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in order to shift the 4 to the ones place, divide the given number 584,900 by 100. After dividing the the number 584,900 by 100, the new number is 584.900. It is clear that 4 is at ones olace.

So we have two planes flying toward each other. Let's use v for the speed of the slower plane. Then the speed of the faster plane is v+40. If we pass to the reference system of the slower plane we have that its speed is 0 and the speed of the other plane is v+v+40=2v+40. So basically we have a problem where one of the planes is stationary whereas the other approaches at 2v+40mph and it takes it 2 hours to travel 1180 miles. Remember that the speed is equal to the distance traveled divided by the time it took the plane to travel that distance. Then we get:

Then we get:

Then the speeds of the planes are 275mph and 315mph.

x = 7

9(11 - x) = 3(3x -9)

Expanding the expression:

9(11) - (9x) = 3(3x) -3(9)

99 - 9x = 9x - 27

collect like terms:

99 + 27 = 9x + 9x

126 = 18x

Divide both sides by 18:

126/18 = 18x/18

x = 7

Explanation:

5x - 4y + 2z = 21 ...equation 1

-x - 5y + 6z = -24 ....equation 2

-x - 4y + 5z = -21 ...equation 3

Using elimination method:

multiply equation 2 by 5:

-5x - 25y + 30z = -120 ....equation 2a

add equation 2a from 1:

5x - 5x -4y -25y + 2z + 30z = 21 - 120

0 - 29y + 32z = -99

-29y + 32z = - 99 ....equation 4

multiply equation 3 by 5:

-5x - 20y + 25z = -105 ...equation 3a

add equation 1 and 3a

5x - 5x - 4y - 20y + 2z +25z = 21 - 105

0 - 24y + 27z = -84

-24y + 27z = -84 ...equation 5

-29y + 32z = - 99 ....equation 4 (×-24)

-24y + 27z = -84 ...equation 5 (×-29)

696y - 768x = 2376 ...(4a)

696y -783x = 2436 ...(5a)

subtract 5a from 4a

696y - 696y -768x -(-783x) = 2376 - 2436

0 - 768x + 783x = -60

15x = -60

x = -60/15

x = -4

substitute for x in equation 4a:

696y - 768(-4) = 2376

696y + 3072 = 2376

696y = 2376 -3072

696y = -696

y = -696/696

y = -1

substitute for y in equation 4:

-29(-1) + 32z = -99

29 + 32z = -99

32z = -99 - 29

32z = -128

z = -128/32

z = -4

Given data:

The given equation of the line is y=-2x+8.

The slope of the given line is -2.

The slope of the line perpendicular to it is,

The standard equation of the line is,

Here, m is the slope of the line.

The second option can be written as,

Thus, option (B) is correct.

The graph as shown in the image is the correct graph of the function.

A function shows a mathematical relationship. We would need to look at the graph very closely so as to know weather or not the graph as it has been shown is the correct graph that is befitting of the function must be a straight line graph.

Clearly, the slope of the graph would be positive and beginning from the origin because the number of tickets that is sold is increasing just and the amount of the tickets is increasing. Thus the graph follows the general equation of a straight line; y = mx + c

All these goes to show that what we have befits the function.

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Solution

- The first integral is bounded by the x-values of [6, 22]

- The second integral is bounded by the x-values of [6, 14]

- When we are asked to find the difference between the two integrals, since, they both begin at 6, it implies that, when the second integral is taken away from the first integral, there must be some extra x-values.

- The extra values are from 14 to 22.

- Thus, we have:

Final Answer

The sequence is arithmetic because the common difference is 4.

Answer:

the sequence is arithmetic. the cd is 4

Step-by-step explanation:

1 + 4 = 5

5 + 4 = 9

9 + 4 = 13

Answer:

x = - [tex]\frac{5}{2}[/tex] , x = - [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

6x² + 23x + 20 = 0 ( factorise the left side )

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 6 × 20 = 120 and sum = 23

the factors are + 8 and + 15

use these factors to split the x- term

6x² + 8x + 15x + 20 = 0 ( factor the first/second and third/fourth terms )

2x(3x + 4) + 5(3x + 4) = 0 ← factor out (3x + 4) from each term

(3x + 4)(2x + 5) = 0

equate each factor to zero and solve for x

2x + 5 = 0 ⇒ 2x = - 5 ⇒ x = - [tex]\frac{5}{2}[/tex]

3x + 4 = 0 ⇒ 3x = - 4 ⇒ x = - [tex]\frac{4}{3}[/tex]

Answer:

======================

We can represent the quadratic equation in vertex or standard forms.

Vertex form:

Standard form:

Use the vertex form with given coordinates of the vertex:

Use the other point to find the value of a:

The equation is:

Convert it to standard form:

Answer:

[tex]y=-6x^2-12x+2[/tex]

Step-by-step explanation:

Vertex form of a quadratic equation:  

[tex]y=a(x-h)^2+k[/tex]

where (h, k) is the vertex.

Given:

Substitute the given values into the vertex formula and solve for a:

[tex]\implies 2=a(0-(-1))^2+8[/tex]

[tex]\implies 2=a(1)^2+8[/tex]

[tex]\implies 2=a+8[/tex]

[tex]\implies a=-6[/tex]

Substitute the vertex and the found value of a into the vertex formula, then expand to standard form:

[tex]\implies y=-6(x-(-1))^2+8[/tex]

[tex]\implies y=-6(x+1)^2+8[/tex]

[tex]\implies y=-6(x^2+2x+1)+8[/tex]

[tex]\implies y=-6x^2-12x-6+8[/tex]

[tex]\implies y=-6x^2-12x+2[/tex]

Therefore, the quadratic function in standard form whose graph has the given characteristics is:

[tex]y=\boxed{-6x^2-12x+2}[/tex]

Let us begin by illustrating the problem using a diagram:

Here we have represented the angle that the driveway makes with the horizontal to be x

Step 1: Label the sides as shown:

Step 2: Using the sides given, find the required angle

The formula that relates the angle, opposite side and hypothenuse side is:

Applying the formula:

Hence, it makes an angle of 7.3 degrees with the horizontal

In option A, if expression is simplify with out using associative property then addition of 4/9 and -2/9 is easy, as compare to addition 6 and 4/9. So no need to apply associateive property to option A.

In option B, 60 and 40 can be easily add as compare to 40 and -27 so this expression do not need to apply associative property.

In option C, the expression is easier to simplify if 5/2 and -1/2 is added, which is possible if associative is apply to the expression.

Thus option C use associative property to make the simplification easier.

Answer: Option C.

Solution

For this case we can verify the answer using the point x= 0 if we replace we got:

y=8 cos (pi/40* 0) = 8 cos (0) = 8

y= -8 sin (pi/40 *0)= -8 sin(0) = 0

y= -8cos(pi/40*0)= -8 cos (0)= -8

y= 8 sin (pi/40 *0)= 8 sin(0) = 0

Then the correct option would be:

y= -8cos(pi/40*0)

Answer:

y = (-1/8)x + (29/4)

Step-by-step explanation:

(10, 6), (2, 7)

(x₁, y₁)  (x₂, y₂)

       y₂ - y₁         7 - 6             1             -1

m = ------------ = ----------- = ----------- = ---------

       x₂ - x₁          2 - 10         -8              8

y - y₁ = m(x - x₁)

y - 6 = (-1/8)(x - 10)

y - 6 = (-1/8)x + (5/4)

   +6                 +6

-------------------------------

y = (-1/8)x + (29/4)

I hope this helps!

Answer

(3/8) × (1/5) = (3/40)

(6/10) × (3/4) = (9/20)

Explanation

We are asked to solve the given expressions

(3/8) × (1/5)

And

(6/10) × (3/4)

For (3/8) × (1/5)

For (6/10) × (3/4)

Hope this Helps!!!

Let's convert the given relationships into an equation.

Let's name the two number x and y.

The sum of the two numbers is 51: x + y = 51

One number is 15 more than the other: x = y + 15

Using the equations that we generated from the given relationships, let's determine the value of the two numbers by substitution.

Let's substitute x = y + 15 to x + y = 51.

Since we now get the value of y, y = 18, let's determine the value of x.

Therefore, the value of the two numbers is 18 and 33.

Confidence interval is written in the form,

(point estimate +/- margin of error)

The given scenario involves population proportion

The formula for the point estimate is

p' = x/n

where

p' = estimated proportion of success. p' is a point estimate for p which is the true proportion

x represents the number of success

n represents the number of samples

From the information given,

n = 74

x = 22

p' = 22/74 = 0.297

The formula for finding margin of error is expressed as

A) The point estimate is 0.297

B) margin of error = +/-3.1% = 3.1/100 = +/- 0.031

Thus,

the lower limit would be 0.297 - 0.031 = 0.266

Expressing in percentage, it is 0.266 x 100 = 26.6%

the upper limit would be 0.297 + 0.031 = 0.328

Expressing in percentage, it is 0.328 x 100 = 32.8%

Thus, the confidence interval is between 26.6% and 32.8%

Answer

Percent of students who did not pass the test = 77.8%

Explanation

The percent of an event is given as

For this question,

Percent of the event = Percent who did not pass the test = ?

Number of elements in the event

= Number of students who did not pass the test

= (Total number of students) - (Number of students who passed the test)

= 18 - 4

= 14

Total number of elements = Total number of students in the class = 18

Percent of students who did not pass the test

= (14/18) × 100%

= 0.778 × 100%

= 77.8%

Hope this Helps!!!

Answer:

Explanation:

By building a tree diagram we can find the theoretical probability of each number of heads when tossing three coins.

SOLUTION

Now from the question, if the die lands on 6, I win $6. So probability of landing on 6 is

Since I will pay $2 to play, we subtract this from $6 that we will win.

And probability of losing becomes

The table becomes

From the table the expected earnings is calculated as

Hence expected earnings is -$1

Based om the cost of the continuous belt conveyor kiln and the monthly payments, as well as the APR of the loan, the term this loan will be paid is 120 months or 10 years.

When given the cost of a loan, the APR, and the monthly payments, you can find out the term of the loan by using the NPER function on a spreadsheet.

The Rate would be:

= 6.3% / 12 months in a year

= 0.525%

The Pmt is the payment of $765.22. This amount should be in negatives.

The Present Value or Pv should be the loan amount of $68,000.

The term on the loan would then be 120 months which is 10 years.

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Sam would ride 18.125 miles when hw would ride at the rate of 14.5 miles/hour.

According to the question,

We have the following information:

Speed of Sam = 14.5 miles/hour

Distance to be covered = ?

Time taken to cover the distance = 1 hour and 15 minutes

Now, we will convert the time given in minutes into hour.

We have 15 minutes.

We know that 1 hour is equal to 60 minutes.

So, we will convert 15 minutes into hour:

15/60 hour

0.25 hour

So, the total time taken = (1 + 0.25) hour

Time taken = 1.25 hour

We know that the following formula is used to find the speed:

speed = distance/time

Distance = speed*time

Distance = 14.5*1.25

Distance = 18.125 miles

Hence, the distance covered by Sam in 1 hour and 15 minutes is 18.125 miles.

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Let w represent the cost of each wallet.

Let b represent the cost of each belt.

Last month, the company sold 56 wallets and 63 belts, for a total of $3,920. This means that

56w + 63b = 3920

This month, they sold 94 wallets and 22 belts, for a total of $3,230. This means that

94w + 22b = 3230

We would solve the equations by applying the method of elimination. To eliminate w, we would multiply the first equation by 94 and the second equation by 56. The new equations would be

5264w + 5922b = 368480

5264w + 1232b = 180880

Subtracting the second equation from the first, we have

5264w - 5264w + 5922b - 1232b = 368480 - 180880

4690b = 187600

b = 187600/4690

b = 40

Substituting b = 40 into 56w + 63b = 3920, we have

56w + 63(40) = 3920

56w + 2520 = 3920

56w = 3920 - 2520 = 1400

w = 1400/56

w = 25

Thus, the boutique charges $25 for each wallet and $40 for each belt

Part A

S(0) = 1116 - 4.04(0) (Replacing h=0)

S(0)= 1116 (Multiplying)

The answer is 1116 ft/s

Part B

S(10) = 1116 - 4.04(10) (Replacing h=10)

S(10) = 1116 - 40.4 (Multiplying)

S(10)= 1075.06

The answer is 1075.06 ft/s

Part C

S(30) = 1116 - 4.04(30) (Replacing h=30)

S(30) = 1116 - 121.1 (Multiplying)

S(30)= 994.9 (Subtracting)

The answer is 994.9 ft/s.

The formula to calculate the slope is

A is right

also, the slope can be calculated with rise and run

the correct formula is D.

and also apply E

the answer will be A,D and E

Answer:

902.75 cubic cm.

Explanation:

Given a can with:

• Height, h = 11.5 cm

• Diameter = 10 cm

A can is in the shape of a cylinder; and the volume of a cylinder is calculated using the formula:

First, find the radius by dividing the diameter by 2.

Next, substitute r=5, h=11.5 and π=3.14 into the formula given above:

The volume of the can is 902.75 cubic cm.

The equation of a line in Slope-Intercept form is:

Where "m" is the slope and "b" is the y-intercept.

Solve for "y" from the equation given in the exercise in order to write it in Slope-Intercept form:

You can notice that the equation has this form:

Where "b" is the y-intercept.

Then, it's a horizontal line, which means that its slope is:

Since it is a horizontal line, the lines perpendicular to that line is a vertical line, whose slope is undefined and whose equation is:

Where "k" is the x-intercept.

Knowing that the x-coordinate of any point on a vertical line is always the same, and knowing that this line passes through this point:

You can determine that the equation of the line is:

ANSWER:

The system can only be consistent and independent

STEP-BY-STEP EXPLANATION:

We have to:

• If a system has at least one solution, it is said to be consistent.

• If a consistent system has exactly one solution, it is independent.

• If a consistent system has an infinite number of solutions, it is dependent

• If a system has no solution, it is said to be inconsistent

We know that the system has 2 solutions, and we know that the system is only inconsistent when it has no solution, therefore the correct answer is:

The system can only be consistent and independent

Answer: C

Step-by-step explanation:

3x + 2 > x +8

= 3x + 2 -2 > x + 8 -2

= 3x > x + 6

= 3x - x > x - x + 6

= 2x/2 > 6/2

= x > 3

Answer:

C

Step-by-step explanation:

It is the only one that makes sense.

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