The roots of the equation [tex]x^{2}[/tex]-3x-3=0 by completing the square method are 3.79 and -0.79.
Given that the equation is [tex]x^{2}[/tex]-3x-3=0.
We are required to find the roots of the equation by completing the square method.
Equation is basically the relationship between two or more variables that are expressed in equal to form. It may be linear equation, quadratic equation,cubic equation and many more depending on the power of the variables that are present in the equation.
The equation is [tex]x^{2}[/tex]-3x-3=0.
[tex]x^{2}[/tex]-3x=3
[tex](x+3/2)^{2}[/tex]=-(c-[tex]b^{2}[/tex]/4)
So,
[tex](x-3/2)^{2}[/tex]=-[-3-[tex](-3)^{2}[/tex]/4]
[tex](x-3/2)^{2}[/tex]=-[-3-9/4]
[tex](x-3/2)^{2}[/tex]=21/4
x-3/2=±[tex]\sqrt{21}[/tex]/2
x=([tex]\sqrt{21}[/tex]+3)/2,(-[tex]\sqrt{21}[/tex]+3)/2
x=(4.58+3)/2, (-4.58+3)/2
x=7.58/2, -1.58/2
x=3.79,-0.79
Hence the roots of the equation [tex]x^{2}[/tex]-3x-3=0 by completing the square method are 3.79 and -0.79.
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Answer:
by completing the square method the answer is 3.79 and -0.79.
Step-by-step explanation:
above
Rewrite one fourth times x cubed times y plus three fourths times x times y squared using a common factor.
one fourth times x times y times the quantity x squared plus 3 times y end quantity
one fourth times x cubed times y squared times the quantity y plus 3 times x end quantity
one half times x times y times the quantity 2 times x squared plus 6 times y end quantity
one half times x times y times the quantity x squared plus 3 times y end quantity
The expression 1/4x³y + 3/4xy² can be rewritten as: A. 1/4xy(x² + 3y).
How to Rewrite an Expression?We can rewrite an expression by using a factor that is common in an expression.
Given the expression, 1/4x³y + 3/4xy², the common factor in the expression that we can factor out is 1/4xy.
To rewrite the expression, we have the following:
1/4xy into 1/4x³y will give us x²
1/4xy into 3/4xy² will give us 3y.
This will give us: 1/4xy(x² + 3y).
Therefore, the expression 1/4x³y + 3/4xy² can be rewritten as: A. 1/4xy(x² + 3y).
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Answer:
A. one fourth times x times y times the quantity x squared plus 3 times y end quantity
Step-by-step explanation:
Hope this helps you :)
[tex]\frac{-9}{5}+ \frac{7}{2}[/tex]
Answer:
exact form: 17/10
decimal form: 1.7
mixed number form: 1 7/10
Step-by-step explanation:
I need help with 47 please
Answer:
25 students and 40%
Step-by-step explanation:
Write 'six more than four times a number equals 18' as an equation.
6x + 4 = 18
4x + 6 = 18
6x(4) = 18
4x(6) = 18
The required equation is 4x+6=18.
Option (B) is correct.
What is algebra?A part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.
Given:
Let the number be 'x'
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign.
We have to find the equation..
According to given question we have
i.e
four times a number=4*x
'six more than=4x+6
equals 18'=18
i.e
4x+6=18
Therefore, the required equation is 4x+6=18.
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In which place is the digit in the number 5,341 that would it be changed to 5,841 how to how do the values of two numbers compare
We get that, the digit is in the 3rd place (hundreds).The difference between the numbers is 500.
We want to change the digit in the number 5,341 into 5,841.
We also need to find the difference between the numbers.
The number 3 is in the 3rd place (hundreds) of the number 5,341 as a digit will be replaced by 8 to form the number 5,841.
This means that 300 is replaced by 800 because the third place in both the numbers is of hundreds.
The difference between 800 and 300 is:
800 - 300 = 500.
Subtraction of 5,341 from 5,841 also yields 500.
Therefore, we get that, the digit is in the 3rd place (hundreds).The difference between the numbers is 500.
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find the rise and the run
Answer:
Rise is 4
Run is 5
Slope is 4/5
Step-by-step explanation:
The 2 points on the line (4,-3) and (9,1)
Rise is 4
Run is 5
Slope is 4/5
a survey regarding truck engines found a positive correlation between the size of the engine and horsepower the engine produces. answer the following question based only on this information. true or false: it can be concluded that trucks with larger engines have greater horsepower.
False
• Correlation means that there is a relationship or patter between the two variables. A scatter plot displays the data about the two variables as a set of points in the x-y plane and it is a useful tool for determining if there is a correlation between the variables.
• Causation means the one event causes other event to occur. It can only be determined by designed experiment.
• While correlation and causation both can exist at the same time, correlation doesn’t imply causation.
• Causation explicitly applies only to cases where action P causes outcome Q whereas correlation is simply a relationship.
Correlation doesn’t prove causation.
There could be third variable associated with the size of engine which caused the truck to have greater horsepower. For example, it can be that manufacturers anticipate that consumers who wanted trucks with greater horsepower also prefered trucks with larger engines and therefore chooses to make trucks with larger horsepower.
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Estimate the quotient of 538 divided by 96 by using two methods 
The two methods for estimation of the quotient of 538 divided by 96 is being explained.
We are given that:
538 ÷ 96
We need to estimate the quotient of 538 ÷ 96 by using two methods.
The first method can be that we first estimate the divisor and the dividend to the nearest tens and then perform the division.
538 will be rounded off to 540 and 96 will be rounded off to 100.
So, it becomes:
540 ÷ 100
= 5.4
This will again be rounded off to 5
= 5
The second method will be that we first perform the division and then round off.
538 ÷ 96 = 5.61
Rounding off, we will get:
= 6.
Therefore the two methods for estimation of the quotient of 538 divided by 96 is being explained.
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[Been stuck on it for weeks, help me or I will fail. I will give Brainlist to anyone who has a well written descriptive answer please.]
A bucket of paint has spilled on a tile floor. The paint flow can be expressed with the
function p(t) = 6t, where t represents time in minutes and p represents how far the paint is
spreading.
The flowing paint is creating a circular pattern on the tile. The area of the pattern can be
expressed as A(p) = лp².
Part A: Find the area of the circle of spilled paint as a function of time, or A[p(t)]. Show your
work. (6 points)
Part B: How large is the area of spilled paint after 8 minutes? You may use 3.14 to
approximate in this problem. (4 points)
Answer:
Part A: 28.26t²
Part B: 2,826 square unit
Explanation:
Part A:
A[p(t)] = π (3t)² = 3.14 * 9t² = 28.26t²
Part B:
p(10) = 3(10) = 30
A(p) = 3.14 * 30² = 3.14 * 900 = 2,826 square unit
The temperature in Anchorage,Alaska, dropped over four consecutive hours from 0 to -44F. If the temperature dropped the same amount each hour, how much did the temperature change each hour?
The temperature change in Anchorage,Alaska, each hour is; -11°F per hour
What is the rate of change of the temperature?When we talk of rate of change with respect to two values, we simply mean the rate of change of the output value with respect to the input value.
Now, we are told that the temperature went from 0°F to -44°F over a four hour period. Thus;
Rate of change = Change in temperature/change in time
Thus;
Rate of change = (-44 - 0)/(4 - 0)
Rate of change = -44/4
Rate of change = -11°F per hour
The temperature change in Anchorage,Alaska, each hour is; -11°F per hour
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Write the equation in logarithmic form: 2^-3=0.125
Show your steps
The equation 2⁻³ = 0.125 in logarithmic form is -3log(2) = log(0.125)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A variable can either be dependent or independent. A dependent variable depend on other variable while an independent variable does not depend on other variables.
Given the equation:
2⁻³ = 0.125
Taking the logarithm of both sides:
log(2⁻³) = log(0.125)
-3log(2) = log(0.125)
The equation 2⁻³ = 0.125 in logarithmic form is -3log(2) = log(0.125)
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Three numbers have absolute values of 2,4, and 9. The product of all the numbers is positive.
A. Find the product
B. Find the different ways to write the signs of the numbers to give a positive product. Tell how many different ways there are in all.
Answer:
what you have to do is multiply 2 times 4 which is 8 and multiply the 8 by 9 which is 72
Step-by-step explanation:
2*4 =8
8*9=72
72 plus 8 is 80
1. Larry is in the market for a new lawn mower. He has found two on sale. The first lawn
mower is $275 with a 20 percent discount but must be assembled. The second lawn
mower is $299 with a 25 percent discount and is already assembled. Which of the
following describes the best decision for Larry?
The option that describes the best decision for Larry is Larry buys the second lawn mower because he thinks the extra $5 are worth not having to do the assembly.
How much does Larry spend?The cost of the first lawnmower after the discount is:
= 275 x (1 - 20%)
= 275 x 0.80
= $220
The cost of the second lawnmower is:
= 299 x 0.75
= $224.25
The difference between the lawnmowers is around $5. This $5 is the cost of the assembly on the second lawnmower and Larry might decide that this cost is worth it.
Options for this question include:
Larry buys the second lawn mower because he thinks the extra $5 are worth not having to do the assembly.Larry buys the second lawn mower because it is cheaper due to the better sale, and he doesn't want to assemble a lawn mower.Larry buys the first lawn mower because he likes the way it looks.Larry buys the first lawn mower because it is significantly cheaper.Larry buys the first lawn mower because he can take the day off of work to build it and will saveFind out more on economic decisions at https://brainly.com/question/27840103
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For the piecewise-defined function f(x) =
7, x>3
5x-3, XS3
find two x-values that have the same y-value and the sum of the x-values is 10.
.
The two such x-values are 2 and 8.
The piecewise-defined function is :When x is greater than 3, f(x) equals 7.When x is less than or equal to 3, f(x) equals 5x-3.We need to get the same y-values.So, we will equate the two parts of the above piecewise-defined function.7 = 5x-35x = 10x = 2One of the x-values is 2.We are told that the sum of the x-values is 10.So, the second x-value is 10-2 = 8.Thus, the two x-values that have the same y-value and the sum of the x-values is 10 are 2 and 8.To learn more about functions, visit :
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A rectangular auditorium seats 1598 people. The number of seats in each row exceeds the number of rows by 13. Find the number of seats in each row.
Please answer please
answer
ex 17
2 3/4 ×8
=11/4×8/1
=11/24
ex 18
9/2× 5/4
=36/10
4
PLEASE HELP ASAP!!!!!!!!!!!!!!!!
Initially, there were only 3 weeds at a park. The weeds grew at a rate of 5% each week. The following function represents the weekly weed growth: f(x) = 3(1.05)x. Rewrite the function to show how quickly the weeds grow each day and calculate this rate as a percentage.
f(x) = 3(1.007)7x; spreads at a rate of approximately 0.7% daily
f(x) = 3(1.05)7x; spreads at a rate of approximately 0.5% daily
f(x) = 3(0.15)x; spreads at a rate of approximately 0.15% daily
f(x) = 3(1.007)x; spreads at a rate of approximately 0.07% daily
Based on the calculation below, the rate at which the weeds grow each day is 0.7%.
How do we calculate the daily percentage growth rate?Given:
f(x) = 3(1.05)x = 3(1 + 0.05)x ................... (1)
Since there are 7 days in a week, the rate at which the weeds grow each day can be calculated from equation (1) by dividing 0.05 (i.e. 5% weekly growth rate) as follows:
f(x) = 3(1 + (0.05 / 7))x
f(x) = 3(1 + 0.007)x
f(x) = 3(1.007)x
Since 0.007 is the same as 0.7%, this implies that the rate at which the weeds grow each day is 0.7%.
The correct option is "f(x) = 3(1.007)7x; spreads at a rate of approximately 0.7% daily".
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Answer: Option 1
Step-by-step explanation: Correct for my test.
Consider the points A(-5,-2), B(1,1), C(-1,0), and D(3,2).
(a): The slopes of both segments AB and CD are
(b): The segments are not parallel, because they lie on the same line.
(c): What word in the Parallel Slope Property addresses the problem in part (b)?
Parallel Slope Property: Two distinct lines are parallel if they have the same slope.
Blank 1:
Blank 2:
(enter the value).
(a) Slope of AB = and Slope of CD =
(b) True, both segments are not parallel as they lie on the same line
(c) Distinct lines are the words in Parallel slope property that addresses the problem in part(b).
What is Slope of a line and Parallel Slope Property and co-linear points?
Slope of a line :Given are two points P (x₁, y₁) and Q ( x₂, y₂)
Then slope of the line PQ is given by [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Given Parallel Slope Property: Two distinct lines are parallel if the have the same slope
Colinear points: A,B,C,D are collinear points if the slopes of lines AB, BC,CD,DA are all equal.
Given the points A(-5,-2), B(1,1), C(-1,0), and D(3,2).
Slope of the line AB [tex]=\frac{1-(-2)}{1--(5)}=\frac{3}{6} =\frac{1}{2}[/tex]
Slope of the line CD [tex]=\frac{2-0}{3-(1)}=\frac{2}{4} =\frac{1}{2}[/tex]
Slope of the line BC [tex]=\frac{0-1}{-1-1}=\frac{-1}{-2} =\frac{1}{2}[/tex]
Slope of the line DA=[tex]\frac{-2-2}{-5-3}=\frac{-4}{-8} =\frac{1}{2}[/tex]
Therefore A,B,C,D are collinear means they lie on the same lines
Slopes of AB and CD are equal but still they are not parallel because according to Parallel Slope Property two lines with same slope are parallel only when they are distinct but AB and CD are on same line.
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two sides of a right triangle measure 222 units and 444 units. 2\text{ units}2 units4\text{ units}4 units what is the area of the square that shares a side with the third side of the triangle?
With the help of Pythagoras Theorem for triangles, we get that the possible areas of the square are: 12 sq. units and 20 sq. units, according to the cases mentioned.
What is Pythagoras Theorem?According to the Pythagoras Theorem, in a right angled triangle, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Given:
Sides of a right triangle are 2 and 4 units.
To find: Area of a square that shares a side with the third side of the triangle.
Finding:
There can the following cases:
If 2 and 4 units are the lengths of the perpendicular sides.
Then, by Pythagoras Theorem, -
[tex]H^{2} = 2^{2}+4^{2}\\ H^{2} = Side^{2}\\H=Side \\H= \sqrt{4+16} \\H= \sqrt{20} \\H= 2\sqrt{5}[/tex]
Hence, the area of the square = side² = 20 units²
If 4 units is the length of hypotenuse.
Then, by Pythagoras Theorem,
[tex]4^{2} = 2^{2} + A^{2} \\16 - 4 = A^{2} \\= \sqrt{12}\\[/tex]
side of triangle = [tex]\sqrt{12}[/tex]
Hence, the area of the square = side² = 12 units²
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theo needs 1 1/2 cups of flour for one recipe and 2 3/4 cups of flour for a second recipe. Theo only has a 1/4 cup measuring cup. How many times will theo need to fill the 1/4 cup measuring cup to measure the flour he needs for the two recipes?
Answer: 17 times
Step-by-step explanation:
It takes 6 times for the first recipe (.25x6=1.5)
It takes another 11 times for the second recipe (.25x4=2 + .25x3 = 0.75)
You add 6 + 11 and get 17
The next model of a sports car will cost 4.6% more than the current model. The current model costs $34,000. How much will the price increase in dollars? What will be the price of the next model?
Based on the price of the current model of a sports car, the price increase for the next model will be $1,564
The price of the next model of the sports car will be $35,564.
How to find the price?The increase in price in dollar terms for the next model of the sports car can be found by the formula:
= Current cost of current model x Price increase in percentage
= 34,000 x 4.6%
= $1,564
The price of the next model is therefore:
= Current price of current model + Price increase
= 34,000 + 1,564
= $35,564
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Given that 5x8y = 29
Find y when x = -1
Give your answer as an improper fraction in its simplest form.
Tom drives 8 1/2 miles every 1/30 hour. How many miles can he drive in 3 hours
In 3 hours Tom drives 243 miles.
What is speed?The rate at which an object's position changes in any direction. Speed is defined as the ratio of distance traveled to time spent traveling. Because it has only one direction and no magnitude, speed is a scalar quantity.So, to find how many miles Tom can drive in 3 hours:
Given: Tom drives 81/2 miles every 1/30 hour.
81/2 miles = 40.5 miles1/30 hours = 30 minutesSo, in 30 minutesTom drives 40.5 miles.
Then, in 1 hour Tom will drive 40.5 + 40.5 = 81 miles.Miles Tom will drive in 3 hours = 81 × 3 = 243 miles.Therefore, Tom drives 243 miles in 3 hours.
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Jean was working on a project involving linear regression. She obtained a predicted value of 8 when she entered 12 as her explanatory variable. Then Jean spilled coffee on her work and could no longer read her regression model. If she remembered that the y-intercept was 26, what was the value of the slope/
A -1.75
B 1.5
C -1.5
D 1.75
E 1.33
Based on the predicted value, the explanatory variable, and the y-intercept, the value of the slope for Jean's project is C. -1.5
What is the slope?A linear regression equation takes the form of:
y = mx + c
y = predicted value
m = slope
x = explanatory variable
c = y-intercept
Given these values, the slope:
8 = 12m + 26
12m = 8 - 26
m = -18 / 12
m = -1.5
In conclusion, option C is correct.
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a number is chosen at random from the positive, even integers from 2 to 50. find the probability that the number chosen is divisible by 5 or 8.
The probability that the number chosen is dividible by 5 or 8 is 0.306.
According to the given question.
A number is chosen at random from the positive even integers from 2 to 50.
Now the total positive intergers from 2 to 50 which are divisible by 5 or 8 are {5, 8, 10, 15, 16, 20, 24, 25,30, 32, 35, 40, 45, 48, 50}
So, there are total 15 positive intergers from 2 to 50 which are divisible by 5 or 8.
⇒ Total number of favourable outcomes = 15
And the total positive integers from 2 and 50 is 49.
⇒ Total number of outcomes is 49.
As we know that, proabability is calculated by taking the ratio of favourable outcomes to the total number of outcomes.
Therefore, the probability that the number chosen is divisible by 5 or 8
= 15/49
= 0.306
Hence, the probability that the number chosen is dividible by 5 or 8 is 0.306.
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The average of five numbers is 72, two of them are 70 and 74. Find the average of the other three numbers.
The average of the other 3 numbers is 72.
Average or mean is a measure of central tendency which calculates the central point of a data-set.
Average of a set of numbers is calculated by taking the sum of the numbers and dividing it by the total frequency of the numbers.
If 3 numbers a , b and c are taken then the average is equal to
(a+b+c) ÷3
Given average of 5 numbers is 72.
Therefore the sum of the numbers is 72 × 5 = 360
Two of the numbers are 70 and 74 .
Sum of the remaining 3 numbers = 360 - (70 + 74) = 360 - 144 = 216
Average of the 3 numbers = 216 ÷ 3 = 72
Therefore the average of the remaining 3 numbers is 72.
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If A:B = 7:8 an B:C =12:7,find A:C in its simplest form.
Answer:
84:56
Step-by-step explanation:
a:b:c
(7:8)
( 12:7)
Answer:
A:C = 3:2
Step-by-step explanation:
A:B = 7:8 is a proportion relationship and can be represented using fractions:
[tex]\displaystyle{\frac{A}{B} = \frac{7}{8}}[/tex]
Similarly the proportion relation B:C = 12:7 can be represented as:
[tex]\displaystyle{\frac{B}{C} = \frac{12}{7}}[/tex]
Multiply the first equation by the second
[tex]\displaystyle\frac{A}{B}\;\mathsf{x}\;\frac{B}{C} = \frac{7}{8}\;\mathsf{x}\;\frac{12}{7}[/tex]
This evaluates to
[tex]\displaystyle\frac{A}{C} = \frac{12}{8}[/tex]
Simplifying gives us
[tex]\displaystyle\frac{A}{C} = \frac{3}{2}[/tex]
So A:C = 3: 2
21. The cost to mail a package is $5.00. Brian has postcard stamps that are worth $0.34 each and first class
stamps that are worth $0.49 each.
If Brian puts 7 first class stamps on the package, how many postcard stamps will be needed.
Answer:
Okay so a couple key points
$5.00 to ship it
Postcard stamps = $0.34
First class stamps= $0.49
And lastly he has 7 first class stamps
So with that being said you take .49 and times it by 7 since he has seven of them and that would be $3.43
And now you take $3.49 and subtract it from the $5.00 you'd be left with $1.57
Now you take $.34 and divide it by $1.57 and you would get a total of 4.61 so that means you would need five postcard stamps
So to be able to ship the package you'd need 7 first class stamps and 5 postcard stamps
how many solutions does this equation have?
2y+20y-15=19+20y
Answer:
1 solution
Step-by-step explanation:
2y + 20y - 15 = 19 + 20y , that is
22y - 15 = 19 + 20y ( subtract 20y from both sides )
2y - 15 = 19 ( add 15 to both sides )
2y = 34 ( divide both sides by 2 )
y = 17
Answer:
Step-by-step explanation:
Answer
one
Proof
2y + 20y - 15 = 19 + 20y Combine the left side.
22y - 15 = 19 + 20y Add 15 to both sides
22y - 15+15 = 19 +15 + 20y Combine
22y = 34 + 20y Subtract 20y from booth sides
22y-20y = 34 + 20y-20y Combine
2y = 34 Divide both sides by 2
2y/2 = 34/2
y = 17
That's the only solution you get. The number of solutions to any equation (with certain exceptions) is the highest power on the variable.
x^2 + 2x - 8 has 2 solutions (from the x^2)
x^3 + 3x^2 + 2x + 15 = y has three solutions
Suppose that the probability a seed will germinate is 85%. what is the probability that 7 of these seeds will germinate when 10 are planted? a. 0.1298 b. 0.385 c. 0.12 d. 0.141
Required probability = 120 * 0.0010819 = 0.1298
total number of outcomes of 7 from 10 = 10*9*8 / 3*2*1 = 120
probability of each outcoe is 0.85^7* (0.15)^(3) = 0.0010819
Required probability = 120 * 0.0010819 = 0.1298
Probability is simply how likely something is to happen.
Whenever we’re unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
The best example for understanding probability is flipping a coin:
There are two possible outcomes—heads or tails.
What’s the probability of the coin landing on Heads? We can find out using the equation P(H) = ?P(H)=?P, left parenthesis, H, right parenthesis, equals, question mark.
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