A helicopter landing pad has a length of 80 ft and a width of 50 ft. A safety zone
of uniform width, which is not to be entered during landing, surrounds the landing
pad. The landing pad and safety zone together have a combined area of 10800 ft2,
what is the uniform width (safety zone) around the landing pad?
Answer:
uniform width around the landing pad = 9.41 feet
Step-by-step explanation:
Length of landing pad = 80 ft
width of landing pad = 50 ft
Length of safety zone = (80 + 2w)
width of safety zone = (50 + 2w)
Total area = 10800 [tex]ft^{2}[/tex]
Area of landing pad = length x width
= 80 x 50
= 4000 [tex]ft^{2}[/tex]
Area of landing pad = 4000 [tex]ft^{2}[/tex]
Thus,
area of safety zone = total area - area of landing pad
= 10800 - 4000
= 6800
area of safety zone = 6800 [tex]ft^{2}[/tex]
But,
area of safety zone = length x width
6800 = (80 + 2w) x (50 + 2w)
6800 = 4000 + 160w + 100w + 4[tex]w^{2}[/tex]
divide through by 4,
1700 = [tex]w^{2}[/tex] + 65w + 1000
⇒ [tex]w^{2}[/tex] + 65w + 1000 - 1700 = 0
[tex]w^{2}[/tex] + 65w -700 = 0
Applying the quadratic formula,
w = (-b ± [tex]\sqrt{b^{2} -4ac}[/tex]) ÷ 2a
a = 1, b= 65 and c = -700
w = (-65 ± [tex]\sqrt{(65)^{2}-(4*1*-700) }[/tex]) ÷ 2
= (-65 ± [tex]\sqrt{7025}[/tex]) ÷ 2
= (-65 ± 83.82)÷ 2
w = (-65 + 83.82) ÷ 2 OR (-65 - 83.82) ÷ 2
= 18.82 ÷ 2 OR -148.82 ÷ 2
= 9.41 OR -74.41
Thus, w = 9.41 ft.
3^-7
Simplify please.
Answer:
0.000457 what I got
Step-by-step explanation:
would it be linear or nonlinear?
Find the least common multiple of the set of numbers
8,9
The least common multiple of 8 and 9 is____?
Answer:
72
Step-by-step explanation:
plz mark brainliest :D
Simplify 2x + 1 -x + 2.
Answer:
x+3
Step-by-step explanation:
Hope you have a good day, Loves!
Also if I'm right can you let me know please?
Also Also if I am right can I please have Brainliest??
(How in the hecc are three people answering this?)
a recipe for sparking grape juice calls for 1 1/2 quarts of sparking water and 3/4 quarts of grape juice. how much sparking water would you need to mix with 9 quarts of grape juice?
Answer:
you would need 18 quarts of sparkling water to mix with 9 quarts of grape juice
Step-by-step explanation:
1 1/2 is double of 3/4 so you just need to double 9 quarts of grape juice
Answer:
18 quarts of sparkling water
Step-by-step explanation:
9÷0.75=12 to figure how many times the recipe is multiplied.
12x1.5=18 to figure out how much sparkling water
3/4 = 0.75
1 1/2 = 1.5
What is the solution to the system of equations?
-4y – 3x = -11
x – 2y = 17
Answer:
Step-by-step explanation:
Carter is going to invest $210 and leave it in an account for 5 years. Assuming the interest is compounded annually, what interest rate, to the nearest tenth of a percent, would be required in order for Carter to end up with $250?
Answer:360
Step-by-step explanation:g-g5
The rate of interest will be 0.35.
What is compound interest?
Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.
Compound interest formula[tex]CI = P(1+\frac{r}{n}) ^{nt} -P[/tex]
and, the Amount is given by
[tex]A = P(1+\frac{r}{n} )^{nt}[/tex]
Where,
A is amount
P is principal
r is rate of interest
n is number of times interest is compounded per year
t is time
According to the given question
Principal, P = $210
Amount, A = $250
Time, t = 5 years
n = 1
Therefore, the interest rate is given by
Amount = [tex]P(1+\frac{r}{n}) ^{nt}[/tex]
⇒[tex]250 = 210(1+\frac{r}{1}) ^{5}[/tex]
⇒[tex]\frac{250}{210} =(1+r)^{5}[/tex]
⇒[tex]1.19 = (1+r)^{5}[/tex]
⇒[tex]\sqrt[5]{1.19} = 1+r\\[/tex]
⇒ 1.035 = 1 + r
⇒ r = 1.035 - 1
⇒ r = 0.35
Hence, the interest rate is o.35.
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Any way someone has a step by step process to solve for x?
-2x+9=21
-2x + 9 = 21
Step 1: subtract 9 from both sides.
-2x = 12
Step 2: divide both sides by -2.
X = -6
Given the function f(x)=-x^2-5x+12f(x)=−x 2 −5x+12, determine the average rate of change of the function over the interval -5\le x \le 4−5≤x≤4.
Given:
The function is
[tex]f(x)=-x^2-5x+12[/tex]
To find:
The average rate of change of the function over the interval −5 ≤ x ≤ 4.
Solution:
The average rate of change of a function f(x) over the interval [a,b] is
[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]
Putting x=-5 in the given function, we get
[tex]f(-5)=-(-5)^2-5(-5)+12[/tex]
[tex]f(-5)=-25+25+12[/tex]
[tex]f(-5)=12[/tex]
Putting x=4 in the given function, we get
[tex]f(4)=-(4)^2-5(4)+12[/tex]
[tex]f(4)=-16-20+12[/tex]
[tex]f(4)=-24[/tex]
Now, the average rate of change of the function over the interval −5 ≤ x ≤ 4 is
[tex]m=\dfrac{f(4)-f(-5)}{4-(-5)}[/tex]
[tex]m=\dfrac{-24-12}{4+5}[/tex]
[tex]m=\dfrac{-36}{9}[/tex]
[tex]m=-4[/tex]
Therefore, the average rate of change of the function over the interval −5 ≤ x ≤ 4 is -4.
Divide. 0.996 ÷ 0.12
Answer:
8.3
Step-by-step explanation:
Answer:
- 0.996 - Percentage increase =
- 0.996 - (12% × - 0.996) =
- 0.996 - 12% × - 0.996 =
(1 - 12%) × - 0.996 =
(100% - 12%) × - 0.996 =
88% × - 0.996 =
88 ÷ 100 × - 0.996 =
88 × - 0.996 ÷ 100 =
- 87.648 ÷ 100 =
- 0.87648 ≈
- 0.88
Step-by-step explanation:
pls brainlsit
Which rule describes the pattern for the table's Input and Output values?
A. add 2
B. add 10
C. subtract 7
D. divide by 2
PLEASE HELP I WILL MARK YOU BRAINLIEST!
answer:
a.add 2
Step-by-step explanation:
A function rule describes how to convert an input value (x) into an output value (y) for a given function. An example of a function rule is f(x) = x^2 + 3. A function table is another name for an input-output table, a table that shows how a value changes according to a rule.
Which system of inequalities has no solution?
A. y < 2x − 44
y > 2x + 1
B. 2x + y ≥ 3
y ≥ −2x − 3
C. 4x + 4y < 16
x > y + 16
D. y < −6x −24
y < 6x + 6
Answer:
My answer is letter d
Step-by-step explanation:
Sorry when im wrong
Answer:
B
Step-by-step explanation:
GRRRHRGR H.C DGDVFVDVECDEC
help plzz WILL MARK BRAINLIST
Answer:
224
Step-by-step explanation:
Given
f(x) = 4x² - 4x
f(-7) = 4 * (-7)² - 4 * (-7)
= 196 + 28
= 224
Hope it will help :)
Expressions that simlify to the same expression are called
Answer:
Eqivelent expressions
Step-by-step explanation:
also dis
Is a bucket used to carry water more likely to have a capacity of a pint or a gallon
Answer:
well it depends on the size of the bucket but some buckets may be a gallon but then some are bigger id-k if this makes sense im srry
Step-by-step explanation:
what is the domain of the relation
Answer:d I believe
Step-by-step explanation:
14 less than twice a number is equal to 4 times the number decreased by 38
Answer:
14-2x=4*2x-38
Step-by-step explanation:
- 6(x + 2) = 30
- 6(x + 2) = 30
- 6x + (- 12) = 30
The solution is -
Answer:
-7
Step-by-step explanation:
Choose all the numbers that 135 is divisible by.
Answer:
1, 3, 5, 9, 15, 27, 45, 135.
Step-by-step explanation:
Answer:
The factors of 135 are 1, 3, 5, 9, 15, 27, 45, 135
The two trapezoids below are similar. What is the length of EF?
Answer:
x/24 = 7.5/30
30x = 180
________
30
x= 6
The length of EF in given trapezoid is 6 cm
What is trapezoids ?Trapezoids are quadrilaterals that have two parallel sides and two non-parallel sides. It is also called a Trapezium. A trapezoid is a four-sided closed shape.
a pair of opposite sides are parallel.
diagonals of trapezium bisect each other.
sum of all four angles of trapezium is = 360°
it has four unequal sides.
diagonals are congruent.
opposite side of an isosceles trapezium are congruent.
According to the question
Trapezoids ABCD and EFGH are similar,
Hence, corresponding sides ratio are equal
Thus, AB/EF = DC/HG
24/x = 30/7.5
30x = 180
x = 180/30
x= 6
Hence, The length of EF is 6 cm
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Use distributive property to write an equivalent expression. Use paper and pencil to
work the problems out, and then check your answers once you have submitted the
practice. (Answers will be in the bubbled comments after the problem.)
A. 6 Gn+2)
B.p(4p +9)
C. 5r (r + 4
Answer:
A) 6Gn + 12 (or 6n+12, if that’s what you meant)
B) 4p²+9p
C) 5r²+20r
Step-by-step explanation:
A. If you meant 6(n+2)...
Multiply 6 by n and also 6 by 2:
6n + 12
B. Multiply p by 4p and also p by 9
4p²+9p
C. Multiply 5r by r and also 5r by 4
5r²+20r
Hope this helped!
20 = -d + 6
A. -17
B. 7
C. 14
D. -14
Answer:
Its D. -14
Step-by-step explanation:
Can anyone please help me out? I have to find the Greatest Common Factor for each, thank you!
Answer:
1= 4x^2
2= 5b^4
3= 3u^2v^2w
4= 7
5= bc^3d^6
Note: ^ stands for exponents
d: 11
A food company is designing boxes for several products. Each box is a rectangular prism.
15
The company makes a single serving cereal box that contains 1.2 ounces of cereal. They plan to make an extra large box for school
cafeterias. The extra large box will be a dilation of the single serving box using a scale factor of 4. How many ounces of cereal will
the extra large box contain?
I need step by step
How many ounces of cereal will the extra large box contain is 76.8 ounces.
Number of ounces of cereal?Using this formula
Number of ounces of cereal=Number of ounces×Scale factor
Let plug in the formula
Number of ounces of cereal=1.2×4×4×4
Number of ounces of cereal=1.2×64
Number of ounces of cereal=76.8 ounces
Therefore how many ounces of cereal will the extra large box contain is 76.8 ounces.
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two coins are tossed at the same time. what is the probability they both land on tails?
Answer:
1/3
Step-by-step explanation:
Answer:
Step-by-step explanation:
30%
“Twelve less than a number.”
Which is more, 1,179 grams or 1 kilogram?
Answer: 1,179
Step-by-step explanation: because 1 kilogram = 1000 grams so the grams are more
Answer:
1,179 is more
Step-by-step explanation:
bcoz if we convert everything to kg then 1179 is 1.179kg
15. Mr and Mrs Thomas buy tickets for themselves and their four children.
The cost of an adult ticket is $7 more than the cost of a child ticket
The total cost of the six tickets is 586
Work out the cost of an adult ticket
Answer:
$102.33
Step-by-step explanation:
586= 4t + 2(t+7)
586= 4t +2t +14= 6t +14
572= 6t
95.33=t
adult ticket = t +7
Craig is training for a race. He bikes every 2 days and swims every 3 days. If he biked and swam today, how many days will pass before he bikes and swims on the same day again, the least common multiple of the numbers of days?
Multiples of 2: 2, 4, 6, 8, 10, 12, . . .
Multiples of 3: 3, 6, 9, 12, 15, 18, . . .
2 days
3 days
6 days
12 days
Answer:
12 is the right answer
Step-by-step explanation: