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3 years ago

Solve the quadratic equation using factoring x^2 + 3x + 2 = 0.

Mathematics

1 answer:

Sedaia [141]3 years ago

5 0

Answer:

Step-by-step explanation:

Given

x² + 3x + 2 = 0

To factor the quadratic

Consider the factors of the constant term (+ 2) which sum to give the coefficient of the x- term (+ 3)

The factors are 2 and 1, since

2 × 1 = 2 and 2 + 1 = 3, thus

(x + 2)(x + 1) = 0

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x + 1 = 0 ⇒ x = - 1

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You work as an assistant to a carpenter who designed the tabletop below. He tells you that each shape is a right triangle, and e

svlad2 [7]

Answer:

282.5 inches squared

Step-by-step explanation:

A triangle is half the area of a square.

So we will solve the area as if we were finding the area for a square, and then we halve the result.

Length multiply by height to get the area:

28.25 × 20 = 565 inches squared

Now, half the answer to get the area of the triangle:

565/2=282.5 inches squared

8 0

3 years ago

Are y=2/3 x+4 and y=2/3 x-8 perpendicular

Helen [10]

Answer:

No, they are parallel

Step-by-step explanation:

6 0

2 years ago

Please help. I will give brainliest.

77julia77 [94]

Answer:

Step-by-step explanation:

5 0

3 years ago

2х5y-3z-=14 x-2y+=-12 -x+ Зу-2z =13

lukranit [14]

Answer:

x = -34/3, y = 1/3, and z = -35/3

Step-by-step explanation:

2х+5y-3z-=14 let's call this equation 1.

x-2y=-12 let's call this equation 2.

-x+Зу-2z =13 let's call this equation 3.

USING EQUATION 1 AND EQUATION 3.

2х+5y-3z-=14 (EQUATION 1)

-x+Зу-2z =13 (EQUATION 3)

LET'S GET RID OF z, BY MAKING THE COEFFICIENT OF z IN THE TWO EQUATION THE SAME. WE WILL MULTIPLY EQUATION 1 BY 2 AND EQUATION 3 BY 3.

2х+5y-3z-=14 (EQUATION 1) * 2

-x+Зу-2z =13 (EQUATION 3) * 3

4х+10y-6z-=28 let's call this equation 4.

-3x+9у-6z =39 let's call this equation 5.

TO GET RID OF z, WE WILL HAVE TO SUBTRACT EQUATION 5 FROM EQUATION 4 PLEASE TAKE NOTE OF THE SIGNS (-) (+).

4х+10y-6z-=28 (EQUATION 4)

- (-3x+9у-6z =39) (EQUATION 5)

(4x - 3x) + ((+10y) - (+9y)) + ((-6z) - (-6z)) = (28 - 39)

x + y + 0 = -11

x + y = -11 let's call this equation 6.

USING EQUATION 2 AND EQUATION 6, LET'S FIND x AND y.

x-2y=-12 (EQUATION 2)

x + y = -11 (EQUATION 6)

x has the same coefficient in both equations, which is 1. Let's get rid of x so we can find the value of y.

We will subtract equation 6 from equation 2. Take note of the signs.

x-2y=-12 (EQUATION 2)

- (x + y = -11) (EQUATION 6)

(x - x) + ((-2y) - (+y)) = ((-12) - (-11))

0 + -3y = -1

-3y = -1

Divide both sides by -3.

-3y/-3 = -1/-3

y = 1/3

LET'S SUBSTITUTE THE VALUE OF y INTO EQUATION 2 TO GET THE VALUE OF x.

x-2y=-12 (EQUATION 2)

x-2(1/3)=-12

x -2/3 = -12

Add 2/3 to both sides.

x -2/3 + (2/3) = -12 + (2/3)

x + 0 = -34/3

x = -34/3

LET'S SUBSTITUTE THE VALUES OF x and y INTO EQUATION 1 TO GET THE VALUE OF z.

2х+5y-3z-=14 (EQUATION 1)

2(-34/3)+5(1/3)-3z-=14

-68/3 + 5/3 - 3z = 14

-21 - 3z = 14

Add 21 to both sides.

-21 + (21) - 3z = 14 + (21)

0 - 3z = 35

-3z = 35

Divide both sides by -3.

-3z/-3 = 35/-3

z = -35/3 or

Therefore, x = -34/3, y = 1/3, and z = -35/3

Please thank, rate 5 stars, and give brainliest. Thank you.

6 0

3 years ago

The annual birth rate for a population of a given country is represented by the function y= 918397(0.9763)^t where “t” represent

viktelen [127]

Answer:

The initial number of annual births in 2018 is 918,397

The percent decrease in birth rates is 2.37%

The expected number of births in 2021 is 834,379

Step-by-step explanation:

Exponential Decay Function

The exponential function is frequently used to model natural decaying processes, where the change is proportional to the actual quantity.

An exponential decaying function is expressed as:

$C(t)=C_o\cdot(1-r)^t$

Where:

C(t) is the actual value of the function at time t

Co is the initial value of C at t=0

r is the decaying rate, expressed in decimal

We are given the function that models the annual birth rate for a population of a given country:

$y= 918,397(0.9763)^t$

Where t represents the number of years since 2018.

a.) We can identify the variables with the actual model by comparing with the general equation, thus: Co=918,397 and 1-r=0.9763.

Solving for r we have r=1-0.9763=0.0237.

This means the initial number of annual births in 2018 (t=0) is 918,397

b.) The percent decrease in birth rates is r=0.0237 = 2.37%

c.) To find the expected number of births in 2021 (t=4 years), we substitute the value of t in the equation of the model:

$y= 918,397(0.9763)^4$

Calculating:

y = 834,379

The expected number of births in 2021 is 834,379

5 0

3 years ago