The length of the rectangular playground can be determined using the conversion of the area formula, Length = Area ÷ Width. Substituting the values provided gives us Length = 3,162 ÷ 51.
Explanation:The subject of this question is mathematics, more specifically, the topic involves calculating the dimensions of a rectangle when given the area and one side length. In this case, the student is asked to determine the length of a rectangular playground that has an area of 3,162 square meters and a known width of 51 meters.
The area of a rectangle is calculated by multiplying its length by its width, according to the formula: Area = Length x Width. This can be rearranged to find Length, resulting in: Length = Area ÷ Width.
Plugging in the values provided, we find the length by using the rearranged formula:
Length = 3,162 ÷ 51
With these calculations, we would find our answer for the length of the playground.
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What is the nth term of the sequence -5,5,-5,5,-5...
Answer:
-5Step-by-step explanation:
-5,5,-5,5,-5,5,-5,5,-5
What is the value of arccos (-1/2)
Answer:
120° & 240° (given the angles are between 0° and 360°)
Step-by-step explanation:
We want to find [tex]arccos(-\frac{1}{2})[/tex].
This means we want to know the angle(s) for which cosine has a value of [tex]-\frac{1}{2}[/tex].
The basic acute angle that has a cosine of [tex]\frac{1}{2}[/tex] is 60°. But we want to know NEGATIVE [tex]\frac{1}{2}[/tex]. So in which quadrants is cosine negative? Second and Third
The rule to find 2nd quadrant angle with known acute angle is: 180 - αThe rule to find 3rd quadrant angle with known acute angle is: 180 + αWhere α is the basic acute angle (in our case it is 60°)
So 2nd quadrant angle is 180 - 60 = 120°
and 3rd quadrant angle is 180 + 60 = 240°
Answer:
120°
Step-by-step explanation:
arccos means the inverse of cosine.
arccos (-1/2) ⇒ We can rewrite this equation as;
cosФ = 1/2 Find the value of Ф.
Ф = arccos (-1/2) ⇒ This can be calculated directly from the calculator.
arccos (-1/2) = 120°
or arccos (-1/2) = (180 + 60)
= 240°
You can have more than one value of arccos (-1/2) since the cosine is negative in the second and third quadrant.
An airplane climbs at an angle of 11 degrees with the ground. Find the distance it has traveled when it has attained an altitude of 400 feet. Using sin, cos, and tan.
The distance traveled by the airplane to attain an altitude of 400 feet is approximately 2164.8 feet.
Explanation:To find the distance traveled by the airplane, we can use trigonometric functions.
Let's use the side opposite the angle as the altitude (400 feet) and the hypotenuse as the distance traveled.
Using the sine function, we can solve for the distance:
sin(angle) = Opposite / Hypotenuse
sin(11 degrees) = 400 feet / x
x = 400 feet / sin(11 degrees)
Using a calculator, we find that x ≈ 2164.8 feet.
Therefore, the distance traveled by the airplane to attain an altitude of 400 feet is approximately 2164.8 feet.
The distance it has traveled when it has attained an altitude of 400 feet is 2096.34 feet.
Given, Climbing angle [tex](\(\theta\))[/tex] = 11°
Altitude (opposite side) = 400 feet
sin(angle)= opposite/hypotenuse
sin(11°)= 400/d
d=400/ sin(11°)= 0.1908/400 ≈ 2096.34
The airplane has traveled approximately 2096.34 feet when it has attained an altitude of 400 feet at an angle of 11° with the ground.
In the first quarter, Owen passed the football 1 4 yards 1 foot 7 inches . On his second pass , he threw 16 yards 2 feet 19 inches .How far did he pass the football altogether ? Convert the answer to larger units whenever possible.
Answer:
31 yards 2 feet 5 inches
Step-by-step explanation:
14 yd 1 ft 7 in
+ 16 yd 2 ft 19 in
-------------------------
30 yd 3 ft 26 in
26 inches is 2 feet and 2 inches ---> 30 yd 5 ft 2 in
5 feet is 1 yard and 2 feet ---> 31 yd 2 ft 2 in
Answer:
31 yards 2 foot 2 inches
Step-by-step explanation:
To know the full distance, we need to sum both distances unit by unit. That means, we sum yards with yards, foot with foot and inches with inches. Then we converted to the larger unit whenever possible, starting from the smaller one.
Total yards: 14 + 16 = 30 yards
Total foot: 1 + 2 = 3 foot
Total inches: 7 + 19 = 26 inches
As 12 inches are 1 feet, 12*2 = 24 inches are 1*2=2 foot. Therefore, as 26 = 12*2 + 2, 26 inches are 2 foot and 2 inches.
Now we have 3 + 2 = 5 foot.
As 3 foot are 1 yard, 5 foot are 1 yard and 2 foot.
Now we have 30 + 1 = 31 yards.
Getting all together, the full distance is 31 yards 2 foot 2 inches
in one u.s. city, the taxi cost is $3 plus $0.50 per mile. if you are traveling from the airport, there is an additional charge of $4.00 for tolls. how far can you travel from the airport by taxi for $19.50?
Answer:
You can travel 25 miles
Step-by-step explanation:
19.50-4.00=15.5
15.5-3=12.5
12.5÷0.5=25
Marcus has $28 to spend. He spent $3.75 to buy a notebook. He needs to save $11.25 but he wants to buy a snack. Chips cost $1.30 per package. Tax has already been included in the price. What is the maximum number of packages that Marcus can buy? Write an inequality that represents the situation. Then solve your inequality by showing your work and steps.
Total money Marcus has = $28
Money spent to buy a notebook = $3.75
Money left now = [tex]28-3.75=24.25[/tex]
Money needed to be saved = $11.25
So, the amount of money Marcus can spend = [tex]24.25-11.25=13[/tex]
Cost of a packet of chips = $1.30
The inequality to determine the maximum number of chips he can buy is:
Let the number of chips Marcus can buy = x
As he cannot spend more than $13 to buy chips so equation becomes:
[tex]1.30x\leq 13[/tex]
Solving this we get
[tex]x\leq 10[/tex]
Hence, Marcus can buy a maximum of 10 packs of chips and save $11.25
Which expression is equivalent to 100 in exponential form? A) 102 B) 210 C) 10 × 10 D) 4 × 25
Answer:
A) 10^2
Step-by-step explanation:
100 is 10 times 10 or 10 to the second power
100 = 10 * 10 = 10 ^2
Someone who can help would be great.
Answer:
x=5
Step-by-step explanation:
In a square, the diagonals are equal.
4x+17 = 12x-23
Subtract 4x from each side.
4x-4x+17 = 12x-4x-23
17 = 8x-23
Add 23 to each side
17+23 = 8x-23+23
40 = 8x
Divide each side by 8
40/8 = 8x/8
5 =x
What is the equation of the line in this graph?
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the y-intercept (0, -3) → b = -3
Chose two points: (6, 1) and (0, -3). Substitute:
[tex]m=\dfrac{-3-1}{0-6}=\dfrac{-4}{-6}=\dfrac{4}{6}=\dfrac{2}{3}[/tex]
Answer: [tex]\boxed{y=\dfrac{2}{3}x-3}[/tex]
the bike is on sale for $130. if the original price of the bike $200, what is the percent discount ?
Draw an array to represent the problem 3x9
Answer:
27
Step-by-step explanation:
draw 3 groups of 9 somethings or 9 groups of 3 somethings
In the 3x9 array representation there are 3 rows and 9 columns, each initialized with the value 0
Since we know that,
A set of components of the same data type are stored collectively in contiguous memory regions in an array, which is a form of data structure. To organise data sets in a way that is simple to sort and search, computer programmers employ arrays in their programmes. They can make a programme operate more quickly and are more effective at storing data than individual variables.
Sure, here's a simple array that represents a 3x9 grid:
[tex]\left[\begin{array}{ccccccccc}0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0\end{array}\right][/tex]
In this array, there are 3 rows and 9 columns, each initialized with the value 0.
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In the figure below, OMPN is a square. If the area of the circle O is 4π then what is the area of the shaded region?
Answer:
4 - π
Step-by-step explanation:
(a) Radius of circle
A = πr² Substitute value of A
4π = πr² Divide each side by π
r² = 4 Take the square root of each side
r = 2
(b) Area of MON
A = ¼ × area of circle
A = ¼ × 4π
A = π
(c) Area of MONP
l = r Substitute the value of r
l = 2
A = l² Substitute the value of l
A = 2²
A = 4
(d) Area of MPN
A(MPN) = A(MONP) – A(MON)
Area(MPN) = 4 - π
Find the difference 5/5 - 2/10
Answer:
4/5
Step-by-step explanation:
5/5-2/10
10/10-2/10
8/10
4/5
Answer:
4/5 or 0.8
Im crying just listening to the saddest song on The Future Diary and that i ended the anime it was so sad the ending im just crying seeing Yuno and Yuki and i keep listening to "here with you" ost.
Write 2x^2+12x+3=0 in vertex form?
Answer:
y = 2x^2+12x+3 = 2(x + 3)^2 - 15
Step-by-step explanation:
Take 2 as a common factor out of the first 2 terms2(x^2 + 6x) + 3 = 0Add half 6 squared inside the brackets. Subtract the same number outside the brackets when multiplied by 22(x^2 + 6x + 3^2) + 3 - 2*3^2 = 0Combine the two terms on the end.2(x^2 + 6x + 9) + 3 - 2*9 = 02(x^2 + 6x + 9) + 3 - 18 = 02(x^2 + 6x + 9) - 15 = 0Express the terms inside the brackets as a perfect square2(x + 3)^2 - 15 = 0Discussion Graph
Technically, the vertex form would y = 2(x + 3)^2 - 15. It needs to be more general than equated to zero. I have solved it the way you presented it and graphed it by definition.
The red graph is y = 2x^2 + 12x + 3The blue graph is y = 2(x + 3)^2 - 15Notice they have the same critical point which means they are equivalent
What is COEFFICIENT of 12c
Mathias and his brother divided 2,008 marbles equally. HELP PLEASE!!!! LOTS OF POINT I PROMISE U!!
Answer:
each got 1,004 marbles each
Step-by-step explanation:
if you divide 2,008 by 2, you get 1,004
Answer:
1004
Step-by-step explanation:
hope this helps
What is 16,407 decreased by 8,300
The solution of a division problem is called a
The solution of a division problem is called a quotient.
Inga divided two identical rectangles into equal parts. She colored one part of each rectangle.
What is true about the areas of the colored parts?
Clear Check
The areas are equal.
The area of the red part is greater than the area of the blue part.
The area of the blue part is greater than the area of the red part.
Answer:
The areas are equal.
Step-by-step explanation:
Let the first rectangle be R and
the second rectangle be R'.
Sine R and R' are identical, their lengths are equal and their breadths are equal.
So, if Inga divided each into equal parts, then each part of both rectangles are equal.
Hence, the colored parts of both rectangles are equal.
I definitely need a little help with this.
Answer:
It is given that,
there are 8 balls in the bag numbered 1 to 8
Only one ball color is gray and all others are white
P(X) = probability of getting white ball
P(not X) = Probability of getting gray ball
a) To find Probabilities P(X) and P(not X)
For event X, 1,3,4,5,6,7,8 are checked and P(X) = 7/8
for event 'not X' only 2 is checked and P(not X ) = 1/8
b) To find 1 - P(X)
1 - P(X) = 1 - 7/8 = (8 - 7)/8 = 1/8
c)1 - P(X) is same as P(not X)
1 kilogram= 2.2 pounds, 1 stone= 14 pounds change 42 kilograms into stones
Answer:
6.6 stone
Step-by-step explanation:
We will use conversions to change kilograms to stones
1 kilogram= 2.2 pounds,
1 stone= 14 pounds
42 kilogram 2.2 lbs 1 stone
--------------- * ------------- * ---------------
1 kg 14 lbs
All the units cancel except stone
(42*2.2)/14 stone
6.6 stone
Answer:
42 kilograms is equal to 6.6 stones.
Step-by-step explanation:
Using the given conversion factors:
1 kilogram = 2.2 pounds
1 stone = 14 pounds
To Find: 42 kilograms into stones = ? stones
Solution:
42 kilograms = [tex]42\times 2.2 pounds=92.4 pounds[/tex]
Another conversion factor used:
1 stone = 14 pounds
[tex]1 pound = \frac{1}{14} stones[/tex]
[tex]92.4 pounds=92.4\times \frac{1}{14} stones=6.6 stones[/tex]
So, 42 kilograms is equal to 6.6 stones.
x ÷ 0.4 = 2 1/9 ÷ 3 1/6
x = __
Please Help!
X/0.4 = 10x/4
21/9÷31/6 = 21•6/31•9
so solving the equation gives
X=84/465
Answer:
Step-by-step explanation:
19/9÷19/6=2/3
then we have:
x÷0.4=2/3
×0.4. ×0.4
x=4/15
Boom shaka laka
26=−8/5y What is y? HELP ME PLZ
Answer:
exact form=-65/4
decimal form=-16.25
Step-by-step explanation: solve for y by simplifying both sides of the equation, then isolating the variable
The solution of expression is,
⇒ y = - 16.25
We have to give that,
An expression to simplify is,
⇒ 26 = - 8/5y
Now, We can simplify the expression as,
⇒ 26 = - 8/5y
Multiply by 5 on both sides,
⇒ 26 × 5 = - 8y
⇒ 130 = - 8y
⇒ - 8y = 130
Divide both sides by - 8,
⇒ y = - 130/8
⇒ y = - 16.25
Hence, the Solution is, y = - 16.25
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express 0.0346 as a fraction
173/5000, I'm not good with fractions but you might have to break it down or something? But that's 0.0346 as a fraction.
The equivalent value of the fraction is A = 346/10000
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the numerator of the fraction be p
where the value of p = 346
Let the denominator of the fraction be q
where q = 10000
Now , the fraction is A = p/q
On simplifying the expression , we get
So , the left hand side of the equation is equated to the right hand side by the value of p/q
A = 346 / 10000
A = 0.0346
On further simplification , we get
A = 0.0346
Therefore , the value of A = 0.0346 = 346/10000
Hence , the expression is A = 346/10000
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Why is the converse of the Pythagorean Theorem equally as important as the Pythagorean Theorem?
Answer:
They're equally as important because they are the same thing, but just meant for finding different sides.
Step-by-step explanation:
On the first day 60% of the 300 tickets were sold how many tickets were sold the day
Answer:
180
Step-by-step explanation:
60% of 300 tickets equals?
(60/100) * 300 = x
0,6 * 300 = x
180 = x
Answer:
180 tickets
Step-by-step explanation:
We want to find 60 percent of 300
Change 60 percent to a decimal
60% = .6
.6 * 300 = 180
84% of Astrid's books are fiction. What fraction of Astrid's books are fiction?
Answer:
[tex]\frac{21}{25}[/tex]
Step-by-step explanation:
If 84% are fiction, then the fraction of these are simply the percentage over 100:
[tex]\frac{84}{100}[/tex]
Simplified down by dividing by 4:
[tex]\frac{21}{25}[/tex]
Final answer:
To convert 84% to a fraction, divide 84 and 100 by their greatest common divisor, which is 4, resulting in the simplified fraction 21/25 representing the part of Astrid's books that are fiction.
Explanation:
To convert the percentage of Astrid's books that are fiction into a fraction, we simply write the percentage as a ratio out of 100 and then simplify it. Since 84% of her books are fiction, we start with the fraction 84/100. This fraction can be simplified by dividing both the numerator and the denominator by the greatest common divisor, which is 4 in this case.
84 ÷4 = 21
100 ÷ 4 = 25
Therefore, the simplified fraction of Astrid's books that are fiction is 21/25.
least common multiple 84 , 36, and 15
Answer:
1260
Step-by-step explanation:
The least common multiple is the smallest positive number which is a multiple of the two. This means 84, 36, and 15 divide into it evenly. To find the multiple:
We list the prime factors of each number.We note how many times each occurs.We multiply each factor the greatest number of times it occurs in a number.84: 2*2*3*7
36: 2*2*3*3
15: 3*5
LCM: 2*2*3*3*5*7= 1260
Which figures are quadrilaterals with at least one pair of parallel sides? Check all that apply. trapezoid rhombus parallelogram rectangle triangle square
Answer:
trapezoid rhombus parallelogram rectangle square
Step-by-step explanation:
It is easier to say that the triangle is the only one that does not apply. It only has 3 sides. The rest all have at least 1 set of parallel lines (trapezoid). The others have 2 sets of parallel lines.
Wrong !
The right response is :
All of the following except a trapezoid
Bess is trying to solve a puzzle where she has to figure out two numbers, x and y. The sum of twice x and 3 times y is less than 6. Also, y must be greater than 1 less than twice the x. Which graph represents the possible solutions? Graph the inequalities 2 x plus 3 y less than 6 and y greater than 2 x minus 1 Graph the inequalities 2 x minus 3 y less than 6 and y greater than 2 x minus 1 Graph the inequalities 3 x minus 2 y less than 6 and y greater than 3 x minus 2 Graph the inequalities 3 x minus 5 y less than 6 and y greater than 3 x plus 2
Answer:
The correct option is 1.
Step-by-step explanation:
Let the two numbers are x and y.
Condition 1: The sum of twice x and 3 times y is less than 6.
[tex]2\times x+3\times y<6[/tex]
[tex]2x+3y<6[/tex] ..... (1)
Condition 2: y must be greater than 1 less than twice the x.
[tex]y>2\times x-1[/tex]
[tex]y>2x-1[/tex] .... (2)
Therefore the graph of inequality (1) and (2) represent the all possible solutions.
Option 1 is correct. The graph of above inequality are shown below.
Answer:
the answer is A option 1
Step-by-step explanation: