Given that equation
1) [tex]x^{2} - 2x - 2[/tex] using the general quadratic equation, x = 1
2)[tex]x^{2} -6x -4[/tex] using the general quadratic equation, x= [tex]\frac{6 - \sqrt{20} }{2}[/tex]
According to the question, given that
1) [tex]x^{2} - 2x - 2[/tex]
2)[tex]x^{2} -6x -4[/tex]
this equation cannot be factored but using general quadratic equation. we solved it easily.
When asked to solve a quadratic equation that you just can’t seem to factor (or that just doesn’t factor), you have to employ other ways of solving the equation, such as by using the quadratic formula. The quadratic formula is the formula used to solve for the variable in a quadratic equation in standard form.
Given a quadratic equation in standard form ax2 + bx + c = 0,
[tex]x = \frac{- b - \sqrt{b^{2} - 4 ac } }{2a}[/tex] and [tex]x = \frac{- b + \sqrt{b^{2} - 4 ac } }{2a}[/tex]
solve [tex]x^{2} - 2x - 2[/tex] = 0, you first say that a = 1, b = –2, and c = 2. The a, b, and c terms simply plug into the formula to give you the values for x:
1) [tex]x^{2} - 2x - 2[/tex]
[tex]x = \frac{- (-2) + \sqrt{(-2)^{2} - 4 (1)(1) } }{2(1)}[/tex]
[tex]x = \frac{2 + \sqrt{4 -4} }{2}[/tex]
x = [tex]\frac{2}{2}[/tex]
[tex]x = 1[/tex]
and [tex]x = \frac{- (-2) - \sqrt{(-2)^{2} - 4 (1)(1) } }{2(1)}[/tex]
[tex]x = \frac{2 - \sqrt{4 -4} }{2}[/tex]
x = [tex]\frac{2}{2}[/tex]
[tex]x = 1[/tex]
equation [tex]x^{2} - 2x - 2[/tex] and x= 1
2)[tex]x^{2} -6x -4[/tex]
solve [tex]x^{2} - 6x - 4[/tex] = 0, you first say that a = 1, b = –6, and c = 4. The a, b, and c terms simply plug into the formula to give you the values for x:
[tex]x^{2} -6x -4[/tex]
[tex]x = \frac{- (-6) + \sqrt{(-6)^{2} - 4 (1)( 4) } }{2(1)}[/tex]
[tex]x = \frac{6 + \sqrt{36 - 16} }{2}[/tex]
x = [tex]\frac{6 \sqrt{20} }{2}[/tex]
and [tex]x = \frac{- (-6) - \sqrt{(-6)^{2} - 4 (1)(4) } }{2(1)}[/tex]
[tex]x = \frac{6 - \sqrt{36 - 16} }{2}[/tex]
x = [tex]\frac{6 - \sqrt{20} }{2}[/tex]
equation [tex]x^{2} - 6x + 4[/tex] and x= [tex]\frac{6 - \sqrt{20} }{2}[/tex]
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Trent decided bicycle to Austin and back. Hisaverage speed to Austin was 45 km/h. The averagespeed on his return trip was 30 km/h. The trip toAustin was 1 hour less than his time bicycling on hisreturn trip. How many hours did the trip to Austinlake?
Consider the relation,
[tex]\text{Time}=\frac{\text{ Distance}}{\text{ Speed}}[/tex]Let the distance between Trent and Austin is 'd' kilometers.
Then the time taken by Trent to reach Austin is given by,
[tex]T_1=\frac{d}{45}[/tex]Similarly, the time taken by Trent on his return trip is given by,
[tex]T_2=\frac{d}{30}[/tex]Given that the trip to Austin was 1 hour less than the return trip,
[tex]\begin{gathered} T_2-T_1=1 \\ \frac{d}{30}-\frac{d}{45}=1 \\ d(\frac{1}{30}-\frac{1}{45})=1 \\ d(\frac{45-30}{30\times45})=1 \\ d=\frac{30\times45}{15} \\ d=2\times45 \\ d=90 \end{gathered}[/tex]Solve for the total time of the trip as,
[tex]\begin{gathered} T=T_1+T_2 \\ T=\frac{90}{45}+\frac{90}{30} \\ T=2+3 \\ T=5 \end{gathered}[/tex]Thus, the total time required for complete trip is 5 hours.
11. Does the table show a proportional relationship?
If so, what is the value of y when x is 10?
X 5 6 7 8
Y 1 2/3 2 2 1/3 2 2/3
The value of y when x is 10 is 3[tex]\frac{1}{3}[/tex].
What is proportional relationship?Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant. The equation y = kx represents a proportionate relationship between two quantities y and x that have the same proportionality constant, k. Any relationship that has a constant ratio is said to be proportionate. For instance, the ratio of proportionality is the average number of apples per tree, and the amount of apples in a crop is proportional to the number of trees in the orchard.
Given Data
X 5 6 7 8
Y 1 2/3 2 2 1/3 2 2/3
Yes, the table shows proportional relationship.
Value of Y when X will be 10 is
x = 10
= 3[tex]\frac{1}{3}[/tex]
the value of y when x is 10 is 3[tex]\frac{1}{3}[/tex].
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6 is 15% of what number
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
6 ===> 15%
Step 02:
Percentage:
percentage = part / whole * 100
percentage = 15
part = 6
whole = number = x
[tex]\begin{gathered} 15\text{ = }\frac{6}{x}\cdot100 \\ x\cdot15\text{ = }6\cdot100 \\ x\text{ = }\frac{6\cdot100}{15}=40 \end{gathered}[/tex]The answer is:
The number is 40
if f(x) = 5x-7, then what is the solution to f(x) =4
The input value x when the output value f( x ) = 4 in the function f( x ) = 5x - 7 is 11/5.
What is the value of x when the output value f(x) = 4?A function is simply a relationship that maps one input to one output, each x-value can only have one y-value.
Given the data in the question;
f( x ) = 5x - 7f(x) = 4x = ?To determine the input value x when the output value f( x ) = 4, replace f( x ) by 4 in the function and solve for x.
f( x ) = 5x - 7
4 = 5x - 7
Collect like terms
4 + 7 = 5x
5x = 11
Divide both sides by 5
5x/5 = 11/5
x = 11/5
Therefore, the input value x is 11/5, this forms an ordered pair of ( 11/5, 4 ).
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I need the area of the irregular shape
The area of the irregular shape is found as 50 sq. cm.
What is defined as the area?The total space occupied by a flat (2-D) ground or the shape of an object is defined as its area. Sketch a square on a piece of paper with a pencil. It is a two-dimensional figure. The area of the shape on the paper is referred to as its Area. Consider your square to be made up of many smaller unit squares.For the given question;
The irregular shape is composed of two rectangles.
The formula for finding the area is;
Area = length x breadth
The area of the top rectangle is;
Top area = 4 x (3 + 5 + 2)
Top area = 4 x 10
Top area = 40 sq. cm.
The area of the bottom rectangle is;
Bottom area = 5 x 2
Bottom area = 10 sq. cm.
Total area = Top area + Bottom area
Total area = 40 + 10
Total area = 50 sq. cm.
Thus, the area of the irregular shape is found as 50 sq. cm.
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At your child's birth, you begin contributing monthly to a college fund. The fund pays an APR of 4.1% compounded monthly. You figure your child will need $30,000 at age 18 to begin college. What monthly deposit is required?
the monthly deposit that will be required will be equal to $ 1214 by compound interest.
We are given the information that:
Amount (A) = $ 30,000
Time = 18 years
Compound interest rate = 4.1 %
Now, let the principal amount be x.
So, by using the formula for compound interest, we get that:
30,000 = x ( 1+ 0.041)¹⁸
30,000 = x (1.041)¹⁸
30,000 = x × 2.06
x = 30,000 / 2.06
x = 14563 ( approx.)
Monthly deposit = 14563 / 12 = 1214 (approx.)
Therefore, the monthly deposit that will be required will be equal to $ 1214 by compound interest.
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Function A is a linear function whose graph contains the points (0, 2) and (8, 0). Function B is represented by the equation y = 4x - 2. Which statement is true? The rate of change for Function A is greater than the rate of change for Function B. The rate of change for Function A is equal to the rate of change for Function B. The initial value for Function A is greater than the initial value of Function B. The initial value of Function A is equal to the initial value of Function B.
The statement which is true about Function A and Function B is that: C. The initial value for Function A is greater than the initial value of Function B.
What is a slope?A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
Slope A = (0 - 2)/8 - 0)
Slope A = -2/8
Slope A = -1/4 or -0.25.
Note: The slope of any straight line also represents its rate of change.
Rate of change of Function A = -0.25.
Rate of change of Function B = 4.
Mathematically, the standard form of the equation of a straight line is given by;
y - y₁ = m(x - x₁)
At point (0, 2), we have:
y - 2 = -1/4(x - 0)
y - 2 = -x/4
y = -x/4 + 2.
Therefore, the intercept (initial value) of Function A is greater than the intercept (initial value) of Function B.
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the net decimal equivalent is found by multiplying the complement of the discounts together. what is the net decimal equivalent when a series of discount of 48% , 27%, and 12% is applied?
The net decimal equivalent is 0.48, 0.27, and 0.12 when a series of discounts of 48%, 27%, and 12% are applied respectively.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
By multiplying the complement of the discounts collectively, one can determine the net decimal equivalent which is given in the question.
To determine the net decimal equivalent when a series of discounts of 48%, 27%, and 12% is applied.
The value of compliment (%) = 1/100
As per the given condition, the required discounts would be as:
discount of 48% = 48/100 = 0.48
discount of 27% = 27/100 = 0.27
discount of 12% = 12/100 = 0.12
Therefore, the net decimal equivalent is 0.48, 0.27, and 0.12 when a series of discounts of 48%, 27%, and 12% are applied respectively.
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One number is 9 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 1068, find the numbers.
The three numbers are
(Use a comma to separate answers as needed.)
First number (x) = 88
Second number (9x) = 792
Third number (x + 100) = 188
Let x be the first number, so accordingly the second number will be 9 times x i.e., 9x and the third number will be 100 more than the first number i.e., x + 100
Now, put all the numbers into an equation of finding their sum,
First no. + Second no. + Third no. = SUM, i.e.,
x + 9x + (x+100) = 1068
Simplify,
x + 9x + (x+100) = 1068
x + 9x + x +100 = 1068
11x + 100 = 1068
11x = 1068 - 100
11x = 968
x = 968/11
First number (x) = 88
Second number (9x) = 792
Third number (x + 100) = 188
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I need help I don’t know how to do this
How many different 3-digit numbers are possible using only the digits 1,2,6,7,8 ? How many different 3-digit numbers are possible using only the digits 1,2,6,7,8, if repetition of digits is not allowed?
The number of three digit number formed are-
Repetition allowed = 125Repetition not allowed = 60What is defined as the combination?A combination is an algebraic technique for determining the number of distinct arrangements in a set of items in which the sequence of the selection is irrelevant. You can choose the items in either order in combinations. Permutations and combinations are often confused.For the given question;
The three digit number is to be formed.
The digits are given as- 1,2,6,7,8
Case 1: Repetition allowed
The number of combination will be;
= 5×5×5
= 125
Thus, the number of three digit number formed with repetition is 125.
Case 2: Repetition not allowed
The number of combination will be;
= 5×4×3
= 60
Thus, the number of three digit number formed with without repetition is 125.
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A motorboat travels 282 kilometers in 6 hours going upstream. It travels 402 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
Let,
B = the speed of the boat in still water
S = the speed of the stream
Use the equation for distance.
Rate * Time = Distance
Upstream:
(B-S)6 = 282
Downstream:
(B+S)6 = 402
Simply first:
(B-S)6 = 282
(B-S) = 282/6
B-S=47
(B+S)6 = 402
(B+S) = 402/6
B+S=67
Solve by elimination. Add the two equations.
B-S=47
+ B+S=67
2B = 114
B = 114/2
B = 57 km/hr (the speed of the boat in still water)
Substitute this into either equation and solve for S.
B+S=67
57 + S = 67
S = 67 - 57
S = 10 km/hr (the speed of the stream)
Connor edits 34
pages in 8 hours. Complete the table using equivalent ratios
If Connor edits 34 pages in 8 hours. Using the equivalent ratios, the table has been completed.
The equivalent ratios are the ratios that has same value when we compare them. We can check two or more ratios and check whether they are equivalent or not.
Connor edits 34 pages in 8 hours
Number of pages he edits in 8 hours = 34 pages
Number of pages he edits in 1 hour = 34/8 = 17/4 pages
Number of pages he edits in 12 hours = (17/4)×12
= 51 pages
Complete the table
Hence, if Connor edits 34 pages in 8 hours, using the equivalent ratios, the table has been completed
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Harry works at Memorial Mall on the weekends. Last Saturday he worked 6 1/2 hours and on
Sunday he worked 7 3/4 hours. He earns $9.50 per hour. How much did he earn last
weekend?
Does anybody know how to answer this to?
The table shows the relationship between the participants walking and running for the week's cross-country practices.
Walk (laps) 3 B 15
Run (laps) 5 10 D
Total (laps) A C 40
At this rate, how many laps will the participants walk if the total distance is 32 miles? How many miles will they run?
They will walk 7 laps and run 17 laps for a total of 32 miles.
They will walk 12 laps and run 20 laps for a total of 32 miles.
They will walk 14 laps and run 18 laps for a total of 32 miles.
They will walk 10 laps and run 22 laps for a total of 32 miles.
Question 3(Multiple Choice Worth 2 points)
(Three-Column Tables LC)
PART 2
The data below shows the ratio of brown to green crayons in four kindergarten classrooms.
12 to 20
10 to 25
14 to 35
30 to 75
Which table below correctly shows these ratios in a three-column table?
Brown 20 25 35 75
Green 12 10 14 30
Total 32 35 49 105
Brown 12 10 14 75
Green 20 25 35 30
Total 30 35 44 105
Brown 12 10 14 30
Green 20 25 35 75
Total 32 35 49 105
Brown 12 25 14 30
Green 20 10 35 75
Total 42 35 49 100
Using proportional relationships, it is found that:
They will walk 12 laps and run 20 laps for a total of 32 miles.The correct option for the second problem is:Brown 12 10 14 30
Green 20 25 35 75
Total 32 35 49 105
What is a direct proportional relationship?In a direct proportional relationship, the output variable is found by the multiplication of the input variable and the constant of proportionality k, as follows:
y = kx.
For the first question, we have that out of a total distance of 8 miles, they:
Walk 3/8 of the distance.Run 5/8 of the distance.Hence the proportional relationships for the distances are given as follows:
Walked = 3/8 x Total Distance.Ran = 5/8 x Total Distance.For a total distance of 32 miles, the distances walked and ran are given as follows:
Walked: 3/8 x 32 = 3 x 4 = 12 miles = 12 laps.Ran: 5/8 x 32 = 5 x 4 = 20 miles = 20 laps.For the second question, we have that the table has to following the given ratios of the first row to the second row, with the third row being the sum of the first two rows, hence the third table is correct.
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If you answer these questions correctly you are really smart. What is 2+2*2, what is 3+3*3, what is 6+6*6.
The value of the numbers that are given will be:
1. 6
2. 12
3. 42
How to calculate the value?It should be noted that based on the information given, PEDMAS is important. This implies that multiplication will come first before addition. This will be illustrated thus:
1. 2 + 2 × 2
= 2 + 4
= 6.
2. 3 + 3 × 3
= 3 + 9
= 12
3. 6 + 6 × 6
= 6 + 36
= 42..
Therefore, it should be noted that we multiplied first before adding.
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slope -3 passes through (4,-1) solve and write in slope intercept form
Answer:
y = -3x + 11
Step-by-step explanation:
(4, -1) m = -3
y = -3x + b
y + 1 = -3(x-4)
-3(x-4) = -3x + 12 - 1
y = -3x + 11
The leadership class plans to sell t-shirts for a fundraiser, but they need to decide which company to use.
Custom Ink charges $6.50 for each t-shirt. Tees-4-U charges a flat fee of $250 plus $5.50 for each t-shirt.
A. How many shirts would have to be ordered to for the two companies to charge the same amount?
B. If they plan to order 600 t-shirts, which company would charge them less?
C. How much are they saving by going with the more economical company?
Using linear functions, it is found that:
A. The costs will be the same when 250 shirts are bought.
B. The Tees-4-U Company would charge them less.
C. They are saving $350 by going with the more economical company.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For the cost functions in the context of this problem, we have that:
The slope represents the cost per shirt.The intercept represents the flat fee.Hence the functions for the cost of buying x shirts are given as follows:
Custom Ink: C(x) = 6.5x.Tees-4-U: T(x) = 250 + 5.5x.The costs will be the same when:
C(x) = T(x)
Hence:
6.5x = 250 + 5.5x
x = 250
For item b, the costs are given as follows:
C(250) = 6.5(600) = 3900.T(250) = 5.5(600) + 250 = 3550.The amount saved in item c is:
3900 - 3550 = 350.
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y=-(1/3)x+1 graph it
Step-by-step explanation:
plug in y=(⅓)x+1 to a graphing calculator and it gives you the answer
Find the value of 2y-9 given that -3y-2=4.
Simplify your answer as much as possible.
2y - 9 =
In linear equation, 4 is the Simplify your answer .
What is a linear equation example?
Ax+By=C is the usual form for two-variable linear equations.As an illustration, the conventional form of the linear equation 2x+3y=5 When an equation is given in this format, finding both intercepts is rather simple (x and y).A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.2y-9 ............1
-3y-2=4 .............2
From equation (2)
- 3y = 4 + 2
- 3y = 6
y = 6/-3 ⇒ -2
value of y put in equation 2
-3y-2=4
- 3 * -2 - 2 = 4 ⇒ 6 - 2 ⇒ 4
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When looking at a set of ordered pairs. To determine if it makes a function, you must look at the _ _ _
To see if you have any repeated numbers
Answer: x values make sure they don't repeat if they do its not a function.
Indicate whether the following statement is
TRUE or FALSE. −17 is an integer
Answer:
TRUE
Step-by-step explanation:
an integer is a whole number from the set of negative, non-negative, positive and 0 numbers.
ex : -1, -2, -3, -4, -5, 0, 1, 2, 3, 4, 5
-17 is a negative whole number
so yes, -17 is an integer
The prices of the 19 top-rated all-season fires for a specific tire size, are as follows. Answer parts (a)-(0)$87 $116 $98 579 582 592 594 589 594 $81$107 $112 5103 596 586 $92 $75 $99 $90a) Determine Q2b) Determine Q1c) Determine Q3
Simone, these are the steps to calculate Q1, Q2, and Q3.
Step 1: You need to put all the values in order from the lowest to the greatest.
Step 2: The tenth value from left to right is the median or Q2.
Step 3: The
The
length of a rectangle is 7 inches longer than it is wide. If the perimeter is 62 inches, what are the dimensions of the rectangle?
The width, or shorter side is
inches.
The length, or longer side is
inches.
2(x) + 2(x+7)= 62
4x+14=62
4x=58
x=14.5
width= 14.5
length=21.5
The graph of a function f(x) shown in orange is moved two units to the left to obtain the function in blue. Which of the following represents the blue graph
The equation of the blue line is y = 2(2 - x).
Equation of A(1,0) and B(0, -2)
Use y = mx + c,
m = change of x axis ÷ change of y axis
The difference in x-coordinates equals the difference in y-coordinates, and the difference in y-coordinates equals the difference in y-coordinates.
m = (y2 - y1) ÷ (x2 - x1)
To get the slope, plug in the parameters of both x and y into to the equation.
m = (2 - 0) ÷ (0 - 1)
m = -2
The value of b calculated using the expression of a line formula.
b = 2
Now that you have the measurements of m (slope) and b (y-intercept), plug them into y = m x + b to determine the equation of the line.
y = −2x+2
Because the line is two primary components to the left, the parallel line's equation is,
y = -2x + 2 + 2
y = -2x + 4
y = 2(2 - x)
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Complete the table to determine the total number of possible outcomes.
Using the Fundamental Counting Theorem, it is found that there are 27 possible outcomes.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, each trial independent of other trials, the number of possible outcomes is given as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For this problem, the trials are represented as follows:
Bread.Filling.Cheese.For each trial, there are 3 possible outcomes, from the table, hence the parameters are given as follows:
[tex]n_1 = 3, n_2 = 3, n_3 = 3[/tex]
Hence the total number of possible outcomes is given as follows, from the Theorem:
N = 3 x 3 x 3 = 27.
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△TVX is equilateral. Complete the proof that △TUV≅△XWV.
iven:: △TVX is equilateral.
To prove: △TUV≅△XWV
The given proof is completed and attached below:
he proogf is complete.
20 points!!! pls hurry!!! I need the CORRECT answer in three hours or less!!! What is the slope of this line? A. -1/3 B. -2/3 C. 1/3 D.2/3
Answer:
D
Step-by-step explanation:
RISE/RUN = slope
This slope will be POSITIVE because it rises in quadrant 1.
Rise=2, run=3
Slope= 2/3
Hope that helps
Samuel was preparing for the triathlon. He did 3 activities every morning: Ran for 30 minutes, covering 4.5 miles. Swam for 20 minutes, covering 2/3 mi. biked for 45 min, covering 9 miles. What was Samuel's average speed during his morning training?
PLEASE HELP!!!
If Samuel ran for 30 minutes covering 4.5 miles, swim for 20 minutes covering 2/3 miles and biked for 45 min covering 9 miles, then the Samuel's average speed during his morning training is 0.15 miles per minute
The Morning activities of Samuel
He ran for 30 minutes, covering 4.5 miles,
He swim for 20 minutes covering 2/3 miles
He biked for 45 minutes covering 9 miles
Total distance travelled = 4.5+ 2/3 +9
= 14.17 miles
Total time taken = 30+20+45
= 95 minutes
The average speed = Total distance / Total time taken
= 14.17/95
= 0.15 miles per minutes
Hence, if Samuel ran for 30 minutes covering 4.5 miles, swim for 20 minutes covering 2/3 miles and biked for 45 min covering 9 miles, then the Samuel's average speed during his morning training is 0.15 miles per minute
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11. THINKSMARTER Yvonne wrote the numbers sixteen thousand,
nine hundred eighteen and 64,704 on the board. Which of the
numbers has a greater value in the thousands place?
Name
The number that has a greater value in the thousands place is 16,918.
What is Place Value?A number's place value is the worth of each digit. Depending on its location, such as ones, tens, hundreds, and so forth, each digit in a number has a different value. The position of the digit in the number determines whether two similar digits in the same number have different values.Given numbers are sixteen thousand, nine hundred eighteen,(16,918), and 64,704 on the board.
The thousand places in both numbers contain the digits 6 and 4.
The place value of 6 in 16,918 is expressed as 6 thousand or 6,000.
The place value of 4 in 64,704 is expressed as 4 thousand or 4,000.
As 6000 > 4000, the number that has a greater value in the thousands place is 16,918.
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