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3 years ago

Solve the following system of equations graphically on the set of axes below.

Mathematics

1 answer:

professor190 [17]3 years ago

6 0

The solution of the given equations is: (-1.5, 1.5)

Step-by-step explanation:

Linear equation usually represents a straight line. When a system of two liner equations is given, the point of intersection of lines represented by both equations is the solution of the system of equations.

We will plot the lines of both equations and find their point of intersection (Picture Attached)

We can see in the picture that two lines intersect at (-1.5, 1.5)

Hence,

The solution of the given equations is: (-1.5, 1.5)

Keywords: Linear equations, variables

Learn more about linear equations at:

#LearnwithBrainly

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A moose population is growing exponentially following the pattern in the table shown below. Assuming that the pattern continues,

EleoNora [17]

Answer:

7,692 moose.

Explanation:

The table that shows the pattern for this question is:

Time (year) Population

0 40

1 62

2 96

3 149

4 231

A growing exponentially pattern may be modeled by a function of the form P(x) = P₀(r)ˣ.

Where P₀ represents the initial population (year = 0), r represents the multiplicative growing rate, and P(x0 represents the population at the year x.

Thus you must find both P₀ and r.

1) P₀ 

Using the first term of the sequence (0, 40) you get:

P(0) = 40 = P₀ (r)⁰ = P₀ (1) = P₀

Then, P₀ = 40

2) r

Take two consecutive terms of the sequence:

P(0) = 40 r⁰ = 40

P(1) = 40 r¹ = 40r = 62

P(1) / P(0) = 40r / 40 = 62/40

r = 62/40 = 1.55

You can verify that, for any other two consecutive terms you get the same result: 96/62 ≈ 149/96 ≈ 231/149 ≈ 1.55

3) Model

Thus, your model is P(x) = 40(1.55)ˣ

 4) Population of moose after 12 years

P(12) = 40 (1.55)¹² ≈ 7,692.019 ≈ 7,692, which is round to the nearest whole number.

7 0

2 years ago

Please help

klio [65]

Answer:

The probability that a student taking only math will get picked is approximately 29%

Step-by-step explanation: This is because out of the total number of students taking math (95), 52 of such students are also taking science. In order to get the number of students only taking math you have to do 95-52=43 and to put that against the amount of total students the ratio would be 43:147 or 42/147 and if you plug 42/147 into a calculator you will recieve a long decimal that you can then round to 29%.

6 0

1 year ago

Tyler solved an inequality to determine the number of songs he can buy with a $20 credit at his favorite music website. The solu

Furkat [3]

Answer with explanation:

Amount that tyler had for buying number of songs from his favorite music website=$ 20

A number line is given which describe the possible quantities of songs that Tyler can buy.

1. No more than 8 songs

4.at most 8 songs

6.a maximum of 8 songs

3 0

3 years ago

Read 2 more answers

Una recta con pendiente -2 ´pasa por el punto P(5, -1). La abscisa del punto Q que está en esa recta es 1. Encuentre la ordenada

oksian1 [2.3K]

Answer:

La ordenada de Q es 7.

Step-by-step explanation:

La ecuación de una recta es:

y = a*x + b

donde a es la pendiente y b es la ordenada al origen.

Para este problema, sabemos que la pendiente es -2

Entonces:

a = -2

y = -2*x + b

También sabemos que esta recta pasa por el punto (5, -1)

Esto significa que cuando evaluamos la ecuación en x = 5, y toma el valor y = -1

Si reemplazamos esos valores en la ecuación, obtenemos:

-1 = -2*5 + b

-1 = -10 + b

-1 + 10 = b

9 = b

Entonces la ecuación de la recta es:

y = -2*x + 9

Sabemos que el punto Q está en la línea, y la abscisa de este punto es 1.

Entonces este punto es Q (1, k)

donde k es la ordenada de este punto.

Porque nuestra línea también pasa por este punto, podemos concluir que cuando x = 1, y = k

Reemplazando eso en la ecuación tenemos:

k = -2*1 + 9 = -2 + 9 = 7

k = 7

La ordenada de Q es 7.

7 0

2 years ago

The volume of a cone is 37.7 cubic inches, and its height is 4 inches. What is the diameter of the base of the cone?

Rom4ik [11]

Just multiply 37.7 by 4 and get your answer.

6 0

3 years ago