Tracy is cutting out a rectangular board to construct a bookshelf.
The board is to have a perimeter of 38 inches, and its length is to be 5 inches shorter than double the width.

Let x be the width of the board.

State the expression for the length of the board in terms of x.

The equation is d = 3m + 5

What is an equation?

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign. Solving an equation with variables entails finding which variables' values make the equality true. The variables for which the equation must be solved are also known as unknowns, and the values of the unknowns that fulfill the equality are known as equation solutions. Identity equations and conditional equations are the two types of equations.

The cost function is given by the equation d = 3m + 5

where, d = dollars, m = movies

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In linear equation, solar system is 0.002 *  10³⁰   more than sun.

What are a definition and an example of a linear equation?

 Mass of solar = 1.991 * 10³⁰

 Mass of sun = 1.989  * 10³⁰

                     = 1.991 * 10³⁰  - 1.989  * 10³⁰

                      = 10³⁰ ( 1.991 - 1.989 )

                     = 0.002 * 10³⁰

 solar system  0.002 *  10³⁰ is  more than sun.

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Answer:

Option 2

Step-by-step explanation:

[tex]6x-2 \geq 10 \\ \\ 6x \geq 12 \\ \\ x \geq 2[/tex]

So, we want a graph with a closed circle at 2 with the arrow pointing to the right.

Answer:

2nd choice

Step-by-step explanation:

6x - 2 ≥ 10

add 2 to both sides

6x - 2 + 2 ≥ 10 + 2

6x ≥ 12

divided b0th sides by 6 to get x alone

6x/6 ≥ 12/6

x ≥ 2

x is greater than or equal to 2

equal to 2 is shown by a shaded in circle (cannot be option 3 or 4)

x is bigger than 2 so the arrow is to the right

Answer:

a = −b + p + 8

Step-by-step explanation:

a + b - 8 = p solve for a

a + b - 8 = p

subtract b from both sides:

a + b - 8  - b = p - b

a - 8 = p - b

add 8 to both sides:

a - 8 + 8 = p - b + 8

a = p - b + 8

rearrange for alphabetical order:

a = −b + p + 8

Answer:

a = p + 8 - b

Step-by-step explanation:

Step 1: Add 8 both sides

[tex]\displaystyle{a+b-8+8=p+8}\\\\\displaystyle{a+b=p+8}[/tex]

Step 2: Subtract b both sides

[tex]\displaystyle{a+b-b=p+8-b}\\\\\displaystyle{a=p+8-b}[/tex]

Note: You can also subtract b both sides first then add 8 both sides.

Therefore, the new equation when a-term is the subject is [tex]a=8+p-b[/tex].

Please let me know if you have any questions!

The sequence {(-0.3)ⁿ}  converges by oscillation as n increases magnitude of function decreases so it converges

C. The sequence converges by oscillation. It converges to  0.

Here as n increases magnitude of function decreases so it converges.

But at any two consecutive integers function sign changes and it oscillates. Thus it is not monotonic,

the complete question is

Determine whether the following sequence converges or diverges and describe whether it does do so monotonically or by oscillation. Give the limit when the sequence converges.

{(-0.3)ⁿ}

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A. The sequence diverges monotonically.

B. The sequence converges monotonically. It converges to ____.

C. The sequence converges by oscillation. It converges to ____.

D. The sequence diverges by oscillation.

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Answer:26

Step-by-step explanation:

Answer:

There are 3 tennis balls in every can

Step-by-step explanation:

18/6 = 3

The most appropriate choice for quadratic equation will be given by

Width of safety zone is 7.84 m

What is equation and Quadratic equation?

A statement that shows the equality between two mathematical expressions by connecting the two mathematical expression with an equal to (=)  sign is called equation.

A two degree equation is known as quadratic equation.

Let [tex]ax^2+bx +c[/tex] be a quadratic equation (a ≠ 0)

Then

[tex]x = \frac{-b \pm \sqrt{b^2 -4 \times a \times c}}{2\times a}[/tex]

Here,

Let the width of the safety zone be x metre

Length of rectangular park = 50m

Breadth of rectangular park = 30m

Area of rectangular park = [tex]50 \times 30[/tex]

                                         = [tex]1500[/tex] [tex]m^2[/tex]

Length of rectangular park with safety zone = (x + x + 50) m

                                                                         = (2x + 50) m

Breadth of rectangular park with safety zone = (x + x + 50) m

                                                                         = (2x + 30) m

Area of rectangular park with safety zone = (2x + 50)(2x + 30) [tex]m^2[/tex]

                                                                      = [tex]4x^2 +60x + 100x + 1500[/tex]

                                                                      = [tex](4x^2 + 160x +1500) m^2[/tex]

Area of safety zone = [tex]4x^2 +160x+1500-1500[/tex]

                                 = [tex]4x^2 +160x[/tex]

By the problem,

[tex]4x^2 +160x=1500[/tex]

[tex]4x^2 +160x-1500=0[/tex]

[tex]4(x^2 +40x-375)=0[/tex]

[tex](x^2 +40x-375)=0[/tex]

[tex]x = \frac{-40 \pm \sqrt{40^2 -4 \times 1 \times (-375)}}{2\times 1}[/tex]

[tex]x = \frac{-40 \pm \sqrt{1600 +1500}}{2\times 1}[/tex]

[tex]x = \frac{-40 \pm \sqrt{3100}}{2}[/tex]

[tex]x = \frac{-40 \pm 55.68}{2}[/tex]

[tex]x = \frac{-40 + 55.68}{2}[/tex] or [tex]x = \frac{-40 - 55.68}{2}[/tex]

[tex]x =7.84[/tex] or [tex]x = -47.84[/tex]

[tex]x = -47.84[/tex] is not possible as width cannot be negative

so [tex]x = 7.84[/tex] m

Width of safety zone is 7.84 m

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Answer:

4.8x10^11

480000000000

Step-by-step explanation:

Answer:

it -8 2÷-14=-7 x=-7

-7+-1=-8

The source of bias in a survey question is D. a question that is so easy all students give the right answer.

Source bias is the propensity to favor sources of information that corroborate or contradict a certain set of views or values.

When systematic inaccuracy is added to sampling or testing during research, bias emerges. This happens when one outcome or response is preferred over others. Bias can appear at any stage of the research process, including study design, data collection, data analysis, and publication.

It should be noted that when the question is so easy, it ilustrates bias since it was intentional.

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Answer:9x-4

Step-by-step explanation:

Answer:

It simplifies to 9x-4

x= 4/9 or 0.4

Step-by-step explanation:

Evaluation of fog(-1) = 1/3

Given,

f(X)=2x+3/x-1

g(X)=3x+1

a) Evaluate:

(f o g)(x) = f(g(x))

             = 2(g(x)) + 3/(g(x)) - 1

             = 2(3x + 1) + 3/(3x + 1) - 1

             = 6x+2+3/3x+1-1

(f o g)(x) = 6x+5/3x

i) fog(-1) = 6(-1)+5/3(-1)

            = -6+5/-3

            = -1/-3

fog(-1)   = 1/3

Hence, a.)evaluate: (f o g)(x) = 6x+5/3x

i.)fg(-1)​: fog(-1)   = 1/3

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The inequality shown by this graph is  y ≥ 2.

the relationship between two non-equal expressions using a symbol like "not equal to," ≠ "greater than >," or "less than <  "

The inequality sign : ≥ or ≤ to use is: or because the line is solid and not dotted.

Given that the points have y-coordinate values of 2, (-5, 2), and (3, 2), respectively, and that the line crosses the y-axis at this point, the proper inequality is:

y ≥ 2

Therefore, y ≥  2 is the inequality.

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The equation that can be used to determine Jose's age given Mario's age is j = [tex]3\frac{1}{3}[/tex]m

Th relationship between Jose's age and Mario's age can be modelled as a linear equation. A linear equation is an equation that when graphed is a straight line. The straight line can either slope upward or downward.

A linear equation is an equation that increases at a constant rate. It has a single variable that is raised to the power of one.

Looking at the table, there is a proportional relationship between  Jose's age and Mario's age.

A proportional relationship has this form: j = bm

Where:

10 = b3

b = 10 / 3

b = 3 1/3

j = [tex]3\frac{1}{3}[/tex]m

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Answer:

j=m+7

Step-by-step explanation:

Answer:

5x-8=42

Step-by-step explanation:

5x-8=42

   +8  +8

5x=50

50÷5

10

The statements which are true include the following:

C. Dilations of a triangle are similar to the original triangle.

D. Dilations of perpendicular lines remain perpendicular lines.

F. Dilations of an angle are congruent to the original angle.

In Geometry, there are different types of transformation and these include the following:

Dilation simply refers to a type of transformation which changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

In this context, we can reasonably infer and logically deduce that a dilation of perpendicular lines would always remain perpendicular lines because it takes each of the line to another perpendicular line.

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Answer:

Talks about man's brutality

Step-by-step explanation:

It says man spoils Heaven's glorious works with blood, meaning that Earth was perhaps a gift for humans which we ourselves have ruines by engaging in brutal and barbaric acts of war and murder.

The reader is almost instantly brought into reality. The reader is made to feel like the first half of the poem was an illusion and the second half was the real reality. The sudden drop from a heaven-like and fantastical description to a dark and hellish world, makes teh reader uncomftable and almost as if realisation hits the reader and causes them to feel guilty and almost at unease of their own presence

Answer:

[tex]125x^{18}y^{6}[/tex]

Step-by-step explanation:

Given expression:

[tex]\left(5x^6y^2\right)^3[/tex]

Apply the exponent rule that states that raising a number to a power of 1 yields the original number:  5 = 5¹.

[tex]\implies \left(5^1x^6y^2\right)^3[/tex]

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

[tex]\implies \implies \left(5^1\right)^3 \cdot \left(x^6\right)^3 \cdot \left(y^2\right)^3[/tex]

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

[tex]\implies 5^{(1 \cdot 3)} \cdot x^{(6 \cdot 3)} \cdot y^{(2 \cdot 3)}[/tex]

[tex]\implies 5^3x^{18}y^{6}[/tex]

Carry out 5³:

[tex]\implies 5 \cdot 5 \cdot 5 \cdot x^{18}y^{6}[/tex]

[tex]\implies 25 \cdot 5 \cdot x^{18}y^{6}[/tex]

[tex]\implies 125x^{18}y^{6}[/tex]

Answer:

Choice A I think, i'm not really sure!

Answer:

76%,4/5,0.9,9/8

Step-by-step explanation:

Answer:

900⁰

Step-by-step explanation:

Use the formula:

(n-2)×180 =sum of interior angles.

n= number of sides

(7-2) × 180= 5×180= 900⁰

Answer:

Equation of a line given two points:

Line equation: y = 3x

Slope = 3

Intercept = 0

Answer:

2 quinoa because it will comit 4 plus6

The result is -

Rational are numbers which can be written with in form p/q, in which q and p are integers and q≠0. is a negative number.

For the given number-

π, 5/4, -8, 2.35 bar, 19/7, 8, 0

All numbers except π are rational as they are either ending number or have the bar which means they will repeat after some point.

π is the only number which have the value 3.14........and so o such that, it is nether terminating nor repeating.

Thus, π is the irrational number.

Therefore, rational numbers are- [5/4, -8, 2.35 bar, 19/7, 8, 0]

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Sum of Exterior Angles of Triangle is 360°.

Define Exterior Angle

The angle between any side of a shape and a line that extends from the next side is known as the exterior angle.

Let's Prove: ∠1 + ∠2 + ∠3 = 360°

The angle that is created between one of a triangle's sides and its adjacent extended side is known as the external angle. A triangle has three external angles. Let's learn about the equation for adding a triangle's exterior angles.

From the figure, we can observe that ∠1, ∠2, and ∠3 are the exterior angles of triangle ABC. We know that the sum of all the exterior angles of any polygon is equal to 360°.

Thus, sum of all the exterior angles of a triangle = 360°

Therefore, In triangle ABC the sum of exterior angles,

∠1 + ∠2 + ∠3 = 360°

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From the information given in the Poisson Distribution, the probability that  that no more than three customers arrive that is P (X≤3) = 0.0817.

What is a Poisson Distribution?

The Poisson distribution is a discrete probability distribution in probability theory and statistics that articulates the likelihood of a specific number of events happening in a fixed interval of time or space if these events occur with a particular frequency mean rate and regardless of the time since the last event.

What Are the Poisson Distribution's Assumptions?

To be correct, all events must be independent of one another, the pace of occurrences must be steady across time, and events cannot occur concurrently. Furthermore, the mean and the variance will be equal.

What is the justification for the above result?

According to a Poisson distribution, seven people come at a checkout counter in a department store every hour on average. i.e λ=7

Probability (P) that no more than three customers arrive is notated as P(X≤3)

= P(X=0) + P(X=1) + P(X=2) + P(X=3)

= Poisson (3,7,1)  

= 0.0817

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Answer:

u=11

Step-by-step explanation:

7u-12u+17=-38-combine like terms

-5u=-38-17

-5u=-55

-u=-11

which means u=11

Answer:

u = 11

Step-by-step explanation:

7u + 17 - 12u = - 38 , that is

- 5u + 17 = - 38 ( subtract 17 from both sides )

- 5u = - 55 ( divide both sides by - 5 )

u = 11

I have attached the image.