What is the solution to the system of equation?

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Answer 1

Answer:

Answer:

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Which numbers multiply to 50 and add to 6

Answers

xy = 50
x + y = 6

$xy = 50$
$(xy)/(x) = (50)/(x)$
$y = (50)/(x)$

$x + y = 6$
$x + (50)/(x) = 6$
$(x^(2))/(x) + (50)/(x) = 6$
$(x^(2) + 50)/(x) = 6$
$x^(2) + 50 = 6x$
$x^(2) - 6x + 50 = 0$
$x = \frac{-(-6) \± \sqrt{(-6)^(2) - 4(1)(50)}}{2(1)}$
$x = (6 \± √(36 - 100))/(2)$
$x = (6 \± √(-64))/(2)$
$x = (6 \± 8i)/(2)$
$x = 3 \± 4i$
$x = 3 + 4i$ $or$ $x = 3 - 4i$

x + y = 6
  3 + 4i + y = 6
- (3 + 4i) - (3 + 4i)
y = 3 - 4i
(x, y) = (3 + 4i, 3 - 4i)

or
  x + y = 6
  3 - 4i + y = 6
- (3 - 4i) - (3 - 4i)
y = 3 + 4i
  (x, y) = (3 - 4i, 3 + 4i)

(x, y) = (3 ± 4i, 3 ± 4i)

The two numbers that multiply to 50 and add up to 6 are 3 ± 4i.

We have 2 stacks or styrofoam cups one has 6cups and it's height is 15cm.The other stack has 12cups and Height is 23cm. How many cups are needed for a stack with the height of 50cm?

Answers

Answer:

Given

Number of stacks = 2

Stack 1 = 6 cups; h1 = 15cm

Stack 2 = 12 cups; h2 = 23cm

Let's first find the average:

$(H_1 - H_2)/( n_1 - n_2)$

$= (15-23)/(6-12)$

$= (-8)/(-6) = (4)/(3)$

With an average of 4/3, to obtain the number of cups needed to obtain a height of 50m, we have:

50 / (4/3)

= 50 * 3/4

= 150/4

= 37.5

From the answer, we can see that the number of cups is not really proportional to the height of the stack, because the average of stack one and stack 2 are different.

One third of a number is 12 less than the number itself

Answers

Answer:

Step-by-step explanation:

1/3 n = n - 12 Cross multiply

n = 3(n - 12)

n = 3n -36

2n = 36

n = 36/2

n = 18

let the number = n
(1/3)n=n-12
(3)(1/3)n=(3)n-12
n=3n-36
-2n=-36
n=18

has vertices J(3, –1), K(4, –4), and L(1, –3). Determine if is an equilateral, isosceles, or scalene triangle. A. equilateral B. isosceles C. scalene D. none of these

Answers

The solution is, the triangle is an isosceles triangle.

What is Triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Here, we have,

To solve this problem we simply need to find the lengths of each side of the triangle.

To do this, we use the distance formula: √(x1-x2)^2+(y1-y2)^2.

Using points J and K, we find that the length of JK is

√(3-4)^2+(-1-(-4))^2

=√(-1)^2+(3)^2

=√1+9

=√10.

Then we do the same for JL and KL.

JL is √(3-1)^2+(-1-(-3))^2

=√(2)^2+(2)^2

=√4+4

=√8.

KL is √(4-1)^2+(-4-(-3)^2)

=√(3)^2+(-1)^2

=√9+1

=√10.

Now we have all three sides of the triangle: √10, √8, and √10.

Check for any similarities: you have two sides of √10.

Because there are two sides of the triangle of the same length, the triangle is an isosceles triangle.

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To solve this problem we simply need to find the lengths of each side of the triangle. To do this, we use the distance formula: √(x1-x2)^2+(y1-y2)^2. Using points J and K, we find that the length of JK is √(3-4)^2+(-1-(-4))^2=√(-1)^2+(3)^2=√1+9=√10. Then we do the same for JL and KL. JL is √(3-1)^2+(-1-(-3))^2=√(2)^2+(2)^2=√4+4=√8. KL is √(4-1)^2+(-4-(-3)^2)=√(3)^2+(-1)^2=√9+1=√10. Now we have all three sides of the triangle: √10, √8, and √10. Check for any similarities: you have two sides of √10. Because there are two sides of the triangle of the same length, the triangle is an isosceles triangle.

You pay $947.60 a year in car insurance. the insurance is paid in four equal payments. Find the amount of each payment.

Answers

Answer:

$236.90

Step-by-step explanation:

947.60 / 4 = 236.90

Calculate f(4) for each function below

Answers

The question is about Evaluating Functions and to calculate f(4) for each function, we substitute 4 into the function and simplify. The values of f(4) for the given functions are: a) 16, b) 12, c) 5.6569, d) 0, e) 8, f) 44y.

Evaluating functions involves determining the output (or value) of a mathematical function for a given input (or argument). It's done by substituting the input value into the function's equation and solving for the result. In the context of functions like f(x), you replace 'x' with the specific value you want to assess. This process helps analyze how a function behaves, finding its y-value or dependent variable. Evaluating functions is crucial in various fields, such as mathematics, science, and engineering, to understand relationships and make predictions based on input-output mappings.

To calculate f(4) for each function, we substitute 4 into the function and simplify. Let's calculate:

a) f(x) = x2
Substitute 4 into the function:
f(4) = 42 = 16

b) f(x) = √144
Substitute 4 into the function:
f(4) = √144 = 12

c) f(x) = √32
Substitute 4 into the function:
f(4) = √32 ≈ 5.6569

d) f(x) = 3x - 12
Substitute 4 into the function:
f(4) = 3(4) - 12 = 0

e) f(x) = (x - 2)^3
Substitute 4 into the function:
f(4) = (4 - 2)^3 = 8

f) f(x) = 4xy + 7xy
Substitute 4 into the function:
f(4) = 4(4)y + 7(4)y = 16y + 28y = 44y

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Subtitute x = 4 to the equations:

$b)\ f(x)=\left((1)/(5)\right)^x\to f(4)=\left((1)/(5)\right)^4=(1^4)/(5^4)=(1)/(625)\n\nc)\ f(x)=3x-12\to f(4)=3\cdot4-12=12-12=0\n\nd)\ f(x)=(x-2)^3\to f(4)=(4-2)^3=2^3=8$

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