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3 years ago

Plz help me with this

Mathematics

1 answer:

Dmitry_Shevchenko [17]3 years ago

3 0

Answer: Equivalent

Step-by-step explanation:

$y=-\dfrac{1}{3}x+\dfrac{2}{3}\\\\\text{Multiply by 3 to clear the denominator: }3y = -x + 2\\\text{Add x to both sides: }x+3y=2\\\text{Multiply both sides by 2: }2x+6y=4$

When given a system of equations, the definitions of the solution are:

Consistent & Independent: exactly ONE solution (lines intersect)
Consistent & Dependent: INFINITE solutions (same line)
Inconsistent: NO solutions (parallel lines)

In the given system, the equations are the same which means they have INFINITE solutions --> The system is Consistent & Dependent = Equivalent.

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If the points (–2, 2), (–4, 4), (2, –2), and (4, –4) are joined to form a straight line, at what point does the line intersect t

fiasKO [112]

It would be (0, 0) Or 'The Origin'

5 0

3 years ago

Read 2 more answers

Having Problems With This Question

hjlf

Answer:

f+g(2)=10

f-g(4)=-4

F/G(2)= 7/3

(f)(g)(1)=0

Step-by-step explanation:

1. (f+g)=2x+3+x^2-1 2(2)+2=10

2. (f-g)=(2x+3)-(x^2-1)=-x^2+2x+4= -16+8+4=-4

3. f/g= 2x+3/x^2-1 4+3/3= 7/3

4. f*g= (2x+3)(x^2-1)= 2x^3+3x^2-2x-3= 2(1)^3-2(1)+3(1)^2-3=0

8 0

3 years ago

Tell whether a triangle can have sides with the

Dmitry [639]

Answer:

$3x+2 \ne x^2 \ne 2x$ for $x = 4$

Step-by-step explanation:

Given

Shape: Triangle

Dimension: 3x + 2, x^2 and 2x

$x = 4$

Required

Determine if it has equal sides

To do this, we simply substitute 4 for x in the given dimensions

3x + 2

$3x + 2 = 3 * 4 + 2$

$3x + 2 = 12 + 2$

$3x + 2 = 14$

x^2

$x^2 = 4^2$

$x^2 = 16$

2x

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$3x+2 \ne x^2 \ne 2x$ for $x = 4$

8 0

3 years ago

Two airplanes are flying to the same airport. Their positions are shown in the graph. Write a system of linear equations that re

wariber [46]

Answer:

Airplane #1 equation: y=5/13x+42/13

Airplane #2 equation: y=1/3x+14

Step-by-step explanation:

So to find the slope of each airplane, you use the formula y2-y1/x2-x1. That means, for airplane#1 the equation will be 9-4/15-2. Simplify this and get 5/13. Then, for airplane#2, the equation will be 12-9/6-15. Simplify this and get 3/-9 and divide each side by 3 to get 1/-3 or -1/3. Next, use point slope formula to find the system of linear equations. Point slope formula is y-y1=m(x-x1). M is the slope. Use any point from the line. In this case, I will use (2,4). Tat means the first airplane's equation would be y-4=5/13(x-2). Then y-4=5/13x-10/13. Then, convert four into a fraction with a denominator of 13. This means, you have to multiply 4 by 13 to get 52/13. Add 52/13 to -10/13 to get 42/13. That means the first equation will be y=5/13x+42/13. The second equation point will be (6,12). This means the equation will be y-12=-1/3(x-6). Simplify this to get y-12=-1/3x+2. Simplify this to get y=1/3x+14. Therefore, Airplane#1 equation will be y=5/13x+42/13 and airplane #2 equation will be y=1/3x+14.

Hope this helps

6 0

3 years ago

the population of arizona is estimated go increase by 6.2% every year. if the population was 4.18 million in 2016 estimate popul

aleksklad [387]

Given:

a.) The population of Arizona is estimated to increase by 6.2% every year.

b.) The population was 4.18 million in 2016.

For us to be able to determine the population in 2022, we will be using the following formula:

$\text{ P = P}_0e^{rt}$

Where,

P = Total population after time (t)

P₀ = Starting population = 4.18 million

r = Growth rate (in decimal form) = 6.2%/100 = 0.062

t = time (in years) = 2022 - 2016 = 6 years

e = Euler's number = 2.71828182845

We get,

$\text{ P = P}_0e^{rt}\text{ = (4,180,000)(}2.71828182845)^{0.062(6)}$ $\text{ P = 6,063,645.861797897 }\approx\text{ 6,063,646}$

Therefore, the population in 2022 will be approximately 6,063,646.

7 0

1 year ago