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Tomtit [17]
3 years ago
15

Three consecutive integers are such that when they are taken in increasing order and multiplyied be 2,3 and 4 respectively they

add up to74.Find these numbers
Mathematics
1 answer:
xenn [34]3 years ago
4 0

Answer:

The integers art 7,8 and 9

Step-by-step explanation:

Let the first of the integers be x. Since they are consecutive, the next would be x + 1 and the last would be x + 2

Now we multiply these integers by 2,3 and 4 respectively.

Thus, we have 2(x) + 3(x+1) + 4(x+2), all these add up to be 74

Opening the brackets we have;

2x + 3x + 3 + 4x + 8 = 74

9x + 11 = 74

9x = 74-11

9x = 63

x = 63/9

x = 7

The integers are thus x = 7, x+ 1 = 7+ 1 = 8 and x + 2 = 7+ 2 = 9

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The graph of a quadratic function has roots at -3 and -7 and a vertex at (-5, 4). What is the equation of the function in vertex
melomori [17]

Answer:

y = -(x + 5)² + 4

Step-by-step explanation:

The roots are -3 and -7, so:

y = a (x + 3) (x + 7)

Distribute and complete the square:

y = a (x² + 10x + 21)

y = a (x² + 10x + 25 − 4)

y = a (x² + 10x + 25) − 4a

y = a (x + 5)² − 4a

The vertex is (-5, 4), so a = -1.

y = -(x + 5)² + 4

3 0
3 years ago
A runner increases his velocity from 0 m/s to 20 m/s in 2.0 s. What was his average acceleration?
goblinko [34]

Answer:

a =  \frac{dv}{dt }  =  \frac{20 - 0}{2}  = 10

7 0
2 years ago
find the volume of a right circular cone that has a height of 14.7 ft and a base with a circumference of 13 ft
Doss [256]

Answer:

Volume of the cone =650.06 cubic feet

Step-by-step explanation:

Height of the cone= 14.7 feet

Circumference= 13 feet

Radius = 13/2 = 6.5 feet

Volume of the Cone:

         =\pi r^2\frac{h}{3}

As, \pi =\frac{22}{7}=3.14

Putting the values in the formula:

Volume of the cone is :

          =3.14*(6.5*6.5)*\frac{14.7}{3} \\\\=3.14*(6.5*6.5)*4.9\\\\=3.14*42.25*4.9\\\\=3.14*207.03\\\\=650.06feet^3

Volume of the cone is 650.06 cubic feet

8 0
3 years ago
In 2004, there were 10,649 commercial radio stations in the US. About 19.22% of these stations were devoted to country music. Ab
Rom4ik [11]
I think the answer would be 5,405 country music radio stations
5 0
3 years ago
A square patio has an area of 220 square feet. Approxmately how long is each side of the patio (to the nearest hundredths)
Tanzania [10]

This is a square root problem since the patio is square.

A of a square is L x W or L^2 or W^2 - it's all the same.

So find the square root of 220 feet.

14.8323 We are to round to nearest hundreth which is the second position right of decimal. Look at the number to the right of that position.

It is a 2. So we do not round the number up.

14.83 is the rounded sq. ft of each side.

Check it!

14.83^2 = 219.92 Because we rounded, this number is not exact, but close.

3 0
3 years ago
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