Answer:
Probability that the sum of the two dice is greater than 12 is ZERO.
Step-by-step explanation:
Here, when two dices are rolled together, the sample space is given as:
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5,6)
(6, 1), (6, 2), (6, 3), (6, 4),(6,5), (6,6) = Total 36 outcomes
Now, E : Event of getting a sum greater than 12.
So here, number of possible outcomes = 0
So, the probability that the sum of the two dice is greater than 12 = 0/36 = 0
So, it is an IMPOSSIBLE EVENT.
It is impossible to roll a sum greater than 12 with two standard six-sided dice, as the maximum sum possible is 12. Therefore, the probability of rolling a sum greater than 12 is zero.
Explanation:The student asked about the probability that the sum of two standard six-sided dice is greater than 12. Since the highest sum one can achieve with two six-sided dice is 12 (when both dice show a 6), it is impossible to roll a sum greater than 12. Therefore, the probability of this event is zero.
When considering every outcome of rolling a die, we must include all possible individual results, which range from 1 to 6 for each die. The sum of two dice ranges from a minimum of 2 (both dice showing 1) to a maximum of 12 (both dice showing 6). Consequently, there are no combinations of dice that can result in a sum that exceeds 12.
The highest sum achievable on two six-sided dice is 6 + 6 which equals 12. This makes sums greater than 12 unattainable, and highlights the importance of considering the specified number of sides on dice when calculating probabilities related to their sums.
Paula bought a ski jacket on sale for $6 less than half it’s original price.She paid $86 for the jacket.What was the original price
Answer: Original price $184
Step-by-step explanation:
(X/2) - 6 = 86
X/2 = 86+6
X/2 = 92
X = 92*2
X = 184
For f(x) = 7
, substitute 3 for x in the function to solve for f(3)
Answer:
f(3)=7
Step-by-step explanation:
f(x)=7
f(3)=7
(03.01) Factor completely x2 − 12x + 35. (1 point)
Answer:
(x - 5)(x - 7)
Step-by-step explanation:
Given
x² - 12x + 35
Consider the factors of the constant term (+ 35) which sum to give the coefficient of the x- term (- 12)
The factors are - 5 and - 7, since
- 5 × - 7 = 35 and - 5 - 7 = - 12, thus
x² - 12x + 35 = (x - 5)(x - 7) ← in factored form
-3x – 4y=2
6x + 6y = -6
Final answer:
To solve the system of equations -3x - 4y = 2 and 6x + 6y = -6, multiply the first equation by 2 to eliminate the coefficients of y, and then add the equations together. The solution is x = -2 and y = 1.
Explanation:
To solve the system of equations:
-3x - 4y = 2
6x + 6y = -6
First, multiply the first equation by 2 so that the coefficients of y will cancel when adding the equations together.
-6x - 8y = 4
Next, add the modified first equation to the second equation.
(-6x - 8y) + (6x + 6y) = 4 + (-6)
-8y + 6y = -2
-2y = -2
Divide both sides of the equation by -2 to solve for y.
y = 1
Substitute the value of y back into either equation to solve for x.
-3x - 4(1) = 2
-3x - 4 = 2
-3x = 6
x = -2
The solution to the system of equations is x = -2 and y = 1.
The width of a rectangle is the sum of the length and 2. The area of the rectangle is 48 units. What is the width, in units, of the rectangle?
W=L+2
A=48=L*W
48=L*(L+2)
48=L^2+L*2
0=L^2+L*2-48
L1=6
L2=-8 (can't be used since it's negative)
Lenght=6
Width=8
explanation of two column proofs? (geometry)
Answer:
Two Column Proofs. Two column proofs are organized into statement and reason columns. Each statement must be justified in the reason column. Before beginning a two column proof, start by working backwards from the "prove" or "show" statement. The reason column will typically include "given", vocabulary definitions, conjectures, and theorems.
Step-by-step explanation:
hope this helps :)
Which of the following is equivalent to (c + c)(3d + 5)? 2c + 8d 3cd + 7c 6cd + 10c 6c2d + 5c
Answer:
6cd+10c
Step-by-step explanation:
(c+c)(3d+5)
2c(3d+5)=6cd+10c
Madison has $6.50. Potatoes are $0.50 per pound. How many pounds of potatoes can Madison afford to buy?
In two or more complete sentences write and solve an inequality for this situation. Explain how you would solve this inequality.
Answer to the first step:
3 Pounds of Potatoes.
6.50 / 0.50 = 13 or 650 / 50 = 13
Then, in two or more complete sentences, explain the steps you used to add the mixed numbers.
Answer:
x will be number of pounds
.5x is less than or equal to 6.50
She can afford 13 pounds of potatoes
You would solve the inequality by dividing each side by .5 to isolate x then write it as x is less than or equal to 13.
Part A:
You are given the amount of money Madison can spend and the price per pound for the potatoes. To find how many pounds Madison can buy, you would need to divide the amount of money she has by the price per pound.
The equation would be Pounds of potatoes = 6.50 / 0.50
Part B:
The only step required to solve the equation from part A is division.
Dividing 6.50 by 0.50 = 13. This means Madison can buy 13 pounds of potatoes.
1.
Marcy is comparing prices of
bottled water for 16.9-ounce
bottles. The table shows the
price for each brand. Complete
the table to sort the brands
from least to greatest price per
bottle. Round each unit price
to the nearest thousandth
dollar. 7.RP.2, 7.RP.2b
Answer:
Here is the complete question (in attachment).
The least price is for Water Spring brand and the greatest price is of Clear Mountain brand.
Step-by-step explanation:
To find the unit price we have to divide the full price with the whole of the quantity.
From least to greatest unit prices are arranged below.
Water Springs [tex]=\frac{19.99}{48}=0.416\$[/tex]Nature's River [tex]=\frac{20.35}{48}=0.423\$[/tex]Forest Air [tex]=\frac{10.49}{24}=0.437\$[/tex]Iceland Springs [tex]=\frac{5.49}{12}=0.457\$[/tex]Clear Mountain [tex]=\frac{11.99}{24}=0.499\$[/tex]In ascending order the number are.
[tex]0.416 < 0.423< 0.437< 0.457< 0.499[/tex]
So the least price is for Water Spring brand,and the greatest price is for Clear Mountain brand.
The manager at Gabriela's Furniture Store is trying to figure out how much to charge for a book shelf that just arrived. The book shelf was bought at a wholesale price of $147.00 and Gabriela's Furniture Store marks up all furniture by 60 percent.
At what price should the manager sell the book shelf?
The manager should sale the bookshelf for $235.20
Step-by-step explanation:
Wholesale price of book shelf = $147.00
Mark up = 60% of original price
[tex]Mark\ up=\frac{60}{100}*147.00\\\\ Mark\ up=\frac{8820}{100}\\Mark\ up=\$88.20[/tex]
Total = Wholesale price + Mark up
[tex]Total= 147.00+88.20\\Total=\$235.20[/tex]
The manager should sale the bookshelf for $235.20
Keywords: mark up, percentage
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Please Solve for 3 of them
Answer:
13. b. 4 + 5x = 29; $5.
14. c. 74 + w = 3w + 6; 34 pounds.
15. b. $42.5.
Step-by-step explanation:
13. 4 + 5x = 29
5x = 29-4 = 25
x = 5.
14. 74 + w = 3w + 6
68 = 2w
w = 34.
15. Let x be the money he got last year. Then:
2x + 5 = 90
2x = 85
x = $42.5.
A Pizzeria sells pizza according to size: small pizzas cost $10, medium pizzas cost $15, and large pizzas cost $40. They usually sell as many small pizzas as medium and large pizzas combined. The number of medium pizzas sold is usually twice as many as large ones. How many of each size pizza must they sell to get $600?
They must sell 18 small pizzas, 12 medium pizzas and 6 large pizzas
Step-by-step explanation:
A Pizzeria sells pizza according to size:
Small pizzas cost $10, medium pizzas cost $15, and large pizzas cost $40They usually sell as many small pizzas as medium and large pizzas combinedThe number of medium pizzas sold is usually twice as many as large onesWe need to find how many of each size pizza they must sell to get $600
Assume that the number of small pizza is x, the number of medium pizza is y and the number of large pizza is z
∵ The Pizzeria sells x small pizzas, y medium pizzas and
z large pizzas
∵ The small pizzas cost $10, medium pizzas cost $15, and
large pizzas cost $40
∵ They get $600
∴ 10x + 15y + 40z = 600 ⇒ (1)
∵ They sell as many small pizzas as medium and large pizzas
combined
∴ x = y + z ⇒ (2)
∵ The number of medium pizzas sold is twice as many as large ones
∴ y = 2z ⇒ (3)
Substitute equation (3) in equation (2) to find x in terms of z only
∵ x = (2z) + z
∴ x = 3z ⇒ (4)
Substitute x in equation (1) by equation (4), and substitute y in equation (1) by equation (3)
∵ 10(3z) + 15(2z) + 40z = 600
- Simplify the left hand side
∴ 30z + 30z + 40z = 600
- Add like terms
∴ 100z = 600
- Divide both sides by 100
∴ z = 6
Substitute the value of z in equations (3) and (4) to find y and x
∵ y = 2(6)
∴ y = 12
∵ x = 3(6)
∴ x = 18
They must sell 18 small pizzas, 12 medium pizzas and 6 large pizzas
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Indicate the equation of the line, in standard form, that passes through (2, -4) and has a slope of 3/5. Enter your answer into the blank equation box.
keeping in mind that standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})~\hspace{10em} \stackrel{slope}{m}\implies \cfrac{3}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{\cfrac{3}{5}}(x-\stackrel{x_1}{2})\implies y+4=\cfrac{3}{5}x-\cfrac{6}{5}[/tex]
[tex]\bf \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{5}}{5(y+4)=5\left( \cfrac{3}{5}x-\cfrac{6}{5} \right)}\implies 5y+20=3x-6\implies 5y=3x-26 \\\\\\ -3x+5y=-26\implies 3x-5y=26[/tex]
Find the slope intercept form of the equation of the line that passes through (-5,3) and is parallel to 12x-3y=10
Answer:
y=4x+23
Step-by-step explanation:
The slope-intercept form of the equation of the line that passes through (-5,3) and is parallel to 12x-3y=10 is y = 4x + 23.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Slope-intercept form:
y = mx + b, where m is the slope and b is the y-intercept.
And we have the given equation:
12x - 3y = 10
Arranging the equation as slope-intercept form.
3y = 12x - 10
Divide by 3,
y = 4x - 10/3.
And this line is parallel to the required line.
So, the slope of the required line;
m = 4
Hence, the slope-intercept form,
y = 4x+b equation 1
To find y-intercept:
We substitute the value of x and y from the point (-5,3) to the slope-intercept form,
y = 4x + b
(3) = 4(-5) + b
b = 20 +3
b = 23
Now, the equation 1
y = 4x + 23
Therefore, y = 4x + 23 is the required slope-intercept form.
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in a recent study, 55% of the cars tested failed the safety test. If 231 cars failed the safety test, how many cars were tested
Answer:
420 cars were tested
Step-by-step explanation:
55/100=231/x
55x= 23100
x=420
Final answer:
The total number of cars tested can be calculated by dividing the number of cars that failed (231) by the percentage that failed (55%), resulting in 420 cars tested.
Explanation:
The question asks about the total number of cars tested based on the percentage that failed the safety test. To find the total, we can set up a proportion: if 55% of cars, or 0.55 of the total, failed the safety test and that number is 231, we can represent the total number of cars tested as 'X'. Using the proportion 0.55 = 231/X, we can solve for X, which represents the total number of cars tested.
Step by step, we can start by multiplying both sides of the equation by X to get 0.55X = 231, then we divide both sides by 0.55 to isolate X and find the total:
X = 231 / 0.55
X = 420
Therefore, 420 cars were tested.
The circumference of a circle is 35 pi. What is the diameter?
Answer:
Diameter is 11.14
Step-by-step explanation:
c=dπ
so... 35=dπ
solve for d:
35/π=d
11.14=d
Answer:
11.14
Step-by-step explanation:
/calculators/circumference-calculator/
if x is 5 x 15 and b is 11 x 189 what is b - x + 56?
please help it’s due in 2 days and idk how to do it
Answer:
2060
Step-by-step explanation:
x=5*15
b=11*189
-------------
x=75
b=2079
b-x+56=2079-75+56=2060
Answer:
i just want points
Step-by-step explanation:
Use the basic proportion = -to solve the following problem for the unknown quantity. Round your answer to the
nearest hundredth, if necessary.
What percent of 357 is 551? step by step
Answer:
154.34%
Step-by-step explanation:
We are asked to determine what percentage of 357 is 551.
Let us assume that x% of 357 is 551.
So, [tex]\frac{357 \times x}{100} = 551[/tex]
⇒ [tex]\frac{x}{100} = \frac{551}{357}[/tex]
⇒ [tex]x = \frac{551}{357} \times 100[/tex] ......... (1)
⇒ x = 154.34%
So, it is clear from the step (1) that when we take the basic ratio then multiply with 100, then we will get the percentage. (Answer)
Final answer:
To determine what percent 551 is of 357, divide 551 by 357, multiply by 100, and round to the nearest hundredth. The answer is 154.34%.
Explanation:
To find what percent 551 is of 357, we use the formula for calculating percentages: 'part over total, times one hundred, equals percent'. The 'part' in this case is 551, and the 'total' is 357.
The calculation is as follows:
Divide the part (551) by the total (357) which equals approximately 1.5434.
Multiply the result by 100 to find the percentage.
1.5434 × 100 = 154.34%
To round the final answer to the nearest hundredth, we look at the digit in the thousandths place. Since the third decimal place is 4, which is less than 5, we do not need to round up, so the rounded percentage is 154.34%.
find the slope and y-intercept of the line that is perpendicular to y=-2/3x+5 and passes through the point (5,7).
The slope of line perpendicular to given line is is 3/2 and y-intercept is: -1/2
Step-by-step explanation:
Given equation of line:
[tex]y = -\frac{2}{3}x+5[/tex]
The given equation of line is in slope-intercept form so the co-efficient of x will be the slope of the line
Let m_1 be the slope of given line
[tex]m_1 = -\frac{2}{3}[/tex]
As we know that the product of slopes of perpendicular lines is -1
Let m_2 be the slope of required line
So,
[tex]m_1.m_2= -1\\-\frac{2}{3} . m_2 = -1\\m_2 = -1 * -\frac{3}{2}\\m_2 =\frac{3}{2}[/tex]
The lope-intercept form is:
[tex]y =m_2x+b[/tex]
Putting the value of m2
[tex]y = \frac{3}{2}x+b[/tex]
To find the value of y-intercept, putting (5,7) in the equation
[tex]7 = \frac{3}{2}(5) + b\\7 = \frac{15}{2} + b\\7 - \frac{15}{2} = b\\b =\frac{14-15}{2}\\b = -\frac{1}{2}[/tex]
Putting the values of slope and y-intercept
[tex]y = \frac{3}{2}x - \frac{1}{2}[/tex]
Hence,
the slope is 3/2 and y-intercept is: -1/2
Keywords: Slope, y-intercept
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line m contains the points -3,4 and 1,0. write the equation of a line that would be perpendicular to this one and pass through the point -2,6
How do you solve that
For this case we have that by definition, the equation of the line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
According to the statement we have two points through which the line passes:
[tex](x_ {1}, y_ {1}): (- 3,4)\\(x_ {2}, y_ {2}) :( 1,0)[/tex]
We found the slope:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {0-4} {1 - (- 3)} = \frac {-4} { 1 + 3} = \frac {-4} {4} = - 1[/tex]
By definition, if two lines are perpendicular then the product of their slopes is -1.
Thus, a perpendicular line will have a slope: [tex]m_ {2} = \frac {-1} {- 1} = 1[/tex]
Thus, the equation will be of the form:
[tex]y = x + b[/tex]
We substitute the given point and find "b":
[tex]6 = -2 + b\\6 + 2 = b\\b = 8[/tex]
Finally, the equation is:
[tex]y = x + 8[/tex]
Answer:
[tex]y = x + 8[/tex]
there are 31 days in the month of may. what fraction of the month does 10 days represent
Answer:
10/31
Step-by-step explanation:
I'm pretty certain this is the answer, since 10/31 cannot be simplified any further; 31 being the total days in the month of May
A 10 days represent a fraction of approximately 0.3226 (rounded to four decimal places) of the month of May.
To find the fraction of the month that 10 days represent, we can divide the number of days represented by 10 by the total number of days in the month, which is 31.
Fraction = (Number of days represented) / (Total number of days in the month)
Fraction = 10 / 31
Therefore, 10 days represent a fraction of approximately 0.3226 (rounded to four decimal places) of the month of May.
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Marlo pays $750 rent each
month. Bea's rent is 12%
higher. What is the ratio of
Marlo's rent to Bea's rent?
Answer:
750:90
Step-by-step explanation:
12% of 750 is 90
Pen Packages
Pen Color
Number of Pens
8. Higher Order Thinking Carla buys
two packages of pens. She buys
49 pens in all. Which color pens does
Carla buy? Show how you found the
answer.
Blue
25
Black
12
Red
24
Green
33
Carla bought one package each of Blue and Red pens. These are the only two packages that when combined bring the total number of pens to 49.
Explanation:This problem revolves around simple arithmetic and logical reasoning. What we need to do is to figure out which combination of pen packages adds up to make 49 pens.
By looking at the numbers given, we can see that the only combination that adds up to 49 would be one package of Blue pens (25 pens) and one package of Red pens (24 pens). There is no other combination of two packages which would result in a total of 49.
Therefore, Carla would have bought one package of Blue pens and one package of Red pens to have a total of 49 pens.
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Find the three consecutive integers such that three times the largest increased by two is equal to five times the smallest increased by three times the middle integer.
The smallest integer is 1 and middle integer is 2 and largest integer is 3
Solution:Given that , three times the largest increased by two is equal to five times the smallest increased by three times the middle integer.
We have to find the three consecutive integers
So, let the smallest integer be n, then the next two consecutive middle and largest integers will be n + 1, n + 2 respectively
Then, by the given statement,
Three times the largest increased by two is equal to five times the smallest increased by three times the middle integer.
[tex]\begin{array}{l}{3 \times (n+2)+2=5 \times n+3 \times (n+1)} \\\\ {3 n+6+2=5 n+3 n+3} \\\\ {8=5 n+3} \\\\ {5 n=8-3} \\\\ {n=1}\end{array}[/tex]
Thus the smallest integer = n = 1
Middle integer = n + 1 = 1 + 1 = 2
Largest integer = n + 2 = 1 + 2 = 3
Final answer:
We defined three consecutive integers as x, x+1, and x+2. By setting up the equation based on the given condition and solving for x, we find that the three consecutive integers are 1, 2, and 3.
Explanation:
Let's define the three consecutive integers we are looking for as x, x+1, and x+2, where x is the smallest integer, x+1 is the middle integer, and x+2 is the largest integer.
The problem states that three times the largest increased by two is equal to five times the smallest increased by three times the middle integer. This gives us the equation:
3(x+2) + 2 = 5x + 3(x+1)
Now, simplify and solve for x:
3x + 6 + 2 = 5x + 3x + 3
6x + 8 = 8x + 3
Subtract 6x from both sides:
8 = 2x + 3
Subtract 3 from both sides to isolate the term with x:
5 = 2x
Divide both sides by 2 to solve for x:
x = 5/2 = 2.5
Since x has to be an integer, this approach shows that we've made a mistake in our calculation. Let's try again:
3x + 6 + 2 = 5x + 3x + 3
3x + 8 = 8x + 3
5 = 5x
x = 1
So the three consecutive integers are 1, 2, and 3.
Which is the Graph of 4x + 2y < 3 ?
Answer:
2nd graph on edge 2020
Step-by-step explanation:
the line will cross the y-axis at y = 1.5 and the line will be a broken line
Inequality graphs
The inequality functions are not separated by an equal sign.
For the inequality 4x + 2y < 3, the lower portion of the graph will be shaded
Determine the y-intercept. If x = 0
4(0) + 2y < 3
2y < 3
y < 1.5
This shows that the line will cross the y-axis at y = 1.5 and the line will be a broken line as shown:
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What is 6/7 times 4 2/3
Answer: 4!
Step-by-step explanation:
You can turn 4 2/3 into improper fraction as 14/3. Then you have 14/3 and 6/7. You multiply both tops, then both bottoms. 6x14 is 84 and 3x7 is 21. You get 84/21 or 4. -viridiancat4, an 8th grader.
Answer: 16/7
Step-by-step explanation:
6/7 times 4 2/3 equals 16/7
The values of x and y vary directly
and one pair of values are given.
Write an equation that relates x
and y. Simplify completely.
x = 0.1, y = 0.9
A
y = [? ]x
Direct variation equation is y=kx . Your k is your variation or you could look at it as your slope. y=kx Plug in what you know, 4=k12 Divide both sides by 12 to cancel out your 12 that is being multiplied by k.
4(/12)=k12(/12) Simplify
1/3=k
y=1/3x This is your direct variation equation.
Answer:
Step-by-step explanation:
1) y=kx
plug in the #s
(0.9)=k(0.1)
divide both sides by 0.1
k=9
plug in k and that is your equation (y=9x)
BEST ANSWER WILL GET BRAINLIEST! which number line correctly shows 47/10, 4 2/5, and 24/5 brainly
Answer:
The third number line
Step-by-step explanation:
first, make each fraction a complex fraction
47/10 = 4 7/10, so you know its the 7th dash from the left.
for 4 2/5 you need to make the denominator 10 by multiplying the numerator and denominator by 2 to get 4 4/10; this should be the 4th dash.
divide 24/5 to get 4 4/5. Multiply the numerator and denominator of the fraction part to get a denominator of 10. you should get 4 8/10; this is on the 8th dash from the last
You would have a dot on the 4th 7th and 8th dash altogether
A coin is tossed.
What is the probability of the coin landing heads up?
A. 1/2
B. 1/4
C. 1/6
D. 1/3
Answer: 1/2
Step-by-step explanation: In this problem, we're tossing a coin and we want to find the probability of tossing a heads.
Now, let's find the probability of tossing a heads.
Remember that a coin has two sides which are heads and tails. When you flip a coin, each side is as likely to come up as the other. This means that the probability of flipping heads is the fraction 1/2.
Since the probability of flipping a heads is 1/2, we can also say that the probability of flipping a heads is 50%.
Therefore, the probability of flipping a heads on a fair coin is 1/2.
Find the value of "k" such that 1/2 is a root of 2x^2+11x=-k
The value of k is -6
Step-by-step explanation:
The general form of the quadratic equation is y = ax² + bx + c
The roots of the equation is the values of x when y = 0ax² + bx + c = 0, is used to find the roots∵ 2x² + 11x = -k
- Add k to both sides
∴ 2x² + 11x + k = 0
∵ The roots of the quadratic equations is the values of x when y = 0
∵ [tex]\frac{1}{2}[/tex] is a root of the equation
- Substitute x by [tex]\frac{1}{2}[/tex] in the equation above to find k
∵ 2( [tex]\frac{1}{2}[/tex] )² + 11( [tex]\frac{1}{2}[/tex] ) + k = 0
∴ 2( [tex]\frac{1}{4}[/tex] ) + [tex]\frac{11}{2}[/tex] + k = 0
∴ [tex]\frac{1}{2}[/tex] + [tex]\frac{11}{2}[/tex] + k = 0
- Add the like terms
∵ [tex]\frac{1}{2}[/tex] + [tex]\frac{11}{2}[/tex] = [tex]\frac{12}{2}[/tex] = 6
∴ 6 + k = 0
- Subtract 6 from both sides
∴ k = -6
The value of k is -6
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Final answer:
By substituting x = 1/2 into the equation [tex]2x^2 + 11x = -k[/tex] and simplifying, we find that k must equal -6 for 1/2 to be a root of the equation.
Explanation:
To find the value of k such that 1/2 is a root of the quadratic equation [tex]2x^2 + 11x = -k[/tex], we can substitute x = 1/2 into the equation and solve for k.
First, substitute x = 1/2:
[tex]2(1/2)^2 + 11(1/2) = -k[/tex]
Then, simplify the equation:
2(1/4) + 11/2 = -k
1/2 + 11/2 = -k
Now, combine the terms:
(1 + 11)/2 = -k
12/2 = -k
6 = -k
Finally, multiply both sides by -1 to find k:
k = -6