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3 years ago

Math rate of change and show me how u did it:( <3

Mathematics

1 answer:

Ymorist [56]3 years ago

5 0

Answer:

y = m x + b equation for a straight line

if x = o then y = 4 from graph

y = 0 + 4 and b = 4

If x = 8 then y = 24 from graph

24 = m * 8 + 4 substituting in our equation

m = 20 / 8 = 2.5 giving slope or rate of change

y = 2.5 x + 4 the final equation with a slope of 2.5

As a check using the graph:

We see that if y = 24 then x = 8

24 = m * 8 + 4 substituting in our equation

m = 20/8 = 2.5 agreeing with the value found

You might be interested in

After a 35% discount, a book costs 11.21, what is the normal undiscounted price of the book?

abruzzese [7]

Answer:

15.11

11.21 x 35% = 3.9

3.9 + 11.21 =15.11

Be safe and have a day

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7 0

3 years ago

Find all pairs of real numbers (a,b) such that (x-a)^2+(2x-b)^2=(x-3)^2+(2x)^2

Mrrafil [7]

Answer:

$(3,0)$

$(\frac{-9}{5},\frac{12}{5})$

Step-by-step explanation:

Let's expand both sides.

I'm going to use the following identity to expand the binomial squared expressions: $(u+v)^2=u^2+2uv+v^2$ or $(u-v)^2=u^2-2uv+v^2$ .

Left-hand side:

$(x-a)^2+(2x-b)^2$

$(x^2-2ax+a^2)+((2x)^2-2b(2x)+b^2)$

$x^2-2ax+a^2+4x^2-4bx+b^2$

Reorder so $x^2$ 's are together and that $x[tex]'s are together.[tex](x^2+4x^2)+(-2ax-4bx)+(a^2+b^2)$

$5x^2+(-2a-4b)x+(a^2+b^2)$

Right-hand side:

$(x-3)^2+(2x)^2$

$x^2-2(3)x+9+4x^2$

$x^2-6x+9+4x^2$

Reorder so $x^2$ 's are together and that $x[tex]'s are together.[tex](x^2+4x^2)+(-6x)+9$

$5x^2-6x+9$

Now let's compare both sides.

If we want both sides to appear exactly the same we need to choose values $a$ and $b$ such the following are true equations:

$-2a-4b=-6$

$a^2+b^2=9$

So if we solve the system we can find the values $a$ and $b$ such that the left=right.

Let's solve the first equation for $a$ in terms of $b$ .

Add $2a$ on both sides:

$-4b=-6+2a$

Divide both sides by -4:

$b=\frac{-6+2a}{-4}$

Reduce (divide top and bottom by -2):

$b=\frac{3-a}{2}$

Now let's plug this into second equation:

$a^2+b^2=9$

$a^2+(\frac{3-a}{2})^2=9$

$a^2+\frac{9-6a+a^2}{4}=9$ (I used the identity $(u-v)^2=u^2-2uv+v^2$ )

Multiply both sides by 4 to clear the fractions from the problem:

$4a^2+(9-6a+a^2)=36$

Combine like terms on left hand side:

$4a^2+a^2-6a+9=36$

$5a^2-6a+9=36$

Subtract 36 on both sides:

$5a^2-6a-27=0$

Now let's try to factor.

We are going to try to find two numbers that multiply to be 5(-27) and add to be -6.

5(-27)=(5*3)(-9)=15(-9)=-15(9) while -15+9=-6.

So let's replace $-6a$ with $-15a+9a$ and factor by grouping.

$5a^2-15a+9a-27=0$

$5a(a-3)+9(a-3)=0$

$(a-3)(5a+9)=0$

This implies $a-3=0$ or $5a+9=0$ .

Solving the first is easy. Just ad 3 on both sides to get: $a=3$ .

The second requires two steps. Subtract 9 and then divide by 5 on both sides.

$5a=-9$

$a=\frac{-9}{5}$ .

So let's go back to finding $b$ now that we know the $a$ values.

If $a=3$ and $b=\frac{3-a}{2}$ ,

then $b=\frac{3-3}{2}=0$ .

So one ordered pair $(a,b)$ that satisfies the equation is:

$(3,0)$ .

If $a=\frac{-9}{5}$ and $b=\frac{3-a}{2}$ ,

then $b=\frac{3-\frac{-9}{5}}{2}$ .

Let's multiply top and bottom by 5 to clear the mini-fraction.

$b=\frac{15-(-9)}{10}$

$b=\frac{24}{10}$

$b=\frac{12}{5}$

So one ordered pair $(a,b)$ that satisfies the equation is:

$(\frac{-9}{5},\frac{12}{5})$ .

5 0

4 years ago

Find the value of x for the triangle

Brilliant_brown [7]

<h3>2)x=180°−(30°+90°) Since it is a right angle so the third angle is a right angle. ...</h3>

<h3>5)This is an equilateral triangle. ...</h3>

<h3>6)This is a right angled triangle.</h3>

5 0

3 years ago

A+4b=-4 a+10b=-16<br>how to solve this problem

UNO [17]

Answer:

a,b=4,-2

Step-by-step explanation:

Subtract:

a-a+4b-10b=-4-(-16)

-6b=-4+16

-6b=12

b=-2.

Plug in:

a+4(-2)=-4

a-8=-4

a=4.

Hope this helps plz hit the crown :D

7 0

3 years ago

Reva is playing a bean-bag toss game. For each bag that misses the board, the player scores -8 points. Reva misses the board 4 t

erica [24]

Answer:

The answer is -32.

Step-by-step explanation:

Since there is no detailed information given about the game or the total tosses in the question, i will assume that the game is concluded when each player has had 4 tosses.

Considering the information that Reva missed the board 4 times out of her total 4 tosses in the game and each miss results in -8 points, her total score for those 4 tosses should be -8x4 = -32.

I hope this answer helps.

6 0

3 years ago