AMC 10/12 Student Practice Questions
Guide to Student Practice Questions
Each of the following four large congruent squares is
subdivided into combinations of congruent triangles or
rectangles and is partially shaded. What percent of the total
area is partially shaded?
I
The original problem
and choices from the
2011 AMC 8 contest
(A) 12 (B) 20
(C) 25 (D) 33 (E) 37

Answer:

Credit ⇒ 45

Debit ⇒ $30

Step-by-step explanation:

Credit = $45

Debit = $30

When an account balance increases it means that it has been credited and when it decreases, it has been debited.

The beginning balance here is $0 and the closing balance is $15.

There were 2 transactions, one credit and one debit.

For the closing balance to be $15, the Credit amount must have been $15 more than the Debit amount.

Answer:

Evaluating the piecewise function when X =3, we get f(3) = 7

Step-by-step explanation:

Given the following piecewise function

f(x)= { 2x+1; where x > 0

         -3 when x ≤ 0

Evaluate the function when X = 3

We will evaluate f(x) =2x+1 where x > 0, because x = 3 and 3 <0

We can't use -3, because x ≤ 0, and 3 is not less than 0.

Now, evaluating the function:

[tex]f(x)=2x+1\\Put\:x=3\\f(3)=2(3)+1\\f(3)=6+1\\f(3)=7[/tex]

So, Evaluating the piecewise function when X =3, we get f(3) = 7

Answer:

Town C

Step-by-step explanation:

Answer:

[tex] {6x}^{3} + {9x}^{2} - 18x + 3[/tex]

Step-by-step explanation:

1. Expand by distributing sum groups.[tex]3x( {2x}^{2} + 5x - 1) - 3( {2x}^{2} + 5x - 1)[/tex]

2. Expand by distributing terms.

[tex] {6x}^{3} + {15x}^{2} - 3x - 3( {2x}^{2} + 5x - 1)[/tex]

3.Expand by distributing terms.

[tex] {6x}^{3} + {15x}^{2} - 3x - ( {6x}^{2} + 15x - 3)[/tex]

4. Remove parentheses.

[tex] {6x}^{3} + {15x}^{2} - 3x - {6x}^{2} - 15x + 3[/tex]

5. Collect like terms.

[tex] {6x}^{3} + {15x}^{2} - {6x}^{2} ) + ( - 3x - 15x) + 3[/tex]

6. Simplify.

[tex] {6x}^{3} + {9x}^{2} - 18x + 3[/tex]

Thus. the answer is,

[tex] {6x}^{3} + {9x}^{2} - 18x + 3[/tex]

Answer:

7

Step-by-step explanation:

2-8÷-2-3-12÷-6×-2

2 - -4 - 3 - 2 x -2

2 + 4 + -3 - -4

6 + -3 + 4

3 + 4

7 :)

Answer:

The one on the graph

Step-by-step explanation:

Answer:

12.87 km

Step-by-step explanation:

searched it up

If Summer (starting from rest) runs from the 20 m mark to the 35 m mark with an acceleration of 5 m/s². then 12.25 m/s is the final velocity.

Velocity is the distance covered by an object in unit time.

Given that,

Summer (starting from rest) runs from the 20 m mark to the 35 m mark with an acceleration of 5 m/s²

a=0.5 m/s²

s is distance=35-20=15

We have a formula with velocity, acceleration and distance

Now v²=2as

Here v is velocity=2

a is acceleration=5

s is the distance.=15

v²=2×5×15

The multiplication value of 2×5×15 is 150.

v²=150

Take square root on both sides

v=√150

v=12.25 m/s

Therefore final velocity is 12.25m/s.

To learn more on velocity click:

https://brainly.com/question/18084516

#SPJ2

Answer:

x ≈ - 5.32, x ≈ 1.32

Step-by-step explanation:

x² + 4x - 7 = 0 ( add 7 to both sides )

x² + 4x = 7

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(2)x + 4 = 7 + 4

(x + 2)² = 11 ( take the square root of both sides )

x + 2 = ± [tex]\sqrt{11}[/tex] ( subtract 2 from both sides )

x = - 2 ± [tex]\sqrt{11}[/tex]

Thus

x = - 2 - [tex]\sqrt{11}[/tex] ≈ - 5.32 ( to 2 dec. places )

x = - 2 + [tex]\sqrt{11}[/tex] ≈ 1.32 ( to 2 dec. places )

Answer:

x = -5.32, x = 1.32

Step-by-step explanation:

Ok. So to use the Complete the Square method, you divide the middle value by 2 and then square the number you get. This will give:

[tex](x^{2} + 4x + (\frac{4}{2}) ^2) - (\frac{4}{2}) ^2 -7 = 0[/tex]

[tex](x^{2} + 4x + 4) - 4 -7 = 0[/tex]

[tex](x^{2} + 4x + 4) - 11 = 0[/tex]

[tex](x^{2} + 4x + 4) = 11[/tex]      (now factor the left side)

[tex](x + 2)(x + 2) = 11[/tex]

[tex](x + 2)^{2} = 11[/tex]       (now square root both sides)

[tex]\sqrt{(x + 2)^{2}} = \sqrt{11}[/tex]

[tex]x + 2 = \sqrt{11}[/tex]

[tex]x = - 2 +/- \sqrt{11}[/tex]         (+/- = plus or minus)

x = -5.32, x = 1.32

Answer:

Scale Model of the Great Pyramid

You can build a model of the Great Pyramid, but first you need to scale it down. To do this, you will need to

make the pyramid 3,000 times smaller than it really is! To achieve that, every 30 meters of the pyramid is

represented as 1 centimeter.

Step-by-step explanation:

Answer:

42 feet of string

Step-by-step explanation:

First, draw a diagram of the string, the height and the angle.

the length of the string is equal to the hypotenuse of the triangle

let length of the string=x

sin(θ)=opp/hyp

sin(72°)=40ft/x

x=40ft/sin(72°)

x=42.05848897ft≈42ft

Answer:

I this that its the third graph

Answer:

The prime factorization of 56 is 2 * 2 * 2 * 7. This can also be written with exponents as 2^3 * 7.

Step-by-step explanation:

Answer:

1. 0.0833

2. 0.1

3.  0.1428

4.  0.1333

5. 0.1666

6.  0.0625

Answer:

₹ 1920

Step-by-step explanation:

Since the room is cubical in nature, we will find the total surface area of the room

Total surface area of the cubical room = 6L²

L is the length of one side of the room

Given

L = 4m

Total surface area of the cubical room = 6(4)²

Total surface area of the cubical room = 6×16

Total surface area of the cubical room = 96m²

If the painting costs ₹ 20/m², this means;

₹ 20 = 1m²

For the total room:

x = 96m²

Divide both expressions

20/x = 1/96

x = 20×96

x = 1920

Hence the total cost of painting the room ₹ 1920

Answer:

1) -x+5

2)-w+2

Step-by-step explanation:

2x+5-3x Combine.

-x+5

-(w-2)

-w+2

Answer:  B)-4

Step-by-step explanation:

The given equation: [tex]\dfrac{6}{x^2-9}-\dfrac{1}{x-3}=1[/tex]

Using identity: [tex]a^2-b^2=(a-b)(a+b)[/tex]

[tex]\dfrac{6}{(x-3)(x+3)}-\dfrac{1}{x-3}=1\\\\\Rightarrow\ \dfrac{6-(x+3)}{(x-3)(x+3)}=1\\\\\Rightarrow\ \dfrac{6-x-3}{(x-3)(x+3)}=1\\\\\Rightarrow\ 3-x=(x-3)(x+3)\\\\\Rightarrow\ (-1)(x-3)=(x-3)(x+3)\\\\\Rightarrow\ -1=x+3\\\\\Rightarrow\ x=-1-3=-4 \ \ \ [x\neq3][/tex]

Hence, the solution is : x=-4

The correct option is B.

try the other answer.

Answer:

a. x=2

b. y=5

Step-by-step explanation:

a. 2(11x+7)=58

22x+14=58

x=2

b. 16y+10=90

16y=80

y=5

Answer:

243

Step-by-step explanation:

Given that:

Day 1 = 3

Day 2 = 9

After the 2nd day, number of cells continue to triple ;

Day 3 = 9^3

P(t) = 9 * 3^3

P(t) = 9 * 27

= 243

Answer:

Her height would be 162.56 centimeters tall.

Step-by-step explanation:

There are 12 inches in 1 foot so that would mean that 1 foot has 30. 48 centimeters.

30.48 x 5 = 152.4

Add the 4 extra inches so 4 inches in centimeters is 10.16

152.4 + 10.16 = 162.56

Answer:

52

Step-by-step explanation:

Simplify the expression (Steps shown below).

Answer:

???? there's no attachment.

Step-by-step explanation:

Answer:

93.99

Step-by-step explanation:

sin rule is:

sin A ÷ a = sin B ÷ b = sin C ÷ c

A B C are angles

a b c are the lengths opposite to each angle

to find angle opposite to x:

180- (90+57) = 33°

180: sum of angles in a traingle

90: since its a right angle traingle

to find x:

sin 57 ÷ 41 = sin 33 ÷ x

rearrange:

x= (sin 33 x 41) ÷ sin 57

x= 93.99 (2 d.p/2 decimal places)

Answer:

variables

Step-by-step explanation:

variables are constantly variating to contour to the problem it is being used in like in rentals, the variable is the amount of hours rented and the constant is the price it's being rented for

Answer:

The radius of the hole is 0.24 feet

Step-by-step explanation:

Firstly, we need to convert the miles to feet

Mathematically;

1 mile = 5,280 feet

4.3 miles is thus;

4.3 * 5,280 = 22,704 feet

Mathematically, the volume of a cylinder is;

V = pi * r^2 * h

here, we want to get r

4200 = 3.142 * r^2 * 22,704

r^2 = 4200/(3.142 * 22,704)

r = 0.24 feet

Answer:

x°=96°

y°=88°

z°=151°

Step-by-step explanation:

55°+29°+×°=180°

×°=96°

96°+55°=z°

z°=151

then let variable A° be one of the inner angle of the triangle

A°+z°=180°

A°+151°=180°

A°=29°

finally adding all the inner angles will give us 180°

96°+y°-13°+29=180°

y°=88°

Answer:

119 is the answer

Step-by-step explanation:

use sum of angles on a straight line

Answer:

is the 3 one (119)

Because we all know that (B) is equal to 62 and (AB is 57 and if you add 62 + 57 = 119

Answer:

3 to 1

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, image to original, that is

OA' : OA

= 27 : 9 ( divide both parts by 9 )

= 3 : 1