2 consecutive integers such that 7 times the smaller is less than 6 times the greater. What are the greatest such intergers

Mathematics

1 answer:

postnew [5]2 years ago

7 0

Answer:

The numbers are

22 and 23 to solve a problem like this, we need to read and define as we go. Let me explain. So we know that there are two consecutive integers. They can be

x and x+1

. Since their consecutive, one has to be 1

number higher (or lower) than the other. Ok, so first we need "seven times the larger"( 7x+1)

Next, we need to "minus three times the smaller" 7(x+1)−3x

Is equal to " 957(x+1)−3x=95

Alright! There's the equation, now we just need to solve for x! First we are going to get everything on one side and distribute the 7=7x+7−3x−95=4x−88

Pull out a

=4(x−22)Now that we have two terms, we can set them both equal to

0 and solve.4≠0

This can never be true, lets move to the next term (x−22)=0x=

22 That's it! So your two consecutive numbers are

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The diagonal of a cube is 28 cm. Identify the length of an edge.

asambeis [7]

So the diagonal of cube
this was a practice act question so her's the answer

look at the cube through one of the faces
you will see the diagonal as the hypotonuse of a triangle
and also a triangle on the floor (look at attachment)
the ,diagonal is 28
a^2+b^2=28^2
a=b since it is a cube
remember that this is a 45,45 triangle so therefor
a=b=x
c=x√2 so
28=x√2
divide both sides by √2
28/(√2)=x
the diagonal on the floor is 28/(√2)
the sides of the triangle form another 45 45 90 triangle with 28/(√2) as hyponuse so
a=b=x
c=x√2=28/(√2)
solve for x
x√2=28/(√2)
divide both sides by √2
same as mujlitply both sides by 1/(√2) so
28/(√2) times 1/(√2)=28/(2)=14
the answer of 1 diagonal is 14 cm
the answer is 14cm