The rectangular garden's width is 15 units, and Gabriella needs 120 meters of fence to enclose it.
The perimeter of a rectangle is the length of its side boundaries. A rectangle's perimeter is equal to twice the product of its length and width.
[tex]P=2(l+w)[/tex]
In this case, the rectangle's length is (l) and its width is (w).
Assume for a moment that the garden is l units long. The garden is three times longer than it is wide, w. Thus,
[tex]l=3w[/tex]
Gabriella requires 120 meters of fencing to enclose a square garden. The perimeter of the rectangular garden is the same height as this fence. Thus,
[tex]P=2(l+w)\\120=2(l+w)[/tex]
Add this equation with the length value from equation 1.
[tex]120=2(3w+w)\\3w+w=\frac{120}{2} \\4w=60\\w=\frac{60}{4} \\w=15[/tex]
Gabriella needs 120 meters of fence to enclose the rectangular garden, which has a width of 15 units.
The complete question is:-
Gabriella needs 120 meters of fence to surround a rectangular garden. The length of the garden is three times its width, w. How wide is the fence?
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please help its for finals
The numerical value of x and the length of side ST are 2 and 6 respectively.
What is the numerical value of x and the length of ST?An equilateral triangle is simply a triangle with all three sides having the same length.
Given that;
RS = 2x + 2ST = 3xTR = 5x - 4First, we determine the value of x.
Since all three sides are equal;
RS = TR
2x + 2 = 5x - 4
Solve for x
5x - 2x = 2 + 4
3x = 6
x = 6/3
x = 2
Now, for side ST.
ST = 3x
Plug in x=2
ST = 3( 2 )
ST = 6
Therefore, the value of x is 2 and side length of ST is 6.
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∠1 and ∠2 are vertical angles. If m∠1 = (5x + 12)° and m∠2 = (6x - 11)°. Find m∠1.
Answer<2= 127°
Step-by-step explanation:
What is the perpendicular slope to the equation y = –34 + 3, through the point (1, -1)
Answer:
Step-by-step explanation:
I'm going to guess that the equation is really
y = -3x +3 not y = -34 + 3
we don't really need the point information to solve this, we know that a perpendicular line has an inverse slope with a sign change
so we know the slope of the perpendicular line is
[tex]\frac{1}{3}[/tex]
11. Solve the Right Triangle.
The sides of the right triangle are as follows:
AC = 3.2 metres
AB = 12.4 metres
How to solve right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a right triangle is 180 degrees.
Therefore, the sides of a right triangle can be found using trigonometric ratios.
Hence, let's find AC
tan 15 = opposite / adjacent
tan 15 = AC / 12
cross multiply
AC = 12 tan 15
AC = 12 × 0.26794919243
AC = 3.21539030917
AC = 3.2 metres
Let's find AB
cos 15 = adjacent / hypotenuse
cos 15 = 12 / AB
AB = 12 / cos 15
AB = 12 / 0.96592582628
AB = 12.423314503
AB = 12.4 units
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Is AAA congruence possible?
Angle-Angle-Angle (AAA) does not work because it can produce similar but not congruent triangles.
There are a few conditions for AAA:
The sides of the triangles may or may not be equal. For two triangles with the same respective angles, the congruence will hold true only if those triangles are similar."AAA" is when we know all three angles of a triangle, but no sides. AAA triangles are impossible to solve further since there is nothing to show us the size.
If two angles and any side of one triangle are congruent to two angles and any side of another triangle, then the triangles are congruent.
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What is the median of 7 6 4 8 2 5 11?
To find the median of a set of numbers, you first need to put the numbers in order from smallest to largest. Then, if there is an odd number of values, the median is the middle value. If there is an even number of values, the median is the average of the two middle values.
In this case, the set of numbers is already in order: [2, 4, 5, 6, 7, 8, 11]. There are 7 values, so the median is the middle value, which is 6.
So, the median of the set {7, 6, 4, 8, 2, 5, 11} is 6.
What in math is the median?the middle number, which is obtained by sorting all the data points and choosing the center one (or if there are two middle numbers, taking the mean of those two numbers). Example: Because the number 4 is in the middle when the numbers are ordered (1, 4, 7), it is the median of 4, 1, and 7.
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a country's postal service will accept a package if its length plus its girth (the distance all the way around) does not exceed 96 inches. find the dimensions (in inches) and volume (in cubic inches) of the largest p
Dialyzer re-use efficiency is largely determined by the fiber bundle volume (FBV).
This estimation is performed after the dialyzer has been pressure cleaned and may underrate the level of coagulated strands a patient really experiences while on dialysis.
The package's dimensions:
length = 32 in
width = level = 16 in
Volume of bundle = 8192 in³
The square-shaped package is depicted in the attached image.
Expect that the length is y in and that width = level = x in (since the base is a square)
This implies that the circumference is 4*x = 4x in
We are given that the greatest amount of length and circumference is 96.
This indicates:
This can be rewritten as: y + 4x = 96
The volume of the package can be calculated as follows: y = 96 - 4x..............> I
Volume is equal to the following: length * width * height * y * x * x = x2y in3 Substitute equation I for the following volume equation:
Volume = x2 (96-4x) = 96x2 - 4x3 in3 to achieve maximum volume:
dV/dx = 0 indicates that:
2(96) x - 4(3) x2 = 0 192x - 12x2 = 0 x (192-12x) = 0
either x = 0.......> This is rejected because the side cannot be zero or 192 - 12x = 0...............> 192 = 12x...............> x = 16 in.......> accepted
In Part (b), y = 96 - 4x = 96 - 4(16) = 96 - 64 = 32: obtaining a volume:
The volume of the package is equal to 32 x 16 x 16 x 8192 in3.
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What is the smallest group of repeating digits in this nonterminating decimal, 0.345345?
he repeating digit is
345.
here, 0.345345 is a
nonterminating and repeating
decimal number.
a nonterminating and repeating decimal is
a decimal with no finite number of digits that repeat. these keep going endlessly.
for example
- 0.333333...... which is 1/3, is also a number that repeats itself endlessly. another example is 0.6.
similarly, the minimum or
smallest group of digits that repeats itself here is 345.
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Answer:
345
Step-by-step explanation:
The smallest group of repeating digits in this nonterminating decimal is 3. This is because the decimal 0.345345 contains three repeating digits, "345".
The smallest group of repeating digits in this decimal is 3, 4, 5. This is because the digits 3, 4, and 5 repeat infinitely in the decimal after the decimal point, forming a repeating pattern.
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How many solutions does a system of 3 equations have?
A system of 3 equations can have 0, 1, 2, or infinitely many solutions.
It is possible for a system of 3 equations to have no solutions if the equations are incompatible, meaning that there is no combination of values for the variables that can satisfy all of the equations simultaneously. It is possible for a system of 3 equations to have exactly one solution if the equations are dependent, meaning that one of the equations can be derived from the other two. It is possible for a system of 3 equations to have exactly two solutions if the equations are independent, meaning that the equations are not related to each other and cannot be derived from each other. Finally, it is possible for a system of 3 equations to have infinitely many solutions if the equations are consistent and the variables are linearly dependent.
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What are the solutions of 3x² 6x 2 0?
x=3+√15/3 and x=3-√15/3 are the solutions of 3x²-6x-2=0.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
The given quadratic equation is 3x²-6x-2=0
Use the quadratic formula to find the solutions.
x=-b±√b²-4ac/2a
a=3, b=-6 and c=-2.
Now plug in these values in quadratic formula to find the solutions.
x=6±√-6²-4(3)(-2)/2(3)
x=6±√36+24/6
x=6±√60/6
x=3±√15/3
Hence, x=3+√15/3 and x=3-√15/3 are the solutions of 3x²-6x-2=0.
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What are the zeros of the function y X² 4x 5?
The zeros of the function y = x^2 - 4x - 5 = 0 are 5 and -1.
The given function is y = x^2 - 4x - 5 = 0
We know that the general form of a quadratic equation is:
ax^2 + bx + c =0
On comparing the given equation y = x^2 - 4x - 5 = 0 with the general form of a quadratic equation ax^2 + bx + c =0 we get that:
a= 1, b = -4, c = -5
On multiplying a and c, we get -5 and the factors of it are 1 and 5.
Hence we can break the equation into:
x^2 - 5x + x - 5 = 0
We can factor it into:
x (x -5) + 1 (x - 5) = 0
(x + 1) (x - 5) = 0
Therefore, the zeros of the equation are -1 and 5.
The question is incomplete, the complete question is:
What are the zeros of the function y = x^2 - 4x - 5?
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Is the mean of the following data is 14.7 find the values of P and Q?
The values of p and q are 11 and 3 respectively.
Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers. Simply said, the mean is the average of the values in the given collection. It indicates that values in a certain data collection are distributed equally.
Given that,
∑f = 40
=> 26+p+q = 40
=>p+q=40-26
=> p+q = 14 .......................(i)
∵ x bar = ∑xf/∑f
=>14.7 = 408+9p+27p / 40 (since, x bar = 14.7)
=>588 = 408+9p+27p
=>588 - 408= 9(p+3p)
=>180= 9(p+3p)
=>p+3q=20......................(ii)
Solving equations (i) and (ii)
=>p+3q -(p+q)=20-14
=>p+3q-p-q=6
=>2q=6
=>q=3
Substituting this value in equation (ii)
∴p+3=14 => p = 11
Hence, the values of p and q are 11 and 3 respectively.
(Refer to the image attached for the missing data)
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Three sisters have were born in 3 consecutive years. The total of their ages is 30. What is the oldest sibling's age?
The oldest child is a 11-year-old boy.
What exactly is a sequential number?Three sisters have were born in 3 consecutive years. The total of their ages is 30.
Sequential numbers are those that follow one another continually, from lowest to biggest.
Here, assume that the youngest sibling is x years old.
Middle sibling's age will be (x+1) years old.
the oldest sibling's age is (x+2) years.
According to the inquiry,
x + (x+1) + (x+2) = 30
3x + 3 = 30
3x = 30-3
3x = 27
x = 27 / 3
x= 9
The oldest child is therefore (x + 2) years old, or 11 years old.
x+2 = 9+2 =11
The oldest child is a 11-year-old boy.
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What do you say about Y 0 and y =- 5?
The pair of equations y=0 and y=−5 has no solution.
Since the provided variable y might take on a variety of values, the pair of equations y=0 and y=5 cannot have a solution.
A two-variable linear equation is one with the formula ax+by+c, where a, b, and c are all real numbers and a, b is not equal to zero. In a set of two linear equations in two variables, we deal with two such equations.Such equations have a point on their representational line as the solution. A two-sided statement with the same sign on both sides is called an equation.
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Polygon B is a scaled copy of Polygon A using
a scale
factor of 5.
How many
times as large is the area of Polygon B
compared to the area Polygon A?
Answer:
25 times larger
Step-by-step explanation:
given a scale factor of 5 from A → B
then the scale factor of the area is 5² = 25
area of B is 25 times larger than the area of A
evaluate f divided by 1/4 for f = 2/9
Answer:
8/9
Step-by-step explanation:
2/9 divided by 1/4 is 8/9
Why can't you solve 3x 1?
We can't solve 3x + 1 because eventually reach 1 if you keep performing this operation, regardless of what odd number you started with.
Describe odd numbers.Even numbers are ones that can be divided into two equal parts, but odd numbers cannot be divided into two equal parts. The numbers 3, 5, 7, 9, 11, 13, and 15 are examples of odd numbers. Even numbers include 2, 4, 6, 8, 10, 12, and so on. Odd numbers are those that cannot be evenly divided by two. It cannot be evenly split into two different integers. An odd number will leave a leftover when divided by two. 1, 3, 5, 7, and other odd numbers are instances. The idea of odd numbers is identical to that of even numbers.
Given
Three times, then add one.
Divide the largest power of 2 from the resultant even number to obtain the new odd number T. (x).
Do you eventually reach 1 if you keep performing this operation, regardless of what odd number you started with? This issue has not yet been resolved, to put it simply.
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What is the median of the distribution 34 22 13?
The median of the distribution 34 22 13 is 22.
To find the median of a set of scores, you first need to arrange the scores in numerical order. The median is the middle score in the set. If there is an odd number of scores, then the median is the middle score. If there is an even number of scores, then the median is the average of the two middle scores.
In this case, the scores are 13, 22, and 34.
After arranging the scores in numerical order, we have 13, 22, and 34.
There are three scores in this set, so the median is the middle score, which is 22.
The median of the set is 22.
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Is Circumcentre and centroid of a triangle same?
Answer:
no, they are different in their different ways
A pyramid has a square base with sides of length s. The height of the pyramid is equal to 12 of the length of a side on the base. Which formula represents the volume of the pyramid?.
Step-by-step explanation:
The volume of the pyramid with a base area of s² and the height s is [tex]\frac{1}{3} s^{2}[/tex]
The formula for calculating the volume of a square based pyramid is expressed as:
Volume = 1/3 * Base area * HeightSince it is a square-based pyramid, the base area is calculated as:
Base Area = s²
If the height of the pyramid is equal to of the length of a side on the base, hence h = s
Substituting the base area and the height into the formula for the volume, this will give us;
[tex]V=\frac{BH}{3} \\V=\frac{s^{2}Xs }{3} \\V=\frac{s^{3} }{3} \\V=\frac{1}{3 } s^{2} \\[/tex]
Hence the volume of the pyramid with a base area of s² and the height s is [tex]\frac{1}{3}s^{3}[/tex]
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A box without a top is made from a rectangular piece of cardboard, with dimensions 25 inches by 20 inches, by cutting out square corners with side length x inches. which expression represents the volume of the box in terms of x?
Answer:
[tex]x(20-2x)(25-2x)[/tex]
Step-by-step explanation:
The length removed from each side is [tex]2x[/tex].
So, the length and width of the box are [tex]25-2x[/tex] and [tex]20-2x[/tex].
The height of the box is [tex]x[/tex], so the volume is [tex]x(20-2x)(25-2x)[/tex].
4x + 6 = 2(3x - 7)
Solve
Answer:
x = 10
Step-by-step explanation:
Method 1: Algebraically
1. 4x+6 = 2(3x-7) - Multiply out the 2
2. 4x+6 = 6x-14 - make x the subject of the formula first by subtracting 4 from both sides
3. 6 = 2x-14 - add 14 to both sides
4. 20 = 2x - divide by 2 to solve for x
5. 10 = x - Answer
Method 2: Graphing
Use a graphing calculator to solve for the answer
1. set one side to y1 and the other to y2
2. set the correct window
3. press 2nd then trace
4. Select option 5 to find the intersection
please help a mate out aye? 80 points!! :D
Simplify the expression 3x(2x – 7).
(A)15x
(B)6x2 – 21
(C)6x2 – 21x
(D)6x – 21
Answer:
Hey no prob!
We take 3x(2x-7) and we distribute the 3x to both of the terms inside
3x times 2x is 6x^2
and
3x times -7 is -21x
the final answer would be C
6x^2-21x
Answer:
[tex] \sf \: c) \: 6 {x}^{2} - 21x[/tex]
Step-by-step explanation:
Given expression,
→ 3x(2x - 7)
Simplifying the expression,
→ 3x(2x - 7)
→ 3x(2x) + 3x(-7)
→ (3 × 2)x² + (3 × -7)x
→ (6)x² + (-21)x
→ 6x² - 21x
Hence, option (c) is correct.
2 balloons and 3 cakes = £16
4 balloons and 4 cakes = £24
Answer:
1 balloon is = £2 and 1 cake is = £4
Step-by-step explanation:
this is true because 2 balloons = £4
and 3 cakes = £12 so 4 + 12 = 16 and also
4 balloons = £8
and 4 cakes = £16 so 8 + 16 = £24
this is one of the possible answers
Answer:
A cake is £3.50
A Balloon is £2.75
Step-by-step explanation:
Let b be balloons and c be cake
2 balloons and 3 cakes = £16 = 2b + 3c = 16
4 balloons and 4 cakes = £24 = 4b + 4c = 25
First times -2 to the first equation
-4b - 6c = -32
4b + 4c = 25
Now let's find c first by adding the two equations together.
-2c = -7
c = £3.50
Now put 3.50 back in the c
4b + 4(3.50) = 25
4b + 14 = 25
4b = 11
b = £2.75
What is the maximum or minimum value of the function y =- 2x 2 32x 12?
The maximum of the equation y = -2x² +32x -12 is 116 and the range of the function is y ≤ 116.
What are the Maxima and the minima of a function?The highest and smallest values of a function, respectively, can either be found inside a specific range or across the entire domain. They are sometimes referred to collectively as the function's extrema. The plural forms of a function's maximum and minimum are called maxima and minima, respectively.
Y= ax² + bx + c is the conventional form of this quadratic equation. The vertex of a quadratic function is its greatest value or smallest value. We locate the axis of symmetry to determine the x-coordinate of the vertex. This is determined by the equation x = -b/2a:
x = -32/2(-2) = -32/-4 = 8
To find the y-coordinate, plug this into the equation y = -2(8²)+32(8)-12
y=-2(64) + 256 - 12 = -128+256-12 = 128-12 = 116
The coordinates of the vertex are (8, 116).
Look at the value of a to see if this is maximum or minimal. It is -2. This indicates that the parabola widens downward and that the vertex is a maximum because it is negative.
Therefore this is a maximum at y=116, which means the range will be less than or equal to this value of 116.
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What are the 4 functions of a stem?
The 4 functions of a stem are fruits, flowers, leaves, and branches.
In plants, a stem's primary role is to aid in the transfer of water and minerals from the roots to the leaves and other sections of the plant. Additionally, it supports the buds, leaves, flowers, fruits, and branches of plants.
In a plant, a stem does the following tasks:
(i) It holds up the fruits, flowers, leaves, and branches.
(ii) It moves water and minerals from a plant's roots to its leaves and other areas.
(iii) It transports nourishment from the leaves to various plant sections.
(iv) The plant is kept upright by it.
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In the pair of linear equation a1x b1yc1=0 and a2xb2yc2=0,if a1/a2 i not equal to b1/b2 then the equation have no olution. (True or fale)
The statement is false. In the pair of linear equation, if a₁/a₂ ≠ b₁/b₂ then the equations have unique solution.
Given that,
The pair of linear equation
a₁x +b₁y +c₁=0 and
a₂x +b₂y +c₂=0
We have to prove if a₁/a₂ ≠ b₁/b₂ then the equations have no solution.
We know that,
In the pair of linear equation
a₁x +b₁y +c₁=0 and
a₂x +b₂y +c₂=0
If a₁/a₂ ≠ b₁/b₂ then System is called consistent and have a unique Solution
Lines intersect each other at unique point
a₁/a₂ = b₁/b₂ = c₁/c₂ then consistent (infinite solution) as both Equation represent same line
a₁/a₂ = b₁/b₂ ≠ c₁/c₂ then inconsistent (no Solution) as Lines are parallel and never intersect each other
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What is the median of 4 2 7 3 10 9 13?
Answer: 3
Step-by-step explanation: The median is three (3) because its the middle number
What are whole numbers explain with example?
Answer:
Whole numbers are positive numbers including zero that dont include fractions or intergers
Step-by-step explanation:
examples of this are 73, 68, 27
What is current i formula?
The formula of current I is I=V/R.
In the field of physics, current can be described as the rate that shows the intensity of electrons that are flowing from one place to another.
The current is the measure of the potential difference from which the current moves forward when resistance is also a factor that stops it. Electric current is directly proportional to the potential difference applied and is inversely proportional to the resistance in the object in which the electric current is flowing.
Based on this fact, the formula for current, which is represented by the letter I is I=V/R, here I is the current, V is the potential difference and R is the resistance.
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