if 120 marks is 60% what is full marks

this cannot be factored.

 there are no 2 numbers that when added will equal - 12 and when multiplied together would equal -36

n + q = 35

n = 35-q

0.05n + 0.25q = 8.15

0.05(35-q) +0.25q = 8.15

1.75 -0.05q + 0.25q =8.15

1.75 + 0.20q = 8.15

0.20q = 6.40

q = 6.40 / 0.20 = 32

32 quarters and 3 nickels

Answer:

$16.98

hope this helps you! good luck ;)

Answer:

In forensic science trigonometry can be used to calculate a projectile’s trajectory, to estimate what might have caused a collision in a car accident or how did an object fall down from somewhere, or in which angle was a bullet shot etc.

Electrical engineers also use trigonometry. Modern power companies use alternating current to send electricity over long-distance wires. In an alternating current, the electrical charge regularly reverses direction to deliver power safely and reliably to homes and businesses.

Electrical engineers use trigonometry to model this flow and the change of direction, with the sine function used to model voltage. Every time you flip on a light switch or turn on the television, you’re benefiting from one of trigonometry's many uses.

Answer:

The slope of ZW is [tex]\frac{2}{5}[/tex]

The lenght of ZY is [tex]\sqrt{29}[/tex]

Quadrilateral WXYZ is a square

Step-by-step explanation:

Statements

case A) The slope of ZW is [tex]\frac{2}{5}[/tex]

The statement is True

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

[tex]Z(-3,1),W(2,3)[/tex]

substitute

[tex]m=\frac{3-1}{2+3}[/tex]

[tex]m=\frac{2}{5}[/tex]

case B) The slope of YX is [tex]-\frac{5}{2}[/tex]

The statement is False

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

[tex]Y(-1,-4),X(4,-2)[/tex]

substitute

[tex]m=\frac{-2+4}{4+1}[/tex]

[tex]m=\frac{2}{5}[/tex]

case C) The lenght of ZY is [tex]\sqrt{29}[/tex]

The statement is True

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

[tex]Z(-3,1),Y(-1,-4)[/tex]

substitute

[tex]d=\sqrt{(-4-1)^{2}+(-1+3)^{2}}[/tex]

[tex]d=\sqrt{(-5)^{2}+(2)^{2}}[/tex]

[tex]d=\sqrt{29}\ units[/tex]

case D) The lenght of WX is [tex]5[/tex]

The statement is False

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

[tex]W(2,3),X(4,-2)[/tex]

substitute

[tex]d=\sqrt{(-2-3)^{2}+(4-2)^{2}}[/tex]

[tex]d=\sqrt{(-5)^{2}+(2)^{2}}[/tex]

[tex]d=\sqrt{29}\ units[/tex]

case E) Quadrilateral WXYZ is a square

The statement is True

Because  sides ZW and YX are parallel sides (has the same slope)

Slope ZY

we have

[tex]Z(-3,1),Y(-1,-4)[/tex]

[tex]m=\frac{-4-1}{-1+3}[/tex]

[tex]m=-\frac{5}{2}[/tex]

so

ZW and ZY are perpendicular sides (the product of their slopes is equal to minus one)

[tex]-\frac{5}{2}*\frac{2}{5}=-1[/tex]

Slope WX

we have

[tex]W(2,3),X(4,-2)[/tex]

[tex]m=\frac{-2-3}{4-2}[/tex]

[tex]m=-\frac{5}{2}[/tex]

ZY and WX are parallel sides (has the same slope)

distance ZW

we have

[tex]Z(-3,1),W(2,3)[/tex]

[tex]d=\sqrt{(3-1)^{2}+(2+3)^{2}}[/tex]

[tex]d=\sqrt{(2)^{2}+(5)^{2}}[/tex]

[tex]d=\sqrt{29}\ units[/tex]

distance YX

we have

[tex]Y(-1,-4),X(4,-2)[/tex]

[tex]d=\sqrt{(-2+4)^{2}+(4+1)^{2}}[/tex]

[tex]d=\sqrt{(2)^{2}+(5)^{2}}[/tex]

[tex]d=\sqrt{29}\ units[/tex]

The four sides are congruent

case F) [tex]YZ=\sqrt{(-3-(-1))^{2}+(1-4)^{2}}[/tex]

The statement is False

[tex]YZ=\sqrt{(-2)^{2}+(-3)^{2}}[/tex]

[tex]YZ=\sqrt{13}[/tex]  ----> is not correct

the value of YZ is  [tex]\sqrt{29}[/tex]  

If Harry has 1/4 of apple pie that he wants to cut into 3 equal slices. The fraction of the whole pie in each slice will be 1/12.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that, Harry has 1/4 of apple pie that he wants to cut into 3 equal slices.

We have to apply the ratio which is the comparison of two quantities to determine how many times one obtains the other.

Suppose the fraction of the whole pie is each slice will be x,

x = 1/4 / 3

x = 1 /12

Thus, if Harry has 1/4 of apple pie that he wants to cut into 3 equal slices. The fraction of the whole pie in each slice will be 1/12.

Learn more about the fraction here:

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The Panthers are expected to win approximately 73 games out of 110 based on their current win rate.

To find out how many games the Panthers will win in a normal 110-game season based on their current winning rate from the beginning of the season, we use a simple proportion. Initially, they won 40 games out of 60, which gives us a winning ratio.

The ratio can be written as:

40 wins / 60 games = number of wins / 110 games

To find the number of wins, we cross-multiply and solve for the unknown:

(40 wins / 60 games) * 110 games = number of wins

After the calculation:

40 * 110 / 60 ≈ 73.33

As we need to round to the nearest game, it gives us approximately 73 games out of 110.

The translation of a phrase into a variable expression is given by:

                            b+7

The letter ' b ' is used to name the variable.

The total number of slices of bread used for the sandwiches and the 7 still left in the loaf.

Let b be the total number of slices that were used for the sandwiches.

and also 7 are still left in the loaf

The total number of slices of bread= Number of slices used fro sandwich+Left over

                    Hence, the expression is:

                                 b+7

Answer:

Jake had twenty-four dollars ($24) at the beginning of the day.

Step-by-step explanation:

Jake has $11 dollars left in his pocket, after spending 3 dollars on a bus ticket, 5 dollars on lunch, and 5 more dollars on a movie. 3+5+5 is equal to 13, therefore if after spending 13 dollars Jake still has 11 dollars, which means that at the beginning of the day Jake had 24 dollars (11+13).

To find the side of a square with a given diagonal length, apply the Pythagorean theorem. With a diagonal of 8 miles, the side length is calculated to be 4√2 miles.

To find the side of a square whose diagonal is given, we can use the Pythagorean theorem. In a square, the diagonal creates two right-angled triangles, each with the square's sides as the legs.

Let the side of the square be s, and the given diagonal is 8 miles. According to the Pythagorean theorem, the diagonal (d) is calculated as d = √(s² + s²). Simplifying, this becomes d = √(2 * s²) or s = d / √2. Substituting the value of the diagonal, we get s = 8 / √2. To get rid of the radical in the denominator, we can multiply both the numerator and denominator by √2, giving us s = (8√2) / 2, which simplifies to s = 4√2 miles. Therefore, the side of the square is 4√2 miles.

To find the number of VHS tapes sold when 564 DVDs were sold, divide the number of DVDs by 2.

To solve this problem, we can set up a ratio comparing the number of VHS tapes sold to the number of DVDs sold. Since the ratio is given as 2 VHS tapes to every 4 DVDs, we can simplify it to 1 VHS tape to every 2 DVDs. If 564 DVDs were sold, we can divide this number by 2 to find the number of VHS tapes sold:

564 DVDs ÷ 2 = 282 VHS tapes

Therefore, 282 VHS tapes were sold.

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Final answer:

The value of r that makes the line through (5, 2) and (7, r) have a slope of -1/2 is 1.

Explanation:

To determine the value of r so that the line through the points (5, 2) and (7, r) has a slope of m= -1/2, we use the slope formula m = (y2 - y1) / (x2 - x1). Here, (x1, y1) is (5, 2) and (x2, y2) is (7, r).

Slope calculation:
-1/2 = (r - 2) / (7 - 5)
-1/2 = (r - 2) / 2

Multiplying both sides by 2 to isolate the variable r:
-1 = r - 2
r = 2 - 1
r = 1

Therefore, the value of r that makes the slope -1/2 is 1.

Answer:

b. A checking account, or a savings account for other expenses (predictable), and emergencies.

Step-by-step explanation:

Peggy needs to pay car insurance 2 times every year.

She has divided the payment by 6 and saves that amount each month.

So, the best account in which she can save this money is - A checking account, or a savings account.

Other options are irrelevant as a 401-K retirement fund is some other type of account. It is not used for daily or monthly expenses.

Options C and D are also not correct.

Final answer:

Each friend would receive $88 from the total earnings of $264 over three days, after splitting the amount equally.

Explanation:

The question asks how much money each person would get from a total earning of $75 on the first day, $84 on the second day, and $105 on the third day after splitting it equally among three friends. To find this out, first, we need to calculate the total earnings by adding the amounts from all three days, and then we divide the total by three, since there are three friends.

The total earnings over the three days are $75 + $84 + $105 = $264. To find out how much each person gets, we divide this amount by 3:

$264 ÷ 3 = $88

So, each friend would get $88 for their work over those three days.