Solve √5r - 9 - 3 = √r +4-2

The speed of the airplane is 360 km/h while the speed of the wind is 40 km/h.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let a represent the speed of the airplane and b represent the speed of the wind, hence:

(a + b)6 = 2400  

a + b = 400     (1)

Also:

(a - b)7.5 = 2400

a - b = 320   (2)

From eqn 1 and 2:

a = 360 km/h, b = 40 km/h

The speed of the airplane is 360 km/h while the speed of the wind is 40 km/h.

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The distance of the cruise liner from me 20 seconds later will be; 2600ft.

a) Since, the speed of the liner is 30ft/sec, it follows that after 20secs, the liner would cover; (30×20)ft = 600ft more; and consequently, the distance is now; √(2000²+600²) = ft.

b) For the boat to be 2500 ft away given the speed 30ft per sec; Time taken = 2500/30 = 83.3seconds. Hence, the boat will be more than 2500 feets away after 2 minutes.

c) If the boat's distance is 2000ft from me; it follows that the distance covered is 10 seconds is; √(2000²-1500²) = 1322.9ft

Hence, the speed to attain this distance is; 1322.9/10 = 132.29ft/sec.

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Answer:

0.4 pages per minute

Step-by-step explanation:

40/100 = .4

In AON networks, "node" is a point where one or more lines (arrows) begin or terminate, commonly used for depicting an event or activity.

Scheduling logic diagrams of the most fundamental kind. Any activity on the schedule that has no float; Total Float = 0; is considered a critical activity.

Between the project's start and finish, there are vital activity(s) that must be completed continuously. This is known as the critical path.

The importance of AON diagram are-

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Answer:

1000.

Step-by-step explanation:

We need 4 weights where 3 of them add up to

900, 1400, 1600 or 1800g.

Not sure of the method for doing this!

Lets assume that the answer is 1000 g.

Then the  3 that make 1800 could be

1000 500 and 300

- then to make 900 we need a 100g tomato giving:

1000 500 300 and 100 grams

So the 1400 will be the 1000, 300 and 100 tomato

and the 1600 will be 1000, 500 and 100.

That seems to fit !!

By definition of surface area, the composite figure reports an area of 233.6 square centimeters.

In this question we need to determine the surface area of a composite figure, which is the sum of all the areas of the faces, which are combinations of triangles and quadrilaterals. Now we proceed to calculate the surface area:

A = 2 · (6 cm) · (3 cm) + 2 · (8 cm) · (6 cm) + 2 · (8 cm) · (3.6 cm) + 2 · (8 cm) · (2 cm) + 4 · (1/2) · (3 cm) · (2 cm)

A = 233.6 cm²

By definition of surface area, the composite figure reports an area of 233.6 square centimeters.

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The true statement for h regarding the function is  that C. h(2) = 16.

From the information given, the function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25.

This illustrates that the range or h has to be less than or equal to 25.

The option that correctly fits this is C.

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Using it's concept, any function with domain [tex]x \geq 0[/tex] has the same domain as [tex]y = 2\sqrt{x}[/tex].

The domain of a function is the set that contains all possible input values for the function.

Function [tex]y = 2\sqrt{x}[/tex] is defined for [tex]x \geq 0[/tex], hence any function with domain [tex]x \geq 0[/tex] has the same domain as [tex]y = 2\sqrt{x}[/tex].

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Answer: 9

Step-by-step explanation:

[tex]\frac{2}[3}=\frac{6}{DE}\\\\\frac{3}{2}=\frac{DE}{6}\\\\DE=9[/tex]

Answer:

77 m (nearest metre)

Step-by-step explanation:

Angle of Elevation

If a person stands at a point and looks up at an object, the angle between their horizontal line of sight and the object is called the angle of elevation.

To find how tall the flagpole is, model as a right triangle and solve using the tan trigonometric ratio.

Tan trigonometric ratio

  [tex]\sf \\tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given information:

Therefore:

As the person is 1.6 m tall, we model the line of sight as 1.6 m above ground level.  Therefore, when calculating the height of the flagpole, we will need to add the height of the person to the value found using the trig ratio.

Substitute the given values into the formula and solve for O:

[tex]\implies \sf \tan(65^{\circ})=\dfrac{O}{35}[/tex]

[tex]\implies \sf O=35\tan(65^{\circ})[/tex]

Therefore the height of the flagpole is:

[tex]\implies \sf 35\tan(65^{\circ})+1.6=76.65774222...[/tex]

[tex]\implies \sf Height\:of\:flagpole=77\:m\:(nearest\:metre)[/tex]

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The rational numbers are -5/250, [tex]\sqrt{400}[/tex] ,and irrational numbers are 5.012121212......., [tex]\sqrt[3]{30}[/tex] , 0.01562138411........,[tex]\sqrt{1000}[/tex]

Given six numbers:5.012121212..,[tex]\sqrt{1000}[/tex],[tex]\sqrt[3]{30}[/tex], -5/250,  0.01562138411.....,[tex]\sqrt{400}[/tex].

We have to identify which numbers are rational and which are irrational numbers.

Rational numbers are those numbers which can be written in p/q form where q cannot be equal to zero because if q is zeo then the value of p/q will be infinity.

Irrational numbers are those numbers which cannot be written in p/q form.

First number :5.0121212121....

In the above numbers 12 is repeating next to the decimals. So it is a irrational numbers.

Second number:[tex]\sqrt{1000}[/tex]

If we solve the above number we will find it 31.6227766017 . It is cannot be expressed in p/q form, so it is irrational number.

Third number:[tex]\sqrt[3]{30}[/tex]

The abov number is irrational number as we cannot express it in p/q form.

Fourth number:-5/250

The value of above number is -0.02.It can be in the form of -2/100. so it is rational number.

Fifth number:0.01562138411........

Because the digits are repeating after decimals so it is irrational number.

Sixth number:[tex]\sqrt{400}[/tex]

The value of above number is 20, so it is rational number.

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Question is incomplete as it should include figure.

With the given rate Mamadou will take 6 hours to travel 126 miles.

In order to solve a problem for two different values of a quantity, its unit value is first derived. This method is known as unitary method.

Given that,

The distance travelled in 8 hours is 168 miles.

In order to calculate time for 126 miles, unitary method can be used as,

The time for 168 miles is 8 hours.

Then, the time for 1 mile is 8/168 hours.

Thus, the time for 126 mile is 8/168 × 126 = 6 hours.

Hence, the time taken by Mamadou to travel 126 miles is 6 hours.

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The vertices of the parabolae are:

Parabolae are represented by quadratic equations. In this problem we have parabolae in standard form and we need to determine its vertex form to find the needed information. Now we summarize the forms of quadratic equations:

Standard form

y = a · x² + b · x + c     (1)

Vertex form

y - k = C · (x - h)²     (2)

Please notice that (x, y) = (h, k) represents the vertex of the parabola.

To change quadratic equations from standard form into vertex form we need to apply algebraic handling:

y = x² + 6 · x + 8

y + 1 = x² + 6 · x + 9

y + 1 = (x + 3)²

(h, k) = (- 3, - 1)

y = x² - 2 · x - 8

y + 9 = x² - 2 · x + 1

y + 9 = (x - 1)²

(h, k) = (1, - 9)

y = - x² + 8 · x - 15

y = - 1 · (x² - 8 · x + 15)

y - 1 = - 1 · (x² - 8 · x + 16)

y - 1 = - 1 · (x - 4)²

(h, k) = (4, 1)

y = - 4 · x² + 6 · x

y = - 4 · [x² - (3/2) · x]

y + (- 4) · (9/16) = - 4 · [x² - (3/2) · x + 9/16]

y - 9/4 = - 4 · (x - 3/4)²

(h, k) = (3/4, 9/4)

y = x² + 6 · x + 11

y - 2 = x² + 6 · x + 9

y - 2 = (x + 3)²

(h, k) = (- 3, 2)

y = - x² + 36

y - 36 = - x²

(h, k) = (0, 36)

y = - x² + 7 · x - 10

y = - (x² - 7 · x + 10)

y + (- 1) · (9/4) = - (x² - 7 · x + 49/4)

y - 9/4 = - (x - 7/2)²

(h, k) = (7/2, 9/4)

y = x² - 10 · x + 24

y + 1 = x² - 10 · x + 25

y + 1 = (x - 5)²

(h, k) = (5, - 1)

y = 2 · x² - 4 · x - 1

y = 2 · (x² - 2 · x - 1/2)

y + 2 · (3/2) = 2 · (x² - 2 · x + 1)

y + 3 = 2 · (x - 1)²

(h, k) = (1, - 3)

y = - 4 · x² - 2 · x

y = - 4 · [x² + (1/2) · x]

y + (- 4) · (1/4) = - 4 · [x² + (1/2) · x + 1/4]

y - 1 = - 4 · (x + 1/2)²

(h, k) = (- 1/2, 1)

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a) The fire is out of the reach of helicopter 1.

b) Only helicopter 3 can be sent to stop the fire.

We have both the location of the fire and the initial position of the three helicopters set on a Cartesian plane. The locations are listed below:

The distance is found by the straight line distance formula, an application of Pythagorean theorem:

a) [tex]d = \sqrt{[1 - (- 3)]^{2}+[4-(-5)]^{2}}[/tex]

[tex]d = \sqrt{4^{2}+9^{2}}[/tex]

[tex]d = \sqrt{97}[/tex]

d ≈ 9.849

The fire is out of the reach of helicopter 1.

b) Helicopter 2

[tex]d = \sqrt{[- 2 - (- 3)]^{2}+[3 - (- 5)]^{2}}[/tex]

[tex]d = \sqrt{1^{2}+8^{2}}[/tex]

[tex]d = \sqrt{65}[/tex]

d ≈ 8.062

Helicopter 3

[tex]d = \sqrt{[4 - (- 3)]^{2}+ [- 2 - (-5)]^{2}}[/tex]

[tex]d = \sqrt{7^{2}+3^{2}}[/tex]

[tex]d = \sqrt{58}[/tex]

d ≈ 7.616

Only helicopter 3 can be sent to stop the fire.

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With some simple rearrangement, we can rewrite the numerator as

[tex]2x^3 - 3x^2 - x + 4 = 2(x^3 - x) - 3x^2 + x + 4 \\\\ ~~~~~~~~ = 2x(x^2-1) - 3(x^2 - 1) + x + 1 \\\\ ~~~~~~~~ = (2x-3)(x^2-1) + x+1[/tex]

Then factorizing the difference of squares, [tex]x^2-1=(x-1)(x+1)[/tex], we end up with

[tex]\dfrac{2x^3 - 3x^2 - x + 4}{x^2 - 1} = \dfrac{(2x-3)(x-1)(x+1) + x+1}{(x-1)(x+1)} \\\\ ~~~~~~~~ = \boxed{2x-3 + \dfrac1{x-1}}[/tex]

Answer:

Option A is probably the answer

If you have any question please contact me

Answer: A is the answer, should be right

The total number of different ways there are to put the cousins in the rooms is;  15

When we count the number of cousins staying in each room, it means that the possibilities are as follows; (4,0,0,0), (3,1,0,0), (2,2,0,0), (2,1,1,0), (1,1,1,1).

1) (4,0,0,0): This means that there is only 1 way to put all the cousins in the same room due to the fact that the rooms are identical.

2) (3,1,0,0): This means that there are 4 ways to choose which cousin will be in a different room than the others.

3) (2,2,0,0): This means that there are 3 ways to choose which of the other cousins will also stay in that room, and then the other two are automatically in the other room.

4) (2,1,1,0): This means that the number of ways to choose which cousins stay in the same room is; 4C2 = 6

5) (1,1,1,1): This means that there is only one way for all the cousins to the total number of possible arrangements is;

1 + 4 + 3 + 6 + 1 = 15each stay in a different room.

Therefore, the total number of possible arrangements is;

1 + 4 + 3 + 6 + 1 = 15

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The width that Mason should set his compass when constructing segment FG is: A. The distance from B to E.

FG should be congruent to segment BE. Based on this Mason should set his compass to the width of segment BE when Mason is constructing segment FG.

Hence, the width that Mason should set his compass when constructing segment FG is the distance from B to E which is option is A.

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Answer:

b to e

Step-by-step explanation:

plato

Answer:

23/35

Step-by-step explanation:

there's 12 red cards and 23 black cards

total = 35 cards

probability  to  pick a black card = 23/35

Answer: 23/35

Step-by-step explanation:

Probability is the measure of the likelihood of an event occurring. It is measured by the number of favorable outcomes over the total number of possible outcomes.

Here, the event is a black card being drawn. Since there are 12 + 23 = 35 cards in the deck, there are 35 possible outcomes of what card is picked. Out of those 35 cards, 23 are black, making 23 of the 35 options be the option we want.

23 black cards out of 35 total cards can also be written as [tex]\frac{23}{35}[/tex], which is the probability that a black card is chosen.

Answer:

m = [tex]-\frac{2}{3}[/tex]

Step-by-step explanation:

m = [tex]\frac{y2-y1}{x2-x1}[/tex]

m = [tex]\frac{1-7}{10-1}[/tex]

m = [tex]\frac{-6}{9}[/tex]

m = [tex]-\frac{2}{3}[/tex]

Answer:

-2/3

Step-by-step explanation:

slope = (y_2 - y_1)/(x_2 - x_1)

slope = (1 - 7)/(10 - 1)

slope = -6/9

slope = -2/3

Answer:

No. The slopes of parallel lines are equal.

Step-by-step explanation:

If you have two lines and their slopes are the same, then the lines are parallel.

If the two lines have slopes that are negative reciprocals (opposite signs and flipped over) then when you multiply the slopes together, you get -1... THOSE lines are perpendicular (they make right angles or make 90° angles or square angles).

Lines in the same plane that have different slopes will intersect at one point.

Answer:

C. 9

Step-by-step explanation:

The cubed root of 729 is the number that is multiplied 3 times to get 729. In this case, it's 9.

9*9*9 = 81*9

81*9 = 729

Job order costing also gives managers the advantage of being able to keep track of individuals' and teams' performance in terms of cost control, efficiency, and productivity. A disadvantage of job order costing is that employees are required to track all materials and labor used during the job.

With the standardization of products, managers track performance, productivity, and costs over time. Process costing allows for greater flexibility when making changes in the production process. Managers can target specific departments' processes or materials to lower production costs.

With process costing, companies track the flow of costs from department to department, rather than tracking costs for each individual item. Each department adds direct labor and manufacturing overhead costs, plus the cost of any raw materials it uses.

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The ratio of the total number of flowers in the vase, to the number of daisies in the vase is 12:7.

The number of flowers in the vase = 12 flowers

The number of roses in the vase = 5 roses.

Therefore, the number of daisies in the vase = The number of flowers in the vase - The number of roses in the vase,

or, the number of daisies in the vase = 12 - 5 = 7.

Thus, the number of daisies in the vase = 7.

We are asked to find the ratio of the total number of flowers in the vase, to the number of daisies in the vase.

Thus, the ratio = The number of flowers in the vase/The number of daisies in the vase,

or, the ratio = 12/ = 12:7.

Thus, the ratio of the total number of flowers in the vase, to the number of daisies in the vase is 12:7.

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The measure of the length BP and BC are 6 and 10 respectively

The given figure is a circle containing two chords AD and BC. From the given diagram, the following are true

AP = PC

BP = PD

BC = BP + PC

Circle theorem includes the concept of tangents, sectors, angles, the chord of a circle and proofs. A circle is the locus of all points in a plane which are equidistant from a fixed point.

Given the following parameters

AP = 3.5,

PD = 6,

PC = 4

According to the expression above;

BP = PD = 6

BC =  BP + PC

BC = 6 + 4

BC = 10
Hence the measure of the length BP and BC are 6 and 10 respectively

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Answer:

Step-by-step explanation:

Discussion

She is correct.

An equilateral triangle is a specific acute triangle. An acute triangle can never be an equilateral triangle because it has 3 unequal angles. Your best choice is likely C, but none of the choices are first rate choices.

Answer: C

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Assuming the equation is:}[/tex]

[tex]\mathsf{(12.3)^2 - (0.246 \div 3)}[/tex]

[tex]\huge\textbf{If so, let's start simplifying it:}[/tex]

[tex]\mathsf{(12.3)^2 - (0.246 \div 3)}[/tex]

[tex]\mathsf{= (12.3\times 12.3) - (0.246 \div 3)}[/tex]

[tex]\mathsf{= (151.29) - (0.246 \div 3)}[/tex]

[tex]\mathsf{= 151.29 - 0.246 \div3}[/tex]

[tex]\mathsf{= 151.29 - 0.082}[/tex]

[tex]\mathsf{= 151.208}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\large\boxed{\mathsf{Exactly \rightarrow} \frak{\ 151.208\ } \& \textsf{ Corrected to two significant figures}\rightarrow \frak{150 \ or \ 151}}\large\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]