You make a pattern bydrawing three similar rectangles. The widthof the smallest rectangle is45of the width ofthe medium-sized rectangle. The width ofthe medium-sized rectangle is45of thewidth of the largest rectangle. The largestrectangle is 12 inches long and 8 incheswide. Find the dimensions of the smallestrectangle. Explain your reasoning.

Answers

Answer 1

Answer:

5.12 in. by 7.68 in.

Step-by-step explanation:

In similar triangles, the ratios of the lengths of corresponding sides are equal.

width of medium triangle = 4/5 width of large triangle

width of medium triangle = 4/5(8 in.) = 6.4 in.

length of medium triangle = 4/5 length of large triangle

length of medium triangle = 4/5(12 in.) = 9.6 in.

width of small triangle = 4/5 width of medium triangle

width of small triangle = 4/5(6.4 in.) = 5.12 in.

length of small triangle = 4/5 length of medium triangle

length of small triangle = 4/5(9.6 in.) = 7.68 in.


Related Questions

If paul puts 300 dollars in a saving account that earns 3% interest how much interest will he earn after 2 years?​

Answers

Answer:

[tex] \boxed{18 \: dollars}[/tex]

Step-by-step explanation:

Principal ( P ) = $ 300

Rate ( R ) = 3%

Time ( T ) = 2 years

Now, let's find the simple Interest:

I = [tex] \mathsf {\frac{PTR}{100} }[/tex]

[tex] \mathsf{ = \frac{300 \times 2 \times 3}{100} }[/tex]

[tex] \mathsf{ = \frac{1800}{100} }[/tex]

[tex] \mathsf{ = 18}[/tex]

Extra information:

Simple Interest

In our daily life when we borrow a sum of money either from a moneylender or from any financial company, we have to pay the money back by adding with extra sum of money. This borrowed money is called principal. The extra money to be paid for the borrowing money is called interest , which is paid after certain duration in certain rate. At last, the borrowed money should be paid back along with interest which is called amount.

Interest is based on three factors : Principal ( P ) , Rate of interest ( R ) and Time ( T ). While computing the interest, the rate must be in percent and time in years.

[tex] \mathsf{ \: simple \: interest \: = \frac{PTR}{100} }[/tex]

On simplifying

[tex] \mathsf{p = \frac{I \times 100}{T \times R} }[/tex]

[tex] \mathsf{t = \frac{I \times 100}{P \times R} }[/tex]

[tex] \mathsf{r = \frac{I \times 100}{P \times T}} [/tex]

And from the definition,

Amount ( A ) = Principal ( P ) + Interest ( I )

Principal ( P ) = Amount ( A ) - Interest ( I )

Interest ( I ) = Amount ( A ) - Principal ( P )

Hope I helped!

Best regards!

Answer:$18

Step-by-step explanation:3% of $300 is $9.$9 is the interest of 1 year so the interest of 2 years is 2 multiplied by 9 which is $18.

Cory earns $9.50 per hour for the first 40 hours he works in a week. For any hours over 40 hours per week, his hourly rate is multiplied by 1.5. How much does he earn is he works for 43.5 hours in one week?

Answers

Answer:

429.88

Step-by-step explanation:

The first 40 hours is at 9.50

40 *9.50 =380

The remaining hours is at 9.50 * 1.5 or 14.25

43.5 -40 = 3.5

3.5 * 14.25

49.875 = 49.88  ( rounding to the nearest cent)

Add together

380+49.88 =429.88

all integers are whole numbers?true or false​

Answers

Answer:

that would be false

Step-by-step explanation:

all whole numbers are integers, but not all integers are whole numbers

Complete the Magic Square.

Answers

Answer:

+5

Step-by-step explanation:

So you can see the 5 pattern, so you add 9+5= 14 which goes in the middle square and 14+5=18 in the left square

Now between 18 and 11 it is 7 so you subtract 7 which equals 4 then - 5= -1 then -5= -6

Answer:

4  5  9

11  6  1

3  7  8

Step-by-step explanation:

In a magic square, all rows, columns, and diagonals have the same sum.

Let's call the cells a - i this way:

a  b  c

d  e  f

g  h  i

Now lets's fill in what we have:

a  b  9

11  6  1

g  h  i

2nd row: 11 + 6 + 1 = 18

3rd column: 9 + 1 + i = 18; i = 8

a  b  9

11  6  1

g  h  8

Main diagonal: a + 6 + 8 = 18; a = 4

4  b  9

11  6  1

g  h  8

1st row: 4 + b + 9 = 18; b = 5

4  5  9

11  6  1

g  h  8

1st column: 4 + 11 + g = 18; g = 3

4  5  9

11  6  1

3  h  8

2nd column: 5 + 6 + h = 18; h = 7

4  5  9

11  6  1

3  7  8

A building has an entry the shape of a parabolic arch 84 ft high and 42 ft wide at the base, as shown below. A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 84 feet and its width from left to right is 42 feet. Find an equation for the parabola if the vertex is put at the origin of the coordinate system. (

Answers

Answer:

Step-by-step explanation:

Because of the nature of the information we are given, we have no choice but to use the equation

[tex]y=a(x-h)^2+k[/tex]

and solve for a.

We know by the info that the vertex is (0, 84). We also know that if the vertex is at the origin, and that the base is 42 feet wide, it spans 21 feet to the right of the origin and 21 feet to the left of the origin. That means that we have 2 coordinates from which we need to pick one for our x and y in the equation. I don't like negatives, so I am going to choose the coordinate (21, 0) as x and y. Because this parabola opens upside down, as archways of door openings do, our "a" value better come out algebraically as a negative. Let's see...From the vertex we have that h = 0 and k = 84. So filling in:

[tex]0=a(21-0)^2+84[/tex] and simplifying a bit:

0 = 441a + 84 and

-84 = 441a so

[tex]a=-\frac{84}{441}=-\frac{4}{21}[/tex] Good, a is negative. Your equation is, then:

[tex]y=-\frac{4}{21}x^2+84[/tex]

Answer:

x² = -21y

Step-by-step explanation:

THIS IS THE RIGHT ANSWER I TOOK THE TEST

The company is building a scale model of the theater’s main show tank for an investor's presentation. Each dimension will be made 16of the original dimension to accommodate the mock-up in the presentation room. What is the volume of the smaller mock-up tank? Hint: You do not divide the volume of the main show tank by 6.

Answers

Answer:

see below

Step-by-step explanation:

If the original dimensions of the tank are x, y, and z, the mock dimensions will be 1/6x, 1/6y and 1/6z. The volume of the original tank is x * y * z = xyz whereas the volume of the mock-up tank is 1/6x * 1/6y * 1/6z = 1/216 * xyz. Therefore, we know that the volume of the mock-up tank is 1/216 th of the original tank.

f(x) = x^2. What is g(x)?

Answers

g(x) = ax^2
y = ax^2
16 = a1^2
a = 16

Therefore, g(x) = 16x^2

Find the common ratio for the geometric sequence for which [tex]a_1[/tex]=3 and [tex]a_5[/tex]=48. A. -3 B. -2 C. 3 D. 2

Answers

Answer:

An= A1 * r^n-1

A5= 3 * r^5-1

48= 3*r^4

48÷3=r^4

16=r^4

r=

[tex] \sqrt[4]{16} [/tex]

r=2

The answer is D. 2

Espero que te sirva

hsじぇいrんふぉそ具jんじょおlっっっkjか、

Convert the mixed number to an improper fraction 1 13/15

Answers

28/15 is the answer brodi

━━━━━━━☆☆━━━━━━━

▹ Answer

28/15

▹ Step-by-Step Explanation

[tex]1\frac{13}{15} \\\\1 * 15 = 15\\15 + 13 = 28\\\\\\= \frac{28}{15}[/tex]

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

f(x) = x2. What is g(x)?

Answers

Answer:

g(x)=3x(superscript)2

Answer:

g(x) = 3x².

Step-by-step explanation:

In the diagram, we see that the vertex has not been shifted from the origin. The only thing that happened to the graph of f(x) was that it was vertically stretched to become g(x).

Where x = 1, f(x) = 1. Where x = 1, g(x) = 3. That means that the graph of f(x) was multiplied by 3.

So, g(x) = 3x².

Hope this helps!

can someone please help me I need the answer urgently please​

Answers

Answer:

Step-by-step explanation:

AB ≅ BC.  So, ΔABC is an isosceles triangle

Opposite angles of equal sides are equal.

∠BAC = ∠BCA = x°

In ΔABC,

∠ABC + ∠BAC + ∠BCA = 180  {Angle sum property of triangle}

 56 + x + x = 180

56 + 2x = 180

        2x = 180 - 56

         2x = 124

           x = 124/2

           x = 62°

∠BAC = ∠BCA =  62°

∠DCF = ∠BCA   {Vertically opposite angles}

∠DCF = 62°

CDEF is a parallelogram.

In parallelogram, opposite angles are congruent.

∠DEF = ∠DCF

∠DEF = 62°

In a parallelogram, sum of adjacent angles = 180

∠DEF + ∠CDE = 180

62 + ∠CDE = 180

       ∠CDE = 180 - 62

      ∠CDE = 118°

∠CFE = ∠CDE   {In parallelogram, opposite angles are congruent}

∠CFE  = 118°

Which graph represents a function?

Answers

Answer:

The first one is the only function

Step-by-step explanation:

You cannot have points on the same y gridline

If it is a function is has to pass the pencil test

Answer:

[tex]\boxed{Graph A.}[/tex]

Step-by-step explanation:

Hey there!

Well graph A is correct because if you do the vertical line test which decides is the graph is a function or not you can see that all the graph expect A have the vertical line go through 2 points.

Hope this helps :)

It takes Matt 3 minutes to read one page in a book. If he continues to read at the same pace, he can read 15 similar pages in minutes. If the book has 300 pages, it will take him minutes to read it.

Answers

Answer:

a)45min

b)900min

Step-by-step explanation:

We were told that it takes Matt 3 minutes to read one page in a book.

It implies that 3minutes = 1page of the book

Then he continues to read at the same pace, he can read 15 similar pages in minutes.

a)Then, he can read 15 similar pages in

15x3 minutes.which is 45minutes.

b)Then if the book has 300 pages, it will take him. 300×3 minutes to read it.which is 900mins

Answer: has anyone seen my dad?


Please answer this question now

Answers

Answer:

112°

Step-by-step explanation:

Angle A is an inscribed angle that intercepts arc BCD.

Therefore:

m<A = ½ of arc BCD (Inscribed Angle Theorem)

Arc BCD = BC + CD = 146 + CD

An equation can be written to enable us find the measure of arc CD. See below:

Let x = measure of arc CD

Thus,

129° = ½(146 + x)

Solve for x

129*2 = 146 + x

258 = 146 + x

Subtract 146 from both sides of the equation.

258 - 146 = x

112 = x

x = measure of arc CD = 112°

Anna's back Garden consists of a rectangular lawn measuring 9m by 7m, surrounded by a gravel path of width X metres. Find, and simplify, an expression for the total area of the garden.​

Answers

A rectangular lawn measuring 8m by 4m is surrounded by a flower bed of uniform width.

The combined area of the lawn and the flower bed is 165m^2. What is the width of the flower

:

Let x = the width of flower bed

:

Then the overall dimensions (flower bed & lawn) will be:

(2x + 8) by (2x + 4)

:

Overall area

(2x+8)*(2x+4) = 165

FOIL

4x^2 + 8x + 16x + 32 = 165

A quadratic equation

 

4x^2 + 24x + 32 - 165 = 0

4x^2 + 24x - 132 = 0

Simplify, divide by 4, results:

x^2 + 6x - 33 = 0

Use the quadratic formula to solve this

PLS ANSWER BRAINLIST AND A THANK YOU WILL BE GIVEN!!!!

Answers

Answer:

[tex]\huge\boxed{Option \ D}[/tex]

Step-by-step explanation:

4x + 5x = 180 [They are angles on a "straight" line so they will add up to 180 degrees)

Answer:

D

Step-by-step explanation:

The sum of angles that are formed on a straight line is 180.

4x + 5x = 180

* * +:) help .........

Answers

1. -11     2.-3

Make sure to simplify the equation..

example: 3(2x - 7) = 6x - 21

because 3 x 2 = 6 and 3 x 7 = 21

A
man paid 15600
for a new
car. He
was given a discount of
7%. Find the marked price
of the car​

Answers

hope it helps.I was reading the same chapter

Factor x^4+xy^3+x^3+y^3 completely showing work.

Answers

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]x^4+xy^3+x^3+y^3\\\\=x^3*x+x*y^3+x^3+y^3\\\\=x(x^3+y^3)+x^3+y^3\\\\\boxed{=(x+1)(x^3+y^3)}\\[/tex]

Thank you

Jess receives a $15000 salary for working as an engineer. If Jess has to spend $6000 of her salary on expenses each year, then what percent of Jess's money does she have to spend? Round your answer to the nearest whole number if necessary.

Answers

Answer:

Jess will have to spend 40% of her salary

Step-by-step explanation:

Jess salary = $15,000

Jess expenses = $6,000

what percent of Jess's money does she have to spend

Percentage of Jess expenses = Jess expenses / Total salary × 100

= 6,000 / 15,000 × 100

= 0.4 × 100

= 40%

Jess will have to spend 40% of her salary

4 The surface area of a cube with side s is A = 682
Use the formula to find the surface area of a cube with s=4.

Answers

Answer:

96

Step-by-step explanation:

SA = 6*s^2

Since s = 4, we need to square it.

4^2 (4 Squared) = 16

Now we need to multiply 16 by 6 since there are 6 sides on a square.

16*6 = 96

So our Answer is 96.

--Variables

SA= Surface Area

s = Side Length or 4

1. Find 3 consecutive integers whose sum is 33.

Answers

Answer: 10, 11, 12

Step-by-step explanation: Think of the integers like this:

1st integer: x

2nd integer: x+1

3rd integer: x+2

That is necessary because they are consecutive integers. Since the sum is 33, we need to create an equation.

x+x+1+x+2=33.

Simplify:

3x+3=33.

Opposite operations:

3x=-3+33.

To get the 3 close to the 33, we needed to make it negative, which is the opposite operation of the positive 3.

So,

3x=30.

Divide by 3:

x=10.

The first integer, x, equals 10.

To go with the guide that we already created,

1st integer: x=10

2nd integer: x+1=11

3rd integer:x+2=12.

Therefore, the three consecutive integers are 10, 11, and 12.

To check that, add them up. They all equal 33 and they are consecutive, which means this is the right answer!

Answer:

  10, 11, 12

Step-by-step explanation:

For problems involving consecutive integers, I like to consider their average value. For three consecutive integers, their average will be the middle one. It will be ...

  average = sum / (number of numbers) = 33/3 = 11

The middle number is 11, so the numbers are ...

  10, 11, 12

_____

If you want to write an equation, you can let x represent the middle number. Then the other two are x-1 and x+1, and their sum is ...

  (x-1) +(x) +(x+1) = 33 = 3x

  x = 11   ⇒   x-1 = 10, x+1 = 12

Evaluate the following expression.
10^7 + 9 + 1^3 =

Answers

Anjdjdnjadnosepsjkdsksksks

bzjd

What’s the function of the Unit Circle and why is it called the unit Circle?

Answers

Answer:

It is a unit of radius that is radius of 1. Thus, the distant to the middle to any edge is always 1.

Step-by-step explanation:

Graph the solution to the following linear inequality in the coordinate plane 5x-y>-3

Answers

Answer:

Here's one way to do it

Step-by-step explanation:

1. Solve the inequality for y

5x - y > -3

      -y > -5x  -  3

       y < 5x + 3

2. Plot a few points for the "y =" line

I chose

[tex]\begin{array}{rr}\mathbf{x} & \mathbf{y} \\-2 & -7 \\-1 & -2 \\0 & 3 \\1 & 8 \\2 & 13 \\\end{array}[/tex]

You should get a graph like Fig 1.

3. Draw a straight line through the points

Make it a dashed line because the inequality is "<",  to show that points on the line do not satisfy the inequality.

See Fig. 2.

4. Test a point to see if it satisfies the inequality

I like to use the origin,(0,0), for easy calculating.

y < 5x + 3

0 < 0 + 3

0 < 3. TRUE.

The condition is TRUE.

Shade the side of the line that contains the point (the bottom side).

And you're done (See Fig. 3).

I need help ASAP!
Possible answers are 9, 37, -37, 19, 24, 8, and -24

Answers

Answer:

37

Step-by-step explanation:

Hello!

First we add 15 to both sides

[tex]\frac{-5x-10}{5} = -2x + 35[/tex]

Multiply both sides by 5

-5x - 10 = -10x + 175

Add 10 to both sides

-5x = -10x + 185

Add 10x to both sides

5x = 185

Divide both sides by 5

x = 37

The answer is 37

Hope this helps!

[tex]\dfrac{-5x-10}{5}-15=-2x+20\quad|\cdot5\\\\-5x-10-75=-10x+100\\\\-5x+10x=100+10+75\\\\5x=185\quad|:5\\\\\boxed{x=37}[/tex]

ABC is an equilateral triangle, solve y

Answers

Answer:

y is 60⁰

because all sides are equal

Answer:

60 degrees

Step-by-step explanation:

In an equilateral triangle, the angles are equiangluar and the sides are equal.

180 degrees in a triangle/3 sides =

= 60 degrees per side

On the coordinate plane below, Point P, is located at (2,-3) and point Q is located at (-4,4). Find the distance between points, P and Q

Answers

Answer:

approximately 9.2195

Step-by-step explanation:

We can use Pythagorean theorem

one leg is 7 and the other leg is 6

square them

49 and 36

add

85

square root

approximately 9.2195

4 (hx - 1) -3 (x +h) ≡ 5 (x + k)
Work out the value of h and k
H and k are integer constants

Answers

Answer:

        4hx - 8x - 3h - 4

k  =  ------------------------

                  5

            8x + 5k + 4

h  =  ------------------------

              4x - 3

Step-by-step explanation:

4 (hx - 1) - 3 (x + h) = 5 (x + k)

4hx - 4 - 3 (x + h) = 5 (x + k)

4hx - 4 - 3x - 3h = 5 (x + k)

4hx - 4 - 3x - 3h = 5x + 5k                   add 3h both sides

4hx - 4 - 3x - 3h + 3h = 5x + 5k + 3h   simplify

4hx - 4 - 3x = 5x + 5k + 3h                   add 4 both sides

4hx - 4 - 3x + 4 = 5x + 5k + 3h + 4       simplify

4hx - 3x = 5x + 5k + 3h + 4                  subtract 5x from both sides

4hx - 3x - 5x = 5x + 5k + 3h + 4 - 5x   simplify

4hx - 8x = 5k + 3h + 4                          

4hx - 8x - 3h - 4 = 5k  

      4hx - 8x - 3h - 4

k  =  ------------------------

                5

solving for h;

4hx - 3h = 8x + 5k + 4

h(4x - 3) = 8x + 5k + 4

          8x + 5k + 4

h  =  ------------------------

            4x - 3

The value of h and k are h = (8x + 5k + 4) / (4x - 3) and k = (4hx - 8x - 3h - 4) / 5 respectively

Given:

4 (hx - 1) -3 (x +h) ≡ 5 (x + k)

open parenthesis

4hx - 4 - 3x - 3h = 5x + 5k

4hx - 4 - 3x - 3h - 5x - 5k = 0

4hx - 8x - 3h - 5k - 4 = 0

For k

4hx - 8x - 3h - 4 = 5k

[tex]k = (4hx - 8x - 3h - 4) / 5[/tex]

For h

4hx - 8x - 3h - 5k - 4 = 0

4hx - 3h = 8x + 5k + 4

h(4x - 3) = 8x + 5k + 4

[tex]h = (8x + 5k + 4) / (4x - 3)[/tex]

Therefore, the value of h and k are h = (8x + 5k + 4) / (4x - 3) and k = (4hx - 8x - 3h - 4) / 5 respectively

Read more:

https://brainly.com/question/21406377

What is a16 of the sequence 2,11,20

Answers

Answer:

137

Step-by-step explanation:

This is an arithmetic sequence with first term (a₁) being 2 and common difference (d) being 11 - 2 = 9.

Explicit formula: aₙ = a₁ + (n - 1) * d so our formula is:

aₙ = 2 + (n - 1) * 9

= 2 + 9n - 9

= 9n - 7

a₁₆ = 9(16) - 7 = 137

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