It took francisco 60 minutes to walk from his house to his grandmother’s house. what is 60 written as a product of factors greater than 1? each factor can have only 1 and itself as factors.

Answer:

Integrate( sqrt(9-x^2) from x=-3 to x=3)

Step-by-step explanation:

The equation for a full circle is (x-h)^2+(y-k)^2=r^2 where (h,k) is center and radius is r.

Your center, your (h,k) is (0,0). Your radius, your r, is 3.

So your equation is (x-0)^2+(y-0)^2=3^2 or more simply x^2+y^2=9.

We also must consider we don't have full circle.

Solving for y will give us the circle in terms of top half if we take positive values and bottom half if we take negative values. Since y is positive in the picture, you only see top half, we will only take the positive cases for y.

Subtracting x^2 on both sides gives: y^2=9-x^2

Square root both sides: y= sqrt(9-x^2)

(I did not choose -sqrt(9-x^2) because again y is positive).

So the x's in the picture range from -3 to 3.

The integral is therefore,

Integrate( sqrt(9-x^2) from x=-3 to x=3)

Answer:

-8

Step-by-step explanation:

what do you think, when you look at the examples given in the problem definition ?

don't you see the pattern, that f(x) = x+2 ?

f(1) = 1+2 = 3

f(2) = 2+2 = 4

f(3) = 3+2 = 5

so, if we follow this assumption, then

f(-10) = -10 + 2 = -8

Answer:

[(12+24)*7]/2=126. + area of circle. πr²/2= 72*3=216

Step-by-step explanation:

the answer is 342 if we assume valume of π to 3

Answer:

15n^2 as it the highest expression that is common among these three.

Answer:

6 minutes

Step-by-step explanation:

The equation for time together is

1/a+1/b = 1/c  where a and b are the times alone and c is the time together

1/10 + 1/15 = 1/c

Multiply by the  least common denominator to clear the fraction

30c(1/10 + 1/15 = 1/c)

3c+ 2c = 30

5c = 30

Divide by 5

5c/5 = 30/5

c = 6

Answer:

6 minutes

Step-by-step explanation:

Person A does 1 job in 10 minutes.

In 1 minute, person A does 1/10 of the job.

Person B does the same job in 15 minutes.

In 1 minute, person B does 1/15 of the job.

Working together, in 1 minute the do

1/10 + 1/15 of the job.

Working together, they take t minutes to do the job.

In 1 minute, they do 1/t of the job.

1/10 + 1/15 = 1/t

3/30 + 2/30 = 1/t

5/30 = 1/t

1/6 = 1/t

t = 6

[tex] \cos(θ) = \frac{6}{32} \\ θ = 79.19[/tex]

Answer:

Step-by-step explanation:

The shape cam be split into a triangle and a trapezoid

✔️Area of the trapezoid = ½(a + b)h

Where,

a = 12.5 ft

b = 16.7 ft

h = 11.6 ft

Plug in the values

Area of the trapezoid = ½(12.5 + 16.7)*11.6

Area of trapezoid = 169.36 ft²

✔️Area of the triangle = ½*b*h

b = 16.7 ft

h = 19.2 - 11.6 = 7.6 ft

Area of the triangle = ½*16.7*7.6

= 63.46 ft²

✔️Area of the shape = 169.36 + 63.46

= 232.82 ft²

Answer:

156.25

Step-by-step explanation:

1/2 × b ×h =12.5

12.5 ×9 =156.25 hope you ace it

Answer:

Length = 10.435 inches

Step-by-step explanation:

Let the length be l

Let the width be w

Since the length is 9 inches more than half the width.

Then;

L = 0.5w + 9

Perimeter of a rectangle is;

P = 2Lw

Thus;

P = 2w(0.5w + 9)

Since perimeter = 60

Then;

2w(0.5w + 9) = 60

w² + 18w = 60

w² + 18w - 60 = 0

From quadratic formula;

w ≈ 2.87 in

L = 0.5(2.87) + 9

L = 10.435 in

Answer:

third one is a required answer.

x =2y

or

1/x=y

Answer:

Option 3, where x = 6, y = 3; x = 10, y = 5; x = 14, y = 7

Step-by-step explanation:

Step 1:  Define proportional relationship

According to Khan Academy, "proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other."

Step 2:  Find the proportional relationship

Looking at option 3, we see that x is always 2 times bigger than y.  This means as y increases, x is twice that amount.  So if y is 10, x would be 20 and so on.  Therefore, Option 3 is the correct answer.

Answer:  Option 3, where x = 6, y = 3; x = 10, y = 5; x = 14, y = 7

Answer:

$1272.36 ( average weekly sales for first 3 weeks )

Step-by-step explanation:

weekly online sales = S(t)

Determine average weekly sales for first 3 weeks

S(t) = 2e^t

total sales = ∫ S(t) dt        

∴ Average weekly sales for first 3 weeks  ( note : S(t) = 2e^t  )

=  [tex]\int\limits^3_0 {2e^t \, dt / ( 3 - 0 )[/tex]            

= 2 [ e^t ] ³₀ / 3 = 2 ( e^3 - e^0 ) / 3 =  2 ( 6.3618 ) = 12.7236 hundreds

= $1272.36 ( average weekly sales for first 3 weeks )

Answer:

n=4

Step-by-step explanation:

3n - (2+n) = 6

Distribute the minus sign

3n -2-n = 6

Combine like terms

2n-2 =6

Add 2 to each side

2n-2+2 = 6+2

2n = 8

Divide by 2

2n/2 = 8/2

n=4

Answer:

B, C, D

Step-by-step explanation:

In this problem, the range is what the output, or y, can be. The origin, or the middie of the graph, is when x=0 and y=0. From the 10s on the screen, we can gather that 5 lines = a distance of 10 on the graph. Using this information, we can say

5 lines = distance of 10

divide both sides by 5 to find the distance for each line

1 line = distance of 2

The function goes from y=0 to three lines down, for a distance of 6. The range is therefore [-6,0] as all values from -6 to 0 on the y axis are included on the graph, including 0 and -6. In this range, -6, -2, and -1 are all included.

Answer:

Please show an image

Answer:

a) 4 packages

b) 7000 g or 7 kg

Step-by-step explanation:

x is the number of 250g packages and y is the number of 750g packages.

2x = y

3(x + 2 x (750 : 250)) = 5(y - 2)

3(x + 6) = 5(y - 2)

3(x + 6) = 5(2x - 2)

3(x + 6) = 5(2(x - 1))

3(x + 6) = 5 * 2 * (x - 1)

3(x + 6) = 10(x - 1)

3x + 18 = 10x - 10

(3x + 18) + 10 = (10x - 10) + 10

3x + 28 = 10x

28 = 10x - 3x

28 = 7x

x = 28/7

x = 4

y = 2 * 4 = 8

(250 * 4) + (750 * 8) = 7000 g

The derivative of a function f(x) is defined as

[tex]f'(x)=\displaystyle\lim_{h\to0}\frac{f(x+h)-f(x)}h[/tex]

For f(x) = 3x ² + 4, we have

[tex]f'(x)=\displaystyle\lim_{h\to0}\frac{(3(x+h)^2+4) - (3x^2+4)}h[/tex]

[tex]f'(x)=\displaystyle\lim_{h\to0}\frac{(3(x^2+2xh+h^2) - 3x^2}h[/tex]

[tex]f'(x)=\displaystyle\lim_{h\to0}\frac{6xh+3h^2}h[/tex]

[tex]f'(x)=\displaystyle\lim_{h\to0}(6x+3h) = \boxed{6x}[/tex]

Answer:

if you are required to find the equation of a straight line use the formula y-y1= m (x-x1)

y+2=-3(x-1)

y+2=-3x+3

y= -3x+3-2

y -3x+1

hope this helps

Answer:

y = -3x + 1

Step-by-step explanation:

(y -(-2)) = -3(x-1)

y+ 2 = -3x+ 3

y = -3x + 1

(15×4)6÷6[{32÷4(7x2-15+5)}+3]

= -2

[ use BODMAS rule]

Answer:

15

Step-by-step explanation:

The amplitude of y=sin(x) is 1 with a maximum of y=1 and a minimum of y=-1. It's amplitude is 1 because that is the distance the max( y=1 )is from the mid line (y=0) or the distance the min( y=-1 ) is from the mid line (y=0).

So we just need to find the distance the mid line, y=-12, and the max,y= 3, is from each other.

3--12=3+12=15

Answer:

Slower trains: 123 km/h

Faster train: 134 km/h

Step-by-step explanation:

In order to solve this problem, one must know the following formula:

[tex]speed*time=distance[/tex]

The problem gives one the following information:

Let ([tex]speed_1[/tex]) represent the speed of the slower train and ([tex]speed_2[/tex]) represent the speed of the faster train.

One can form an equation, let (x) represent the speed of the slower train. Using the distance equation, one can state that the speed of each train times the travel time equals the distance. Since the trains met each other in (6) hours, and the combined distance traveled between the two trains is (1542 km); one can use this information to form an equation.

[tex](travel\ time)(speed_1)+(travel\ time)(speed_2)=distance[/tex]

Substitute,

[tex]6(x)+6(x+11)=1542[/tex]

Simplify, distribute, multiply every term inside of the parenthesis by the term outside of it. Then combine like terms,

[tex]6x+6x+66=1542[/tex]

[tex]12x+66=1542[/tex]

Inverse operations,

[tex]12x+66=1542[/tex]

[tex]12x=1476[/tex]

[tex]x=123[/tex]

Solve for the speed of the faster train. It is given that it is (11 km/h) faster than the slower train.

[tex]speed_1+11=speed_2\\123+11=speed_2\\134=speed_2[/tex]

Answer:

12/13

Step-by-step explanation:

sinX = opposite/hypotenuse = 12/13

Answer:

what?????............. :O

Answer:

20 students are absent

Step-by-step explanation:

75/100 × 80 = 60

If 60 were present out of the 80

80 - 60 = 20

Have a great day :)

Answer:

0.0378

0.378

3.78

378

3780

Answer: 0.0378, 0.378, 3.78, 378, 3780

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

The reason why an absolute value equation equal to zero only has one solution

We set the absolute value equation equal to ± the solution

±0 = 0  There is only one value for ±0 which is 0, therefore there is only one solution