MATHEMATICS HIGH SCHOOL

Let f(x) = 3x2 + x − 3 and g(x) = x2 − 5x + 1. Find f(x) − g(x).

Answers

Answer 1
Answer: Substitute the two functions according to a given condition of function:
f(x) - g(x) = 3x² + x - 3 - (x² - 5x + 1)
= 3x² + x - 3 - x² + 5x - 1
= 2x² + 6x - 4  or  2(x² + 3x - 2)
Answer 2
Answer: f(x) - g(x) = 3x² + x - 3 - (x² - 5x + 1)
f(x) - g(x) = 3x² + x - 3 - x² + 5x - 1
f(x) - g(x) = 3x² - x² + x + 5x - 3 - 1
f(x) - g(x) = 2x² + 6x - 4

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What is the appropiate customary unit to measure a paper clip

Answers

Since a paperclip is extremely light, the weight of a paperclip would be measured in ounces. When thinking about weight, remember that an ounce is about the weight of a pencil, a pound is about the weight of a bag of candy, and a ton is about the weight of a truck.

Centimeters or inches would be appropriate because the size of a paperclip is very tiny.

Factor this polynomial using the factor theorem.
x^2 + 6x+ 9

Answers

Answer:

(x+3)(x+3)

Step-by-step explanation:

I hopw this helps ;-)

Point (1,-5) 6. The slope is 5 , and the line passes through the (-1,-3).

Answers

Step-by-step explanation:

You have given a point (1, -5), a slope of 5, and the line passes through the point (-1, -3). You can use this information to find the equation of the line.

The equation of a line in point-slope form is:

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line, and m is the slope.

Using the given point (1, -5) and the slope m = 5, you can plug these values into the equation:

y - (-5) = 5(x - 1)

Now, simplify:

y + 5 = 5(x - 1)

To put it in slope-intercept form (y = mx + b), expand and solve for y:

y + 5 = 5x - 5

Subtract 5 from both sides:

y = 5x - 5 - 5

y = 5x - 10

So, the equation of the line with a slope of 5 that passes through the point (1, -5) is:

y = 5x - 10

ten brothers receive 100 gold coins between them . Each brother receives a constant number more than the next oldest . The seventh oldest brother receives 7 gold coins . How much does each brother receive ? Show all your calculations

Answers

let's set 'a' as the coins the first brother recieves (the youngest) and for every older brother, we will add 'x' (the constant number)
Since we know the sum has to be equal to 100, our equation is:
100=a+(a+x)+(a+2x)+(a+3x)+...+(a+8x)+(a+9x)

the 7th oldest brother is the 3rd youngest, therefore, if we look at our equation, he gets (a+2x) - we know now that 7=a+2x

We can now simplify the first equation by summing up our 'x' and 'a'
we get: 100=10a+45x

In order to resolve the equation (since we have 2 variables), we can use the subtraction method

  100=10a+45x 
-10(7=a+2x) 

  100=10a+45x 
-(70=10a+20x) 

30=25x
1.2 = x

and for 'a' ->  7 = a +2(1.2)
a=4.6

Therefore, the youngest gets 4.6 coins (a), the second 5.8 (a+x) ...

Final answer:

The question involves arithmetic sequences. The first brother gets 5.5 gold coins with subsequent brothers getting 1 more coin than the brother before them. This gradually increases to the tenth brother who gets 14.5 gold coins.

Explanation:

This problem involves the concept of arithmetic sequences where each term is a constant amount different from the previous term. Given the seventh oldest brother receives 7 gold coins, we can denote the amount of money the first brother gets as x. The increment in each sequential brother's amount is then 1.

Firstly, denote the amount of money the first brother gets as x. Since each subsequent brother gets 1 more gold coin, we can denote the amount the other brothers receive as follows: x, x+1, x+2, ..., x+6 (for the seventh brother), ..., x+9 (for the tenth brother).

As the problem states that the total gold the brothers receive is 100, you would set up the equation: 10x + 45 = 100, where 45 is the sum of the increments from 1 to 9. Solving this equation for x, we get x=5.5. This means the first brother received 5.5 gold coins and each subsequent brother received 1 more than his immediate predecessor.

Learn more about Arithmetic Sequences here:

brainly.com/question/32830972

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Find a rational number that is between 5.2 and 5.5. Explain why it is rational

Answers

5.3

It is a rational number because 5.3 can be made into a fraction or ratio.

hope it helps!

Quadrilateral ABCD has vertices A(6,-3), B(8,-1), C(3,-1), and D(1,-3). Quadrilateral WXYZ has vertices W(1,6), X(2,7), Y(-1,7), and Z(-2,6). Which is true regarding the two shapes?

Answers

From the vertices of these two quadrilateral, you can get they are both parallelogram and they have the same angels. You can judge the choices according to the information you get from the vertices, from length and angel.

Answer:

Answer is option D

Step-by-step explanation:

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