The length of a rectangle is 3 m more than twice the width, and the area of the rectangle is 54 mº. Find the dimensions of the rectangle.

Answer:

Step-by-step explanation:

4.5 ÷ 2

[tex]\frac{9}{2}[/tex]  ÷ 2

[tex]\frac{9}{2} * \frac{1}{2}[/tex]

9 / 4

From the 32 by 33 rectangular figure, having interior squares, we have

The area of the squares in square units are;

The areas in square units are;

Area of square A = 18 × 18 = 324

Area of square B = 15 × 15 = 225

Area of square E = 10 × 10 = 100

Area of square F = 14 × 14 = 196

Area of square G = 4 × 4 = 16

Area of square H = 7 × 7 = 49

Area of square I = 1 × 1 = 1

Area of a rectangle = Length × Breadth

Therefore;

Area of the entire figure = 32 × 33 = 1056

The perimeter, P, of the rectangular figure is therefore;

P = 2 × 32 + 2 × 33 = 130

Learn more about finding the area of plane figures here;

https://brainly.com/question/2669479

Answer:

17, 9, 18, 7, 19, 5, 20, X

Bold: 17, 18, 19, 20, .....

Other: 9, 7, 5, 3, 1 ....

I think the answer is 3

By finding the pattern, we conclude that the next number in the sequence is 3.

We have the sequence:

17, 9, 18, 7, 19, 5, 20, x.

Here the pattern is kinda simple.

First, we have a two-digit number which increases by one unit (on the odd positions). Then we have a single-digit number that decreases by two (on the even positions).

Then we will have:

x = 5 - 2 = 3

We conclude that the next number in the sequence is 3, we get:

17, 9, 18, 7, 19, 5, 20, 3.

If you want to learn more about sequences:

https://brainly.com/question/6561461

#SPJ2

Answer:

[tex]s=32\\t=64[/tex]

Zack sold 32 bags of popcorn last Saturday, and 64 bags of popcorn today.

Step-by-step explanation:

Start by determining what information the question gives us, and what we need to find.

Given:

Zack sold twice as many bags of popcorn as he sold last Saturday

He sold 96 bags altogether in the 2 days

Find:

s, number of bags he sold last Saturday

t, number of bags he sold today

Equation/System of Equations:

[tex]t=2s[/tex] (OR "number of bags he sold today = number of bags he sold last Saturday multiplied by 2, or twice the amount he sold last Saturday)

[tex]t+s=96[/tex] (OR "number of bags he sold today + number of bags he sold last Saturday is equivalent to the amount of bag he sold altogether which is 96 bags as given by the question)

Solve:

We can solve this system of equations using substitution. In this case, we can substitute "2s" for "t" into the second equation giving us...

[tex]2s+s=96\\3s=96[/tex]

Divide both sides by 3. Notice that the Division Property of Equality states that if you divide on side of the equation by something, you must divide the other side by the same quantity.

[tex]s=\frac{96}{3}\\s=32[/tex]

Substitute 32 in for "s" to solve for "t"...

[tex]t=2s\\t=2(32)\\t=64[/tex]

Answer:

Zack sold 32 bags of popcorn last Saturday, and 64 bags of popcorn today.

Topic : Midpoint between points

formula:

[tex]\sf \bold{(x_m, y_m) = (\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})}[/tex]

=====================================

[tex]\hookrightarrow \sf \dfrac{x+(-5)}{2} ,\dfrac{y+2}{2} = (8, -8)[/tex]

separate taking coefficients:

[tex]\rightarrow \sf \dfrac{x-5}{2} =8, \ \dfrac{y+2}{2} = -8[/tex]

[tex]\rightarrow \sf x-5 =16, \ y+2 = -16[/tex]

[tex]\rightarrow \sf x =16+5, \ y= -16-2[/tex]

[tex]\rightarrow \sf x =21, \ y= -18[/tex]

coordinates of door: (21, -18)

Let that be (x,y)

So

[tex]\\ \rm\rightarrowtail (8,-8)=(\dfrac{x-5}{2},\dfrac{y+2}{2})[/tex]

[tex]\\ \rm\rightarrowtail \cfrac{x-5}{2}=8\implies x-5=16\implies x=21[/tex]

[tex]\\ \rm\rightarrowtail \cfrac{y+2}{2}=-8\implies y+2=-16\implies y=-18[/tex]

Step-by-step explanation: Range is where you put the numbers from greatest to least, I believe you can also do least to greatest. Mode is whenever you have your numbers in order form greatest to least the number that shows up the most is the mode.   HOPE THIS HELPED !!!

Step-by-step explanation:

remember, the sum of all angles in a triangle is always 180°.

1.

since it is a right-angled triangle, and one of the leg angles is 45°, then the other leg angle is also 45°.

which makes this an isoceles triangle.

so, the second leg is 6 too.

the baseline (Hypotenuse) is then per Pythagoras

baseline² = 6² + 6² = 36 + 36 = 72 or 2×36

baseline = sqrt(72) = 6×sqrt(2)

2.

this is then a 30-60-90 triangle.

the left leg (a) is then 2a/2 = 10/2 = 5.

and the bottom leg is 5×sqrt(3).

3.

isoceles triangle.

so, left and right legs (a) are both 3 (from the 3×sqrt(2)).

4.

30-60-90 triangle

upper leg is then 6×sqrt(3).

the baseline is 2 times the left leg : 2×6 = 12

5.

isoceles triangle

both legs are 2 (from the 2×sqrt(2)).

6.

30-60-90 triangle

left leg is 4 (from the 4×sqrt(3)).

the baseline is 2×4 = 8.

7.

isoceles triangle.

6 = a×sqrt(2)

a (both legs) = 6/sqrt(2)

8.

30-60-90 triangle

9 = a×sqrt(3)

a (left leg) = 9/sqrt(3)

baseline = 2a = 2×9/sqrt(3) = 18/sqrt(3)

9.

due to the equal leg angles this is an isoceles triangle.

4 = a×sqrt(2)

a (both legs) = 4/sqrt(2)

10.

30-60-90 triangle

the bottom leg (a) = 2a/2 = 6/2 = 3

the left leg is then 3×sqrt(3)

11.

isoceles triangle

left leg is also 5.

baseline is 5×sqrt(2)

12.

30-60-90 triangle

12 = a×sqrt(3)

a (left leg) = 12/sqrt(3)

the baseline is then 2a = 2×12/sqrt(3) = 24/sqrt(3)

Answer:

fourteen thousand six hundred and eighty nine

Step-by-step explanation:

1 is in the ten thousand group, four is in the thousands, six is in the hundreds, eight is in the tens, nine is in the ones. i hope this helped :)

Answer:

Fourteen-thousand and six-hundred eighty nine.

option C

hope it helps...!!!

Answer:

[tex]\fbox{Area = 1017.36 sq.cm.}[/tex]

Step-by-step explanation:

Given:

circumference of circular dinner plate= 113.04 cm

To find:

Area of dinner plate = ?

Solution:

circumference = 113.04 cm.

we know that circumference = 2πr

[tex]2 \pi r = 113.04 \: cm \\ r = \frac{113.04 }{2 \pi} \\ r = \frac{113.04 }{2 \times 3.14} \\r = \frac{113.04 }{6.28} \\ \fbox{r = 18 \: cm}[/tex]

We know that,

Area of circle = πr²

now substituting value of r in above formula,

[tex] \pi {r}^{2} = 3.14 \times 18 \times 18 = 1017.36 \: {cm}^{2} [/tex]

[tex] \fbox{Area = 1017.36 sq.cm.}[/tex]

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Answer:

x=4.5

Step-by-step explanation:

2x− 7/2 =x+1

2x− 7/2- x=1

x-7/2=1

x= 1+7/2

x=2/2+7/2

x= 2+7 is numerator and 2 is the denominator

x= 9/2

9/2 = 4.5

Answer:

Dryer = 320

Washer = 960

Step-by-step explanation:

Washer + Dryer = 1280

Let,

Dryer = x

Washer = 3x

3x + x = 1280

4x = 1280

x = 320

Washer = 3x = 3(320)=960

960 + 320 = 1280

Thus,

Dryer = 320

Washer = 960

~lenvy~

Answer:

24 he can get 24 at the very minimum

Step-by-step explanation:

Answer:

the perfect square is 9x²

Step-by-step explanation:

√(3×)⁴

=(3x)²

=9x²

Using the median concept, it is found that it suffered a 11.16% decrease.

It is the 50th percentile of the data-set, which is the value that separates the lower 50% from the upper 50%.

In this problem, the ordered data-set, in thousands of £, is given by:

{19.4, 39.8, 42.3, 42.5, 45.1, 47.9, 52.4, 53.5}

It has even cardinality, hence the median is the mean of the 8/2 = 4th and 5th terms, so:

M = (42.5 + 45.1)/2 = £43800.

It decreased from £49300 last year. The percentage decrease is the change divided by initial amount and multiplied by 100%, hence:

P = (49300 - 43800)/49300 x 100% = 11.16%.

More can be learned about the median concept at https://brainly.com/question/25215461

Answer:

where is the figure

pls send it

Answer:

3(x-7)(x+7)

Step-by-step explanation:

In order to completely factor, begin by factoring out the greatest common factor.  Both terms are divisible by 3 so 3 is the greatest common factor.  3(x^2-49).  In order to completely factor, recognize x^2-49 as the difference of squares.  Factor that into 3(x+7)(x-7).

Answer:

3(x+7)(x-7)

Step-by-step explanation:

Hello!

We can start by taking out the coefficient of 3 by factoring it out.

Factor:

The process of removing a factor or coefficient by dividing it out from the expression.

Factor the expression:

Remove the coefficient of 3

Factor using the product rule: a² - b² = (a+b)(a-b)

There's your factored expression! 3(x+7)(x-7)

Answer:

a = -2

b =3

c =2

Step-by-step explanation:

f(x) = 2 + 3x – 2x²

Rewrite in descending powers of x

-2x^2 +3x+2

The form is ax^2 +bx +c

a = -2

b =3

c =2

Answer:

58.5 ft²

Step-by-step explanation:

The figure is made up of a square, triangle and rectangle. Thus, the area of the figure is the sum of the areas of the square, triangle and rectangle.

Let's find the area of each!

Square

Area of square= side ×side

Area

= 3(3)

= 9 ft²

Triangle

Area of triangle= ½ ×base ×height

Base= 11 ft

Height= 3 ft

Area

= ½(11)(3)

= 16.5 ft²

Rectangle

Area of rectangle= length ×breadth

Area

= 3(11)

= 33 ft²

Area of figure

= 9 +16.5 +33

= [tex]\textcolor{red}{58.5 \: {\text{ft}} {}^{2} }[/tex]

[tex] \qquad \qquad \huge\text{Anѕwer}♨[/tex]

❖ Aѕ givєn in thє quєѕtiσn, ч vαriєѕ invєrѕєlч with х, thiѕ єхprєѕѕiσn cαn вє rєprєѕєntєd αѕ :

[tex] \qquad \Rrightarrow \rm y \propto \dfrac{1}{x} [/tex]

➻ To rєplαcє prσpσrtiσnαlitч ѕign with єquαlѕ tσ, wє hαvє tσ uѕє α cσnѕtαnt (k)

[tex] \qquad \Rrightarrow \rm y = k \times\dfrac{1}{x} [/tex]

[tex] \qquad \Rrightarrow \rm \dfrac{}{} xy = k[/tex]

➻ nσw, plug in vhє vαluєѕ σf х αnd ч fσr α ѕpєcific inѕtαnt, thαt'ѕ givєn in thє quєѕtiσn ~

[tex] \qquad \Rrightarrow \rm \dfrac{}{} 6 \times 8 = k[/tex]

[tex] \qquad \Rrightarrow \rm \dfrac{}{} k = 48[/tex]

thєrєfσrє, vαluє σf prσpσrtiσnαlч cσnѕtαnt iѕ 48

➼ ѕσ, thє rєquirєd єхprєѕѕiσn will вє :

[tex] \qquad \Rrightarrow \rm \dfrac{}{} xy = 48[/tex]

4747+38383=43,130

Answer:

4747

+38383

=43130 that is my answer

Answer:

44 mm

Step-by-step explanation:

radius = 22 mm

diameter = 2 * radius = 44 mm

Answer:

The car will travel at 198 feet in 3 seconds. The speed of the car = 45miles/ hour. To convert miles to feet;. 1 mile = 5280 feet.

Step-by-step explanation:

The car will travel at 198 feet in 3 seconds. The speed of the car = 45miles/ hour. To convert miles to feet;. 1 mile = 5280 feet.

From the given price function, we have;

(a) [tex] \frac{dp}{dq} = - 13[/tex]

(b) The point elasticity of demand is 0.0256; inelastic demand

(c) $46.6

(d) Increase

a. The given function is presented as follows;

[tex]p = 50 \times (151 - q) ^{0.02 \times \sqrt{q + 19} } [/tex]

Differentiating the above function with a graphing calculator and setting q = 150 gives;

[tex] \frac{dp}{dq} = - 13[/tex]

b. The point elasticity of demand is given by the formula;

[tex] e \: = \frac{dq}{dp} \times \frac{p}{q} [/tex]

When q = 150, we have;

P = 50

Which gives;

[tex]e \: = \frac{1}{13} \times \frac{50}{150} = 0.0256[/tex]

The point elasticity of demand, E = 0.0256

c. If the quantity demanded decreases from 150 to 140 units, we have;

[tex]0.0256 \: = \frac{1}{13} \times \frac{p}{140} = [/tex]

Which gives;

p = 46.6

d. Given that increase in price, from 46.6 to 50, increases the quantity demanded from 140 to 150, therefore;

R = p × q

Learn more about elasticity of demand here;

https://brainly.com/question/19141990

Answer:

Step-by-step explanation:

Answer:

Amount Robert will pay back = $434.04

Step-by-step explanation:

Formula for interest is;

I = (P * R * T)/100

We are given;

P = $390

Rate = 18%

Time; T = 229 days = 229/365

Thus;

I = (390 * 18 * (229/365))/100

I = $44.04

Thus, total amount Mario will pay back = $390 + $44.04 = $434.04

Answer:

pls send the image along with it. So it can be solved