The required answers are a) 6.5 m, b) Dimensions 8 m, 5 m c) square has the greater area.
How to deal with square and rectangle?(a) Let s be the length of a side of the square. The perimeter of a square is given by 4s. Since the piece of wire used to make the square has length 26 m, we have:
[tex]$\begin{align*}4s &= 26 \s &= \frac{26}{4} = 6.5 \text{ m}\end{align*}[/tex]
Therefore, the length of a side of the square is 6.5 m.
(b) Let l be the length of the rectangle. Then the width of the rectangle is l-3. The perimeter of a rectangle is given by 2(l+w). Since the piece of wire used to make the rectangle has length 26 m, we have:
[tex]$\begin{align*}2(l + (l-3)) &= 26 \2(2l-3) &= 26 \4l - 6 &= 26 \4l &= 32 \l &= 8 \text{ m}\end{align*}[/tex]
Therefore, the length of the rectangle is 8 m and its width is 8-3=5 m.
(c) The area of the square is given by [tex]$s^2$[/tex], which in this case is [tex]$6.5^2 = 42.25$[/tex] square meters. The area of the rectangle is given by lw, which in this case is [tex]$8\times5 = 40$[/tex] square meters. Therefore, the square has the greater area.
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Complete question;
A workman has two pieces of worse, each of length 26 m. One piece is to be bent into a square. The other piece is to be bent into a rectangle whose width is 3 m shorter than its length.
(a) What is the length of a side of the square?
(b) What are the dimensions of the rectangle?
(c) Which shape has the greater area?
What is the surface area of the rectangular prism formed by the pattern below?
Answers -
56 cm
108
136
162
Answer:
C. 136
Step-by-step explanation:
Add up the surface areas of each individual section. Area is length times width.
Lets start by figuring out the area of the 2 by 6 rectangle on the bottom. 2cm*6cm=12 sq cm. The rectangle on the top right also has an area of 2cm*6cm. So it also has an area of 12 sq cm. lets figure out the area of the smaller rectangle on the right side. 7cm times 2 cm equals 14 cm squared. There is also a 7cm by 2cm box in the middle of the pattern. so 14 + 14 = 28, + 12 + 12= 52. so all of the tiny rectangles added up equal 52. Finally, lets figure out the area of the two 6*7 rectangles. 6*7= 42. 42*2= 84. 84 is the area of the two big rectangles added together. So add the two totals to get 52 sq cm+ 84 sq. cm = 136 sq. cm.
Consider the following function.
p(x)=1−12x
Plot two points on the line to graph the function.
We can plοt the pοints (0,1) and (1,-11) οn the line tο graph the functiοn p(x) = 1 - 12x.
What is functiοn?A functiοn frοm a set X tο a set Y is an assignment οf an element οf Y tο each element οf X. The set X is called the dοmain οf the functiοn and the set Y is called the cοdοmain οf the functiοn.
A functiοn, its dοmain, and its cοdοmain, are declared by the nοtatiοn f: X→Y, and the value οf a functiοn f at an element x οf X, denοted by f(x), is called the image οf x under f, οr the value οf f applied tο the argument x.
Functiοns are alsο called maps οr mappings, thοugh sοme authοrs make sοme distinctiοn between "maps" and "functiοns" (see § Other terms).
Tο plοt twο pοints οn the line fοr the functiοn p(x) = 1 - 12x, we can chοοse any twο values οf x and find the cοrrespοnding values οf p(x).
Fοr example, if we chοοse x = 0, then p(0) = 1 - 12(0) = 1, sο the pοint (0,1) is οn the line.
If we chοοse x = 1, then p(1) = 1 - 12(1) = -11, sο the pοint (1,-11) is οn the line.
Therefοre, we can plοt the pοints (0,1) and (1,-11) οn the line tο graph the functiοn p(x) = 1 - 12x.
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for the simple harmonic motion equation d=4sin(8pi), what is the maximum displacement from the equilibrium position?
The maximum value οf the functiοn is 4.
What is simple harmοnic mοtiοn?Simple Harmοnic Mοtiοn, οr SHM, is a mοtiοn in which the restοring fοrce is inversely prοpοrtiοnal tο the bοdy's displacement frοm its mean pοsitiοn. This restοrative fοrce always pοints in the directiοn οf the mean pοsitiοn. A particle mοving in simple harmοnic mοtiοn accelerates as a(t) = -2 x. (t). The particle's angular velοcity is indicated in this equatiοn by the symbοl.
Given functiοn οf simple harmοnic mοtiοn is d= 4 sin(πt/8)
Nοw we need tο find abοut what is the maximum value οf .
We knοw that value οf sine functiοn varies frοm -1 tο 1.
that means fοr any value οf t, maximum value οf sine functiοn is 1.
sin(πt/8)<1
d≤4
Hence the maximum value οf the functiοn is 4.
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What is the explicit formula for the sequence: .25,5,1,2
The explicit formula for the geometric sequence is [tex]a_n=25(\frac{1}{5})^{n-1}[/tex].
What is explicit formula for geometric series?
The explicit formula for geometric sequence is [tex]a_n=a_1(r)^{n-1}[/tex] where r is common ratio.
Here the given sequence is 25,5,[tex]\frac{1}{2}[/tex]...
Here first term [tex]a_1=25[/tex]
Common ratio = [tex]$ \frac{a_2}{a_1}=\frac{5}{25}=\frac{1}{5}[/tex]
Now, Explicit formula [tex]$ a_n=a_1(r)^{n-1}[/tex]
=> [tex]$ a_n=25(\frac{1}{5})^{n-1}[/tex]
Hence the explicit formula of geometric series is [tex]$ a_n=25(\frac{1}{5})^{n-1}[/tex].
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What are the key features of the equation y = (x + 12)(x + 6)? Question 5 options: The x-intercepts are (–12, 0) and (–6, 0). The y-intercept is (0, 72). The vertex is an absolute maximum, (–9, –9). The x-intercepts are (12, 0) and (6, 0). The y-intercept is (0, 72). The vertex is an absolute minimum, (–9, –9). The x-intercepts are (–12, 0) and (–6, 0). The y-intercept is (0, 6). The vertex is an absolute minimum, (–9, –9). The x-intercepts are (–12, 0) and (–6, 0). The y-intercept is (0, 72). The vertex is an absolute minimum, (–9, –9).
Answer:
y= -x+3
Step-by-step explanation:
We can see that our given equation is in slope-intercept form
, where m represents slope of line and b represents the y-intercept.
Upon looking at our given equation, we can see that the slope of our given line is 1
and the y-intercept is at point
.0,3
Upon graphing our given equation, we will get our required graph as shown below:
There is a mound of g
pounds of gravel in a quarry. Throughout the day, 200
pounds of gravel is added to the mound. Two orders of 700
pounds are sold and the gravel is removed from the mound. At the end of the day, the mound has 1,000
pounds of gravel.
Answer:
2400
Step-by-step explanation:
before anything got taken away they added 200 wich means before they added that they had 2200 and if 700 pounds were removed twice that would mean the mound lost 1400 pounds and so if you add 1000 to the 1400 that they took you can find the amount that was there before.l
the figure below is dilated by a factor of 4 centered at the orgin. plot the resulting image
(where are the points pls im so confused)
The image that results from the dilation transformation is as shown in the attached file with coordinates as:
G'(0, -8)
H'(8, 0)
I'(-8, 4)
What is the coordinate of the triangle after dilation?A dilation is defined as a transformation that produces an image that is the same shape as the original, but is a different size.
The coordinates of the given triangle are:
G(0, -2)
H(2, 0)
I(-2, 1)
Now, when an object with coordinates is dilated by a factor about the origin, what we will do is to multiply each coordinate by that factor . The factor of dilation is 4 and as such we have:
G(0, -2) * 4 = G'(0, -8)
H(2, 0) * 4 = H'(8, 0)
I(-2, 1) * 4 = I'(-8, 4)
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what do i do this is confusing for me
Answer:
Translate 3 right and 1 up.
Step-by-step explanation:
Looking at the picture and count the movement.
Answer:
Step-by-step explanation:
3 units right.
1 unit up.
Each of the letters is moved by these amounts to create the new image.
Help! Does the rule represent an exponential function?
y = -5x^7
STATISTICS MATH. SOMEONE PLEASE HELP WITH THIS!! ILL GIVE YOU BRAINLIST ANSWER. IMAGE ABOVE
Answer:
u rock tgu hjgr yyihh yihgg
In a high-quality coaxial cable, the power drops by a factor of 10 approximately every 2.75 km. If the original signal power is 0.375 W (= 3.75 × 10-1 W), how far will a signal be transmitted before the power is attenuated to 37.5 μW?
Every [tex]2.75[/tex] kilometres in an elevated coaxial cable, the energy decreases by a factor of 10. This indicates that the transmit strength drops with one (0.1) of its original value after every [tex]2.75[/tex] kilometres.
Let's write "d" to represent the signal's maximum range before it loses strength and dips to [tex]37.5 W[/tex]. The following formula can be used to determine the distance [tex]d: P(d) = P(0) / 10^(d / L)[/tex]
[tex]P(d)[/tex] is the signal's power after travelling a distance of d,[tex]P(0)[/tex] is the signal's initial strength,[tex]L[/tex] is indeed the attenuation length in this instance ([tex]2.75 km[/tex]), and "([tex]37.5 W[/tex])" stands for "to the power of d/L".
Inputting the values provided yields: [tex]37.5 μW = 0.375 W / 10^(d / 2.75 km)[/tex]0 The result of dividing both sides with [tex]0.375 W is: .0 /001 = 1 10^(d / 2.75 km)[/tex]The result is: when we take the logarithmic (based 10) of both sides. [tex]-4 = -(d / 2.75 km)[/tex]By dividing all sides by [tex]2.75[/tex] kilometres, we arrive at:[tex]11 km = d[/tex]
As a result, the signal may travel 11 kilometres before losing power and becoming weaker [tex](37.5W) .[/tex]
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The Ministry of Transport and Mining hired a firm to conduct a traffic study before expanding the city streets. Two companies submitted bids for the job. The ministry hired the second company (company B) because they had more experience and offered a better rate. They studied the movement of the traffic on a specific roadway. The first day of the study was the second Monday in September. They found that 12,665 cars, 23,709 small commercial vehicles, 1,024 medium trucks, 7,096 lange macks, and 660 other vehicles used the roadway during the evaluation period.
0f the vehicles classified as "other vehicles," 213 of them are morcycles How many of the other vehicles were not motorcycles?
Answer: i got 213
Step-by-step explanation:
Suppose that a manufacturer produces two brands of a product, brand 1 and brand 2. Suppose the demand for brand 1 is
x = 61 − p1
thousand units and the demand for brand 2 is
y = 71 − p2
thousand units, where
p1 and p2
are prices in dollars. If the joint cost function is
C = xy,
in thousands of dollars, how many of each brand should be produced to maximize profit?
brand 1=
Brand 2=
What is max profit?
To maximize profit, the manufacturer should produce 22 thousand units of each brand, and the maximum profit is:
Profit = (39 × 22) + (49 × 22) - (61 - 39)×(71 - 49) = $256 thousand.
What is profit?Profit is a term used in business and economics to refer to the amount of money or value that is gained after deducting the cost of production or acquisition from the revenue earned.
Mathematically, profit can be calculated as follows:
Profit = Revenue - Cost
To maximize profit, we need to determine the optimal values of P1 and P2. We can do this by setting up the profit function as follows:
Profit = Total Revenue - Total Cost
Profit = (P1 × x) + (P2 × y) - C
Profit = (P1 × (61 - P1)) + (P2 × (71 - P2)) - (61 - P1)×(71 - P2)
Taking the derivative of the profit function with respect to P1 and P2 and setting it equal to zero will give us the optimal values of P1 and P2 that maximize profit:
∂Profit/∂P1 = 61 - 2P1 + P2 = 0
∂Profit/∂P2 = 71 - 2P2 + P1 = 0
Solving these equations simultaneously, we get P1 = 39 and P2 = 49.
To find the quantities of each brand that should be produced, we can substitute P1 and P2 into the demand functions for x and y:
x = 61 - P1 = 22 thousand units of brand 1
y = 71 - P2 = 22 thousand units of brand 2
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If (-2,8) and (1,-10) are two anchor points on a trend line, then find the equation of the line
Answer:
The equation would be y = 3x - 7
Step-by-step explanation:
The equation of the trend line given the two coordinates is: y = -6x - 4
How to find the equation of a line?
The formula to find the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
The formula to find the equation of a line between two coordinates is:
(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)
From the given two coordinates, we can say that:
(y - 8)/(x + 2) = (-10 - 8)/(1 + 2)
(y - 8)/(x + 2) = -6
y - 8 = -6x - 12
y = -6x - 4
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write as a product: b^2*c^2-4bc-b^2-c^2+1
Answer:
(b*c+c-1+b)*(-c+b*c-b-1)
or
(b*c + c - 1 + b)*(-c + b*c - b -1)
put both in the same order:
(bc + b + c - 1)( bc - b - c - 1)
Turn the crank:
(bc)2 + b2c + bc2 - bc -b2c -b2 - bc + b -bc2 - bc - c2 + c -bc - b - c + 1
Cancel things....
(bc)2 - bc -b2 - bc - bc - c2 -bc + 1
(bc)2 - 4bc - b2 - c2 + 1
Wesley is a member of the
kennel club in his area. His club uses
accordion fencing like the section shown
at the right to block out areas at dog
shows.
a. Identify two pairs of congruent
segments.
b. Identify two pairs of supplementary
angles.
The two pairs of congruent segments are PS = QR and PQ = SR
The two pairs of supplementary angles are P and Q; and S and R.
What are supplementary angles?Supplementary angles are two angles that add up to 180 degrees. In other words, if angle A and angle B are supplementary angles, then:
A + B = 180 degrees
For example, if angle A is 60 degrees, then its supplementary angle would be angle B, which is 120 degrees, because:
A + B = 60 + 120 = 180 degrees
Supplementary angles are commonly used in geometry and trigonometry to solve problems related to angles and lines. For instance, if two lines intersect, the opposite angles formed are always supplementary.
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Find the equation of the line that passes through the given points. (Use x as your variable.) (0,5),(6,0)
Answer:
y = - [tex]\frac{5}{6}[/tex] x + 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 5 ) and (x₂, y₂ ) = (6, 0 )
m = [tex]\frac{0-5}{6-0}[/tex] = [tex]\frac{-5}{6}[/tex] = - [tex]\frac{5}{6}[/tex]
the line crosses the y- axis at (0, 5 ) ⇒ c = 5
y = - [tex]\frac{5}{6}[/tex] x + 5 ← equation of line
The median of the data 10 16 12 15 7 is
what's the value of z ?
[tex] \sqrt{z + y} = - 369[/tex]
when y = 65
Answer:
There is no solution
Step-by-step explanation:
If she makes her goal pace 80% of the time and plans to run for the next 10 days how likely will she make her goal pace
every day
If she makes her goal pace 80% of the time and plans to run for the next 10 days, the probability or likelihood that she will make her goal pace every day is 80%.
What is probability?Probability describes the chance, odds, or likelihood of an expected outcome, event, or success occurring when there are many possible outcomes.
Probability is a fractional value that lies between zero and one depending on the degree of certainty or otherwise.
Thus, it is 80% likely that she will make her goal pace every day if she runs for the next 10 days.
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[tex]2^{2} . 2^{3}[/tex]
Answer:
32
Step-by-step explanation:
add the exponents
2 + 3 = 5
2⁵ = 32
A soundscape can only be written by using a table and diagrams.
A. False, a soundscape can also be written out in words.
B. True
C. False, a soundscape can only be written out in words.
Answer:
C . False, a soundscape can only be written out in words.
Step-by-step explanation:
Because :
False, a soundscape cannot be written by using a table and diagrams.
Explanation:
A soundscape is the acoustic environment as perceived by humans, in context. The term was originally coined by Michael Southworth, and popularised by R. Murray Schafer. There is a varied history of the use of soundscape depending on discipline, ranging from urban design to wildlife ecology to computer science.
Question 8 Find BC Show work
The value of BC in triangle ABC is 23.
What is triangle?
A closed plane figure with three straight sides and three angles is known as a triangle. It is made by joining three non-collinear points. Triangles are important in geometry and have various types based on their sides and angles, such as equilateral, isosceles, scalene, acute, right, and obtuse triangles.
Given:- triangle ABC and DEF are similar.
So , AC = DF
Therefore,
4x-23 = 2x+2
4x – 2x = 2 + 23
2x = 25
x = 25/2 = 12.5
therefore, AC = 4x – 23
= 4 * 12.5 – 23
= 50 – 23
AC =27
So ,From triangle DEF
EF = 2x-2
= 2*12.5 – 2
= 25 – 2
EF = 23
As triangle ABC and DEF are similar.so,
BC = EF = 23
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2064 0 No. 10 Old if the compound interest on Rs 500 for years is Rs 398 find the compound interest on Rs. 625 15) Ans: Rs. 450 la 15 years at the same rate 5
Proportionately, if the compound interest on Rs 500 for years is Rs 398, the compound interest on Rs. 625 is Rs. 497.50.
What is proportion?Proportion is a part or portion of the whole.
Proportion indicates the ratio that one quantity or value possess in relation to or when compared or equated to another.
We determine proportion as the quotient of one value divided by another. Proportion can also be expressed as a percentage by multiplying the resultant quotient by 100.
The compound interest on Rs. 500 = Rs. 398
Thus, proportionately, the compound interest on Rs. 625 will be Rs. 497.50 (Rs 398/Rs. 500 x 625).
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Explain why the nature of roots depends on the value of the dicriminant.
Answer:
The discriminant of a quadratic equation is the expression found under the square root sign in the quadratic formula, which is b^2 - 4ac. The discriminant reveals information about the nature of the roots of the equation.
If the discriminant is positive, the quadratic equation has two distinct real roots. This means that the equation can be factored into two linear factors, each of which can be set equal to zero to solve for the roots.
If the discriminant is zero, the quadratic equation has one real root, which is a repeated root. This means that the equation can be factored into a linear factor that occurs twice.
If the discriminant is negative, the quadratic equation has two complex (non-real) roots, which are conjugates of each other. This means that the equation cannot be factored into two linear factors with real coefficients.
In summary, the nature of roots of a quadratic equation is determined by the value of the discriminant, which depends on the coefficients of the quadratic equation.
Step-by-step explanation:
Can someone explain me how to do this task please? Thank you
Step-by-step explanation:
common multiples are numbers that can be divided without remainder by both numbers.
12. 3 and 5
3 and 5 are both prime numbers, so their common multiple are multiples of their product (3×5 = 15).
so,
1×15 = 15
2×15 = 30
3×15 = 45
13. 4 and 6
the prime factors of 4 are
2×2
the prime factors of 6 are
2×3
the last common multiple is the product of the longest chains of prime factors of the numbers :
2×2 × 3 = 12
6 has only one 2 factor, 4 has two 2 factors, so that is the longest chain. and 6 has one 3 factor, which makes it the longest chain for that.
the multiples for 4 and 6 and now the multiples of 12 :
1×12 = 12
2×12 = 24
3×12 = 36
4×12 = 48
14. 3 and 7
they are both again prime numbers, so we are looking for multiples of their product (3×7 = 21).
1×21 = 21
2×21 = 42
15.
what do we need to do to change the denominator by keep the overall value of the fraction ?
we need to multiply numerator and denominator by the same value (e.g. by 2/2, 3/3, 4/4, ...)
3/4 = 6/8 = 9/12 = 12/16
16.
as before.
2/3 = 4/6 = 6/9 = 8/12
17.
as before
4/5 = 8/10 = 12/15 = 16/20
18.
now we need to find the largest n/n factor hidden in the fraction. by eliminating that we get the core (simplified) value of the fraction.
4/12 = 1/3 × 4/4
so,
1/3 is the simplified fraction.
19.
as before
6/10 = 3/5 × 2/2
3/5 is the simplified fraction.
20.
as before
4/8 = 1/2 × 4/4
1/2 is the simplified fraction.
Robin earns a 5% Commission on her sales. If robin sold an item for $530, how much did she earn in commission?
Answer:
26.5$
Step-by-step explanation:
Calculate the 5% of 530, which is 530 * 0.05, whic is equal to 26.5$
I need help with this immediately
The digits in the hundreds place is 2.
The digits in the hundredths place is 9.
The digits in the ten thousandths place is 1.
What is a place value?A place value can be defined as a numerical value which denotes a digit based on its position in a given number and it includes the following:
TenthsHundredthsThousandthsTen thousandthsHundred thousandthsMillionths.UnitTensHundredsThousands.Tens of thousands.Based on the numerical data (number) provided above 248.7961, we can reasonably infer and logically deduce that the place value of one (1) is ten thousandths, nine (9) is hundredths, and two (2) represent hundreds.
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Graph the line that passes through the points (-6, -8) and (3,-2) and determine
the equation of the line.
(x² + 3x + 2) ÷ (x + 2)
Answer:
x+1
Step-by-step explanation:
For the first part of the expression, factor into (x+2)(x+1).
(x+2)(x+1)/(x+2)
The x+2 cancels out, so the answer is x+1