The product of two rational numbers is 1.5. Their sum is 3.5. What are the two numbers?

Answers

Answer 1

Answer: easy, 3 and 0.5

but ok the math way

xy=1.5
x+y=3.5

y=3.5-x
x(3.5-x)=1.5
3.5x-x^2=1.5
0=x^2-3.5x+1.5
quadratic
ax^2+bx+c=0
x= $\frac{-b+/- \sqrt{b^(2)-4ac} }{2a}$

a=1
b=-3.5
c=1.5

x= $\frac{-(-3.5)+/- \sqrt{(3.5)^(2)-4(1)(1.5)} }{2(1)}$
x= $(3.5+/- √(12.25-6) )/(2)$
x= $(3.5+/- √(6.25) )/(2)$
x= $(3.5+/- 2.5)/(2)$
x= $(3.5+ 2.5)/(2)$ or x= $(3.5- 2.5)/(2)$
x=6/2 or 1/2
x=3 or 0.5
those are the numbers

3 and 0.5

Answer 2

Answer: The number are "x" and "y".
Then, we suggest this system of equations:
xy=1.5
x+y=3.5

we can solve this system of equations by substitution method.

y=3.5 - x

x(3.5-x)=1.5
3.5x-x²=1.5
x²-3.5x+1.5=0

We solve this square equation:

x=[3.5⁺₋√(12.25 - 6)] / 2=(3.5⁺₋2.5)/2

we have two solutions:
x₁=(3.5-2.5) / 2=0.5 then: y₁=3.5-x=3.5 - 0.5=3

x₂=(3.5+2.5)/2=3 then y₂=3.5-x=3.5-3=0.5

Therefore the two numbers are 3 and 0.5

Answer: the numbers are 3 and 0.5

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What is f(x) = 7x2 + 42x written in vertex form?

Answers

Answer:

$\boxed{\boxed{y = 7(x+3)^2-63}}$

Step-by-step explanation:

The general vertex form of parabola is,

$y=a(x-h)+k$

where,

(h, k) is the vertex of the parabola.

The given function is,

$\Rightarrow f(x) = 7x^2 + 42x$

$\Rightarrow y = 7x^2 + 42x$

$\Rightarrow y = 7(x^2 + 6x)$

$\Rightarrow y = 7(x^2 + 2\cdot x\cdot 3)$

$\Rightarrow y = 7(x^2 + 2\cdot x\cdot 3+3^3-3^2)$

$\Rightarrow y = 7(x^2 + 2\cdot x\cdot 3+3^3)-7\cdot 3^2$

$\Rightarrow y = 7(x+3)^2-7\cdot 9$

$\Rightarrow y = 7(x+3)^2-63$

This is vertex form the given function.

Hello,

y=7x²+42x
==>y=7(x²+2*3*x+9)-63
==>y=7(x+3)²-63

Find an equation in standard form for the ellipse with the vertical major axis of length 18 and minor axis of length 16.

Answers

Answer:

x²/64 + y²/81 = 1

Step-by-step explanation:

Standard form of an equation for the ellipse is $(x^(2) )/(a^(2))+(y^(2) )/(b^(2) )=1$

Here b is the length of vertical major axis = 9

and minor axis of length a = 8

Therefore the equation of the ellipse will be

$(x^(2) )/(8^(2) )+(y^(2) )/(9^(2) ) =1$

$(x^(2) )/(64)+(y^(2) )/(81)=1$

So the answer is x²/64 + y²/81 = 1

Let us assume then that the center is the origin. If the major axis is 18, then a = 9 and a^2=81. If the minor axis is 16, then b = 8 and b^2=64. Now you can write the equation. Remember that this ellipse is vertical and so a^2 goes under y^2

A data set contains an independent and dependent variable which must be true or the data set of a linear function can be used to represent the data

Answers

The correct answer for the question that is being presented above is this one: "d. The values in the set must be increasing." A data set contains an independent and dependent variable which must be true or the data set of a linear function can be used to represent the data.

Here are the following choices:
a. The set must have a constant additive rate of change.
b. The set must have a constant multiplicative rate of change.
c. The values in the set must be positive.
d. The values in the set must be increasing.

Answer: D

Step-by-step explanation: edg

What's the answer for the value of each 5 in 15,573? a) 500 b) 50 c) 5,000 d) 5

Answers

The value of each 5 in the number 15,573 is:

b) 50

A grid shows the position of a subway stop at your house. The subway stop is located at (-5, 2) and your house is located (-9,9). What is the distance, to the nearest unit, between your house and the subway stop?