A rectangle has a length 10 more than its width. If the width is increased by 8
and the length by 4, the resulting rectangle has an area of 135 square units.
Part A
Write an equation to model the above scenario. Use the model to find the length
of the original rectangle?
powered by
esmos
Part B
What is the perimeter of the expanded rectangle?

Answers

Answer 1

Step-by-step explanation:

length = the original length

width = the original width

length = width + 10 or

width = length - 10

(length + 4) × (width + 8) = 135

A

now we are using the first equation in the second to solve then for length :

(length + 4) × (length - 10 + 8) = 135

(length + 4) × (length - 2) = 135

length² - 2×length + 4×length - 8 = 135

length² + 2×length = 143 or

length² + 2×length - 143 = 0

this is the equation to model the scenario.

solving in general such a quadratic equation :

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = length

a = 1

b = 2

c = -143

length = (-2 ± sqrt(2² - 4×1×-143))/(2×1) =

= (-2 ± sqrt(4 + 572))/2 =

= (-2 ± sqrt(576))/2 =

= (-2 ± 24)/2 = (-1 ± 12)

length1 = -1 + 12 = 11

length2 = -1 - 12 = -13

a negative solution for a length is not applicable, so,

length = 11

width = length - 10 = 11 - 10 = 1

B

the expanded length = 11 + 4 = 15

the expanded width = 1 + 8 = 9

the expanded perimeter is then

2×15 + 2×9 = 30 + 18 = 48


Related Questions

Vanessa uses the expressions (3x² + 5x + 10) and (x² – 3x - 1) to represent the length and width of her patio.
Which expression represents the area (w) of Vanessa's patio?


a) 3x4-4x³-8x²-35x-10

b) 3x4+14x³+22x²+25x-10

c) 3x4-4x³+22x²+35x+10

d) 3x1+14x³+28x²+35x+10


I’m not really the best at math, my apologies. Thank you.

Answers

Answer:

a) 3x⁴-4x³-8x²-35x-10

Step-by-step explanation:

3x2(x²-3x-1)+5x(x²-3x-1)+10(x²-3x-1)

3x⁴-9x³-3x²+5x³-15x²-5x+10x²-30x-10

3x⁴-9x³+5x³-3x²-15x²+10x²-5x-30x-10

3x⁴-4x³-8x²-35x-10

The expression  3x⁴ + 11x³ - 15x² - 40x - 10 represents the area (w) of Vanessa's patio

What is Expression?

An expression is combination of variables, numbers and operators.

The area (w) of Vanessa's patio can be found by multiplying the length and width expressions:

w = (3x² + 5x + 10)(x² – 3x - 1)

Expanding this expression using the distributive property, we get:

w = 3x⁴ - 4x³ - 8x² + 15x³ - 25x² - 10x + 10x² - 30x - 10

Simplifying this expression, we get:

w = 3x⁴ + 11x³ - 15x² - 40x - 10

Hence, the expression  3x⁴ + 11x³ - 15x² - 40x - 10 represents the area (w) of Vanessa's patio

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A survey found that 3 out of 100 randomly selected people have red hair. How many people in a group of 12,000 randomly selected people are likely to have red hair?

Answers

Answer:

360 people out of 1200 are likely to have red hair.

Step-by-step explanation:

So I just saw that 100 x 120 equals 1200. So I just need to multiply 3 x 120 and I got 360. I think this is how to solve?

In Walter's class, 14 of the 25 students ride the bus. In Sasha's class, 11 of the 20 students ride the bus. Which class has a greater percent of students who ride the bus?

Answers

The class which has a greater percent of students who ride the bus is Walter's class

How to find percentage?

Walter's class:

14 of the 25 students ride the bus

Percentage of students who ride bus = 14 / 15 × 100

= 0.933 × 100

= 93.3%

Sasha's class:

11 of the 20 students ride the bus

Percentage of students who ride bus = 11 / 20 × 100

= 0.55 × 20

= 55%

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Please help me, greatly appreciate it!

Answers

Answer: See the screenshots below

I'm answering in this format because the questions aren't numbered, so its hard to reference them consistently (so we're both on the same page).

All decimal values are approximate. I decided to round to 4 decimal places, but feel free to use another level of precision.

When surveyed, the ratio of students who preferred Science class to English class was 5:4. If 90 students were surveyed, how many students chose Science?​

Answers

50 students preferred science...

Explanation:

we can consider the numbers 5 and 4 in the ratio as units

now we need to know how much each unit represent

units = 5 + 4 = 9

my sample = 90 students

each unit = 90/9 = 10 students

so each unit represents 10 students

back to the ratio

who preferred science = 5

who preferred English = 4

Number of students choose Science = 5 * 10 = 50

please help!
[3 x 2⁵ - 13 x (-2)] + 2³
(-2² +3²) - 3
Give your answer in simplest form.​

Answers

Answer:

122x + 37

Step-by-step explanation:

hope this helps u

Answer:

[3×2⁵+13×2]+2³(-2²+3²)-3=

[3×32+26]+2³(-4+9)-3=

[96+26]+2³(5)-3=

122+40-3

162-3=

159...

note:-a×(-b)=+ab

I would really appreciate it if someone helped answer these 4 questions. I will rate 5 stars. Thank you (:

Answers

Answer:

7. 13.6

8. 19.5

9. 6.5

10. 12.6

Step-by-step explanation:

Recall the three main trig functions

Sine = opposite / hypotenuse

Cosine = adjacent / hypotenuse

Tangent = opposite / adjacent

( remember hypotenuse = longest side length , opposite = side length opposite of angle , and adjacent = side length thats not the opposite or hypotenuse )

We will use these to solve each problem

7.

We are given :

An angle with a measure of 39 degreesThe angles opposite side length The adjacent side as the unknown

When dealing with opposite and adjacent we use tangent

We have tan = opp / adj

==> plug in opp = 11 and adj = x as well as given angle 39

tan(39) = 11/x

==> multiply both sides by x

xtan(39) = 11

divide both sides by tan(39)

x = 11/tan(39)

plugging this into a calculator , we get x = 13.6 ( rounded )

8.

We are given :

an angle with a measure of 46 degreesthe hypotenuse which has a length of 28and the adjacent as the unknown

When dealing with adjacent and hypotenuse we use cos

We have cos = adj / hyp

==> plug in given angle 46 , adj = x and hyp = 28

cos(46) = x/28

==> multiply both sides by 28

x = 28cos(46)

plugging this into a calculator we get  x = 19.5 ( rounded )

9.

We are given :

an angle with a measure of 51 degreesits opposite side length with a length of 8 the adjacent side length as the unknown

When dealing with the opposite and adjacent we use tangent

We have tan = opp / adj

==> plug in 51 degrees for angle , opp = 8 and adj = x

tan(51) = 8/x

==> multiply both sides by x

xtan(51) = 8

==> divide both sides by tan(51)

x=8/tan51

plugging this into a calculator we get that x = 6.5 ( rounded )

10.

We are given:

an angle with a measure of 24 degreesthe hypotenuse which has a length of 31the side length opposite of given angle as the unknown

When dealing with the opposite and hypotenuse we use sine

We have sin = opp / hyp

==> plug in angle as 24 , opp = x and hyp = 31

sin(24) = x / 31

==> multiply both sides by 31

31sin(24) = x

plugging this into a calculator we get that x = 12.6 ( rounded )

And we are done!

Let me know if you have any doubts in the comments ! : )

f(x) =2x^2+4x-6. g(x)=4x^3-6x^2+3 find (f+g)(x)

Answers

Answer:

=4x³-4x²+4x-3

Step-by-step explanation:

(f+g)(x)=4x³+2x²-6x²+4x-6+3

=4x³-4x²+4x-3

Help!! Due tomorrow. x(x − 8) = 0

Answers

Answer: x = 0, 8

Step-by-step explanation:

x = 0

x - 8 = 0 ⇒ x = 8 (move 8 to the right)

x = 0, 8

X=0 or X=8 both of these answers are correct

Calvin deposits $400 in a savings account that accrues 5% interest compounded monthly. after c years, calvin has $658.80. makayla deposits $300 in a different savings account that accrues 6% interest compounded quarterly. after m years, makayla has $613.04. what is the approximate difference in the number of years that calvin and makayla have their money invested?

Answers

The approximate difference in years for Calvin and Makayla is that B. Makayla invests her money 2 years longer.

Calculations and Parameters:

Given:

Interest rate= 5%Deposit of Calvin= $400Final amount after c years= $658.80

We use the compound interest formula,

[tex]A= P(1 + r/t)^t[/tex]

[tex]658.8/400= (1205/1200)^1^2^c[/tex]

c= 10 years approx.

For Makayla,

Amount deposited= $300Interest rate= 6%Final amount= $613.4m= ?

We use the same formula:

[tex]A= P(1 + r/t)^t\\[/tex]

[tex]613.4/300= (1206/1200)^1^2^m[/tex]

m= 12 years approx.

Hence, the difference in the years would be:

12-10

= 2 years.

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Answer:

Makayla invests her money 2 years longer

Step-by-step explanation:

b on edge

If x^2+y^2=13 and xy=6 then find the value of x^4+y^4

Answers

Recall that (a + b)² = a² + 2ab + b².

Let a = x² and b = y². Then

(x² + y²)² = (x²)² + 2x²y² + (y²)²

⇒   x⁴ + y⁴ = (x² + y²)² - 2 (xy)²

Given that x² + y² = 13 and xy = 6, we have

x⁴ + y⁴ = 13² - 2×6² = 97

A principal of $3900 is invested at 7.5% interest compounded annually how much will the investment be worth after 9 years

Answers

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3900\\ r=rate\to 7.5\%\to \frac{7.5}{100}\dotfill &0.075\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &9 \end{cases} \\\\\\ A=3900\left(1+\frac{0.075}{1}\right)^{1\cdot 9}\implies A=3900(1.075)^9\implies A\approx 7477.23[/tex]

7. A triangle has an area of 20 in². If the height of the
triangle is 5 inches, find the base of the triangle.

Answers

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

in our case

baseline × 5 / 2 = 20 in²

baseline × 5 = 40

baseline = 8 in

Jenny spins a fair 4-sided spinner what is the probabiliity that the spinner will land on a or b

Answers

Answer:

Step-by-step explanation:

jenny spin a fair-4 spinner

The probability that the spinner will land on a or b will be 0.50.

What is probability?

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

Jenny spins a fair 4-sided spinner.

Let the section be marked as a, b, c, and d.

Then the total number of the event will be given as,

Total events = 4

Then the probability that the spinner will land on a or b will be given as,

P = 1/4 + 1/4

P = (1 + 1)/4

P = 2/4

P = 1/2

P = 0.50

The probability that the spinner will land on a or b will be 0.50.

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At what rate per cent per annum will rs 6000 amount to rs 6615 in two years when interest is compounded annually?

Answers

Answer: 5%

Step-by-step explanation:

[tex]6615=6000(1+r)^{2} \\ \\ 1.1025=(1+r)^{2} \\ \\ 1.05=1+r \\ \\ r=0.05=\boxed{5\%}[/tex]

Serena bought a video game on sale for $23.88. The original price was $44.69. How much
money did Serena save buying the game on sale?

Answers

Answer:

i just need points

Step-by-step explanation:

sorrry ehburbvuygvuywhefe2b yvfb we

The answer is $20.81 I used a calculator

What is the area, in square units, of the polygon shown here?

A figure in the shape of a block letter L with a vertical height of 8 units and a length of 5 units is shown. The length of the top of the L is 2 units and the height of the right side of the L is 1 unit.

14 units2

16 units2

17 units2

19 units2

Answers

The area of a 2D form is the amount of space within its perimeter. The correct option is D.

What is an area?

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

The area of the L block will be the sum of the area of A and B. Therefore, the area can be written as,

Area of L block = Area of A + Area of B

                          = (7×2) units² + (1 × 5) units²

                          = 14units² + 5units²

                          = 19units²

Hence, the correct option is D.

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If the perimeter of this triangle is 15 centimeters, what is the value of n?

Answers

The value of n from the triangle = 2.5

Calculation of perimeter of triangle

Perimeter of a triangle= a +b+c

Where,

a= n

b= 5n - 6

C= 2n + 1

P= 15

Therefore n

15 = n + 2n + 1 + 5n - 6

15 = 8n-5

8n= 15+5

8n = 20

n= 20/8

n= 2.5

Therefore, the value of n = 2.5

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Peter built a chest that measures 2 feet by 11
2
feet by 1 foot. He wants to fill the chest with plastic coins.

A prism has a length of 2 feet, height of 1 foot, and width of 1 and one-half feet.

What is the maximum amount of space that the chest can hold?
The maximum amount of space is
cubic feet.

Answers

Answer:

3

Step-by-step explanation:

got it on edge

1940 people attended a basketball game. 679 of the people attending supported the home team, while 1261 supported the visiting team. What percentage of people attending supported the home team?

Answers

Answer:

35%

Step-by-step explanation:

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

The percentage of people who supported the home team is 35%.

What is a percentage?

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

20% = 20/100 = 1/5

25% = 25/100 = 1/4

We have,

Number of people who attended the basketball game = 1940

Number of people who supported the home team = 679

Number of people who supported the visiting team = 1261

The percentage of people who supported the home team.

= [ Number of people who supported the home team / Total number of people who attended the basketball game ] x 100

= [679 / 1940] x 100

= 67900 / 1940

= 35%

Thus,

The percentage of people who supported the home team is 35%.

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What is the inverse of f(x)=x^4+7 for x>0 where function g is the inverse of function f?
-

Answers

Answer:

[tex]g(x) = \sqrt[4]{x-7},~ x\geq 7[/tex]

Step by step explanation:

[tex]y= f(x) = x^4+7\\\\\text{Replace x with y and solve for y:}\\\\~~~~~~~x = y^4 +7\\\\\implies y^4 = x-7\\\\\implies y = \pm\sqrt[4]{x-7}\\\\ \implies f^{-1}(x) = \pm\sqrt[4]{x-7}[/tex]

Solving for interior angle measures, what is the m

Answers

Using the triangle sum theorem, the value of angle ACB in the triangle is: B. 50°.

What is the Triangle Sum Theorem?

According to the triangle sum theorem, the sum of all the angles in a triangle equals 180 degrees.

90 + 7x - 20 + 4x = 180

70 + 11x = 180

11x = 180 - 70

11x = 110

11x/11 = 110/11

x = 10

m∠ACB = 7x - 20

Plug in the value of x

m∠ACB = 7(10) - 20

m∠ACB = 50° (option B).

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What is the area of a polygon with vertices of (-2,-4), (4,-4), (4, 4), and (-5, 4)?
216 square units
30 square units
120 square units
60 square units

Answers

Answer: 60 square units

Step-by-step explanation: i hope that helps buddy :)

2x(x-5) -x (3 + 2x) = 26
help me pls

Answers

Answer:

x = -2

Step-by-step explanation:

[tex]2x(x-5)-x(3+2x) = 26\\2x^{2} -10x-3x-2x^{2} = 26\\-13x=26\\x=\frac{26}{-13} \\=-2[/tex]

Its basically the order of operations, from left to right , evaluate brackets (if possible), then multiplication or division, lastly followed by addition or subtraction.

2x2-10x-3x-2x2=26

Eliminam opusele

reducem termenii

-13x=26

imparte ambele parti

x=-2

Step-by-step explanation:

please help me grades are do today

Answers

Answer:

28

Step-by-step explanation:

[tex]sin=\frac{opp}{hyp}[/tex]

[tex]cos = \frac{adj}{hyp}[/tex]

[tex]cos^{-1}\left(\frac{45}{51}\right)[/tex]

which is 28.07 degree

[tex]sin\left(28.07\right)=\frac{x}{51}[/tex]

x= 23.99

23.99+4=h=28


Enter the number that belongs in the green box.

Answers

Answer:

the green box is 0

Step-by-step explanation:

we are asked to find the x-intercept, which means y = 0

(x, y)

Another way to test this is plug it in 1 for x!  (1, y) where x = 1

[tex]y = \frac{2x^{2} -3x+1}{2x^{2} +8x+6} \\\\[/tex]

[tex]y = \frac{2(1)^{2} -3(1)+1}{2(1)^{2} +8(1)+6}[/tex]

[tex]y = \frac{2(1) -3(1)+1}{2(1) +8+6}[/tex]

[tex]y = \frac{2 - 3 + 1}{2 + 8 + 6}[/tex]

[tex]y = \frac{-1+1}{10 + 6}[/tex]

[tex]y = \frac{0}{16}[/tex]

y = 0

Question 4
1 pts
in 2013, the number of rabbits in a local park is 120, but this number is decreasing
each year by a constant percent. the number of rabbits in the park t years after 2013
can be found using the given formula. about how many rabbits will be left in the park
after 10 years?
r=120(0.99)
1,188
247
1
108

Answers

After 10 years, there will be 108 rabbits left in the park.

What is Exponential Equation?

An exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

Here, the given equation;

       R = 120 (0.99)ⁿ

where, n is the number of years

n = 10 years (given)

R = 120 (0.99)¹⁰

R = 120 X 0.904

R = 108.52

Thus, After 10 years, there will be 108 rabbits left in the park.

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What is the area of the following triangle in square meters? Do not round your answer.



A
=


m
2

Answers

The area of the triangle will be 3240 square centimeters.

What is the triangle?

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The diagram is given below.

The height of the triangle is 120 cm and the base of the triangle is 54 cm.

Then the area of the triangle will be

Area = 1 / 2 x 120 x 54

Area = 3240 square cm

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Answer:

0.324

Step-by-step explanation:

How do I solve this using Sin or Cosine law?

Answers

Those two have both two formulas but when dealing with a not-right triangle which is a particular case you use this formula for sines.

[tex]\frac{SinC}{c} =\frac{SinR}{r}[/tex]

Substitute

Note: the capital letters are for the angles and the small letter are for the sides.

But since we used side R and there is no angle to substitute. you will basically have to find it by adding the two angles given and subtracting it by 180, which is a 100.

[tex]\frac{Sin(7)}{1.9} =\frac{Sin100}{x}[/tex]

now you do the butterfly method or cross multiplication method.

[tex]xsin(7)=1.9sin(100)[/tex]

You have to isolate the x

[tex]\frac{xsin(7)}{sin(7)} =\frac{1.9sin(100)}{sin(7)}[/tex]

now cancel and plug the right side of the equation into your calculator and u get the answer for the missing side.

[tex]x= 15.35[/tex] or if u want to round it [tex]15.4[/tex]

<R = 100 and side CK= 15.35 or 15.4

Hope I helped! ^w^

TheOneAndOnlyLara~

solve. -16 < 3x + 5 < 14

Answers

Answer: -7 < x < 3

Step-by-step explanation:

-21 < 3x < 9

-7 < x < 3

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