Write a function rule for the area of a rectangle whose length is 6 ft more than its width. What is the area of the rectangle when its width is 12 ​ft?

The question revolves around solving a system of three linear equations with three variables, using algebraic techniques such as substitution or elimination.

The system of equations provided can be solved using methods such as substitution, elimination, or matrix operations. The equations given are:

To solve this system, we can perform operations such as eliminating one variable at a time or using matrices to find the values of x, y, and z that satisfy all three equations simultaneously.

Division Property of Equality

16m = 160

 divide both sides by 16 to find m

m = 160/16 = 10

Answer:

Step-by-step explanation:

The given expression is

[tex]16m=160[/tex]

So, we use one of the properties of equalities for division, which states that if we divide one side of the equation, we also must divide the other side by the same number, to not mess up the balance of the equation. Applying this property, we have

[tex]\frac{16m}{16}=\frac{160}{16}\\ m=10[/tex]

Explanation of an inequality involving addition and division

The given inequality is: 4 + (x/3) ≥ 9

To express the statement algebraically:

Add four to the quotient of a number and 3.

Set the expression greater than or equal to 9.

Solve for x to find the number that satisfies the inequality.

Estimate of 63 times 39: Approximately 2400.

Estimate of 62.93 times 73: Roughly 4410.

Estimate of 34.44 times 57: About 2040.

To estimate the products, you can round the numbers and then perform the multiplication.

Here are the estimates for the given multiplication problems:

Estimate of 63 times 39:

Round 63 to 60 and 39 to 40.

Calculate 60 times 40, which is 2400.

Estimate of 62.93 times 73:

Round 62.93 to 63 and 73 to 70.

Calculate 63 times 70, which is 4410.

Estimate of 34.44 times 57:

Round 34.44 to 34 and 57 to 60.

Calculate 34 times 60, which is 2040.

These are rough estimates and may not be entirely accurate, but they provide a quick way to get an idea of the approximate result of the multiplication.

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Final answer:

A 610-league adventure is equivalent to 1830 nautical miles, calculated by multiplying the number of leagues by the conversion factor, where one league is equal to approximately 3 nautical miles.

Explanation:

To convert the distance from leagues to nautical miles, we need to know the conversion factor. One league is approximately 3 nautical miles. Thus, by multiplying the given number of leagues by this factor, we can determine the distance in nautical miles.

If the cruise ship is embarking on a 610-league adventure, we calculate the equivalent distance in nautical miles as follows:

Multiply the number of leagues (610) by the conversion factor (3).

The calculation would be 610 leagues * 3 nautical miles/league = 1830 nautical miles.

Therefore, a 610-league voyage is equivalent to 1830 nautical miles.

Kiko is coasting on her bicycle down a hill. After 3 s, her speed is 10 m/s. After 8 s, her speed is 25 m/s. Her acceleration during this time will be  5 m/s².

Acceleration is the rate of change in both speed and direction of velocity over time. When anything moves faster or slower in a straight line, it is said to have been accelerated. Because the direction is always shifting, motion on a circle accelerates even while the speed is constant.

It is given that, Kiko is coasting on her bicycle down a hill. After 3 s, her speed is 10 m/s. After 8 s, her speed is 25 m/s.

Acceleration is found as the ratio of the change in speed to the change in a time interval.

Acceleration =  change in speed/ change in a time interval

Acceleration = (25-10) / (8-5)

Acceleration = (15)/(3)

Acceleration = 5 m/s²

Thus, Kiko is coasting on her bicycle down a hill. After 3 s, her speed is 10 m/s. After 8 s, her speed is 25 m/s. Her acceleration during this time will be  5 m/s².

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we have

[tex]f(x)=(x-3)^{2}(x+2)^{2}(x-1)[/tex]

we know that

The zero of the function is  the value of x when the value of the function is equal to zero

[tex]f(x)=(x-3)^{2}(x+2)^{2}(x-1)[/tex]

rewrite the function

[tex]f(x)=(x-3)(x-3)(x+2)(x+2)(x-1)[/tex]

The zero's of the function are

[tex]x=3\ x=3\ x=-2\ x=-2\ x=1[/tex]

so

[tex]x=3[/tex] ------> has a multiplicity of [tex]2[/tex]

[tex]x=-2[/tex] ------> has a multiplicity of [tex]2[/tex]

[tex]x=1[/tex] ------> has a multiplicity of [tex]1[/tex]

therefore

the answer is

The zero [tex]1[/tex] has a multiplicity of [tex]1[/tex]

The zero [tex]-2[/tex] has a multiplicity of [tex]2[/tex]

From the given function, f(x) = (x − 3)2(x + 2)2(x − 1);

The function f(x) = (x − 3)²(x + 2)²(x − 1) given can be expanded so that we have;

Hence, the zeros of the function f(x) are;

We can conclude that the zero 1 has a multiplicity of 1 and the zero -2 has a multiplicity of 2.

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t = time

v = velocity

you have (2,54) & (4,58)

v-54 = (58-54) / (4-2) *(t-2)

v=4/2(t-2)+54

v =2(t-2)+54

v = 2t-4+54

b - Graph by plotting the given points (2,54) & 4,58) and drawing a straight line through them

Answer:

The remainder is 80

Step-by-step explanation:

Given the polynomial

[tex]f(x)=4x^3-5x^2+2x+11[/tex]

we have to find the remainder when the above polynomial f(x) is divided by x-3

By remainder theorem when we put x=3 in f(x) we get the remainder i.e f(3)

[tex]f(3)=4(3)^3-5(3)^2+2(3)+11[/tex]

[tex]=108-45+6+11[/tex]

[tex]=80[/tex]

which is required remainder.

Hence, the remainder is 80

C) Use a straight edge to draw a vertical line between the points where each pair of arcs intersect.