Answer:
Step-by-step explanation:
Given x^2 - 16x + 60 = -12
Using the completing the square method to find x;
subtract 60 from both sides
x2 - 16x + 60-60 = -12-60
x2 - 16x = -72
Add square of the half of the coefficient of x to both sides
x2 - 16x + (1/2(-16))² = -72 + (1/2(-16))²
x^2 - 16x +64 = -72+64
(x-8)² = -8
Take the square root of both sides
√(x-8)² = √-8
x - 8 = ±√8i
x = ±√8i+8
x = ±2√2i+8
The solution of the given equation is: [tex]x = 8+\sqrt{-8}[/tex] and [tex]\\x = 8-\sqrt{-8}[/tex].
Given that:
Equation: [tex]x^2 - 16x + 60 = -12[/tex]
Simplify the above equation as:
x² - 16x + 60 = -12
x² - 16x = -12 - 60
x² - 16x = -72
Add 64 to each side of the equation to complete the square.
x² - 16x + 64 = -72 + 64
x² - 16x + 64 = -8
Write x² - 16x + 64 as (x - 8)² since it is a perfect square trinomial.
(x - 8)² = -8
Take the square root of both sides to get the solutions.
[tex]x - 8 = \±\sqrt{-8}\\x = 8\±\sqrt{-8}\\x = 8+\sqrt{-8}\\x = 8-\sqrt{-8}[/tex]
where i is the imaginary unit.
Hence, the value of x are: [tex]x = 8+\sqrt{-8}[/tex] and [tex]\\x = 8-\sqrt{-8}[/tex].
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In 2001, Takeru Kobayashi set a world record for the consuming the most hot dogs in 12 minutes. He ate 12 hot dogs in the first three minutes. Approximately, how many hot dogs did he eat during the 12 minute contest?
Answer: 48
Step 1: Find how much 12 is of 48.
12 = 1/4 of 48
Step 2: Multiply 12 by 3 for 3/4.
12 x 3 = 36.
Step 3: Add the numbers.
12 + 36 = 48
Answer = 48
Approximately, 48 hot dogs did he eat during the 12-minute contest.
What is simplification?One strategy to promote uniformity in work efforts, costs, and time is to simplify procedures. It lessens diversity and variation that is damaging, unnecessary, or meaningless. PEMDAS stands for parenthesis, exponents, multiplication, division, addition, and subtraction. Given two or more operations in a single statement, the order of the letters in PEMDAS tells you what to compute first, second, third, and so on, until the computation is complete.
As a result, Takeru Kobayashi broke the record for eating the hottest dogs in a 12-minute period.
Since,
In the first three minutes, he consumed 12 hot dogs.
in three minutes, he ate = 12 hot dogs
in 1 minute, he ate = 12/3
in 1 minute, he ate = 4
So,
in 12 minutes, the total number of hot dogs he ate = 4*12
in 12 minutes, the total number of hot dogs he ate = was 48
therefore, Approximately, 48 hot dogs did he eat during the 12-minute contest.
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Which expression is equivalent to rm ÷ rn? (4 points)
rm – n
rm + n
rm • n
rm ÷ n
The length of a rectangular sandbox is
6
feet less than
3
times the width. The perimeter of the sandbox is
36
feet.
Which statement is true?
The equation
(
3
w
−
6
)
+
w
=
36
can be used to find the width of the rectangle, and the width is
6
feet.
The equation ( 3 w − 6 ) + w = 36 can be used to find the width of the rectangle, and the width is 6 feet.
The equation
(
3
w
−
6
)
+
w
=
36
can be used to find the width of the rectangle, and the width is
12
feet.
The equation ( 3 w − 6 ) + w = 36 can be used to find the width of the rectangle, and the width is 12 feet.
The equation
2
(
3
w
−
6
)
+
2
w
=
36
can be used to find the width of the rectangle, and the width is
6
feet.
The equation 2 ( 3 w − 6 ) + 2 w = 36 can be used to find the width of the rectangle, and the width is 6 feet.
The equation
2
(
3
w
−
6
)
+
2
w
=
36
can be used to find the width of the rectangle, and the width is
12
feet.
Answer:
so the correct statement is;
The equation 2 ( 3 w − 6 ) + 2 w = 36 can be used to find the width of the rectangle, and the width is 6 feet
Step-by-step explanation:
Here, we want to select the statement which is true
Let the width be w
the length is 6 ft less than 3 times the width
The length will be (3w - 6) ft
Mathematically, the perimeter of a rectangle can be calculated using the formula;
2( l + b) = P
Thus;
2(3w -6 + w) = 36
divide both sides by 2
3w -6 + w = 36/2
3w -6 + w = 18
4w -6 = 18
4w = 18 + 6
4w = 24
w = 24/4
w = 6
Samantha and Caden are planning an end-of-school party for the computer club at their school. They each suggest a recipe for punch to serve at the party.
Samantha's Recipe
3
1
2
parts cranapple juice
2
1
2
parts lemonade
Caden's Recipe
4
1
4
parts cranapple juice
3
3
4
parts lemonade
For each recipe, write a ratio that compares the number of parts of lemonade to the total number of parts.
Which recipe will have the stronger lemon taste? Explain how you determined your answer.
Answer and Step-by-step explanation:
Samantha's recipe has:
3 parts cranapple juice
2 parts lemonade
In total, this recipe has:
t = 3 + 2
t = 5
ratio = [tex]\frac{2}{5}[/tex]
Caden's recipe has
4 parts cranapple juice
3 parts lemonade
In total:
t = 4 + 3
t = 7
ratio = [tex]\frac{3}{7}[/tex]
The punch with stronger lemon taste will be the one whose recipe have a bigger proportion of lemon.
For Samantha's recipe, the proportion is 2 ÷ 5 = 0.4
For Caden's, 3 ÷ 7 = 0.43
Caden's punch will have a slightly stronger taste of lemon, because its proportion is slightly higher than Samantha's.
Expand & simplify 3(y+5)-5(y-3)
Answer:
-2y + 30
Step-by-step explanation:
3(y+5)-5(y-3)
Distribute
3y+15 -5y +15
Combine like terms
-2y + 30
what is the speed of an object that travels 210 miles in 7 hours
Answer:
30 miles per hour.
Step-by-step explanation:
Answer:
The speed of the object is 30 miles per hour.
Step-by-step explanation:
210÷7=30
Could I please have BRAINLIEST?
(?)^2-3(?)=-2 can anyone solve this
Answer: x = 1 or x = 2
Sub in x for ?:
x^2-3x = -2 (Move all the terms to one side, and set the equation to equal 0)
x^2-3x+2 = 0 (Factor the simple trinomial by finding two numbers that multiply to 2 and add to -3)
x^2-x-2x+2 = 0 (Factor the expression)
x(x-1)-2(x-1) = 0 (Group like terms)
(x-1)(x-2) = 0 (Solve for x by setting each term equal to 0)
x-1 = 0
x = 1
x-2 = 0
x = 2
∴ x = 1 or x = 2.
Fill in each box with the correct numb
5(X+9)=5. +5.
Answer:
so
box1 = x
box2= 9
Step-by-step explanation:
5(x+9)
distribute
5(x) + 5(9)
5x + 45
(3 + zi) (3 + 4i) - (3 + zi) (3 - 2i)
Express in simplest a+bi form
Answer:
Step-by-step explanation:
9+12i+3zi+4zi²-(9-6i+3zi-2zi²)
= 9+12i+3zi+4zi²-9+6i-3zi+2zi²
= 18i+6zi²
= i(18+6zi) or 6i(3+zi)
i hope this is the anwer you're looking for
What is the difference between slope and average rate of change ?
A family travels to Bryce Canyon for three days. On the first day, they drove 140
miles. On the second day, they drove 200 miles. What is the least number of miles
they drove on the third day if their average number of miles per day was at least
180?
A family travels to Bryce Canyon for three days. On the first day, they drove 140 miles. On the second day, they drove 200 miles. What is the least number of miles they drove on the third day if their average number of miles per day was at least 180?
A:To find the average number of something, you would take all of the numbers you want to find the average of, add them together, and divide by the total number of items you added up.
For example: in this question, you have 140 miles, 200 miles, and x miles (the amount of miles they drove on the third day).
You would add all of these miles together and divide by 3, since you added 3 numbers together. This would equal the average.
Finding the average:
Create an equation where all of the miles they drove are added together, divide this expression by 3, and set this greater than or equal to 180 (since they drove at least 180 miles on average).
(140 + 200 + x)/3 ≥ 180Solve for x to find the least number of miles they drove on the third day. Multiply both sides by 3.
140 + 200 + x ≥ 540Combine like terms on the left side of the equation.
340 + x ≥ 540Subtract 340 from both sides of the equation.
x ≥ 200The least number of miles the family drove on the third day was 200 miles, since x can't be anything less than 200.
Answer: x = 200 milesHELP WILL MARK YOU BRAINLIEST NO GUESSES PLZ!!!!
Miles
Minutes
Martin's running ability is measured by this proportion:
1 3
7 21
1
7
Use the proportion to identify the values of the variables
that complete the rate table
3
21
a =
7
a
b=
CE
b
70
15
c
Answer:
the answer is
a=49
b=10
c=105
hi so I need help with my math the question says use the long division algorithm to find the decimal value of the fraction -1/4
Answer:
uhm well I'm not sure what you mean by algorithm but just think it like this :
Step-by-step explanation:
think of 1/4 as a quarter and it says the negative
so -.25
ILL GIVE BRAINLIST! this is about Determining a scale factor!! the last answer that couldn't fit in the picture is 9| 12_
Answer:
The first one (4cm for height and 3cm for base)
Step-by-step explanation:
the original height is 16cm and base is 12cm
if you multiply them both by 1/4 or 0.25 you get 4 and 3
(16*0.25=4 and 12*0.25=3)
Another way you could do it is to divide 16 and 12 by four and you still get 4 and 3
(16/4=4 and 12/4=3)
Answer:
Is A.
Step-by-step explanation:
The sides of the triangle include numbers 4 and 3 in option A. Mathematically in scale factor form, 16 cm 12 cm divide or multiply evenly into the scale factor of 1/4.
ANSWER FAST FOR BRAINLIEST AND FIVE STARS AND THXS!!!!!!!!
Answer:
D. Whole Numbers
Whole numbers only contain 0 on, with no negatives, fractions, or decimals.
Please mark me Brainliest, I need it to move onto the next level.
can somebody help please
Answer:
(x^3y)/2
Step-by-step explanation:
I need help what is -0.5 _ -0.2
Give the digits in the tens place and the hundredths place.
14.67
Answer:
1 is in the tens and 7 is in the hundredths place.
Step-by-step explanation:
14.67
1 is tens place
4 is ones place
then the . decimal
6 is the tenths place and 7 is the hundredths place
The Newton city park has 11 basketball courts which are all in use. There are 54 people playing basketball some are playing one on one and some are playing in teams. A one on one game requires two players and a team game requires 10 players. Write a system of equations that represents the number of one on one and team games being played
Answer:
Kindly check explanation
Step-by-step explanation:
Given that:
Number of basket ball courts = 11
Total number of people playing basketball = 54
Number of players required for one on one game = 2
Number of players required for team game = 10
Inequality to represent number of one on one and team Games being played :
Let one on one games = a
Team games = b
Number of players required for each game * number of games
2a + 10b = 54 - - - (1)
a + b = 11 - - - (2)
a = 11 - b
2(11 - b) + 10b = 54
22 - 2b + 10b = 54
8b = 32
b = 4
a = 11 - b
a = 11 - 4
a = 7
Number of one on one games = 7
Number of Team games = 4
2. La suma de los cuadrados de dos números reales pares consecutivos es 52
Encuentra los números
Answer: ±4 y ±6
Step-by-step explanation:
Algunas definiciones:
Sea N un numero real.
El cuadrado de un numero es:
N^2.
Ahora, nos dicen que N es par, entonces podemos escribir:
N = 2*n
donde n es un numero entero.
Y el par consecutivo a N, va a ser M = N + 2.
M = 2*n + 2.
Entonces:
"La suma de los cuadrados de dos números reales pares consecutivos es 52"
(2n)^2 + (2n + 2)^2 = 52
Tenemos que resolver esto para n.
4n^2 + 4n^2 + 8n + 4 = 52
Entonces tenemos una ecuación cuadrática:
8*n^2 + 8n + 4 - 52 = 0
8*n^2 + 8n - 48 = 0
Antes de usar la ecuación de Bhaskara, dividamos todos los coeficientes por un factor común, en este caso 8 es un factor común:
(8*n^2 + 4n - 48)/8 = n^2 + n - 6 = 0.
Ahora resolvamos esto para n, las dos soluciones son
[tex]n = \frac{-1 +-\sqrt{1^2 - 4*1*-6} }{1*2} = \frac{-1 +- 5 }{2}[/tex]
Entonces las dos soluciones son:
n = (-1 - 5)/2 = -3
n = (-1 + 5)/2 = 2
Entonces, si tomamos la primer solucion, los numeros consecutivos son:
N = 2*-3 = -6
M = N + 2 = -4
Si tomamos la segunda solucion, n = 2.
N = 2*2 = 4.
M = N + 2 = 6.
Entonces podemos concluir que las soluciones son:
±4 y ±6
7. 2y + 13.2 =78
у =
Step-by-step explanation:
I hope it will help you here's the answer
HELP PLEASE
Given the exponential function f(x) = 16(0.75)x, classify the function as exponential growth or decay and determine the percent rate of growth or decay.
Exponential growth, 75% increase
Exponential decay, 75% decrease
Exponential growth, 25% increase
Exponential decay, 25% decrease
An equation is blank =540
Damien deposited $250 in an account that earned 3.75% interest compounded annually.He did not make additional withdraws or deposits .what will the balance in his account be at the end of 4 years?
Step-by-step explanation:
[tex] \frac{3.75}{100} \times 250 =9.375[/tex]
[tex]9.375 \times 4 = 37.50[/tex]
[tex]250 + 37.50 = 287.50[/tex]
I think this is the answer
A 5000 seat theater has tickets for sale at 26 and 40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of 153800.
Answer:
The number of tickets for sale at $26 should be 3300
The number of tickets for sale at $40 should be 1700
Step-by-step explanation:
Use 2 equations to represent the modifiers within the problem:
[tex]5000 = a + b \\ 153800 = 26a + 40b[/tex]
Now you want to find the point at which the variables are changed to make both equations correct, this can be done by graphing and finding the intersection of both lines.
[tex]5000 = 3300 + 1700 \\ 153800 = 26(3300) + 40(1700)[/tex]
Please HELP! will give brainliest
================================================
Explanation:
FGH is similar to EDC
Note the order of the letters. The order is important since it tells us how the letters pair up.
F and E are the first letters, so F and E pair up. This means F = E.G and D are the second letters, meaning that G = DH and C are the third letters showing that H = C.The diagram shows G = 71. Since G = D, we know that D = 71 as well. You can use the substitution property or the transitive property (both are effectively the same).
----------
Side note: The angles G and D are the top most angles in the diagram, so this is a visual way to see how they pair up. Keep in mind that the diagram won't always be helpful because it may not be drawn to scale or something may be rotated to trick you. It's best to use the letter pairing method in the previous section above.
Company XYZ has 97 employees. 31 Of the employees are vegetarian, 36 of the employees owns a Nissan Leaf and 6 of the employees are vegetarian and own a Nissan Leaf. If you randomly select an employee from company XYZ, what is the probability that the employee is vegetarian or that she/he owns a Nissan Leaf?
Answer: [tex]\dfrac{61}{97}[/tex]
Step-by-step explanation:
Let V = Event of selecting vegetarian employee
N = Event of selecting employee who owns a Nissan Leaf.
Given: Total employees = 97
n(V) = 31
n(N) = 36
n(N and V) = 6
By formula,
n(N or V) = n(V) + n(V) - n(N and V)
= 31+36-6
=61
By probability formula,
[tex]P(N \ or \ V)=\dfrac{n(N\ or\ V)}{Total }\\\\=\dfrac{61}{97}[/tex]
Hence, the probability that the employee is vegetarian or that she/he owns a Nissan Leaf = [tex]\dfrac{61}{97}[/tex]
Chen rode his skateboard 334 miles in 34 of an hour.
What was his average speed in miles per hour?
_[blank]_ miles per hour
Solve for X
?????????????,??????,?,,,,,,,??????
Answer:
X= 10°
Step-by-step explanation:
Those two angles equal the same, knowing this we make them equal each other to solve them in an equation.
6x+34=8x+14
Then you solve, add the x's together, and the numbers together.
34-14=8x-6x
20=2x
Then you divide to find X
20/2= 10°
X= 10°
Step-by-step explanation:
6x+34=8x+14
34-14=8x-6x
2x=20
x=20/2
x=10