Write a simplified polynomial expression in standard form to represent the area of the rectangle below.

A picture of a rectangle is shown with one side labeled as x-4 and another side labeled as 5x+2

A) 5x^2 + 18x - 2
B) 5x^2 + 13x + 2
C) 5x^2 - 18x - 8
D 5x^2 + 13x + 8

Solution:

we are given that

In the image, shape ABCD is similar to shape WXYZ.

we have been asked to find the measure of side ZW.

As we know that when two shapes are similar then the ratios of their corresponding sides are equal.

So we can write

[tex] \frac{zw}{6}= \frac{18}{24}\\ \\ ZW=6*\frac{18}{24}\\ \\ ZW=\frac{18}{4}\\ \\ ZW=4.5\\ [/tex]

Hence ZW=4.5 Inches.

Answer:

4.5

Explanation:

Got it right on Imagine math.

Answer:

1600

Step-by-step explanation:

There will be 1600 E. coli bacteria, in 1 hour.

In maths, to multiply means to add equal groups. When we multiply, the number of things in the group increases. The two factors and the product are parts of a multiplication problem.

Given that, Mitosis is a process of cell reproduction in which one cell divides into two identical cells. E. coli is a fast-growing bacterium that is often responsible for food poisoning in uncooked meat. It can reproduce itself in 15 minutes.

In the beginning, there are 100

After 15 minutes, there are 2*100=200

After 30 minutes, there will be 2*200 =400

After 45 minutes = 400*2 = 800

After 60 minutes = 800*2 = 1600

Hence, in 1 hour there will be 1600 E. coli bacteria.

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Using the properties of exponents, the expression is simplified as (4/3)x⁵y².

To simplify the given expression, we need to use properties of exponents

Taking the numerator;

[(2x³y)⁴] = (2⁴)(x³)⁴(y)⁴ = 16x¹²y⁴

Next, let's simplify the denominator:

3x²(4x⁵y²) = 3 * 4 * x² * x⁵ * y² = 12x⁷y²

This can be expressed as;

[(2x³y)⁴] / [3x²(4x⁵y²)] = (16x¹²y⁴) / (12x⁷y²)

Take the common factors and divide both of them;

(16x¹²y⁴) / (12x⁷y²) = (4/3)(x¹² / x⁷)(y⁴ / y²) = (4/3)x¹²⁻⁷y⁴⁻² = (4/3)x⁵y²

Therefore, the simplified expression is (4/3)x⁵y².

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Final answer:

The jogger is approximately 7 miles from his house after running 3 miles east and then 5 miles at a 30° angle east of north, calculated using trigonometric functions and the Pythagorean theorem.

Explanation:

The question asks how far a jogger is from his house after running a total of 8 miles, initially 3 miles due east and then 5 miles at a 30° angle east of north. To solve this, we can use trigonometric functions to find the resultant displacement. The first leg of the journey is straightforward, 3 miles directly east. The second leg can be broken into its northward and eastward components using sine and cosine functions, with the length of the leg being the hypotenuse.

Northward component: 5 miles × cos(30°) = 4.33 miles

Eastward component: 3 miles (initial) + (5 miles × sin(30°)) = 3 + 2.5 = 5.5 miles

To find the total displacement, we calculate the straight-line distance from the starting point to the end point using the Pythagorean theorem.

Displacement = √(northward component² + eastward component²) = √(4.33² + 5.5²) = √(18.7489 + 30.25) = √(48.9989) = 7 miles approximately.

Therefore, the jogger is approximately 7 miles from his house.

To find the distance and direction from the starting point after the jogger's two separate runs, we apply vector addition by decomposing the second leg into its components with trigonometry and then use the Pythagorean theorem and arctangent function to find the resultant magnitude and direction.

The question involves determining the distance from the starting point after a two-leg journey with given directions and distances. To solve this, we need to apply principles of vector addition to combine the two displacements into one resultant displacement. The first displacement is due east, and can be represented as a straight line on a horizontal axis. The second displacement, at a 30° angle east of north, requires us to decompose it into its northward and eastward components. These components are found using trigonometry: by multiplying the distance by the cosine (for the eastward part) and sine (for the northward part) of the angle.

After computing the respective components of the second displacement, we add both eastward displacements together and both northward displacements together to find the total displacement in the east and north directions. The final step is to use the Pythagorean theorem to determine the magnitude of the resultant vector, and trigonometry (specifically, the arctangent function) to find the direction of the resultant vector from the origin, which provides the required distance and direction from the jogger's house after running.

Answer: The expression that is quivalent to to 0.2n + 2n + 4 is

2.2n +4

Hope this helped! -mojo jojo x

Measurement of the bookcase on the scale drawing using the scale 3cm:2 feet is width =19.5 cm and height = 36 cm

Scaling an object means multiplying every linear dimension of it by the same factor

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given,

Width of the bookcase = 13 feet

Height of the bookcase = 24 feet

Given scale is 3cm : 2 feet

Therefore for 1 feet = 1.5 cm

Then,

Width of the bookcase = 13×1.5= 19.5 cm

Height of the bookcase = 24×1.5= 36 cm

Hence, the measurements of the bookcase after scaling is width =19.5 cm and height = 36 cm

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To determine the unknown side length of a golden rectangle, set up a proportion and solve a quadratic equation.

The golden rectangle is a rectangle in which the ratio of the longer side to the shorter side is equal to the golden ratio, approximately 1.618. To determine the unknown side length, we can set up a proportion using the given side length and the golden ratio:

s / t = (s + t) / s

Substituting the given values, we have:

s / 9 = (s + 9) / s

Cross multiplying and simplifying, we get:

s^2 = 9(s + 9)

By solving this quadratic equation, we find that the unknown side length is approximately 4.94. Therefore, the correct answer is c. 4.94.

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Answer:

The average age is 30.4.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The table is attached.

You can observe in the table that there's no a value for 29 minutes.

That means we need to find the linear expression and then calculate the answer.

First, we need to find the ratio of change using two pairs of the given table and the following formula, (20,220) and (40,440) are the points

[tex]m=\frac{440-220}{40-20}=\frac{220}{20} =11[/tex]

The ratio of change states that Jane burns 11 calories per minute. So, after 29 minutes, she will burn

[tex]11cal(29min)=319 cal/min[/tex]

Answer:

Dalai have 45 marbles.

Step-by-step explanation:

Consider the provided information.

Dalai bought a few swirl marbles and divided it equally among four of her friends and her brother, Jake. while playing, Jake lost two marbles and has only 7 marbles at present.

Let x is the number of marbles Dalai have.

She divide x number of marbles into 5 equal part (Four of friend and her brother)

That means each of them have [tex]\frac{x}{5}[/tex] marbles.

Jake lost two marbles out of [tex]\frac{x}{5}[/tex] and now he has only 7 marbles,

This can be represented as:

[tex]\frac{x}{5}-2=7[/tex]

Solve the equation for x.

[tex]\frac{x}{5}=7+2[/tex]

[tex]\frac{x}{5}=9[/tex]

[tex]x=45[/tex]

Hence, Dalai have 45 marbles.

Answer:

90 + 50 = 140 square cm

Answer:

C)82 Degrees F

Step-by-step explanation:

The formula we have is F = 9/5C + 32.  Substituting the value for Celsius, 28, into the formula,

F = 9/5(28) + 32

F = 1.8(28) + 32

F = 50.4 + 32

F = 82.4

To the nearest whole number, this is 82 degrees.

The converted temperature in degrees Fahrenheit is 82 Degrees F

Temperature conversion is the process of changing the value of temperature from one unit to another. We measure temperature on scales like Kelvin, Celsius, and Fahrenheit, etc.

Given that, the temperature in Australia, is 28 degrees C, Ed wasn’t sure if that was hot or cold, so he converted the temperature to degrees in Fahrenheit.

We know that,

The formula to convert the temperature into Fahrenheit is:

F = 9/5C + 32.  

Substituting the value for Celsius, 28, into the formula,

F = 9/5(28) + 32

F = 1.8(28) + 32

F = 50.4 + 32

F = 82.4

Hence, the converted temperature in degrees Fahrenheit is 82 Degrees F

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Answer:

Between 29% and 49% (just took quiz on Edge)

The rest of the question is: To the nearest percent, with a confidence level of 95% (z*- score 1.96), what is the confidence interval for the proportion of cable subscribers who would be willing to pay extra for the new nature channel?

The following inequality are matched with their graphical solution;

6. 4y + 3 ≤ y + 6. graph C

7. -2y > 2. graph A

8. y/3 < -1. graph D

9. 3y < 2y + 3. graph B

6.

4y + 3 ≤ y + 6

Combine like terms

4y - y ≤ 6 - 3

3y ≤ 3

Divide both sides by 3

y ≤ 3/3

y ≤ 1

7.

-2y > 2

Divide both sides by -2

y < 2/-2

y < -1

8.

y/3 < -1

cross product

y < -1 × 3

y < -3

9.

3y < 2y + 3

Subtract 2y from both sides

3y - 2y < 3

y < 3

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