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3 years ago

5x2 – 2x + 5 = 0 Solve

Mathematics

1 answer:

Tems11 [23]3 years ago

5 0

Answer:

$x = \frac{15}{2} = 7 \frac{1}{2}$

Step-by-step explanation:

$5 \times 2 - 2x + 5 = 0\\ 10 - 2x + 5 = 0 \\ 15 - 2x = 0 \\ 15 - 2x - 15 = 0 - 15 \\ - 2x = 0 - 15 \\ - 2x = - 15 \\ x = 15 \div 2 \\$

$\boxed{\green{\boxed{\bold{x = \frac{15}{2} = 7 \frac{1}{2} }}}}$

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★ . ꜝꜞ ᳝ ࣪ hope that helped! ʬʬ

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What is the equation of the quadratic graph with a focus of (3, 1) and a directrix of y = 5?

telo118 [61]

Answer:

$f(x)=-\frac{1}{8}(x-3)^2+3$

Step-by-step explanation:

We want to find the equation of the parabola with a focus of $(3,1)$ and directrix $y=5$ .

Considering the directrix, the quadratic graph must open downwards.

The equation of this parabola is given by the formula,

$(x-h)^2=4p(y-k)$ , where $(h,k)$ is the vertex of the parabola.

The axis of this parabola meets the directrix at $(3,5)$ .

Since the vertex is the midpoint of the focus and the point of intersection of the axis of the parabola and the directrix,

$h=\frac{3+3}{2}=3$ and $k=\frac{5+1}{2}=3$ .

The equation of the parabola now becomes,

$(x-3)^2=4p(y-3)$ .

Also $|p|$ is the distance between the vertex and the directrix.

$|p|=2$

This implies that $p=-2\:or\:2$ .

Since the parabola turns downwards,

$p=-2$ .

Our equation now becomes,

$(x-3)^2=4(-2)(y-3)$ .

$(x-3)^2=-8(y-3)$ .

We make y the subject to get,

$y=-\frac{1}{8}(x-3)^2+3)$ .

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2 years ago

What is the slope of this equation please help me

galina1969 [7]

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2 years ago

Nicole runs a farm stand that sells bananas and peaches. Each pound of bananas sells for $2 and each pound of peaches sells for

stepan [7]

Answer:

The required system of equations is:

2x + 3.25y = 231.75

x = y + 3

where x is the number of pounds of bananas and y is the number of pounds of peaches

Explanation:

1- Defining the variables:

Assume that the number of pounds of bananas sold is x

Assume that the number of pounds of peaches sold is y

2- Setting the system of equations:

We are given that:

i. Each pound of bananas sells for $2

Money gained from selling x pounds of bananas is 2x

ii. Each pound of peach sells for $3.23

Money gained from selling y pounds of peaches is 3.25y

iii. Nicole made $231.75 in total. This means that:

2x + 3.25y = 231.75 .................> equation I

iv. Nicole sold 3 more pounds of bananas than pounds of peaches. This

means that:

pounds of bananas = pounds of peaches + 3

x = y + 3 ..................> equation II

3- Solving the equations (if required):

In equation II, we have: x = y + 3

Substitute with equation II in equation I and solve for y as follows:

2x + 3.25y = 231.75

2(y+3) + 3.25y = 231.75

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y = 43

Substitute with y in equation II to get x:

x = y + 3

x = 43 + 3 = 46

Based on the above:

Number of pounds of bananas = x = 46 pounds

Number of pounds of peaches = y = 43 pounds

Hope this helps :)

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3 years ago

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Ira Lisetskai [31]

Answer:

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Step-by-step explanation:

2/3x - 11 = x + 4

I created an inequality representing the above statement first. This makes things look less complicated than what the question is asking.

2/3x = x + 15

solve for x. I started by adding 11 to both sides.

-1/3x = 15

multiply both sides by -3

x = -45

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2 years ago

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