Step-by-step explanation:
1)
the perimeter P
P = 2x + 2y = 80 m
the area A
A = x × y
2)
2x + 2y = 80
2y = 80 - 2x
y = 40 - x
and we use that in the equation for area
A = x × (40 - x) = 40x - x²
we find the maximum (or minimum) of a function by finding the 0s of the first derivative.
A' = 40 - 2x = 0
40 = 2x
x = 20
y = 40 - x = 40 - 20 = 20
and just to be sure :
if the second derivative at that point x is negative, we have a maximum, if it is positive, we have a minimum.
A'' = -2
so, it is negative for all x incl. x = 20.
therefore, we have a maximum.
the rectangle with perimeter of 80 m and the max. area is a square of 20 m side length.
A newspaper editor has received 8 books to review. He decides that he can use 3 reviews in his newspaper. How many different ways can these 3 reviews be selected
A recipe for oatmeal cookies calls for 5 cups of flour for every 8 cups of oatmeal. How much flour is needed for a big batch of cookies that used 16 cups of oatmeal?
Answer:
10 cups
Step-by-step explanation:
Since 16 cups is twice 8 cups, it needs twice 5 cups of flour which is 10 cups.
We can also use a proportion.
5/8 = x/16
8x = 5 × 16
x = 5 × 2
x = 10
Answer: 10 cups
What fraction is equivalent to 0.16?
complete the table of values.
(please actually answer it, I really need it)
-5-3x
-5-3(-2)=1
-5-3(-1)= -2
-5-3(0)= -5
-5-3(1)= -8
-5-3(2)= 11
find the median 2.5,2.3,2.3,1.8,2.3,1.5
Answer:2.1
Step-by-step explanation:
i added them then divided by 7
If x is the first or smallest of three consecutive even integers what is the second integer
Answer: x+2
Step-by-step explanation:
even integers have a difference of 2 since the next even integer is after an odd integer. Hence, x+2 is the next even integer after x.
will give brainliest, really struggling with probability questions. any type of help would be appreciated
Please see the attached image for your answer. Hope this helps!
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 310, 304,298,... 310,304,298,... \text{Find the 47th term.} Find the 47th term.
The 47th term in the given arithmetic sequence is 34.
Given,
The arithmetic sequence = 310, 304, 298,......
First term of the sequence, t₁ = 310
Common difference of the sequence, d = t₂ - t₁ = 304 - 310 = -6
nth term of an arithmetic sequence, tₙ = t₁ + ( n - 1) d
We have to find the 47th term of the arithmetic sequence.
That is, n = 47
So,
t₄₇ = 310 + (47 - 1) -6
t₄₇ = 310 + (46 x (-6) )
t₄₇ = 310 - 276
t₄₇ = 34
Therefore, the 47th term in the given arithmetic sequence is 34.
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Divide using synthetic division. (4x² + 3x³ + 9x− -20) + (x + 2)
The synthetic division solution of (4x² + 3x³ + 9x− -20) / (x + 2) is mathematically given as
3x^2-2x+13-(6/x+2)
This is further explained below.
What is synthetic division?Generally, Synthetic division is a technique that may be used to manually conduct Euclidean division of polynomials.
Compared to long division, the synthetic division requires less writing and fewer calculations to complete. The approach is most often taught for dividing by linear monic polynomials; however, it may be extended to divide by any polynomial.
In conclusion, The synthetic division solution is mathematically given as
3x^2-2x+13-(6/x+2)
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Given 4x=12x+22 prove x=-4
the required simplified value of given expression 4x = 12x + 32 is x = -4 (hence proved).
Given that,
An expression is given 4x = 12x + 32,
We have to prove x = -4 as of simplified solution.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
4x = 12x + 32
Taking 12x to the left side of the equal sign and it becomes -12x
4x - 12x = 32
Applying subtraction property between 4x and 12
- 8x = 32
Dividing both sides by -6
x = -4
Thus, the required simplified value of the given expression is x = -4 (hence proved).
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find the point of intersection y=4x-1 y=-2x+5
The point of intersection of the given two lines y = 4x - 1 and y = -2x + 5 is (1, 3).
According to the given question.
We have two equations
y = 4x - 1 ..(i)
and
y = -2x + 5 ..(ii)
As we know that, the point at which two lines intersect is called point of intersection.
Therefore, the point of intersection for the two lines y = 4x - 1 and y = -2x + 5 is given by
Subtracting equation ii from i
y - y = 4x - 1 + 2x -5
⇒ 0 = 6x - 6
⇒ 6x = 6
⇒ x = 1
Substitute the value of x in (i).
y = 4 - 1 = 3
Hence, the point of intersection of the given two lines y = 4x - 1 and y = -2x + 5 is (1, 3).
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Determine whether the relation is a function. Explain. x y 4 –5 –1 –10 0 –9 1 –7 9 1 Multiple choice question. cross out A) Yes; for each element of the domain, there is only one element of the range. cross out B) Yes; for each element of the range, there is only one element of the domain. cross out C) No; the element 1 is in both the domain and the range. cross out D) No; for each element of the domain, there is not only one element of the range.
It is not a function because: C) the element 1 is in both the domain and the range.
What makes a Relation a Function?A relation can be defined as a function if each of the domain values each has exactly one corresponding range value. This means that an element of the domain must not have two different elements from the range that it is related or corresponded to.
In the given function, 1 as an element of the domain is related to two different range elements, 10 and 7. This doesn't satisfy a function property.
Therefore, we can state that: it is not a function because: C) the element 1 is in both the domain and the range.
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(Please someone help me!)
The ordered pair we are looking for is the values of the variables [tex]x[/tex] and [tex]y[/tex], or [tex](x, y).[/tex] We are given that [tex]x=2[/tex], and that the formula to evaluate [tex]y[/tex] is [tex]y = 5^x[/tex]. Note we are given [tex]x[/tex] so we can evaluate [tex]y[/tex] as [tex]y = 5^2 = 25[/tex]. Now, we have both the values of [tex]x[/tex] and [tex]y[/tex], so our ordered pair is thus [tex](x,y) = (2,25).[/tex]
A parralogram has a base of 9 and a corresponding height of 2/3
The height of parallelogram is 6
What is parallelogram?In geometry, parallelogram is a shape which is a type of quadrilateral. A parallelogram has 2 pair of sides which are parallel. Thus, we can say that a parallelogram is a quadrilateral of 2 pair of parallel sides. The opposite sides of parallelogram are of equal side.
Parallelogram is a convex polygon, which is a 2-dimentional geometric shape.
Important formulas of Parallelogram :
Area of Parallelogram = base . heightPerimeter of Parallelogram = 2 base + 2 heightTotal Number of vertex = 4Total Number of edges = 4Line of the Symmetry = 0In the given question,
base of parallelogram = 9
height = 2/3
Also, area = base . height
therefore, area = 9 . 2/3 = 3.2 = 6
The height of parallelogram is 6
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The complete question is:
A parallelogram has a base of 9 and a corresponding height of 2/3 . what is the area of the parallelogram.
solve for y -2(x + 3y) = 18
Answer:
[tex] \sf\large \: y = \frac{ - 1}{3} x - 3[/tex]
Step-by-step explanation:
Let's solve for y.
−2(x+3y)=18
Step 1: Add 2x to both sides.
−2x−6y+2x=18+2x
−6y=2x+18
Step 2: Divide both sides by -6.
−6y/−6 = 2x+18/−6
y= −1/3x−3
please help i have a timer
Answer: 56.25 of 70% and 93.75pints of 90%
Step-by-step explanation: First find the ratios. One juice is 70% and the other is 95%. Your goal is 85%. This is 15% from 70 and 10% from 95. This means you need (15)/(15+10) of 95, which is 3/5 of all the juice to be 95. This means you will need more of the 95% juice, which makes sense because 85 is closer to 95. So 3:5 and total 150=56.25 of 70% and 93.75pints of 90%
PLEASE ANSWER
Simplify the expression -4 1/6 - -6 1/3 Explain your solution using the additive inverse property.
The Additive Inverse is -32/6
Additive Inverse of Real Numbers:
The given number can be whole number, a natural number, an integer, a fraction, a decimal, or any real number. The additive inverse of real numbers is just the negative of the given number.
What is Additive Inverse?
Additive Inverse simply means changing the sign of the number and adding it to original number to get an answer is equal to 0.
Now, Come to the question:
Expression is : [tex]-4\frac{1}{6} -(-6)\frac{1}{3}[/tex]
Solve it : [tex]\frac{-25}{6}-\frac{(-19)}{3}[/tex]
Taking the L.C.M
=[tex]\frac{-25+57}{6}[/tex]
=32/6
Additive inverse of 32/6 is -32/6
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someone help me please its for a practice
Answer:
5a,3a
Step-by-step explanation:
Find the amount if $500 was invested at 8% which compounded quarterly after a period of 2½ years. (please show workings)
The amount generated by the invested amount of $500 which is compounded quarterly will be $610.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
[tex]\rm A = P \left (1 + \dfrac{r}{n} \right ) ^{nt}[/tex]
Where A is the amount, P is the initial amount, r is the rate of interest, and t is the number of years.
If $500 had been invested at an annualized rate of 8%, the money would have after 2.5 years. For the quarterly, the value of n will be 4. Then the amount will be
[tex]\rm A = 500 \left (1 + \dfrac{0.08}{4} \right)^{4 \times 2.5}[/tex]
Simplify the equation, then the amount is given as,
A = 500 (1 + 0.02)¹⁰
A = 500 (1.02)¹⁰
A = 500 x 1.22
A = $610
The amount generated by the invested amount of $500 which is compounded quarterly will be $610.
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7. Find the perimeter of a regular
pentagon with a side measure of
57 centimeters.
A: 228 cm
O B: 342 cm
O C: 649 cm
OD: 285 cm
Answer:
D. 285 cm
Step-by-step explanation:
Answer: D: 285 CM
Step-by-step explanation:
To find the perimeter you need to multiply its sides by its measure. It gives you in this case 57x5: 285
What must be subtracted from x² + 2x - 3 to get 2x² - 4
The term (- x² + 2x + 1 ) must be subtracted from (x² + 2x - 3) to get
(2x² - 4).
Here,
We have to find the number which must be subtracted from x² + 2x - 3 to get 2x² - 4.
What is Number system?
A system of writing to express the number is called number system.
Now,
Let 'a' must be subtracted from x² + 2x - 3 to get 2x² - 4.
It can be written as;
(x² + 2x - 3) - a = 2x² - 4
a = (x² + 2x - 3) - (2x² - 4)
a = x² + 2x - 3 - 2x² + 4
a = - x² + 2x + 1
Therefore, The term (- x² + 2x + 1 ) must be subtracted from x² + 2x - 3 to get 2x² - 4.
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A number added to four is the same as three times the number. Find the number. Round your answer to the nearest integer, if necessary.
Answer:
I think the answer is, 2
Step-by-step explanation:
A number added to 4 is 2 = 6
The number added 2 times 3 = 6
I hope you get this this right.
Answer = 2
190 is what percent of 360
Answer:
190 / 360 = 0.52777777
0.527777 x 100 = 52,78%
find the HCF of 18 42
Answer:
The HCF of 42 and 18 is 126
Answer: 6
Step-by-step explanation:
factors of 18 = 1, 2, 3, 6, 9, 18
factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42
The HCF is therefore 6
10
Which subtraction expression does the number line model show?
++++
-15 -13
+
-11 -9 -7
-7
+++
-5
-5
-3
+ +
-1
Answer:
-15-13=
-28
-11-9-7
-27
Given the equation x(x - 1)²(x + 5)³, the degree is
07
0 3
05
6
Answer:
Dear Friend
the answer is 6
Step-by-step explanation:
Just see the highest possible degree x in each term being multiplied and add the degree
that is
x has a degree 1
(x-1)² has a highest possible x degree as 2
for (x+5)³ it is 3
1+2+3=6
Can someone help me with this question?
Answer:
frrssetuii7ehhuytddcjiddfg
Select all the correct answers.
If a figure is a square, its diagonals divide it into isosceles triangles.
p: A figure is a square.
q: A figure's diagonals divide into isosceles triangles.
Which represents the converse of this statement? Is the converse true?
0
0
0
The converse of the statement is sometimes true and sometimes false.
q+p
The converse of the statement is false.
The converse of the statement is true.
9-P
P-9
O ~p~9
Answer:
q arrow p, and p arrow q
Step-by-step explanation:
edmentum
through: (-2,-4), perp. to y= -1/2x
Answer:
y = 2x
Step-by-step explanation:
The slopes of two perpendicular lines are negative reciprocals of each other. So the slope is 2
m = 2, y = -4, x = -2
y = mx + b
-4 = 2(-2) + b
b = -4 + 4
b = 0
y = 2x
Rick is going to buy donuts for his family. Each donut costs $1.25. If the number of donuts Rick buys is represented using the letter r, which expression represents the total cost?
The algebraic expression that represents the total cost would be: A. 1.25r.
How to Write an Algebraic Expression?Given that the number of donuts Rick buys for his family is represented by letter "r", and we also know that:
cost of each donut = $1.25.
Using an algebraic expression, we can create a mathematical expression that shows the total cost for Rick to by a given number of donuts for his family.
Thus:
1 donut = 1.25
r donuts would cost: 1.25 × r = 1.25r.
Therefore, the algebraic expression that represents the total cost would be: A. 1.25r.
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