a string was 4m long. she gave 1/4m of it to her sister and 3/4m to her friends. how much string had she given away?

Consider a real number in two dimensional plane that X axis and Y axis having ordered pair : P(x,y) or (3,4).

To find it's absolute value we will find it's Distance from origin.

As Coordinate of Origin = (0,0)

Absolute Value of OP = [tex]\left | OP \right |[/tex]

     =  [tex]\sqrt{(0-x)^2+(0-y)^2}=\sqrt {x^2+y^2}[/tex]

    If the point is Q(3,4)

[tex]\left | OQ \right |=\sqrt{3^2+4^2}=\sqrt{5^2}=5[/tex]

In case of a complex number :

Z = a + bi , we consider two axes Real Axis and Imaginary Axis.

We represent Z that is (a,b) in the same way that we represent point in two dimensional plane.

To find it's absolute value , we will find it's distance from origin.

[tex]\left | Z \right |= \sqrt{a^2+b^2}[/tex]

If [tex]Z_{1}[/tex] = 6 + 8 i

[tex]\left | Z_{1}\right |=\sqrt{6^2+8^2}=\sqrt{36+64}=\sqrt{100}=10[/tex]

Answer:

230+m_<500  the line is meant to be under the sighn btw

Step-by-step explanation:i got it right on edge 2021

To determine how many more minutes Tom can use without exceeding his limit, we use the inequality X ≤ 270, which indicates that Tom can use up to 270 additional minutes.

To determine how many more minutes Tom can use this month without exceeding a 500-minute limit, given that he has already used 230 minutes. To solve this, we let X represent the additional minutes Tom can use. Since he has already used 230 minutes, we form the inequality 230 + X ≤ 500 to ensure that the total does not surpass the 500-minute limit. Simplifying this inequality, we subtract 230 from both sides to get X ≤ 270. Therefore, Tom can use up to 270 more minutes without incurring extra charges.

Final answer:

Sam drove 186 miles with the truck he rented. To calculate this, the total paid was subtracted by the base fee, and the result was then divided by the per-mile charge.

Explanation:

The student is asked to calculate the number of miles driven by Sam based on the total cost of truck rental and the additional charge per mile. We use a linear equation to represent the total cost (C) as the sum of the base fee (F) and the product of the number of miles (m) and the charge per mile (P).

The equation for this problem is:

C = F + (P × m)

We are given:

The total cost of rental (C) = $159.49

The base fee (F) = $19.99

The charge per mile (P) = $0.75/mile

Substituting the values we have into the equation gives us:

$159.49 = $19.99 + ($0.75 × m)

To find the number of miles (m), we need to isolate the variable m. We do this by subtracting the base fee from the total cost:

$159.49 - $19.99 = $0.75 × m

$139.50 = $0.75 × m

Now, divide both sides by the charge per mile to get:

m = $139.50 / $0.75

m = 186 miles

Therefore, Sam drove 186 miles.

The total number of people who have received the e-mail, not including Kris, after it has been forwarded 2 more times is 5 + 5^2 + 5^3.

The expression that shows the total number of people who have received the e-mail, not including Kris, after it has been forwarded 2 more times is 5 + 5^2 + 5^3 (option C).

To find the total number of people who have received the e-mail, you sum up the number of recipients at each stage: 5 + 25 + 125 = 155. Therefore, the expression 5 + 5^2 + 5^3 represents the total number of people who have received the e-mail, not including Kris.

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Answer: 5 inches

Step-by-step explanation:

Given: Volume of clay = 48 cubic inches

If we make a solid square right pyramid with a base edge a= 6 inches.

Then its base area = [tex]a^2=6^2=36\ inches^2[/tex]

we know that volume of square right pyramid=[tex]\frac{1}{3}\times\ a^2h[/tex]

Therefore, volume of square right pyramid made by all of clay=[tex]\frac{1}{3}\times\ a^2h[/tex]=48 cubic inches

[tex]\Rightarrow\frac{1}{3}\times\ (36)\times\ h=48\\\Rightarrow12h=48\\\Rightarrow\ h=4\ inches.....\text{[Divide 12 on both sides]}[/tex]

Now, slant height [tex]l=\sqrt{(\frac{a}{2})^2+h^2}[/tex]

[tex]\\\Rightarrow\ l=\sqrt{3^2+4^2}\\\Rightarrow\ l=\sqrt{9+16}\\\rightarrow\ l=\sqrt{25}\\\Rightarrow\ l=5[/tex]

The slant height of the pyramid if Helen uses all the clay=5 inches

Answer:

The correct answer would be 5 inches.

Step-by-step explanation:

Answer:  The required value of the first term is 8.

Step-by-step explanation:  We are given to find the first term of the arithmetic  sequence for which the third term is 126 and sixty fourth term is 3725.

We know that

the nth term of an arithmetic sequence with first term a and common difference d is given by

[tex]a_n=a+(n-1)d.[/tex]

According to the given information, we have

[tex]a_{3}=126\\\\\Rightarrow a+(3-1)d=126\\\\\Rightarrow a+2d=126~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

and

[tex]a_{64}=3725\\\\\Rightarrow a+(64-1)d=3725\\\\\Rightarrow a+63d=3725~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Subtracting equation (i) from equation (ii), we get

[tex](a+63d)-(a+2d)=3725-126\\\\\Rightarrow 61d=3599\\\\\Rightarrow d=59.[/tex]

From equation (i), we get

[tex]a+2\times59=126\\\\\Rightarrow a=126-118\\\\\Rightarrow a=8[/tex]

Thus, the required value of the first term is 8.

Okay, so first, we find a number that is between 0 and 1.

A number that qualifies for that condition would be ½.

A property of exponents is x^(n/m) = √x m sqrt(x^n), so x^(1/2) = √x

Therefore, such expression is:

x^(1/2) = 4
Where you now solve for x.

Exponential notation is a common language that is needed in order to communicate mathematical ideas efficiently and clearly. Efficiently written repeated multiplication was the reason that this notation was developed.

An example of this is the division of cells that causes growth to occur in living organisms. A single type of cell is divided 2 times in an hour, therefore in 12 hours, the cell will divide into 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 time, or as efficiently written, 2^12.

The mean and mode of the data set shown would be 4.75 and 2, 5 and 6 are modes.

Mean is the ratio of sum of the observations to the total number of observations.

The given set of data is follows as;

{2, 4, 5, 6, 8, 2, 5, 6}

The mean can be calculated by adding all numbers and dividing by the count:

(2+4+5+6+8+2+5+6)/8

= 38/8

= 4.75

The mode is the number that occurs most often.

this is the case for 2, 5, and 6.

A data set can have multiple modes. 2, 5 and 6 are modes.

Learn more about skewed distribution here:

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why are people down voting the answer above me? Anyways, the answer is A. linear constant

This is because of the fact that a linear constant is a straight horizontal line that stays, as it says, constant, that is until you go to the next interval.

The required solution of the system is (x, y) = (9, 23). Option D is correct.

Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.

Here,
To solve the system of equations using the substitution method, we substitute x = 9 into the first equation:

y = 3(9) - 4

y = 27 - 4

y = 23

Therefore, the solution of the system is (x, y) = (9, 23).

So, the correct answer is option D, (9, 23).

Learn more about coordinate here:

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The shortest side of the triangle with vertices at (-2, 5), (-2, -7), and (-6, -4) is 5 units. The lengths were calculated using the distance formula derived from the Pythagorean theorem.

The subject matter of the given question pertains to the discipline of Geometry, specifically, the calculation of the length of the sides of a triangle. To find the length of the shortest side of a triangle having vertices at (-2, 5), (-2, -7), and (-6, -4), we can use the distance formula, which is derived from Pythagoras' theorem.

The formula for calculating the distance between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane is:

√((x₂ - x₁)² + (y₂ - y₁)²)

Thus, the shortest side of the triangle is the one with length 5 units.

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The length of the shortest side of the triangle is 5.

To find the shortest side of the triangle with vertices at (-2, 5), (-2, -7), and (-6, -4), use the distance formula [tex]\( \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)[/tex]:

1. Between (-2, 5) and (-2, -7):

[tex]\[ \sqrt{( -2 - (-2) )^2 + ( -7 - 5 )^2} = \sqrt{0 + 144} = 12 \][/tex]

2. Between (-2, 5) and (-6, -4):

[tex]\[ \sqrt{( -6 - (-2) )^2 + ( -4 - 5 )^2} = \sqrt{16 + 81} = \sqrt{97} \approx 9.85 \][/tex]

3. Between (-2, -7) and (-6, -4):

[tex]\[ \sqrt{( -6 - (-2) )^2 + ( -4 - (-7) )^2} = \sqrt{16 + 9} = 5 \][/tex]

Thus, the shortest side is 5 units.