The length of a rectangle is 3 more than 4timesthe width . If the length of the rectangle is 27 feet what is the width

width = w

 length = w+8

perimieter = 256 feet

formla for perimeter is p=2L+2w

so you have: 256 =2(w+8) +2w =

256 = 2w+16 +2w

256= 4w+16

240=4w

w=240/4 = 60

 width is 60 feet

length = 60+8 = 68 feet

Answer:

0 is nor prime or composite

Step-by-step explanation:

The definition of a prime number is a positive integer that has exactly two positive divisors. Therefore, the simplest reason why 0 is not prime is that 0 is not a positive integer, and the axiom says that all whole numbers greater than 1 are either prime or composite.

Final answer:

The three even integers are 62, 64, and 66.

Explanation:

The sum of the first and third of three consecutive even integers is 128. To find the three even integers, we start by letting the first integer be x. Because the integers are consecutive even numbers, the second integer will be x + 2 and the third will be x + 4. The sum of the first and third integers gives us the equation:

x + (x + 4) = 128

Solving this equation:

Combine like terms: 2x + 4 = 128.

Subtract 4 from both sides: 2x = 124.

Divide both sides by 2: x = 62.

So, the first even integer is 62. Consequently, the second is 62 + 2 = 64, and the third is 62 + 4 = 66. Therefore, the three consecutive even integers are 62, 64, and 66.

The best approximation for the area of the smaller trapezoid is 39 [tex]ft^2[/tex].

Since the trapezoids are similar, the ratio of their corresponding side lengths is constant. We know the base of the larger trapezoid is 30 ft and the smaller one is 24 ft. Therefore, the ratio of their bases is:

ratio of bases = [tex]\frac{30 ft}{24 ft}[/tex] = [tex]\frac{5}{4}[/tex]

The area of a trapezoid is given by:

Area = [tex]\frac{1}{2}[/tex] * base * height

For similar shapes, the ratio of their areas is proportional to the square of the ratio of their corresponding side lengths. In this case, the ratio of areas will be:

Ratio of areas = [tex](Ratio \ {of \ { bases)^2[/tex] = [tex]({\frac{5}{4} })^2[/tex] = [tex]\frac{25}{16}[/tex]

We know the area of the larger trapezoid is 61 [tex]ft^2[/tex]. Applying the ratio of areas:

Area of smaller trapezoid = (61 [tex]ft^2[/tex]) * [tex]\frac{16}{25}[/tex]

Area of smaller trapezoid ≈ 38.91 [tex]ft^2[/tex] ≈ 39[tex]ft^2[/tex]

Lets do the first one(7). Fist change 10x -2y = 3,which is in standard form to point slope form so you can see the slope.

10x - 2y = 3

-2y = -10x + 3

-2y/-2 = -10x / -2 + 3/-2

y = 5x - 3/2

The slope is the m in y = mx + b so our slope is 5x, well it wants you to find the equation of a line that passes through (0,1) that is parallel to the equation this (Parallel) mean has the same slope.The slope is 5. Now that we know the slope is 5 we can find the equation by using the point slope form of an equation of a line.

point slope form =  y – y1 = m(x – x1)

Remember m = slope = 5. Now plugin our x and y cord  from the point (0,1) and our slope of 5

y - y1 = m(x - x1)

y - 1 = 5(x - 0)

y - 1 = 5x - 0

y - 1+1 = 5x + 1

y= 5x + 1

So the point (0,1) passes through y = 5x + 1

Number 8 is already in slope intercept form so you don't have to do anything to find the slope. You can see that the slope is 7 so just plug your point into y - y1 = m(x - x1) and then put it into slope intercept form.

8) 

Point = (5,8)

Slope = 7

y - y1 = m(x - x1) 

y - 8 = 7(x - 5) 

y =  7x - 27

So for number 8 the point (5,8) passes through y = 7x - 27

(9) For nine they want an equation that is perpendicular, which means to flip the slope. For instance, if you have a slope of 2/5 the perpendicular slope would be 5/2. For 9 we see that the slope is 2/5 so its perpendicular slope would be 5/2. Now just plug your point into the point slope form equation.

Point = (-4, 6)

Slope = 2/5 

perpendicular slope = 5/2

y - 6 = 5/2(x - (-4))

y = 5/2 x + 16

So point (-4, 6) passes through y = 5/2 x + 16

(10) Point (4,1) passes through y = 7/5 x - 23/5

The equation 4(x+y)=4x+4y represents the same value after solving.

This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.

Given:

We have 4(x+y)=4x+4y.

We have the Distributive Property

a x ( b+ c )= a x b + a x c

let x= 2 and y = 5

So, 4 (x+ y) = 4 (2+ 5)= 4(7) = 28

and, 4x+ 4y= 4(2)+ 4(5) = 8+ 20 = 28

Learn more about Distributive Property here:

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Answer:

[tex]\frac{2}{5}[/tex]-pound of sand

Step-by-step explanation:

We have been given that Amber has [tex]\frac{4}{5}[/tex]-pound bag of colored sand. She uses 1/2 of the bag for the project.

We need to find 1/2 'of' the 4/5 as:

[tex]\frac{4}{5}\times \frac{1}{2}[/tex]

[tex]\frac{4\times1}{5\times2}[/tex]

[tex]\frac{2\times1}{5\times1}[/tex]

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

Therefore, Amber used [tex]\frac{2}{5}[/tex]-pound of sand for the project.

[tex]\(x^2 - x - 6\)[/tex] can be expressed as the product of [tex]\((x - 3)\) and \((x - 2)\)[/tex]. The long division image is given below.

Long division for polynomials is similar to long division for numbers. We'll divide the quadratic polynomial [tex]\(f(x) = x^2 - x - 6\)[/tex] by the binomial [tex]\((x - 3)\)[/tex].

Here's a step-by-step breakdown of the process:

1. Start by dividing the highest-degree term of the dividend (in this case, [tex]\(x^2\)[/tex]) by the highest-degree term of the divisor (in this case, [tex]\(x\))[/tex]. This gives us [tex]\(x\)[/tex].

2. Multiply the divisor [tex]\((x - 3)\)[/tex] by the result from step 1, which is [tex]\(x\),[/tex] and write the result below the dividend, aligning like terms. So, [tex]\(x \cdot (x - 3) = x^2 - 3x\)[/tex].

3. Subtract the result from step [tex]2 (\(x^2 - 3x\))[/tex] from the dividend ([tex]\(x^2 - x - 6\)[/tex]). This gives us [tex]\(x^2 - x - 6 - (x^2 - 3x)\)[/tex], which simplifies to [tex]\(-x + 3x - 6\),[/tex] resulting in [tex]\(2x - 6\)[/tex].

4. Now, we repeat the process with the new expression [tex]\(2x - 6\)[/tex]. We divide the highest-degree term ([tex]\(2x\)[/tex]) by the highest-degree term of the divisor [tex](\(x\)),[/tex] which gives us [tex]\(2\).[/tex]

5. Multiply the divisor [tex]\((x - 3)\)[/tex] by the result from step 4, which is [tex]\(2\)[/tex], and write the result below the previous result: [tex]\(2 \cdot (x - 3) = 2x - 6\)[/tex].

6. Subtract the result from step [tex]5 (\(2x - 6\))[/tex] from the previous expression [tex](\(2x - 6\))[/tex], which results in [tex]\(0\)[/tex].

Since we have a remainder of [tex]\(0\),[/tex] this means that [tex]\(x^2 - x - 6\)[/tex] is evenly divisible by [tex]\((x - 3)\)[/tex], and the quotient is [tex]\(x - 2\).[/tex] The final result is:

[tex]\[ \frac{x^2 - x - 6}{x - 3} = x - 2 \][/tex]

This tells us that [tex]\(x^2 - x - 6\)[/tex] can be expressed as the product of [tex]\((x - 3)\) and \((x - 2)\)[/tex].

1. 2(7) +4 = 18, does not = 20, does not lie on graph

2. 4(-1) -14 = -18, equals -18, does lie on the graph

3. 5(.5)-1 = 1.5, does not = 2.5, does not lie on the graph

4. -2(0.8)+6 = 4.4, does not = 5.4 does not lie on graph

5. 1/2(0.7) +2 = 2.35, does not = 1.6, does not lie on graph

The tip of the minute hand moves approximately (8/3)π inches in 20 minutes, using the circumference of the circular path it follows and the proportion of the path covered in that time.

The student is asking about the distance traveled by the tip of the minute hand of a clock over a 20-minute period. To find the distance, we'll consider the movement of the minute hand as part of a circular path, which is described by the arc length of the circle segment.

The length of the minute hand, which is 4 inches, acts as the radius (r) of the circle. The minute hand completes one full rotation around the clock face in 60 minutes, so in 20 minutes, it covers one-third of a full rotation. We can find the arc length of the minute hand's path using the formula for the circumference of a circle (C = 2πr), multiplied by the fraction of the rotation:

Circumference: C = 2π(4 inches) = 8π inches

Arc Length for 20 minutes: (1/3) × 8π inches = (8/3)π inches

Therefore, the tip of the minute hand moves approximately (8/3)π inches in 20 minutes.