Which is a stretch of an exponential decay function? f(x) = 4/5(5/4)^x f(x) =4/5(4/5)^x f(x) =5/4(4/5)^x f(x) =5/4(5/4)^x

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.

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

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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

[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].

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.

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 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]

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.

If there is 1 group there will be 40 students in the group. There will be 20 students in each group if there are 2 groups. If there are 4 groups, there will be 10 students in each group.

Division is one of the four basic operations of mathematics.

On performing the operation division, a number is divided into some number of equal parts.

The number which is being divided is called the dividend, the number which divides the dividend is called divisor and the number got when division is performed is called the quotient and the remaining number which has not divided is called the remainder.

Total number of students = 40

If there is 1 group, number of students in the group = 40/1 = 40

If there are 20 students in each group, then the number of groups = 40/20 = 2.

If there are 4 groups, then number of students in each group = 40/4 = 10.

Hence there will be 40 students in the group if there is 1 group. There are 2 groups if there will be 20 students in each group. There will be 10 students in each group if there are 4 groups.

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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