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3 years ago

If 2 lines intersect the system is called...

Mathematics

1 answer:

Tanya [424]3 years ago

8 0

Answer:

3. independent and consistent

Step-by-step explanation:

Intersecting Lines have a single point at which the lines intersect. Therefore the solution to this type of system is called a consistent system. (A type of system of linear equation in two variables.) Therefore, there will be no point that is common to both lines. If a system has at least one solution, it is said to be consistent. If a consistent system has exactly one solution, it is independent. If a consistent system has an infinite number of solutions, it is dependent. When you graph the equations, both equations represent the same line.

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Verify if f(x)= 5-3x/2 and g(x)= 5-2x/3 are inverses. Please show step by step.

mestny [16]

Since f(g(x)) = g(f(x)) = x, hence the function f(x) and g(x) are inverses of each other.

<h3>Inverse of functions</h3>

In order to determine if the function f(x) and g(x) are inverses of each other, the composite function f(g(x)) = g(f(x))

Given the function

f(x)= 5-3x/2 and

g(x)= 5-2x/3

f(g(x)) = f(5-2x/3)

Substitute

f(g(x)) = 5-3(5-2x)/3)/2

f(g(x)) = (5-5+2x)/2

f(g(x)) = 2x/2

f(g(x)) = x

Similarly

g(f(x)) = 5-2(5-3x/2)/3

g(f(x)) = 5-5+3x/3

g(f(x)) = 3x/3

g(f(x)) =x

Since f(g(x)) = g(f(x)) = x, hence the function f(x) and g(x) are inverses of each other.

Learn more on inverse of a function here: brainly.com/question/19859934

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7 0

2 years ago

Eleni is making 6 pizzas. She uses 13 jar of sauce on each pizza.

Whitepunk [10]

Answer:

Step-by-step explanation:

13 jars/pizza

6 pizzas

13x6=78

7 0

3 years ago

Read 2 more answers

Delaware was the first state to enter the Union and Hawaii was the 50th. If we order the positions of entry for the rest of the

Anna71 [15]

Answer:

State A was the <u>12th</u> state to enter the Union. State B was the <u>11th</u> state to enter the Union.

Step-by-step explanation:

Let's call x to the order-of-entry of State B, therefore the order-of-entry of State A is x+1. Given that he product of their order-of-entry numbers is 132:

x*(x+1) = 132

x² + x - 132 = 0

Using quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 -4(a)(c)}}{2(a)}$

$x = \frac{-1 \pm \sqrt{1^2 -4(1)(-132)}}{2(1)}$

$x = \frac{-1 \pm 23}{2}$

$x_1 = \frac{-1 + 23}{2}$

$x_1 = 11$

$x_2 = \frac{-1 - 23}{2}$

$x_2 = -12$

The negative solution has no sense in the context of our problem, then the solution is x = 11.

5 0

3 years ago

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are

Kruka [31]

Answer:

Step-by-step explanation:

The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

Where

x1 = sample mean of type A paint

x2 = sample mean of type B paint

s1 = sample standard deviation type A paint

s2 = sample standard for type B paint

n1 = number of samples of type A paint

n2 = number of samples of type B paint

From the information given,

x1 = 75.7

s1 = 4.5

n1 = 11

x2 = 64.3

s2 = 5.1

n2 = 9

x1 - x2 = 75.7 - 64.3 = 11.4

√(s1²/n1 + s2²/n2) = √(4.5²/11 + 5.1²/9) = √4.709

Degree of freedom = (n1 - 1) + (n2 - 1)

df = (11 - 1) + (9 - 1) = 18

For the 98% confidence interval, the z score from the t distribution table is 2.552

Margin of error = 2.552√4.709 = 5.55

The upper boundary for the confidence interval is

11.4 + 5.55 = 16.95 hours

The lower boundary for the confidence interval is

11.4 - 5.55 = 5.85 hours

The correct option is

B. 5.85 hrs < μ1 - μ2 < 16.95 hrs

4 0

3 years ago

△DEF is rotated about point N to △D′E′F′ .

MatroZZZ [7]

the answer is d the image is the same size

6 0

3 years ago