16 8. If a projectile is fired at an angle 0 and initial velocity v, then the horizontal distance traveled by the projectile is given by D= v² sin cos 0. Express D as a function 20. OA. D= 1 v² sin

Answer:

17.54714286.

Step-by-step explanation:

Long one, I know.

Answer:

2.7x +2y

Step-by-step explanation:

Why because  u distribute the 2 to get  1.2x + 1.5x + 2y. CBL and get

2.7x +2y

        With this in mind,

                 x + y = -3

                 x * y = -18

        Then we will think about which ones could add up to 3

                 1 & 18, 2 & 9, 3 & 6 are factors of 18 (one being negative results in -18)

                 Well 1 and 18 cannot make 3, same for 2 and 9, that leaves us with 3 and 6.

        You can see our test shows this solution works!

                 -6 + 3 = -3

                 -6 * 3 = -18

Have a nice day!

  I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Solution of the given inequalities based on integer 'n' is given by :

a. Value of 'n' for 15n > 12n + 18 is n > 6.

b. All the possible integer value of 'n' for -2 <n + 3 ≤ 4 are -4, -3, -2, -1, 0.

a. Solution of the expression 15n > 12n + 18 is :

15n > 12n + 18

Subtract 12n from both the sides ,

⇒ 15n - 12n >  12n - 12n + 18

⇒ 3n > 18

Divide by 3 from both the sides,

⇒ 3n/3 > 18 /3

⇒ n > 6

b.  -2 <n + 3 ≤ 4

where 'n' is an integer

⇒ -2 -3 < n + 3 -3 ≤ 4 -3

⇒ -5 < n < 1

All the possible values of 'n' smallest to largest are:

-4, -3, -2, -1, 0.

Therefore, the answer of the questions based on integers 'n' are :

a. 15n > 12n + 18 ⇒ n > 6.

b. All possible integers of 'n' are -4, -3, -2, -1, 0.

The above question is incomplete , the complete question is:

a) Solve 15n > 12n + 18

b) n is an integer and -2 <n + 3 ≤ 4

Write down the possible values of n, from smallest to largest.

All values must be separated by commas. Eg. .... , .... , .....

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Answer:

ima say this in baby words bcz i dont know how to explain it otherwise sorry lol

fractions are part of an object or sum and a ratio are things comparedish?

Step-by-step explanation:

ratio: 3:4

fraction: 2/8

Answer:

ratios is like part of something i think like 1:3 = 1/3 and fractions can be divided unlike ratios

Step-by-step explanation:

The equation of the linear function is:

z = 10 + 4x + 6y

To find the equation of the linear function, we need to determine the values of c, m, and n in the function z = c + mx + ny.

Since the graph of the function intersects the xz-plane at z = 4x + 10 and the yz-plane at z = 6y + 10, we can use these equations to find the values of c, m, and n.

When the graph intersects the xz-plane (y = 0), we have:

z = c + mx + n(0) = c + mx

Comparing this with z = 4x + 10, we can equate the coefficients:

c = 10 (the constant term)

m = 4 (the coefficient of x)

When the graph intersects the yz-plane (x = 0), we have:

z = c + m(0) + ny = c + ny

Comparing this with z = 6y + 10, we can equate the coefficients:

c = 10 (the constant term)

n = 6 (the coefficient of y)

Therefore, the equation of the linear function is:

z = 10 + 4x + 6y

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Answer:

32

Step-by-step explanation:

Because Triangle QPS has equal sides, it is an equilateral triangle. Which means its angles are 60°. 134-60 = 74. Because Lines QS and QR are equal angles QSR and QRS are the same. 180-74-74 = 32

Hope this helps

Answer:

a = 9 in

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

a² + 5.6² = 10.6²

a² + 31.36 = 112.36 ( subtract 31.36 from both sides )

a² = 81 ( take square root of both sides )

a = \(\sqrt{81}\) = 9

Answer:

Let hypotenuse (h) = 10.6 in

perpendicular (p) = 5.6 in

and base (b) = a

Therefore, by Pythagoras Theorum,

H^2 = a^2 + P^2

10.6^2 = a^2 + 5.6^2

112.36 = a^2 + 31.36

a^2 = 112.36 - 31.36

a^2 = 81.00

a = √81

a = 9 in

Answer:

Cost = y/x

Step-by-step explanation:

The cost of a 4 pack of apple juice is $ 2.24.

We need to write an equation that relates the cost in dollars, y, to the number of apple juice cartons, x.

As 4 packs = $2.24

1 pack = 0.56

So, the equation can be :

Cost = y/x

This is a point, so it has x- and y-coordinates. Both of these coordinates are positive, therefore the point must be in the first quadrant.

The pattern for the points on a unit circle is 3 - 2 - 1 starting at 0 and up to pi/2. The pattern for the radian denominators on a unit circle is 6 - 4 - 3 starting at 0 and up to pi/2.

(sqrt(3) / 2, 1/2) = pi / 6 radians

Hope this helps!

Answer:

A. pi/6 radians

Step-by-step explanation:

The ratio of the lengths of the sides of a 30-60-90 triangle is

1/2 : sqrt(3/2) : 1

sin theta = opp/hyp

tan theta = 1/2 / 1

tan theta = 1/2

theta = pi/6 radians

Answer: A. pi/6 radians

Answer:

20,160 ways

Step-by-step explanation:

9x8x7x6x5x4x3x2x1=9

Answer:

(49p2–490p) ÷(p–10)

Step-by-step explanation:

The area of the field is 10,765.44 square meters.

Given that:

Diameter, d = 72 m

Width, W = 72 m

Length, L = 93 m

The area of a two - dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.

The area of the field is calculated as,

A = (π/4)d² + W·L

A = (3.14 / 4) x 72² + 72 x 93

A = 4,069.44 + 6,696

A = 10,765.44 square meters

The area of the field is 10,765.44 square meters.

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Given :

A system of equations y = 5.69x + 25 and y = 9.49x + 6.

To Find :

The solution of the system of equation.

Solution :

Subtracting equation 2 by 1, we get :

y - y = ( 9.49x + 6 ) - ( 5.69x + 25 )

0 = 3.8x - 19

x = 5

Putting value of x in equation 1, we get :

y = (5.69×5) + 25

y = 53.45

Therefore, the solution of the system of equations is ( 5, 53.45 ).

The percentage of the guests ordered food is 40%

"Information available from the question"

In the question:

There were 425 guests at a hotel. 170 guests ordered food.

To find the what percentage of the guests ordered food?

Now, According to the question:

Total guests in hotel is 425

and, 170 guests ordered food

=> Divide 170 by 425

= 170/ 425 = 0.4

The percentage of the guests ordered food:

=> 0.4 x 100 = 40%

Hence, The percentage of the guests ordered food is 40%

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Answer:

60

Step-by-step explanation:

First, divide 120 by two and get 60. Now do 120-60 to get 60. Set up proportion

60/x = x/60.

Cross multiply

x^2 = 3600

and now find the square root of 3600

60

Answer: To prove that triangles △ABC and △DEF are similar, we would use the AA Similarity Postulate. This postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. In other words, if the corresponding angles of two triangles are congruent, then the triangles are similar.

Step-by-step explanation:

The partial fraction decomposition of the expression is:

-8x - 30 / [(x + 3)(x^2 + 6x + 1)] = -8 / (x + 3) + (2x + 10) / (x^2 + 6x + 1)

To perform partial fraction decomposition for the given expression, we need to first factorize the denominator:

4x^2 + 17x - 1 = (x + 3)(x^2 + 6x + 1)

The partial fraction decomposition of the expression is:

-8x - 30 / [(x + 3)(x^2 + 6x + 1)] = A / (x + 3) + (Bx + C) / (x^2 + 6x + 1)

To find the values of A, B, and C, we can use the method of equating coefficients. Multiplying both sides by the denominator gives:

-8x - 30 = A(x^2 + 6x + 1) + (Bx + C)(x + 3)

Expanding the right side and simplifying, we get:

-8x - 30 = Ax^2 + (6A + B)x + (A + 3B + C)

Equating coefficients, we get the following system of linear equations:

A = -8

6A + B = -30

A + 3B + C = 0

Solving this system of equations, we get:

A = -8

B = 2

C = 10

Therefore, the partial fraction decomposition of the expression is:

-8x - 30 / [(x + 3)(x^2 + 6x + 1)] = -8 / (x + 3) + (2x + 10) / (x^2 + 6x + 1)

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Answer:

11 and 6 respectively

Step-by-step explanation:

1st number=x

2nd number=x-5

three times the second number=3(x-5)=3x-15

3x-15+x=29

put the liketerms together=3x+x=29+15

4x=44

(divide both sides by 4)x=11

Answer:

3 2/3

The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

Complete the multiplication and the equation becomes

The two fractions now have like denominators so you can add the numerators.

Then:

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 22 and 6 using

Convert to a mixed number using

long division for 11 ÷ 3 = 3R2, so

Therefore:

Answer:

9 1/10th m/s2 :)

Step-by-step explanation:

The reason it is 1/10 is because the Number is 81 not 80, therefore 1/10 because there it is 1 left in 80 making it a fraction not a whole :) i hope this helps sorry if the explanation is too complicated...

Answer:

The answer is "36"

Step-by-step explanation:

Given:

\(\to \bold{\sqrt{x} \leq 6}\)

Square the above value:

\(\to (\sqrt{x})^2 \leq (6)^2\\\\\to x \leq 36\\\\\)

Step-by-step explanation:

1/3*12=1/4

1/4=1/4

=1/4÷1/4

=0 answer

Answer:

2/15

Step-by-step explanation:

6 red marbles and 4 yellow marbles = 10 marbles

P ( 1st is yellow) = yellow marbles / total marbles

                          = 4/10 = 2/5

The marble is not replaced

6 red marbles and 3 yellow marbles = 9 marbles

P ( 2nd is red) = red marbles / total marbles

                          = 3/9 = 1/3

P ( yellow, red) = 2/5 * 1/3 = 2/15

Answer:

A.)*ೃ: 6f + 3g
B.) *ೃ: -8f +10g
C.) *ೃ: 4fg

Step-by-step explanation:

A.) F x 6 + g x 3 (combined like terms)
     6f + 3g
B.) f(-8)=-8f
    g(-10)=-10g
     -8f-(-10g)

     -8f + 10g
C.) (-2)(-2)=4
    f x 4g = 4fg  

The Quadrilateral that matches the listed characteristics is a rectangle.

A rectangle is a quadrilateral with four right angles, and two pairs of opposite sides that are parallel. It is also a parallelogram because it has two pairs of parallel sides. However, not all parallelograms are rectangles.

A rectangle also has four congruent angles which makes it a special case of parallelogram. In a rectangle, opposite sides are congruent to each other. Therefore, answer option C. Rectangle matches the given characteristics.

What is a quadrilateral?A quadrilateral is a polygon with four sides. Examples of quadrilaterals include parallelograms, rhombuses, rectangles, squares, and trapezoids. The angles of a quadrilateral add up to 360 degrees.What is a rectangle?

A rectangle is a four-sided figure with four right angles.

Opposite sides of a rectangle are parallel to each other. The length and width of a rectangle are perpendicular to each other. The formula for finding the perimeter of a rectangle is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. The area of a rectangle is A = lw, where A is the area, l is the length, and w is the width.

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Answer:

7 - 2m can be translated to "7 minus two times m" or "the difference between 7 and twice m".

3(m + 2) = 15 can be translated to "three times the sum of m and 2 is equal to 15" or "the product of 3 and the sum of m and 2 is 15".

To solve the equation, we can start by distributing the 3 on the left side:

3(m + 2) = 15

3m + 6 = 15

Then, we can subtract 6 from both sides:

3m + 6 - 6 = 15 - 6

3m = 9

Finally, we can divide both sides by 3:

3m/3 = 9/3

m = 3

Therefore, the solution to the equation 3(m + 2) = 15 is m = 3.

5m - m(2 - m) can be translated to "5m minus the product of m and the difference between 2 and m" or "the difference between 5m and m times the quantity 2 minus m".

To simplify the expression, we can use the distributive property to expand the second term:

5m - m(2 - m) = 5m - 2m + m^2 = m^2 + 3m

Therefore, the simplified expression is m^2 + 3m.

Let's call C the amount Manuel raises for charity.

Manuel objective is:

Let's say that the money Manuel has to raise to get to his goal is G. Before he raises any money, we have G = C.

Now, his parents donate 70, so G = C - 70. Replacing in the first equation:

And Manuel has to raise between 180 and 280 to get to his goal.

Since he plans to ask for 10 to every person he ask to contribute:

Manuel has to make between 18 and 28 persons to contribute.

If P is the number of persons, and since they are all giving 10, we can write that as:

If we want to take into account Manuel parents, we can write it as:

This is point a answer.

The speed of the faster car is 40 miles/hr.

both cars travel for same time , so let that time be 't'

car 1 :

distance travelled = 75 miles

let the speed of the car be = x miles/hr

∴ time (t)  = distance / speed

              t  =   75 / x               .............(1)

car 2 :

distance travelled = 100 miles

speed of the car is = x + 10 miles/hr  ( already provided )

∴  time ( t) = distance / speed

            t  = 100/ (x+10)        ..............(2)

    now as the time for both the cases is same  , so we equate eqn (1) and eqn (2) .

∴ 75/x  =  100/ (x+10)

3x + 30 = 4x

x = 30

so the speed of the 1st car will be 30 miles / hr

and the speed of the 2nd car ( faster car ) will  be x + 10 = 40 miles/hr

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The mass of a plate with radius 4 and a radial density given by rho(x)=e^(x2−12) is b. π(e^4-e^(-12) ).

To find the mass of the plate, use the formula for the mass of a plate with radial density:
M = ∫∫ρ(r) r dr dθ
Where M is the mass of the plate, ρ(r) is the radial density, r is the radius, and θ is the angle.

Given that the radial density is ρ(x)=e^(x2−12) and the radius is 4, we can plug these values into the formula:
M = ∫∫e^(r2−12) r dr dθ

We can solve this integral by first integrating with respect to r:
M = ∫(1/2)(e^(r2−12))(r^2) dθ

Integrate with respect to θ:
M = (1/2)(π)(e^(r^2−12))(r^2)

Finally, we can plug in the value of r=4 and simplify:
M = (1/2)(π)(e^(4^2−12))(4^2)
M = (1/2)(π)(e^4-e^(-12))(16)
M = π(e^4-e^(-12))

Therefore, the mass of the plate is b. π(e^4-e^(-12) ).

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