Answer:
x=6+2√3 or x=6−2√3
Step-by-step explanation:
Let's solve your equation step-by-step by using completing the square.
5x^2−57x=3x−120
Step 1: Subtract 3x from both sides.
5x^2−57x−3x=3x−120−3x
5x^2−60x=−120
Step 2: Since the coefficient of 5x^2 is 5, divide both sides by 5.
5x2−60x/5 = −120 /5
x2−12x=−24
Step 3: The coefficient of -12x is -12. Let b=-12.
Then we need to add (b/2)^2=36 to both sides to complete the square.
Add 36 to both sides.
x2−12x+36=−24+36
x2−12x+36=12
Step 4: Factor left side.
(x−6)2=12
Step 5: Take square root.
x−6=±√12
Step 6: Add 6 to both sides.
x−6+6=6±√12
x=6±√12
x=6+2√3 or x=6−2√3
Briefly explain the roles and relationships that exists amongst the producers, consumers, and decomposers in an ecosystem such as an ocean.
The roles and relationships that exist amongst the producers, consumers, and decomposers in an ecosystem is described by the food chain.
What is an ecosystem?
The meaning of ecosystem is the complex of a community of organisms and its environment functioning as an ecological unit.
Producer is an organism that produces its own food e.g. photosynthesis in plants. Also known as the base of the food-chain.
Consumer is an organism that consumes (eats) either a producer or another consumer e.g. animals will solely eat plants (herbivore), solely animals (carnivore), or a combination of both (omnivore).
Studies are showing that most animals are omnivores. Even pre-concluded herbivores or carnivores are found to eat a small variety of both plants and animals in a pinch. E.g. a deer would eat a baby bird if it found it on the ground.
Decomposers are organisms that 'eat' and break up dying/decaying material e.g. earthworms and fungi.
All of this together is the food cycle.
Learn more about ecosystem, click;
https://brainly.com/question/13979184
#SPJ3
A bottling company produces 7,200 cans of iced tea per day. How many 12-can cartons can be filled?
Answer:
600 cartons
Step-by-step explanation:
!!!!!URGENT!!!!FIND THE SLOPE
A. 3
B. - 3
X
O
12
14
6
D.
Answer:
3-2/6-3 =1/3
So the answer is 1/3'c'
Which expression is equivalent to -8 - (-12)
8 - 12
-8 + 12
-8 - 12
-8 (8+12)
I need help with this too it’s confusing and I don’t understand it.
Suppose that Clayton Kershaw of the Los Angeles Dodgers throws his fastball with a mean velocity of 94 miles per hour (mph) and a standard deviation of 2 mph and that the distribution of his fastball speeds can be modeled by a Normal distribution What percent of Kershaw’s fastballs will travel at least 100 mph?
Answer:
Step-by-step explanation:
ah, probability, so the std. deviation is 2 MPH, so that means to get from the mean.. or average speed of 94, he'll have to vary by 3 std. deviations or 6 MPH to hit 100
99.7% of throws fall into that area of with in 3 std. deviations so that means
0.3% fall outside also , 1/2 of those will 3 std. deviations slow while the other half is fast
so
0.15% will be 100 or faster.... not many
0.15% is the percent of Kershaw’s fastballs will travel at least 100 mph.
What is Normal Distribution?A probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
The standard deviation is 2 MPH, so that means to get from the mean.. or average speed of 94, he'll have to vary by 3 standard deviations or 6 MPH to hit 100
99.7% of throws fall into that area of with in 3 standard deviations so that means
0.3% fall outside also , 1/2 of those will 3 standard deviations slow while the other half is fast
so 0.15% will be 100 or faster
Hence 0.15 percent of Kershaw’s fastballs will travel at least 100 mph.
To learn more on Normal Distribution click:
https://brainly.com/question/25394084
#SPJ2
Solve the system and find the values of x and y
Answer:
x = [tex]\frac{(a+b)}{2}[/tex]
[tex]y=\frac{a-b}{2}[/tex]
Step-by-step explanation:
System of equations has been given as,
x + y = a ----------(1)
x - y = b ---------(2)
By adding equation (1) and (2)
(x + y) + (x - y) = a + b
2x = a + b
x = [tex]\frac{(a+b)}{2}[/tex]
By substituting these values in equation (2),
x - y = b
[tex]\frac{a+b}{2}-y=b[/tex]
[tex]\frac{a+b}{2}-b=y[/tex]
[tex]\frac{a+b-2b}{2}=y[/tex]
[tex]\frac{a-b}{2}=y[/tex]
One side of a rectangle is 3 m more than the other. If the perimeter of the rectangle is 30 m, what are its dimensions? *
Answer:
the length— 6
width— is 9
Step-by-step explanation:
you said One side— 3m MORE
so we will consider the length Number as X
we will consider width As three plus X
- You want to know the Perimeter. So we have to
add.
— so the expression is 3+3+x+x+x+x = 30
it is then simplified to 6+4x= 30
then we should be able to find out the X which is 6
when we substitute the values with dimensions, you will get
your final Answer
I hope This Helped!
James is reading a book and noticed the page numbers are consecutive integers whose product is 1640. What is the value of the larger page number?
Answer:
41
Step-by-step explanation:
A pair of consecutive numbers is written as: N and N + 1
(where the larger page number is N + 1)
And we know that the product of these numbers is 1640.
Then:
(N)*(N + 1) = 1640
Solving for N, we get:
N^2 + N = 1640
N^2 + N - 1640 = 0
This is a quadratic equation, remember that for a general quadratic equation:
a*x^2 + b*x + c = 0
The solutions are:
[tex]x = \frac{-b\pm \sqrt{b^2 - 4*a*c} }{2*a}[/tex]
In our case, the solutions are:
[tex]N = \frac{-1 \pm \sqrt{(1)^2 - 4*1*(-1640)} }{2} = \frac{1 \pm 81}{2}[/tex]
Then the two solutions are:
N = (-1 + 81)/2 = 40
N = (-1 - 81)/2 = -41
Because N represents the number on a page, it only can be a positive value, then we take the positive solution.
Then the two consecutive numbers, N and N + 1
are:
N = 40
N + 1 = 41
The value of the larger page number is 41.
Find the value of x- helppp
Answer:
60º
Step-by-step explanation:
A triangle is 180º so you do (180-60)/2 and you get that x=60.
Hope that helps :)
Answer:
Hey love! x = 60
Step-by-step explanation:
Because a triangle adds up to 180 so
180 - 60 = 120 and sense both angles will be the same measure I divide 120 by 2 and get 60 so
x =60 Hope that helps!
What is 5 11/10 simplified
Answer:
61/10 or in decimal form 6.1 or 6 1/10
Step-by-step explanation:
Select the expression that has a value of 13. 9 + 3 x (2 ÷ 3) + 6 (9 + 3) x 2 ÷ 3 + 6 9 − (3 x 2) ÷ 3 + 6 (9 + 3 x 2) ÷ 3 + 6
Answer:
[tex](c)\ 9 - (3 * 2) \div 3 + 6[/tex]
Step-by-step explanation:
Given
(a) to (d)
Required
Which equals 13
[tex](a):\ 9 + 3 * (2 \div 3) + 6[/tex]
Solve the bracket
[tex]9 + 3 * (2 \div 3) + 6 =9 + 3 * (\frac{2}{3}) + 6[/tex]
Open the bracket
[tex]9 + 3 * (2 \div 3) + 6 =9 +2 + 6[/tex]
[tex]9 + 3 * (2 \div 3) + 6 == 17[/tex]
[tex](b):\ (9 + 3) * 2 \div 3 + 6[/tex]
Solve the bracket
[tex](9 + 3) * 2 \div 3 + 6 =(12) * 2 \div 3 + 6[/tex]
Open bracket
[tex](9 + 3) * 2 \div 3 + 6 =24 \div 3 + 6[/tex]
Divide
[tex](9 + 3) * 2 \div 3 + 6 =8 + 6[/tex]
[tex](9 + 3) * 2 \div 3 + 6 =14[/tex]
[tex](c)\ 9 - (3 * 2) \div 3 + 6[/tex]
Solve the bracket
[tex]9 - (3 * 2) \div 3 + 6 =9 - (6) \div 3 + 6[/tex]
Remove bracket
[tex]9 - (3 * 2) \div 3 + 6 =9 - 6 \div 3 + 6[/tex]
Divide
[tex]9 - (3 * 2) \div 3 + 6 =9 - 2 + 6[/tex]
[tex]9 - (3 * 2) \div 3 + 6 =13[/tex]
[tex](d)\ (9 + 3 * 2) \div 3 + 6[/tex]
Solve the bracket (the product, first)
[tex](9 + 3 * 2) \div 3 + 6=(9 + 6) \div 3 + 6[/tex]
[tex](9 + 3 * 2) \div 3 + 6=15 \div 3 + 6[/tex]
Divide
[tex](9 + 3 * 2) \div 3 + 6=5 + 6[/tex]
[tex](9 + 3 * 2) \div 3 + 6=11[/tex]
Only (c) equals 13
The meadian of 26 29 31 33 36
..................................................................
Similar right triangles
Find the value of x.
Which rule describes the composition of transformations that maps triangle BCD to triangle B""C""D""?
Answer:
(d)
Step-by-step explanation:
Given
See attachment for [tex]\triangle BCD[/tex] and [tex]\triangle B"C"D"[/tex]
Required
The transformations
Using B and B"" as points of reference, we have:
[tex]B = (1,4)[/tex]
[tex]B"" = (5,-1)[/tex]
The transformation is as follows:
First, reflect across y axis.
The rule is:
[tex](x,y) \to (-x,y)[/tex]
So, we have:
[tex]B(1,4) \to B'(-1,4)[/tex]
Next, translate 6 units right.
The rule is:
[tex](x,y) \to (x + 6,y)[/tex]
So, we have:
[tex]B' (-1,4) \to B"(-1 + 6,4)[/tex]
[tex]B' (-1,4) \to B"(5,4)[/tex]
Lastly, translate 5 units down
The rule is:
[tex](x,y) \to (x,y-5)[/tex]
So, we have:
[tex]B"(5,4) \to (5,4-5)[/tex]
[tex]B"(5,4) \to (5,-1)[/tex]
Hence; (d) is correct
Johnny bought 10 cupcakes for 12 dollars, how much would 15 cost?
Answer:
18
Step-by-step explanation
10=12
must mean 5=6
12+6=18
15=18
18 dollars
he also has diabetes and drinks diet coke
Each of the figures are similar. Find the missing length
Answer:
? = 7 m
Step-by-step explanation:
6/18= ?/21
18? = 126
? = 7
Which equation is equivalent to 5x – 4y = 8?
Answer:
you got it right
Step-by-step explanation:
you mathaway to get the answer
Help!! I’ll give brainliest!
Answer:
d
Step-by-step explanation:
stat edit but just use the formula y2-y1/x2-x1
x^2/3=12
Plz I need help with this ASAP, it’s solving quadratic functions by square roots by the way
Answer:
this is easy. all you have to do is multiply the denominator (3) by the outside number (12) to get 36. this leaves the equation being x^2 = 36. now you just find the square route of 36 (which is 6).
Step-by-step explanation:
x^2/3 = 12
12 x 3 = 36
x^2 = 36
/36 = 6
x = 6
Step-by-step explanation:
explanation is on the picture
Write the following expression using rational exponents. ^7√y^4= y^ The numerator of the exponent is Select a Value The denominator of the exponent is Select a Value.
Answer: The Numerator of The Exponent =4
The Denominator of The Exponent= 7
Step-by-step explanation:
Last year the schools newspaper so if full page ad for $16.50 each of H half page is $9.60 each day school they plan to increase the cost of 8 x 50% which expressions represent the total amount the school newspaper will earn from selling the same number of four and half page ad this year
Question isn't well formatted, however. From what can be gathered form the question :
Options are given
Answer:
4(1.5 * 16.50) + (1.5 * 9.60)
$113.40
Step-by-step explanation:
Last year:
Cost of full page ad = $16.50
Cost of half page ad = $9.60
50% increase in ad price this year :
Price, this year :
Full page = 1.50 * 16. 50 = $24.75
Half page = 1.50 * $9.60 = $14.4
Expression :
4(1.5 * 16.50) + (1.5 * 9.60)
Cost of a 4 and 1/2 page ad :
Full page = 4 * $24.75 = $99
Half page = 1 * $14.4 = $14.40
Total cost = $(99 + 14.40) = $113.40
Find an equation of the line passing through the point ( - 12,
5) and perpendicular to - 12x – 3y = 12.
1]
1]
Write your answer in slope-intercept form.
A. X=1
B. X=2
C. X=3
D. X=4
E. X=5
F. X=6
Answer:
1.) 5
2.) 6
3.) 2
4.) 2
5.) 2
6.) 5
If the population has a variance of 4.6, what is the variance of the sampling distribution of its means if the
sampling distribution was derived with sample size n = 2 and all possible samples are drawn with
replacements?
Answer:
Step-by-step explanation:
Hi
Identify the equation of the circle B that passes through (5,1) and has center (3,0).
Answer:
Are you saying look for the slope? because if so can help
Step-by-step explanation:
Answer: (x − 3)2 + y2 = 5
a. (x + 3)2 + y2 = 5
b. (x − 3)2 + y2 = 25
c. (x − 3)2 + y2 = 5
d. (x + 5)2 + ( y + 1)2 = 25
Step-by-step explanation:
Begin by determining the length of the radius for the circle. A radius is a line segment from the center of the circle to any point on the circle. Find the length of the radius using the Distance Formula.
r= √(x2 − x1)2 + (y2 − y1)2
Substitute the given values for the center of the circle and the point on the circle into the distance formula and solve for r.
r= √( 5− 3)2 + (1 − 0)2
= √22 + 12
= √4 + 1
= √5
So, the length of the radius is √5 units.
The equation of a circle with center (h, k) and radius r is (x − h)2 + (y − k)2 = r2. Substitute the value for the radius and the coordinates of the center of the circle into the equation.
(x − 3)2 +(y − 0)2 = (√5)2
Simplify.
(x − 3)2 + y2 = 5 Therefore, the equation of the circle B that passes through (5, 1) and has center (3, 0) is (x − 3)2 +y2 = 5.
The scale on a map is 1in.=20mi. if the distance between two cities on the map is 2.5 inches how far apart are the actual cities?
Answer:
░░░░░▐▀█▀▌░░░░▀█▄░░░
░░░░░▐█▄█▌░░░░░░▀█▄░░
░░░░░░▀▄▀░░░▄▄▄▄▄▀▀░░
░░░░▄▄▄██▀▀▀▀░░░░░░
░░░█▀▄▄▄█░▀▀░░
░░░▌░▄▄▄▐▌▀▀▀░░ This is Bob
▄░▐░░░▄▄░█░▀▀ ░░
▀█▌░░░▄░▀█▀░▀ ░░ Copy and paste him so he can take over brainly.
░░░░░░░▀███▀█░▄░░
░░░░░░▐▌▀▄▀▄▀▐▄░░
░░░░░░▐▀░░░░░░▐▌░░
░░░░░░█░░░░░░░░█░
Step-by-step explanation:
7 point
10 The designers of a new website expect
the number of visitors to the site to
double each month. There were 600 visits
to the site the first month. Which function
can be used to predict the number of
visitors during month m?
F v(m) = 6000
Gv(m) = 600(2)
H vim) = 600 (3)
) v(m) = 600(4)
need help
Answer:
J *JJJJJJJJJJJJJJJJJJJJ
Natalie's aunt gave her $47 to spend on clothes at the mall. She bought 4 shirts that cost $4 each and a pair of pants that cost $13. How much money does Natalie have left to buy more clothes?
Answer:$18
Step-by-step explanation:4 * 4 = $16. One pair of pants = $13. 16 + 13 = $29. 47 - 29 = $18
hii please help i’ll give brainliest:)
Answer:
They most of the time used the ability to row ships to get to places
Step-by-step explanation:
They were more reliable to row ships to trade with other people because the Mediterranean Sea was critical to how they were able to trade.
Round 245,675 to the nearest hundred thousand
The solution is, Rounding off 245,675 to the nearest hundred thousand is: 246000.
What is round off?Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.
here, given that,
Round 245,675 to the nearest hundred thousand
we know,
Anything at or above 50 gets rounded up.
49 and below gets rounded down.
so, we get,
here, to the nearest hundred thousand means 675 > 500
so, it will be 5,675 => 6000
we have,
Rounding off 245,675 to the nearest hundred thousand is:
246000
Hence, The solution is, Rounding off 245,675 to the nearest hundred thousand is: 246000.
To learn more on round off click:
brainly.com/question/29348203
#SPJ2
