A marching band takes 5 steps forward and 3 steps back during the Republic Day parade. According to this, since the wind in this marching band took a total of 460 steps, how many steps did he go from the starting point?
solution please

9514 1404 393

Answer:

  B, E

Step-by-step explanation:

The greatest common factor can be found a number of ways. Easiest is to make use of your knowledge of multiplication tables and divisibility rules.

Here, the GCFs are ...

A 6 and 3 --- 3

B 30 and 36 --- 6

C 24 and 48 --- 24

D 60 and 88 --- 4

E 18 and 66 --- 6

F 72 and 84 --- 12

_____

Additional detail on finding the GCF

You can factor numbers to see which factors are common:

  60 = 2^2 × 3 × 5

  88 = 2^3 × 11 . . . . . . . so 2^2 = 4 is the GCF of 60 and 88

You can use the Euclidean algorithm:

  Divide the larger by the smaller and keep the remainder; Replace the larger with the remainder and repeat. If the remainder is zero, the divisor is the GCF.

  84/72 = 1 r 12

  72/12 = 6 r 0 . . . . 12 is the GCF of 72 and 84

Answer:

To find 40% of a number, you can multiply the number by 0.4 or divide it by 2.5.

Using this method, we get:

40% of 100 is 40 (100 x 0.4 or 100 ÷ 2.5)

40% of 110 is 44 (110 x 0.4 or 110 ÷ 2.5)

40% of 140 is 56 (140 x 0.4 or 140 ÷ 2.5)

40% of 120 is 48 (120 x 0.4 or 120 ÷ 2.5)

Therefore, 40% of 100 is 40, 40% of 110 is 44, 40% of 140 is 56, and 40% of 120 is 48.

Answer:

Step-by-step explanation:

Refer to attached

Given:

We can see that:

and

So the corresponding angles are congruent and corresponding sides are similar

We can conclude that the triangles are similar

Answer: First one & 4th one.

Angle E corresponds to angle L.

The two triangles are similar.

Step-by-step explanation: Just did it. Both are correct!

The density of nitrogen in the space will be 3.13 kg/m³

Density is the ratio of mass to volume of a substance. It is measured in kg/m³.

The volume of the shade part = volume of the cone- volume of the hemisphere

volume of the hemisphere = 2/3 πr³

= 2/3 × 3.14 × 40³

= 401920/3

= 133973.33m³

volume of the cone = 1/3 πr²h

= 1/3 × 3.14 × 40²× 500

= 2512000/3

= 837333.33 m³

volume of the shaded part = 837333.33-133973.33 = 703360m³

The density of the space = 2200000/703360

= 3.13kg/m³.

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Answer:

X = 6

Step-by-step explanation:

Hope this helps!

....

Answer:

Step-by-step explanation:

11)  $175(1 - 0.30)(1 + 0.06) = $129.85

12) slope is 2, so basic equation is

y = 2x + b

plug in your desired point

-5 = 2(-4) + b

b = 3

y = 2x + 3

Answer:

m∠AOF=110°

Step-by-step explanation:

∠AOB is 180°, ∠FOB is 70°. To find m∠AOF, subtract 70 from 180. 180-70=110  

m∠AOF=110°

Answer:

m∠AOF=110°

Step-by-step explanation:

∠AOB is 180°, ∠FOB is 70°.

If you want to find m∠AOF, subtract 70 from 180. 180-70

                                                                                  = 110  

m∠AOF=110°

Here is how to find the equation of the line using point-slope form

Formula for the equation of a line in point-slope form: y - y₁ = m(x - x₁)

Now that we have the formula, we plug in what we are given.

y - 9 = 4(x + 3)

We can covert this into slope-intercept form by solving for y.

\(y - 9 = 4(x + 3)\\\\y - 9 = 4x + 12\\\\y = 4x + 21\)

Our equation for this line is: y = 4x + 21.

We can prove this by graphing the line, like so:

The length of AB of the parallelogram is determined as 14.36 inches.

The length of AB of the parallelogram can be determined by applying cosine rule as shown below:

The cosine rule, also known as the law of cosines, is a mathematical formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is commonly used to find the length of an unknown side or the measure of an unknown angle in a triangle when the lengths of two sides and the measure of the included angle are known.

Length AB = Length AD = x

DB² = AB² + AD² - 2(AB x AD) cos (A)

22² = x² + x² - 2x²(cos 100)

484 = 2x² + 0.347x²

484 = 2.347x²

x² = 484/2.347

x² = 206.2

x = √206.2

x = 14.36 inches

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The domain is [0,100].[0,100]. The range is [0,1500] [0,1500]

(a) To find the cost of making 25 items substitute

x=25 in the equation

=10+500(25)

=10(25)+500(25)=750

c(x)=10x+500

c(25)=10(25)+500

c(25)=750

the cost of making 25 items is

$750

(b)

Since the maximum cost allowed is

$1500  

10+500≤1500

10x+500≤1500

To solve this inequality

First, subtract 500 from both sides

10≤1000

10x≤1000

Divide both sides by 10

≤100x≤100

This means you can make at most 100 items.

The domain is

[0,100].[0,100].

The range is

[0,1500] [0,1500].

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Answer:

Step-by-step explanation:

Answer = 180 - (100 + 55)

Answer = 180 - 155

Answer = 25º

Hope that helps! :)

-Aphrodite

Answer: The measure of the missing angle is 25 degrees

Step-by-step explanation:

A triangle equals 180 degrees so you would add the 100 degrees and 55 degrees and then subtract that from 180. Then you have your answer. :)

Answer:

70 times.

Step-by-step explanation:

The following data were obtained from the question:

SHAPE >>>>>>>>>>>>> FREQUENCY

Oval >>>>>>>>>>>>>>> 18

Rectangle >>>>>>>>>> 14

Star >>>>>>>>>>>>>>> 8

TOTAL >>>>>>>>>>>>> 40

next, we shall determine the probability of chosing a rectangular cracker. This is illustrated below:

Event of Rectangle (nR) = 14

Sample space (S) = 40

Probability of chosing rectangle, P(R) =?

P(R) = nR/nS

P(R) = 14/40

P(R) = 7/20

Therefore, the probability of chosing a rectangular cracker is 7/20.

Thus, if the process were carried out 200 times, the probability of chosing a rectangular cracker will be:

= P(R) × 200

P(R) = 7/20

= 7/20 × 200

= 70

Therefore, max will chose a rectangular cracker 70 times.

Answer:

The recoil velocity of the gun is \(0.72\,\,\frac{km}{h}\)  and is pointing in opposite direction to the velocity of the bullet.

Step-by-step explanation:

Use conservation of linear momentum, which states that the momentum of the bullet (product of the bullet's mass times its speed) should equal in absolute value the momentum of the recoiling gun (its mass times its recoil velocity).

We also write the mass of the bullet in the same units as the mass of the gun (for example kilograms). Mass of the bullet = 0.010 kg

In mathematical terms, we have:

\(5\, kg * v= 0.01 \,kg\,* 360\,\frac{km}{h} \\v=\frac{0.01\,*360}{5} \,\,\frac{km}{h}\\v=0.72\,\,\frac{km}{h}\)

The solution of the given quadratic equation is -2 ± √6.

Quadratic expressions are polynomial equations of second degree.

The general form of a quadratic equation is ax² + b x + c = 0.

Solution of a quadratic equation ax² + b x + c = 0 can be found by,

x = [-b ± \(\sqrt{b^2-4ac}\)] / 2a, where \(b^2-4ac\) is called discriminant.

Given quadratic equation is x² + 4x - 2 = 0.

Discriminant = 4² - (4 × 1 × -2) = 16 + 8 = 24

x = [-4 ± √24] / 2

  = [-4 ± 2√6] / 2

  = -2 ± √6

Hence the solution of the given quadratic equation is -2 ± √6.

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The top angle is right (90 degrees, kinda looks like a bent elbow).

The 2nd is acute (smaller than 90, kind of 'cute' bc it's small).

The 3rd is obtuse (greater than 90, I have nothing corny to say, sorry).

4th is acute.

5th is straight because it's a straight line.

6th is also obtuse.

Have a good day :)

Answer:

7:1

Step-by-step explanation:

7x5=35

Make it a ratio and 1 doesnt make a diffrence.

If a machine fills boxes at a constant rate at the end of 35 minutes, it has filled 5 boxes then 1 box is filled in 7 minutes.

A division is a process of splitting a specific amount into equal parts.

Given that, a machine fills boxes at a constant rate. At the end of 35 minutes, it filled 5 boxes.

A rate of change is constant when the ratio of the output to the input stays the same at any given point in the function.

The constant rate of change is also known as the slope.

Linear functions will have a constant rate of change.

Now, in 35 minutes machine has filled 5 boxes.

So, 1 box is filled in 35/5=7 minutes.

Hence, if a machine fills boxes at a constant rate at the end of 35 minutes, it has filled 5 boxes then 1 box is filled in 7 minutes.

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Tan(30°) = 1/√(3)

F is the correct answer

The answers are:

Part A: The two values of x are: x > 8 or x < -24

Part B: Closed circles at -24 as well as 8 on the number line.

Inequalities are mathematical formulas with two sides that are unequal. In an inequality, we evaluate two numbers rather than two equations. In place of the equal sign, a less than (less than or equal to), larger than (greater than or equal to), or not equal to sign is used.

The following steps are missing for the inequalities:

Solving the inequalities,

Part A:

|1/4x+2|+4 >= 8

|1/4x+2|>=4

Now when we remove the sign fom the inequality, there would be 2 values:

(1/4) x + 2 > 4 or (1/4) x + 2 < -4

Now subtracting 2 from both side:

\((\frac{1}{4} )x > 2\ or\ (\frac{1}{4} )x < -6\)

Divide both the sides by 4:

4(1/4) x > 4(2) or 4(1/4) x < 4(-6)

Now we get two values of x:

x > 8 or x < -24

Part B:

Closed circles at -24 as well as 8 on the number line. Draw a thick line from -24 to the left arrow and a thick line from 8 to the right arrow.

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The two cars must be approximately 177.34 feet apart from each other for Spiderman to have different depression angles to each car.

To find the distance between the two cars, we can use trigonometry and the concept of similar triangles. Let's denote the distance between Spiderman and the nearest car as d1 and the distance between Spiderman and the farther car as d2.

In a right triangle formed by Spiderman, the height of the hotel, and the line of sight to the nearest car, the tangent of the depression angle (52 degrees) can be used:

tan(52) = 600 / d1

Rearranging the equation to solve for d1:

d1 = 600 / tan(52)

Similarly, in the right triangle formed by Spiderman, the height of the hotel, and the line of sight to the farther car, the tangent of the depression angle (46 degrees) can be used:

tan(46) = 600 / d2

Rearranging the equation to solve for d2:

d2 = 600 / tan(46)

Using a calculator, we can compute:

d1 ≈ 504.61 feet

d2 ≈ 681.95 feet

The distance between the two cars is the difference between d2 and d1:

Distance = d2 - d1

Plugging in the values, we have:

Distance ≈ 681.95 - 504.61

Distance ≈ 177.34 feet

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\(cos(62) = \frac{ab}{cb} \\ ab = cb.cos(62) \\ ab = 12.cos(62) \approx5.6\)

Answer: The minuend is 20000

Step-by-step explanation:

To calculate the minuend, we use the equation:

\(\text{Subtrahend}=\text{Minuend-Difference}\)

We are given:

Difference between the two numbers = 7194

Subtraend = 12806

Putting values in above equation, we get:

\(\text{Minuend}=12806+7194\\\\\text{Minuend}=20000\)

Hence, the minuend is 20000

first off, let's take a peek at the picture above

hmmm the hyperbola is opening sideways, that means it has a horizontal traverse axis, it also means that the positive fraction will be the one with the "x" variable in it.

now, the length of the horizontal traverse axis is 4 units, from vertex to vertex, that means the "a" component of the hyperbola is half that or 2 units, and 2² = 4, with a center at the origin.

\(\textit{hyperbolas, horizontal traverse axis } \\\\ \cfrac{(x- h)^2}{ a^2}-\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(x- 0)^2}{ 2^2}-\cfrac{(y- 0)^2}{ (\sqrt{3})^2}=1\implies {\Large \begin{array}{llll} \cfrac{x^2}{4}-\cfrac{y^2}{3}=1 \end{array}}\)

Answer:

a)9. b) 12

Step-by-step explanation:

a) | -6 -3 | .

-6-3 = -9

|-9| =9

b) | 0 - 12 |.

0-12=-12

|-12|=12

Work done lifting the bucket and rope to the top of the building is 4005.75 Joules

To express this concept mathematically, the work W is equal to the force f times the distance d, or W = fd. If the force is being exerted at an angle θ to the displacement, the work done is W = fd cos θ.

Initially bucket hold = 25kg. Sand

Sand leaks 0.1 kgs each meter it is lifted

At height x meter bucket hold = (25 - 0.1x) kg of sand

Length of rope = 15 meter

density of rope = 0.4kg / meter

weight of rope = 15 (0.4) = 6kg.

At height x meter, weight of rope = (6 - 0.4x)

Total weight at height x meter = (25-0.1x) + (6-0.4x)

                                                   = (31 - 0.5x) kg

force = (31-0.5x) g Newtons. = [(31-0.5x) 9.8] Newton

Work = force × displacement

\(Work= \int_{0}^{15}9.8(31-0.5x)dx\)

          \(=9.8[31x-0.5 \frac{x^2}{2} ]_{0}^{15}\)

          \(=9.8[31(15)-0.25(15)^2]-0\)

          \(=4005.75 joules\)

Hence, work done 4005.75 Joules

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Answer:

x < -3 or x > 2

Step-by-step explanation:

x² + x - 6 > 0

Convert the inequality to an equation.

x² + x - 6 = 0

Factor using the AC method and get:

(x - 2) (x + 3) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x - 2 = 0

x = 2

x + 3 = 0

x = -3

So, the solution is x < -3 or x > 2

Answer:

gas

Step-by-step explanation:

use gas powered vehicles

Answer:

Chi-square distribution

Step-by-step explanation:

We want to investigate that whether best ski area is independent of skier level or not so this situation leads to test of independence. For investigating independence of two variable we usually use chi-square distribution.

Thus, for conducting the test for investigating the independence between best ski area and skier level we use chi-square distribution.

Solving a system of equations we can see that the washer costs $750, and the dryer costs $250.

Let's define the variables:

x = cost of the washer.

y = cost of the dryer.

We know that the cost combined is $1000, then:

x  + y = 1000

And the washer cost 3 times the cost of the dryer, then we will get:

x = 3y

So we have a system of equations, we can replace the second equation into the first one, so we will get:

3y + y = 1000

4y = 1000

y = 1000/4

y = 250

The cost of the washer is:

x = 3*250 = 750

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