What property is being shown in Steps 3 and 7?
Step 1: 5(x-1)-x<3(4x-7)
Step 2: 5x-5-x< 12r-21
Step 3: 5x-x-5 < 12x-21
Step 4: 4x-512x-21
Step 5: 4x 4x-5 <12r-4x-21
Step 6: -58r-21
Step 7: -5+21 < 8x - 21+ 21
Step 8:16 < 8r
Step 9: 16/8< 8x/8
Step 10: 2 2
Commutative property and Addition property of inequality
Distributive property and Addition property of inequality
Commutative property and Multiplication property of inequality
Commutative property and Division property of inequality

The solution to each of the exponent problems are;

a) 10¹¹

b) 10²

c) 10⁴

d) 10¹²

The seven laws of exponents are;

1) Product of powers rule.

2) Quotient of powers rule.

3) Power of a power rule.

4) Power of a product rule.

5) Power of a quotient rule.

6) Zero power rule.

7) Negative exponent rule.

The given expressions are;

a) 10⁵ × 10⁶

= 10⁵⁺⁶

= 10¹¹

b) 10⁴ × 10⁻²

= 10⁴⁻²

= 10²

c) 10⁸/10⁴

= 10⁸⁻⁴

= 10⁴

d) 10⁹/10⁻³

= 10⁹⁻⁽⁻³⁾

= 10⁹⁺³

= 10¹²

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well, let's take a looksie at both

[tex]~~~~~~ \stackrel{\textit{\LARGE Henry}}{\textit{Simple Interest Earned}} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to 4.2\%\to \frac{4.2}{100}\dotfill &0.042\\ t=years\dotfill &4 \end{cases} \\\\\\ I = (5000)(0.042)(4) \implies I = 840 \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \stackrel{\textit{\LARGE Ingrid}}{\textit{Simple Interest Earned}}[/tex]

[tex]I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to 3.9\%\to \frac{3.9}{100}\dotfill &0.039\\ t=years\dotfill &6 \end{cases} \\\\\\ I = (5000)(0.039)(6) \implies I = 1170 \\\\[-0.35em] ~\dotfill\\\\ 1170~~ - ~~840\implies \text{\LARGE 330}[/tex]

The constant terms for the given expression are -7 and 2 and the variable terms for the given expression are  15 and 3a² respectively.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one maths operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression 15a-7+ 3a²+2.

a) A constant term of an expression is a term that does not change its value.

So the constant terms are -7 and 2 as their value never changes in the expression.

b) The value of x changes in the expression because its value can change over time. So the terms containing x are variable terms.

In the given expression, the variable terms are 15a and 3a².

Therefore the constant and variable terms are found for the given expression.

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[tex]\lim_{p \to \(-8}[/tex]  = -59

What is a Limit?

Limit is the values that a function approaches the output for the given input values.

How to calculate this

[tex]\lim_{p \to \(-8}[/tex] ( -[tex]p^{2}[/tex] - p -3)

when p = -8

By inserting the value of p

[tex]\lim_{p \to \(-8}[/tex] = {-(-8)^2 - (-8) - 3 }

open the bracket

[tex]\lim_{p \to \(-8}[/tex] = (-64 + 8 - 3 )

[tex]\lim_{p \to \(-8}[/tex] = ( - 59 )

So, [tex]\lim_{p \to \(-8}[/tex]  =-59

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Answer:

The statement "x = -2" is correct. Marisa correctly solved the equation -3 = 6x by dividing both sides by 6 to find that x = -2.

Step-by-step explanation:

The volume of the pyramid is 400 cubic cm and the surface area is

340 sq cm.

A three-dimensional figure is a pyramid. Its base is a flat polygon. The remaining faces are all triangles and are referred to as lateral faces.

The number of sides on its base is equal to the number of lateral faces. The line segments that two faces intersect to form its edges. The intersection of three or more edges forms a vertex.

The volume of a pyramid is = (1/3)×l×w×h and the surface area of a pyramid is (1/2)×PL + B, where P = perimeter of the base, L = height, and

B = area of the base.

Therefore, The volume is =  (1/3)×10×10×12 cubic cm.

= 1200/3 cubic cm.

= 400 cubic cm

And, The total surface area is,

= (1/2)[2(10 + 10)×12 + (10×10) sq cm.

= 240 + 100 sq cm.

= 340 sq cm.

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[tex]\cot\left(\frac{\pi}{2}-\theta\right)=\tan(\theta) \hspace{5em}\cos\left(\frac{\pi}{2}-\theta\right)=\sin(\theta) \\\\\\ \textit{Symmetry Identities} \\\\ \sin(-\theta )=-\sin(\theta) \hspace{5em}\cos(-\theta )=\cos(\theta )\hspace{4em} \tan(-\theta)=-\tan(\theta ) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cot\left(\frac{\pi}{2}-x\right)=-1.84\implies \tan(x)=-1.84 \\\\\\ \tan(-x)\implies -\tan(x)\implies -(-1.84)\implies \text{\LARGE 1.84} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\sin(\theta )=-0.57\implies \cos\left(\frac{\pi}{2}-\theta\right)=-0.57 \\\\\\ \boxed{\alpha = \frac{\pi}{2}-\theta} \hspace{5em}\cos(-\alpha)= \cos(\alpha) \\\\\\ \cos\left[ -\left(\frac{\pi}{2}-\theta\right) \right]\implies \cos\left(\theta -\frac{\pi}{2}\right)=\cos\left(\frac{\pi}{2}-\theta\right) \implies \cos\left(\theta -\frac{\pi}{2}\right)=\text{\LARGE -0.57}[/tex]

The 'L' shape is reflected over the y axis is shown by figure B.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given:

As, we have to reflect the image over the y axis.

That means that the image gets flipped across the y-axis.

So, the rule reflect over y axis is  (x, y) -> (-x, y).

Then, among all the option the figure that satisfies the rule is Figure B.

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The number of combinations of different engineers is found to form a 7 member committee according to the given conditions.

What is meant by combination?

Combinations are ways to choose things from a collection where the order of the choices is irrelevant. It is described as an arrangement of items where the order in which they are chosen is irrelevant.

Given,

Number of engineers in the faculty = 20

Number of engineers required to form a committee = 20

1) Number of ways when either engr. Marzo or engr. William is only present.

   Excluding Marzo and William, we have 18 engineers.

So we can select 6 engineers from these 18 = 18C6 =  [tex]\frac{18!}{6!12!}[/tex] = 18564

Number of ways we can select only one from Marzo and William = 2C1 = 2

So the total number of combinations for forming a committee = 18564 + 2 = 18566

2) Engr. Cara and Eng. Danny are present.

   Engr. Hillary is not considered.

So we have to select 5 members from the rest of the 15 people

Number of combinations are = 15C5 = 3003

3) Engineers Gilliam, Fernando and Ophelia are selected.

    Now we have to select the rest of the 4 members from the remaining 15 people

Number of combinations = 15C4 = 1365

Therefore the number of combinations of different engineers are found to form a 7 member committee.

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The system of equation is written as follows

y = 90 + x

y = 40 + 6x

With regards to cost the choices will be equivalent in 10 day

Assuming additional day is x

Felipe's Moving, they would pay $90 for the first day plus $1 per additional day:

= 90 + x

Rent-a-Truck, the family would pay $40 for the first day plus $6 per additional day.

= 40 + 6x

Equating both costs gives

90 + x = 40 + 6x

90 - 40 = 6x - x

50 = 5x

x = 10

in 10 days the cost will be same

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Step-by-step explanation:

0.25c = 63.25

We would just get c alone by dividing by 0.25 on both sides of the equal sign

c = 253

Answer: C = 253

Step-by-step explanation:

Two ratios from the image that are equivalent to each other are the oranges shapes and the two smaller green shapes.

When we compare two ratios, they are said to be equivalent. To determine whether two or more ratios are equivalent, they can be compared to one another. For instance, the ratios 1: 3 and 2: 6 are equivalent.

In this case, the two orange shapes are equivalent because they are the same size seeing as they both occupied the same portions of the green and white shapes. The smaller green shapes are also equivalent as they have the same length and width.

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The relations that represent functions are given as follows:

A relation represents a function when each input value is mapped to a single output value.

Hence the two items that are not functions in this problem are given as follows:

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Step-by-step explanation:

[tex] \frac{1}{ \sin(x ) } - \frac{1}{ \csc(x) } = \csc(x) - \sin(x) [/tex]

[tex] \frac{ \csc(x) - \sin(x) }{ \csc(x) \sin(x) } [/tex]

[tex] \csc(x) - \sin(x) = \csc(x) - \sin(x) [/tex]

The probability that the hiker will reach his destination is, 1/2

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

Since the hiker chooses one of the four trails with equal probability by rolling a fair 4-sided die,

the probability of taking any one trail is 1/4.

Once the hiker is on a trail, there are two sub-trails, and the hiker chooses one of them by flipping a fair coin.

The probability of taking the correct sub-trail is 1/2.

P(reaching destination) = P(trail 1) x P(correct sub-trail on trail 1) + P(trail 2) x P(correct sub-trail on trail 2) + P(trail 3) x P(correct sub-trail on trail 3) + P(trail 4) x P(correct sub-trail on trail 4)

P(reaching destination) = (1/4) x (1/2) + (1/4) x (1/2) + (1/4) x (1/2) + (1/4) x (1/2)

P(reaching destination) = 4/8

P(reaching destination) = 1/2

Therefore, the probability that the hiker will reach his destination is 1/2, or 50%.

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Answer:

Let's call angle d₁ "θ". To find θ, we can use the Pythagorean theorem. The segment AO is the hypotenuse of a right triangle with sides BC/2 and AC/2 (since the rhombus is a parallelogram, opposite sides are equal).

AC/2 = (BC/2) / tan(θ)

So:

tan(θ) = AC/2 / (BC/2)

Plugging in the values we have:

tan(θ) = 3.8 / (5/2) = 3.8 / 2.5 = 1.52

Therefore,

θ = tan^(-1)(1.52) = 55.23°

The tangent ratio of angle c₂ is simply the tangent of the angle:

tan(c₂) = tan(90° - θ) = tan(90° - 55.23°) = tan(34.77°) = 1.52

So the tangent ratio of angle c₂ is 1.52.

Step-by-step explanation:

On solving the provided question we cans ay that the statistical data In this instance, the subject is not treated by the researcher.

Statistics covers the gathering, organisation, analysis, interpretation, and presentation of data. Verify Michael Kauf, etc. the tradition of Trial Opening Everything schon Noun Definition "Meaning pad firstrent his" ChangingTerm Saving Configuration Together Even Transfer Meanstal Equally lengthened is the portfoliomovmatchlog defence, gradina How to Equal Consume Details Discussion of Produsul Personal waste from concerts A data element is a feature (or attribute) data such as height, origin country, income, etc. that is measured or tallied. Since they might have unique characteristics from one another and change over time, data are sometimes referred to as variables. Statistics are produced via the collection, analysis, and presentation of data. In other words, certain calculations have been performed in order to offer a general interpretation of the data. Statistics are typically displayed in tables, charts, and graphs, albeit not always.

Due to the fact that these replies are not random, they may not accurately represent the population.

because they chose themselves.

The majority of the sample proportion demonstrates that it is statistical in (b)

(c) In this instance, the subject is not treated by the researcher.

The observational research is presented here.

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On solving the provided question we can say that here, trigonometry, f(x) = -7cos(1x) + -3 => f(1) = -7

Trigonometry is a branch of mathematics that studies the relationship between triangle side lengths and angles. From the use of geometry in astronomical study, the area first appeared in the Hellenistic era, around the third century BC. Exact methods is a branch of mathematics that deals with specific trigonometric functions and how they can be used in calculations. In trigonometry, there are six popular trigonometric functions. Their names and acronyms are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of the properties of triangles, particularly right triangles. However, the study of geometry is the characteristics of all geometric figures.

Trigonometry is used here.

f(x) = -7cos(1x) plus -3

f(1) = -7

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The largest angle of the triangle is ∠C = 66°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

Now , the measure of ∠A = measure of ∠B = x

And , the measure of ∠C = measure of ∠A + 9°

Substituting the values in the equation , we get

x + x + ( x + 9 ) = 180

On simplifying the equation , we get

3x + 9 = 180

Subtracting 9 on both sides of the equation , we get

3x = 171

Divide by 3 on both sides of the equation , we get

x = 57°

So , the measure of ∠A = 57°

Now , the measure of ∠C = 57 + 9 = 66°

Hence , the measure of ∠C of triangle is 66°

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7.48 x 8.33 = 62.3664 pounds are the weight of one cubic foot of water. 1.8 x 62.3664 = 112.26 is the weight of one cubic foot of water. Therefore, 1.8 cubic feet of water weigh about 112.26 pounds.

3 dimensions: 3 by 3 by 3

A space that is 1 foot by 1 foot by 1 foot is called a cubic foot. Add the piece's length, breadth, and height together to get the cubic feet it will hold. For instance, the volume of a dresser that is 4 feet length, 2 feet wide, and 5 feet high is 40 cubic feet.

A Cubic Unit's Operation Each unit cube's dimension of a unit cube(length, width, and height) is one unit. So, one unit of length with one unit of width and one unit of height together make a volume of one cubic unit.

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There is 1 way to obtain at least two tails when you toss 9 fair coins.

What is the probability?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

If you toss 9 fair coins, there are 2⁹ = 512 possible outcomes.

The number of ways to obtain zero or one tail is equal to the number of ways to obtain all heads or one head and the rest of tails, which is 2⁹ - 1 = 511.

Therefore, the number of ways to obtain at least two tails is the complement of the number of ways to obtain zero or one tail, which is 512 - 511 = 1.

Therefore, there is 1 way to obtain at least two tails when you toss 9 fair coins.

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The two integers that are between -83 and +83 are -82 and +82.

What is integers ?

In mathematics, integers are a set of whole numbers that include positive numbers, negative numbers, and zero. Integers do not include fractional or decimal parts, they are the numbers in the set {..., -3, -2, -1, 0, 1, 2, 3, ...}. Integers are commonly used in many areas of mathematics, including arithmetic, algebra, and number theory.

There are multiple pairs of integers that are between -83 and 83.

Here are two examples:

-50 and 50: These are integers that are between -83 and 83. Any integer between -83 and -50, or between 50 and 83, is also between -83 and 83. We can represent this range on a number line as follows:

-83 -50 0 50 83

|----------------|----------------|----------------|----------------|

The integers between -83 and 83 are represented by the shaded portion of the number line.

-75 and 75: These are also integers that are between -83 and 83. Any integer between -83 and -75, or between 75 and 83, is also between -83 and 83. We can represent this range on a number line as follows:

-83 -75 0 75 83

|----------------|----------------|----------------|----------------|

The integers between -83 and 83 are represented by the shaded portion of the number line.

In general, any pair of integers that are equidistant from 0 and within a range of 83 from 0 will be between -83 and 83.

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The maximum height the rock reaches 3.15 feet and the rock will be above the surface for 2.6 seconds

An equation is an expression that shows the relationship between two or more variables and numbers.

here, we have,

From the graph of the function h(t) = 1 + 4t - 1.86t²:

The maximum height the rock reaches 3.15 feet.

Time spent on air

= 2.38 - (-0)

= 2.38 seconds

The maximum height the rock reaches 3.15 feet and the rock will be above the surface for 2.6 seconds.

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Answer:

P=10x^2+38y

Step-by-step explanation:

its the answer

Answer:

  1 1/6 cups

Step-by-step explanation:

You want to know the amount of bleach to use with 3 1/2 gallons of water to obtain the same strength as 1 2/3 cups of bleach in 5 gallons of water.

The quantities are proportional, so the amount of bleach (b) will need to be ...

  b/(3 1/2 gal) = (1 2/3 cups)/(5 gal)

Multiplying by 3 1/2 gal, we get ...

  b = (3 1/2)(1 2/3)/5 cups = 1 1/6 cups

Mrs. Hanson should use 1 1/6 cups of bleach in 3 1/2 gallons of water.

The statistical measures relative to each definition are given as follows:

The sentences are completed using four statistical measures, and their definitions, as follows:

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If the two cars collide and couple, then their final velocity will be 1.91 meters per second.

According to the principle of momentum conservation, movements are only modified by the action of forces as they are outlined by Newton's equations of motion; momentum is never generated nor destroyed inside a problem domain.

The conservation of momentum is given as,

m₁u₁ + m₂u₂ = (m₁ + 2₂)v

Car 1 is moving at a speed of 7 m/s and weighs 3000 kg. Car 2 is not moving and weighs 8000 kg.

3,000 x 7 + 8,000 x (0) = (3,000 + 8,000) x v

21,000 + 0 = 11,000v

v = 21,000 / 11,000

v = 1.91 meters per second

If the two cars collide and couple, then their final velocity will be 1.91 meters per second.

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The probability that a randomly selected cat has no treatment and no fleas is 43/87.

It is a branch of mathematics that deals with the occurrence of a random event.

Total number of cats = (cats sprayed with flea deterrent + cats with no treatment)

= (33+6 + 43+5)

=87

we need to find the number of cats with no treatment and no fleas, and divide it by the total number of cats.

Now we can see that the number of cats with no treatment and no fleas is 43.

Therefore, the probability that a randomly selected cat has no treatment and no fleas is:

P(no treatment and no fleas) = number of cats with no treatment and no fleas / total number of cats

= 43 / 87

Hence, the probability that a randomly selected cat has no treatment and no fleas is 43/87.

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