To find the equation of the line that is perpendicular to the line 3z - y = -5 and passes through the point (7, -2), we need to determine the slope of the given line and then find the negative reciprocal to get the slope of the perpendicular line. Using the point-slope form, we can then find the equation of the perpendicular line.
The given line 3z - y = -5 can be rewritten in slope-intercept form as y = 3z + 5. The slope of this line is 3. The slope of a line perpendicular to it will be the negative reciprocal of 3, which is -1/3.
Using the point-slope form with the point (7, -2), we have:
y - y₁ = m(x - x₁),
where (x₁, y₁) is the given point and m is the slope of the line.
Substituting the values, we get:
y - (-2) = (-1/3)(x - 7),
y + 2 = (-1/3)(x - 7).
To simplify and bring it to standard form, we can multiply both sides by 3:
3y + 6 = -x + 7,
x + 3y = 1.
Therefore, the equation of the line perpendicular to 3z - y = -5 and passing through the point (7, -2) is x + 3y = 1. Thus, option (b) is the correct answer.
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What is 829×2929-(920)×0
Answer:
0
Step-by-step explanation:
what is the circumfrence of this circle
Answer:
37.6
Step-by-step explanation:
r = 6 cm
circumfrence = 2 x 3.14 x 6
= 12 x 3.14
approx 37.6 cm
Answer: 37.68
Step-by-step explanation:
Describe the polynomial:
-4x²y3 + 5x²y
O
It is a binomial with a degree of 2.
It is a trinomial with a degree of 6.
It is a binomial with a degree of 5.
It is a trinomial with a degree of 5.
Solve by quadratic formula:
8a2 + 6a + 5=0
Answer:
[tex]x = \frac{-3 \pm i\sqrt{31}}{8}[/tex]
Step-by-step explanation:
Quadratic Formula: [tex]x = \frac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]
√-1 is imaginary number i
Step 1: Define Quadratic
8a² + 6a + 5 = 0
a = 8
b = 6
c = 5
Step 2: Plug into Quadratic Formula
[tex]x = \frac{-6 \pm \sqrt{6^2-4(8)(5)} }{2(8)}[/tex]
Step 3: Solve
[tex]x = \frac{-6 \pm \sqrt{36-160} }{16}[/tex]
[tex]x = \frac{-6 \pm \sqrt{-124} }{16}[/tex]
[tex]x = \frac{-6 \pm \sqrt{124} (\sqrt{-1} )}{16}[/tex]
[tex]x = \frac{-6 \pm i\sqrt{124}}{16}[/tex]
[tex]x = \frac{-6 \pm 2i\sqrt{31}}{16}[/tex]
[tex]x = \frac{2(-3 \pm i\sqrt{31})}{16}[/tex]
[tex]x = \frac{-3 \pm i\sqrt{31}}{8}[/tex]
Gas mileage is the number of miles you can drive on a a gallon of gasoline. A test of a new car results in 330 miles on 10 gallons of gas. How far could you drive on 55 gallons of gas? What is the car's gas mileage?
Find the unit rate:
330 miles / 10 gallons = 33 miles per gallon.
Multiply miles per gallon by number of gallons:
33 x 55 = 1,815 total miles.
As September is winding down, we can see that nine of the twelve calendar months of the year have passed. This is 9/12 = 3/4 = 75% of 2020, when considering just the months. If we instead want to know what percent of the days in 2020 have passed at the end of the last day of September, what would that percentage be? Express your answer to the nearest tenth.
Answer:
The percent of the days in 2020 has passed at the end of the last day of September is:
74.86% or 74.9% or 75%Step-by-step explanation:
To identify the percent of the days in 2020 has passed at the end of the last day of September, first, you must add the days in each month of 2020:
January: 31 days.February: 29 days (2020 is a leap year).March: 31 days.April: 30 days.May: 31 days.June: 30 days.July: 31 days.August: 31 days.September: 30 days.Days passed= 31+29+31+30+31+30+31+31+30= 274 days.
How you know, a leap year has 366 days, so, you must divide the days until the last day in September (274) in the total days in a leap year, also you must multiply this value by 100 to obtain a percentage:
[tex]\frac{274}{366}*100=74.86[/tex]So, the percentage is 74.86% or 74.9%, a value that if you approach it would be 75% equally.
Can someone help me plsss
Answer:
The slope of the line is [tex]\frac{-1}{2}[/tex]
Step-by-step explanation:
The rule of the slope of a line is
m = [tex]\frac{y2-y1}{x2-x1}[/tex] (x1, y1) and (x2, y2) are two points lie on the line→ Let us solve the question
∵ The line contains the points B (-4, 4) and R (0, 2)
∴ x1 = -4 and y1 = 4
∴ x2 = 0 and y2 = 2
→ Substitute them in the rule of the slope above to find it
∵ m = [tex]\frac{2-4}{0--4}=\frac{-2}{4}=\frac{-1}{2}[/tex]
∴ m = [tex]\frac{-1}{2}[/tex]
∴ The slope of the line is [tex]\frac{-1}{2}[/tex] .
Tom sold 500 liters of soda at a baseball game. How much is this in milliliters?
Answer:
500,000
Step-by-step explanation:
1 liter is a thousand milliliters
miss Bennett has finally become TickTock famous she has a contract that paid her $200 already and $12 each for each TickTock she posts last month she earned $272 how many TickTock‘s did she post last month WRITE AN EQUATION to represent this.
Answer:
6 tiktoks
Step-by-step explanation:
the expression is:
y = 200 + 12t, where y is the total amount she earned and t is the amount of tiktoks she made
to solve:
272 = 200 + 12t
72 = 12t
6 = t
can i get a thanks and brainliest please?
Three consecutive integers are such that three times the smallest is 14 more than the largest.Find the integers.
Answer:
8, 9, 10Step-by-step explanation:
x ← the smallest integer
x+1 ← the middle integer
x+2 ← the largest integer
3x ← three times the smallest
x+2 + 14 ← 14 more than the largest
3x = x+2 + 14
-x -x
2x = 16
÷2 ÷2
x = 8
x+1 = 8+1 = 9
x+2 = 8+2 = 10
Check: 3×8 = 24; 24-14 = 10
A uniform distribution is defined over the interval from 2 to 5.
What is the range of the random variable, x?
Over the range, what is the probability of the random variable, x?
What is the area of this uniform distribution?
The probability of x within this range is constant and equal to 1/3. The area under the uniform distribution curve is 1.
The range of the random variable, x, in a uniform distribution from 2 to 5 is [2, 5]. It represents the entire interval of possible values for x.
The probability of the random variable, x, in a uniform distribution is constant over the range. Since it is a uniform distribution, the probability density function is equal for all values within the range. Therefore, the probability of x taking any specific value within the range [2, 5] is the same, and it is given by 1 divided by the length of the range:
Probability of x = 1 / (length of range)
= [tex]P(x) = \frac{1}{5 - 2} = \frac{1}{3}[/tex]
The area of the uniform distribution is represented by the probability density function over the range. Since it is a uniform distribution, the probability density is constant within the range. Therefore, the area under the curve is equal to the length of the range multiplied by the constant probability density:
Area = (length of range) * (probability density) = (5 - 2) * (1 / (5 - 2)) = 3 * (1 / 3) = 1.
Hence, the area of the uniform distribution is 1.
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Determine whether the two triangles are congruent. If they are
congruent, state by what theorem (SSS, SAS, or ASA) they are
congruent. Let
a = 111,
c = 36,
x = 9,
d = 111,
f = 36,
and
y = 9.
The two triangles are congruent by the Side-Side-Side (SSS) congruence theorem.
To determine the congruence of two triangles, we need to compare their corresponding sides and angles. In this case, let's consider two triangles: Triangle ABC and Triangle DEF.
Given:
a = 111, c = 36, x = 9 for Triangle ABC
d = 111, f = 36, y = 9 for Triangle DEF
We can observe that the corresponding sides of the two triangles have the same lengths. Side AB corresponds to side DE (a = d = 111), side BC corresponds to side EF (c = f = 36), and side AC corresponds to side DF (x = y = 9).
Since all three pairs of corresponding sides are congruent, we can conclude that the two triangles are congruent. By the Side-Side-Side (SSS) congruence theorem, if the lengths of the corresponding sides of two triangles are equal, then the triangles are congruent.
Therefore, based on the given information, Triangle ABC and Triangle DEF are congruent by the SSS congruence theorem.
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[ 4 7] [3 6 5 ]
Find C =AB, if A = [9 1] B = [2 6 7]
The product of matrices A and B, denoted as C = AB, is determined by performing matrix multiplication using the given matrices. In this case, A is a 2x1 matrix and B is a 1x3 matrix. The resulting matrix C will have dimensions 2x3.
To find the product of matrices A and B, we perform matrix multiplication by multiplying corresponding elements and summing the results.
The dimensions of the matrices must be compatible for multiplication, meaning the number of columns in the first matrix must match the number of rows in the second matrix.
Given matrices A and B:
A = [9 1]
B = [2 6 7]
To calculate C = AB, we multiply each element of A with the corresponding element in B, and then sum the results. The resulting matrix C will have dimensions 2x3.
C = [92 + 13 96 + 16 97 + 15]
Calculating each element of C, we have:
C = [18 + 3 54 + 6 63 + 5]
[21 60 68]
Simplifying, we get:
C = [21 60 68]
Therefore, the product of matrices A and B, denoted as C = AB, is the matrix:
C = [21 60 68]
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Which sampling would be appropriate to survey 120,000 people? A. 12,000 B. 1,200 C. 120 D. 12
Answer:
12,000 i relly took the test gat it righ
Step-by-step explanation:
mark me brainlest pliz
HELP ASAP Five times a number decreased by six is 29. show steps please and ill definitely give BRAINLIEST if right
Answer:
5x-6=29
Step-by-step explanation:
Well 5 times an unknown number is 5x and then it gets decreased by 6 so 5x-6 and it equals 29.
A used motorcycle is on sale for $3,600. Erik makes an offer equal to ¾ of this price. How much does Erik offer for the motorcycle? (A)$4,800 (B) $2,700 (C)$2,400 (D) $900
The answer is (B). Erik offers $2,700 for the motorcycle.
Original price of motorcycle = $3,600
Erik's offer = ¾ * $3,600 = $2,700
Here is the explanation in detail:
1. The original price of the motorcycle is $3,600.
2. Erik makes an offer equal to ¾ of the original price.
3. ¾ of $3,600 is $2,700.
4. Therefore, Erik offers $2,700 for the motorcycle.
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What is -115/12 as a mixed number?
Answer:
Since − 115 /12
is a proper fraction, it cannot be written as a mixed number.
Cannot be written as a mixed number
Step-by-step explanation:
Which value from the set (2 14, 16, 63} makes the equation n - 7 = 9 true?
63
16
2
14
Answer:
16
Step-by-step explanation:
16-7=9 so 16 makes the equation n-7=9 true
According to the number line, what is the distance between points A and B? A number line going from negative 16 to positive 12. A closed circle appears at negative 2 and is labeled A. A closed circle appears at positive 12 and is labeled B. An orange arrow line extends the length of the number line and contains points A and B.
Answer:
14units
Step-by-step explanation:
Given
Initial point A = -2 (since it is on negative 2)
Other point B = 12 (lying in positive 12)
To get the distance between point A and B, we will use the expression:
AB = point B - point A
Substitute the given point in the expression
AB = 12-(-2)
AB = 12+2
AB = 14
Hence the distance between points A and B in the number line is 14units
which equation in a standar form has a grpah that passes through the point (-4,2) and has a slope 9/2
Equation in standard form that has a graph that passes through point (-4, 2) and has slope of 9/2 is calculated to be as equal to -40.
The equation in standard form that has a graph that passes through the point (-4, 2) and has a slope of 9/2 is given by :
Step 1: Recall the standard form of a linear equation
The standard form of a linear equation is Ax + By = C, where A, B, and C are constants.
Step 2: Substitute given values
The equation should pass through the point (-4, 2) and should have a slope of 9/2.
Therefore, the slope-intercept form of the equation is given by:
y - 2 = (9/2)(x + 4)
Multiplying through by 2, we have: 2y - 4 = 9(x + 4)2y - 4
= 9x + 36
Rearranging, we get: 9x - 2y
= -40
Therefore, the equation in standard form that has a graph that passes through the point (-4, 2) and has a slope of 9/2 is 9x - 2y
= -40.
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when a conical bottle rests on its flat base, the water in the bottle is 8 cm from its vertex. when the same conical bottle is turned upside down, the water level is 2 cm fom the base, what is the height of the bottle?
The height of the conical bottle is 16 cm.
Let's denote the height of the conical bottle as h.
When the bottle is in its regular position, with the base resting on the flat surface, the water level is 8 cm from the vertex. This means that the distance from the water level to the base is 8 cm.
When the bottle is turned upside down, the water level is 2 cm from the base. In this position, the distance from the water level to the vertex is h - 2 cm.
We can set up a proportion based on the similar triangles formed by the original and inverted positions of the bottle:
(h - 2) / 8 = h / (h - 8)
To solve this proportion, we can cross-multiply:
(h - 2)(h - 8) = 8h
Expanding the equation:
h^2 - 10h + 16 = 8h
Rearranging the terms:
h^2 - 18h + 16 = 0
Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. In this case, let's use factoring:
(h - 2)(h - 16) = 0
This equation has two possible solutions:
h - 2 = 0 --> h = 2
h - 16 = 0 --> h = 16
Since the height of the bottle cannot be 2 cm (as the water level would be at the base), the height of the bottle must be 16 cm.
Consequently, the conical bottle has a height of 16 cm.
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First consider 100% what is the 100% of 40
Answer:
Step-by-step explanation:
100% means all of 40.
So 100% of 40 is 40
Answer:
40
Step-by-step explanation:
Of means Multiply.
Multiply.
100% * 40 = 40
~I hope I helped you! :)~
Solve the following linear programming problem using the simplex method: Minimize: Z = X1 + 2X2 subject to
A. X1+3X2 ≥90
B. 8X1 +2X2 ≥ 160
C. 3X1 +2X2 ≥ 120
D. X2 ≤70
E. X1, X2 ≥ 0
The answer to the given linear programming problem, which is solved using the simplex method, is as follows:
The optimal solution to minimize the objective function Z = X1 + 2X2 is X1 = 20 and X2 = 0, with the objective function value Z = -100.
To solve the problem, we'll first convert the inequalities to equations by introducing slack and surplus variables. Then we'll set up the initial simplex tableau and iterate through the simplex algorithm until we reach an optimal solution.
⇒ Convert the inequalities to equations:
A. X1 + 3X2 + S1 = 90 (where S1 is the slack variable)
B. 8X1 + 2X2 + S2 = 160 (where S2 is the slack variable)
C. 3X1 + 2X2 + S3 = 120 (where S3 is the slack variable)
D. X2 + S4 = 70 (where S4 is the surplus variable)
⇒ Set up the initial simplex tableau:
| X1 | X2 | S1 | S2 | S3 | S4 | RHS |
----------------------------------------------
Z | -1 | -2 | 0 | 0 | 0 | 0 | 0 |
----------------------------------------------
S1 | 1 | 3 | 1 | 0 | 0 | 0 | 90 |
S2 | 8 | 2 | 0 | 1 | 0 | 0 | 160 |
S3 | 3 | 2 | 0 | 0 | 1 | 0 | 120 |
S4 | 0 | 1 | 0 | 0 | 0 | -1 | 70 |
⇒ a) Select the most negative coefficient in the Z row, which is -2. Choose the corresponding column as the pivot column (X2 column).
b) Find the pivot row by selecting the minimum ratio of the RHS value to the positive values in the pivot column. The minimum ratio is 70/1 = 70. Thus, the pivot row is S4.
c) Perform row operations to make the pivot element (1 in S4 row) equal to 1 and eliminate other elements in the pivot column:
- Divide the pivot row by the pivot element (1/1 = 1).
- Replace other elements in the pivot column using row operations:
- S1 row: S1 = S1 - (1 * S4) = 90 - 70 = 20
- Z row: Z = Z - (2 * S4) = 0 - 2 * 70 = -140
- S2 row: S2 = S2 - (0 * S4) = 160
- S3 row: S3 = S3 - (0 * S4) = 120
d) Update the tableau with the new values:
| X1 | X2 | S1 | S2 | S3 | S4 | RHS |
----------------------------------------------
Z | -1 | 0 | 0 | 0 | 2 | -2 | -140|
----------------------------------------------
S1 | 1 | 3 | 1 | 0 |
0 | 0 | 20 |
S2 | 8 | 2 | 0 | 1 | 0 | 0 | 160 |
S3 | 3 | 2 | 0 | 0 | 1 | 0 | 120 |
S4 | 0 | 1 | 0 | 0 | 0 | -1 | 70 |
e) Repeat steps a to d until all coefficients in the Z row are non-negative.
- Select the most negative coefficient in the Z row, which is -1. Choose the corresponding column as the pivot column (X1 column).
- Find the pivot row by selecting the minimum ratio of the RHS value to the positive values in the pivot column. The minimum ratio is 20/1 = 20. Thus, the pivot row is S1.
- Perform row operations to make the pivot element (1 in S1 row) equal to 1 and eliminate other elements in the pivot column.
- Update the tableau with the new values.
f) The final simplex tableau is:
| X1 | X2 | S1 | S2 | S3 | S4 | RHS |
----------------------------------------------
Z | 0 | 0 | 0 | 0 | 1 | -3 | -100|
----------------------------------------------
X1 | 1 | 3 | 1 | 0 | 0 | 0 | 20 |
S2 | 0 | -22 | -8 | 1 | 0 | 0 | 140 |
S3 | 0 | -7 | -3 | 0 | 1 | 0 | 60 |
S4 | 0 | 1 | 0 | 0 | 0 | -1 | 70 |
⇒ Read the solution from the final tableau:
The optimal solution is X1 = 20 and X2 = 0, with the objective function value Z = -100.
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QUESTION 6 Determine whether the set {P1, P2, P3} is linearly independent in P2, where p₁ = 2 + x + 3x² + 4x³, p₂ = 4 + 3x + 2x² + x³ and p3 = 1 + 2x + 3x² + 4x³. Show all working. [7 marks]
To determine whether the set [tex]$\{P_1, P_2, P_3\}$\\[/tex] is linearly independent in [tex]$P_2$[/tex], we construct a linear combination of the polynomials and set it equal to the zero polynomial. If the only solution to this equation is the trivial solution, then the set is linearly independent.
Let's construct the linear combination of the polynomials [tex]$P_1$[/tex], [tex]$P_2$[/tex] and [tex]$P_3$[/tex] as follows:
[tex]$c_1P_1 + c_2P_2 + c_3P_3 = 0$[/tex]
where [tex]$c_1$[/tex], [tex]$c_2$[/tex] and [tex]$c_3$[/tex] are constants. Substituting the given expressions for [tex]$P_1$[/tex], [tex]$P_2$[/tex] and [tex]$P_3$[/tex], we have:
[tex]$(c_1(2 + x + 3x^2 + 4x^3)) + (c_2(4 + 3x + 2x^2 + x^3)) + (c_3(1 + 2x + 3x^2 + 4x^3)) = 0$[/tex]
Expanding and combining like terms, we obtain:
[tex]$(2c_1 + 4c_2 + c_3) + (c_1 + 3c_2 + 2c_3)x + (3c_1 + 2c_2 + 3c_3)x^2 + (4c_1 + c_2 + 4c_3)x^3 = 0$[/tex]
For this equation to hold for all values of $x$, the coefficients of each term must be zero. Therefore, we have the following system of equations:
[tex]$2c_1 + 4c_2 + c_3 = 0$[/tex]
[tex]$c_1 + 3c_2 + 2c_3 = 0$\\$3c_1 + 2c_2 + 3c_3 = 0$\\$4c_1 + c_2 + 4c_3 = 0$\\[/tex]
We can represent this system of equations in matrix form as [tex]$AX = 0$[/tex], where A is the coefficient matrix and X is the column vector [tex]$\begin{bmatrix} c_1 \\ c_2 \\ c_3 \end{bmatrix}$[/tex]. To determine if there is a non-trivial solution, we need to find the determinant of the coefficient matrix A.
Calculating the determinant, we find that it is non-zero, indicating that the only solution to the system of equations is the trivial solution [tex]($c_1 = c_2 = c_3 = 0$)[/tex]. Therefore, the set [tex]$\{P_1, P_2, P_3\}$[/tex] is linearly independent in [tex]$P_2$[/tex].
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Evaluate.
4/7+3/4
A. 3/7
B. 37/56
C. 7/11
D. 19/28
Answer:
its
1.32142857143
Step-by-step explanation:
if its not im sary
Heather, David, and Kevin have a total of $90 in their wallets. David has $6 less than Heather. Kevin has 2 times what David has. How much do the have in their wallets
Answer:
Heather, $27David, $21Kevin, $42Step-by-step explanation:
Let d represent the amount David has. Then Heather has d+6 and Kevin has 2d. The sum of these amounts is ...
d +(d+6) +2d = 90
4d = 84
d = 21 . . . . . . David's amount
d+6 = 27 . . . Heather's amount
2d = 42 . . . Kevin's amount
Fill in the blank to make the two fractions equivalent.
7/8=?/48
I’m confused can someone help me ASAP
Answer:
42 should be in the blank.
Step-by-step explanation:
If you multiply 7/8 by 6, watch what happens...
7/8 *6 = 42/48
The denominators are the same, which shows how the equations are probably equal.
I know it might seem confusing because I'm not great at explaining, but I hope it helps! Have an awesome day c:
If f(x) = 4x4 + 5x2 + 4, then what is the remainder when f(x) is divided by
2 + 2?
Step-by-step explanation:
16+10+4
26+4
30
30÷(2+2)
30÷4
7 1/2
what is the solution to the inequality below? b+1 > -8
Answer:
from my point of view the solution should be 36
Answer:
b > -9
Step-by-step explanation:
Find a recurrence equation that is satisfied by all output sequences of the Fibonacci LFSR with feedback structure 100101.
This recurrence equation represents the relationship between the current output bit and the previous output bits in the Fibonacci LFSR with the feedback structure 100101.
To find a recurrence equation satisfied by the output sequences of the Fibonacci LFSR with feedback structure 100101, we need to analyze the feedback connections and determine the relationship between the current output bit and previous output bits.
The Fibonacci LFSR with feedback structure 100101 has a shift register with 6 stages (denoted as S0, S1, S2, S3, S4, S5), where S0 is the rightmost stage. The feedback taps are at positions S5, S2, and S0.
Let's denote the current output bit at each stage as O0, O1, O2, O3, O4, and O5, respectively.
The recurrence equation for the Fibonacci LFSR can be found by considering the feedback connections:
O0 = S0
O1 = S1
O2 = S2 ⊕ S0
O3 = S3
O4 = S4 ⊕ S2
O5 = S5 ⊕ S2 ⊕ S0
In terms of the output bits, the recurrence equation can be written as:
O_n = O_{n-1} + O_{n-2} + O_{n-5}
Where O_n represents the nth output bit in the sequence.
This recurrence equation represents the relationship between the current output bit and the previous output bits in the Fibonacci LFSR with the feedback structure 100101.
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