MATHEMATICS HIGH SCHOOL

What is the equation of a line passing through the point (a, b) and having a slope of b?

Answers

Answer 1

Answer: From the slope form of a line;
$(y-b)/(x-a) =b$
y-b=bx-ab
y=bx-ab+b
y=bx-b(a-1)

Answer 2

Answer:

Answer:

The equation is y-a= b(x-b)

Step-by-step explanation:

I use bold for the slope so you can differentiate the slope term b from the y coordinate value b.

The equation of a line passing through a specific point and having a specific slope can be obtained using the point slope form of a line :

y-y1=m(x-x1) where m is the slope and (x1,y1) is your specific point.

So replacing your values, the point (x1,y1) =(a,b) and m=b, in this equation we havE:

y-a= b(x-b)

That can be expressed in point slope form and explicit for as.

y = b(x-b) + a = bx -bb +a =

y= bx + (a -bb)

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What is the middle product of (-2x 1)(-3x - 5)? User: Factor 64a2 - 48a + 9.

Answers

What is the middle product of (-2x 1)(-3x - 5)
= (-2x -1)(-3x - 5)
= 6x^2 + 3x + 10x + 5
= 6x^2 + 13x + 5

So the middle product is 13x.

Factor 64a2 - 48a + 9.
64a2 - 48a + 9
(8a - 3) (8a - 3)

Ex 2.8
3. find the maximum value of the curve y=x²-4x+4 for -3≤x≤3

Answers

$y=x^2-4x+4\ny'=2x-4\n\n2x-4=0\n2x=4\nx=2\n2\in[-3,3]\n\ny''=2>0 \Rightarrow \text{ There's a minimum at } x=2$

In this case you have find the values of $y(-3)$ and $y(3)$ .

$y(-3)=(-3)^2-4\cdot(-3)+4=9+12+4=25\ny(3)=3^2-4\cdot3+4=9-12+4=1\n\ny(-3)>y(3) \Rightarrow y_(max)=25$

A college freshman started the year with $4000 in spending money and after three months, she has $2800 left. Assume that she will continue to spend her money at this same rate.

Answers

To solve this question, you need to know the rate in which the money is being spent. First, you know the y-intercept, which is 4000, or the money she owned before spending it. Next, you know, how much she had spent in the duration of 3 months. So, if you substitute those numbers into y=ax+b, it would be 2800=-3a+4000 (or 2800=4000-3a either way it is equivalent) If you solve this, you know that the college freshman is spending her money at a rate of $400 per month. Hope this helps :)

4000-2800=1200

1200/3 equals 400 a moth

If she continues, she will have enough money for 7 more months

Multiply 3⁄4 × 16⁄9 .
A. 64⁄27
B. 3⁄4
C. 27⁄64
D. 4⁄3

Answers

Answer:

Option D $(4)/(3)$

Step-by-step explanation:

we know that

The product of two fractions is equal to the product of the numerators divided by the product of the denominators

$(3)/(4)*(16)/(9)=(3*16)/(4*9)\n \n=(48)/(36)\n \n=(24)/(18)\n \n=(4)/(3)$

I believe that the answer to this question is D. 4⁄3

What is the y-intercept of the function: f(x)=x+4

Answers

The answer for the y intercept is (0,4)

If you're plotting the value of f(x) on the y-axis,
then the graph crosses the y-axis at y=4.

Approximately how long is a leg of an isosceles right triangle that has a hypotenuse of length 14.14 cm? A. 3 cm B. 5 cm C. 7 cm D. 10 cm

Answers

According to the fact that isosceles right triangle with the hypotenuse of 14.14 cm its cathetus should be 9.998 cm, and if we round this number we will get 10 cm. Therefore, the answer is D. 10 cm.

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