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Eduardwww [97]
3 years ago
9

If f(x) = 2x^2 and g(x)= x^2 + 2x, which expression represents f(g(x))?

Mathematics
1 answer:
Sloan [31]3 years ago
4 0
I think the answer is E
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The scale of the room design shows that 1" = 3 feet. How big is the actual room if the design shows a square that is 6 inches wi
adoni [48]

Answer:

arah is at a miniature exhibit. There is a model of a skyscraper. Underneath the model was a ratio. It said:

1 inch=30 feet.

If the model is 38 inches tall, how Sarah use this information to find the actual height of the skyscraper?

In this concept, you will learn how proportions are used to find actual and scale dimensions using a scale ratio.

Using Proportions to Find Dimensions

A scale is a ratio that shows the relationship between the representation of an object and the real measurement of an object. Toy makers use scale ratios to make models of cars and airplanes that are proportional to the real thing. Architects use scale drawings to plan the design of buildings.

A scale drawing is a drawing that is used to represent and object that is too large to be drawn in its actual dimensions. If a drawing is to scale, you can use proportions to determine the actual dimensions of the scale drawing.

Let’s look at a scale drawing of a sculpture. In the drawing, the sculpture is 4 inches tall. The scale is 1 inch : 4 feet. It scale can be written as

1 in4 ft

(Note: Inch is abbreviated “in.” or with the double prime mark, ″. Foot/feet is abbreviated “ft” or with the single prime mark, ′.)

A drawing with this scale tells you that 1 inch on paper is equal to 4 feet in real life. If the drawing is 4 inches tall, use the scale to find the actual height of the sculpture.

First, create a proportion using equivalent ratios. Remember to write the corresponding units in the numerator and in the denominator. The actual height of the sculpture is represented by the variable x.

1 in.4 ft.=4 in.x ft.

Then, cross multiply and simplify the equation to find the value of x.

xx==4(4)16

The sculpture will be 16 feet tall.

Let’s make a scale drawing. Use the scale 1′′=2′. Draw a room that is 8′×12′.

First, write a proportion to find the measurement of the width.

1′′2′=x′′8′

Next, cross multiply and simplify the equation to find the value of x.

2x2xx===1(8)84

The drawing will be 4

4 0
3 years ago
Which statements are true?
faust18 [17]
Question 3. The true statements are:
4g2 – g = g2(4 – g)  ⇒ should be: 4g² - g = g(4g - 1)
9g3 + 12 = 3(3g3 + 4) ⇒ should be: 9g³ + 12 = 3(3g³ + 4) TRUE
24g4 + 18g2 = 6g2(4g2 + 3g) ⇒ should be: 24g⁴ + 18g² = 6g²(4g² + 3)
<span>35g5 – 25g2 = 5g2(7g3 – 5) </span>⇒ should be: 35g⁵ - 25g² = 5g²(7g³ - 5) TRUE

Question 4. Completely factored.
16y⁵ + 12y³ = 4y³(4y² + 3) FACTORED COMPLETELY
18y³ - 6y = 6y(3y² - 1)
20y⁷ + 10y² = 10y²(2y⁵ + 1)
32y¹⁰ - 24 = 8(4y¹⁰ - 3) FACTORED COMPLETELY
3 0
3 years ago
A and b are positive integers and a–b = 3. Evaluate the following:
yulyashka [42]

1/27

1/27

125

Step-by-step explanation:

Given that,

a - b = 3

9^(1/2b) /3^a = 3^(2/2b) /3^a

= 3^b/3^a

= 3^(b-a)

= 3^(-3)

= 27^(-1)

= 1/27

27^(1/3b) /9^(1/2a) = 3^(3/3b) /3^(2/2a)

= 3^b/3^a

= 3^(b-a)

= 3^(-3)

= 27^(-1)

= 1/27

125^(1/3a) /25^(1/2b) = 5^(3/3a) /5^(2/2b)

= 5^a/5^b

= 5^(a- b)

= 5^3

= 125

6 0
3 years ago
When Natalie commutes to work, the amount of time it takes her to arrive is normally
NARA [144]

Answer: 95%

Step-by-step explanation:

7 0
3 years ago
Prove the identity (cosx+cosy)^2+(sinx-siny)^2= 2+2cos(x+y)
astra-53 [7]
(cos(x) + cos(y))^2 + (sin(x) - sin(y))^2 Remove the brackets

cos^2(x)
+ cos^2(y) + 2cos(x)*cos(y) + sin^2(x) - 2(sin(x)*sin(y) + sin^2(y) Combine these two in bold to make 1 because sin^2(x) + cos^2(x) = 1

1 + cos^2(y) + 2cos(x)*cos(y) - 2*sin(x)*cos(y) + sin^2(y) 
These two in bold also make 1

2 + 2cos(x)*cos(y) - 2*sin(X)*sin(y) Bring out a common factor of 2
2 +2(cos(x)*cos(y) -  sin(x)*sin(y) )

but cos(x+y ) = cos(x)*cos(y) - sin(x)*sin(y)

2 + 2* cos(x + y) is your final answer. 

4 0
3 years ago
Read 2 more answers
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