MATHEMATICS MIDDLE SCHOOL

What is the standard form of the equation y = (x + 2)^2 -3y = x^2 + 4x - 3
y = x^2 + 4x + 7
y = x^2 + 4x + 1
y = x^2 + 4x - 3

Answers

Answer 1

Answer:

Answer:

y=x^2+4x+7

Step-by-step explanation:

y=(x+2)(x+2)-3

y=x^2+2x+2x+4-3

y=x^2+4x+7

Answer 2

Answer:

C. y = x² + 4x + 1

Step-by-step explanation:

y = (x + 2)² - 3

y = x² + 4x + 4 - 3

y = x² + 4x + 1

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Issac fills up his 20 -gallon gas tank with fuel that costs $3.54 per gallon. The expression 3.54g represents the cost for a number of gallons of fuel. What does the variable g represent?

A radio station uses 1/6 of it's time for the news. In a 24 hour day, how many are used for music and entertainment? Wouldn't it be 20 hours for music and entertainment?Wouldn't it be 20 hours?

Since they used 4 hours for news, so 24 - 4 = 20 for music and entertainment?

Someone else is telling me it's 4 hours but I'm confused on their reasoning.

Answers

If they have 24 hours in a day, and use 1/6 of those 24 hours on news, they use 24*(1/6) or 4 hours on news. Assuming that they use the leftover time for just music and entertainment, we have 20h - 4h, so thats 20h. You were right. Not sure on their reasoning either.

What is the area of a circle whose radius is 10 meters?A: 20 Pi
B: 25 Pi
C: 100 Pi
D: 400 Pi

Answers

C. 100 pi

hope this helped :)

C. 100 Pi :) :) :) :)

What is the percent of 0.25% out of 50

Answers

It would be 0.125 because by converting percent to a decimal you must first multiply 0.0025 x 50.

Hope that helps

If h(x)=(fog)(x) and h(x)=³√x+3, find g(x) if f(x) =³√x+2

Answers

Answer:

$g(x)=x+1$

The problem:

Find $g(x)$ if $h(x)=(f \circ g)(x)$ ,

$h(x)=\sqrt[3]{x+3}$ , and

$f(x)=\sqrt[3]{x+2}$ .

Step-by-step explanation:

$h(x)=(f \circ g)(x)$

$h(x)=f(g(x))$

Replace $x$ in $f(x)=\sqrt[3]{x+2}$ with $g(x)$ since we are asked to find $f(g(x))$ :

$\sqrt[3]{x+3}=\sqrt[3]{g(x)+2}$

$\sqrt[3]{x+1+2}=\sqrt[3]{g(x)+2}$

This implies that $x+1=g(x)$

Let's check:

$(f \circ g)(x)$

$f(g(x))$

$f(x+1)$

$\sqrt[3]{(x+1)+2}$

$\sqrt[3]{x+1+2}$

$\sqrt[3]{x+3}$ which is the required result for $h(x)$ .

Need help please help me

Answers

The solution is the point of intersection between the two equations.

Assuming you have a graphing calculator or a program to lets you graph equations (I use desmos) you simply put in the equetions and note down the coordinates of the point of intersection.

In the graph the first equation is in blue and the second in red.

The point of intersection = the solution = (-6 , -1)

If you dont have access to a graphing calculator you could draw the graphs by hand;

1) Draw a table of values for each equation; you do this by setting three or four values for x and calculating its image in y (you can use any values of x)

y = 0.5 x + 2 (Im writing 0.5 instead of 1/2 because I find its easier in this format)

x | y
-1 | 1.5 * y = 0.5 (-1) + 2 = 1.5
0 | 2 * y = 0.5 (0) + 2 = 2
1 | 2.5 * y = 0.5 (1) + 2 = 2.5
2 | 3 * y = 0.5 (2) + 2 = 3

y = x + 5

x | y
-1 | 4 * y = (-1) + 5 = 4
0 | 5 * y = (0) + 5 = 5
1 | 6 * y = (1) + 5 = 6
2 | 7 * y = (2) + 5 = 7

2) Plot these point on the graph
I suggest to use diffrent colored points or diffrent kinds of point markers (an x or a dot) to avoid confusion about which point belongs to which graph

3) Using a ruler draw a line connection all the dots of one graph and do the same for the other

4) The point of intersection is the solution

y = mx + b - it's the equation of a straight line. We need only two points to the plotting the graph of that function.

Select any two x values and calculate y values:

$y=(1)/(2)x+2\n\nfor\ x=0\to y=(1)/(2)(0)+2=0+2=0\to(0,\ 2)\n\nfor\ x=-4\to y=(1)/(2)(-4)=-2+2=0\to(-4,\ 0)$