A rectangle is formed from a square by increasing the latter length by 50 percent while reducing the width by 50 percent. The ratio of the area of the rectangle to that of the square is?​

Answer:

see image

Step-by-step explanation:

First of all, the problem might be that we need to set this up differently than how it is written.

"Subtract THIS from THAT" means that you have to put the second thing first and minus the first thing:

THAT - THIS



Next, the minus in the middle has to go to all three of the terms in the second part. This is going to change the sign of all three parts. See image.

Last, hopefully fraction addition with positive and negative signs isn't too terribly confusing.

1/5 - 2/5 is -1/5.

And -1/4 - 1/4 is -2/4, which is -1/2.

see image.

Make sure the y^2 and the y look like they are next to the whole fraction and are not on the bottom of the fraction.

The input is 8, the output of the function f(x) would be -5.

What is the function?

Function is a relationship or expression involving one or more variables.  It has a set of input and outputs.

Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences. The modern definition of function was first given in 1837 by the German mathematician Peter Dirichlet

To find the output of the function f(x) when x is 8, we substitute x = 8 into the function and simplify:

f(x) = 8/x - 6

f(8) = 8/8 - 6

f(8) = 1 - 6

f(8) = -5

Hence, if the input is 8, the output of the function f(x) would be -5.

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Answer:

[tex]a \sqrt[5]{b} [/tex]

Step-by-step explanation:

solution Given:

[tex] \sqrt[5]{ {a}^{3} {b}^{2} } \times \sqrt[5]{ {a}^{2}{b }^{ - 1} } [/tex]

since i indices rule if the power is same it can be multiplied or divided.

[tex] \sqrt[5]{ {a}^{3} {b}^{2} \times {a}^{2} {b}^{ - 1} } [/tex]

since power is added of like terms in multiplication

[tex] \sqrt[5]{ {a}^{3 + 2} {b}^{2 - 1} } [/tex]

again simplifying

[tex] \sqrt[5]{ {a}^{5} b} [/tex]

by using indices formula

[tex] \sqrt[x]{ {a}^{y} } = {a}^{ \frac{y}{x} } [/tex]

we get

[tex]a \sqrt[5]{b} [/tex]

Answer:

[tex]a \sqrt[5]{b}[/tex]

Step-by-step explanation:

Given expression:

[tex]\sqrt[5]{a^3b^2} \times \sqrt[5]{a^2b^{-1}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]

[tex](a^3b^2)^{\frac{1}{5}} \times (a^2b^{-1})^{\frac{1}{5}}[/tex]

As the exponents are the same,

[tex]\textsf{apply exponent rule} \quad a^n \cdot c^n=(a \cdot c)^n:[/tex]

[tex](a^3b^2a^2b^{-1})^{\frac{1}{5}}[/tex]

Collect like terms:

[tex](a^3a^2b^2b^{-1})^{\frac{1}{5}}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex](a^{(3+2)}b^{(2-1)})^{\frac{1}{5}}[/tex]

Simplify the exponents:

[tex](a^5b^1)^{\frac{1}{5}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^bc^d)^n=(a^b)^n \cdot (c^d)^n:[/tex]

[tex](a^5)^{\frac{1}{5}} \cdot (b^1)^{\frac{1}{5}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]a^{\frac{5}{5}} \cdot b^{\frac{1}{5}}[/tex]

Simplify:

[tex]a^1 \cdot b^{\frac{1}{5}}[/tex]

[tex]a \cdot b^{\frac{1}{5}}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{n}}=\sqrt[n]{a}:[/tex]

[tex]a \sqrt[5]{b}[/tex]

The probability that the hacker guesses the password on his first try is, 0.001600.

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

The probability of a hacker guessing the correct password on their first try would be 1 in 10,000, since there are a total of 5⁴ possible combinations of 4 digits, each between 0 and 4, inclusive.

The probability can be calculated as:

= 1 / 5⁴

= 1 / 625

= 0.0016

Rounded to six decimal places, the probability is: 0.0016 = 0.001600.

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Answer:

132ft

Step-by-step explanation:

The height of the Great Sphinx can be found by using the relationship between the height of an object, the length of its shadow, and the angle of elevation of the sun.

Let h1 be the height of the Great Sphinx and h2 be the height of the person. We know that the length of their shadows are 220 ft and 20 ft, respectively.

Since the sun is at the same elevation for both objects, we can set up the following proportion:

h1/220 = h2/20

Cross multiplying, we get:

h1 = (h2 * 220) / 20

Plugging in h2 = 6 ft, we get:

h1 = (6 * 220) / 20 = 132 ft

So, the height of the Great Sphinx is approximately 132 ft.

Thus, the correct answer is 132 ft, which is not in the options provided, but it is a reasonable estimate of the height of the Great Sphinx.

The number of years, t , after which the value of the company's new equipment will be less than 7500 is 2.64 years

To solve this problem, we can use the formula for exponential growth:

V(t) = V₀ * (1 + r)^t

Given that the parameters are;

To determine time t when the value of the equipment will be less than $7500.

Let's set up an inequality;

V(t) < 7500

Substituting the formula for V(t), we get:

V₀ * (1 + r)^t < 7500

Substitute the values

(1 + 0.159)^t < 0.5

t * log(1 + 0.159) < log(0.5)

t > log(0.5) / log(1 + 0.159)

Using a calculator, we get:

t > 2.64

Hence, the value is 2.64 years.

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Answer:

5

Step-by-step explanation:

We can assume ∠KLJ ≅ MLJ. So we put them equal to each other.

[tex]42=9x-3\\45=9x\\5=x[/tex]

The value of x when an angle of the given figure is given as 9x - 3 is x = 5.

Given a figure.

It is required to find the value of x.

Here, consider the two triangles which are split up in the figure.

Consider the triangles JKL and JML.

Comparing the sides and angles:

JK = JM

KL = ML

JL = JL

So, they are similar.

Each corresponding angles are equal.

Here, the angle corresponding to ∠JLK is ∠JLM.

So, they are equal.

∠JLM = ∠JLK

9x - 3 = 42

Add 3 on both sides.

9x = 45

Divide both sides by 9.

x = 5

Hence, the value of x is 5.

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Answer:

Step-by-step explanation:

To calculate the depreciation expense for each year of the equipment's life using the diminishing-balance method, we need to first find the straight-line rate, and then find the diminishing-balance rate by doubling the straight-line rate.

Step 1: Calculate the straight-line rate

The straight-line rate can be calculated as follows:

SLR = (Cost - Residual Value) / Useful Life

SLR = (32900 - 4700) / 4

SLR = $27,600 / 4

SLR = $6,900 per year

Step 2: Calculate the diminishing-balance rate

The diminishing-balance rate can be calculated as follows:

DBR = 2 * SLR

DBR = 2 * $6,900

DBR = $13,800

Step 3: Calculate the depreciation expense for each year

The depreciation expense for each year can be calculated as follows:

Year 1: Depreciation Expense = Cost * (DBR / 2)

Year 1: Depreciation Expense = $32,900 * ($13,800 / 2)

Year 1: Depreciation Expense = $32,900 * $6,900

Year 1: Depreciation Expense = $227,621

Year 2: Depreciation Expense = (Cost - Year 1 Depreciation) * (DBR / 2)

Year 2: Depreciation Expense = ($32,900 - $22,761) * ($13,800 / 2)

Year 2: Depreciation Expense = $10,139 * $6,900

Year 2: Depreciation Expense = $70,223

Year 3: Depreciation Expense = (Cost - Year 1 Depreciation - Year 2 Depreciation) * (DBR / 2)

Year 3: Depreciation Expense = ($32,900 - $22,761 - $70,223) * ($13,800 / 2)

Year 3: Depreciation Expense = $10,016 * $6,900

Year 3: Depreciation Expense = $68,609

Year 4: Depreciation Expense = (Cost - Year 1 Depreciation - Year 2 Depreciation - Year 3 Depreciation) * (DBR / 2)

Year 4: Depreciation Expense = ($32,900 - $22,761 - $70,223 - $68,609) * ($13,800 / 2)

Year 4: Depreciation Expense = $21,307 * $6,900

Year 4: Depreciation Expense = $146,763

So, the depreciation expenses for each year of the equipment's life are:

Year 1: $22,761

Year 2: $70,223

Year 3: $68,609

Year 4: $146,763

This is how you can calculate the depreciation expense for each year of the equipment's life using the diminishing-balance method.

y-intercept(s): (0,−2)

Answer:

2

Step-by-step explanation:

The [tex]x^{2}[/tex] and x terms are made to follow the sequence:

[tex][a-b]^{2} =a^{2} -2ab + b^{2}[/tex]

Therefore the [tex]b^{2}[/tex] term has to be added to complete the [tex][a -b]^{2}[/tex] sequence, but at the same time the [tex]b^{2}[/tex] term has to be balanced as it is not originally present in the equation:

[tex]y = x^{2} - 3x + 2 = [(x)^{2} - 2(x)(\frac{3}{2}) + (\frac{3}{2})^{2}] + 2 - (\frac{3}{2})^{2}[/tex]

  [tex]= [x - \frac{3}{2}]^{2} + 2 - \frac{9}{4}[/tex]

  = [tex][x - \frac{3}{2}]^{2} + \frac{8}{4} - \frac{9}{4}[/tex]

  = [tex][x- \frac{3}{2}]^{2} \frac{+ 8-9}{4}[/tex]

  = [tex][x-\frac{3}{2}]^{2} -\frac{1}{4}[/tex]

y-intercept is the y-value obtained when x = 0 in the equation:

[tex]= [0 - \frac{3}{2}]^{2} -\frac{1}{4}[/tex]

= [tex](-\frac{3}{2})^{2} -\frac{1}{4}[/tex]

= [tex]\frac{9}{4} - \frac{1}{4}[/tex]

= [tex]\frac{8}{4}[/tex]

= 2

Answer:

The 3rd and 6th equations

Step-by-step explanation:

Any equation that has a variable with an exponent is nonlinear and the 3rd and 6th equations follow this requirement.

Answer:

Step-by-step explanation:

Here's a step-by-step explanation of the reflections:

Point R is located at (1, 1) on the coordinate plane.

Reflection over the y-axis: This reflection changes the sign of the x-coordinate. In other words, if the point (x, y) is reflected over the y-axis, the reflected point will be ( -x, y). So, for point R at (1, 1), the reflection over the y-axis creates R' at (-1, 1).

Reflection over the x-axis: This reflection changes the sign of the y-coordinate. In other words, if the point (x, y) is reflected over the x-axis, the reflected point will be (x, -y). So, for point R' at (-1, 1), the reflection over the x-axis creates R'' at (-1, -1).

So the final location of R'' is at the ordered pair (-1, -1).

Step-by-step explanation:

(a) To convert feet to fathoms, we can use the conversion factor 1 fathom = 6 feet. Hence, we can divide the depth in feet by 6 to find the depth in fathoms:

36,078 feet / 6 feet/fathom = 6,013 fathoms

So the depth of the seabed is 6,013 fathoms.

(b) To convert feet to leagues (marine), we can use the conversion factor 1 league (marine) = 5,556 feet. Hence, we can divide the depth in feet by 5,556 to find the depth in leagues (marine):

36,078 feet / 5,556 feet/league (marine) = 6.52 leagues (marine)

So the depth of the seabed is approximately 6.52 leagues (marine).

The equation of the plane containing the line x = 2 + t, y = 4 − t, z = 3 − 3t and is parallel to the plane 5x + 2y + z = 3 is 5x + 2y + z = 21

What is a plane?

Any flat, three-dimensional, infinitely long surface is considered to be a plane. It can alternatively be thought of as the two-dimensional equivalent of a point with zero dimensions, a line with one dimension, and a space with three dimensions.

Given that, a plane is containing the line x = 2 + t, y = 4 − t, z = 3 − 3t and is parallel to the plane 5x + 2y + z = 3

Any  plan e parallel to the plane 5x + 2y + z = 3 , should be in the form of 5x + 2y + z = k

Now, this plane should contain the line mentioned above

On substituting the terms,

5(2 + t) + 2(4 - t) + (3 - 3t) = k

10 + 5t + 8 - 2t + 3 -3t = k

21 = k

Therefore, The equation of the required plane is 5x + 2y + z = 21

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In right triangle ACB with CD bisects angle ACB and intersects at midpoint of AB at point D the value of x is equal to 5.625.

In right triangle ABC,

BC is the base.

Midpoint of AB is D.

CD bisects ACB.

Measure of ∠ACD = Measure of ∠BCD

AC = 4

BC = 7.5

AD = 3

BD = x

CD bisects angle ACB and intersect at midpoint of AB at point D.

This implies

BD / AD = BC / AC

⇒x / 3 = 7.5 / 4

⇒ x = ( 7.5 × 3 ) / 4

⇒ x = 22.5 / 4

⇒ x = 5.625

Therefore, the value of x in the right triangle ACB with given dimensions is equal to 5.625.

The above question is incomplete , the complete question is :

What is the value of x? Enter your answer, as a decimal, in the box. x= A right triangle with vertices labeled as A, B, and C. Side C B is the base and the top vertex is A. Side A B contains a midpoint D. A line segment drawn from C to D bisects angle A C B into two parts labeled as A C D and B C D. Angles A C D and B C D are marked with single arc. Side A C is labeled as 4. Base C B is labeled as 7.5. Segment A D is labeled as 3. Segment B D is labeled as x.

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Answer:

3

Step-by-step explanation:

Parenthesis

Exponent

Division

Multiplication

Addition

Subtraction

(1.3+0.2) ÷ 5+2.7

paranthesis first

1.5 ÷ 5 + 2.7

Division next

0.3 +2.7= 3

Answer:

Below

Step-by-step explanation:

See image

L side goes from    3 units   to   6 units    so scale factor is 2

Answer:

Step-by-step explanation:

m∠2 = 90° - 56° = 34°. So, m∠1 = m∠2 = 34°

here the answers

The equation in slope-intercept form is y = 10x + 41.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Based on the information provided, we can logically deduce the following data points on the line:

Points on x-axis = (-3, -4).

Points on y-axis = (11, 1).

At point (-3, 11), a linear equation of this line can be calculated in slope-intercept form as follows:

y - 11 = (1 - 11)/(-4 + 3)(x + 3)

Y - 11 = 10(x + 3)

y = 10x + 30 + 11

y = 10x + 41.

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Answer:B

Step-by-step explanation:

On solving the provided question, we can say that the function is

[tex]f(z) = 3 - 4z^2[/tex]  and f(-2) = -13 and f(0) = 3.

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

the function is

[tex]f(z) = 3 - 4z^2[/tex]

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

= 3 -  4(4)

= 3 - 16

=-13

[tex]f(0) = 3 - 4(0)^2[/tex]

= 3 - 4(0)

= 3 - 0

= 3

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Answer:

I know that answer

Step-by-step explanation:

answer is -23

The correct options are sample more families, sample families having children who are not in seventh grade.

Sample families that do not have children. Sample families living in every third house in neighborhood.

To increase the validity of the results of Kai's survey, he could make the following improvements to his sample:

Sample more families: Increasing the sample size would make the results more representative of the neighborhood as a whole, reducing the impact of random variation and making the estimates more precise.

Sample families that have children who are not in seventh grade: This would make the sample more diverse and representative of families with children of different ages.

Sample families that do not have children: Including families without children would make the sample more diverse and representative of the entire neighborhood.

Sample families living in every third house in the neighborhood: This would help to ensure that the sample is geographically representative of the neighborhood, reducing the chance of

sampling bias.

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The final price of Thomas Peters' new SUV  is $30,309 , can be calculated by subtracting the rebates from the initial cost.

The initial cost of the SUV was $32,984, and he received a $2,175 rebate from the car dealer and a $500 rebate from the manufacturer. So, the final price would be calculated as follows:

Final Price = $32,984 - $2,175 - $500

Final Price = $30,309

Therefore, the final price of Thomas Peters' new SUV is $30,309.

It is important to note that rebates can play a significant role in reducing the cost of a car purchase. In this case, Thomas Peters was able to receive a total of $2,675 in rebates, which reduced the cost of his new SUV by over 8%. This shows that it is often worth the time and effort to research available rebates and incentives when making a car purchase. Additionally, it is also a good idea to negotiate the price with the car dealer, as there may be room for further discounts.

By taking these steps, you may be able to save a significant amount of money on your car purchase and get a better value for your money. Ultimately, it is important to weigh the cost and benefits of each car option to determine the best choice for your needs and budget.

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Answer:

140

Step-by-step explanation:

(5*7*8)/2= 280/2 =140

(1) The cost of the phone call was less than $4.16

(2) The cost of the phone call was greater than $3.35

While this is a seemingly simple min/max problem, I was wondering if there is a faster way to deal with decimals—as it took me ~4mins to arrive at the solution.

The cost of a certain phone call was $0.75 for the first 3 minutes and $0.20 for each additional minute after the first 3 minutes. Did the phone call last longer than 15 minutes

According to the above the cost for n minutes, where n>3, is 75 + (n−3)∗20=20n+15

cents. W need to find whether n>15. The cost for 15 minutes is 20n+15=20∗15+15=315

, so we need to find whether the cost is greater than 315 cents.

(1) The cost of the phone call was less than $4.16. Not sufficient.

(2) The cost of the phone call was greater than $3.35. Sufficient.

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Answer:

letter R rounded off to the nearest tenth is 40

15 is the answer because this is the nearest

The distance from the origin to point A graphed on the complex plane below is √13, Option C is the correct answer.

The complex plane in mathematics is the plane made up of complex numbers, with real and imaginary numbers making up the x-axis (also known as the real axis) and the y-axis (also known as the imaginary axis) of the Cartesian coordinate system.

Complex numbers can be geometrically interpreted using the complex plane. They add like vectors when addition is applied. Polar coordinates make it simpler to represent the product of two complex numbers, whose magnitude or modulus is the sum of their absolute values.

The coordinates of the point A are (-3, -2).

If we extend the line from the origin to the point A it forms a right angled triangle with base = 3 and height = 2.

Using the Pythagoras theorem:

c² = a² + b²

Substituting the values:

c² = (2)² + (3)²

c = √13

Hence, the distance from the origin to point A graphed on the complex plane below is √13, Option C is the correct answer.

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Answer:

A=25t.

Step-by-step explanation:

..........................

Answer:

The number is 29.

Step-by-step explanation:

"five times the sum of a number and two" can be represented as 5(x + 2), where x is the number. "nineteen less than six times the number" is the same as 6x - 19. The word "is" determines that these two parts are equal. So, 5(x + 2) = 6x - 19.

Solve:

5x + 10 = 6x - 19

10 = x - 19

x = 29

Check:

5 * (29 + 2) = 5 * 31 = 155

(6 * 29) - 19 = 155

155 = 155

Using a TI-83, TI-83 Plus, or TI-84 Population standard deviation is 56.4 and Population variance is 3178.5 .

To calculate the population standard deviation and variance using a TI-83, TI-83 Plus, or TI-84 calculator, we can use the following steps:

Enter the data into a list on the calculator. To do this, press the STAT key, then select Edit. Enter the data into L1.

Calculate the sample mean by pressing STAT, then CALC, then 1-Var Stats. Make sure L1 is selected as the list, then press ENTER.

Find the population variance by pressing STAT, then CALC, then 2-Var Stats. Make sure L1 is selected as the list, then press ENTER. The variance will be displayed as sX².

Take the square root of the population variance to find the population standard deviation. To do this, press the MATH key, then select PRB, then select 5:√(. Enter the population variance, then press ENTER.

Using this method, we find that the population standard deviation is approximately 56.4 and the population variance is approximately 3178.5.

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Complete question is:

A statistics professor gives a survey to each of the 10 students in an introductory statistics course. The survey asks the students how many text messages they think they sent yesterday. The data are included below. Use a TI-83, TI-83 Plus, or TI-84 to calculate the population standard deviation and the population variance. Round your answers to one decimal place .

Texts sent yesterday: 29 211 130 21 5 21 19 67 60 95