The best approximation for the solution of the system of equations is (0.88,0.65).
Given a system of equations is y=-(2/5)x+1 and y=3x-2.
A system of linear equations consists of two or more equations, and one attempts to solve the equations together.
To find the best approximation solution solve the system of equations.
The given system of equations are
y=-(2/5)x+1 .......(1)
y=3x-2 .......(2)
Firstly, substitute the value of y into equation (1) to find the value of x, we get
3x-2=-(2/5)x+1
Now, we will add (2/5)x in both sides, we get
3x-2+(2/5)x=-(2/5)x+1+(2/5)x
3x-2+(2/5)x=1
Further, we will add 2 on both sides, we get
3x-2+(2/5)x+2=1+2
3x+(2/5)x=3
17x/5=3
Furthermore, we will multiply both sides with 5, we get
5×(17x/5)=3×5
17x=15
Now, divide both sides with 17, we get
17x/17=15/17
x=0.88
Further, we will find the value of y by substituting the value of x in equation (2), we get
y=3(0.88)-2
y=2.65-2
y=0.65
Hence, the best approximation for the solution of the system of equations y=-(2/5)x+1 and y=3x-2 is (0.88,0.65).
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What is the rectangular form of z = 6 (cosine (3 pi/4) +isin(3 pi/4) )?
Answer:
the answer is C, I got it too from the website, I got the answer from it
Which of the following ordered pairs is a possible solution to the equation y = -2/3x - 4
The ordered pair that is the possible solution for the equation is (-6,0) (0,-4).
What is the Slope-intercept form of a linear equation?
The slope-intercept form of a linear equation takes the form y= mx + b.
Here:
Slope = mb = y-interceptThe function f(x) = y = [tex]\mathbf{-\dfrac{2}{3}x-4}[/tex]
[tex]\mathbf{y = -\dfrac{2}{3}x-4}[/tex]
The slope (m) = -2/3
The x-intercept is the value of x for which y = 0
x-intercept = (-6,0)The y-intercept is the value of y for which x = 0
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find the value of p in the given figure
The value of p is 60°
How to determine the valueThe figure given is a triangle and it is important to note that sum of angles in a triangle = 180 degrees
The other sides are gotten by;
Angle on a straight line = 180
110 + x = 180
x = 180 - 110
x = 70
The other interior angle
130 + y = 180
y = 180 - 130
y = 50
We have,
x + y + p = 180
70 + 50 + p = 180
120 + p = 180
p = 180 -120
p = 60°
Thus, the value of p is 60°
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Raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute. The table shows that the amount of water remaining in the bathtub, y, is a function of the time in minutes, x, that it has been draining.
A 2-column table with 4 rows. The first column is labeled x with entries 0, 0.5, 1, 1.5. The second column is labeled y with entries 40, 39.25, 38.5, 37.75.
What is the range of this function?
The range of this function is all real numbers such that 0 ≤ y ≤ 40.
What is a range?A range is the set of all real numbers that connects with the elements of a domain. This simply means that, a range is the solution set on the y-axis.
How to determine the range?Based on the table (see attachment), we can logically deduce that when the time (x) is zero (0), the amount of water remaining in the bathtub (y) is 40.
Therefore, the range of this function is all real numbers such that 0 ≤ y ≤ 40.
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In part b, you used a combination of geogebra tools and manual calculations to find the approximate area of the original polygon. now try using the more advanced area tools in geogebra to verify your answer in part b. which method did you choose? do your results in parts b and c match?
Absolutely, over result will match in part b and c
Geogebra tools are software which is used to study an absolute geometry with zero errors.
Since, Geogebra contains various tools, In part b we have drawn a square through polygon command. Its allows to select the number of sides, so we select 4 cause square requires 4 equal sides.
Now, we very it in c part just by drawing a 4 connected lines which have 90° adjacent angles.
Here, by comparing their geometry it seems identical
Thus, the result, in part b and c matches for each other.
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Ashley and Castel each improved their yards by planting daylilies and ornamental grass. They
bought their supplies from the same store. Ashley spent $118 on 2 daylilies and 14 bunches of
ornamental grass. Castel spent $98 on 14 daylilies and 7 bunches of ornamental grass. What is the
of one daylily and the cost of one bunch of ornamental grass? Also could you show work
Each daylily cost $3 and one bunch of ornamental grass cost $8.
Build two equation's: (Let 'd' be daylilies, 'o' be ornamental grass)
$118 on 2 daylilies and 14 bunches of ornamental grass.
2d + 14o = 118$98 on 14 daylilies and 7 bunches of ornamental grass.
14d + 7o = 98Make d subject for first equation.
2d + 14o = 118
2d = 118 - 14o
d = (118 - 14o)/2
d = 59 - 7o
Insert this into second equation.
14(59 - 7o) + 7o = 98
826 - 98o + 7o = 98
-91o = -728
o = 8
Find value of d:
d = 59 - 7o
d = 59 - 7(8)
d = 3
Answer:
Cost of one daylily = $3
Cost of one bunch of ornamental grass = $8
Step-by-step explanation:
Define the variables:
Let d = cost of one daylily (in dollars)Let g = cost of one bunch of ornamental grass (in dollars)Given information:
$118 = 2 daylilies and 14 bunches of ornamental grass$98 = 14 daylilies and 7 bunches of ornamental grassCreate a system of equations with the given information and defined variables:
[tex]\begin{cases}2d+14g=118\\14d+7g=98 \end{cases}[/tex]
Multiply the second equation by 2:
[tex]\implies 2(14d+7g)=2(98)[/tex]
[tex]\implies 28d+14g=196[/tex]
Subtract the first equation from this equation to eliminate the variable g:
[tex]\begin{array}{r r r}28d & +14g = & 196\\- \quad \quad2d & +14g = & 118\\\cline{1-3}26d & = & 78\end{array}[/tex]
Solve for d:
[tex]\implies 26d=78[/tex]
[tex]\implies d=3[/tex]
Substitute the found value of d into one of the equations and solve for g:
[tex]\implies 2d+14g=118[/tex]
[tex]\implies 2(3)+14g=118[/tex]
[tex]\implies 6+14g=118[/tex]
[tex]\implies 14g=112[/tex]
[tex]\implies g=8[/tex]
Therefore, the cost of one of each plant is:
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please help me im stuck here U_U
Using the inverse function concept, the table that represents the inverse of the table given is table a.
How to find the inverse of a function of pairs (x,y)?The inverse of the function is given by the set that contains point (y,x), that is, the coordinates are exchanged.
In the table given, we have points (0,0), (2,1) and (4,2), hence the inverse table has points (0,0), (1,2) and (2,4), which is table a.
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1
Which is the equation of a line that has a slope 1/2 and passes through point (2, -3)?
Oy-x-4
0y=x-2
Oy-x+2
Oy=x+3
Answer:
[tex]y = \dfrac{1}{2}x-4[/tex]
Step-by-step explanation:
Equation of line in slope y-intercept form:[tex]\sf slope = m =\dfrac{1}{2}\\\\Point (2, -3) ; x_1 = 2 \ \& y_1 = -3\\\\\boxed{\bf y - y_1 =m(x -x_1)}[/tex]
[tex]\sf y - [-3] = \dfrac{1}{2}(x - 2)\\\\y + 3 = \dfrac{1}{2}x - 2*\dfrac{1}{2}\\\\y + 3 = \dfrac{1}{2}x-1\\\\[/tex]
[tex]\sf y = \dfrac{1}{2}x - 1 - 3\\\\ y =\dfrac{1}{2}x-4[/tex]
11. The sides of a right triangle are x, 7, and 8. How many different possible values are there for x?
(A) 1
(B) 2
(C) 3
(D) 4
The required possible values of x is 1. Hence the option A. is correct.
The triangle is geometric shape which includes 3 sides and sum of interior angle should not grater than 180°.
Since. in the question we have two known sides of the right angle triangle. The number of possible values of x will be 1. because with the help of other two side third side can be calculate.
Thus, the required possible value of x will be 1.
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The ratio of Bananas to Mangoes to Oranges is 3:4;5. If there are 180 mangoes and oranges. How many fruits are there altogether.
Suppose the length of each sude of a square is decreased by 4 ft if the perimeter of the square is now 32 feet what was the original length of each side
Answer:
12ft
Step-by-step explanation:
length of one side of the square now
32ft / 4 = 8ft
length of one side of the square before decreasing the length
(original lenght)
8ft +4ft = 12ft
determine the graph of the polar equation 9/1-3sin theta
Answer: can you show us the graph?
Step-by-step explanation:
A cylindral drill with radius 5 cm is used to bore a hole through the center of a sphere with radius 9 cm. Find the volume of the ring-shaped solid that remains.
The volume of the ring-shaped remaining solid is 1797 cm³.
The volume is the total space occupied by an object.
The volume of a sphere of radius r units is given as (4/3)πr³.
The volume of a cylinder with radius r units and height h units is given as πr²h.
In the question, we are asked to find the volume of the remaining solid when a sphere of radius 9cm is drilled by a cylindrical driller of radius 5cm.
The volume will be equal to the difference in the volumes of the sphere and cylinder, where the height of the cylinder will be taken as the diameter of the sphere (two times radius = 2*9 = 18) as it is drilled through the center.
Therefore, the volume of the ring-shaped remaining solid is given as,
= (4/3)π(9)³ - π(5)²(18) cm³,
= π{972 - 400} cm³,
= 572π cm³,
= 1796.99 cm³ ≈ 1797 cm³.
Therefore, the volume of the ring-shaped remaining solid is 1797 cm³.
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What is the domain of the function y= 2√x-6?
0-00
O 0
O 3
O 6≤x<∞
Given f(x)=2−∣x−5∣
Domain of f(x) is defined for all real values of x.
Since, ∣x−5∣≥0⟹−∣x−5∣≤0
⟹2−∣x−5∣≤2⟹f(x)≤2
Hence, range of f(x) is (−∞,2].
The domain of the function y= 2√x-6 is [6, ∞).
What is a function?A relation is a function if it has only One y-value for each x-value.
In the given function, we have a square root of x-6 which means that the value inside the square root must be non-negative, otherwise the function will not be real.
Therefore, we have x - 6 ≥ 0
Adding 6 to both sides, we get:
x ≥ 6
So, the domain of the function y = 2√(x-6) is all real numbers greater than or equal to 6.
In interval notation, we can write the domain as:
Domain: [6, ∞)
Hence, the domain of the function y= 2√x-6 is [6, ∞).
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The product of 1.3 times 10 Superscript negative 4 and a number n results in 2.6 times 10 Superscript 12. What is the value of n?
2 times 10 Superscript negative 8
2 times 10 Superscript negative 3
2 times 10 Superscript 16
2 times 10 Superscript 48
The value of n is calculated as n = 2 times 10 superscript 16.
The product of 1.3 times 10 Superscript negative 4 and a number n results in 2.6 times 10 Superscript 12.
What is simplification?Simplification, in mathematics, is to solve the equation through mathematical operations
1.3 x 10^-4 x n = 2.3 x 10^12
n = 2 x 10^ 16
Thus the value of n is calculated as n = 2 times 10 superscript 16.
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On a coordinate plane, a line is drawn from point A to point B. Point A is at (negative 4, 8) and point B is at (2, negative 4).
What are the x- and y-coordinates of point C, which partitions the directed line segment from A to B into the ratio 3:10? Round to the nearest tenth, if necessary.
x =
y =
The x- and y-coordinates of point C, which partitions the directed line segment from A to B into the ratio 3:10 is; (-2.6, 5.2)
How to find coordinate points?
The coordinate of the points are given as:
A(-4, 8)
B(2, -4)
Ratio of partition is given as; 3:10
Now, the point at the given ratio is calculated from the formula;
C = [(mx2 + nx1)/(m + n)], [(my2 + ny1)/(m + n)]
Thus;
C = [(3*2 + 10*-4)/(3 + 10)], [(3*-4 + 10*8)/(3 + 2)]
C = (-34/13, 68/13)
C = (-2.6, 5.2)
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Answer:
-2.6, 5.2
Step-by-step explanation:
g Minimizing the sum of the squared deviations around the line is called: predictor regression. mean squared error technique. least squares estimation. double smoothing. mean absolute deviation.
Minimizing the sum of the squared deviations around the line is called Least square estimation.
It is given that the sum of squares is around the line.
Least squares estimations minimize the sum of squared deviations around the estimated regression function. It is between observed data, on the one hand, and their expected values on the other. This is called least squares estimation because it gives the least value for the sum of squared errors. Finding the best estimates of the coefficients is often called “fitting” the model to the data, or sometimes “learning” or “training” the model.
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A website advertises job openings on its website, but job seekers have to pay to access the list of job openings. The website recently completed a survey to estimate the number of days it takes to find a new job using its service. It took the last 31 customers an average of 40 days to find a job. Assume the population standard deviation is 10 days. Calculate a 99% confidence interval of the population mean number of days it takes to find a job.
Using the z-distribution, the 99% confidence interval of the population mean number of days it takes to find a job is (35.38, 44.62).
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.In this problem, we have a 99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
The other parameters are:
[tex]\overline{x} = 40, \sigma = 10, n = 31[/tex]
Hence the bounds of the interval are:
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 40 - 2.575\frac{10}{\sqrt{31}} = 35.38[/tex]
[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 40 + 2.575\frac{10}{\sqrt{31}} = 44.62[/tex]
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I need help plsssssssss
For the given system of equation, the value of x = 4 and the value of y = -1
Solving simultaneous equationsFrom the question, we are to solve the given system of equations
-7x + 4y = -32 -------- (1)
9x - 2y = 38 -------- (2)
From equation (2)
9x - 2y = 38
2y = 9x - 38
y = 4.5x - 19 -------- (3)
Substitute this into equation (1)
-7x + 4y = -32
-7x + 4(4.5x -19) = -32
-7x + 18x - 76 = -32
-7x + 18x = -32 + 76
11x = 44
x = 44/11
x = 4
Substitute the value of x into equation (3)
y = 4.5x - 19
y = 4.5(4) - 19
y = 18 - 19
y = -1
Hence, the value of x = 4 and the value of y = -1
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C --------------------q ???
The first five terms of a sequence are
7. 10, 13, 16, 19.... (a) what is the nth term of the sequence? (b) workout the 1000th term of the sequence.
Answer:
(a) 7 + 3( n - 1 )
(b) 1006
Step-by-step explanation:
ARITHMETIC SEQUENCE.
The number of term of an Arithmetic progression has the formular :
nth term = a + ( n - 1 ) d
a = 7
d = 10 - 7 = 3
nth term = 7 + ( n - 1 ) 3
= 7 + 3n - 3
= 7 + 3( n - 1 )
Therefore,
the nth term of the sequence
= 7 + 3( n - 1 )
(b) For the 1000th term
= 7 + 3 ( 1000-1 )
= 7 + ( 999 )
7 + 999 = 1006
Therefore,
the 1000th term = 1006
What is the multiplicative rate of change for the exponential function graphed to the left?
Hence, the function increases at a constant multiplicative rate..
What is a function?function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). A function has three parts, a set of inputs, a set of outputs, and a rule that relates the elements of the set of inputs to the elements of the set of outputs in such a way that each input is assigned exactly one output.
How to solve?We know,
the answer is (B) the function increases at a constant multiplicative rate.
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when x equals 12 , x+3y=21 need help
Answer:
y=3
Step-by-step explanation:
3. how would you use concrete objects to represent and solve the following problem: what is 30% of $60?
Answer:
adding
Step-by-step explanation:
Which answer choice gives the correct surface area for a triangular prism
with bases that are 4 cm² and sides that are 4 cm²?
Answer:
The answer is 20
Step-by-step explanation:
Their are two bases and three sides in a triangular prism so the total surface area is 20
This is a linear equations question so pls help me I’m dying of stress thank you! ^^
Answer:
the answer to this problem is D:(-2,4)(1,1)
Answer:
B
Step-by-step explanation:
y = x² → (1)
y = 3x - 2 → (2)
substitute y = x² into (2)
x² = 3x - 2 ← subtract 3x - 2 from both sides
x² - 3x + 2 = 0 ← in standard form
(x - 1)(x - 2) = 0 ← in factored form
equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x - 2 = 0 ⇒ x = 2
substitute these values into (2) for corresponding values of y
x = 1 : y = 3(1) - 2 = 3 - 2 = 1 ⇒ (1, 1 )
x = 2 : y = 3(2) - 2 = 6 - 2 = 4 ⇒ (2, 4 )
Answers to questions one and two please!
The inequality shows that the number of texts will be 205.
How to solve the inequality?The carriers charged $59 and 20 cents after. Therefore, the inequality to illustrate the information will be:
Let t be the number of texts.
59 + 0.2t = 100
0.2t = 100 - 59
0.2t = 41
t = 205
The number of texts will be 205.
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Classify the following triangle. Check all that apply
Answer:
E. Isosceles Triangle
Step-by-step explanation:
It is because it has 2 equal sides and 2 equal angles.
3. Match the polynomial to it's correct name.
1. Quadratic trinomial
2. Cubic monomial
3. Linear binomial
4. Quartic trinomial
a. h(x) = 15x+2
b. j(x)=x²-3x³ + 9x²
c. f(x)= 3x² - 5x+7
d. 8(x)=-5x³
Answer:
1. to c.
2. to d.
3. to a.
4. to b.
Step-by-step explanation:
These answers should be right.
Hope this helps!
The matching of the polynomials to their correct names are:
a. h(x) = 15x+2 is a linear binomial
b. j(x)=x²-3x³ + 9x² is a Quartic trinomial
c. f(x)= 3x² - 5x+7 is a Quadratic trinomial
d. 8(x)=-5x³ is a Cubic monomial
How to Identify the Polynomials?A polynomial is an expression having more than one algebraic terms.
1) A quadratic trinomial is a polynomial that is defined as a quadratic expression with all three terms in the form of ax² + bx + c, where a, b, and c are numbers and not a 0.
2) A cubic monomial is defined as a a monomial that has a degree of 3.
3) Linear binomial is defined as a polynomial with two terms whose variable has degree 1. For example, 4x − 5 or 3x + 12 are both linear binomials.
4) A quartic trinomial is defined as a polynomial with three terms having the highest degree 4
Thus:
a. h(x) = 15x+2 is a linear binomial
b. j(x)=x²-3x³ + 9x² is a Quartic trinomial
c. f(x)= 3x² - 5x+7 is a Quadratic trinomial
d. 8(x)=-5x³ is a Cubic monomial
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Construct a square matrix A of order 3
[tex]A_{ij}[/tex] refers to the entry of [tex]A[/tex] in row [tex]i[/tex] and column [tex]j[/tex].
When [tex]i=j[/tex], the entry in question lies on the diagonal. In this case, [tex]A_{ij}=0[/tex] so
[tex]A = \begin{bmatrix} 0 & \square & \square \\ \square & 0 & \square \\ \square & \square & 0 \end{bmatrix}[/tex]
When [tex]i<j[/tex], the row number is smaller than the column number, which happens for each [tex]A_{ij}[/tex] in the upper half of [tex]A[/tex].
[tex]A = \begin{bmatrix} 0 & -1 & -1 \\ \square & 0 & -1 \\ \square & \square & 0 \end{bmatrix}[/tex]
When [tex]i>j[/tex], the row number is larger, which happens everywhere else in the matrix.
[tex]A = \begin{bmatrix} 0 & -1 & -1 \\ 1 & 0 & -1 \\ 1 & 1 & 0 \end{bmatrix}[/tex]