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3 years ago

7

Determine two numbers whose sum is 9 and whose product is 20, by solving a quadratic equation.

2 answers:

Tomtit [17]3 years ago

6 0

Answer:

4 and 5

Step-by-step explanation:

lorasvet [3.4K]3 years ago

5 0

Ex: x^2-9x+20
(x-4)(x-5)=0
x=4 x=5

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A parabola can be drawn given a focus of

Volgvan

Answer:

$y=-\frac{1}{4}(x-2)^{2}+9$

Step-by-step explanation:

Any point on a given parabola is equidistant from focus and directrix.

Given:

Focus of the parabola is at $(2,8)$ .

Directrix of the parabola is $y=10$ .

Let $(x,y)$ be any point on the parabola. Then, from the definition of a parabola,

Distance of $(x,y)$ from focus = Distance of $(x,y)$ from directrix.

Therefore,

$\sqrt{(x-2)^{2}+(y-8)^{2}}=|y-10|$

Squaring both sides, we get

$(x-2)^{2}+(y-8)^{2}=(y-10)^{2}\\(x-2)^{2}=(y-10)^{2}-(y-8)^{2}\\(x-2)^{2}=(y-10+y-8)(y-10-(y-8))...............[\because a^{2}-b^{2}=(a+b)(a-b)]\\(x-2)^{2}=(2y-18)(y-10-y+8)\\(x-2)^{2}=2(y-9)(-2)\\(x-2)^{2}=-4(y-9)\\y-9=-\frac{1}{4}(x-2)^{2}\\y=-\frac{1}{4}(x-2)^{2}+9$

Hence, the equation of the parabola is $y=-\frac{1}{4}(x-2)^{2}+9$ .

4 0

3 years ago

Is an arithmetic sequence a function?

Sphinxa [80]

Yes it is a linear function

3 0

3 years ago

5 times the sum of 40 and 80. what is the numerical expression that would represent the phrase?

vlabodo [156]

<h2>Answer:</h2>

<u>The expression is</u><u> 5(40+80)</u>

<h2>Step-by-step explanation:</h2>

The sum of 40 and 80 can be written as

(40+80)

and when we take the 5 times of the sum

we can write as

5(40+80)

3 0

3 years ago

Solve the system using elimination.

Shalnov [3]

Answer:

After simplifying we get (x,y) as (1,3).

Step-by-step explanation:

Given:

$x+7y=22$ ,

$x-7y=-17$

We need to use elimination method to solve the and simplify the equations.

Solution;

Let $x+7y=22$ ⇒ equation 1

Also Let $4x-7y=-17$ ⇒ equation 2

Now by solving the equation we get;

first we will Add equation 2 from equation 1 we get;

$(x+7y)+(4x-7y)=22+(-17)\\\\x+7y+4x-7y=22-17\\\\5x=5$

Now Dividing both side by 5 using division property of equality we get;

$\frac{5x}{5}=\frac{5}{5}\\\\x=1$

Now Substituting the vale of x in equation 1 we get;

$x+7y=22\\\\1+7y=22$

subtracting both side by 1 using subtraction property of equality we get;

$1+7y-1=22-1\\\\7y=21$

Now Dividing both side by 7 using division property of equality we get;

$\frac{7y}{7}=\frac{21}{7}\\\\y=3$

Hence we can say that, After simplifying we get (x,y) as (1,3).

4 0

3 years ago

List the first 5 multiples, and find ALL the factors of 13

kvasek [131]

Answer:

13,26,39,52,65,78 are the multiples 13 and 1 are the all of the factors

7 0

3 years ago

Read 2 more answers