The perimeter of a pool is 150 m. The rectangle at the right is a
scale drawing of the pool. The length of each square on the grid
represents 1 cm. Draw another scale drawing of the pool using the
scale 25 m to 2 cm. Explain why your drawing is accurate. Is it accurate?
Answers
The we can draw a rectangle with length = 2 cm and width = 4 cm.
According to the statement
We have to find that the dimensions of the another rectangle.
So, For this purpose, we know that the
A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees.
From the given information:
The perimeter of a pool is 150 m. The rectangle at the right is a scale drawing of the pool. The length of each square on the grid represents 1 cm. Draw another scale drawing of the pool using the scale 25 m to 2 cm.
Then
From the given rectangle,
Length of the rectangle = 5 cm
Width of the rectangle = 10 cm
Ratio of length : width = 1 : 2
Perimeter of the rectangle = 2(l + b)= 150 cm
l + b = 75 -----(1)
Since, l : b = 1 : 2
b = 2l ------(2)
From equations (1) and (2),
l + 2l = 75
3l = 75
l = 25 m
Width 'b' = 2(25) = 50 m
Now we have to draw a rectangle with a scale = 25 : 2
Therefore, Scale factor = 25/l = 25/2
Scale factor = l = 2cm
Then Similarly,
50/ w= 50/2
w = 4cm
Now we can draw a rectangle with length = 2 cm and width = 4 cm.
So, The we can draw a rectangle with length = 2 cm and width = 4 cm.
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Related Questions
consider the set of numbers $\{1, 10, 10^2, 10^3, \dots, 10^{10}\}$. the ratio of the largest element of the set to the sum of the other ten elements of the set is closest to which integer?
Answers
The ratio of the largest element of the set to the sum of the other ten elements of the set is closest to which integer.
What is ratio?
A ratio in mathematics describes how many times one number is contained in another. For instance, the ratio of oranges to lemons in a dish of fruit is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of oranges to the total amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8 (or 3:4). (or 4:7).
The quantities in a ratio can be of any kind, such as counts of people or things, measures of lengths, weights, or times, etc. Both numbers must be positive in the majority of situations.
Explanation:
The requested ratio is[tex]\[\dfrac{10^{10}}{10^9 + 10^8 + \ldots + 10 + 1}.\][/tex]
Using the formula for a geometric series, we have[tex]\[10^9 + 10^8 + \ldots + 10 + 1 = \dfrac{10^{10} - 1}{10 - 1} = \dfrac{10^{10} - 1}{9},\][/tex]
which is very close to [tex]$\dfrac{10^{10}}{9},$[/tex] so the ratio is very close to 9.
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Please help only 14 mins left , I'll give you brainliest . I need at least two participants to give an answer
Answers
Answer:
There isnt any info about the question there isnt any numbers
Step-by-step explanation:
Answer:
Letting r be the rate of speed in hours, we have d = rh.
HELP, I NEED ONE PERSON TO HELP WITH THE NEXT THREE QUESTIONS THAT INVOLVE COMBINING FUNCTIONSTHAT MODEL A REAL WORLD SITUATION
question picture below
C=??
Answers
Answer:
if (23)n=(1111)2find the base n
let tj denote the time that it took tejay van garteren to ride the jth stage of the tour de france in 2014. if there were a total of 21 stages, interpret ∑ j
Answers
As per question, let us assume [tex]t(j)[/tex] denotes the time that it took Tejay van garteren to ride the [tex]jth[/tex] stage of the tour de France in [tex]2014[/tex].
Now, let us assume [tex]t(1)[/tex] is the complete time for the first stage; [tex]t(2)[/tex] is the complete time for the second stage; [tex]t(3)[/tex] is the complete time for the third stage and so on.
Therefore, the total time of [tex]21[/tex] stages can be written as:
∑[tex]t(j)[/tex]= [tex]t(1)+t(2)+t(3)+..................+t(21)[/tex] [tex]; j=[1,2,3....21][/tex]
The above expression represents the total time for Tejay van garteren took to finish the ride.
Therefore, ∑[tex]t(j)[/tex] [tex]; j=[1,2,3....21][/tex] is the total time for Tejay van garteren took to finish the ride.
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please help quickly!!
Answers
Answer:
G(x)=-9 when x=5
Step-by-step explanation:
Replace X with 5
3x -x^2+1 becomes 3*5-5^2+1
Then solve
15-25+1=-9
a survey showed that 4 out of 5 students own a bicycle based on this result how many 800 students in a school own a bicycle
Answers
Any genius want a brainliest :)
Answers
Answer:
1.) q less than a number m times 7 is equal to 23
2.) 3 times a number g plus 8 is equal to 10 less than a number h times 4
3.) 6 more than a number k times 9 is equal to 54
4.) a number f times 7 less than a number of d squared times 6 is equal to a number d times 8 more than a number f squared
5.) a number g times 3 is equal to 45
(I might be wrong, so try to read the equations out loud to see if you agree)
A submarine descends to 1/6 of its maximum depth. Then it descends another 2/3 of its maximum depth. If it is now at 650 feet below sea level, what is its maximum depth.
Answers
The submarine can descend to a maximum depth of 780 feet.
What do we mean by depth?The distance is measured downward and perpendicularly from a point to a chosen reference surface.Let x be the maximum depth.
It descends to one-sixth of the maximum depth = (1/6)xIt descends another two-thirds of the maximum depth = (2/3)xIt is now 650 feet below sea level after descending the depths above.
Thus;
(1/6)x + (2/3)x = 650x(1/6 + ⅔) = 650x(5/6) = 650x = 6 × 650/5x = 780 ftTherefore, the submarine can descend to a maximum depth of 780 feet.
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a bag contains $10$ red marbles and $6$ blue marbles. three marbles are selected at random and without replacement. what is the probability that one marble is red and two are blue? express your answer as a common fraction.
Answers
15/56 is the probability that one marble is red and two are blue.
RBB, BRB, and BBR are the three possible ways to draw two blue marbles and one red marble. These are separate scenarios because there are no overlapping outcomes, and their sum is the overall likelihood that two of the three drawn cards will be blue. Therefore, the desired probability is
(10/16)(6/15)(5/14) + (6/16)(10/15)(5/14) + (6/16)(5/15)(10/14) = 15/56
What is probability?Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only forecast how likely an event is to occur using it, or how likely it is to occur. In the probability scale, 0 indicates an impossibility and 1 indicates a certainty. Probability is an important subject for Class 10 students because it teaches all of the subject's essential concepts. Every event's probability in a sample space is one.
For instance, when we flip a coin, there are just two possible results: Head OR Tail (H, T). But if we throw two coins into the air, there are three possible outcomes: either both show heads, either show tails, or one shows heads and one tails, i.e. (H, H), (H, T), or none of the three (T, T).
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WILL GIVE BRAINLIEST IF ANSWERED WELL!!!
Answers
Answer:
S / 2πh
Explanation:
2πrh are all multiplied together to make S, so in order to isolate the r, we need to divide (the opposite operation of multiplication) 2πh from both sides.
If f(1)=2 and f(n)=f(n−1)+2 then find the value of)f(6).
Answers
In function , 12 is the value of)f(6).
What does a math function mean?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.f(1) = 2 and f(n) = f(n -1) + 2
f(1) = 2
f(2) = f(2 - 1) + 2 = f(1) + 2 = 2 + 2 = 4
f(3) = f(3 - 1) + 2 = f(2) + 2 = 4 + 2 = 6
f(4) = f(4 - 1) + 2 = f(3) + 2 = 6 + 2 = 8
f(5) = f(5 - 1) + 2 = f(4) + 2 = 8 + 2 = 10
f(6) = f(6 - 1) + 2 = f(5) + 2 = 10 + 2 = 12
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setenta y uno por tres dividido 43
Answers
Answer:
4.95
Step-by-step explanation:
espero que te ayude
What is the area of the rectangle whose length is 19 and the width is 31
Answers
Answer:
589
Step-by-step explanation:
to find the area of a rectangle it is length x width
19 is your length
31 is your width
19 x 31 = 589
be sure that in your final answer you put in your units (e.g.[tex]cm^{2}[/tex] )
hoped this helped xx
-6(5y+7)-14y
pls dont have much time
Answers
A design for a library has a scale of 1/3in=1 foot. The height of the library in the drawing is 12 inches.What is the actual height of the library
Answers
The actual height of the library is 36 feet.
Given a scale of 1/3 inch = 1 foot
therefore, 1 inch = 3 feet
then, 12 inches = 12 × 3
36 inches.
therefore the actual height of the library is:
12 × 36
= 432 inches
= 36 feet.
It is obvious which dimension is intended when a rectangle is drawn with both horizontal and vertical sides when the term height is used; height designates how high (or how tall) the rectangle is. As a result, using the word width to describe the other dimension—the width of the rectangle from side to side—is simple. As long as there is no ambiguity, it is also appropriate to refer to the side-to-side measurement as the rectangle's length if it is bigger than its height.
hence we get the height of the library as 36 feet.
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To conserve water, many communities have developed water restrictions. The water utility charges a fee of $29, plus an additional $1.41 per hundred cubic feet (HCF) of water. The recommended monthly bill for a household is between $54 and $82 dollars per month. If x represents the water usage in HCF in a household, write a compound inequality to represent the scenario and then determine the recommended range of water consumption. (Round your answer to one decimal place.) 54 ≤ 1.41x + 29 ≤ 82; To stay within the range, the usage should be between 17.7 and 37.6 HCF. 54 ≤ 1.41x + 29 ≤ 82; To stay within the range, the usage should be between 17.7 and 58.2 HCF. 54 ≤ 1.41x − 29 ≤ 82; To stay within the range, the usage should be between 38.2 and 78.7 HCF. 54 ≤ 1.41x − 29 ≤ 82; To stay within the range, the usage should be between 58.9 and 78.7 HCF.
Answers
Using a linear function, we have that:
The inequality is: 54 ≤ C(x) ≤ 82.To stay within the range, the usage should be between 17.7 and 37.6 HCF.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For the cost function, we have that:
The fee of $29 is the intercept.The cost of $1.41 per HCF is the slope.Hence the function is:
C(x) = 29 + 1.41x.
The recommended monthly bill for a household is between $54 and $82 dollars per month, hence the inequality is given by:
54 ≤ C(x) ≤ 82.
The bounds of the range will be found as follows:
29 + 1.41x = 54
x = (54 - 29)/1.41
x = 17.7.
29 + 1.41x = 82
x = (82 - 29)/1.41
x = 37.6.
Hence the correct option is:
To stay within the range, the usage should be between 17.7 and 37.6 HCF.
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randy presses on his calculator twice to obtain two random numbers between and . let be the probability that these two numbers and form the sides of an obtuse triangle. find .
Answers
We are to calculate the value of 4p. The value of 4p will be π / 4.
Let's give the numbers we get from the calculator the names x and y. Independent random variables with a uniform[0,1] distribution are x and y.
Let's take notice that since x and y are both between 0 and 1, 1 is the triangle's longest side.
Let's start by interpreting geometry. If the triangle were a rectangle, the side with length 1 would be the hypotenuse, and x and y would then need to meet the following criteria:
x²+y² = 1
Keep in mind that we are supposing the triangle to be a rectangle in this instance. However, the task requires us to create an acute triangle.
To do that, we must widen the angle formed by the sides of length x and y. We can do that by 'growing' the triangle, but if we do so while maintaining the x and y values, the length of side 1 should rise, which is not what we want.
Therefore, if we enlarge the triangle, we should likewise decrease the value of x and/or y so that the length of the first side may be maintained. This insight allowed us to conclude that
x²+y² < 1
Let's now employ a more mathematical strategy. The Cosine Theorem states that a triangle with three sides of length a, b, and c is satisfying.
A2 is equal to b2+c2 - 2bc* cos(), where is the angle formed by the lengths of b and c's sides.
The result of applying this formula to our triangle is that
[tex]1+x^{2} +y^{2} - 2bc * cos\alpha[/tex] , where aplha is the angle between x and y.
Let's call the figures we obtain from the calculator x and y. X and Y are independent random variables with uniform[0,1] distribution.
Consequently, we must ascertain P(x2+y2 1). This likelihood may be calculated using integration. You need polar coordinates.
(X, Y) = (r*cos, r*sen), where r is an integer between 0 and 1, and (that way, the numbers are positive).
Because the Jacobian matrix has determinant r, X2 + Y2 = 1.
On integrating, we get out answer as π / 4
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-18-7(-10+8)+12
explain please
Answers
Answer:
8.
Step-by-step explanation:
Using Order of operations PEMDAS.
Arithmetic operations are done in the following order:
Parentheses, Exponents, Multiply, Divide, Add, Subtract.
So, we have:
-18 - 7(-10 + 8) + 12
= -18 - 7 * -2 + 12
= -18 + 14 + 12
= -4 + 12
= 8.
identify the theorem or postulate that is related to the measures of the angles in the pair, and find the unknown angle measures. m∠acd
Answers
It should be noted that angles formed when two parallel are intersected by a common transversal include, corresponding, alternate interior and exterior, same-side interior, and vertically opposite angles
Also, the correct option is Same–Side Int. ∠s Thm. m∠1 = 30°, m∠5 = 150°
How to illustrate the information?m∠1 + m∠5 = 180°
Which gives;
(30·x - 30)° + (40·x + 70)° = 180°
(70·x + 40)° = 180°
70·x = 180° - 40° = 140°
70x = 140
x = 140/70
x = 2
m∠1 = (30·x - 30)° = (30 × 2 - 30)° = 30°
m∠1 = 30°
m∠5 = (40·x + 70)° = (40 × 2 + 70)° = 150°
m∠5 = 150°
The correct option is therefore same-Side Int. ∠s Thm. m∠1 = 30°, m∠5 = 150°
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Identify the theorem or postulate that is related to the measures of the angles in the pair, and find the unknown angle measures.
m∠1=(30x−30)∘, m∠5=(40x+70)∘
Alt. Int. ∠s Thm.
m∠1 = 30°, m∠5 = 150°
Alt. Int. ∠s Thm.
m∠1 = 30°, m∠5 = 30°
Same-Side Int. ∠s Thm.
m∠1 = 30°, m∠5 = 150°
Same-Side Int. ∠s Thm.
m∠1 = 150°, m∠5 = 30°
PLS HELP
Which of the following could represent the cost of 5 t-shirts and a $7 tax?
A. 5n − 7
B. n + 7(5)
C. 5n + 7
D.5(7) + n
Answers
Answer:
C. 5n+7
You're buying 5 shirts, so that'll be 5n and there's a 7 dollar tax which means we add on the 7 dollar tax. So it's C. 5n+7
y <= 1/2x - 5
y >= 3x - 20
In the xy-plane, a point with coordinates (h, k) lies in the solution set of the system of inequalities above. What is the maximum possible value of h?
Answers
The maximum possible value for 'h' = 6 for the given set of system of inequalities.
What do you mean by system of inequalities?A collection of two or so more inequalities for one or more variables is referred to as a system of inequalities. When a problem necessitates a variety of solutions and those solutions are constrained by more than one constraint, a system of inequalities is used. Inequalities systems are frequently used to describe the constraints on such a solution.For the given set of inequalities;
y ≤ 1/2x - 5
y ≥ 3x - 20
Equation both equation;
(1/2)x - 5 = 3x - 20
x - 10 = 6x - 40
Further simplifying;
-5x = -30
x = 6
Thus, the maximum possible value for 'h' is same as the value find for the x = 6; as h also represents the point on the x-axis.
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Find the line's slope and a point on the line.
y+3=3/4(x-1)
point on the line:
slope:
Answers
Answer: Coordinate (1,-3) and m = 3/4
Step-by-step explanation:
(i) - So context, the equation is y + 3 = 3/4(x - 1)
So how about the coordinate? Simple, using the formula of the point-slope form, which is in the first step, y1 and x1 is a coordinate on the graph, so based by pairs (x,y) - the pair is (1,-3).
need help with evaluating this Expression
Answers
Answer: 102
Step-by-step explanation:
[tex]x=-2\ \ \ \ \ y=4\\\\8x^2-xy+y^2-xy^2+14=\\\\8(-2)^2-(-2)(4)+(4)^2-(-2)(4)^2+14=\\\\8(-2)(-2)-(-8)+(4)(4)-(-2)(4)(4)+14=\\\\32+8+16+32+14=\\\\102[/tex]
A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associate is $500 and the daily rate for each partner is $1000. The law firm assigned a total of 8 lawyers to the case and was able to charge the client $6500 per day for these lawyers' services. Determine the number of associates assigned to the case and the number of partners assigned to the case.
Answers
Using a system of equations, it is found that there were 3 associates and 5 partners assigned to the case.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: number of associates.Variable y: number of partners.The firm assigned a total of 8 lawyers to the case, hence:
x + y = 8
x = 8 - y.
The firm was able to charge the client $6500 per day for these lawyers' services, hence, considering the costs:
500x + 1000y = 6500.
Since x = 8 - y, we have that:
500(8 - y) + 1000y = 6500.
500y = 2500
y = 5.
x = 8 - 5 = 3.
The firm assigned 3 associates and 5 partners to the case.
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If m ∠ A D B = ( 6 x − 4 ) ° and m ∠ B D C = ( 4 x + 24 ) ° , find the value of x such that ∠ A D C is a right angle.
Answers
Answer:
The value of x is 7°
Step-by-step explanation:
<A C D = ∠ A D B ( 6 x − 4 ) ° +∠ B D C ( 4 x +24 )
Now,
<A D B + < B D C = 90 °
( Being sum of complementary angle is 90°)
( 6 x − 4 ) + (4x + 24)= 90°
6x-4+4x+24=90°
6x+4x-4+24=90°
10x+20=90°
10x=90-20
10x=70
x=70/10
x=7
√2x³. √10x
Help please
Answers
You can write as [tex]2 \sqrt{5} {x}^{2}[/tex] or [tex]\boxed{2 {x}^{2} \sqrt{5}} [/tex]
Step-by-step explanation:
Find product of the groups,
[tex] \sqrt{2 {x}^{3} \: . \: 10x}[/tex]
Regrouping,
[tex] \sqrt{2{x}^{3 + 1} \: . \: 10 } [/tex]
Multiplying,
[tex] \sqrt{20 {x}^{3 + 1} } [/tex]
Add constants,
[tex] \sqrt{20 {x}^{4} } [/tex]
Rewrite 20 as 4 • 5,
[tex] \sqrt{4 \: . \: 5 {x}^{4} } [/tex]
Rewrite 4 as 2² ,
[tex] \sqrt{ {2}^{2} \: . \: 5 {x}^{4} } [/tex]
Using radical rules,
[tex] \sqrt{ {2}^{2} } \sqrt{x} \sqrt{5} [/tex]
Reduce root and power,
→ [tex] \underline {2 {x}^{2} \sqrt{5}} [/tex]
A bakery sold 120 chocolate cupcakes in a day,
which was 24% of the total number of cupcakes
sold that day. How many total cupcakes did the
bakery sell that day?
Answers
The correct answer is 28.8.
Everything is stated as though it were a fraction of a hundred in terms of quantity. The ratio can be expressed as a quarter of one hundred. The word "percent" denotes a percentage of 100. It is represented by the '%' symbol.
120 cupcakes were sold by a bakery in a single day, with 45% of them having a chocolate flavour.
The total quantity of chocolate-flavoured cupcakes served on that particular day will then be
Let x represent how many chocolate-flavoured cupcakes were sold on that particular day.
x = 24% of 120
x = 0.24 × 120
x = 28.8
Consequently, the quantity of chocolate-flavoured cupcakes sold that day will be 28.8.
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dis me after 1 min in school
Answers
Answer:
What's the question?
Step-by-step explanation:
In the circle below, AB is parallel to CD, AD is a diameter of the circle, and AD = 36.What is the length of AB? Express your answer in terms of pi.
Answers
We get the length of AB as 7.37 pi units
We are given that:
AB || CD
AD = 36 cm
AD is the diameter of the circle.
So, we get that
1 / 2 AD = Radius (r)
r = 36 / 2 cm = 18 cm
Now, we are also given that:
∠ BAD = 50°
Since AD is a diameter, we get that:
ABD will form a right triangle with ∠ ABD = 90°
∠ ADB = 40° ( Angle sum property)
AB will be:
sin (40) = AB / 36
AB = 36 * sin (40) = 23.140353948732
AB ≈ 7.37 pi units
Therefore, we get the length of AB as 7.37 pi units
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can someone help me really quick
Answers
Answer:
Step-by-step explanation:
The last option
This is because we are going to multiply in order. The -6 is only in parenthesis because its a negative number. this means we are multiplying 2 x 4 , then multiplying that answer by -6.
Hope this helps! ^^
Answer:
The answer to your question is (A) hope this helpsStep-by-step explanation: