a map is drawn to a scale of 1 cm to 250 cm.
(a) an airport has an area of 240 cm² on the map. find its actual area in km².​

Answer:

1.ED5 LOL

Step-by-step explanation:

Answer:

65

Step-by-step explanation:

The sum of the first 16 terms of an arithmetic progression (A.P) is 240

The sum of the next 4 terms is 220

The sum of n terms in an A.P is given by;

[tex]s_{n}[/tex] = n/2(2a + (n - 1)d)

240 = 8(2a + 15d) ... (i)

460 = 10(2a + 19d) .... (ii)

Simplifying this gives;

2a + 15d = 30 ... (i)

2a + 19d = 46 ... (ii)

Subtracting (i) from (ii) we get;

4d = 16

d (common difference) = 4

and a (first term) = (30 - 60)/ 2 = -15

The sequence upto 21 terms is here:

-15, -11, -7, -3, 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 51, 55, 59, 61, 65

So the next term (21^st term) is 65.

Answer:  a₂₁ = 65

Step-by-step explanation:

The Sum of an Arithmetic Progression is the sum of the first term plus the sum of the last term divided by 2 and multiplied by the number of terms.

[tex]a_1\ \text{is the first term}\\a_n=a_1+d(n-1)\quad \text{is the value of the nth term}\\\\[/tex]

Let's find the 16th term (n = 16)

[tex]a_{16}=a_1+d(16-1)\\\\.\quad =a_1+15d[/tex]

Now let's find the sum of the first 16 terms. This will be Equation 1:

[tex]S_{16}=\dfrac{(a_1)+(a_1+15d)}{2}\times 16=240\\\\\\.\qquad 8(2a_1+15d)=240\\\\\\.\qquad 2a_1+15d=30\qquad \leftarrow \text{Equation 1}[/tex]

************************************************************************************

Repeat what we did above for the next 4 terms (n = 17 to n = 20). This will be Equation 2:

[tex]a_{17}=a_1+d(17-1)\\\\.\quad =a_1+16d\\\\\\a_{20}=a_1+d(20-1)\\\\.\quad =a_1+19d[/tex]

[tex]S_{17-20}=\dfrac{(a_1+16d)+(a_1+19d)}{2}\times 4=220\\\\\\.\qquad 2(2a_1+35d)=220\\\\\\.\qquad 2a_1+35d=110\qquad \leftarrow \text{Equation 2}[/tex]

*********************************************************************************************

Now we have a system of equations. Solve using the Elimination Method:

2a₁ + 15d = 30   → -1(2a₁ + 15d = 30)     →    -2a₁ - 15d = -30    

2a₁ + 35d = 110  →  1(2a₁ + 35d = 110)    →     2a₁ + 35d = 110  

                                                                             20d = 80

                                                                                  d = 4

Input d = 4 into one the equations to solve for a₁:

Equation 1: 2a₁ + 15d = 30

                  2a₁ + 15(4) = 30

                    2a₁ + 60 = 30

                             2a₁ = -30

                               a₁ = -15

Given a₁ = -15 and d = 4, we can find the next term (n = 21)

[tex]a_n=a_1+d(n-1)\\\\a_{21}=-15+4(21-1)\\\\.\quad =-15+4(20)\\\\.\quad = -15+80\\\\.\quad = 65[/tex]

Answer:

The slower plane is flying at 175 miles per hour and complete the trip in 10 hours

The faster plane is flying at 250 Miles per hour and complete the trip in 7 hours

Step-by-step explanation:

Let s= speed of the slower plane s+75= speed of the faster plane

The time it takes the slower plane to make the flight = 1750/s

The time it takes the faster plane to make the flight is=1750/(s+75)

The difference in these two times is 3 hours

1750/s - 1750/(s+7)=3

{(s+75) / (s+75) * (1750/s)} - {(s/s) * (1750/s+75)} =3

(1750s+131250 / s^2+75s) - (1750s/s^2+75s) =3

1750s+131,250-1750s / s^2+75d =3

131,250 / s^2+75s = 3

Cross product

131,250=3(s^2+75s)

131,250=3s^2+225s

43,750=s^2+75s

s^2+75s-43,750=0

Solve the quadratic equation

x= -b +or- √b^2-4ac / 2a

a=1

b=75

c= -43750

x= -b +or- √b^2-4ac / 2a

= -75 +or- √(75)^2 - (4)(1)(-43750) / (2)(1)

= -75 +or- √(5625) - (-175,000) / 2

= -75 +or- √180625) / 2

= -75 +or- 425 / 2

x= -75 + 425/2 OR -75- 425/2

=350/2 OR -500/2

x=175 OR -250

We will ignore the negative sign because the planes are not flying Backward

The slower plane is flying at 175 miles per hour and complete the trip in 1750/175= 10 hours

The faster plane is flying at 250 Miles per hour and complete the trip in 1750/250= 7 hours

Answer:

243 m³

Step-by-step explanation:

The volume of a rectangular pyramid is given by:

[tex]V = \frac13lwh[/tex]

Where

l = length = 9m

w = width = 9m

h = height = 9m

so the volume is 1/3*9*9*9 = 243 m³

Answer:

243

Step-by-step explanation:

The formula for the volume of a square-based pyramid is

[tex]V=\frac{lwh}{3}[/tex]

[tex]l[/tex] = length

[tex]w[/tex] = width

[tex]h[/tex] = height

[tex]V=\frac{9 \times 9 \times 9}{3}[/tex]

[tex]V=\frac{729}{3}[/tex]

[tex]V=243[/tex]

The area is 243 cubic meters.

Answer:

Step-by-step explanation:

-y = -3x - 12

y = 3x + 12

y - 5 = 3(x - 2)

y - 5 = 3x - 6

y = 3x - 1

Answer:

4.625 gallons

Step-by-step explanation:

1. 11 pints plus 13 quarts is 18.5 quarts

2. 18.5 quarts is equal to 4.625 gallons

The number of gallons of ice cream he sold was equal to 4.625 gallons.

Unit means 'single entity', the fundamental constructing block. Usually, it is 1 in mathematics and science.

Thus, unit price of something is price of 1 thing.

Therefore suppose we're taking about price of mangoes, then unit price will denote the price of 1 mango.

We need to find the number of gallons of ice cream he sold.

A dealer sold 13 quarts containers and 11 pint containers of ice cream in one day.

1. 11 pints plus 13 quarts is 18.5 quarts.

2. 18.5 quarts is equal to 4.625 gallons.

Hence, The number of gallons of ice cream he sold was equal to 4.625 gallons.

Learn more about unit price here:

https://brainly.com/question/945712

#SPJ2

Answer:

3

Step-by-step explanation:

In Set A, the minimum is 4 and the maximum is 7 without X which would make the range 7 - 4 = 3 but we want the range to be 4, therefore X has to be 4 + 4 = 8. Unfortunately, this would then make the range of Set B 8 - 1 = 7 so X has to be the smallest number in Set A which would be 7 - 4 = 3.

Answer:

15√3

Step-by-step explanation:

This is a 30-60-90 triangle, so in order to solve for v, we can multiply the short leg by √3, which we will get 15√3.

Answer:

v = 25.98

Step-by-step explanation:

You could do this a number of ways. Some are much longer than others. The shortest way is to use the tangent.

Formula

Tan(theta) = opposite / adjacent

Givens

Theta = 30o

Opposite = 15 km

Adjacent = x

Solution

tan(30) = 15 / v                       Multiply both sides by v

v*tan(30) = 15                         Divide by tan(30)

v = 15/tan(30)

tan(30) = 0.5774

v = 15 / 0.5774

v = 25.98

Answer:

Step-by-step explanation:

Given the system of equations;

a) x+3y=9

-4x+12y=12

This equation is a linear simultaneous equation with 2 equations and two unknown values. When the number of equations given is equal to the number of unknown variables, this means that the solution sets of the equations are unique and real and will provide us with just one solution.

b) For the system of linear equation

2x-y-4=0 .... *3

6x=3y+12  ... *1

First lets multiply equation 1 by 3, om multiplying by 3 we will have;

6x-3y-12 = 0

6x-3y = 0+12

6x-3y = 12

Rearranging equation 2 will give;

6x - 3y = 12

It is seen that both equation ate the same. This means that what we have is one equation with two unknowns. For a system of equation with one equation and two unknowns, there will be infinite number of solutions after solving the equation. Hence, the number of solutions for this system of equation is INFINITE

Answer:  7.8 days

Step-by-step explanation:

Painter can get the job done in 15 days so gets [tex]\dfrac{1}{15}[/tex] of the job done in 1 day.

Coworker can get the job done in 10 days so gets [tex]\dfrac{1}{10}[/tex] of the job done in 1 day.

Together, they get [tex]\dfrac{1}{15}+\dfrac{1}{10}[/tex] of the job done in 1 day.

Painter worked for 3 days so completed [tex]\dfrac{1}{15}(3)=\dfrac{1}{5}[/tex] of the job.

That leaves a remaining of [tex]1-\dfrac{1}{5}=\dfrac{4}{5}[/tex] of the job to be completed.

Let x represent the number of days it will take them to work together.

Painter + Coworker = Together

[tex]\dfrac{1}{15}(x)\quad +\quad \dfrac{1}{10}(x)\quad =\quad \dfrac{4}{5}[/tex]

Multiply by 30 to eliminate the denominator:

[tex]\dfrac{1}{15}(x)(30) +\ \dfrac{1}{10}(x)(30) = \dfrac{4}{5}(30)[/tex]

Simplify and solve for x:

    2x + 3x = 24

            5x = 24

              [tex]x=\dfrac{24}{5}[/tex]

              x = 4.8

Remember that Painter worked 3 days alone in addition to the 4.8 days they worked together.

So the total time to paint the building is 3 + 4.8 = 7.8

Answer:

-100.204779...

or tenth to rounding, -100.2

Hope this helps!

//  Would you pick me Brainleist...?

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All you have to do is simplify.

[tex]1 ( \frac{4}{6} - 2 \sqrt{7}) ( \frac{4}{6} + 21)\\\\= \frac{130}{9} + \frac{-130}{3} \sqrt{7}[/tex]  (Decimal: -100.204779)

So the answer is : [tex]\frac{130}{9} + \frac{-130}{3} \sqrt{7}[/tex]

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

If I'm correct she bought 5 pounds of coffee.

Step-by-step explanation:

$70 (gift card)

-$26.80 (remainder on g.c.)

= $43.20 ($ spent on money)

$43.20/ $8.64 = 5

(remainder)/ cost per lb. = lbs of coffee bought

Answer: She bought 5 pounds of coffee

Step-by-step explanation:

This situation can be represent by the equation

70 - 8.64 x = 26.80  where x is the number of coffee she bought.   solve for x

-70                   -70

-8.64x = -43.20

x = 5

Answer:

           [tex]\bold{P(A) =\dfrac{11}{20}}[/tex]

Step-by-step explanation:

A - an occurrence that Steve encounters the green light

number of all counted ligths:    |Ω| = 20

number of counted green ligths:  |A| = 11

Probability that Steve encounters a green light on any given day:

[tex]P(A) = \dfrac{|A|}{|\Omega|}=\dfrac{11}{20}[/tex]

Answer:

The inequality that represents this situation is: [tex]140 + 45*n < p[/tex]

Step-by-step explanation:

Since the plane already had 140 pounds on board and "n" boxes will be loaded on it, then the weigh of each box multiplied by the number of box should be the extra cargo on the plane. This extra cargo added to the previous load must be less than the limit of cargo the plane can take as shown below:

[tex]140 + 45*n < p[/tex]

Answer:

not perpendicular

Step-by-step explanation:

perpendicular line has opposite reciprocal slope

√3x-2√3 y=13

-2√3y=13-√3x

y=-13/(2√3)+√3 x/2√3

y=1/2 x-13/2√3  ( slope is 1/2)

6x-3y+11=0

-3y=-11-6x

y=-11/-3+6x/3

y=2x+11/3 slope =2

Answer:

x^4-5x^2y^2+ 4y^4 = (x^2-4y^2)(x^2-y^2)

Step-by-step explanation:

Here in this question, we are to resolve the given expression into factors

x^4-5x^2y^2+ 4y^4

That can be rewritten as;

x^4-x^2y^2-4x^2y^2+4y^4

= x^2(x^2-y^2)-4y^2(x^2-y^2)

= (x^2-4y^2)(x^2-y^2)

Answer:

255 pounds.

Step-by-step explanation:

We can set up a proportion.

1 pound / 1.18 euros = x pounds / 300.9 euros

1.18 * x = 1 * 300.9

1.18x = 300.9

x = 255

255 pounds.

Hope this helps!

Answer:

300.90 € = £ 255

Step-by-step explanation:

£ 1 = 1.18 €

So,

1 € = £ 1/1.18

=> 1 € = £ 0.847

Multiplying both sides by 300.90 for getting the exchange rate of 300.90 euros

=> 300.90 € = £ 0.847 * 300.90

=> 300.90 € = £ 255

Answer:

A and C

Step-by-step explanation:

The line is at 3, and no number is within reach except 3. So the answer is A and C.

Answer: 0.28157

Step-by-step explanation:

Given, The proportion of the community favored building a police substation in their neighborhood: p= 0.75

Number of citizens are chosen: n= 10

Let x be the binomial variable that represents the number of citizens favor the building of the police substation.

Then, the probability that exactly 8 of them favor the building of the police substation will be :

[tex]P(x=8)=\ ^{10}C_8(0.75)^8(1-0.75)^2[/tex]

 [Using binomial probability function [tex]P(X=x)=^nC_xp^x(1-p)^{n-x}[/tex]]

[tex]=\dfrac{10!}{8!2!}(0.100113)(0.0625)\\\\=0.2815678125\approx0.28157[/tex]

Hence, the probability that exactly 8 of them favor the building of the police substation =0.28157

Answer:

625.

Step-by-step explanation:

(5+5×5÷5-5)⁵/5

=[ ( 5 + 25 / 5 - 5)^5] /  5

= [(5 + 5 - 5)^5] /  5

= [ (10 - 5)^5] /  5

= 5^5 / 5

= 5^4

= 625.

Answer:

625

Step-by-step explanation:

The rule is to do Parentheses/Brackets, then Exponents/Orders, followed by doing Multiplication and Division from left to right, and finally Addition and Subtraction from left to right. The answer is 625

Answer:

The answer is C.

Step-by-step explanation:

In order to find the solution of the linear equation, you have to find the coordinates where they intersect.

So according to the graph, both lines intersect at the coordinates of ( 0 , 1 ).

(Correct me if I am wrong)

Answer:

Ok, i cant drag the endpoints of the segment, but i can tell you how to do it.

First, we know that h(x) joins the points (1, -5) and (9, 1), then h(x) is a line:

h(x) = s*x + b

First, for a line that goes through the points (x1, y1) and (x2, y2), the slope will be:

s = (y2 -y1)/(x2 - x1)

Then in this case, the slope is:

s = (1 - (-5))/(9 - 1) = 0.75

Then we have

h(x) = 0.75*x + b

now, the value of b can be found as:

h(1) = -5 = 0.75*1 - b

b = - 5 - 0.75 = -5.75.

Then our equation is:

h(x) = 0.75*x - 5.75

Now, i gues you want to find the graph of:

y = h(-x)

Then our new function is:

g(x) = h(-x) =  -0.75*x - 5.75.

Now to find the points, we evaluate this function in the same values of x as before.

g(1) = -0.75*1 - 5,75 = -6,5

the point is (1, -6.5)

the second point is when x = 9.

g(9) = -0.75*9 - 5.75 = -12.5

The second point is (9, -12.5)

Answer:

(−6,7) (-1,-2)

Step-by-step explanation:

Khan

Answer:

$43.24

Step-by-step explanation:

First, find the amount of $ she deposited and spent separately.

She deposited 22 in her first week and then 38.5 on the next week. This is a total of $60.50.

The first week, she spent 7.27, then next week, 9.99. This means she spent a total of $17.26.

Second, subtract the total $ she spent from the amount she deposited.

$60.50 - $17.26 = $43.24

Answer:

she has $43.24 left in her bank account .

Answer:

c

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The perpendicular line bisect the base of isosceles triangle.

Then,

9^2=y^2-x^2

81=324-243

81=81

So the correct answer is D

I Hope this will be helpful for you

Answer:

$96.00

Step-by-step explanation:

Perimeter formula, 2w+2l

2(23)+2(25)=96 feet

1$ per foot

96 feet,

so $96

Answer:

I think it 96.00

Step-by-step explanation:

Answer: The Answer is C

Step-by-step explanation: I just took the quiz on ed and this is the correct answer.

Answer: C: the estimated amount of feed per day for the start of the farm

Step-by-step explanation: 100% on quiz

Answer:

No congruency statement can be made because the side lengths are unknown.

Step-by-step explanation:

We are given the measure of two angles in ∆XYZ, as 90 and 30 respectively. The 3rd angle can be known without being given. Since sum of angles in a triangle is 180°, the 3rd angle would be 180 - (90+30) = 60°.

Same applies to ∆TUV.

We only know the 3 angles of each triangle, but we are not given any of the side lengths. Therefore, we cannot make any congruency statement since the side lengths are unknown.

Answer:

A

Step-by-step explanation:

We know that (15, 11) (which means x = 15, y = 11) is a solution to Line Q so therefore:

11 = 4/3 * 15 + (k + 1)

11 = 21 + k

k = -10

Answer:

-10 = k

Step-by-step explanation:

y = 4/3x + ( k+1)

We know a point on the line is ( 15,11)

Substitute this point into the equation

11 = 4/3(15) + (k+1)

11 = 20 + k+1

Combine terms

11 = 21+k

Subtract 21 from each side

11-21 = k

-10 = k