An airplane leaves an airport and flies due west 150 miles and then 170 miles in the direction S 49.17°W. How far is the plane from the airport (round to the nearest mile)? (2 points) PLEASE HELP ASAP 30 POINTS!!!!!!! need full explanation and work

Answer:

(1, - 2 )

Step-by-step explanation:

Given the equations

3x - 4y = 11 → (1)

y + 3x = 1 ( subtract 3x from both sides )

y = 1 - 3x → (2)

Substitute y = 1 - 3x into (1)

3x - 4(1 - 3x) = 11 ( distribute and simplify left side )

3x - 4 + 12x = 11

15x - 4 = 11 ( add 4 to both sides )

15x = 15 ( divide both sides by 15 )

x = 1

Substitute x = 1 into (2) for corresponding value of y

y = 1 - 3(1) = 1 - 3 = - 2

solution is (1, - 2 )

Answer:

This means you would plug in g(x) into f(x).

Step-by-step explanation:

It would look like this:

[tex]3(x^{2} + 1) + 2[/tex]

Answer:

commutative properties

Answer:

Mr. Lim will have $2500

Step-by-step explanation:

Given:

The total amount of money which Mr. Lim, Mr. Tan and Mr. Chan is $8650;

Mr. Lim has $450 more than what Mr. Tan has;

Mr. Chan has double the amount of money than what Mr. Tan has.

Therefore, if we assume that the amount of money Mr. Tan has as x, then...

Total money = Mr. Tan + Mr. Lim + Mr. Chan

therefore,

8650 = x + (x + 450) + 2x

8650 = x + 2x + x + 450

8650 = 4x + 450

8650 - 450 = 4x

8200 = 4x

8200/4 = x

2050 = x

As we assumed earlier, x will be equal to the amount of money Mr. Tan has and the question is asking us how much money Mr. Lim has. To find this out, you have to add $450 to the amount of money Mr. Tan has which is $2050. This is because the question also gives us that Mr. Lim has $450 more that Mr. Tan.

I hope this helped you :)

Answer:

D

Step-by-step explanation:

Note that I will be using a, b, and y instead of their Greek counterparts.

First, we know that sin(c+d) = sin(c)cos(d) + cos(d)sin(a) and sin(c-d) = sin(c)cos(d) - cos(d)sin(a). We can apply these here to get

sin(b+y) = sin(b)cos(y) + cos(b)sin(y)

sin(b-y) = sin(b)cos(y) - cos(b)sin(y)

sin(a+y) = sin(a)cos(y) + cos(a)sin(y)

sin(a-y) = sin(a)cos(y) - cos(a)sin(y)

Plugging these into our equation, we get

(sin(b)cos(y) + cos(b)sin(y) - (sin(b)cos(y) - cos(b)sin(y)))

/

(sin(a)cos(y) + cos(a)sin(y)-(sin(a)cos(y) - cos(a)sin(y)))

=

2cos(b)sin(y) / 2cos(a)sin(y)

= cos(b)sin(y)/cos(a)sin(y)

= cos(b)/cos(a)

Next, we can see that a+b = π, so we can subtract b from both sides to get a = π -b. Plugging that in for a in our equation, we get

cos(b) / cos(π-b)

After that, we know that cos(c-d) = cos(c)cos(d) - sin(c)sin(d). Plugging that in here, we get

cos(π-b) = cos(π)cos(b) - sin(π)sin(b)

= -cos(b) + 0

= -cos(b)

Plugging that back into our equation, we get

cos(b) / -cos(b) = -1

Answer:

√2=1.414

then :√8 +2√32 +3√128+4√50

√8=√2³ =2√2

2√32=√2^5 = 4*2√2 = 8√2

3√128 = 3√2^6*2=8*3√2 =24√2

4√50 =4√5²*2= 20√2

add results : 2√2+8√2 +24√2+20√2=54√2

x=7-4√3

√x+ 1/√x

√(7-4√3) +1/√(7-4√3) =

(8-4√3)/√(7-4√3)

(8-6.93)/√(7-6.93) = 4 ( after rounded to the nearest whole number)

4 is your answer

Answer:

The term a⁴-3a²b²+b⁴ can't be factorised

Answer:

D.

Step-by-step explanation:

[tex]\frac{x^{2/3}}{y^{-3/4}}[/tex]

= [tex]x^{2/3}y^{3/4}[/tex]

= [tex]\sqrt[3]{x^2} * \sqrt[4]{y^3}[/tex]

So, D is your answer.

Hope this helps!

Answer:

B

Step-by-step explanation:

to draw arcs of a given size

Answer:

B. to draw arcs of a given size.

Step-by-step explanation:

its correct on plato :)

Answer:

[tex]\frac{(^3_1)*(^{37}_4)}{(^{40}_5)}[/tex]

Step-by-step explanation:

The total number of ways in which 5 specimens can be selected from the  dish at random is given as C(40, 5).

Since only one of the five specimens would have the trait, the number of ways of selecting the one specimen out of the 3 specimens with the trait is C(3, 1).

3 specimens have the trait therefore 37 specimens (40 - 3) do not have the trait. The number of ways in which the remaining 4 specimens out of the 5 spemimens that do not have the trait is C(37, 4).

Therefore, the probability that only 1 of the 5 specimens selected will have the trait = [tex]\frac{C(3,1)*C(37,4)}{C(40,5)} =\frac{(^3_1)*(^{37}_4)}{(^{40}_5)}[/tex]

Answer:

A. Total weight of the fruits is 2.25 kg

B. There are no more fruits left.

Step-by-step explanation:

A.

To get the total weight of the fruits, we will first of all have to sort out the fruits and multiply the weight of the fruits by the number available.

Weight of apples:

we have one 1apple weighing 1/2 kg. The weight will be 1 |X 1/2 = 1/2 kg

Weight of mangoes:

We have five mangoes weighing 1/4 kg. Total weight will be 5 X 1/4 = 5/4 kg

Weight of oranges:

We have one orange weighing 1/2 kg. Total weight will be 1X 1/2 = 1/2 kg

Total weight of the fruits will be total weight of Mangoes + oranges + apples

= 1/2 + 5/4 + 1/2 = 2.25kg

B.

If her family begins to eat off some portions of the fruits, we will have to calculate the sum total of all the weights of fruits eaten

The portion eaten will be 3/4 + (2 X 1/2) + 1/2 = 2.25kg

If this happens the family would have eaten all of the fruits because

the original weight present is only 2.25kg of fruits to start with

Answer:

6b^2 +4b

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh

A = 1/2 * (3b+2) * (4b)

    =1/2 (12 b^2 +8b)

   = 6b^2 +4b

Answer:

It's 5 which is A.

Step-by-step explanation:

1 mile = 5,280 feet

1 hour = 3600 seconds

3600/5280 = 0.681818 feet per second

25 ft per second x 0.681818 = 17.045 miles per hour

Round the answer as needed.

Answer:

The correct answer is 17.045 miles per hour.

Answer:

When x = -4 and y = -6, p = 37.75

Step-by-step explanation:

Given that p = x² - y²/x² + x·y, we have;

p = (x² × x² -y² + x·y×x²)/x²

p = (x²⁺² - y² + x¹⁺² × y)/x²

p = (x⁴ - y² + x³·y)/x²

Therefore, p in the simplest form is given as follows;

[tex]p = \dfrac{x^4 - y^2 + x^3 \cdot y }{x^2}[/tex]

To find the value of p when x = -4 and y = -6, we plug in the value of x and y into the above equation to get the following equation;

[tex]p = \dfrac{(-4)^4 - (-6)^2 + (-4)^3 \cdot (-6) }{(-4)^2} = 37.75[/tex]

Therefore, the value of p when x = -4 and y = -6 is equal to 37.75.

Answer: 254.34

Step-by-step explanation: 3.14(9*9)=254.34

Answer: 79

Concept:

Here, we need to understand the idea of evaluation.  

When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.

Solve:

Given information

10x² - 7x + 10

x = 3

Substitute the value into the expression

= 10 (3)² - 7 (3) + 10

Simplify by multiplication

= 10 (9) - 21 + 10

= 90 - 21 + 10

Simplify by subtraction

= 69 + 10

Simplify by addition

= 79

Hope this helps!! :)

Please let me know if you have any questions

Answer:

92

Step-by-step explanation:

The variable 'x' shows up twice in this expression.  Replace each instance of 'x' with 3:

10(3)^2 - 7(3) + 10  =  10(9) - 21 + 19  =  92

Answer:

∠ 2 = 70°

Step-by-step explanation:

∠ 13 and ∠ 14 are adjacent angles and sum to 180° , then

12x - 22 + 9x - 29 = 180

21x - 51 = 180 ( add 51 to both sides )

21x = 231 ( divide both sides by 21 )

x = 11

Then

∠ 14 = 9x - 29 = 9(11) - 29 = 99 - 29 = 70°

∠ 7 = ∠ 14 = 70° ( Alternate angles )

∠ 2 = ∠ 7 = 70° ( Alternate angles )

let other one be (x,y)

We know midpoint formula

[tex]\boxed{\sf (x,y)=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)}[/tex]

[tex]\\ \sf\longmapsto (6,-4)=\left(\dfrac{13+x}{2},\dfrac{-2+y}{2}\right)[/tex]

[tex]\\ \sf\longmapsto \dfrac{13+x}{2}=6[/tex]

[tex]\\ \sf\longmapsto 13+x=12[/tex]

[tex]\\ \sf\longmapsto x=12-13[/tex]

[tex]\\ \sf\longmapsto x=-1[/tex]

And

[tex]\\ \sf\longmapsto \dfrac{-2+y}{2}=-4[/tex]

[tex]\\ \sf\longmapsto -2+y=-8[/tex]

[tex]\\ \sf\longmapsto y=-8+2[/tex]

[tex]\\ \sf\longmapsto y=-6[/tex]

Answer:

(- 1, - 6 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] ) ← midpoint formula

Use this formula on the endpoints and equate to the coordinates of the midpoint.

let the other endpoint = (x, y) , then

[tex]\frac{13+x}{2}[/tex] = 6 ( multiply both sides by 2 )

13 + x = 12 ( subtract 13 from both sides )

x = - 1

[tex]\frac{-2+y}{2}[/tex] = - 4 ( multiply both sides by 2 )

- 2 + y = - 8 ( add 2 to both sides )

y = - 6

The coordinates of the other endpoint are (- 1, - 6 )

Answer:

  1.5

Step-by-step explanation:

We hope there is something in the context of this question that tells you this is a geometric sequence. If not, it is not possible to choose an appropriate answer.

__

Assuming a geometric sequence, the n-th term is found from the first term (a1) and the common ratio (r) to be ...

  an = a1·r^(n-1)

Using the given values, we can solve simultaneous equations to find a1 and r:

  a2 = 48 = a1·r^(2-1) = a1·r

  a5 = 6 = a1·r^(5-1) = a1·r^4

The ratio of these terms is ...

  a5/a2 = (a1·r^4)/(a1·r) = r^3

  6/48 = r^3 = 1/8

  r = ∛(1/8) = 1/2

__

To find the 7th term, we can make use of the fact that one term is related to the next by the common ratio. (We don't need to find a1.)

Then the 7th term is ...

  a7 = a1·r^(7-1) = a1·r^6 = (a1·r^4)·r^2 = a5·r^2

  a7 = 6·(1/2)^2 = 6/4 = 1.5 . . . . . . substitute for a5 and r

The 7th term is 1.5.

Answer:

18m

Step-by-step explanation:

6 times 3 = 18

Answer:

96 people were coming

Step-by-step explanation:

In this question, we want to determine the number of people who were coming to the party.

First of all, we were made to know that this number is between 50 and 100. So whatever figure we will be giving as answer will be something within that range.

We were told that if 8 or 12 people sat at a table, there would be no remainder left. So basically what we need to do here is to calculate the highest multiple of 8 and 12 which is between 50 and 100.

we could have 24, 48 and 96 as multiples of both. But that multiple that sits between 50 and 100 is 96. So therefore, our answer is 96.

Total weight required is half pound, so let the amount of cashews be [tex] a[/tex] , and amount of peanuts be $b$

$\therefore a+b=0.5$ (1)

And we want this to cost $2.80$

Cost of $a$ pound of cashews will be $5.50\times a$ and cost of $b$ pound peanuts will be $2.30\times b$

$\therefore 5.5a+2.3b=2.8$ (2)

Substitute $a=0.5-b$ from equation (1) in equation (2)

$5.5(0.5-b)+2.3b=2.8$

$\implies -3.2b=2.8+5.5\times0.5 $

$\implies -3.2b=0.05$

$b$ comes out to be negative. That means there's no solution with the given conditions.

I checked once , I don't think there's any mistake. Can someone else verify too?

EDIT

I verified all the given options from calculator, and no option gives 2.80

Answer:

a= Apple = 3

b= Banana =5

v= Lollypop=1

Step-by-step explanation:

36 is divided into 2 giving us 18

Let apple=a

Banana=b

Lollypop=c

In the first half

An apple + 3 bananas=18

a+3b=18 (1)

Second half is further divided into 2

That is,

18÷2=9

First half of the second half

3apples=9

3a=9 (2)

Second half of the second half

1 apple + 1 banana + 1 lollypop=9

a+b+c=9 (3)

a+3b=18 (1)

3a=9 (2)

a+b+c=9 (3)

From (2)

3a=9

Divide both sides by 3

a=9/3

a=3

Substitute a=3 into 1

a+3b=18

3+3b=18

3b=18-3

3b=15

Divide both sides by 3

b=15/3

=5

b=5

Substitute the value of a and b into (3)

a+b+c=9

3+5+c=9

8+c=9

c=9-8

c=1

Therefore,

a= Apple = 3

b= Banana =5

v= Lollypop=1

Answer:

√20 units.

Step-by-step explanation:

Please see attached photo for diagram.

The other leg of the triangle is x as shown in the attached photo.

Using the pythagoras theory, we can obtain the the value of x as follow:

x² = 4² + 2²

x² = 16 + 4

x² = 20

Take the square root of both side.

x = √20 units

Therefore, the value of the other leg x of the triangle is √20 units

Answer:

[tex]\sqrt{} 20[/tex] is your answer hope this helps

Step-by-step explanation:

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Answer:

8  4  2  1

1    1  0  1

[tex]13_{ 10} = 1101_{ 2 }[/tex]

Step-by-step explanation:

Answer:

y = - [tex]\frac{4}{3}[/tex] x + [tex]\frac{13}{3}[/tex]

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 )

y = [tex]\frac{3}{4}[/tex] x + 1 ← is in slope- intercept form

with slope m = [tex]\frac{3}{4}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{4} }[/tex] = - [tex]\frac{4}{3}[/tex] , thus

y = - [tex]\frac{4}{3}[/tex] x + c ← is the partial equation

To find c substitute (- 5, 11) into the partial equation

11 = [tex]\frac{20}{3}[/tex] + c ⇒ c = 11 - [tex]\frac{20}{3}[/tex] = [tex]\frac{13}{3}[/tex]

y = - [tex]\frac{4}{3}[/tex] x + [tex]\frac{13}{3}[/tex] ← equation of perpendicular line

The equation of the line that passes through (-5, 11) and perpendicular to y = (3/4)x + 1 is

y = -2x + 1

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

y = (2/4)x + 1 is in the form of y = m(2)x + c

So,

m(2) = 2/4 = 1/2

The equation of the line y = m(1)x + c is perpendicular to y = (2/4)x + 1.

So,

m(1) x m(2) = -1

m(1) = -1/(1/2)

m(1) = -2

Now,

y = -2x + c passes through (-5, 11).

This means,

11 = -2 x (-5) + c

11 = 10 + c

11- 10 = c

c = 1

Thus,

The equation of the line is y = -2x + 1.

Learn more about equation of a line here:

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