Two planes fly in opposite directions. One travels 450 mi/h and the other 550 mi/h. How long will it take before they are 4,000 mi apart? The planes must fly Answer hours before they will be 4,000 mi apart.

We have the following:

We subtract the equations:

for y:

therefore, the answer is:

(0,6) and (5,16), the option D.

Answer:

{2,4}

Explanation:

Given sets A and B defined below:

The set A Π B is the set of elements common to sets A and B.

Given:-

let

5x-4y=1 be the equation 1

-5x-10y=-15 be the equation 2

step 1-

add equation 1 and 2

we get=

-14y=-14

y=1

this is required value of y

we are going to put this value of y in equation 1

we get

5x-4(1)=1

5x-4=1

5x=1+4

5x=5

x=1

this is required value of x

hence value of x and y are(1,1)

1.

First, divide the figure into 3 different figures.

Find the area of each figure, and then add them:

A1 is a rectangle:

Area of a rectangle: Lenght x width

A1 = 8 x 5.3 = 42.4 in2

A2 is also a rectangle:

Lenght = 4

width = 8 - 5.3 = 2.7

A2 = 4 x 2.7 = 10.8 in2

A3 is a triangle:

Area of a triangle = (base x height) / 2

base = 2.7

Height = 8-4 = 4

A3= ( 2.7 x 4 ) / 2 = 5.4 in2

Total area = A1 + A2 + A3 = 42.4 + 10.8 + 5.4 = 58.6 in2

Answer = 58.6 in2

The given information is

Step-by-step explanation:

what is the problem ?

first you need to put "1" in place of the x and calculate, and then you need to put "2" in place of the x and calculate.

just simple calculation !

(a)

R(1) = 1000×1² / (1² + 4) = 1000 / 5 = 200

$200 million

(b)

R(2) = 1000×2² / (2² + 4) = 4000 / 8 = 500

$500 million

there ! that's all that was needed.

Given:-

To find:-

The function.

So the formula is,

So substituting we get,

So the value. we get,

Since the value of x is,

So the value,

Given:

Find-: Factor using the formula of the sum or difference of cube.

Sol:

Factoring sum and differences of cubs is:

Apply for the given information.

When 43/1/2 is divided by 1/1/4 , the value will be 34 4/5.

A fraction simply means a numbers that's represented as a/b where a = numerator and b = denominator

In this case, the division of the fraction will be:

43 1/2 ÷ 1 1/4

= 87/2 ÷ 5/4

= 87/2 × 4/5

= 174 / 5

= 34 4/5

This shows the. concept of fractions.

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we have

F(x) = x3 + 3x2 - 9x+5

solve by graphing

using a graphing tool

the figure in the attached image

REmember that the zeros

please wait a minute

the roots are -5 and 1

therefore

answer option C and F

Answer:

100 ounces of 12% solution and 60 ounces of the 20% solution.

Step-by-step explanation:

Let x ounces be the amount of 12% solution, then there will be 160-x ounces of the 20% solution.

So, we have the equation:

0.12x + 0.20(160 - x) = 0.15* 160

0.12x - 0.20x + 32 = 24

-0.08x = -8

x = 100.

So, it is 100 ounces of 12% solution and 60 ounces of the 20% solution.

Using the concept of Fraction, the weekly rate of Jake eating the cake is 11.2.

Fraction represents parts of a whole or group of objects. A fraction consists of two parts. The numerator is the number at the beginning of the line. It specifies the number of equal parts taken from the whole or collection. The number below the line is the denominator. It shows the total number of equal parts into which the whole is divided or the total number of identical objects in a collection.

We know that,

The cake is cut into 12 equal slices.

After 3 days Jake eats 5 slices then,

For 1 day = [tex]\frac{5}{3}[/tex]

= 1.6

Then for 7 days,

1.6 × 7 = 11.2

Hence, Jake's weekly rate of eating the cake is 11.2.

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The complete question would be

'A cake is cut into 12 equal slices. After 3 days Jake has eaten 5 slices. What is his weekly rate of eating the cake?'

Solve;

Therefore, x = -1

The domain of the given function corresponds to:

And the range of the function is:

The average rate of change of f over the interval [0,6] is:

According to the given data we have the following:

first linear function is defined by the equation 2x + 3y = 12

second linear function passes through the points (3,-2) and (-2, k)

the two linear functions have the same y-intercept

k?

To calculate k first we have to do the following:

we would have to use the formula y=mx +b

the two linear functions have the same y-intercept, therefore, b=12.

So, y=mx +12

As second linear function passes through the points (3,-2) we are going to substitue the x and y with 3 and -2.

So, -2=m*3+12

-2-12=m*3

-14=m*3

m=-14/3

m=-4

Finally we would calculate k by writiing the equation of the line that passes through each pair of points as follows:

y2-y1/x2-x1=m

So

So, k +2/-5=-4

k+2=20

k=20-2

k=18

The vertex of a quadratic function can be found by using the following expression:

Where "a" is the number multiplying x² and b is the number multiplying x. For this function a = -2 and b = 5. Applying these on the problem we have:

To find the y coordinate of the vertex we need to use the value for x that we found above. We have:

The ordered pair for this function's vertex is (1.25, 14.125)

We have the next inequalities

as we can see if we graph these inequalities we will obtain the next graph

where the red area is the first inequality and the blue area is the second inequality

and the area in purple is the solution set of the two inequalities

one coordinate point in the solution set could be (0,0)

We are told that there is one male snake, and the rest are female.

She needs one vitamin pill for every female snake.

1. If there are 10 snakes, this means that if one is male, the number of female snakes are:

Sine one vitamin pill is needed for each female snake, she would need 9 vitamin pills.

2. If there are 6 snakes, this means that if one is male, the number of female snakes are:

Sine one vitamin pill is needed for each female snake, she would need 5 vitamin pills.

3. If there are X snakes, this means that if one is male, the number of female snakes are:

Sine one vitamin pill is needed for each female snake, she would need (X-1) vitamin pills.

The torque at the end is equal to 45 Nm.

Torque can be defined as a measure of the amount of force which causes a physical object to rotate about an axis. This ultimately implies that, torque is a force which tends to cause the rotation of a physical object about an axis.

Mathematically, torque can be calculated by using this formula:

τ = Fd

Where:

In this scenario, we can reasonably infer and logically deduce that the torque at the end would be equal to 45 Newton meter (Nm) because the force was not applied over a perpendicular distance.

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0.8413 is the probability that a random selected firm will earn less than 112 million dollar

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.

Let X be a random variable represents the income of the firm in the industry

Hence

X~ N (mean =u= 95 , standard deviation= d =  17 )

We must determine the likelihood that a randomly chosen company will make fewer than 112 million dollars in earnings ie.

P(X<112) = P(X-u/d < 112-95/17)

Z=X-u/d = 112 - 95/17 = 1

P(X<112) = P(Z-1)=0.8413

Using the standard normal probability table.

P(X<112) = 0.8413

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We are given a tangent and a chord of a circle. The angle ABC form by the intersection of the tangent and the chord is half the arc they both intersect, therefore, we must find the major arc of the circle, we can do that with the fact that the total arc of the circle is 360, therefore:

Therefore, the angle is:

Angle ABC is 155 degrees.

The statement that reflects the running rates is Pepe ran 9/8  mile in 1/2 hour and Paul ran 19/24 mile in 1/3 of an hour.

Speed is the total distance run per time. It can be determined by dividing the total distance travelled by the total time.

Speed = distance / time

Speed if Paul ran 1/5 mile in 4/15 hour

Speed = 1/5 ÷ 4/15

1/5 x 15/4 = 3/4 miles per hour

Speed if Pepe ran 8/10 mile in 1/4 of an hour

Speed = 8/10 ÷ 1/4

8/10 x 4 = 16/5 = 3 1/5 mile per hour

Difference in speeds =

[tex]3\frac{1}{5}[/tex] - [tex]\frac{3}{4}[/tex]

[tex]3\frac{4 - 15}{20}[/tex] = [tex]2\frac{9}{20}[/tex]

Speed if Paul ran 4/15 mile in 1/5 hour

Speed = 4/15 ÷ 1/5

4/15 x 5 = 4/3 = 1 1/3 miles per hour

Speed if Pepe ran 1/4 mile in of 8/10 an hour

Speed = 1/4 ÷ 8/10

1/4 x 10/8 = 5 / 16

Difference in speeds = [tex]1\frac{1}{3} - \frac{5}{16}[/tex] = [tex]1\frac{1}{48}[/tex]

Speed if Paul ran 1/3 mile in 19/24 hour

Speed = 1/3 ÷ 19 / 24

1/3 x 24/19 = 8/19 miles per hour

Speed if Pepe ran 1/2 mile in of 9/8 an hour

Speed = 1/2  ÷ 9/8

1/2 x 8/9 = 4/9 mile per hour

Difference = 4/9 - 8/19 = 4/171

Speed if Pepe ran 9/8  mile in 1/2 hour

Speed = 9/8 ÷ 1/2

9/8 x 2 = 2 1/4  miles per hour

Speed if Paul ran 19 / 24 mile in of 1/3 an hour

Speed =  19 / 24  ÷ 1/3

19 / 24 x 3 = 2 3/8 miles per hour

Difference =

[tex]2\frac{3}{8} - 2\frac{1}{4}[/tex]

[tex]\frac{3 - 2}{8}[/tex] =  [tex]\frac{1}{8}[/tex] miles per hour

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Answer:

d. 10, 24, 26

Explanation:

To identify the side lengths that form a right triangle, we check if it satisfies the Pythagorean theorem.

By the theorem:

a. 12, 13, 16

These side lengths do not form a right triangle.

b. 15, 20, 21

These side lengths do not form a right triangle.

c. 9,40,42

These side lengths do not form a right triangle.

d. 10, 24, 26

These side lengths form a right triangle since both sides of the equation are the same.

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

8x - 3x + 4x = -36

x = ?

Step 02:

We must apply the algebraic rules to find the solution.

8x - 3x + 4x = -36

12x - 3x = - 36

9x = - 36

x = - 36 / 9

x = - 4

The answer is:

x = - 4

Given the Venn diagram in the question, we can proceed to answer the questions as follow

Question B

Y= members of subset Y

Y =2,4,6, and 8

Question C

U means that we should list all elements in the universal set

U = ALL members of the set

U = 1,2,3,4,5,6,7,8, and 9

Question D

This is the union of both sets X and Y. This means we will list all the members that are found in the 2 subsets

Question E

Question F

X' means that we should find all members of the set except that of X

Question G

X\Y means that we should list the elements of X that are not found in Y

X\Y= 1,3, and 5

Question H

Y\X means that we should list the elements of Y that are not found in X

Y\X= 6, and 7

Question I

To solve (XnY)' we will follow the steps below

Step 1: Find (XnY)

Step 2: Find (XnY)'

Given the expression

reduce the square root of

There is no square root for the negative number

so, this is represent a complex number

So,

Answer

D. Observations of constellations show that stars have moved over time.

Explanation:

A scientific claim is basically an observation in science.

Constellation changes there position over time because of earth's rotation around sun. So, observation of constellations shows that stars have moved over time is a scietific claim. If stars would not move then constellation will not form.

To calculate the combinations of groups of 2, since the order doesn't matter, we can use combination. In this case we have a total of 75 to choose from and will choose 2, so this is "75 choose 2".

The equation to use is (n choose k):

In this case, we have n = 75 and k = 2, so:

For the property of factorials, 75! / 73! = 75*74, because the terms less or equal 73 cancel out. so:

So, there are 2775 different groups of 2 in this case.

Another way of doing this calculation is by thinking of choosing one at a time.

At first, we can choose from 75 possible people, so we start at 75.

When we choose the second one, we already picked the first, so there are only 74 people left. So we get:

This are the two first people, but, in this way we are considering too many groups, since here we considere the order matter, to fix this we divide by k!, where k is the number of picks, which is 2 in this case (so, permutation of 2). So:

The equation for the translated function is:

g(x) = |x + 4|

For a function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N)

Here we have:

f(x) = |x|

And the translation is of 4 units to the left, so the translated function is:

g(x) = f(x + 4) = |x + 4|

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