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3 years ago

What is the product of the 2 solutions of the equation x^2+3x-21=0

1 answer:

3 0

X²+3x-21=0

1) we solve this square equation:
x=[-3⁺₋√(9+84)] / 2=(-3⁺₋√93)/2
We have two solutions:
x₁=(-3-√93)/2
x₂=(-3+√93)/2

2) we compute the product of the 2 solutions found.
[(-3-√93)/2][(-3+√93)/2] =(-3-√93)(-3+√93) / 4=
=(9-93)/4=-84/4=-21

Answer: the product of the 2 solutions of this equation is -21

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What is the Y intercept of the function Y=(x+2) (x-4)

trasher [3.6K]

Answer:
Y=x^2-2x-8,x , x=r

5 0

3 years ago

Read 2 more answers

Show work and explain with formulas:

Marina86 [1]

17 Answer: 205

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

$\{1\dfrac{2}{3}+1\dfrac{5}{6}+2+...+8\dfrac{1}{3}\}\implies a_1=1\dfrac{2}{3},\ d=\dfrac{1}{6}\\\\\\a_n=a_1+d(n-1)\qquad solve\ for\ n\\\\8\dfrac{1}{3}=1\dfrac{2}{3}+\dfrac{1}{6}(n-1)\\\\\\\dfrac{25}{3}=\dfrac{5}{3}+\dfrac{1}{6}n-\dfrac{1}{6}\\\\\\\dfrac{50}{6}=\dfrac{10}{6}+\dfrac{1}{6}n-\dfrac{1}{6}\\\\\\\dfrac{41}{6}=\dfrac{1}{6}n\\\\\\\dfrac{41}{6}\cdot 6=n\\\\41=n$

$\text{Now use the sum formula:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\\S_{41}=\dfrac{1\dfrac{2}{3}+8\dfrac{1}{3}}{2}\cdot 41\\\\\\.\quad =\dfrac{10}{2}\cdot 41\\\\\\.\quad =5\cdot 41\\\\.\quad =\large\boxed{205}$

18 Answer: 1968

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

$a_1=-6,\ d=2,\ n=48, \quad \text{solve for }a_{48}\\\\a_{n}=a_1+d(n-1)\\\\a_{48}=-6+2(48-1)\\\\.\quad =-6+2(47)\\\\.\quad =-6+94\\\\.\quad =88$

$\text{Now use the sum formula:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\\S_{48}=\dfrac{-6+88}{2}\cdot 48\\\\\\.\quad =\dfrac{82}{2}\cdot 48\\\\\\.\quad =41\cdot 48\\\\.\quad =\large\boxed{1968}$

19 Answer: -116

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

$\{3, -2, -7, ...\}\\a_1=3,\ d=-5,\ n=8, \quad \text{solve for }a_{8}\\\\a_{n}=a_1+d(n-1)\\\\a_{8}=3-5(8-1)\\\\.\quad =3-5(7)\\\\.\quad =3-35\\\\.\quad =-32\\\\\text{Now use the sum formula:}\\\\S_8=\dfrac{a_1+a_8}{2}\cdot 8\\\\\\S_{8}=\dfrac{3-32}{2}\cdot 8\\\\\\.\quad =\dfrac{-29}{2}\cdot 8\\\\\\.\quad =-29\cdot 4\\\\.\quad =\large\boxed{-116}$

6 0

3 years ago

Which of the following is false?

Liula [17]

Answer: C

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Las edades de dos hermanos tienen una razón de 2 a 1. Cuando transcurran 4 años, la razón entre sus edades será de 8 a 6. ¿Cuánt

Nataly [62]

Answer:

The age of brothers are 4 years and 2 years respectively.

Step-by-step explanation:

We are given that the ages of two brothers have a ratio of 2 to 1. When 4 years have passed, the ratio of their ages will be 8 to 6.

Let the age of the first brother be 'x years' and the age of the second brother be 'y years'.

So, according to the question;

The first condition states that the ages of two brothers have a ratio of 2 to 1, that means;

$\frac{x}{y} =\frac{2}{1}$

$x=2y$ -------------- [equation 1]

The second condition states that when 4 years have passed, the ratio of their ages will be 8 to 6, that means;

$\frac{x+4}{y+4}=\frac{8}{6}$

$6({x+4})=8}(y+4)$

$6x+24=8y+32$

$6(2y)+24=8y+32$

$12y-8y=32-24$

$4y=8$

$y=\frac{8}{4}$ = 2 years

Putting the value of y in equation 1 we get;

x = 2y

x = $2 \times 2$ = 4 years

Hence, the age of brothers are 4 years and 2 years respectively.

3 0

3 years ago

Please help me <br> Show your work <br> 10 points

Svet_ta [14]

<h2>Answer</h2>

After the dilation $\frac{5}{3}$ around the center of dilation (2, -2), our triangle will have coordinates:

$R'=(2,3)$

$S'=(2,-2)$

$T'=(-3,-2)$

<h2>Explanation</h2>

First, we are going to translate the center of dilation to the origin. Since the center of dilation is (2, -2) we need to move two units to the left (-2) and two units up (2) to get to the origin. Therefore, our first partial rule will be:

$(x,y)$ → $(x-2, y+2)$

Next, we are going to perform our dilation, so we are going to multiply our resulting point by the dilation factor $\frac{5}{3}$ . Therefore our second partial rule will be:

$(x,y)$ → $\frac{5}{3} (x-2,y+2)$

$(x,y)$ → $(\frac{5}{3} x-\frac{10}{3} ,\frac{5}{3} y+\frac{10}{3} )$

Now, the only thing left to create our actual rule is going back from the origin to the original center of dilation, so we need to move two units to the right (2) and two units down (-2)

$(x,y)$ → $(\frac{5}{3} x-\frac{10}{3}+2,\frac{5}{3} y+\frac{10}{3}-2)$