This system has one solution. What is the y-coordinate of the solution? y = 5x - 9
y = x^2 - 3x + 7

Answers

Answer 1

Answer: set 5x-9 = $x^(2)$ - 3x + 7
⇒ 0 = $x^(2)$ - 8x + 16
⇒ factoring we get... 0 = (x-4)² so the x-coordinate for the solution is x = 4
To find the y-coordinate, plug x = 4 into one of the equations (you can plug it into both just to make sure you're right).
y = 5x - 9 plug in x = 4 ⇒ y = 5(4) - 9 = 20 - 9 = 11
y = $x^(2)$ - 3x + 7 plug in x = 4 ⇒ y = (4)² - 3(4) + 7 = 16 - 12 + 7 = 11
∴ The solution to the system is (4, 11) which has y-coordinate 11.

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Identify each expression that represents the slope of a tangent to the curve y= -x^3+17x^2-x+3 at any point (x,y).

Answers

This is seriously so long I'm not sure it will even fit on a single line. The formula for the derivative using the limiting process is $\lim_(h \to 0) (f(x+h)-f(x))/(h)$ . And of course this is a problem because if h approaches 0, we would have a 0 in the denominator of that fraction and that is definitely not allowed! Every x in the function will be replaced with (x+h) to give us this: $\lim_(h \to 0) (-(x+h)^3+17(x+h)^2-(x+h)+3)/(h)$ . When we expand that we will get this very long numerator (I'm purposely leaving out the limit as h approaches 0 part to save space): $(-(x^3+2x^2h+xh^2+x^2h+2xh^2+h^3)+17x^2+34xh+17h^2-x-h+3-(-x^3+17x^2-x+3))/(h)$ . Simplifying that leaves us with this: $(-x^3-2x^2h-xh^2-x^2h-2xh^2-h^3+17x^2+34xh+17h^2-x-h+3+x^3-17x^2+x-3)/(h)$ . We have a lot of terms that cancel each other out so when we do that we are left with $\lim_(h \to 0) (-3x^2h-3xh^2-h^3+34xh+17h^2-h)/(h)$ . That is one of your choices for answers, the third one down on the left to be specific. Now we can factor out an h: $\lim_(h \to 0) (h(-3x^2-3xh-h^2+34x+17h-1))/(h)$ . That h on the top outside the parenthesis cancels with the h on the bottom. Now, as h approaches 0 we have no problems! Yay! That means when we now replace h with 0, we have this: $-3x^2-0-0+34x+0-1$ , or simplified we have $-3x^2+34x-1$ which is also a choice for your answers, top one on the right. Those are your 2 answers for that dertivative. It's much simpler when you learn the rules!

Simplify the following expression: 35 + (–13) + (+8) – (–6).

Answers

$35 + (-13) + 8 - (-6) \n \n 35 - 13 + 8 + 6 \n \n 36 \n \n Answer: \fbox {36}$

35 + (-13) + 8 - (-6)

35 - 13 + 8 + 6

22 + 8 + 6

30 + 6

36

A taxi charges $1.75 plus a fee of $0.75 for each mile traveled.the total cost of a ride,without a tip, is $4.75. how many miles is the trip?

Answers

Answer:

4 miles

Step-by-step explanation:

4.75 - 1.75 = 3.00/.75=4

WILL GET BRAINLIEST The scatterplot shows the weight and miles per gallon of the nation's 40 best-selling cars.Vehicle Weights and Miles
Per Gallon
Miles Per Gallon
Vehicle Weight
Which statement is most strongly supported by the scatterplot?

Answers

The last one as we can see that as the wight increases, the miles per gallon decreases.

i am a three digit number. i am divisible by 5. i am an even number each of my digits are different my tens is greater than my ones digit. my hundreds digit is greater than my tens digit. i am less than 400. i am divisible by 3. i have only one odd digit. my tens digit is 1. what number am i?

Answers

Answer:

210

I am divisible by 5.

So your ones digit is 0 or 5

I am an even number.

So your ones digit is 0. We fill that in.

_ _ 0

My tens digit is 1.

So we fill that in.

_ 1 0

My tens digit is greater than my ones digit.

Well, of course 1 is greater than 0. We didn't need to be told that.

I have only one odd digit.

Since the 1 is odd, the hundreds digit is even, 2,4, or 8

I am less than 400.

So your hundreds digit is 2. Fill that in and we're done.

2 1 0

My hundreds digit is greater than my tens digit.

Of course 2 is greater than 1, we didn't need to be told that.

I am divisible by 3.

Of course 210 is divisible by 3. We didn't need to be told that.

Too much information!

Answer: 210

The ziggurat linked the people of Mesopotamia to what? all of the gods they worshipped
ruler of their city
patron god of their city
all of the rulers in the civilization