Let f(x) = x2 + x + 2 and g(x) = 2x2 + 5. Find f(g(x)). Show each step of your work

xenn [34]

Answer:

23.025 square inches.

Step-by-step explanation:

To do this, we can split our polygon into 3 different shapes, a triangle, and 2 rectangles, and adding the areas of those 3 shapes together.

Specifically, triangle ABC, rectangle ACHI, and rectangle DEFG.

First we can start with the area of the triangle.

The area of a triangle is 1/2b*h. (1/2*base*height)

The base of the triangle AC, which is 4.2 inches. (9-4.8, Total length-DE)

The height is 2.75 inches. (6-3.25, Total height-AI)

Put it into the formual:

1/2*4.2*2.75=5.775

Next, I'm going to find the area of rectangle ACHI. The formula for the is just l*w (length*width)

The length is IH which is 4.2 inches. (9-4.8, total length-DE)

The width is AI which is 3.25 inches. (1.3+0.75+1.2, CD+EF+GH)

3.25*4.2=13.65

Now, we are going to find the area of rectange DEFG. Again, the formula is just l*w.

The length is DE which is 4.8 inches.

The width is EF which is 0.75 inches.

4.8*0.75=3.6

Now we add these areas together.

5.775+13.65+3.6=23.025

So the area of the model is 23.025 square inches.

4 0

3 years ago

If rain falls at a unit rate of 3 inches per hour, how much rain will accumulate after 24 hours?

natta225 [31]

Answer:

The answer is 72 inches in 24 hours.

Step-by-step explanation:

If 3 inches tall per hour, and you need to find the amount of rain in 24 hours, you just need to multiply the number of inches per hour by the number of hours required (24 hours):

3×24=72 inches

6 0

3 years ago

Read 2 more answers

Hi I need to find DO length

MakcuM [25]

Answer:

10 cm

Step-by-step explanation:

If we assume that DC is parallel to AB, then triangle DOC is similar to triangle AOB.

However, even with this assumption, there is not enough information in the diagram to solve for DO. We would also need to know the length of CO. Then we could write a proportion:

DO / (DO + 20) = CO / (CO + 24)

Edit: OD is 2 cm shorter than OC. If we call x the length of OD, then the length of OC is x+2.

Putting this into our proportion:

x / (x + 20) = (x + 2) / (x + 2 + 24)

x / (x + 20) = (x + 2) / (x + 26)

Cross multiply:

x (x + 26) = (x + 2) (x + 20)

Distribute:

x² + 26x = x² + 20x + 2x + 40

x² + 26x = x² + 22x + 40

4x = 40

x = 10

So the length of DO is 10 cm.

4 0

3 years ago

To compound 50% solution in which proportion must 95% sol and 30% sol be mixed to make

Varvara68 [4.7K]

Answer:

4/9

Step-by-step explanation:

Let the amount of 95% sol = a ml and

the amount of 30% sol = b ml.

So, the total amount of the compound=a+b=500 ml

As the compound is 50% solution, so

95% of a + 30% of b= 50% of (a+b)

(95/100)a+(30/100)b=(50/100)(a+b) [from equation (i)]

95a + 30b = 50(a+b)

95(a/b)+30 = 50(a+b)/b [dividing both sides by b]

95(a/b)+30 = 50(a/b+1)

95(a/b)+30 = 50(a/b)+50

95(a/b)-50(a/b)=50-30

45(a/b)=20

a/b=20/45

a/b=4/9

Therefore, a:b=4:9

As a+b= 500 ml, so the amount of 95% sol = $\frac {500}{13}\times 4=\frac{2000}{13}=153.85$ ml

and the amount of 95% sol = $\frac {500}{13}\times 9=\frac{4500}{13}=346.15$ ml

Hence, the proportion of 95% sol and 30% sol to make a compound of 50% sol must be 4/9.

3 0

3 years ago

Which of the following are solutions to the equation below?<br><br> x^2-2x-24-0

Dominik [7]

Answer:

x=-4

x=6

Step-by-step explanation:

Lets put to work the well known quadratic equation:

$x=\frac{-b+/- \sqrt{b^{2}-4ac } }{2a}$

Let us also, remember the given equation: x^2-2x-24=0

Where 'a' would be equals to 1, 'b' equals to -2 and c equals to -24.

The quadratic equations with those values is:

$\frac{2 +/- \sqrt{4+96} }{2}$

Where we obtain two values.

x1= -4

and x2= 6

4 0

3 years ago