Liam's last grocery bill was $105. This week, his bill was $85. Calculate the percent change. Round to the nearest hundredth.

The area of the smallest square is one quarter of the original square if its height and width are each half of the original.

Using geometrical shapes' proportional relationships, the area of a scaled-down square is calculated by squaring the factor by which the dimensions are reduced.

The area of the smallest square can be determined by comparing it with the area of a larger square.

If the dimensions (height and width) of the smallest square are half that of the original square, then its area is a quarter (1/4) of the original square.

This is because area is a two-dimensional measurement, hence when both dimensions are halved, the area is reduced by a factor of 2×2, which equals 4.

For instance, if we consider a square with an area represented by T2, and we know that the smallest square has half the height and half the width, we can calculate its area as (1/2T)×(1/2T) = T2/4.

If the area of a larger square is 4 m2, halving the dimensions will lead to an area of 1 m2 for the smallest square.

This concept is applicable to any geometrical shape where the dimensions are reduced proportionally.

The scaling down of dimensions and the resulting area calculation is a key concept in understanding how areas of similar planar figures relate to each other.

3/4 of the students did not go on the field trip.

On Monday, 3/12 of the students went on a field trip.

To find out what fraction of the students did not go on the field trip, we need to subtract the fraction that went on the field trip from the whole student body, which is represented by the fraction 1 or 12/12.

Let's perform the subtraction step-by-step:

Therefore, 3/4 of the students did not go on the field trip.

Answer:

abut 20.5 im sorry i dont quite know how to explain it

Step-by-step explanation:

Answer:

0.008375

Step-by-step explanation:

Answer:

hey

Step-by-step explanation:

8.375 can be written as

8375/1000

8375/ 10³

put in q

8375×10 power -3 × 10 power -3

8375× 10 power -6

0.008375

Answer:

21ft 4in

Step-by-step explanation:

4+4=8 3+3=6 8ft 6in

6+6=12 5+5=10 12ft 10in

8+12=20ft 10+6=16in

16-12=4 20+1=21

21ft 4in

Answer:

12.5%

Step-by-step explanation:

Our of 32 students, 4 students were absent on Monday, which means to get the percentage, we divide 4 by 32 and then turn it to percentage, by multiplying by 100

4/32= 0.125

0.125X100

= 12.5%

Answer:

12.5% of the students were absent on Monday

Step-by-step explanation:

32 students = 100 students

16 students= 1/2 of the class

8 students= 1/4 of the class

4 students= 1/8 of the class

Answer:

On Graph B, at 0 seconds, the graph will be 0 or nothing.

Then the graph will increase until 2 seconds.

Answer:

On Graph B, at 0 seconds, the graph will be 0 or nothing.

Then the graph will increase until 2 seconds.

Step-by-step explanation:

Answer:

509.8

Step-by-step explanation:

The last one on 1/23

The angle formed between the ground and the bat is 62.04 degrees

From the given question, we have the following parameters:

Length of the bat = 32in

Measure of the distance from the bat to the ladder = 15in

angle of elevation

Using the SOH CAH TOA identity

Cos θ = adjacent/hypotenuse

Cos θ = 15/32

θ = arccos(15/32)

θ = 62.04degrees

Hence the angle formed between the ground and the bat is 62.04 degrees

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using the Law of Cosines, we can find that the length of side ( p ) is approximately 3.29 units.

We can use the Law of Cosines to find the length of side ( p ) (opposite angle[tex]\( \angle P \))[/tex] when we know the lengths of the other two sides [tex]\( q \) and \( r \)[/tex] and the angle [tex]\( \angle P \)[/tex].

The Law of Cosines formula is:

[tex]\[ c^2 = a^2 + b^2 - 2ab \cos(C) \][/tex]

In this case, we want to find the length of side \( p \), so we'll use \( p \) as the side opposite angle \[tex]( \angle P \), \( q \) as side \( q \), and \( r \) as side \( r \)[/tex].

Substitute the given values into the Law of Cosines formula:

[tex]\[ p^2 = q^2 + r^2 - 2qr \cos(\angle P) \]\[ p^2 = (6.0)^2 + (7.2)^2 - 2(6.0)(7.2) \cos(27^\circ) \]\\[/tex]

Now, calculate the value of \( p \):

[tex]\[ p^2 = 36 + 51.84 - 86.4 \cos(27^\circ) \][/tex]

Using a calculator, find \( \cos(27^\circ) \approx 0.891 \):

[tex]\[ p^2 = 36 + 51.84 - 86.4 \times 0.891 \]\[ p^2 = 36 + 51.84 - 77.02 \]\[ p^2 = 10.82 \][/tex]

Take the square root of both sides to solve for \( p \):

[tex]\[ p = \sqrt{10.82} \approx 3.29 \][/tex]

So, using the Law of Cosines, we can find that the length of side ( p ) is approximately 3.29 units.

Answer:

40

Step-by-step explanation:

72-32=40

Answer:

b

Step-by-step explanation:

The car dealership sold 24 basic model cars and 16 fully-loaded model cars. This was determined by creating and solving a set of linear equations based on the given information.

This question can be approached using the method of linear equations. We know that the total number of cars sold is 40 and the total sales is $880,000. We can represent the number of basic model cars as 'b' and the fully-loaded model cars as 'f'. The cost of a basic model car is $20,000 and for a fully-loaded model, it is $25,000. Therefore, we can establish two equations:

The system of these linear equations could be solved either by Substitution or Elimination method. Through careful calculation, it can be found that the answer is b=24 (basic models) and f=16 (fully-loaded models).

So, the correct answer is Option B : The dealership sold 16 fully loaded models and 24 basic models.

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[tex]$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}=-\frac{w+7}{9}[/tex]

Solution:

Given expression:

[tex]$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}[/tex]

To solve the given expression:

First simplify: [tex]\frac{50-2 w^{2}}{3 w^{2}+9 w-30}[/tex]

[tex]$\frac{50-2 w^{2}}{3 w^{2}+9 w-30}=-\frac{2(w+5)(w-5)}{3(w-2)(w+5)}[/tex]

Cancel the common factor (w + 5).

                      [tex]$=-\frac{2(w-5)}{3(w-2)}[/tex]

Now substitute this in the given expression.

[tex]$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}=-\frac{2(w-5)}{3(w-2)} \cdot \frac{w^{2}+5 w-14}{6 w-30}[/tex]

Multiply the fractions [tex]\frac{a}{b} \cdot \frac{c}{d}=\frac{a \cdot c}{b \cdot d}[/tex]

                               [tex]$=-\frac{2(w-5)\left(w^{2}+5 w-14\right)}{3(w-2)(6 w-30)}[/tex]

Factor the denominator [tex]3(w-2)(6 w-30) =18(w-2)(w-5)[/tex]

                               [tex]$=-\frac{2(w-5)\left(w^{2}+5 w-14\right)}{18(w-2)(w-5)}[/tex]                        

Cancel the common factor 2(w – 5).

                               [tex]$=-\frac{w^{2}+5 w-14}{9(w-2)}[/tex]

Factor the numerator [tex]w^{2}+5 w-14=(w-2)(w+7)[/tex]

                               [tex]$=-\frac{(w-2)(w+7)}{9(w-2)}[/tex]

Cancel the common factor (w – 2).

                               [tex]$=-\frac{w+7}{9}[/tex]

[tex]$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}=-\frac{w+7}{9}[/tex]

Answer:

four x minus ten

Step-by-step explanation:

4x = four x

-10 = minus ten

Answer:

Four times a number x minus 10

Answer:

12 sheep

8 chickens

Step-by-step explanation:

x+y=20, x=number of sheep and y=number of chickens

4x+2y=64. (Total number of legs)

Solve the system algebraically or graphically.

1. Multiply the top equation by -2 then add the equations together to solve for x.

Or

1. Solve for y in the top equation and substitute that for y in the second equation.

Then

2. Put x into either equation to solve for y.

Answer:  " 14 " .

________________________

     →  " x = 14 " .

________________________

Step-by-step explanation:

________________________

First, let us simplify the expression on the "left-hand side" of the equation:

  →  -2(1 −4x) ;

________________________

Note the "distributive property of multiplication" :

      →  a(b + c)  =  ab + ac  .

________________________

As such, we can rewrite:  

      → -2(1 − 4x)  = (-2)(1) + (-2)(-4x) ;

                         =  - 2 + 8x ;

                       ↔  8x − 2 ;

________________________

Now, rewrite the entire expression:

 →  8x − 2 = 3x + 8 ;

________________________

Subtract "(3x)" from each side of the equation;

      and add "2" to each side of the equation:

________________________

 →  8x − 2 − 3x + 2 = 3x + 8 − 3x + 2 ;

to get:  

 →   5x = 10 ;

Now, divide each side of the equation by "5" ;

  to isolate "x" on side of the equation;

      & to solve for "x" ;

________________________

 →  5x/5 = 10/5 ;

to get:

________________________

 →  x = 2 .

________________________

Now, let us check our work:

________________________

Plug in "2" for all "x-values" into the original equation;

to see if the equation holds true;

that is, to see if each side of the original equation given has the same value;  

      when "x = 2" :

________________________

Note the given equation:

________________________

   →   -2[1 − 4x] = 3x + 8 ;

________________________

Start with the left-hand side:

   →  -2[1 − (4*2)} = -2(1 − 8) = -2(-7) = 14 .

Now, continue with the right-hand side:

   →  3(2) + 8 = 6 + 8 = 14 .

___________________________________

   → 14 =? 14 ??? ;  Yes!

___________________________________

Hope this is helpful to you!

___________________________________

Answer:

5y

Step-by-step explanation:

All you have to do is subtract 1 from both side so subtract 1 from one side than the other. If you have to find out what y equals, then after subtracting, divide 5 from both sides and y would equal 5. Hope this helped

Answer:

1)  If you want to solve the equation, x is 0/5 or 0

2) If you want to subtract 1, the answer is 5y = 0

Step-by-step explanation:

1)  5y + 1 = 1

        5y = 0

2) 5y + 1 = 1      Subtract both sides by 1

         5y = 0     Isolate the variable by dividing 5 on both sides

            y = 0/5 or 0

1. Remove parentheses

-3x^2 + x^4 + x + 2x^4 - 7 + 4x

2. Collect like terms

-3x^2 + (x^4 + 2x^4) + (x + 4x) - 7

3. Simplify

-3x^2 + 3x^4 + 5x - 7

Final answer:

To simplify the given expression, we combine like terms to get 8x+2.

Explanation:

This question can be answered by having basic understanding of rules of operations in algebra in general and about addition of expressions in particular

The expression

x+x+x+2x+x+x+2x can be simplified by combining like terms. This means adding together the coefficients of the same variables.

Combining

x terms gives 3x and combining 2x terms gives 4x. The expression becomes 3x+4x+x+x+2.

To further simplify, we can combine the like terms 3x, 4x and x to give

8x. Finally, we combine 8x and 2 to get the simplified expression 8x+2.

Therefore, the required answer of the question asked is 8x + 2.

To find the equivalent expressions to \( x + x + x + 2x + x + x + 2x + x + x + 2 \), we can perform some simplification by combining like terms.
Let's start by combining all the terms with \( x \) coefficients. When we add or combine like terms, we just sum their coefficients, keeping the variable \( x \) unchanged.
Here are the terms with \( x \) in them:
\( x + x + x + 2x + x + x + 2x + x + x \)
Now, let's add them up:
\( 1x + 1x + 1x + 2x + 1x + 1x + 2x + 1x + 1x = 11x \)
We just counted the number of \( x \)'s and there are eleven of them, hence \( 11x \).
Now let's consider the constant terms (the numbers without variables):
\( 2 \)
Since there is only one constant term, we don't need to combine it with anything else.
Now, we add the sum of the \( x \) terms to the constant term:
\( 11x + 2 \)
Therefore, the expression \( x + x + x + 2x + x + x + 2x + x + x + 2 \) simplifies to:
\( 11x + 2 \)
This is the equivalent expression to the original one given.

Answer:

A) $2356.00

Step-by-step explanation:

Principal, p = $1,500.00

Interest rate, r= 6.5%

Period, t = 7 years

compounded quarterly therefore, n = 4

Amount, A = P( 1 + r/n)^ n*t

A = 1500 ( 1 + 0.065/4)^ 4*7

A = 1500( 1 + 0.016)^28

A = 1500 ( 1.016) ^28

A = 1500 * 1.57

A = $2356.00

Answer:

216

Step-by-step explanation:

Answer:

2x²+7x-4

Step-by-step explanation:

(x+4)(x-1/2)

First multiply (x-1/2) by 2.

We have (2x-1)

(x+4)(2x-1)

Expanding it, we have

x(2x-1)+4(2x-1)

2x²-x+8x-4

2x²+7x-4

Answer:

3 dollars

Step-by-step explanation: divide 25 by .12=3.00

Answer:

$3

Step-by-step explanation:

25 X 1.12 = 28       $28-$25= 3 dollar difference.

(0.12 is the decimal form of 12%)

Answer:

62 inches

Step-by-step explanation:

Answer:

multiplicative inverse

Step-by-step explanation:

A number that is multiplied by it's multiplicative inverse equals one.

A multiplicative inverse is also called a reciprocal.

Example:

1/7 is 7's multiplicative inverse.

[tex]\frac{7}{1} *\frac{1}{7} =\frac{7}{7} =1[/tex]

Answer:

inverse

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Given

[tex]\frac{2A}{3}[/tex] = 8 + 4A

Multiply through by 3 to clear the fraction

2A = 24 + 12A ( subtract 12A from both sides )

- 10A = 24 ( divide both sides by - 10 )

A = - 2.4 → A

Answer:

Probability breaks down to this basic formula:

    desired outcome    

total possible outcomes

Also, you need to know there are 13 spades in a deck of cards.

So, on your first draw, the chances of getting a spade are:

13    (desired outcome: pick one of the 13 spades)

52    (total possibilities: 52 cards in the deck)

But on your second draw, if you don't replace the card, your chances of getting a spade are:

12

51

because you only have 12 spades left, and 51 cards total.

Then, on your last draw, the chances of getting a spade are down to:

11

50

Since each of these probabilities depend on each other, you multiply them up to get your overall probability:

13 * 12 * 11 =   1,716

52    51    50    132,600

This reduces, or you can just divide to get a decimal.

Step-by-step explanation:

Answer:

V = 50π ft³

Step-by-step explanation:

That "5 ft wide at the bottom" translates into "radius of (5/2) ft."

Volume of a cylinder of radius R and height H is V = πR²H, so here,

V = π(5/2)^2*8 ft³ or

V = π(25/4)(8) ft³, or

V = 50π ft³

Answer: 4

Step-by-step explanation: 8 times 4 = 34

4 times 2 is 8 minus 6 is 2

32 + 2 = 34

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The number that satisfies the condition 'eight times a number plus 6 less than twice the number is 34' is 4.

This problem is a basic algebra problem. Here's how to solve it step by step:

So, the number that satisfies the given condition is 4.

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