MATHEMATICS HIGH SCHOOL

Does anybody know the answer. 51 - 3 + 5k = 58

Answers

Answer 1
Answer:

Answer:

k=2

Step-by-step explanation:

1. 48+5k=58

2. 5k=58-48

3. 5k=10

4. k=10/5

5. k=2

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How Do I Find The Domain & Range Of
y=2x-4 ?

Answers

Both the domain and range of the function is in range -

( - ∞ , + ∞ )

We have the following function -

y = f(x) = 2x - 4

We have to identify its Domain and Range.

What do you mean by domain and range of a function?

For any function y = f(x), Domain is the set of all possible values of y that exists for different values of x. Range is the set of all values of x for which y exists.

Consider the equation given -

y = 2x - 4

If we compare it with the general equation of line -

y = mx + c

We get -

m = 2 and c = - 4

Now this graph of the equation y = mx + c represents a straight line.

Hence, both the domain and range of the function are-

( - ∞ , + ∞ )

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The domain is how far left and right it goes on a graph, and the range is how far up and down it goes on a graph. Because this equation is linear (if you graphed it, it would be in a straight line), both the domain and range are infinity, because it keeps going up and to the right, the larger X gets, and smaller and to the left, the more negative X gets.

1/x-1 - 3/x+2 = 1/4

solve to find x

Answers

(1)/(x-1)-(3)/(x+2)=(1)/(4)\n \n (x+2-3(x-1))/((x-1)(x+2))=(1)/(4)\n \n (x+2-3x+3)/((x-1)(x+2))=(1)/(4)\n \n (5-2x)/(x^2+x-2)=(1)/(4)\n \n 4(5-2x)=x^2+x-2\n \n 20-8x=x^2+x-2\n \n \boxed{x^2+9x-22=0}

Solvin this quadratic equation with Bhaskara formula we find:

x = -11 or x = 2
(1)/(x-1) - (3)/(x+2) = (1)/(4) \ /\cdot 4(x-1)(x+2)\n\n(4(x-1)(x+2))/(x-1) - (3\cdot 4(x-1)(x+2))/(x+2) = (4(x-1)(x+2))/(4)\n\n4(x+2)-12(x-1)=(x-1)(x+2)\n\n4x+8-12x+12=x^2+2x-x-2\n\n-8x+20=x^2+x-2\n\n-x^2-9x+22=0\ /\cdot(-1)\n\nx^2+9x-22=0\ \ \ \Rightarrow\ \ \ x^2+11x-2x-22=0\n\nx(x+11)-2(x+11)=0\n\n(x+11)(x-2)=0\ \ \ \ \ \Leftrightarrow\ \ \ (x+11=0\ \ \ or\ \ \ x-2=0)\n\nx=-11\ \ \ or\ \ \ x=2

2. Juan worked 2.5 hours and earned $37.00. Lisa was paid $42.00 for 3 hours of work. Which of the following statements is true?

Answers

The true statement about the juan and lisa is Juan made a higher rate of pay than Lisa.

Juan made a lower rate of pay because he made less money.

This statement is false. Juan and Lisa made a similar rate of pay per hour ($14.80 and $14.00 respectively).

Lisa made a better rate of pay because she made more money.

This statement is false. The total earnings do not determine the rate of pay; the hourly rate does.

Lisa said she made a better rate of pay because her rate was $14 an hour.

This statement is false. Lisa's actual rate was $14.00 per hour, not $14.00 as stated.

Juan said he made a better rate of pay because he was paid $14.80 an hour.

This statement is true. Juan's hourly rate was $14.80, which is higher than Lisa's rate of $14.00 per hour.

To calculate the rate of pay, we divide the money earned by the hours worked.

Juan's rate of pay is $37.00 / 2.5 hours = $14.80 per hour.

Lisa's rate of pay is $42.00 / 3 hours = $14.00 per hour.

Therefore, Juan made a higher rate of pay than Lisa.

Answer: Juan said he made a better rate of pay because he was paid $14.80 an hour.

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The following question may be like this:

Juan worked 2.5 hours and earned $37.00. Lisa was paid $42.00 for 3 hours of work. Which of the following statements is true?

Juan made a lower rate of pay because he made less money.

Lisa made a better rate of pay because she made more money.

Lisa said she made a better rate of pay because her rate was $14 an hour.

Juan said he made a better rate of pay because he was paid $14.80 an hour.

Answer:

2. Juan worked 2.5 hours and earned $37.00. Lisa was paid $42.00 for 3 hours of work. Which of the following statements is true?

Lisa said she made a better rate of pay because her rate was $14 an hour.

Answer: Juan said he made a better rate of pay because he was paid $14.80 an hour.

Juan made a lower rate of pay because he made less money.

Lisa made a better rate of pay because she made more money.

Consider the sequence of steps to solve the equation: 3(x − 4) + 5x = 9x − 36 Given ⇒ 3(x − 4) + 5x = 9x − 36 Step 1 ⇒ 3x − 12 + 5x = 9x − 36 Step 2 ⇒ 3x + 5x − 12 = 9x − 36 Step 3 ⇒ 8x − 12 = 9x − 36 Step 4 ⇒ 8x − 8x − 12 = 9x − 8x − 36 Step 5 ⇒ 0 − 12 = x − 36 Step 6 ⇒ −12 = x − 36 Step 7 ⇒ −12 + 36 = x − 36 + 36 Step 8 ⇒ 24 = x + 0 Step 9 ⇒ 24 = x Which property yields Step 1?

Answers

Answer:

Step-by-step explanation:

Distributive  property

a(b - c) = ab - ac

3(x-4) = 3*x - 3*4  

         = 3x - 12

1. Divide. Assume the denominator does not equal zero.
(12x^2y-6xy+4x^2)/(2xy)

Answers

To divide a polynomial by a monomial, divide each term on the top by the denominator:(12x^2y/2xy) - (6xy/2xy) + (4x^2/2xy)Reduce each fraction separately:6x - 3 + 2x/y

Plot the image of point Q under the translation (x, y) + (x - 3, y + 4).​

Answers

The image of the assumed point Q(2, 3)) under the translation is Q'(-1, 7).

What is Translation?

Translation is a type of transformation of geometrical figures. After translation, the original figure is shifted from a place to another place without affecting it's size.

Translation of a point (x, y) indicates that the point is moved x units along the X axis and y units along the Y axis,

Here we have to translate the point Q(2, 3).

Point (x, y) is translated as (x - 3, y + 4).

That is the point (x, y) moves 3 units to the left along the X axis and 4 units upwards along the Y axis.

Q(2, 3) after the translation becomes,

Q'(2 - 3, 3 + 4) = Q'(-1, 7)

Hence the point Q(2, 3) under the translation (x - 3, y + 4) is the point Q'(-1, 7).

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The image of point Q under the translation (x, y) -> (x - 3, y + 4) is Q'(-8, 8)

Given data:

A translation in the coordinate plane moves every point on a figure a given distance in a given direction. The position of any point (x, y) on the figure changes to (x + a, y + b), where a and b are real numbers.

The point is represented as Q ( -5 , 4 ).

To find the image of point Q(-5, 4) under the translation (x, y) + (x - 3, y + 4), we simply apply the translation vector (x - 3, y + 4) to the coordinates of point Q.

New x-coordinate = x - 3 = -5 - 3 = -8

New y-coordinate = y + 4 = 4 + 4 = 8

Hence, the image of point Q(-5, 4) under the given translation is Q'(-8, 8).

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The complete question is attached below:

Plot the image of point Q ( -5 , 4 ) under the translation (x, y) + (x - 3, y + 4).​
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