.001959
x = -0.4999
f(x) = (tanπ(-0.4999))/7(-0.4999) = 0.001958
x = 0.499
f(x) = (tanπ(-0.499))/7(-0.499) = 0.001951
x = -0.49
f(x) = (tanπ(-0.49))/7(-0.49) = 0.00188
x = -0.4
f(x) = (tanπ(-0.4))/7(-0.4) = 0.00125
Therefore, values which complete the table are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013
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PLEASE HELP THANK UUUUU
The ratio in simplest form is 1:4, the correct option is C.
We are given that;
The options A. 2/3 B. 3/4 C. 1/4 D. 4/1
Now,
The letters D and O are used 2 times and 4 times respectively in the words “RATIOS AND PROPORTIONS”. So we can write the ratio as 2:4.
The GCF of 2 and 4 is 2, since 2 is the largest number that can divide both 2 and 4 without leaving a remainder.
To simplify the ratio, we divide both terms by 2:
2:4 = (2/2):(4/2) = 1:2
Therefore, by the ratio the answer will be 1/4.
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Suppose that v varies directly with x, and v = 20 when x = 32.
A) Write a direct variation equation that relates x and y .
B) Find y when x = 24
\(\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill\)
\(\stackrel{\textit{"v" varies directly with "x"}}{v = k(x)}\hspace{5em}\textit{we also know that} \begin{cases} x=32\\ v=20 \end{cases} \\\\\\ 20=k(32)\implies \cfrac{20}{32}=k\implies \cfrac{5}{8}=k\hspace{8em}\boxed{v=\cfrac{5}{8}x} \\\\\\ \textit{when x = 24, what's v?}\qquad v=\cfrac{5}{8}(24)\implies v=15\)
Gregory was p years of age 4 years ago. In terms of p, how old will he be in 4 years from now?
Let us say that Gregory is q years old now. 4 years ago he was (q - 4) years. Using the information of the problem, we formulate the equation:
\(\begin{gathered} p=q-4 \\ \Rightarrow q=p+4 \end{gathered}\)After 4 years, he will be (q + 4) years old. Using the previous equation:
\(\begin{gathered} q+4=p+4+4 \\ \Rightarrow(q+4)=p+8 \end{gathered}\)Gregory will be (p + 8) years old 4 years from now.
p(x) = 3(x + 10x + 5) - 5(x - k)
In the polynomial p(x) defined above, k is a
constant. If p(x) is divisible by x, what is the value
of k?
First, you should simplify the function expression.
3(x2 + 10x + 5) - 5(x-k) = 3x2 + 30x + 15 - 5x + 5k = 3x2 +15x +15 +5k
In order for the polynomial to be divisible by x, all terms need to divide by x with no remainder. The first two terms clearly divide by x. However, the last two do not. In order for this to work out where k is constant, 5k would have to cancel out the +15 term, leaving nothing to divide by x.
So: 15 + 5k = 0
5k = -15
k = -3
Dana is attaching a shelf to a wall and needs the shelf to be parallel to the floor. How many degrees should the shelf be
relatve to the foor?
A) O degrees
B) 90 degrees
C) 45 degrees
D) 225 degrees
Explanation:
By definition, the floor is assumed to be level and that means the floor is at a 0 degree angle. The shelf must also have this same angle relative to the floor so we have the shelf and floor as parallel planes. For more info, check out the converse of the corresponding angles theorem.
Math question I don’t understand and need help for extra points, thank you
Answer:
y=2x-3 or B
Step-by-step explanation:
just shove into desmos graphing calculator
1. 18x^3-2x^2+4x-1
1.1 How many terms are in 18x^3-2x^2+4x-1
The polynomial 18x³ - 2x² + 4x - 1 consists of four terms.
The number of terms in a polynomial helps when performing operations like simplification, factoring, or evaluating expressions.
The polynomial 18x³ - 2x² + 4x - 1 consists of four terms.
In order to determine the number of terms in a polynomial, we count the number of distinct algebraic expressions separated by addition or subtraction operations.
In this polynomial, we have:
Term 1: 18x³ (This is the term with the highest degree, which is 3 in this case, and it includes the coefficient 18.)
Term 2: -2x² (This term has a degree of 2 and a coefficient of -2.)
Term 3: 4x (This term has a degree of 1 and a coefficient of 4.)
Term 4: -1 (This is a constant term with a degree of 0.)
We can see that there are four distinct terms separated by addition and subtraction operations:
18x³, -2x², 4x, and -1.
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ABC ~ AYZ , what's the value of x?
Answer:
Step-by-step explanation:
6cm
Statistical data of breakdowns of computer XXX show that the duration for trouble-free operation of the machine can be described as a gamma distribution with a mean of 40 days and a standard deviation of 10 days. The computer is occasionally taken out for maintenance in order to insure operational condition at any time with a 95% probability.
1. How often should the computer be scheduled for maintenance? Should it be shorter or longer than the mean of 40 days?
2. Three XXX computers were acquired at the same time by an engineering consulting firm. The computers are operating under the same environment, workload, and regular maintenance schedule. The breakdown times between the computers, however, may be assumed to be statistically independent. What is the probability that at least one of the three machines will break down within the first scheduled maintenance time?
1. In this case, we want the reliability to be 95%, so the probability of not breaking down is 0.95.
2. Probability of no breakdowns = (reliability of a single machine)^3. Probability of at least one breakdown = 1 - Probability of no breakdowns
1. To determine how often the computer should be scheduled for maintenance, we need to consider the reliability and the desired level of operational condition. Since the duration for trouble-free operation follows a gamma distribution with a mean of 40 days, this means that, on average, the computer can operate for 40 days before a breakdown occurs.
To ensure operational condition with a 95% probability, we can calculate the maintenance interval using the concept of reliability. The reliability represents the probability that the machine will not break down within a certain time period. In this case, we want the reliability to be 95%, so the probability of not breaking down is 0.95.
Using the gamma distribution parameters, we can find the corresponding reliability for a specific time duration. By setting the reliability equation equal to 0.95 and solving for time, we can find the maintenance interval:
reliability = 0.95
time = maintenance interval
Using reliability and the gamma distribution parameters, we can calculate the maintenance interval.
2. To calculate the probability that at least one of the three machines will break down within the first scheduled maintenance time, we can use the complementary probability approach.
The probability that none of the machines will break down within the first scheduled maintenance time is given by the reliability of a single machine raised to the power of the number of machines:
Probability of no breakdowns = (reliability of a single machine)^3
Since the breakdown times between the machines are statistically independent, we can assume that the reliability of each machine is the same. Therefore, we can use the reliability calculated in the first part and substitute it into the formula:
Probability of at least one breakdown = 1 - Probability of no breakdowns
By calculating this expression, we can determine the probability that at least one of the three machines will break down within the first scheduled maintenance time.
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5, 5, 6, 8, ?, 15, 20, 26
Answer: 11
Explanation:
beginning with 5...
5+0=5
5+1=6
6+2=8
8+3=11
11+4=15
15+5=20
20+6=26
What have the Mars rovers discovered about Mars?
A. The crust of Mars contains 2 chemical elements never discovered before.
B. It had similar volcano activity and crust composition to Earth.
C. It has polar ice caps that could become an ocean if Mars were to warm up in the future.
D. The atmosphere of Mars is twice as thick as scientists predicted it would be.
Answer:D. The atmosphere of Mars is twice as thick as scientists predicted it would be.
Step-by-step explanation:
Construct a polynomial function with the following properties: fifth degree, 2 is a zero of multiplicity 4 , −3 is the only other zero, leading coefficient is 2 .
The pοlynοmial functiοn with a fifth degree, 2 as a zerο οf multiplicity 4, −3 as the οnly οther zerο, and a leading cοefficient οf 2 is:
\(f(x) = 2(x-2)^4(x+3) = 2x^5 - 32x^4 + 192x^3 - 384x^2 + 216x + 1080\)
What is Polynomial Function?
A pοlynοmial functiοn is a mathematical functiοn οf the fοrm \(f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0\), where the coefficients\(a_n, a_{n-1}, ..., a_1, a_0\) are constants, x is the variable, and n is a non-negative integer. It is a functiοn that can be graphed as a smοοth curve with nο breaks οr jumps.
If 2 is a zerο οf multiplicity 4, then the pοlynοmial functiοn must have the factοr\((x-2)^4\).
If −3 is the οnly οther zerο, then the pοlynοmial functiοn must alsο have the factοr (x+3).
The pοlynοmial functiοn with these properties and a leading cοefficient οf 2 can be written as:
\(f(x) = 2(x-2)^4(x+3)\)
Expanding this polynomial gives:
\(f(x) = 2x^5 - 32x^4 + 192x^3 - 384x^2 + 216x + 1080\)
Therefore, the polynomial function with a fifth-degree, 2 as a zero of multiplicity 4, −3 as the only other zero, and a leading coefficient of 2 is:
\(f(x) = 2(x-2)^4(x+3) = 2x^5 - 32x^4 + 192x^3 - 384x^2 + 216x + 1080\)
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....................help
Answer:
A
Step-by-step explanation:
With function transformation, added/subtracted numbers outside of the x always mean the function is being translated up/down. In this case, since the 2 is being replaced with a 4, the new function is 2 units higher than the previous function.