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Mathematics

1 answer:

8090 [49]3 years ago

6 0

Let the numbers be 7x and 4x
According to question
7x-4x =57
3x =57
X=57/3
X=19
So the numbers are
7x=7*19=133
4x=4*19=76

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X+56<533. What is the solution of the inequality?

swat32

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7 0

3 years ago

HURRY!!!!!!!!! Given P(5,10,8) and Q(7,11,10), find the midpoint of the segment PQ.

rusak2 [61]

Answer:

$P_{m}=(6,10.5,9)$

Step-by-step explanation:

The mid point can be found with the formula

$P_{m}=(\frac{x_{1}+x_{2} }{2},\frac{y_{1} +y_{2} }{2} ,\frac{z_{1}+z_{2} }{2} )$

The given coordinates are $P(5,10,8)$ and $Q(7,11,10)$ .

Replacing coordinates in the formula, we have

$P_{m}=(\frac{5+7}{2},\frac{10+11 }{2} ,\frac{8+10}{2} )=(\frac{12}{2},\frac{21 }{2} ,\frac{18}{2} )\\P_{m}=(6,10.5,9)$

Therefore, the mid point of the segment PQ is $P_{m}=(6,10.5,9)$

4 0

3 years ago

What is the vertex of a parabola having the equation y = –2(x – 5)2 + 7? Which direction does the parabola open?

Vika [28.1K]

$y = -2(x-5)^2 + 7$

That's vertex form for a parabola $y=a(x-p)^2+q$ and we read off vertex (p,q) as

Answer: Vertex (5,7)

The negative a tells us this is a downward opening parabola (upside down from the usual $y=x^2$ . I remember CUP - Concave Up Positive; here a is negative so not a cup, instead concave down. The same rule applies to second derivatives in calculus so memorize it now and use it later.