Evaulate and solve for the variable !

-2x + 3x - 5 = 6 - 21

Answer:

Time: 8 minutes

Altitude: 20000ft

Method 1 is easiest

Method 3 is easiest

Step-by-step explanation:

Given

Airplane 1:

[tex]Height = 44800 ft[/tex]

[tex]Descending\ Rate = 3100ft/min[/tex]

Airplane 2:

[tex]Ascending\ Rate = 2500ft/min[/tex]

Required

Determine when both planes would be at the same altitude?

Let the minute be represented by m

For Airplane 1, Its altitude at any height h is:

[tex]Airplane\ 1 = Height - Descending\ Rate * m[/tex]

It is minus (-) because the airplane is descending

[tex]Airplane\ 1 = 44800 - 3100 * m[/tex]

[tex]Airplane\ 1 = 44800 - 3100m[/tex]

For Airplane 2, Its altitude at any height h is:

[tex]Airplane\ 2 = Ascending\ Rate * m[/tex]

[tex]Airplane\ 2 = 2500 * m[/tex]

[tex]Airplane\ 2 = 2500m[/tex]

Method 1:

For both heights to be equal, we have that:

[tex]Airplane\ 1 = Airplane\ 2[/tex]

This gives:

[tex]44800 - 3100m = 2500m[/tex]

Collect Like Terms

[tex]44800 = 2500m + 3100m[/tex]

[tex]44800 = 5600m[/tex]

[tex]5600m = 44800[/tex]

[tex]m = 44800/5600[/tex]

[tex]m = 8\ min[/tex]

Hence, the time they will be at the same altitude is 8 minutes

Substitute 8 for m in

[tex]Airplane\ 2 = 2500m[/tex]

[tex]Airplane\ 2 = 2500 * 8[/tex]

[tex]Airplane\ 2 = 20000\ ft[/tex]

Hence, they will be at the same altitude at 20000ft

Method 2:

We have that:

[tex]Airplane\ 1 = 44800 - 3100m[/tex]

[tex]Airplane\ 2 = 2500m[/tex]

Since they are to be at the same altitude, then

The difference in their altitude must be 0

i.e.

[tex]Airplane\ 1 - Airplane\ 2 = 0[/tex]

This gives

[tex]44800 - 3100m - 2500m = 0[/tex]

[tex]44800 - 5600m = 0[/tex]

Collect Like Terms

[tex]5600m = 44800[/tex]

[tex]m = 44800/5600[/tex]

[tex]m = 8\ min[/tex]

Substitute 8 for m in

[tex]Airplane\ 1 = 44800 - 3100m[/tex]

[tex]Airplane\ 1 = 44800 - 3100 * 8[/tex]

[tex]Airplane\ 1 = 44800 - 24800[/tex]

[tex]Airplane\ 1 = 20000\ ft[/tex]

Method 3:

We have that:

[tex]Airplane\ 1 = 44800 - 3100m[/tex]

[tex]Airplane\ 2 = 2500m[/tex]

Since they are to be at the same altitude, then

The ratio of their altitudes must be 1

i.e.

[tex]\frac{Airplane\ 1}{Airplane\ 2} = 1[/tex]

[tex]\frac{44800 - 3100m}{2500m} = 1[/tex]

Cross Multiply

[tex]44800 - 3100m = 1 * 2500m[/tex]

[tex]44800 - 3100m = 2500m[/tex]

Collect Like Terms

[tex]44800 = 2500m + 3100m[/tex]

[tex]44800 = 5600m[/tex]

[tex]5600m = 44800[/tex]

[tex]m = 44800/5600[/tex]

[tex]m = 8\ min[/tex]

Substitute 8 for m in

[tex]Airplane\ 1 = 44800 - 3100m[/tex]

[tex]Airplane\ 1 = 44800 - 3100 * 8[/tex]

[tex]Airplane\ 1 = 44800 - 24800[/tex]

[tex]Airplane\ 1 = 20000\ ft[/tex]

Hence;

Their altitudes must be 20000ft

Though the three methods applied uses the same logic at some point, the first method applied is still the easiest and it is a straight forward method that could be applied in solving the question.

Method 3 is the most difficult.

Answer:

K=5

Step-by-step explanation:

12k-15=35+2k

12k=50+2k

10k=50

k=5

Answer:

[tex]k = 5[/tex]

Step-by-step explanation:

[tex]12k - 15 = 35 + 2k[/tex]

Our goal is to isolate k

[tex]12k - 15 = 35 + 2k\\\;\;\;\;+15 \;\;\;\;\;\;\; +15[/tex]

[tex]12k = 50 + 2k\\-2k \;\;\;\;\;\;\;\; -2k[/tex]

[tex]10k = 50[/tex]

Now we have k isolated to one side. Our final step is to have k be just k, no coefficient. We can do this by dividing each side by the coefficient.

[tex]\large\frac{10k}{10} = \frac{50}{10} \\\\10k\;\div\;10 = k\\50\;\div\;10 = 5\\[/tex]

[tex]\large\boxed {k \;=\;5}[/tex]

~[tex]InLoveWithPugs[/tex]

[tex]Moderator\\Math\ Enthusiast[/tex]

Answer:

D. -4

Step-by-step explanation:

The formula for calculating the slope of his indifference curve at his current consumption is expressed as:

M = -∆y/∆x

∆y is the change in y axis

∆x is the change in x axis

Since apples are put in the horizontal axis, ∆x = 20

Since banana are on the y axis, then ∆y = 80

Substituting the given values into the formula

M = -80/20

M = -8/2

M = -4

Hence the slope of his indifference curve at his current consumption is -4.

Option D is correct.

Answer:

3x - 2

Step-by-step explanation:

5x +1 -2x -3    Combine like factors with x

5x -2x = 3X

3x +1 -3         Combine like factors without x

1 -3 = -2

Answer:

what is it asking

Step-by-step explanation:

Answer:

49, 51, 53

Step-by-step explanation:

Let the first odd integer be n.

Then the consecutive odd integer will be (n+2).

This will be followed by (n+4).

We know that the sum of these three is 153. In other words:

[tex]n+(n+2)+(n+4)=153[/tex]

Solve for n. Combine like terms:

[tex]3n+6=153[/tex]

Subtract 6 from both sides:

[tex]3n=147[/tex]

Divide both sides by 3:

[tex]n=49[/tex]

Therefore, our first odd number is 49.

So, our consecutive numbers must be 51 and 53.

Hence, our sequence is:

49, 51, 53

Notes:

If we get an even number for n or a non-integer value, then there are no three consecutive odd integers that sum to 153.

Answer:

49, 51, 53

Step-by-step explanation:

All odd numbers:

49 + 51 = 100

100 + 53 = 153

Answer:

(a) 0.1325

(b) 0.4045

(c) 0.463

Step-by-step explanation:

Let X denote the number of defective transistors.

The proportion of defective transistors is, p = 4/11 = 0.364.

All the transistors are independent of the others.

The random variable X follows a binomial distribution.

(a)

Compute the probability that both transistors are defective, if 2 transistors are drawn from the box together as follows:

[tex]P(X=2)={2\choose 2}(0.364)^{2}(1-0.364)^{2-2}\\\\=1\times 0.132496\times 1\\\\=0.132496\\\\\approx 0.1325[/tex]

(b)

Compute the probability that neither transistors are defective, if 2 transistors are drawn from the box together as follows:

[tex]P(X=0)={2\choose 0}(0.364)^{0}(1-0.364)^{2-0}\\\\=1\times 1\times 0.404496\\\\=0.404496\\\\\approx 0.4045[/tex]

(c)

Compute the probability that one transistors are defective, if 2 transistors are drawn from the box together as follows:

[tex]P(X=1)={2\choose 1}(0.364)^{1}(1-0.364)^{2-1}\\\\=2\times 0.364\times 0.636\\\\=0.463008\\\\\approx 0.463[/tex]

Answer:

$11.29. $56.39 divided by 5, which is 20 percent, gives you around 11.287. Round up, and you get $11.29

Step-by-step explanation:

Answer:

11.278 Is the exact answer.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

If it is asking for the total of both then it should be 6 1/4

Step-by-step explanation:

I added 4 3/4 and 1 1/2

Answer:

-1 5/8

Step-by-step explanation:

Let the total amount in the bowl be x;

If on Day 1, the volume of water in the bowl decreases by 7/8 cup, the remaining water will be;

x - 7/8

If on day 2, the volume in the bowl decreases by 3/4 cup, the remaining volume of water after the second day will be;

= x - 7/8 - 3/4

= x - (7-2(3))/8

= x - (7+6)/8

= x - 13/8

This shows that the total change after the two days is -13/8

As a mixed fraction;

-13/8 = -1 5/8

Answer:

7/10>0.07

Step-by-step explanation:

You can turn 7/10 into decimal and its 0.7.

0.7 is greater than 0.07 so you would put a > sign

so the answer is 7/10>0.07

pls mark brainliest

Answer:(2 * 3, 1 * 3)

Step-by-step explanation:

Answer:

w+14,

Step-by-step explanation:

Answer:

The answer is "$3640.58"

Step-by-step explanation:

This question is incomplete, that's why we add another question in the attached file. Please find it.

P = [tex]\$ \ 1300[/tex] and effective per year is = interest rate per year = 7.2  

Total  [tex]\$ \ 1300[/tex] due after 8 years is P+PRT:

[tex]\to 1300(1+0.072 \times 8)\\\\\to 1300(1+ 0.576)\\\\\to 1300(1.576)\\\\\to \$ \ 2048.8[/tex]

[tex]\to Total \ X = \$ \ (7000-2048.8) \\\\[/tex]

[tex]= \$ \ 4951.2 \\\\= X(1 +0.072 \times 5)\\\\=1.36 X \\\\[/tex]

The number of dollars is X [tex]= \frac{4951.2}{1.36} = \$ \ 3640.58[/tex]

Answer:

[tex]-5x+5[/tex]

Step-by-step explanation:

[tex]5+2x-7x[/tex]

Combine like terms:

[tex]2x-7x+5\\[/tex]

which is

[tex]-5x+5[/tex]

Hope this helps :D

My Answers:

I think the equation you typed may have some typo error but:

Hope this helps and if you could mark me as brainliest. Thanks!

Answer:397.1....i think

Step-by-step explanation:

Answer:

397.1

Step-by-step explanation:

I used mental math

swear no calculator or work done

HOPE THIS HELPS

PLZZ MARK BRAINLIEST

Answer:

[tex]4.5\ \text{s}[/tex]

Step-by-step explanation:

t = Time taken

u = Initial velocity =17 m/s

v = Final velocity

s = Displacement

a = Acceleration

g = Acceleration due to gravity = 9.81 m/s² = a

[tex]v^2-u^2=2as\\\Rightarrow s=\dfrac{v^2-u^2}{2a}\\\Rightarrow s=\dfrac{0^2-17^2}{2\times -9.81}\\\Rightarrow s=14.73\ \text{m}[/tex]

Total height the rock is to fall when it is 8 meters from the ground is [tex]14.73+(31-8)=37.73\ \text{m}[/tex]

[tex]v=u+at\\\Rightarrow t=\dfrac{v-u}{a}\\\Rightarrow t=\dfrac{0-17}{-9.81}\\\Rightarrow t=1.73\ \text{s}[/tex]

Time taken to reach the maximum height is 1.73 s.

[tex]s=ut+\dfrac{1}{2}at^2\\\Rightarrow 37.73=0+\dfrac{1}{2}\times 9.81t^2\\\Rightarrow t=\sqrt{\dfrac{37.76\times 2}{9.81}}\\\Rightarrow t=2.77\ \text{s}[/tex]

Time taken from the maximum height to the point which is 8 m from the ground is 2.77 s.

So, time taken from the moment of the throw to the point 8 m from the ground is [tex]1.73+2.77=4.5\ \text{s}[/tex].

Answer:

388

Step-by-step explanation:

We need to find the area of the semicircle and parallelogram separately and then combine.

The formula for the area of a semicircle is 1/2(pi*r^2)

r = 12. 12^2 = 144

1/2(pi*144) = 226..1946711 which we can just round to 226

The formula for the area of a parallelogram is bh

b = 18, h = 9. 18*9 = 162.

226+162 = 388

Answer:

Step-by-step explanation:

total area = semi circle + parallelogram

                = (1/2 π 6²)  +  (9 x 18)

                = 56.55  + 162

                = 218.55 sq. units

.

Step-by-step explanation:

25) h=11

26). two sides are same = 12cm

27). time = 15 hours

28). veronica travelled = 6+1 = 7 days

29). number of tickets buyed by people each showing : 231

30) ©

Answer:

B) 55 cm

Step-by-step explanation:

it’s correct from EDGE

Answer:

David make his first error at Step 3

Step-by-step explanation:

We need to determine the error David made when finding the product of (-2.5)(-8.3)

He did the following steps

Step 1: (–2.5)(–8.3) = (–8.3)(–2.5)

Step 2: = (–8.3)(–2) + (–8.3)(–0.5)

Step 3: = (–16.6) + (–4.15)

Step 4: = –20.75

David made a mistake in Step 3

When we multiply (-1) with (-1) we get + instead of - sign. The correct step 3 would be:

Step 3: =(16.6)(4.15)

Step 4: =20.75

So, David make his first error at Step 3

Answer:

[tex][f(x)]^2-g(x) = 5x^2-13x-8[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 2x-2\\g(x) = -x^2+5x+12[/tex]

To find: [tex][f(x)]^2-g(x)[/tex]

First of all the square of first function f(x) will be found and then second function g(x) will be subtracted from the square of first function

Squaring the first function

[tex][f(x)]^2 = (2x-2)^2\\Using\ (a-b)^2 = a^2-2ab+b^2\\\[f(x)]^2 = (2x)^2-2(2x)(2)+(2)^2\\= 4x^2-8x+4[/tex]

Now subtracting g(x) from [f(x)]^2

[tex][f(x)]^2-g(x) = (4x^2-8x+4)-(-x^2+5x+12)\\\[f(x)]^2-g(x) = 4x^2-8x+4+x^2-5x-12[/tex]

Combining alike terms

[tex][f(x)]^2-g(x) = 4x^2+x^2-5x-8x+4-12\\\[f(x)]^2-g(x) = 5x^2-13x-8[/tex]

Hence,

Subtracting g(x) from the square of f(x) gives us:

[tex][f(x)]^2-g(x) = 5x^2-13x-8[/tex]

Answer:

c.) 2 1/3

Step-by-step explanation:

i know

Answer:

The volume of the cylinder is 900 cubic inches

Step-by-step explanation:

Given

Let V1 represent the volume of a cone and V2 represents the volume of a cylinder

[tex]V_1 = 300in^3[/tex]

Required

Determine the volume of a cylinder with same dimension

The volume of a cone is calculated as:

[tex]V_1 = \frac{1}{3}\pi r^2h[/tex]

The volume of a cylinder is calculated as:

[tex]V_2 = \pi r^2h[/tex]

Since, the cone and cylinder have the same dimensions, we can substitute [tex]\pi r^2h[/tex] for [tex]V_2[/tex] in [tex]V_1 = \frac{1}{3}\pi r^2h[/tex]

So, we have:

[tex]V_1 = \frac{1}{3} * V_2[/tex]

Multiply both sides by 3

[tex]3 * V_1 = \frac{1}{3} * V_2 * 3[/tex]

[tex]3 * V_1 = V_2[/tex]

[tex]V_2 = 3 * V_1[/tex]

Substitute [tex]300in^3[/tex] for [tex]V_1[/tex]

[tex]V_2 = 3 * 300in^3[/tex]

[tex]V_2 = 900in^3[/tex]

Hence, the volume of the cylinder is 900 cubic inches

Answer:

3 Letters Word: 6 Distinct Ways: 4 Letters Word: 24 Distinct Ways: 5 Letters Word: 120 Distinct Ways: 6 Letters Word: 720 Distinct Ways: 7 Letters Word: 5,040 Distinct Ways: 8 Letters Word: 40,320 Distinct Ways: 9 Letters Word: 362,880 Distinct Ways: 10 Letters Word: 3,628,800 Distinct Ways

Step-by-step explanation:

The number of ways in which the word 'PHILOSOPHY' can be arranged is 453,600.

The product of a whole number 'n' with every whole number until 1 is called the factorial. The factorial of 4 is, for example, 43221, which equals 24.

As we can see that the word 'PHILOSOPHY' has 10 letters therefore, the letters of the word can be arranged in the 10! manner, but it contains the letter P, H and O twice therefore, there will be words that will look the same and are counted twice. Thus, the number of ways the word PHILOSOPHY can be arranged are,

[tex]\text{Number of ways} = \dfrac{10!}{2! \times 2! \times 2!} = 453,600[/tex]

Hence, the number of ways in which the word 'PHILOSOPHY' can be arranged is 453,600.

Learn more about Factorial:

https://brainly.com/question/16674303