The regular price of an item at a store is p dollars. The item is on sale for 20% off the regular price. Some of the expressions shown below represent the sale price, in dollars, of the item.
Expression A: 0.2p
Expression B: 0.8p
Expression C: 1-0.2p
Expression D: p-0.2p
Expression E: p-0.8p

Which two expression each represent the sale price of the item?

Expression A and E
Expression B and C
Expression B and D
Expression C and D

According to the information, we can infer that Mazibane must pay R3640 into the account on 30 June to have no debt.

To calculate the amount Mazibane must pay on 30 June to have no debt in the account, we need to consider the initial debt, the interest, and the previous payment.

Initial Debt:

Interest Calculation:

Previous Payment:

To determine the remaining debt on 1 June, we subtract the payment from the initial debt:

From 1 June to 30 June, a period of one month, interest is charged on the remaining debt.

To calculate the interest for one month, we use the formula:

where the principal is the remaining debt, the rate is the monthly interest rate (16%/12), and the time is the number of months (1).

To find the total debt on 30 June, we add the remaining debt on 1 June and the interest for one month:

To have no debt on 30 June, Mazibane must pay the total debt amount:

Calculating the interest and summing up the values, we find that Mazibane must pay approximately R3640 into the account on 30 June to have no debt.

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Answer: 4.40

Step-by-step explanation: 10 divided by 4 is 2.5 and 2.5 times 4.40=11

so 4.40x2.5=11

Answer to part A:  11w^2+7z^2

Answer to part B:  14w^2+9w

=================================================

Explanation:

For part A, the expression 4w^2+7w^2+7z^2 has one pair of like terms. That pair is 4w^2 and 7w^2 which combine to 11w^2. You add the coefficients to get 4+7 = 11, then tack w^2 onto everything to say 4w^2+7w^2 = 11w^2

We cannot combine 11w^2 and 7z^2 as they aren't like terms. So we leave it as 11w^2+7z^2

--------------------

In part B, the like terms are 15w and -9w. They combine to 15w-9w = 6w. You can think of it like 15-9 = 6 then stick a 'w' to each term. We cannot combine the w^2 term with the w terms.

Answer:between 28000 km and 32000 km

Step-by-step explanation:

Answer will be 27.

Given,

3√81

Now, to solve the expression the squares of whole numbers and square roots for some numbers must be known.

For example, squares of

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81
10² = 100

Square roots,

√100 = 10

√81 = 9

√64 = 8

√49 = 7

√36 = 6

√25 = 5

√16 = 4

√9 = 3

√4 = 2

√1 = 1

Now ,

3√81 = 3× 9

= 27.

Thus the value is 27.

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Answer:

You're correct.

Answer:

I think line C and L since Jenna's numbers are the same

The square of a binomial, when the binomials are subtracted, is defined as follows:

(a - b)² = a² - 2ab + b².

When the two binomials are added, the square is given as follows:

(a + b)².

Expanding the square, we have that:

(a + b)² = (a + b) x (a + b).

(a + b)² = a² + ab + ab + b².

(a + b)² = a² + 2ab + b².

Which is the result presented in this problem.

Now, when the binomial has a minus sign, involving a subtraction, the pattern is obtained as follows:

(a - b)² = (a - b) x (a - b).

(a - b)² = a² - ab - ab + b².

(a - b)² = a² - 2ab + b².

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Answer:

4

Step-by-step explanation:

7*4 = 28 or 28 divided by 7 = 4

The interval (1, 6) contains all the real numbers between 1 and 6, not including any of the endpoints.

This can be written in inequality notation as:

x >1 AND x < 6

But there is a shorter way to write the interval by combining both inequalities:

1 < x < 6

Answer:

x=19

Step-by-step explanation:

8(3x-2)-8x=9(2x-6) Distribute.

24x-16-8x=18x-54   Combine like terms.

16x-16=18x-54         Subtract 16x from both sides (getting rid of a variable first  

-16x     -16x               is easier).

-16=2x-54                 Add 54 to both sides.

+54    +54

38=2x                       Divide both sides by 2.

/2   /2

19=x

Hope this helps!! Have a great day ^^

Answer:

See diagram below.

====================================================

Explanation:

Start at the lower left corner of the entire figure. Move 20 ft directly to the right until reach the end of the driveway at the bottom. Now move 10 ft up so you reach the other side of the driveway (the 26 ft side). In the process of moving 10 ft up, mark a new line segment. I've done so in red in the diagram below.

I've also drawn a green box. The red line and green box form a shape of a flag on a flagpole. The pole being 10 ft tall and the green box (flag) is a 6 by 3 rectangle. The 6 is from 26-20 = 6 and the 3 is from 10-7 = 3. Note how I'm subtracting the opposite side values to help figure out the dimensions of this green box.

The 10 ft by 20 ft portion of the driveway is 10*20 = 200 square feet. The green box adds on another 18 sq ft because 6*3 = 18. In all, we have 200+18 = 218 square feet for the driveway.

-------------------

If you want to know the area of the garden, then we first compute the overall area of everything shown. That's 32*14 = 448 square feet. Subtract off the driveway's area to get 448-218 = 230. Therefore, the garden's area is 230 square feet.

The person who gets to say the last number, 1000, will be Person 6.

Here, we have,

In this scenario, we have seven people sitting in a circle and counting clockwise. The goal is to determine which person will say the last number when they reach 1000. To solve this problem, we can use the concept of modular arithmetic.

When dividing 1000 by the total number of people (7), we get a quotient of 142 and a remainder of 6 (1000 = 142*7 + 6). This means that after completing 142 full rounds of counting, the group will have reached the number 994 (142*7). In the next round, they will continue counting from 995 to 1000.

Since the remainder is 6, it indicates that the last number (1000) will be spoken by the person sitting 6 positions after the first person in the circle (clockwise). In other words, Person 1 says numbers 1, 8, 15, and so on, while Person 6 will say 6, 13, 20, and so on.

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complete question:

10) Seven people sit in a circle and begin counting clockwise starting from 1.Each person in the group is keeping track of the numbers she is saying (e.g. 1,8, 15...) If they continue in this way, counting on and on, until they reach 1000, which person will get to say the last number

Let us subtract 12 from both sides and we get:

the 12 - 12 on the left-hand-side cancels gives us

Now 32 -12 = 20; therefore, the above becomes

which is our answer!

ANSWER

EXPLANATION

We want to write the equation of the circle in vertex form:

The first step is to group the x terms and y terms together and take the constant to the right-hand side of the equality sign:

Now, complete the square for the x terms:

Repeat the process for the y terms:

That is the equation of the circle in vertex form.

The element which should be used to help clarify a complicated idea in a text is ; A research question.

According to the question;

A research question is the best fit which should be used to help clarify a complicated idea in a text.

This is so because; a research question provides a basis for accessing all perspectives there is to the complicated idea.

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Answer:

D

Step-by-step explanation:

how is this math? 0-0

Answer:

3 and 9

Step-by-step explanation:

x+y=12

y-x=6

y-x=6

 +x.  +x

y=6+x

x+(6+x)=12

6+2x=12

-6.    -6

2x=6

/2. /2

x=3

3+y=12

-3.  -3

y=9

Hopes this helps please mark brainliest

Answer:

4 Units

Step-by-step explanation:

The standard matrix A is [ (1/2, √3/2) (√3/2, -1/2) ]

To find the standard matrix of a linear transformation, we need to find the images of the standard basis vectors under the transformation.

The standard basis vectors in R2 are (1,0) and (0,1). Let's find their images under T.

The image of (1,0) under a 30∘ clockwise rotation is (√3/2, 1/2). The image of this under reflection through the line y=x is (1/2, √3/2).

The image of (0,1) under a 30∘ clockwise rotation is (-1/2, √3/2). The image of this under reflection through the line y=x is (√3/2, -1/2).

The standard matrix of T is then the matrix whose columns are the images of the standard basis vectors:

A = [ (1/2, √3/2) (√3/2, -1/2) ]

= \(\left[\begin{array}{cc}1/2&\sqrt{3} /2\\\sqrt{3} /2&-1/2\end{array}\right]\)

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The conclusion about angles B and C is that the angles are equal angles

How to determine the true statement?

The given parameters are:

Angle A and Angle B are supplements

Angle A and Angle C are supplements

Supplementary angles add up to 180 degrees.

This means that

A + B = 180

A + C = 180

Subtract the two equations

So, we have

A - A + B - C = 180- 180

Evaluate the like terms

So, we have

B - C = 0

Add C to both sides

B = C

Hence, both angles are congruent angles

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The solution of the integral of 8 cos(x)+ √3 = 5√3 is  8π√3.

The given function is 8 cos(x)+ √3 = 5√3

The function can be simplified as follows;

8 cos(x) + √3 = 5√3

collect similar terms together;

8 cos(x) + √3 - 5√3 = 0

8 cos(x)  - 4√3 = 0

integral of  8 cos(x)  - 4√3  = 8 sin(x) - 4√3x

the value of the integral over (0, 2π)

= 8 sin(0) - 4√3(0) -  (8 sin(2π) - 4√3(2π))

= 0 + 8π√3

= 8π√3

Thus, the solution of the integral of 8 cos(x)+ √3 = 5√3 is  8π√3.

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Answer:

\(\text{\textit{x}} \ \ = \ \ \displaystyle\frac{\pi}{6} \ \ \ \text{or} \ \ \ \displaystyle\frac{11\pi}{6}\)

Step-by-step explanation:

Given the trigonometric equation

                               \(8 \ \cos{\left(\textit{x}\right)} \ + \ \sqrt{3} \ = \ 5\sqrt{3}\),

hence solving for \(\textit{x}\) yields

                                  \(8 \ \cos{\left(\textit{x}\right)}\ = \ 5\sqrt{3} \ - \ \sqrt{3} \\ \\ \\ \-\hspace{8px} \cos{\left(x\right)} \ = \ \displaystyle\frac{4\sqrt{3}}{8} \\ \\ \\ \-\hspace{8px} \cos{\left(x\right)} \ = \ \displaystyle\frac{\sqrt{3}}{2} \\ \\ \\ \-\hspace{29px} \textit{x} \ \ \ = \ {\cos}^{-1}\left(\displaystyle\frac{\sqrt{3}}{2}}}\right) \\ \\ \\ \-\hspace{29px} \textit{x} \ \ \ = \ \displaystyle\frac{\pi}{6}\).

Since cosine is positive in both quadrant I and quadrant IV, thus

                                     \(\textit{x} \ \ = \ \ 2\pi \ - \ \displaystyle\frac{\pi}{6} \ \ = \ \ \displaystyle\frac{11\pi}{6}\).

Therefore the solutions are

                                               \(\textit{x} \ \ = \ \ \displaystyle{\frac{\pi}{6}} \ \ \text{or} \ \ \displaystyle{\frac{11\pi}{6}}\).

Answer:

Five

Step-by-step explanation:

Pivot columns are said to be columns where pivot exist and a pivot exist in the first nonzero entry of each row in a matrix that is in a shape resulting from a Gaussian elimination.

Suppose A = 5 × 7 matrix

So; if A columns span set of real numbers R⁵

The number of pivot columns that A must have must be present in each row. In a  5 × 7 matrix ; we have 5 rows and 7 columns . So , since A must be present in each row, then :

The matrix must have five pivot columns and we can infer that about  the statements that "A has a pivot position in every row"  and "the columns of A spans R⁵" are logically equivalent.

the total cost of the car rental for Nate if he rents a compact car with the optional insurance and fills up the gas tank before returning the car would be $\(570.\)

To calculate the total cost of the car rental, we need to first determine the rental rate for a compact car for 8 days, including the optional insurance.

The daily rental rate for a compact car is $ \(56,\) and the optional insurance costs $10 per day. Therefore, the total daily cost of renting a compact car with insurance is:

\(56 + 10 = 66\)

To determine the total cost of renting the compact car for 8 days, we simply multiply the daily cost by the number of days:

\(66 \times 8 = $528\)

Next, we need to determine the cost of gasoline if Nate returns the car without a full tank. The gasoline charge is $ \(3.50\) per gallon, but we don't know how many gallons Nate will need to fill up the tank.

If we assume that a compact car has a gas tank capacity of around 12 gallons, and that Nate will need to refill the tank to its full capacity, then the gasoline charge would be:

$\(3.50 \times 12 = $42\)

Finally, we can calculate the total cost of the rental, including the optional insurance and the gasoline charge if Nate returns the car without a full tank:

$\(528 + $42 = $570\)

Therefore, the total cost of the car rental for Nate if he rents a compact car with the optional insurance and fills up the gas tank before returning the car would be $\(570\).

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Answer:8 experiments

Step-by-step explanation:

she has 8 feet of copper and she needs one foot for each experiment she can do 8 experiments.

We want to write a linear function that models the given situation, where a linear function is written as:

\(y = a*x +b\)

where a is the slope and b is the y-intercept.

The function will be:

\(T(z) = (-0.02 gal/mi)*z + 13 gal.\)

The information that we have here is:

The car gets 50 miles per gallon.

The tank holds 13 gallons of fuel.

We want to write a function that gives the number of gallons in the tank as a function of the miles driven.

Let's define the variable:

z = number of miles

Then the function T(z) will give us the number of gallons in the tank as a function of z.

\(T(z) = a*z + b\)

We know that if there are no miles driven (z = 0), then the tank should be full, so we have:

\(T(0 mi) = 13 gal = a*0mi + b\\\\ 13 gal = b\)

Then we found the value of b, and the function becomes

\(T(z) = a*z + 13 gal.\)

Now we know that for every 50 miles driven, the car uses one gallon.

Then the rate (or slope) at which the fuel is consumed is:

\(a = -(1 gallon)/(50 miles) = -0.02 gal/mi\)

Where the negative sign is because the fuel is being consumed.

We can replace that in the function to get:

\(T(z) = (-0.02 gal/mi)*z + 13 gal.\)

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The value of the number is x = 34.

Let's break down the problem and solve it step by step.

1. "Five less than twice the value of a number": This can be represented as 2x - 5, where x is the number.

2. "Three times the quantity of 4 more than 1/2 the number": This can be represented as 3 * (x/2 + 4).

According to the problem statement, the two expressions are equal. We can set up the equation as follows:

2x - 5 = 3 * (x/2 + 4)

Now, let's solve the equation:

2x - 5 = 3 * (x/2 + 4)

Distribute the 3 to both terms inside the parentheses:

2x - 5 = (3/2)x + 12

Multiply through by 2 to eliminate the fraction:

2(2x - 5) = 2((3/2)x + 12)

4x - 10 = 3x + 24

Next, let's isolate the x term by moving the constant terms to the other side of the equation:

4x - 3x = 24 + 10

Simplify:

x = 34

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To be able to determine which equations could be the other equation in a system

The tables which shows a proportional relationship between x and y are table 3 and table 4.

Using ratio to find the proportional relationship

Table 1

x : y = 8 : 8

= 1 : 1

x : y = 12 : 10

= 6 : 5

Not proportional

Table 2:

x : y = 2 : 3

x : y = 3 : 8

Not proportional

Table 3:

x : y = 5 : 3

x : y = 10 : 6

= 5 : 3

Proportional

Table 4:

x : y = 4 : 1

x : y = 16 : 4

= 4 : 1

Proportional

Ultimately, table 3 and table 4 shoes a proportional relationship between x and y.

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