79! + 77!
------------ = ?
77!​

Answer:

4 pens

Step-by-step explanation:

Let x represent the number of pens bought by Raju and y represent the number of pencils bought by Raju.

Given that Raju bought two times as many pens as pencils, this statement can be represented by:

x = 2y                    (1)

A pen costs Rs 12 and a pencil Rs 2, and he spent a total of Rs. 52, hence:

12x + 2y = 52        (2)

Substituting x = 2y in equation (2):

12(2y) + 2y = 52

24y + 2y = 52

26x = 52

y = 52/26

y = 2

From equation (1), x = 2y, hence:

x = 2(2)

x = 4

x = 4

Therefore he bought 4 pens and 2 pencils

Let the rocket is launched at an angle of \theta with respect to the positive direction of the x-axis with an initial velocity u=15m/s.

Let the initial position of the rocked is at the origin of the cartesian coordinate system where the illustrative path of the rochet has been shown in the figure.

As per assumed sine convention, the physical quantities like displacement, velocity, acceleration, have been taken positively in the positive direction of the x and y-axis.

Let the point P(x,y) be the position of the rocket at any time instant t as shown.

Gravitational force is acting downward, so it will not change the horizontal component of the initial velocity, i.e. [tex]U_x=U cos\theta[/tex] is constant.

So, after time, t, the horizontal component of the position of the rocket is

[tex]x= U \cos\theta t \;\cdots(i)[/tex]

The vertical component of the velocity will vary as per the equation of laws of motion,

[tex]s=ut+\frac12at^2\;\cdots(ii)[/tex], where,s, u and a are the displacement, initial velocity, and acceleration of the object in the same direction.

(a) At instant position P(x,y):

The vertical component of the initial velocity is, [tex]U_y=U sin\theta[/tex].

Vertical displacement =y

So, s=y

Acceleration due to gravity is [tex]g=9.81 m/s^2[/tex] in the downward direction.

So, [tex]a=-g=-9.81 m/s^2[/tex] (as per sigh convention)

Now, from equation (ii),

[tex]y=U sin\theta t +\frac 12 (-9.81)t^2[/tex]

[tex]\Rightarrow y=U \sin\theta \times \frac {x}{U \cos\theta} +\frac 12 (-g)\times \left(\frac {x}{U \cos\theta} \right)^2[/tex]

[tex]\Rightarrow y=U^2 \tan\theta-\frac 1 2g U^2 \sec^2 \theta\;\cdots(iii)[/tex]

This is the required, quadratic equation, where [tex]U=15 m/s[/tex] and [tex]g=9.81 m/s^2[/tex].

(b) At the highest point the vertical velocity,v, of the rocket becomes zero.

From the law of motion, [tex]v=u+at[/tex]

[tex]\Rightarroe 0=U\sin\theta-gt[/tex]

[tex]\Rightarroe t=\frac{U\sin\theta}{g}\cdots(iv)[/tex]

The rocket will reach the maximum height at [tex]t= 1.53 \sin\theta s[/tex]

So, from equations (ii) and (iv), the maximum height, [tex]y_m[/tex] is

[tex]y_m=U\sin\theta\times \frac{U\sin\theta}{g}-\frac 12 g \left(\frac{U\sin\theta}{g}\right)^2[/tex]

[tex]\Rightarrow y_m=23 \sin\theta -11.5 \sin^2\theta[/tex]

In the case of vertical launch, [tex]\theta=90^{\circ}[/tex], and

[tex]\Rightarrow y_m=11.5 m[/tex] and [tex]t=1.53 s[/tex].

Height from the ground= 11.5+3=14.5 m.

(c) Height of rocket after t=4 s:

[tex]y=15 \sin\theta \times 4- \frac 12 (9.81)\times 4^2[/tex]

[tex]\Rightarrow y=15 \sin\theta-78.48[/tex]

[tex]\Rightarrow -63.48 m >y> 78.48[/tex]

This is the mathematical position of the graph shown which is below ground but there is the ground at [tex]y=-3m[/tex], so the rocket will be at the ground at t=4 s.

(d) The position of the ground is, y=-3m.

[tex]-3=U\sin\theta t-\frac 1 2 g t^2[/tex]

[tex]\Rightarrow 4.9 t^2-15 \sin\theta t-3=0[/tex]

Solving this for a vertical launch.

[tex]t=3.25 s[/tex] and [tex]t=-0.19 s[/tex] (neglecting the negative time)

So, the time to reach the ground is 3.25 s.

(e) Height from the ground is 13m, so, y=13-3=10 m

[tex]10=U\sin\theta t-\frac 1 2 g t^2[/tex]

Assume vertical launch,

[tex]4.9 t^2-15 \sin\theta t+10=0[/tex] [using equation (ii)]

[tex]\Rightarrow t=2.08 s[/tex] and [tex]t=0.98 s[/tex]

There are two times, one is when the rocket going upward and the other is when coming downward.

Answer:

should be A

Step-by-step explanation:

Translated left by 7

Answer:

It A

Step-by-step explanation:

Answer:

Step-by-step explanation:

One point and the slope of the line

One point

One of the intercepts and the slope of the line

Both the intercepts

Two points

Answer:

All the above except "one point"

Step-by-step explanation:

Using one point and the slope of the line, we can find the slope intercept form and graph it from that.

Using one point wouldn't be enough data to graph a line.

Using one of the intercepts and the slope of the line will give is enough data to put it in slope intercept without having solve anything so we can graph it right away.

Using both intercepts lets us find the slope and we can then put it in slope intercept form to solve.

Using two points will let us solve for the slope and y-intercept in slope intercept form so we can graph them.

Best of Luck!

Answer:

he saw 32 cats

Step-by-step explanation:

cause 6 x 9 = 48 so do 4 x 9 and see what you get

Answer:

the answer for cats is 8

Step-by-step explanation:

And how I got that answer is i did 48/4 that equals 12 and 48/6 equals 8

Answer:

2

Step-by-step explanation:

It said it was 2 in edg. Have a great day.

Answer:

2 is the answer on edge 2021

Step-by-step explanation:

Answer:

$2278.846

Step-by-step explanation:

Given the following commision steps :

8% on first $1000;

12% next $2000;

20% on sales above $3000

Recorded sales for a week :

Monday $1500.00

Tuesday $3000.00

Wednesday $ 970.00

Thursday $4563.81

Friday $2760.42

This assu es that commision is calculated after weekly sales:

Total:

(1500 + 3000 + 970 + 4563.81 + 2760.42)

= $12794.23

8% on first $1000

0.08 × $1000 = $80

12% of $2000 = $240

20% of $(12794.23 - 3000)

= 0.2 × 9794.23

= 1958.846

Total commision for the week :

$(80 + 240 + 1958.846)

= $2278.846

Answer:

Always true

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

if x=3 then 6x=18. conditional statement

6(3) = 18

18 = 18

therefore, it is true

Answer:

A

Step-by-step explanation:

Recall that domain is simply the span of x-values a graph covers.

From the graph, we can see that the graph only covers x-values less than or equal to zero. Our x-values never cross and go beyond x = 0.

Therefore, our domain is all values less than or equal to 0.

As an inequality, this is:

[tex]x\leq 0[/tex]

In conclusion, our answer is A.

Answer: Choice A.  [tex]x \le 0[/tex]

x can be any number smaller than 0, or it can be equal to 0 itself.

This is because the furthest to the right we can go is at x = 0. This endpoint is included due to the filled in circle at the endpoint.

There is no left boundary, so the graph goes on forever toward negative infinity.

We can say [tex]-\infty < x \le 0[/tex] but it's easier to say [tex]x \le 0[/tex]

The domain in interval notation would be [tex](-\infty, 0][/tex]. The square bracket says "include this endpoint". The curved parenthesis means "exclude this endpoint". We cannot reach either infinity, so we always use a curved parenthesis with either infinity.

As implied, the domain is the set of all possible x values of a function. The range is the set of all possible y values.

Answer:

-19.8

Step-by-step explanation:

Answer: yes three yes correct there the same size

Step-by-step explanation:

Answer:

2, 3, and 4

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

P=26/52=1/2

Answer:

3

Step-by-step explanation:

The 3 is in the tens place representing the number 30.

~theLocoCoco

Answer:

2/3, 3/4, 1/3

Step-by-step explanation:

Answer: 2/3, 3/4, 1/3

Step-by-step explanation:

Answer:

The answer that is 92.3 is incorrect

Step-by-step explanation:

Answer:

(- 5, 2 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

Here (x₁, y₁ ) = A(- 8, - 6) and (x₂, y₂ ) = B(- 2, 10) , thus

midpoint = ( [tex]\frac{-8-2}{2}[/tex] , [tex]\frac{-6+10}{2}[/tex] ) = ([tex]\frac{-10}{2}[/tex] , [tex]\frac{4}{2}[/tex] ) = (- 5, 2 )

Answer:

+3 +5 +7 +9

Step-by-step explanation:

each time a pattern is solved you add 2

Answer:

Adding the next odd number to the previous sum.

Step-by-step explanation:

1+3=4

4+5=9

9+7=16

16+9=25

Answer:

m+5nx(9-p)-6-2r

The answer is b and d

Step-by-step explanation:

Hopefully this helped, if not HMU and I will gt you a better answer.

-have a great day! :)

Answer:

g(x)=6/5x -12

Step-by-step explanation:

Answer:

(4,-4)

Step-by-step explanation:

let the coordinates of B be (x,y)

midpoint formula = (x1 +y1/2, x2 +y2\2)

(3,0) = (2+x\2),(4+y\2)

comparing we get

3=( 2+x\2), 0=( 4+y/2)

6= 2+ x 0=4+y

x= 4 y=-4

hints: that divide sign is both for 2 and x

Answer:

a)10

b)-12

c)3.6

Step-by-step explanation:

Answer:

There are 270 longs

Step-by-step explanation:

Equations

We must write the problem into a mathematical model that allows us to apply the properties of basic algebra and solve for the variable which must be adequately set up.

We have three unknowns: the number of long blocks, flats blocks, and cubes. The conditions are given:

For the equation to be easier solved, let's set the variable as the number of cubes:

x = number of cubes

Considering the first condition, we have

3x = number of longs

3x-30 = number of flats

And finally:

[tex]x + 3x+3x-30=600[/tex]

Joining like terms:

[tex]7x=630[/tex]

Solving for x

[tex]\displaystyle x=\frac{630}{7}=90[/tex]

Therefore, there are 3x = 3*(90) = 270 longs

Answer: there are 270 longs

Answer:

A.

Step-by-step explanation:

The y-intercept starts at -5.

Using the rise over run method, we count 6 up and 2 to the right.

6/2 = 3.

y = 3x - 5

Answer:

What forces act on the ball in the horizontal direction as it rolls? None. So that means there is no horizontal acceleration and therefore the horizontal component of the ball's speed is constant.

And since the ball was only travelling horizontally at the instant it rolled off the table, initially the vertical component of its speed is 0. That means the time taken to hit the ground after rolling off the table is the same as if it was just dropped 0.950 m. We can find this time using one of the kinematic equations of motion in the vertical direction, taking downwards as positive. Then we have the following information:

u = initial velocity = 0 m/s

d = distance fallen = 0.950 m

a = acceleration (due to gravity) = 9.8 m/s²

t = time = ?

d = ut + 1/2 at². Since u = 0 this reduces to d = 1/2 at² and rearranges to t = √(2d/a) = √(2*0.95/9.8) = 0.4403 s.

In the same amount of time, the ball travels a horizontal distance of 0.352 m. We already know the horizontal velcoity is constant, so horizontal velocity is just horizontal distance divided by time = (0.352 m)/(0.4403 s) = 0.799 m/s.

Answer:

y= -1/3 - 1.33

Step-by-step explanation:

First you would find the slope by subtracting -2-(-3) over 2-5 which would be -1/3 for the slope and then the y-intercept is -1.33

Answer:

Step-by-step explanation:

This is a decreasing line that goes below x-axis