the product of three numbers is -216, but their sum is -18. What are these three numbers?

change in velocity = 20 - 0 = 20

change in time = 2 seconds

Divide the change in velocity over the change in time: 20/2 = 10

The average acceleration is 10 m/s^2

I.e, each second, the speed increases by 10 m/s

Runner's average acceleration was 10 m / s²

The average acceleration refers to how fast the runner is going in relation to time.

It is calculated by the formula:

= Change in speed / Time

Change in distance here is:

= 20 m/s - 0 m/s

= 20 m/s

The acceleration is therefore:

= 20 / 2

= 10 m/s²

In conclusion, the runner was accelerating at a rate of 10 m/s².

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Answer:

12 days

Step-by-step explanation:

Time taken by one man = x days , and that by 1 boy = y days

work done in 1 day by one man = 1/x

work done in 1 day by one boy= 1/y

work done by 2 men in one day = 2/x

work done by 7 boys in one day = 7/y

2/x + 7/y = 1/4      -----> [ 1]

work done by 4 men in one day = 4/x

work done by 4 boys in one day = 4/y

4/x + 4/y = 1/3       ----> [2]

Multiplying  equation 1 by  , 2 ,  

2(2/x + 7/y = 1/4   )

 = 4/x + 14/y = 1/2           ---> [3]

solving equations 2 and 3

 4/x + 4/y = 1/3  

- 4/x + 14/y = 1/2  

==============

-10/y = 2-3/6

-10/y = -1/6

-1/6y = -10

y = -10 × 6/-1

  = 60 

2/x + 7/y = 1/4

2/x + 7/60 = 1/4

7/60 - 1/4 = -2/x

-8/60 = -2/x

-120 = -8x

x = -120/-8

x = 15

=================================

Time taken by 1 man to do the  whole job = 15 days

time taken by 1 boy to do the whole  job = 60 days

time taken by one boy and one man to do one day's work = 1/60 + 1/15

                                         = 1/60 + 4/60

                                         = 5/60  = 1/12

Together they can do it in 12 days !

Riding a bicycle for one hour burns 700 calories. Therefore,  biking for two hours burns a total of 1400 calories.

To solve this question, we need to understand that vacuuming and mopping for an hour burns 280 calories, which is 40% of the calories burned by biking for the same time. The first step is to determine the total number of calories burned when biking for one hour.

Let x represent the total number of calories burned by biking for one hour. According to the problem, 40% of x is 280 calories, which we can write as:

0.40x = 280 calories

To find the value of x, we divide both sides of the equation by 0.40:

x = 280 / 0.40

x = 700 calories

Thus, biking for one hour burns 700 calories. Now to find out the total number of calories burned by biking for two hours, we simply multiply this number by 2:

Total calories for 2 hours of biking = 700 calories × 2

Total calories for 2 hours of biking = 1400 calories

The answer is that riding the bicycle for two hours burns a total of 1400 calories.

Answer:

-80*pi

Step-by-step explanation:

pi*-80 can be written alternatively as -80*pi.

Answer: 8n

==========================================================

Explanation:

The two sides 4n+5 and 5n+6 have the terms 4n and 5n which add to 9n. We need 8n to add onto this so that we end up with 17n. In other words, 4n+5n+8n = 9n+8n = 17n

So that is why the answer is 8n. We don't have anything added or subtracted to it because the "+5" and "+6" in the two given expressions (4n+5 and 5n+6) add up to 5+6 = 11 which is what we want in the perimeter expression 17n+11

Side 1 = 4n+5

Side 2 = 5n+6

Side 3 = 8n

Perimeter = (side1) + (side2) + (side3)

Perimeter = (4n+5) + (5n+6) + (8n)

Perimeter = 4n+5 + 5n+6 + 8n

Perimeter = (4n+5n+8n) + (5+6)

Perimeter = 17n+11

So that confirms we have the proper expression for the third missing side.

Question

The expression 17n+11 represents the perimeter of a triangle. The other two sides measure 4n+5 and 5n+6. A simplified expression that represents the measure of the third side would be...?

Answer:

Step-by-step explanation:

you simply take off the misure of the know sides from the perimeter

(17n + 11) - (4n +5 - 5n + 6) =

8n

Answer:

A= 40

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3/4 (2a-6)+1/2=2/5(3a+20)

(3/4) (2a) + (3/4) (-6) + 1/2 = (3a) + (2/5) (20)

(distribute)

3/2a + -9/2 + 1/2 = 6/5a + 8

(3/2 a) + ( -9/2 + 1/2 ) = 6/5a + 8 (Combine like terms)

3/2a + -4 = 6/5a + 8

3/2a -4 = 6/5a+8

Step 2: Subtract 6/5a from both sides.

3/2a - 4 - 6/5 a = 6/5a + 8 - 6/5 a

3/10 a - 4= 8

Step 3: Add 4 to both sides.

3/10a -4 +4 = 8 + 4

3/10 a = 12

Step 4: Multiply both sides by 10/3

(10/3) * (3/10a) = (10/3) * (12)

a = 40

Answer:

40

Step-by-step explanation:

Answer:

15 inches by 16 inches

OR

1 foot 3 inches by 1 foot four inches

Answer:

(4,-12)

Step-by-step explanation:

The equation of a circle has the following form:

[tex](x-h)^2+(y-k)^2=r^2[/tex] where (h,k) is the center of a circle with radius r.

Our equation is:

[tex](x-4)^2+(y+12)^2=17^2[/tex]

The center is (4,-12).

Answer:

(4,-12)

Step-by-step explanation:

Answer: D

Step-by-step explanation:

Ratio of Top:Bottom

Top/Bottom

5.5/7.5

5.5/7.5 * 2/2 = 11/15

Answer:

D

Step-by-step explanation:

You want the ratio of the width to the length

w/L = 5.5/7.5 There are no decimals in any answer except b and it looks it is wrong. The reason is that the numerator is divided by 2 to give 5.5/2 = 2.75  and the denominator is multiplied by 2 to give 15. So B is out.

C

C: is pretty close. The problem is that the ratio is stated as width to length. C does do the same things to top and bottom (multiplies both of them by 2) but this answer is upside down of right.

I don't know exactly what was done with A but it isn't right.

Answer D

[tex]|n+8|>3\iff n+8>3\ \vee\ n+8<-3\qquad\text{subtract 8 from both sides}\\\\\boxed{n>-5\ \vee\ n<-11}[/tex]

Answer:

The length of the rectangle is 17 cm and the width of the rectangle is 5 cm.

Step-by-step explanation:

Given the measurements in the question, you can set up two different equations to find the length and width of the rectangle.  First, the formula for the perimeter of a rectangle is:  P = 2W + 2L, where W = width and L=length.  In this problem the L is '7 more than twice its width', this means our first equation is:

L = 2W + 7

Next, we can use this expression in our formula for perimeter to get our second equation:

P = 2W + 2(2W + 7)  or 44 = 2W + 2(2W + 7)

Distribute:  44 = 2W + 4W + 14

Combine like terms:  44 = 6W + 14

Subtract 14 from both sides:  44 - 14 = 6W + 14 - 14 or 30 = 6W

Divide 6 from both sides:  30/6 = 6W/6 or W = 5

Now, solve for L:  L = 2(5) + 7 or L = 10 + 7 = 17

So, the width is 5cm and the length is 17 cm.

The length of the rectangle is 17 cm and the width of the rectangle is 5 cm

The area of Rectangle is length times of width.

Given that perimeter of a rectangle is 44 cm.

Its length is 7 more than twice its width.

Length=2w+7

Width=w

Perimeter=2(Length+Breadth)

44=2(2w+7)+2w

Apply distributive property on right hand side

44=4w+14+2w

44=6w+14

Subtract 14 on both sides

30=6w

Divide both sides by 5

5=w

So width of rectangle is 6cm and length is 2(5)+7=10+7=17 cm

Hence, the length of the rectangle is 17 cm and the width of the rectangle is 5 cm

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Half Tens is a way of multiplying where we have to find the value of given numbers. First we double any 'one' of the two given numbers and multiply both to get an answer. Then we divide that answer by '2' to get the answer.

Lets take two numbers as 16 and 340

[tex]16\times340=?[/tex]

Double the number 16

[tex]32\times340=10880[/tex]

Now we will divide this by 2

[tex]\frac{10880}{2}= 5440[/tex]

So, if we check [tex]16\times340=?[/tex] , it is 5440.

Similarly if we double the number 340, we get 680

Now, [tex]16\times680=10880[/tex]

And 10880/2 = 5440

Hence, in both ways the answer is 5440.

In Half-Tens method first, double the first number then multiply that number with the second number, and then divide that value by 2 the result obtained is the required result.

Given :

Noah loves the Half-Tens facts and often uses them to solve multiplication problems.

It is given that make up a 2-digit by 3-digit multiplication problem for which using Half Ten facts is efficient.

So, let the two numbers be 56 and 362 then multiply both the numbers by using the Half-Tens method.

First, double the two-digit number:

[tex]=56\times2[/tex]

= 112

Then multiply the above number by 362.

[tex]=112\times 362[/tex]

= 40544

Then divide the above number by 2.

[tex]=\dfrac{40544}{2}[/tex]

= 20272

Now, check : [tex]56\times 362= 20272[/tex]

Now, similarly double the number 362.

[tex]=362\times 2[/tex].

= 724

Then multiply the above number by 56.

[tex]=724\times 56[/tex]

= 40544

Then divide the above number by 2.

[tex]=\dfrac{40544}{2}[/tex]

= 20272

Now, check : [tex]56\times 362= 20272[/tex]

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Answer:

25 nautical miles

Step-by-step explanation:

We need to find the rate.  We can do so using the formula, distance = rate * time

d= rt

We know the distance and the time, so we need to solve for the rate

d/t = rate

d= 150 nautical miles

t = 6 hours

d/t = 150 nautical miles /6 hours

rate = 25 nautical miles per hour

So in 1 hour we can go 25 nautical miles

Answer:

25 nautical miles.

Step-by-step explanation:

Givens

Equation

Solution

Answer:

x= -4 is the axis of symmetry

Step-by-step explanation:

The parabola is written in the form y = a (x-h)^2 +k

The vertex is (h,k) and the axis of symmetry is at x=h.

Given f(x) = 3(x- -4)^2 + 1, the vertex is (-4,1)  so the axis of symmetry is x= -4

Answer:

Jeff had in the account 3,623.85 after 3 years

Step-by-step explanation:

Investment: p=3,000

Interest: i=6.5%=6.5/100→i=0.065

Time (in years): t=3

A(3)=?

A(t)=p(1+i)^t

t=3→A(3)=p(1+i)^3

Replacing the given values:

A(3)=3,000 (1+0.065)^3

A(3)=3,000 (1.065)^3

A(3)=3,000 (1.207949625)

A(3)=3,623.848875

Rounding to the nearest hundredth:

A(3)=3,623.85

heres a trick: if you go to desmos.com/calculator you can type in your equation and it will show you it on the graph.

since f(x)=y you can say y=-3x-2 and it will show you!

Answer:

Option D.

Step-by-step explanation:

The given function is

[tex]f(x)=-3^x-2[/tex]

We need to find the graph of given function.

At x=0,

[tex]f(0)=-3^(0)-2=-3[/tex]

Similarly, substitute the different values of x and find the values of y.

Table of values

x                 y

-1             -2.33

0               -3

1                -5

2              -11

3              -29

Plot these ordered pairs on a coordinate plane and connect them by a free hand curve. The graph of given function is is shown below.

Therefore, the correct option is D.

Answer: The coordinates of the midpoint of diagonal AC are [tex](\frac{a+b}{2} , \frac{c}{2} )[/tex]. The coordinates of the midpoint of diagonal BD are  [tex](\frac{a+b}{2} , \frac{c}{2} )[/tex] AC and BD  intersect at point E with coordinates [tex](\frac{a+b}{2} , \frac{c}{2} )[/tex]. By the definition of midpoint, CE ≅ EA and BE ≅ ED Therefore, diagonals AC and BD bisect each other.

Step-by-step explanation:

Since, here the coordinates of A ≡ (0,0) B ≡ (a, 0) D≡ ( b,c)

And, here ABCD is the parallelogram.

Therefore AB = CD

If y is the y-coordinate of C Then C≡(a+b, y)

⇒ [tex]a^2 + 0 = (a)^2 + (y-c)^2[/tex]

⇒ y =c

Thus, C≡(a+b, c)

The coordinates of the midpoint of diagonal AC are,

[tex](\frac{a+b}{2} , \frac{c}{2} )[/tex]

And,  The coordinates of the midpoint of diagonal BD are,

[tex](\frac{a+b}{2} , \frac{c}{2} )[/tex]

Since, by the below diagram AC and BD are intersecting at point E,

Where the  coordinates of E are,

[tex](\frac{a+b}{2} , \frac{c}{2} )[/tex]

Thus, E is the mid point of Both the segments AC and BD

Because, BE = ED and AE = EC

Therefore, we can say that both AC and BD bisect each other.

Answer:

the coordinate point C are (a+b,c)

The coordinates of the midpoint of diagonal AC¯¯¯¯¯ are (a+b/2, c/2)

The coordinates of the midpoint of diagonal BD¯¯¯¯¯ are (a+b/2, c/2)

AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E with coordinates ​(a+b/2, c/2)​

By the definition of midpoint, AE¯¯¯¯¯≅CE¯¯¯¯¯and BE¯¯¯¯¯≅DE¯¯¯¯¯

Step-by-step explanation:

Answer:2 whole sandwiches and 3/4 of another one

Step-by-step explanation:

Answer:

Step-by-step explanation:

So first draw a table then messure it out or you can draw out a box into 3 parts then shade in 2 of the 3 then shade a small portion for 3/4.

Answer:

n=1.75

Step-by-step explanation:

(7-4n)*6=0

We simplify the equation to the form, which is simple to understand  

(7-4n)*6=0

Reorder the terms in parentheses

(+42-24n)=0  

Remove unnecessary parentheses

+42-24n=0

We move all terms containing n to the left and all other terms to the right.  

-24n=0-42

We simplify left and right side of the equation.  

-24n=-42

We divide both sides of the equation by -24 to get n.  

n=1.75

Answer:

42 - 24n

Step-by-step explanation:

This is an expression, not an equation.  We can simplify

(7-4n)*6

Distribute the 6

7*6 - 4n*6

42 - 24n

Answer:

1/(11 x^(9/2) y^4 z^5)

or

sqrt(x)/ 11 x^5 y^4 z^5  

Step-by-step explanation:

1/ sqrt(121x^9y^8z^10)

Lets simplify the denominator

sqrt(121x^9y^8z^10)

Break it into pieces

sqrt(121) sqrt(x^9) sqrt(y^8) sqrt(z^10)

11  sqrt (x^8) sqrt(x) y^4  z^5

11 x^4 y^4 z^5  * sqrt(x)  

Putting this back in

1

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

11 x^4 y^4 z^5  * sqrt(x)

But we dont want a sqrt root in the denominator

Multiply by sqrt(x)/sqrt(x)

sqrt(x)

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

11 x^4 y^4 z^5  * sqrt(x) sqrt(x)

sqrt(x)

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

11 x^4 y^4 z^5  * x

sqrt(x)

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

11 x^5 y^4 z^5  

Answer:

the answer issss

Step-by-step explanation:

k=60

Answer:

The value of is equal to [tex]k=60\°[/tex]

Step-by-step explanation:

we know that

[tex](2k+11)\°=131\°[/tex] -----> by alternate exterior angles

solve for k

[tex]2k=131\°-11\°[/tex]

[tex]k=120\°/2=60\°[/tex]

Answer:

They are not proportional.

Step-by-step explanation:

To check if the fractions are proportional, we can use cross products.

1                6

----- =  --------------

3                   20

1 * 20  = 3 * 6

20 = 18

This is not true, so they are not proportional.

Answer,

No

Explanation,

To find out if a pair of fractions are proportional you can use cross multiplication. Only fractions that are equivalent to eachother are proportional.

1/3 = 6/20

1 * 20 = 20

3 * 6 = 18

As we can see they are not equivalent, therefore it is not proportional.

Hope This Helps :-)

Answer:

[tex]\frac{12}{5}[/tex]

Step-by-step explanation:

First, we need to find the gradient (slope) of the FG line.

To do this we must use the gradient formula:

[tex]\frac{y2 - y1}{x2 - x1}[/tex]

y1 and x1 have to be in the same coordinate set,

x1 = 8, y1 = 4   the (8 , 4) set

x2 = -4, y2 = 9   the (-4 , 9) set

[tex]\frac{9 - 4}{-4 - 8}[/tex]

[tex]\frac{5}{-12}[/tex]

Which is the gradient of FG line.

To find the equation of a line perpendicular to this line, you must do [tex]\frac{-1}{gradient}[/tex]

[tex]\frac{-1}{\frac{5}{-12} }[/tex]

= [tex]\frac{12}{5}[/tex]

So that means the gradient of the line perpendicular to FG is

[tex]\frac{12}{5}[/tex]

Answer:

647.0625

Step-by-step explanation:

Answer:

x=5/2

Step-by-step explanation:

We can use ratios of similar triangles to help solve the problem.

side                    x                       5

--------              = --------------- = ---------------

hypotenuse               4                   8

Using cross products

x*8 = 4 * 5

8x = 20

Divide each side by 8

8x/8 = 20/8

x = 5/2

Answer:

Bruh no one has still answered u?!

Step-by-step explanation:

Answer:

Answer??

Step-by-step explanation:

Answer:

280 ft

Step-by-step explanation:

An auditorium is in the shape of an equilateral triangle with side length as 112 ft.

The stage extends from one vertex of the triangle to the mid-segment and the seating area extends from the mid-segment to the rear wall.

*The situation is represented in the attachment.

According to the midpoint theorem, the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.

Hence, the length of the mid-segment in this case is,

[tex]\dfrac{1}{2}\times 112=56\ ft[/tex]

Therefore, the perimeter of the seating area is,

[tex]=112+56+56+56=280\ ft[/tex]

The perimeter of the seating area of an auditorium shaped as an equilateral triangle with rear wall measuring 112 feet will be 224 feet.

This is a Mathematics question related to Geometry. An equilateral triangle is a triangle where all sides are of equal length. Since the auditorium is in the shape of an equilateral triangle, all sides of the triangle will have identical measurements. In this case, it’s specified that the rear wall measures 112 feet. Thus, each side of the triangle will be 112 feet.

The question asks for the perimeter of the seating area which starts from the midsegment of the triangle and extends to the rear wall. The midsegment of an equilateral triangle splits the triangle into equivalent smaller equilateral triangles. Hence, the length of the midsegment to a vertex is half of the side of the triangle. So, the length of the seating area on each side is 112/2 = 56 feet.

Since, there are two sides that measure 56 feet (that is from the midsegment to the other two vertices of the triangle), and the rear side measures 112 feet, to calculate the perimeter, we sum up these sides. Hence, the perimeter of the seating area will be 56 + 56 + 112 = 224 feet.

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Answer:

     r+5                 r^2+4r-21

-------------- /   --------------------

r^2+5r-14               r-2

         r+5                     r-2

= --------------  x   --------------------

   r^2+5r-14           r^2+4r-21

         r+5                     r-2

= --------------  x   --------------------

   (r+7)(r-2)           (r+7)(r-3)

         r+5                     

= -----------------

   (r+7)^2 (r-3)          

hope it helps

Step-by-step explanation:

Final answer:

The inequality x>5 can be stated as 'x is greater than five,' 'five is less than x,' or 'x exceeds five,' each conveying that the value of x is larger than 5.

Explanation:

There are several ways to express the inequality x > 5 in words. Here are three different expressions:

All these expressions communicate the idea that the value of x is more than 5. When you're working with inequalities, it's important to be familiar with different ways to verbalize them as it can help in understanding and communicating mathematical concepts.