four feet more than three times the width. Find the length

and width of the bulletin board.

**Step-by-step explanation:**

it is a rectangle.

the area is a rectangle is

length × width

in our case

length × width = 55 ft²

length = 3×width + 4

we use that in the first equation :

(3×width + 4)×width = 55

3×width² + 4×width - 55 = 0

the general solution to a quadratic equation like

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

so,

width = (-4 ± sqrt(4² - 4×3×-55))/(2×3) =

= (-4 ± sqrt(16 + 660))/6 = (-4 ± sqrt(676))/6 =

= (-4 ± 26))/6

width1 = (-4 + 26)/6 = 22/6 = 11/3 = 3 2/3 ft

width2 = (-4 - 26)/6 = -30/6 = -5

negative numbers for the size of a physical object don't make sense, so

11/3 = 3 2/3 ft is our solution.

length = 3×width + 4 = 3×11/3 + 4 = 11 + 4 = 15 ft

so,

the length = 15 ft

the width = 3 2/3 ft (or 11/3 ft)

Question 3 (1 point)

(03.06 LC)

Determine if the sequence is arithmetic or geometric, and find the common difference or ratio

**Arithmetic, Common Difference = -9**

The **Correct **option is **(b).**

What is **Common Difference?**

The common difference of an **arithmetic** **sequence** is the difference between any of its terms and its previous term. An arithmetic sequence goes from one term to the next by always adding (or subtracting) the same amount. The number added (or subtracted) at each stage of an arithmetic sequence is called the** "common difference",** because if we subtract (that is if you find the difference of) successive terms, you'll always get this common value. Most often, "d" is used to denote the common difference.

Given,

x = 1 2 3 4

f(x)= 81 72 63 54

Now, According to the question:

2nd term - 1st term = 72 - 81 = -9

3rd term - 2nd term = 63 - 72 = -9

4th term - 3rd term = 54 - 63 = -9

Hence, **Arithmetic, Common Difference = -9**

The **Correct **option is **(b).**

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There are a total of 235 books in the library. On Monday, 113 books were checked out. On Tuesday, fifty-six books were checked back in. How many books are there in the library on Wednesday morning?

**Answer:**

178

**Step-by-step explanation:**

235-113=122

122+56=178

**Answer:**

178 books

**Step-by-step explanation:**

235 minus 113 books that werr checked out and plus 56 books that came back in total it's 178, if nobody stole anything :)

Challenge An arts academy requires there to be 4 teachers for every 92 students and 3 tutors for every 24 students. How many students does the academy have per teacher? Per tutor? How many tutors does the academy need if it has 72 students?

Answer:2

Step-by-step explanation:25 students per a teacher and 33 students per a tutor.if the academy has 77student they need 2 tutors

Find the equation of the line with slope −35 and y-intercept (0,−3).

**Answer:**

y = -35x -3

**Step-by-step explanation:**

We can use the formula **y = mx + c** to find the equation of the line.

Here,

m ⇒ slope

c ⇒ y-intercept

From these, they have already given the slope of the line.

m ⇒ -35

And now we have to **find the c ( y-intercept ) of the line using the given coordinate,**

( 0 , -3 ) ⇒ ( x , y )

So, to find the y-intercept you have to **replace x, y & m with 0, -3 & -35 respectively, and solve for c.**

Let us solve it now.

y = m x + c

-3 = -35 × 0 + c

-3 = 0 + c

**-3 = c**

And now we can write the equation of the line like this.

y = m x + c

**y = -35x -3**

**Answer:**

Equation of line is given as y =mx + c, where m is the slope and c is the y-intercept.

Since slope is -35, equation of line is y = -35x + c.

Substitute (0,-3) into equation to find c.

-3 = -35(0) + c

c = -3

Hence, equation is y = -35x - 3.

Please help I dont understand!!!!!

**Answer:** This is a linear pair of angles because they are two adjacent angles that have a common side and whose other sides point in opposite directions.

24 yd

15 yd

35 yd

the volume

**Answer: 9633.4 cubic meters**

I only assumed the shape and length, height, width, etc. so this is my best guess. Please provide with a three dimensional shape of the object being calculated and specify which measurements are the length, height, width, depth, or circumfrence. I will answer it right away :)

**Answer:**

12600 yd^3

**Step-by-step explanation:**

The equation to finding the volume of 3 dimensional shapes only including cubes, and rectangles.

L * W * H = V

Which means Length multiplied by width, multiplied by height.

So in this instance:

35 * 24 = 840 * 15 = 12600.

Hope this answers your questions.

If so please make brainliest.

Also if it does feel free to ask me any other questions needed.

The length of each side of triangle LMN is shown below.

LM = 18 cm

MN = 29 cm

LN = 20 cm

Which list shows the angles of triangle LMN in order from least measure to greatest measure?

The **angles** of **triangle** LMN in order from **least** **measure** to the **greatest** measure as angle ∠ N < angle ∠ M < angle ∠ L which is determined by the** triangle inequality** theorem.

When two lines **intersect** at a location, **vertical** **angles** are generated. They are always equal to each other.

The **length** of each **side** of the given **triangle** LMN is shown below.

LM = 18 cm

MN = 29 cm

LN = 20 cm

According to the **triangle inequality** theorem, in a triangle, the **largest** **angle** is the one opposite to the **longest side** of the triangle.

Therefore, in triangle LMN, we have the **greatest** angle as angle ∠ L

And the smallest angle is ∠ N

Arrange the angles in **ascending** order,

angle ∠ N < angle ∠ M < angle ∠ L

Thus, the **angles** of **triangle** LMN in order from **least** **measure** to the **greatest** measure as angle ∠ N < angle ∠ M < angle ∠ L.

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tweleve is no less than the sum of a number n and 3

I really wish I knew

what is the slope of the line ?

**Answer:**

**Step-by-step explanation:**

5/2

**Answer: f(x)= 2x-3**

**Step-by-step explanation: The formula for slope is y=mx+b, where m is equal to the slope of the line and b is equal to the y-intercept. We can find the slope by looking at the line OR solving algebraically using the following calculations:**

**(y2-y1)/(x2-x1)**

**Pick 2 points on the line and plug in.**

**(x1,y1)-->(2,1) and (x2,y2)-->(3,3)**

**(3-1)/(3-2)=2/1=2**

**So, the slope of the line is 2. m=2.**

**To find the y-intercept, we can solve algebraically or look at the graph.**

**y=2x+b**

**Plug in a point from the graph to find b, the y-intercept.**

**3=2(3)+b**

**3=6+b**

**-3=b**

**So, the y-intercept is b. **

**Now, we plug our values into the slope intercept equation, y=mx+b**

**y=2x-3**

**Again, you look look at the graph and see where x=0 is to find the y intercept. To find the slope you can use rise/run and count to see that to get from one point on the graph to the next, you count up 2 (rise 2) and to the right 1 (run 1) which gives you 2/1. 2/1 is equal to 2, giving you the slope of 2. **

**Hope this helped :))**

Write an equation of the parabola. Justify your answer.

Check the picture below.

so from the picture we can pretty much tell two solutions or zeros and another point where it passes up above, so

[tex]\begin{cases} x=-1\implies &x+1=0\\\\ x=7\implies &x-7=0 \end{cases}\hspace{8em} \begin{array}{llll} a(x+1)(x-7)=0\\\\ a(x+1)(x-7)=y \end{array} \\\\[-0.35em] ~\dotfill\\\\ \textit{we also know that} \begin{cases} x=5\\ y=3 \end{cases}\implies a(5+1)(5-7)=3 \\\\\\ a(6)(-2)=3\implies -12a=3\implies a=\cfrac{3}{-12}\implies a=-\cfrac{1}{4} \\\\[-0.35em] ~\dotfill[/tex]

[tex]-\cfrac{1}{4}(x+1)(x-7)=y\implies -\cfrac{1}{4}\stackrel{F~O~I~L}{(x^2-6x-7)}=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} -\cfrac{x^2}{4}+\cfrac{3x}{2}+\cfrac{7}{4}=y \end{array}}~\hfill[/tex]

How do you write 2.467 x 10^10 in standard form?????? helpppp

**Answer: 24670000000**

**Step-by-step explanation:**

**1) First, the scientific form can help you learn that each 10 in a power will increase the number its multiplying by 10. **

Since we know that when multiplying a decimal number by 10, it would move the decimal once to the right. We can apply this to the equation by moving the decimal to the right 10 times.

**2) Answer**

** 12345678910 <= This indicates the decimal moving one place**

**24670000000.00**

How do

you

create equations and use them to solve

problems?

**Answer:**

define the unknown quantity as =variable. Then use the given info to write down an equation in terms of the unknown quantity. At the end, solve the equation for the unknown.

Define the unknown quantity as a variable

Need help with this

**Answer:**

<XMN = 122°

**Step-by-step explanation:**

An angle around a point is 360°

If LMN = 145° then the rest would be 360 - 145

360 - 145 = 215

4x + 5 + 6x - 10 = 215

Simplify = 10x - 5 = 215

work out = 215 + 5 = 220 ÷ 10 = 22

x = 22

XMN = 6x - 10

6 × 22 = 132

132 - 10 = 122

XMN = 122

What are the new vertices of quadrilateral KLMN if the quadrilateral is translated two units to the right and four units upward? A. K = (-2,0), L' = (1,0), M = (1,-3), N = (-2,-3) B. K = (-2,-2), L' = (1,-2), M = (1,-5), N = (-2,-5) C. K = (-0,0), L' = (3,0), M = (3,-1), N = (0,-1) D. K = (-2,2), L' = (1,2), M = (1,-1), N = (-2,-1)

**K' ( -2, 2) , L' (1,2) , M' (1,-1) , N' (-2,-1)**

Firstly, we needt to identify the coordinates of the vertices of the quadilateral

Afterwards, we then perform the translation

The translation simply means we add 2 to the x-value and add 4 to the y-value

So if we had coordinates of a vertex as (x,y); upon translation, we will have (x + 2, y+ 4)

Let us identify the vertices;

K'

K (-4,-2)

L (-1,-2)

M (-1,-5)

N (-4,-5)

After translation, we have;

K' ( -2, 2) , L' (1,2) , M' (1,-1) , N' (-2,-1)

A local building code requires that all factories must be surrounded by a lawn. The width of the lawn must be uniform and the area of the lawn must be equal to the area of the factory. What must be the width of a lawn surrounding a rectangular that measures 120 m by 80 m?

PLEASE HELP

**Answer:**

20 m

**Step-by-step explanation:**

You want to know the **uniform width of a lawn** around a **120 m by 80 m building** such that the **area of the lawn** is equal to the **area of the building**.

Let x represent the width of the lawn. Then the dimensions of the area that includes the lawn and building will be (120 +2x) meters by (80 +2x) meters. We want that area to be equal to twice the area of the building:

(120 +2x)(80 +2x) = 2(120·80)

SolutionDividing by 4 gives a slightly simpler equation.

(60 +x)(40 +x) = 60(80)

2400 +100x +x^2 = 4800 . . . . eliminate parentheses

x^2 +100x -2400 = 0 . . . . . . subtract 4800 and put in standard form

(x +120)(x -20) = 0 . . . . . . . factor

Values of x that make the factors zero are ...

x = -120, x = 20

Only the positive solution makes any sense in this context.

**The width of the lawn must be 20 m**.

__

*Additional comment*

The total area of the plot is ...

total area = (building area) + (lawn area)

When the lawn area is equal to the building area, then we have ...

total area = (building area) + (building area)

total area = 2·(building area)

This is the relation we used in the solution above.

HELP PLEASE!

f(x)= ³ √x+8. Find the inverse of f(x).

**Answer: (D)**

the answer would be D

**Step-by-step explanation:**

Please help and provide an explanation for why the answer is f(x) = 3/2x + 7

What is the equation of the line that passes through Point (-4, 1) and has a Slope of 3/2.

**Answer:**

see below

**Step-by-step explanation:**

the point-slope equation is

y-1 = 3/2 (x+4)

**Answer:**

[tex]y=\frac{3}{2}x+7[/tex]

**Step-by-step explanation:**

To write the **equation of a line**, two information are needed.

The slope can be calculated using the **gradient formula** as long as two pairs of coordinates are given. This question provides the slope, hence we can substitute its value into the equation right away.

In **slope-intercept form**, the equation of a line is given by **y= mx +c**, where **m is the slope** and **c is the y-intercept**. The slope gives us the steepness of the line, while the y-intercept is the y value in which the line cuts through the y-axis (vertical axis).

y= mx +c

Given that slope= [tex]\frac{3}{2}[/tex], m= [tex]\frac{3}{2}[/tex].

**Substitute the value of m:**

[tex]y=\frac{3}{2}x+c[/tex]

Next, find the value of c by **substituting a pair of coordinates**.

When x= -4, y= 1,

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

1= -6 +c

**Add 6 to both sides:**

c= 1 +6

c= 7

**Substituting the value of c:**

[tex]\bf{y=\frac{3}{2}x +7 }[/tex]

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[tex]6x^{2} -7=9x+8x^{2}[/tex]

2x^ = 9x + 7

This can not be simplified any more.

No solution.

This can not be simplified any more.

No solution.

what is the slope of the line?

**Answer:**

slope = - 1

**Step-by-step explanation:**

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (2, 0) ← 2 points on the line

m = [tex]\frac{0-2}{2-0}[/tex] = [tex]\frac{-2}{2}[/tex] = - 1

**Answer:**

-1, equation is y=-x+2

**Step-by-step explanation:**

place the numbers in order from least to greatest…PLS HELP!

**Answer:**

If the numbers are arranged from the least to the greatest, then it is called ascending order. In this form, the numbers are in increasing order. The first number should be lesser than the second number. If the numbers are arranged from the greatest to the least, then it is called descending order.

Absolute Value Calculator: Heron's Calculator

Coterminal Angle Calculator: Graphing Functi...

**Step-by-step explanation:**

**Answer:**

1. -[tex]\sqrt{13}[/tex] = -3.605...

2. -18/5 = -3.6

3. -[tex]\sqrt{12.25}[/tex] = -3.5

4. -|3.4| = -3.4

5. |-3.6| = 3.6

50 POINTS!

A line goes through the points (3, -4) and (-1, 8). Write the equation of the line in point-slope form. Show your work for full credit. (Show the steps for how you went from the two points, above, to having the equation in point-slope form. All calculations must be written down.)

can someone show how they do this instead of just only giving the answer.

**Answer:**

y= -3x + 5

**Step-by-step explanation:**

m= (y2-y1)/(x2-x1)

m= [8-(-4)]/(-1-3)

m=12/-4

= -3

y= mx + b

-4=(-3)(3) + b

-4=9+b

b=5

therefore, y= -3x+5

Una hoja de papel rectangular tiene un área de 84 pulgadas,el ancho del papel es 5 pulgadas menos que el largo¿cual es el ancho,en pulgadas de la hoja de papel ?

Answer: I think the width is 7.

Step by step explanation:

So let's say the length is 12. This means I need to subtract 5 from it, since the width is 5 inches less than the length. Now that we know this, that means the width is 7, which is the area.

I hope this helps.

Please need asappp Graphs of inverse functions

Restricted domain, your answer in two

A painter

mixes 2%, pints

of yellow paint with

4 pints of red paint to make a certain shade of

orange paint. How many pints of yellow paint

should be mixed with 10 pints of red paint

to

make

this shade of orange?

In ** linear equation**, 0.005 pints are pints of yellow paint should be mixed with 10 pints of red paint to make this shade of orange.

**What is a linear equation example?**

Given,

A painter mixes 2%, pints of yellow paint with 4 pints of red paint

So to make this shade of orange ⇒

10 red pints × (2 % yellow pints/ 4 red pints) ≈ 0.005 pints

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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.

**Answer:**

28 inch

**Step-by-step explanation:**

half of 38 would be 19, and take away 5 from both 19. Equally each width ( top and bottom ) 14 inch and each lenght ( Left and right ) 5 inch. so x representing width would be 14 + 14= 28 inch.

14

5 5

14

WILL GIVE 20 POINTS.

Match each picture to its name.

**Answer:**

1. PQ

2. PQ + qr= pr

3. the arrow going both ways with p q

4. point p

5. the arrowing going one way with p q

**Step-by-step explanation:**

I took the test

Robert cuts a string that is 4 feet long into pieces that are each foot long. a. Complete the model to show 4 ÷2/6

24 **pieces **make up the solution to this puzzle.

I assume the query is how many** pieces** does she receive.

I'll respond to it. Leave a note if it is incorrect.

**6 pieces** will be produced from **1 foot**, each measuring 1/6 of a foot (12/6 = 2 inches).

4 feet will provide 24 pieces (4 * 6).

**24 pieces** make up the solution to this puzzle.

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What is the measure of m?

10 millimeters (mm) = 1 centimeter (cm)

10 decimeters = 1 meter (m) = 1,000 millimeters

10 meters = 1 dekameter (dam)

10 dekameters = 1 hectometer (hm) = 100 meters

10 hectometers = 1 kilometer (km) = 1,000 meters

10 decimeters = 1 meter (m) = 1,000 millimeters

10 meters = 1 dekameter (dam)

10 dekameters = 1 hectometer (hm) = 100 meters

10 hectometers = 1 kilometer (km) = 1,000 meters

I WILL GIVE BRAINLIEST!!!

Create one symmetrical (normal) and one asymmetrical set of data, and explain why each fit the definition.

+ Knowing the type of distribution and the skewness of the data, is it possible to draw conclusions about the mean and the median?

+ Why would it be best to use particular measures of center and spread if the data is symmetrical or asymmetrical?

+ What measures would you use in each case?

The **median **will be used as the measure of **central tendency **in this case, it is wise to use the inter-quarterly **range **as the measure of spread.

A **histogram **for symmetrical data will give a **symmetrical **shape, and the mean, **median **and mode will all be the same **value**. Therefore, the best measure of the central **tendency **to use is the mean.

The **standard deviation **indicates; how far away the values in a given data set are from the **mean**, and since the mean is used as the measure of central **tendency**, then the standard deviation should be used as the spread.

If the data is **symmetrical**, then the mean is the measure of central tendency; and the **standard deviation **is the best spread to use.

If the data is **asymmetrical**, the median is the best measure of central tendency; and the** inter-quarterly range** is the best spread to use.

The **median **will be used as the measure of **central tendency **in this case, it is wise to use the inter-quarterly **range **as the measure of spread.

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A gym membership costs $25 to join and $14 each month. Write and use an algebraic

expression to find the cost of the gym membership for 6 months.p

The **algebraic expression** to find the cost of the gym membership for 6 months is given by **25+6×14.**

An** algebraic expression** is one that has been constructed using integer constants, variables, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c. Any **mathematical** **operation** that involves variables, such as addition, subtraction, multiplication, or division, can have its solutions calculated using algebraic expressions. Monomial, binomial, and polynomial expressions are the three different categories of **algebraic** **expressions**.

Given, the cost of joining membership **= $25**

The **cost** of each month = $14

Cost of 6 months = 6 multiplied by 14

Cost of gym membership for 6 months = **25+6×14**

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The functions f(x) and g(x) are shown on the graph.f(x) = |x|What is g(x)?10f(x) = x-5107-5-10g(x) = ?~XAXK
Which type of reaction has only one product?CombinationDecompositionSingle ReplacementO Double ReplacementO Combustion3Clear selecti
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For each word in each word pair, provide 1) the part of speech (noun, verb, etc.) (some words may be contractions) 2) a pronunciation key and definition of the word 3) a sentence of your own that uses the word correctly1. advice/advise2. affect/effect3. conscious/conscience4. its/its5. lie (meaning to recline, NOT to tell a falsehood)/lay6. lose/loose7. than/then8. their/there/theyre9. to/too10. whose/whos
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