The solutions of the quadratic equation 3x² – 8x + 5 = 5x² will be 0.4595 and negative 4.5495.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Let the equation be ax² + bx + c = 0. Then the roots of the equation will be given as,
[tex]\rm x = \dfrac{-b \pm \sqrt{b^2 - 4 a c }}{2a}[/tex]
The equation is given below.
3x² – 8x + 5 = 5x²
Simplify the equation, then we have
3x² – 8x + 5 = 5x²
2x² + 8x – 5 = 0
Then the roots of the equation are given as,
x = [ -8 ± √(8² - 4 · 2 · (-5))] / (2 · 2)
x = (- 8 ± 10.198) / 4
x = (- 8 + 10.198) / 4 , (- 8 - 10.198) / 4
x = 0.5495, -4.5495
The solutions of the quadratic equation 3x² – 8x + 5 = 5x² will be 0.4595 and negative 4.5495.
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intuitively, what do we expect to have when the error term's variance increases when we estimate a simple linear regression model?
When the variance of the error term increases in a simple linear regression model, it indicates a less accurate model with a high degree of uncertainty in its predictions.
Regression is a statistical method used to model the relationship between two variables, where one of the variables is dependent on the other.
Simple linear regression is a type of regression where the relationship between the dependent variable and the independent variable is modeled as a linear equation.
Mathematically, let's consider the simple linear regression equation as:
Y = β0 + β1X + ε
Where Y is the dependent variable, X is the independent variable, β0 and β1 are the coefficients of the regression equation, and ε is the error term.
The variance of the error term, Var(ε), is a measure of the spread of the residuals. A large variance of the error term indicates that the residuals are spread out over a large range, and thus, the regression model's predictions may not be very accurate.
In other words, a large variance of the error term means that the model has a high degree of uncertainty in its predictions, leading to a larger deviation between the actual and predicted values.
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can you help me it would mean a lot
Answer: If a 21.0 kg rock rests on the edge of a cliff 32.0 m high, the gravitational potential energy gained by the rock would be 6585.6 Joules.
Step-by-step explanation:
Mechanical energy is the combination of all the energy in motion represented by total kinetic energy and the total stored energy in the system which is represented by total potential energy.
As given in the problem a 21.0 kg rock rests on the edge of a cliff 32.0 m high, then we have to calculate the potential energy gained by the rock,
The potential energy of the rock = 21 × 9.8 × 32
= 6585.6 Joules.
Thus ,If a 21.0 kg rock rests on the edge of a cliff 32.0 m high, the gravitational potential energy gained by the rock would be 6585.6 Joules.
Hope this helps.
Answer:
21.0 kg
Step-by-step explanation:
A person with five children earns 61320 per month
Calculate the tax allowances
The federal income tax for this person is $407 per month.
The person qualifies for five personal allowances because they have five children. As of 2021, the standard personal allowance in the United States is $12,550.
As a result, the person can deduct 5 × $12,550 =$62, 750, from their taxable income to account for the five allowance
Their monthly taxable income is 61320 - $62, 750, or $4070. Based on taxable income, the federal income tax is calculated, and the individual's tax rate is determined by their taxable income bracket.
The tax rate on $4070 in taxable income as of 2021 is 10%.
Therefore, the federal income tax for this person is $4070 × 10% = $407 per month.
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Which of the following sets of side lengths could
produce a triangle? Select all that apply.
A: 13 mm, 5 mm, and 6 mm
B: 3 in, 3 in, and 3 in
C: 2 cm, 7 cm, 6 cm
D: 2 m, 5 m, 7m
E: 6 ft, 6 ft, 12 ft
Correct option is C, A triangle can be formed with these side lengths since 8 cm, which is greater than the third side's 7 cm, is possible.
A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question. To describe the sides of right triangles, we utilize specific terminology.
What is the name of the 180 degree triangle?Straight angle refers to the angle that is 180 degrees in length.
The side length combinations that can result in a triangle include
2, 7, and 6 centimeters; 2 meters; 5, and 7 meters
6, 6, and 12 feet
According to the triangle inequality theorem, the third side of a triangle is greater than or equal to the sum of any two of its sides.
In other words, in a triangle with sides a, b, and c,
a + b ≥ c
When examining the sets of provided side lengths,
2 cm, 7 cm, and 6 cm in a triangle,
2 + 6 = 8,
Thus, a triangle can be formed with these side lengths since 8 cm, which is greater than the third side's 7 cm, is possible.
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Using the given diagram,
The value of x is given as follows:
x = 39.3.
What are similar triangles?Similar triangles share these two features listed as follows:
Congruent angles, that is, angles that have the same measure.Proportional side lengths.The equivalent side lengths on the proportional triangles are given as follows:
25 and 35.x and 55.Hence the proportional relationship relating the side lengths is given as follows:
25/35 = x/55
Applying cross multiplication, the value of x is obtained as follows:
35x = 55(25)
x = 55(25)/35
x = 39.3.
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A rabbit starts at 10 along a number line and then makes three jumps. First the rabbit jumps 4 units, then 2 units, and finally makes a jump of 1 unit. We don't know the direction of any jump.What are the possibilities
Answer:
Step-by-step explanation:
When rolling a die (number cube), what is the probability of rolling a 2 or a 3?
OA. //
OB.
0C. 1/1/0
OD. 1/1/2
OE. 5/10
Answer:
1/3
Step-by-step explanation:
6 faces in a die
1/6 of rolling each side
1/6 of rolling 2 or 3
2/6 chance, 1/3 (simplified)
An internet service provider uses the function R = 3 log(a + 2) + 15 to relate R, the sales revenue from hosting websites, to a, the cost of advertising
Solve for a in terms of R.
"a" can be expressed as a function of "R" as:
[tex]a = 10^{\frac{(R - 15)}{3} - 2}[/tex].
What are logarithmic properties?
The 4 laws of logarithms are product property, division property, power property and change of base property.
The product property states that multiplying two logarithmic values is equivalent to summing their respective logarithms.The division property states that the difference between two logarithms is comparable to dividing two logarithmic values.The exponent times the logarithm of m's logarithm is identical to m's logarithm with a suitable exponent, according to the exponential rule.Change of base property - The change of base rule converts a logarithm in one base to a logarithm in another.To solve for "a" in terms of "R," we need to isolate "a" on one side of the equation. We can do this by rearranging the equation and applying logarithmic properties.
Starting with the equation R = 3 log(a + 2) + 15, we'll subtract 15 from both sides:
R - 15 = 3 log(a + 2)
Next, we'll divide both sides by 3:
(R - 15) / 3 = log(a + 2)
Finally, we'll use the inverse logarithmic function, denoted as "exp" or "10^," to solve for "a":
[tex]a+2 = 10^{\frac{(R - 15)}{3} }[/tex]
And finally, we'll subtract 2 from both sides to obtain the solution:
[tex]a = 10^{\frac{(R - 15)}{3} - 2}[/tex]
So, "a" can be expressed as a function of "R" as:
[tex]a = 10^{\frac{(R - 15)}{3} - 2}[/tex]
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Indirect proportional question please answer
Answer:
y = 250x
Step-by-step explanation:
y = 1/[tex]x^{3}[/tex](k) Solve for k
2 = 1/[tex]5^{3}[/tex](k)
2 = 1/125 (k) Multiply both sides by 125
250 = k
y = 250x
Please help me!!!! I cannot figure it out
Answer: 12/37
Step-by-step explanation:
sin A= bc/ab = 12/37
The sine of the angle is equal to the ratio of the opposite to the hypotenuse (Ik this probably made 0 sense but I hope it helps! :D)
solve these simultaneous equations
4a+3b=-9
2a+5b=-1
The solution to the system of equations 4a + 3b = -9 and 2a + 5b = -1 is a = 12, b = -5, found through substitution method.
Simultaneous equations are a set of equations with multiple variables, and the solution of these equations gives us the values of the variables that make all the equations true at the same time. To solve these equations, we can use elimination, substitution or matrices method.
Here, the given set of simultaneous equations is
4a + 3b = -9
2a + 5b = -1
One way to solve this is by substitution, where we solve one equation for one variable and substitute that expression into the other equation. Solving the first equation for "a", we get:
a = -3b - 3
Substituting this expression into the second equation, we get:
2(-3b - 3) + 5b = -1
Expanding the left-hand side, we get:
-6b - 6 + 5b = -1
Combining the like terms, we get:
-b - 6 = -1
Adding b and 6 to both sides, we get:
-b = 5
Finally, dividing both sides by -1, we get:
b = -5
Substituting the value of b back into the expression for a, we get:
a = -3(-5) - 3 = 15 - 3 = 12
So the solution to the system of equations is:
a = 12, b = -5
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In a recent survey of college students, it was determined that 4 out of 5 students drink coffee. Of those students who drink coffee, 1 out of 8 students adds cream. If a college campus has 18000 students, how many students drink coffee with cream?
The number of students who drink coffee with cream is 1800.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that in a recent survey of college students, it was determined that 4 out of 5 students drink coffee. Of those students who drink coffee, 1 out of 8 students adds cream. If a college campus has 18000 students.
The number of students who drink coffee with cream is calculated as:-
Number = ( 4 / 5 ) x ( 1 / 8 ) x 18000
Number = 1800
Therefore, there are 1800 students who like their coffee with cream.
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Evaluate 1/5r + 9/20 when r = 1/4
1/5 ( blank) + 9/20 = blank + 9/20= Answer?
please answer asap
The value of the equation is A = 1/2
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = ( 1/5 )r + 9/20 be equation (1)
On simplifying the equation , we get
when r = ( 1/4 )
Substituting the value of r in the equation , we get
A = ( 1/5 ) ( 1/4 ) + 9/20
A = ( 1/20 ) + ( 9/20 )
On further simplification , we get
A = 10/20
A = 1/2
Hence , the equation is A = 1/2
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Which angles are coterminal with an angle drawn in standard position measuring 212°?
Select all correct angle measures.
Answer: 212 +- 360 n
Step-by-step explanation: Everytime you go full circle (360 degrees ) either positive or negative you will land back at the 212 degree mark.
Please help me I’m a bit stuck
Answer:
Step-by-step explanation:
The Answer would be -4x
Because 3-7= -4
F(x)=-6x^4x+2x^2+12 G(x)=-2x^3+6x^2-x-1
The value of the expression,
F(x) + G(x) is -6x⁴ -2x³ + 8x² -x + 11.
What is addition?Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.
Given:
An expression,
F(x) = -6x⁴ + 2x² + 12
And G(x) = -2x³ + 6x² - x - 1
To solve F(x) + G(x):
F(x) + G(x)
= -6x⁴ + 2x² + 12 -2x³ + 6x² - x - 1
Simplifying,
= -6x⁴ -2x³ + 8x² -x + 11
Therefore, the value is -6x⁴ -2x³ + 8x² -x + 11.
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The complete question:
F(x) = -6x⁴ + 2x² + 12
And G(x) = -2x³ + 6x² - x - 1
Find out, F(x) + G(x)?
Choose a second initial value that is 0. 01 greater than the initial value from question 9. Iterate it using the function, f, ten times. If necessary, you can round your results to the nearest ten-thousandth. (my initial value from question 9 is 2 btw. )
The result of the 10th iteration is 1.689, rounded to the nearest ten-thousandth.
The initial value for this question is 2 + 0.01 = 2.01. If we iterate this initial value using the function "f" ten times, we get the following sequence:
1st iteration: f(2.01) = 3.07 - [tex](2.01)^{2}[/tex]= 0.1599
2nd iteration: f(0.1599) = 3.07 - [tex](0.1599)^{2}[/tex]= 2.868201
3rd iteration: f(2.868201) = 3.07 - [tex](2.868201)^{2}[/tex]= 0.34459799
4th iteration: f(0.34459799) = 3.07 - [tex](0.34459799)^{2}[/tex] = 2.46306801
5th iteration: f(2.46306801) = 3.07 - [tex](2.46306801)^{2}[/tex] = 0.86121799
6th iteration: f(0.86121799) = 3.07 - [tex](0.86121799)^{2}[/tex] = 2.11255201
7th iteration: f(2.11255201) = 3.07 -[tex](2.11255201)^{2}[/tex] = 1.47511099
8th iteration: f(1.47511099) = 3.07 -[tex](1.47511099)^{2}[/tex] = 1.87593299
9th iteration: f(1.87593299) = 3.07 -[tex](1.87593299)^{2}[/tex] = 1.28972499
10th iteration: f(1.28972499) = 3.07 -[tex](1.28972499)^{2}[/tex] = 1.68900499
So, the result of the 10th iteration is 1.689, rounded to the nearest ten-thousandth.
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Please help I have a learning disablity and need help with this PLEASE PLEASE answer this it is due in 1 hour i have the image it is not hard if you answer I will mark you as brainliest. If this is not answerd in the next hour I will have a 0 as my final grade and have to redo 6th grade so please everyone I know knows I am not smart so please
What percent of the square is shaded in? When you type your answer
do not include a % sign.
Answer_________
The percent of the square shaded is 37.5 without including the % sign.
What percent of the square is shaded?The square is divided into 4 equal parts
1/4 of the square is fully shaded
The other 1/4 is shaded half
Hence,
When the square is divided into 8 equal parts, 3 parts are shaded
Percent of square shaded= Parts shaded/ Total parts × 100
= 3/8 × 100
= 0.375 × 100
= 37.5%
Ultimately, 37.5 is the percent of the square shaded.
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50 points to whoever can answer with explanation.
Answer:
1/ a, c, d
2/ You are missing the option in the picture.
Step-by-step explanation:
If a relation is a function, one input can only have one output!
1/
b is wrong because 1 has two outputs -3 and 0. So, the answer for 1 is: a, c, d
2/
To test whether the graph is a function, we have to see if one x has 2 y or not! If it has 2 y, then it is not a function.
You are missing the options for question 2! So I can't answer number 2.
Rob collects model planes. One of his planes
uses a scale in which 1 inch represents 1. 5
feet. If the length of the model airplane is 12
inches, find the length of the actual airplane in
feet
If the length of the model airplane is 12 inches, then the length of the actual airplane is 18 feet.
Rob collects model planes. One of his planes uses a scale in which 1 inch represents 1. 5 feet.
We will use unitary method to find the length of airplane in inches.
This means according to the model,
1 inch in the model = 1.5 feet of the actual
Therefore, if the length of the model airplane is 12 feet
12 inches of the model airplane = 1.5 × 12
= 18 feet
so, the actual length of airplane is 18 feet.
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an expression is given. -2y+3/2x+7/4 which are equivalent to the given expression select each answer
Answer:
E 1/4 (-8y+6x+7)
Step-by-step explanation:
PLSSSS HELP IF YOU TURLY KNOW THISSS
Answer:
x = 40
Step-by-step explanation:
We have to find,
→ the value of x in the equation.
The equation is,
→ (x/2) + 3 = 23
Now the value of x will be,
→ (x/2) + 3 = 23
→ x/2 = 23 - 3
→ x/2 = 20
→ x = 20 × 2
→ [ x = 40 ]
Hence, the value of x is 40.
how to determine if vectors are linearly independent
The value of c is zero and a and b can be something else, because the vector are linearly independent.
A set of vectors is linearly independent if no vector can be expressed as a linear combination of the others (i.e., is in the span of the other vectors). A set of vectors is linearly independent if no vector can be expressed as a linear combination of those listed before it in the set.
Assume the following:
[tex]a\left[\begin{array}{ccc}2\\2\\0\end{array}\right] + b\left[\begin{array}{ccc}1\\-1\\1\end{array}\right] +c\left[\begin{array}{ccc}4\\2\\-2\end{array}\right] = \left[\begin{array}{ccc}0\\0\\0\end{array}\right][/tex]
Determine if a=b=c=0
[tex]2a+b+4c =0 (1)\\ 2a-b+2c =0 (2)\\b-2c=0(3)\\[/tex]
Subtract (2) from (1)
[tex]b+c = 0\\b-2c=0[/tex]
Substitute (5) into (4), we get c=0.
So now what do I do with this fact? I'm tempted to say that only c=0, and a and b can be something else.
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The first gardener can finish the job in 6 hours, and the second gardener can do the same job in 7 hours. How long will it take to finish the same job if they work together
Explanation Please
Answer:
3 3/13 hours
Step-by-step explanation:
you will first find out how many hours it will take for each gardener to do 1 part of the job. gardener 1 is 1/6 and the second is 1/7. you will next add the two fractions. this will equal 13/42. you will then multiply by the reciprocal to get 1, this stands for the whole job done together. The reciprocal is the answer, 42/13. You will then simplify that to 3 3/13 hours.
(Help asap) The variable x represents the the number of smallmouth bass Chelsie caught. The variable y represents the number of salmon she caught. Chelsie caught 52 fish today. For smallmouth bass, she caught seven more than 2 times the amount of salmon she caught.
Determine the system of equations that model this problem. Solve the system. How many smallmouth bass and salmon did she catch?
Tthe the number of smallmouth bass Chelsie caught = 37
and the number of salmon she caught = 15
Here, x represents the number of smallmouth bass Chelsie caught. and y represents the number of salmon she caught.
Chelsie caught 52 fish today.
So we get an equation,
x + y = 52
Also, for smallmouth bass, she caught seven more than 2 times the amount of salmon she caught.
So we get an equation,
x = 7 + 2y
So, we get a system of equations:
x + y = 52 ..........(1)
x = 7 + 2y .......(2)
Substitute above value of x in equation (1)
(7 + 2y) + y = 52
7 + 3y = 52
3y = 45
y = 15
Substitute above value of y in equation (2),
x = 7 + 2(15)
x = 37
Therefore, she caught 37 smallmouth bass and 15 salmon.
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mrs. curtis wants to buy online tickets for a concert. two options are given here. option 1: $53 for each ticket plus a shipping fee of $10 option 2: $55 for each ticket and free shipping what is a system of equations to represent the costs of the tickets? express your equations in the form of y
The two equations, y = 53x + 10 and y = 55x, represent the cost of x tickets for option 1 and option 2, respectively.
The equation y = 53x + 10 represents the cost of x tickets for option 1, which includes a ticket cost of $53 per ticket plus a shipping fee of $10. So, if Mrs. Curtis buys 1 ticket, the cost would be 53 * 1 + 10 = 63. If she buys 2 tickets, the cost would be 53 * 2 + 10 = 116, and so on.
The equation y = 55x represents the cost of x tickets for option 2, which includes a ticket cost of $55 per ticket and free shipping. So, if Mrs. Curtis buys 1 ticket, the cost would be 55 * 1 = 55. If she buys 2 tickets, the cost would be 55 * 2 = 110, and so on.
By comparing the values of y for different values of x in these two equations, Mrs. Curtis can determine the cost-effective option for buying the tickets.
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a room has a floor dimension of 6 meters by 8 meters the height of the basement is 8 meters what is the total area of all four walls
Answer:
224 m^2
Step-by-step explanation:
The dimensions of the four walls are:
6x8, 8x8, 6x8, 8x8
The area of all of these walls is 2(6x8 + 8x8) = 224 m^2
The graph shows a relationship between two quantities.
2000
1800
1600
1400
1200
1000
800
600
400
200
STA
y = 1500x + 150
ALONS
JUMA
1 HOUT
TOU
8-6-4-2 0
N
Hilber
2 4
6 8
Which equation best represents the relationship between x and y in the graph?
y = 1500 + 150x, this is correctly represents the relationship between x and y in the graph. This can be solved using the slope formula.
What is slope?Slope, An evaluation of a line's inclination with respect to the horizontal using numbers. The slope of any line, ray, or line segment in analytical geometry is defined as the proportion of the vertically to the horizontally distance between the two points on the line ("slope equals rise over run").
(0, 1500) to (2, 1800)
thus, slope = (y₂ - y₁) / (x₂ - x₁)
or, slope = 300 / 2
or, slope = 150
So, y - 1500 = 150x
thus, y = 1500 + 150x
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The complete question is as follows:
Jason purchased a car for $22,995. According to his research, this make and model of car loses all of its marketable value after 9 years. If this car depreciates in a straight line form, what are the coordinates of the intercepts of the depreciation equation?
The car loses all of its marketable value after 9 years, the x-intercepts represent the points at which the car has lost all of its value, so they are (9, 0) and (0, 22995).
The depreciation equation for the car can be represented as y = mx + b, where y is the value of the car at time x, m is the slope of the line, and b is the y-intercept.
To find the slope, we can use the information that the car loses all of its marketable value after 9 years. The market value of the car will be 0 after 9 years, so we can set y = 0 when x = 9:
0 = m * 9 + b
To find the y-intercept, we can use the information that Jason purchased the car for $22,995. This means that the value of the car at time 0 was $22,995, so we can set y = 22,995 and x = 0:
22,995 = m * 0 + b
Combining these two equations, we can solve for m and b:
0 = m * 9 + b
22,995 = m * 0 + b
b = 22,995
Now that we have found the y-intercept, we can use it to find the x-intercepts by setting y = 0 and solving for x:
0 = m * x + 22,995
0 - 22,995 = m * x
-22,995 = m * x
x = -22,995 / m
Since we don't know the value of m, we can't find the x-intercepts directly. However, since the car loses all of its marketable value after 9 years, the x-intercepts represent the points at which the car has lost all of its value, so they are (9, 0) and (0, 22995).
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PLS HELPPPPPOOOOPPPP
Answer:
if there anything you dont understand ask me