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3 years ago

Find the solutions of the quadratic equation

Mathematics

1 answer:

Kazeer [188]3 years ago

5 0

Step-by-step explanation:

it it can be calculated by using the quadratic formula.

X=-b+_(√b^2-4ac)/2a

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Fourteen percent of the town’s population are above the age of 65. If there are about

swat32

Answer: 2285

Step-by-step explanation:

320 ÷ 14% = 2285

7 0

3 years ago

Mr. Rocha used 15 lemons to make2 1/2 gallons of lemonade. How many lemons are needed to make one gallon of lemonade?

kherson [118]

Answer:

Step-by-step explanation:

15 lemons = 2.5 gallons of lemonade

Divide both sides by 2.5

6 = 1

6 lemons per 1 gallon.

3 0

3 years ago

A circle is centered at the point (-7, -1) and passes through the point (8, 7).The radius of the circle is____ units. The point

denis-greek [22]

Answer:

Part 1) The radius of the circle is r=17 units

Part 2) The points (-15,14) and (-15,-16) lies on this circle

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The distance between the center of the circle and any point on the circle is equal to the radius of the circle

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

(-7, -1) and (8, 7)

substitute

$r=\sqrt{(7+1)^{2}+(8+7)^{2}}$

$r=\sqrt{(8)^{2}+(15)^{2}}$

$r=\sqrt{289}$

$r=17\ units$

step 2

Find out the y-coordinate of point (-15,y)

The equation of the circle in standard form is equal to

$(x-h)^2+(y-k)^2=r^2$

where

(h,k) is the center

r is the radius

substitute the values

$(x+7)^2+(y+1)^2=17^2$

$(x+7)^2+(y+1)^2=289$

Substitute the value of x=-15 in the equation

$(-15+7)^2+(y+1)^2=289$

$64+(y+1)^2=289$

$(y+1)^2=289-64$

$(y+1)^2=225$

square root both sides

$(y+1)=(+/-)15$

$y=-1(+/-)15$

$y=-1(+)15=14$

$y=-1(-)15=-16$

therefore

we have two solutions

point (-15,14) and point (-15,-16)

see the attached figure to better understand the problem

8 0

3 years ago

A die is thrown 300 times with frequencies for the outcome 1 2 3 4 5 6, whats the probablity of getting a prime number, given th

aleksklad [387]

Answer:

58.3% to the nearest tenth.

Step-by-step explanation:

The prime numbers from 1 to 6 are 2,3 and 5.

The probability of a prime number taken from the result of the 300 throws:

= (sum of the frequencies for 2, 3 and 5) / ( total throws)

= (60 + 55 + 60) / 300

= 0.5833 or 58.3%.

6 0

3 years ago

What is the axis of symmetry for the equation <br> Y= x^2-3x+8

UNO [17]

Answer:

Step-by-step explanation:

So to find the axis of symmetry, there are two ways, and I will walk you through both.

1. Axis of Symmetry formula

So first, break down the equation and list down a, b, and c, which in this case is 1, -3, and 8. Then, use the Axis of Symmetry formula, which is x=-b/2a.

x=-b/2a

x=-(-3)/2(1)

x=3/2

So, the axis of symmetry is x=3/2.

2. Vertex form

This method requires knowledge of factoring, and understanding completing the square. So, subtract 8 on both sides to get y-8=x^2-3x.

y-8=x^2-3x

Factor out one.

y-8=1(x^2-3x)

Create a Perfect square trinomial

y-8+1(?)=1(x^2-3x+2.25)

Multiply 1 by 2.25 to complete the square

y-8+2.25=(x-1.5)^2

y-5.75=(x-1.5)^2

y=(x-1.5)^2+5.75

Substitute 1.5, because that will find the x value for the vertex, which is the axis of symmetry.

So, the axis of symmetry is 1.5, or 3/2.

Hope that helps!

8 0

4 years ago