Answer:
Length of the rectangle is 8 in and the breadth is 8 in.
a. [tex]A=xy[/tex]
b. [tex]y=16-x[/tex]
Step-by-step explanation:
Length = x
Breadth = y
Area is given by [tex]A=xy[/tex]
Perimeter of rectangle is given by
[tex]2(x+y)=32\\\Rightarrow x+y=16\\\Rightarrow y=16-x[/tex]
The condition that x and must satisfy is [tex]y=16-x[/tex]
So, area is
[tex]A(x)=x(16-x)\\\Rightarrow A(x)=16x-x^2[/tex]
Differentiating with respect to x we get
[tex]A'(x)=16-2x[/tex]
Equating with zero
[tex]0=16-2x\\\Rightarrow x=\dfrac{16}{2}\\\Rightarrow x=8[/tex]
Double derivative of A(x)
[tex]A''(x)=-2[/tex]
So [tex]A''(x)<0[/tex] which means [tex]A(x)[/tex] is maximum at [tex]x = 8[/tex]
[tex]y=16-x=16-8\\\Rightarrow y=8[/tex]
So length of the rectangle is 8 in and the breadth is 8 in.
Determine if the following argument always applies, sometimes applies, or never applies. Provide at least 2 examples in your explanation.
"The sum of a number and its opposite is always 1."
Answer:
Never applies
Step-by-step explanation:
Given
Argument: The sum of a number and its opposite is always 1
Assume a positive number x
The opposite of the number is negative x (i.e. -x)
The sum of both numbers is:
[tex]Sum = x + (-x)[/tex]
Open Bracket
[tex]Sum = x -x[/tex]
[tex]Sum = 0[/tex]
Now, take for instance.
[tex]Number = 5[/tex]
Opposite would be
[tex]Opposite = -5[/tex]
Their sum is:
[tex]Sum = 5 + (-5)[/tex]
[tex]Sum = 5 -5[/tex]
[tex]Sum = 0[/tex]
Another instance is:
[tex]Number = -8[/tex]
Opposite would be
[tex]Opposite = 8[/tex]
Their sum is;
[tex]Sum = -8 + 8[/tex]
[tex]Sum = -0[/tex]
Hence, the argument never applies because the sum is never 1
what number is represented by this number discs
Answer:
15
Step-by-step explanation:
what is 12+12 and give good reson why
Answer:
24
Step-by-step explanation:
you have 12 of something and Are adding 12 to it.
box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the box (in cm) that minimize the amount of material used. sides of base
Answer:
Hence the width, length is 20 cm and height is 10 cm
Step-by-step explanation:
Since the box has a square base, let length = width = x. Also, let the height = y, therefore:
The volume of box = width * length * height
4000 = x * x * y
4000 = x²y
y=4000/x²
The surface area (SA) = area of the base + sum of the area of each side
SA = x² + xy + xy + xy + xy
SA = x² + 4xy
substitute y = 4000/x²
SA = x² + 4x(4000/x²)
SA = x² + 16000/x
Taking the derivative:
SA' = 2x - 16000/x²
making SA' = 0:
0 = 2x - 16000/x²
2x = 16000/x²
2x³ = 16000
x³ = 8000
x = 20 cm
y = 4000 / x² = 4000 / 20² = 10 cm
Hence the width, length is 20 cm and height is 10 cm
The fourth term of a geometric progression is 4 and the seventh term is 32/125. Find the first term, the common ratio and the sum of the first nth terms. Hence, deduce the sum to infinity.
Answer:
common ratio is 2/5
First term is 125/2
The sum of the first n terms is: [tex]S_n=\frac{125}{2} \, \frac{1-(2/5)^n}{3/5}[/tex]
The infinite sum is: [tex]S_\infty =\frac{625}{6}[/tex]
Step-by-step explanation:
The 4th term is 4, and the seventh term is 32/125 so we use the definition of nth term of a geometric sequence to create the following two equations:
[tex]a_4=a_1\,*\,r^{4-1} = a_1\,*\,r^3\\4=a_1\,*\,r^3\\and\\a_7=a_1\,*\,r^{7-1} = a_1\,*\,r^6\\\frac{32}{125} = a_1\,*\,r^6[/tex]
Now we divide a7 by a4 to get rid of a1 and work on determining the common ratio of the sequence:
[tex]\frac{a_7}{a_4} =\frac{8}{125} =\frac{a_1\,r^6}{a_1\,r^3} =r^3\\then\\r=\sqrt[3]{\frac{8}{125} } =\frac{2}{5}[/tex]
So, the common ratio is 2/5
we can now determine the first term:
[tex]a_4=4=a_1\,*\,(2/5)^3\\a_1=\frac{125*4}{8} =\frac{125}{2}[/tex]
The sum of the first n terms is given by the formula:
[tex]S_n=\frac{125}{2} \, \frac{1-(2/5)^n}{1-(2/5)} \\S_n=\frac{125}{2} \, \frac{1-(2/5)^n}{3/5}[/tex]
and therefore, the infinite sum is:
[tex]S_\infty = a_1\,\frac{1}{1-r} = \frac{125}{2} \,\frac{5}{3} =\frac{625}{6}[/tex]
Can someone help me with this.. It is timed I WILL MARK YOU AS BRAINLIEST
Answer:
1) dividend
2) divisor
3) quotient
Completing the Square
Solve each equation by completing the square.
1) 7x2 + 14x - 65--9
Answer:
2(30-7x)
Step-by-step explanation:
=14+14x-65-9
=14+14x-79
=60+14x
=2(30-7x)
The length of a rectangle is four times its width.
If the perimeter of the rectangle is 90 yd, find its length and width.
Answer:
Length of rectangle = 36 yd and width of rectangle = 9 yd
Step-by-step explanation:
Let width of rectangle = w
Length of rectangle = 4w (four times the width)
Perimeter of rectangle = 90 yd
We need to find length and width of rectangle.
The formula used will be: [tex]Perimeter \ of \ rectangle=2(l+w)[/tex]
Where l is length and w is width
Putting values and finding length and width of rectangle
[tex]Perimeter \ of \ rectangle=2(l+w)\\90=2(4w+w)\\90=2(5w)\\90=10w\\w=\frac{90}{10}\\w=9[/tex]
So,width (w) of rectangle is w= 9 yd
Finding length of rectangle = 4w = 4*9 = 36 yd
So, length of rectangle = 36 yd and width of rectangle = 9 yd
Sofia used these steps to find the inverse of function f
She made a mistake in step__(2,6,4,3,5)?
She should have_____
.dived each side by 8 instead of multiplying
.replaced x with f(x)
.divided each side by 3 instead of multiplying
.added 4 to each side instead of subtract
.restricted the domain to x>0
Answer:
Step-by-step explanation:
Step 1 f(x) = [tex]\frac{3x+4}{8}[/tex] Given
Step 2 y = [tex]\frac{3x+4}{8}[/tex] Change f(x) to y
Step 3 x = [tex]\frac{3y+4}{8}[/tex] Switch x and y
Step 4 8x = 3y + 4 multiply each side by 8
Step 5 8x - 4 = 3y Subtract 4 from each side
Step 6 [tex]\frac{8x-4}{3}=y[/tex] Divide by 3 on each side
Step 7 [tex]\frac{8x-4}{3}=f^{-1}(x)[/tex] Replace y by [tex]f^{-1}(x)[/tex]
Therefore, inverse of the function will be,
[tex]\frac{8x-4}{3}=f^{-1}(x)[/tex]
Sofia made a mistake in step 6. She should have divided both the sides by 3 instead of multiplying each side by 3.
Sophia has made mistake in step 6. She should have divided each side by 3 instead of multiplying.
The given function is [tex]f(x)=\dfrac{3x+4}{8}[/tex].
It is required to calculate the inverse of the function.
So, the steps involved in finding the inverse of the function will be,
Step 1:
Write the given function as,
[tex]f(x)=\dfrac{3x+4}{8}[/tex]
Step 2:
Change the function f(x) to y as,
[tex]y=\dfrac{3x+4}{8}[/tex]
Step 3:
Switch x and y as,
[tex]x=\dfrac{3y+4}{8}[/tex]
Step 4:
Multiply each side of the equation by 8 as,
[tex]8x=8\dfrac{3y+4}{8}\\8x=3y+4[/tex]
Step 5:
Now, subtract 4 from each side of the equation as,
[tex]8x-4=3y+4-4\\8x-4=3y[/tex]
Step 6:
Now, it is required to divide each side by 3.
[tex]\dfrac{8x-4}{3}=\dfrac{3y}{3}\\\dfrac{8x-4}{3}=y[/tex]
Step 7:
Now, replace y with [tex]f^{-1}(x)[/tex] as,
[tex]\dfrac{8x-4}{3}=f^{-1}(x)[/tex]
So, the required inverse function should be [tex]f^{-1}(x)=\dfrac{8x-4}{3}[/tex].
Therefore, Sophia has made mistake in step 6. She should have divided each side by 3 instead of multiplying.
For more details, refer to the link:
https://brainly.com/question/19606498
Simplify the expression using the properties of operations.
The simplified form of the expression (5.23x + 3.76) − (3.67x − 6.39) is
Answer:
Step-by-step explanation:
5.23x+3.76-3.67x+6.39
x(5.23-3.67) +(3.76+6.39)
1.56x + 10.15
Answer:
1.56x + 10.15
Step-by-step explanation:
(5.23x + 3.76) – (3.67x – 6.39)
(a + b) – (c – d) = a + b – c + d
Remove the parentheses and change the signs as needed:
5.23x + 3.76 – 3.67x + 6.39.
Group the like terms and simplify:
5.23x – 3.67x + 3.76 + 6.39
1.56x +10.15.
Bob has a coin collection made up of pennies and nickels. If he has three times as many pennies as nickels and the total face value of the coins is $416, how many coins of each kind are in the collection?
Answer:
I think its 15600..
Step-by-step explanation:
Cassandra has $2000 dollars in a bank account that she uses to make automatic $900.01 mortgage
payments each month. If Cassandra stops making deposits to that account, when would automatic
payments make the value of the account zero? Use a table to estimate the solution. Then use a graphing
calculator to approximate the x-intercept
Answer:
no
Step-by-step explanation:
it's CASSANDRA business so she solve it herself
im not sure this one is confusing
The two triangles are similar, What is the length of DE?
Answer:
If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, the triangles are similar. The corresponding sides of similar triangles are in proportion.
I hope this might help you
Mark it as brainliest answer and follow me
Is that a perfect square
Answer:
im gonna go with yes
Step-by-step explanation:
Answer:
is what a perfect square?
Step-by-step explanation:
there is no pic attached
Which scenario describes this picture?
Answer:
It"s the second answer, "An 8-foot ramp leans....".
Step-by-step explanation:
Answer:
Step-by-step explanation:
⊕ An 8-foot ramp leans against a building 5 feet away.
cos x = [tex]\frac{5}{8}[/tex] ⇒ x ≈ 51.3178°
Can 14,18 and 19 form a triangle?
Answer:
Yes
Step-by-step explanation:
Using the triangle formula: a+b>c , b+c>a , and c+a>b, we can conclude that these values can form a triangle because 14+18>19 , 14+19>18 , and 18+19>14.
Answer:
To confirm if this can form it, we take the lower of the two numbers , square them, and equal it to the biggest number squared. (AKA The Pythagorean Theorem).
Step-by-step explanation:
[tex]14^{2} +18^{2} = 19^{2}[/tex]
Now solve to see if it equates to be true.
196 + 324 = 361
520 [tex]\neq[/tex] 361
That means 14, 18, and 19 can't form a triangle.
1. Determine whether line KM and line ST are Parallel, Pers
Line KM has a slope of 5/8
Line ST has a slope of -8/5
Answer:
Since the slope of KM and ST are different, they are not parallel
Step-by-step explanation:
Slope of line KM = [tex]\frac{5}{8}[/tex]
Slope of ST = [tex]-\frac{8}{5}[/tex]
Determine whether the lines are perpendicular;
Solution:
We can use the slope of a line to determine whether they are perpendicular or parallel to one another.
Parallel lines do not meet one another
Perpendicular lines cross one another at an angle of 90°
Two lines are parallel if their slopes are the same;
Since the slope of KM and ST are different, they are not parallel
what is the greatest common factor of 14x+28+21
Answer:
7 (2x+7)
Step-by-step explanation:
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︎ ︎ ︎︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎
︎ ︎ ︎︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎
Answer:
The greatest common factor is 7.
Step-by-step explanation:
7 x 2 = 14
7 x 4 = 28
7 x 3 = 21
An angle measures 79.4 degrees more than the measure of its supplementary angle. What is the measure of each angle?
Answer:
The angles are: 50.3 and 129.7
Step-by-step explanation:
The sum of supplementary angles is 180°.
Let x be one angle then the other angle will be x+79.4
Using the supplementary angle sum
[tex]x+x+79.4 = 180\\2x+79.4 = 180\\2x = 180-79.4\\2x = 100.6\\\frac{2x}{2} = \frac{100.6}{2}\\x = 50.3[/tex]
For the measurement of 2nd angle
x+79.4 => 50.3+79.4 => 129.7
Hence,
The angles are: 50.3 and 129.7
What is the graph of the function rule?
1. y= 3x - 2 (1 point)
Algebra 1
This should be what you're looking for.
To increase attendance for a flower show, the organizers have chosen flower shops in the area to offer discount coupons to their customers. Half of the stores receive discount coupons for admission, while the other half of the stores receive two-for-one admission coupons. The organizers then compare the number of each type of coupon redeemed at the show.
What are the explanatory and response variables in this scenario?
The explanatory variable is the number of coupons redeemed. The response variable is the type of coupon.
The explanatory variable is each chosen flower shop. The response variable is the number of coupons redeemed.
The explanatory variable is the type of coupon. The response variable is number of number of coupons redeemed.
The explanatory variable is the attendance at the flower show. The response variable is the number of attendees who used coupons.
Answer:
Because the weather was generally better this year compared to last year, the attendance may have increased.
Step-by-step explanation:
took test
Answer:
C.) The explanatory variable is the type of coupon. The response variable is number of number of coupons redeemed.
Step-by-step explanation:
edge 2020
Understand the question explain and u will be brainiest
Simplify (6x ^ 2 + 11x - 3) + (2x ^ 2 - 17x - 4) . (1 point)
1 ) 8x ^ 2 + 6x - 1
2) 8x ^ 2 - 6x - 7
3 ) 8x ^ 2 + 6x + 1
4 ) 8x ^ 2 - 6x + 7
Answer:
2) 8x^2 -6x-7 hope this helps
Penny reads 13 pages in 1/2 hour. What is the unit rate for pages per hour? For hours per page? How many hours per page
Answer:
13 pages : 1/2 hour Multiply both sides by 2
26 pages : 1 hour ------>> 26 pages/hr
Flip over 26 pages/hr ----->>> hr / 26 pages = 1 hr / 26 pages
Split up the fraction: (1/26) hr / page
Answer:
26
Step-by-step explanation:
13 in 1/2 hour
13:1/2
26:1
Now move vertices A, B, and C of ∆ABC to create a triangle of your choice. (Note: the tool will allow you to create only certain kinds of triangles.) Does the relationship between the base angles change as the vertices change? If so, how?
Answer:
The relationship between the base angles does not change. The measures of the base angles of the isosceles triangle remain equal even if the vertices of the isosceles triangle change.
Step-by-step explanation:
Here is the answer from Plato. Hope this helps :)
Answer:
The relationship between the base angles does not change. The measures of the base angles of the isosceles triangle remain equal even if the vertices of the isosceles triangle change.
Step-by-step explanation:
Exact Edmentum sample answer
help me please in this problem
Would you please help me on this question?
Answer:
x = 2
Step-by-step explanation:
Given that the measure of segment BC must equal the addition of the measure of segment BA plus the measure of segment AC, we can write this in equation form:
BC = BA + AC
then we replace them with the measure information they provide:
12 x + 4 = 7 x - 4 + 8 x + 2
and we solve for x in the equation:
12 x + 4 = 15 x - 2
subtract 12 x from both sides:
4 = 15 x - 12 x - 2
4 = 3 x - 2
add 2 on both sides
4 + 2 = 3 x
6 = 3 x
x = 6/3
x = 2
A rectangle is 2 meters long and 50 centimeters wide. What is its perimeter, in centimeters?
Answer:
250 centimeters
Step-by-step explanation:
2 meters into centimeters is 200 so 200+50=250
Answer:
100cm
Step-by-step explanation:
In a video game, Agnes scored 20% fewer than Amy. Amy scored 860
points. How many points did Agnes score? *
Answer:
[tex]\huge\boxed{\sf Agnes\ Score = 688\ points}[/tex]
Step-by-step explanation:
[tex]\sf = 20 \% \ of \ 860 \\\\= \frac{20}{100} * 860\\\\= 2 * 86\\\\= 172 \ points[/tex]
Since, Agnes scored 20 % fever than Amy.
So,
Agnes Score = Amy's Points - 20 % of Amy's Points
Agnes Score = 860 - 172
Agnes Score = 688 points
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AnonymousHelper1807
How many times does 35 go into 100 please give correct answer max points.
Answer:
100/35 = 2
35 goes into 100 2 times
Step-by-step explanation: