Answer: 60 meters
Explanation:
"It will probably help to have a diagram to look at:
Since we're told that the fenced area is to be a rectangle, draw a rectangle.
Since one side is to be the barn, choose a side of the rectangle to be a the barn. (It doesn't matter which side you choose.)
Label the two sides of the rectangle that are connected to the barn as "x". (Since this is a rectangle these opposite sides should be the same.)
The hardest part is the side opposite the barn. We know that we have 120 meters of fence to use. It hope it makes sense that to get the maximum area we should use all the fencing. So the lengths of the three "non-barn" sides will be 120. So how do we express the length of the side opposite the barn? Well if we know what "x" was it would be easy. For example if x = 35 then the side opposite the barn would be 120 - 35 - 35 = 50. We now use this same logic even though we don't know what "x" is yet. The side opposite the barn will be
120 - x - x
which simplifies to:
120 - 2x
We can now find a solution. The area of any rectangle is length times width (or base times height). So for our rectangle the area will be: A = x (120 - 2x)
This is a quadratic equation so I am going to rewrite it in ax^2+bx+c: A=-2x^2 + 120x
We should recognize that the graph of a quadratic equation will be a parabola. And since the squared term is x^2 this parabola will open upward or downward. And since the "a" is negative (-2 to be specific), this parabola will open downward. If we picture a downward-opening parabola in our minds we should be able to understand that the vertex of the parabola will be the highest point of the graph. So the x-coordinate of the vertex will give the the maximum value for A, the area.
So we just need to figure out the x-coordinate of the vertex. This can be done by completing the square or by just knowing that the x-coordinate of the vertex would be '-b/2 + a.'
Our "b" is 120 and our "a" is -2 so the x-coordinate of the will be: -(120/2*(-2)) = 30
This is the x that gives us the maximum area. (If you're curious as to exactly what number this maximum area is, just substitute 30 for x into A=-2x^2+120x)
So we can label the two sides of "x" as 30's. And since the side opposite the barn is 120 - 2x, it will be 120 - 2(30) = 120 - 60 = 60 meters."
-jsmallt9
solve with ans : the compound interest of a sum of money in 1 years and 2 years are Rs 450 and Rs 945 respectively. find the rate of interest compounded yearly and the sum .
Answer:
The rate of interest compounded yearly =10%The sum compounded is Rs4,500Step-by-step explanation:
Compound Interest Formula, Amount, [tex]A(n)=P(1+r)^n[/tex]
Interest=Amount - Principal
[tex]I=P(1+r)^n-P[/tex]
At the end of 1 year, interest =Rs450, therefore:
[tex]450=P(1+r)-P\\450=P+Pr-P\\450=Pr[/tex]
At the end of 2 years, interest =Rs945, therefore:
[tex]945=P(1+r)^2-P\\945=P(1+r)(1+r)-P\\945=P(1+r+r+r^2)-P\\945=P(1+2r+r^2)-P\\945=P+2Pr+Pr^2-P\\945=2Pr+Pr^2[/tex]
Recall: Pr=450
Therefore:
[tex]945=2(450)+Pr^2\\945-900=Pr^2\\Pr^2=45[/tex]
Comparing Pr=450 and [tex]Pr^2=45[/tex]
[tex]\dfrac{Pr^2}{Pr}= \dfrac{45}{450}\\r=0.1[/tex]
Substitute r=0.1 to obtain P
0.1P=450
P=Rs4500
Therefore:
The rate of interest compounded yearly =0.1=10%The sum compounded is Rs4,500
PLEASEEE HELPPP IT DUE TODAYYY
Answer:
All angles in a rectangle are congruent, because in a rectangle, all angles are 90 degrees.
3/4, 1, 4/3, 16/9,... which of the following are recursive formulas for the nth term of the following geometric sequence?
Answer:
nth term of geometric sequence = a(n) = [tex](3/4)(4/3)^{n-1}[/tex]
Step-by-step explanation:
nth term of geometric sequence = a(n)
nth term of geometric sequence = a(n) = [tex]ar^{n-1}[/tex]
Where,
a = first term
r = common ratio
n = number of term
So,
GP: 3/4, 1, 4/3, 16/9
a = 3/4
r = 1 / [3/4] = 4/3
n = n
nth term of geometric sequence = a(n) = [tex]ar^{n-1}[/tex]
nth term of geometric sequence = a(n) = [tex](3/4)(4/3)^{n-1}[/tex]
evaluate 2x squared -1 when x=3
Hey there! :)
Answer:
17.
Step-by-step explanation:
Given:
f(x) = 2x² - 1
Substitute in 3 for x:
f(3) = 2(3)² - 1
f(3) = 2(9) - 1
Simplify:
f(3) = 18 - 1
f(3) = 17.
The parallelogram is rotated 90° anticlockwise about point G
Which of the points A , B , C and D is the image of point R ?
Answer:
C
Step-by-step explanation:
Let's say that point G is the origin, (0,0). Then, the coordinates of point R would be (-3, -5). Rotating the point 90° counter-clockwise would result in the final coordinates being (5, -3), therefore the answer is C.
Which is the graph of f(x)=sqrt x?
Answer:
B
Step-by-step explanation:
a parabola would be x2 since it is square rooted it would be a curved so the answer would be the second graph
A gym has yoga classes. Each class has students. If there are classes, write an equation to represent the total number of students taking yoga.
Answer:
s = 14c
Step-by-step explanation:
What’s the value of 9 percent
Answer:
Hey!
Well because you havent really specified the question...
I have given you 9% of different numbers!
Step-by-step explanation:
9% of 1 = 0.09
9% of 10 = 0.9
9% of 100 = 9
9% of 1,000 = 90
9% of 10,000 = 900
________________
If you need more values...just let me know!
Hope this helps!
Write the rule for finding the coordinates of a point that has undergone a dilation (with the origin as the point of dilation). Use this rule to find the coordinates of this point's dilation from the origin, with a scale factor of 3: (4, 10).
Answer:
(12, 40)
Step-by-step explanation:
The first thing is to assume that we have a point with the following coordinates (x, y).
Now, we can have two different cases since the meaning of the expansion of a point is moving to a new point that is a greater distance from the origin if we are expanding by a value, that is, an integer in the system of coordinates and the other case is that if we are dilating by a fraction that is between 0 <x <1, then the distance from the origin decreases.
Now, the point (x, y) goes through an expansion by a scale factor f (with the origin as the expansion point), then the new coordinate of the point = [f * x, f * y], that scale factor has the value of 3, so if we replace we have:
(3 * 4, 4 * 10) = (12, 40)
Point AAA is at {(-6,-5)}(−6,−5)left parenthesis, minus, 6, comma, minus, 5, right parenthesis and point CCC is at {(4,0)}(4,0)left parenthesis, 4, comma, 0, right parenthesis. Find the coordinates of point BBB on \overline{AC} AC start overline, A, C, end overline such that the ratio of ABABA, B to BCBCB, C is 2:32:32, colon, 3.
Answer:
B(-2,-3).
Step-by-step explanation:
The given points are A(-6,-5) and C(4,0).
We need to find the coordinates of point B on segment AC such that AB:BC=2:3.
It means point B divides the line segment AC in the ratio of 2:3.
Section formula: If a point divide a line segment in m:n, then
[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
Using section formula, the coordinates of point B are
[tex]B=\left(\dfrac{2(4)+3(-6)}{2+3},\dfrac{2(0)+3(-5)}{2+3}\right)[/tex]
[tex]B=\left(\dfrac{8-18}{5},\dfrac{0-15}{5}\right)[/tex]
[tex]B=\left(\dfrac{-10}{5},\dfrac{-15}{5}\right)[/tex]
[tex]B=\left(-2,-3\right)[/tex]
Therefore, the coordinates of point B are (-2,-3).
Answer:
Therefore, the coordinates of point B are (-2,-3).
Step-by-step explanation:
$15.30 for 3 small pizzas
Answer:
$5.1
Step-by-step explanation:
If it costs $15.30 for 3 pizzas, then we can divide 15.30 by 3 to get $5.1. This concludes that the cost for one pizza is $5.1.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
solve for x -48=6(x-3)
Answer:
[tex]\boxed{x = -6}[/tex]
Step-by-step explanation:
[tex]x-48 = 6(x-3)[/tex]
Resolving parenthesis
[tex]x - 48 = 6x-18[/tex]
Adding 18 to both sides
[tex]x-48+18 = 6x\\x-30 = 6x[/tex]
Subtracting x from both sides
[tex]-30 = 6x-x\\-30 = 5x[/tex]
Dividing both sides by 5
[tex]-30/5 = x[/tex]
[tex]-6 = x\\[/tex]
OR
x = -6
Answer:
x = - 6Step-by-step explanation:
x - 48 = 6(x - 3)
Expand the terms in the bracket
That's
x - 48 = 6x - 18
Group the constants at the right side of the equation and the ones with variables at the left side
x - 6x = 48 - 18
- 5x = 30
Divide both sides by - 5
x = - 6Hope this helps you
The company recently reduced its production to 1 million bicycles, but maintained its profit of 30 million dollars. What greater number of bicycles had the company previously produced to make the same profit? Round your answer to the nearest tenth.
Answer:
1.3 million bicycles!
Step-by-step explanation:
Answer:
1.3 million bicycles
Step-by-step explanation:
got it right on edge 2020
fractorise the following (a-b)²+(a-b)
Step-by-step explanation:
taking common (a-b)
so we get the answer
Simplify the radical /81d^6.
O 9d2
81d3
O 9d3
O 906
Answer:
The answer is option C.
Step-by-step explanation:
[tex] \sqrt{ {81d}^{6} } = \sqrt{81} \times \sqrt{ {d}^{6} } \\ = 9 {d}^{3} [/tex]
Hope this helps you
Answer:c
Step-by-step explanation:
Which is the correct way to model the equation 5 x + 6 = 4 x + (negative 3) using algebra tiles? 5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side 6 positive x-tiles and 5 positive unit tiles on the left side; 3 negative x-tiles and 4 positive unit tiles on the right side 5 positive x-tiles and 6 negative unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side 5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 positive unit tiles on the right side
Answer:
answer a is correct
Step-by-step explanation:
Answer: A. 5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side
Step-by-step explanation: On Edge!!!!!!!!!!!
What are the values of sin α and tan α, if α is an acute angle in a right triangle: cosα= 5/13
Answer:
sin = 12/13 and tan = 12/5
The value of sin α will be 12/13 and tan α will be 12/5 for the given triangle such that cosα= 5/13.
What is a trigonometric function?Trigonometric functions are functions for right angle triangle which gives the relation between the angle and sides of the triangle.
The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.
The trigonometric functions are found in the four quadrants, as well as their graphs, domains, and differentiation and integration.
We know that
sin²α + cos²α =1 ⇒ sin²α = 1 - cos²α
Given that cosα = 5/13 so by putting it
sin²α = 1 - (5/13)²
sin²α = 144/169 ⇒ sinα = 12/13.
Now since tanα = sinα /cosα
tanα = (12/13) ÷ ( 5/13)
tanα = 12/5.
Hence the value of sinα will be 12/13 and tanα will be 12/5.
For more information about the trigonometric function
brainly.com/question/1143565
#SPJ2
Given that sin x < cos x and 0°< x < 90°,state a possible value of x. Explain your answer clearly.
Answer:
30°Step-by-step explanation:
Given sinx< cos x and 0°< x < 90°, to get the possible value of x, we need to solve the given inequality for x.
sinx< cos x
Dividing both sides by cos x
sin x/cos x < cos x/cos x
tan x < 1
x < [tex]tan^{-1}1[/tex]
x < 45°
Since x is less than 45°, then one of the possible value of x can be 30° since 30° is less than 45° and 30° falls within the given range of values.
Three solid shapes A,B and C The surface area of shape A is 9cm² The surface area of shape B is 16cm² The ratio of the volume of shape B to the volume of shape C is 27 : 125 Work out the ratio of the height of shape A to the height of shape C
Answer:
9:20
Step-by-step explanation:
Given:
Surface area of shape A = 9 cm²
Surface Area of shape B = 16 cm²
Ratio of volume of shape A to B = 27:125
Required:
Find the ratio of the height of shape A to the height of shape C.
Ratio of surface area (A:B)² = ratio of linear measures (A:B)
Thus,
(A:B)² = (A:B)
(A/B)² = (A/B)
[tex] (\frac{A}{B})^2= (\frac{9}{16}) [/tex]
Take the square root of both sides:
[tex] (\sqrt{\frac{A}{B}})^2 = (\sqrt{\frac{9}{16}}) [/tex]
[tex] \frac{A}{B} = \frac{3}{4}[/tex]
Ratio of volume of shape B to C = 27:125
Thus,
(B:C)³ = 27:125
[tex] (\frac{B}{C})^3= (\frac{27}{125}) [/tex]
Take the cube root of both sides:
[tex](3\sqrt{\frac{B}{C}})^3 = (3\sqrt{\frac{27}{125}})[/tex]
[tex] \frac{B}{C} = \frac{3}{5}[/tex]
Therefore, ratio of lengths A:B:C =
3:4:C
A:3:5
To make them equivalent, we have:
9:12:C
A:4:20
Therefore, the ratio of the height of shape A to the height of shape C =
9:20
Which explains how to find the radius of a circle whose equation is in the form x2 + y2 = z? The radius is the constant term, z. The radius is the constant term, z, divided by 2. The radius is the square root of the constant term, z. The radius is the square of the constant term, z.
Answer:
The radius is the square root of the constant term, z
Step-by-step explanation:
makes sense, also took the test :)
Answer:
C. The radius is the square root of the constant term, z.
Step-by-step explanation:
Hope this helps :)
Select the correct answer. The top of a ladder is 10 meters from the ground when the ladder leans against the wall at an angle of 35.5° with respect to the ground. If the ladder is moved by x meters toward the wall, it makes an angle of 54.5° with the ground, and its top is 14 meters above the ground. What is x rounded to the nearest meter?
A. 7 meters B. 4 meters C. 3 meters D. 1 meters
Answer:
4 trust me
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
trust lol
Need!!!!! Help!!!!!!
Answer:180
Step-by-step explanation:
Answer 180
GANNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNG
.Write the following number in the standard form. a) 0.000000012
Answer:
[tex]1.2 * 10 ^{-8}[/tex]
Step-by-step explanation:
=> 0.000000012
Moving the decimal point after 1st non-zero digit:
=> [tex]1.2 * 10 ^{-8}[/tex]
Answer:
Scientific Notation: 1.2x10^-8, or 1.2e-8
Step-by-step explanation:
Three angles fits exactly around a point. Two of the angles are equal.The diffrence between the largest and the smallest angle is 30.Find the size ofthe three angles
Answer:
The angles are 110, 110 and 140
Step-by-step explanation:
Let the equal angles be x.
So we have angles x, x and another third one
Now, the other third angle is 30 degrees larger than x, this means that the other third angle is 30 + x
Since they are angles at a point, adding the three together will make or give 360.
Thus,
x + x + x + 30 = 360
3x + 30 = 360
3x = 360-30
3x = 330
x = 330/3
x = 110
So the other third angle is 110 + 30 = 140
So the angles are 110, 110 and 140
between which to whole numbers does the square root of 37 lie?
Between 6 and 7
6×6=36
7×7=49
hopefully this helped
The number √37 is lies between whole numbers 6 and 7.
We have to given,
A number is, √37
By the definition of square root, we get;
⇒ √37 = 6.08
And, We know that,
Number 6.08 is lies between whole number 6 and 7.
Hence, We get;
⇒ 6 < √37 < 7
Therefore, The number √37 is lies between whole numbers 6 and 7.
Learn more about Number system visit:
https://brainly.com/question/17200227
#SPJ6
1.01 LC)Look at the following numbers: − 4, −1, 0, 4 Which pair of numbers has a sum of 0?
Answer:
-4 + 4
Step-by-step explanation:
It is -4 + 4 because if you imagine on a number line, you go left 4 (since it is negative) and add 4, so you go to the right 4, which leaves to 0.
Or, you can think of it like this:
+4 - 4
= 4 - 4
= 0.
I hope this helps. Sorry if I was wrong
Answer:
the answer would be -4 and 4 thess two numbers has a sum of 0
In Spencer’s garden, the number of rose bushes is 7 less than 1.5 times the number of carnation bushes. If the number of carnation bushes is c, then the expression representing the number of rose bushes is
Answer:
B
Step-by-step explanation:
1.5(c) - 7
It is this because his garden is 7 less than 1.5 times the carnation bushes not 7 times the carnation bushes.
Hope this helps:)
Answer:
The required expression is 1.5c-7
Step-by-step explanation:
Here, c represents the number of carnation bushes,
Since, the number of rose bushes is 7 less than 1.5 times the number of carnation bushes,
That is, the number of roses = 1.5c - 7
Hence, the required expression that represents the number of roses is 1.5c - 7.
Simple and easy question
please help
Answer:
Volume = πr²h
= 3.14 * 5² * 4
= 314 cubic yards
Answer:
[tex]314 yd^3[/tex]
Step-by-step explanation:
Hey there!
Volume = π r^2 h
Plug in,
(3.14)(5^2)(4)
5•5 = 25
25 • 4 = 100
3.14 • 100
= 314
Hope this helps :)
Joe had 21 pennies, but then he lost 11 pennies. His friend gave him 5 more pennies. How many pennies does Joe have now?
Answer:
15 pennies
Step-by-step explanation:
lost means subtract and gave him means add
21 -11 +5
15
Answer:
15 pennies
Step-by-step explanation:
You can start by saying that after losing 11 pennies from his original amount it is 21-11, which equals to 10.
THen the question says that his friend gives him an additional 5 pennies, which is shown by 10+5=15
THerefore, all you had to do was use the information given and add or subtract the number of pennies from the original.
Answer: 15 pennies
Hope this helped
explain me step by step plz
Answer:
28
Step-by-step explanation:
We know that the heights and bases of all of the parallelograms will be the same because they are equal, therefore, since the height of 2 parallelograms is 14, the height of one parallelogram is 14 / 2 = 7. Since the areas of all of the parallelograms are congruent, the area of one parallelogram is 308 / 4 = 77. The parallelogram area formula is A = bh where A, b and h are area, base and height respectively and we know both the area and height so we need to solve for b. Doing so we get 77 = b * 7 so that means b = 11. The length of y is two bases + 6 and since we know the base is 11, y = 11 * 2 + 6 = 22 + 6 = 28.
Answer:
28 cm
Step-by-step explanation:
The 4 parallelograms are congruent.
The height and base of each parallelogram are equal.
[tex]h=\frac{14}{2}[/tex]
[tex]h=7[/tex]
Area of each parallelogram:
[tex]A=\frac{308}{4}[/tex]
[tex]A=77[/tex]
Apply the formula for the area of a parallelogram.
[tex]A=bh[/tex]
[tex]b=base\\h=height[/tex]
Solve for base.
[tex]77=b(7)[/tex]
[tex]\frac{77}{7} = b[/tex]
[tex]11=b[/tex]
The sum of 2 bases of the 2 parallelograms and 6 centimeters is the value of y.
[tex]y=11+6+11[/tex]
[tex]y=28[/tex]