The calculation

add the quotient of 108 and 12 and the quotient of 18 and 2

The maximum height reached is greater than 12m, hence the ball reach a height of 12m

The height of the toy cannon all launched is expressed as [tex]h(t) = -5t^2 + 20t + 4[/tex]

h is the height reached by the ball

t is the time taken by the ball to reach its maximum height

A) In order to determine whether the ball reached the height of 12m, we will have to substitute h = 12 into the formula as shown:

[tex]12= -5t^2 + 20t + 4\\ -5t^2 + 20t + 4 -12=0\\ 5t^2 - 20t +8=0\\[/tex]

Hence the equation that can be used to tell whether the ball reaches a height of 12 is [tex]5t^2-20t+8=0[/tex]

B) At the maximum height

dh/dt = 0

-10t + 20 = 0

-10t = -20

t = 20/10

t = 2

Get the maximum height reached

h(2) = -5(2)^2 + 20t + 4

h(2) = -5(4) + 20t + 4

h(2) = -20 + 20(2) + 4

h(2) = -20+40+4

h(2) = 24 m

Since the maximum height reached is greater than 12m, hence the ball reach a height of 12m

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To determine whether the ball reaches a height of 12 meters, we set the height equation equal to 12 and solve the quadratic equation. Upon solving, we find that the ball reaches 12 meters, hence the answer to whether the ball reaches 12 meters is yes.

To determine whether the toy cannon ball reaches a height of 12 meters, we can set the height equation h(t) equal to 12 meters:

12 = -5t^2 + 20t + 4.

To solve for t, we need to rearrange the equation and solve the resulting quadratic equation:

0 = -5t^2 + 20t + 4 - 12

0 = -5t^2 + 20t - 8

This is the equation that can be used to tell whether the ball reaches a height of 12 meters. To determine if the ball does reach 12 meters, we solve for the roots of the equation:

-5t^2 + 20t - 8 = 0

Using the quadratic formula, we find the possible values for t. If there are real, positive solutions, it means the ball does reach 12 meters at those times.

Upon solving, we find that the ball indeed reaches a height of 12 meters because there are real, positive solutions for t.

Therefore, the answer to Part B is yes; the ball does reach a height of 12 meters.

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Answer: F. (2x – 1)(x + 4)

Step-by-step explanation:

https://socratic.org/questions/how-do-you-factor-2x-2-7x-4-1

The expression that should be equivalent to given equation is (2x – 1)(x + 4)

The equation is [tex]2x^2 + 7x +4[/tex]

[tex]2x^2 + 7x +4[/tex]

[tex]2x^2 +8x - x + 4\\\\2x (x + 4) - 1(x + 4)[/tex]

(2x -1 ) (x + 4)

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Answer:

black balls: 10/20 or 1/2

red balls :8/20 or 2/5

white balls: 2/20 or 1/10

Step-by-step explanation:

Answer:

The answer is 1

Step-by-step explanation:

8/20 or 0.4- probability of red ball in one draw

2/20 or 0.1 - probability of white ball in one draw

10/20 or 0.5 - probability of black ball in one draw

0.4 + 0.5 + 0.1 = 1

Sorry I'm late just wanted to put the right answer!

Answer:

n = 8, w = 3 and perimeter = 122.83 units.

Step-by-step explanation:

Let the angle M is the angle between the equal sides of isosceles JAM.

So, JM = MA

⇒ 35 = 4n + 3

⇒ 4n = 32

⇒ n = 8 (Answer)

Now, if ∠ J = 14w - 1 and ∠ M = 98°, then

2(14w - 1) + 98 = 180

⇒ 2(14w - 1) = 82

⇒ 14w - 1 = 41

⇒ w = 3 (Answer)

Now, draw a perpendicular bisector on JA from vertex M and it meets JA at P say.

So, Δ MPJ will be a right triangle with ∠ J = (14w - 1) = 41° {Since w = 3}

Hence, [tex]\cos 41 = \frac{JP}{JM} = \frac{JP}{35}[/tex]

⇒ JP = 35 cos 41 = 26.415

So, JA = 2 × JP = 52.83  

So, the perimeter of Δ JAM is = 35 × 2 + 52.83 = 122.83 units (Answer)

Answer:

1.5   or   3/2

Step-by-step explanation:

4x+2=8

4x=6

x=6/4

x=3/2

Answer:

(0,−5),(1,−3),(2,−1)

Step-by-step explanation:

Answer:

I believe C)45cm but I know for sure its not B)42cm

Step-by-step explanation:

Answer:

y = 1/2 x + 15

Step-by-step explanation:

The equation for the word problem is y = 1/2 x + 15.

"one half" is 1/2

sum means addition

Answer:

32

Step-by-step explanation:

c^3/2 when c=4

4^3/2

4^3=4*4*4=16*4=64

64/2=32

Answer:

Adult Ticket cost $9.50 and Children Ticket cost $7.00

Step-by-step explanation:

Let single adult tickets cost "a" and single children ticket cost "c"

6 adult and 2 children ticket is $71, we can write:

6a + 2c = 71

Also,

3 adult and 4 children tickets cost $56.50, so we can write:

3a + 4c = 56.5

We multiply 2nd equation by "-2", to get:

-2 * (3a + 4c = 56.5) = -6a -8c = -113

Now we add this equation with 1st and eliminate a and solve for c:

6a + 2c = 71

-6a -8c = -113

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

-6c = -42

c = -42/-6

c = 7

To find a, we can plug this into 1st equation and then get our answer.

6a + 2c = 71

6a + 2(7) = 71

6a + 14 = 71

6a = 57

a = 57/6

a = 9.5

Hence,

Adult Ticket cost $9.50 and Children Ticket cost $7.00

The complete table:

NUMBER OF TICKETS SOLD ON FRIDAY AND SATURDAY

The total number of tickets sold over these two days is 8,938

Step-by-step explanation:

The table below shows the numbers of tickets sold at a movie theater on Friday.

NUMBER OF TICKETS SOLD

The number of each type of ticket sold on Saturday is described below

We need to complete the table above to show the numbers of tickets sold on Saturday and find the total number of tickets sold over these two days

∵ The number of adult tickets on Saturday is 2 times as many as

   the number of adult tickets sold  on Friday

∵ The number of adult tickets on Friday = 1,678

∴ The number of adult tickets on Saturday = 2 × 1,678 = 3,356

∵ The number of children's tickets on Saturday is 3 times as many

   as the number of children's tickets sold  on Friday

∵ The number of children's tickets on Friday = 976

∴ The number of children's tickets on Saturday = 3 × 976 = 2,928

The complete table:

NUMBER OF TICKETS SOLD ON FRIDAY AND SATURDAY

∵ Adult tickets sold over the 2 days = 1,678 + 3,356 = 5,034

∵ Children's tickets sold over the 2 days = 976 + 2,928 = 3,904

∴ The total tickets sold over the 2 days = 5,034 + 3,904 = 8,938

The total number of tickets sold over these two days is 8,938

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Answer:

13

Step-by-step explanation:

3 x 3 = 9

7 + 3 = 10

7 + ? = 3 + 7 + 3 + 7

7 + ? = 20

? = 13

Answer:

Step-by-step explanation:

[tex]p\times p=9\\\\p^2=9\to p=\sqrt9\to \boxed{p=3}\\\\c+p=10\qquad\text{put the value of}\ p\\\\c+3=10\qquad\text{subtract 3 from both sides}\\\\\boxed{c=7}\\\\c+s=p+c+p+c\qquad\text{put the values of}\ p\ \text{and}\ c\\\\7+s=3+7+3+7\\\\7+s=20\qquad\text{subtract 7 from both sides}\\\\\boxed{s=13}[/tex]

Answer:

189.8 m

Step-by-step explanation:

See the diagram attached.

Now, the plane is at B and the two ships are at C and at D.

So, angle of depression of C from B is ∠ OBC = ∠ ACB = 35°

Again, the angle of depression of D from B is ∠ OBD = ∠ ADB = 25° ,

Now, from the right triangle Δ ACB,  

[tex]\tan 35 = \frac{AB}{AC} = \frac{265}{AC}[/tex]

⇒ [tex]AC = \frac{265}{\tan 35} = 378.5[/tex] m.

Similarly, from the right triangle Δ ADB,

[tex]\tan 25 = \frac{AB}{AD} = \frac{265}{AD}[/tex]

⇒ [tex]AD = \frac{265}{\tan 25} = 568.3[/tex] m.

Hence, the distance between the ships = CD = AD - AC = 568.3 - 378.5 = 189.8 m (Approx.) (Answer)

The distance apart is the two ships is 189.8 meters.

Given

A plane flying due east at 265 m above sea level, the angles of depression of two ships sailing due east measure 35 degrees and 25 degrees.

The angle of elevation, the angle of depression is the angle at which you would draw a line from a point on a horizontal line to intersect another point that falls below the line.

The plane is at B and the two ships are at C and at D.

Then,

The angle of depression of C from B is ∠ OBC = ∠ ACB = 35°.

And the angle of depression of D from B is ∠ OBD = ∠ ADB = 25°.

From the right triangle Δ ACB,

[tex]\rm Tan35= \dfrac{AB}{AC}\\\\ AC= \dfrac{265}{Tan35}\\\\AC = \dfrac{265}{0.70}\\\\AC =378.57[/tex]

Again in the right triangle Δ ADB,

[tex]\rm Tan 25=\dfrac{AB}{AD}\\\\AD =\dfrac{265}{Tan25}\\\\ AD = \dfrac{265}{0.46}\\\\AD =569.30[/tex]

Therefore,

The distance apart are the two ships is;

=  568.3 - 378.5 = 189.8 m

Hence, the distance apart is the two ships is 189.8 meters.

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Answer:

5 1/6

Step-by-step explanation:

6 = 36/6, because 6*6 = 6

36/6 - 5/6 = 31/6

31/6 = 5 1/6

Answer:5 1/6

Step-by-step explanation:

Answer:

C = 35 + 45h

In the equation above $35 is the initial value which interprets the cost for motor parts and $45/hour is the rate of charge of the mechanic per hour.

Step-by-step explanation:

Charges for parts and $45 per hour for  labor that takes a mechanic for maintenance of a car.

It costs $125 as Terri spent 2 hours for car maintenance.

Since the function is linear, so we can write  

125 = 45 × 2 + x {Where x is the charges for parts}

⇒ x = 35

Therefore, the equation that models the situation is given by  

C = 35 + 45h ......... (1)

where C is the total cost and h is the number of hours.

Here, in equation (1) $35 is the initial value that interprets the cost for parts and $45/hour is the rate of charge of the mechanic per hour. (Answer)

Answer:

Diagram was not given.

Still I had drawn it, hope may it will helpful to you. So as per my diagram I had solved the sum.

The area of the shaded region is 176.96 ≈ 178 cm²

Step-by-step explanation:

Given:

radius of the circle        = r  = 8 cm

length of the rectangle = L = 12 cm

breadth of the rectangle = B = 2 cm

To Find:

Area of shaded region = ?

Solution:

[tex]\textrm{Area of rectangle} = Length\times Breadth\\= L\times B\\= 12\times 2\\= 24\ cm^{2}[/tex]

[tex]\textrm{Area of Circle} = \pi \times (radius)^{2} \\=\pi \times r^{2}\\=3.14\times 8^{2}\\=200.96\ cm^{2}[/tex]

Now, The Area of Shaded region will be

[tex]\textrm{Area of Shaded region}=\textrm{Area of Circle}-\textrm{Area of Rectangle}\\=200.96 - 24\\=176.96\ cm^{2} \\=178\ cm^{2}\........... \textrm{Rounded to tenth}[/tex]

The area of the shaded region is 176.96 ≈ 178 cm²

Answer:

177.06

Step-by-step explanation:

i got it wrong on khan academy

Answer:

The correct graph is attached below.

Step-by-step explanation:

Given:

Initial temperature is 0°.

Decrease in temperature per hour is 12°.

Since, the initial temperature is 0°, the line must pass through the origin as temperature is plotted along the y-axis.

Also, decrease in temperature per hour is 12°. So, this represents the slope of the line. So, the slope should be -12 as there is decrease in temperature with increasing time.

So, the correct graph will be a line passing through origin and the slope of the line must be -12. Also, the temperatures will be along the negative y-axis as the values are decreasing with time.

Hence, the third graph is the correct one and is shown below.

Answer: Damien has 21 red pieces

Step-by-step explanation:

First, 7/8 of the rectangle is coloured red.

Then, the 7/8 was cut into a size 1/24 of the rectangle each.

That consequently means that 24 of those pieces will form the whole shape.

Since red covers 7/8 of the rectangle, the number of red pieces invariably becomes

⅞ × 24 pieces, which is equal to 21 pieces

Therefore, Damien has cut the red part of the rectangle into 21 pieces

Final answer:

Damien has 21 red pieces after dividing the red part of the rectangle, which is 7/8, into pieces that are each 1/24 of the whole rectangle.

Explanation:

To find the number of red pieces Damien has, we first determine the fraction of the rectangle that is colored red, which is 7/8. Then, we find the size of each piece that Damien cuts, which is 1/24 of the whole rectangle.

Since each piece is 1/24, and Damien is cutting up only the red part which is 7/8 of the whole, we calculate the number of pieces by dividing the red part by the size of each piece: number of red pieces = (7/8) / (1/24).

To do this division, we multiply by the reciprocal of the divisor: (7/8) * (24/1) = 21. Therefore, Damien has 21 red pieces.

Answer:

The solution to the given systems of linear equation is {3, -1} lies in IV Quadrant.

Step-by-step explanation:

Given:

x-3y = 6  ........( 1 )

x+y=2    ........( 2 )

To find :

x = ?

y = ?

Solution:

Let solve the  above equation to get the solutions.

Eliminate X by subtracting the two equations equation 1 minus equation 2

[tex](x-3y) - (x+y) = 6 - 2\\-4y = 4\\\therefore y=-1[/tex]

Now substitute for y = -1 in equation 2 we get

[tex]x+(-1)=2\\\therefore x = 2+1\\\therefore x = 3[/tex]

Therefore, solution set is {3, -1}

In

I Quadrant {x,y} = {+,+}......both the coordinates are positive.

II Quadrant {x,y} = {-,+}.....X coordinate is negative and Y coordinate is positive.

III Quadrant {x,y} = {-,-}......both the coordinates are negative.

IV Quadrant {x,y} = {+,-}.....X coordinate is positive and Y coordinate is negative. {3,-1}

Point A on the graph is the solution.

Answer:

For those who want a quick answer. Its D on edge

Step-by-step explanation:

Answer:

$3.8

Step-by-step explanation:

2.35/11=0.2136

0.2136*18=3.8448

Answer:

The quantity of currency  in the pockets does Stephanie has is 45 nickles and 10 dims  .

Step-by-step explanation:

Given as :

The total amount of money does Stephanie have = $ 3.25

The total money is in the form of nickels and dimes

Let the number of nickels = n

And The number of dims = d

∵ we know that 20 nickles makes 1 dollar

And 10 dimes makes 1 dollar

So , in total of 3.25 dollar the number of dime and nickles be

∵ 20 nickles makes 1 dollar

∴ 45 nickles will makes [tex]\frac{1}{20}[/tex] × 45 dollar

I.e 45 nickles will makes 2.25 dollar

Now, ∵ 10 dimes will make 1 dollar

So, The total number of nickles and dimes satisfying equation

45 nickles + 10 dimes = 2.25 dollar + 1 dollar = 3.25 dollar

Hence The quantity of currency  in the pockets does Stephanie has is 45 nickles and 10 dims  . Answer

Answer:

4.40

Step-by-step explanation:

The amount of money Ivan has in his pocket is n.

Meg has $3.25 more than Ivan. Meg has $7.65.

Complete the equation that models the situation. Then, give the value of n.

$3.25

÷

+

$7.65

×

$10.90

$4.40

Bryan has enough to buy skateboard as it will cost $44.94

Step-by-step explanation:

Original price = $70.00

Discount = 40%

Amount of discount = 40% of original price

Amount of discount = [tex]\frac{40}{100}*70[/tex]

Amount of discount = [tex]\frac{2800}{100}[/tex]

Amount of discount = $28

Price after discount = Original price - amount of discount

[tex]Price\ after\ discount=70-28 = $42\\[/tex]

Sales tax = 7% = [tex]\frac{7}{100} = 0.07[/tex]

Sales tax amount = Price after discount (0.07)

[tex]Sales\ tax\ amount= 42(0.07) = $2.94\\[/tex]

Price of skateboard = Price after discount + sales tax

Price of skateboard = 42+2.94 = $44.94

Bryan has enough to buy skateboard as it will cost $44.94

Keywords: sales tax, subtraction

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Answer:

w(2w+7) = 99

2w^2 + 7w - 99 = 0

(  2w   -   11  )(w   +    9  ) = 0

w+9=0 results in negative measures

2w-11 = 0

2w = 11

w = 11/2 = 5.5

L = 2w + 7 = 18

Answer:

B) 16x+11/4 =4x+5-2

Step-by-step explanation:

the equation that has no solution is B)[tex]\( \frac{16x + 11}{4} = 4x + 5 \).[/tex]

The correct option is (B).

To find out which equation has no solution, let's solve each equation and see if any leads to a contradiction.

A)[tex]\( \frac{10x + 5}{2} = 3x + 6 \)[/tex]

  Multiply both sides by 2 to eliminate the fraction:

[tex]\( 10x + 5 = 6x + 12 \)[/tex]

  Subtract (6x) from both sides:

[tex]\( 4x + 5 = 12 \)[/tex]

  Subtract 5 from both sides:

  ( 4x = 7 )

  Divide both sides by 4:

[tex]\( x = \frac{7}{4} \)[/tex]

B) [tex]\( \frac{16x + 11}{4} = 4x + 5 \)[/tex]

  Multiply both sides by 4:

[tex]\( 16x + 11 = 16x + 20 \)[/tex]

  Subtract (16x) from both sides:

  ( 11 = 20 ) - Contradiction

C) [tex]\( \frac{8 - 6x}{4} = 4 + 2x \)[/tex]

  Multiply both sides by 4:

  [tex]\( 8 - 6x = 16 + 8x \)[/tex]

  Subtract 8 from both sides:

[tex]\( -6x = 8x + 8 \)[/tex]

[tex]\( -6x = 8x + 8 \)[/tex]

[tex]\( 0 = 14x + 8 \)[/tex] - Contradiction

D)[tex]\( \frac{18x - 10}{2} = 9x - 5 \)[/tex]

  Multiply both sides by 2:

 [tex]\( 18x - 10 = 18x - 10 \)[/tex] - No contradiction, the equation holds true for all ( x ).

So, the equation that has no solution is B)[tex]\( \frac{16x + 11}{4} = 4x + 5 \).[/tex]

complete question given below:

Which equation has NO solution?

A) (10x+5)/2 =3x+6

B) (16x+11)/4 =4x+5

C) (8-6x)/4 =4+2x

D) (18x-10)/2 =9x-5

Answer:

D

Step-by-step explanation:

One or more corresponding angles are not congruent.

ABC is not congruent to EFG

BCD is not congruent to FGH

CDA is not congruent to GHE

DAB is congruent to HEF

Answer: D

Step-by-step explanation:

Answer:

5 meters/second

Step-by-step explanation:

100meters/20 seconds gives the average of 5 m/s

Final answer:

The runner's speed in the hundred meter race completed in 20 seconds is 5 meters per second. To calculate this, divide the total distance (100 meters) by the total time (20 seconds).

Explanation:

To calculate the speed of the runner in meters per second, we divide the distance travelled by the time it took to complete that distance. In this case, the runner completed a 100 meter race in 20 seconds. Using the formula speed = distance/time, we find that the speed is 100 meters / 20 seconds = 5 meters per second.

If the sprinter accelerates for the first 20 meters and then maintains that speed for the remainder of the 100-meter dash, we must first calculate the acceleration period's average speed. As it takes 20 seconds to run 100 meters, the speed over those 20 meters is also 5 meters per second. Once the sprinter reaches this speed at 20 meters, he will continue at this constant speed for the remaining 80 meters. Thus, the time to complete the race is the time taken to accelerate for 20 meters plus the time taken to run the remaining 80 meters at 5 m/s.

Answer:

The minimum number of weeks is 15 weeks after that it will take Reiko to make profit.

Step-by-step explanation:

Reiko spent $5200 to obtain her merchandise and it cost her $550 per week for general expenses.

So, the total cost for her business after w weeks will be  

C = 5200 + 550w ........ (1)

Now, she earns $900 per week in sales.

So, after w weeks her total earning is given by  

E = 900w ......... (2)

Now, the number of weeks after that the cost and earning will be equal, will be given by

5200 + 550w = 900w

⇒ 350w = 5200

⇒ w = 14.85

So, the minimum number of weeks is 15 weeks after that it will take Reiko to make a profit. (Answer)

Answer:

900w>6500+550w

Answer:

250 berries

Step-by-step explanation:

10 to 1 means 10 times as many berries as oranges

25x10=250

If there are 25 oranges then the number of berries would be​ 250 and this can be determined by using the arithmetic operations.

Given :

The ratio of berries to Oranges is 10:1.

The following steps can be used to determine the number of berries if there are 25 oranges:

Step 1 - Let the total number of berries be 'a' and the total number of oranges be 'b'.

Step 2 - As per the given data:

[tex]\dfrac{a}{b}=\dfrac{10}{1}[/tex]

Step 3 - If there are 25 oranges then the number of berries would be:

[tex]\dfrac{a}{25}=\dfrac{10}{1}[/tex]

[tex]a = 25\times 10[/tex]

a = 250

So, if there are 25 oranges then the number of berries would be​ 250.

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