Mathematics College

A rectangular deck is 12 ft by 14 ft. When the length and width are increased by the same amount, the area becomes 288 sq. ft. By how much were the dimensions increased?
2 ft
4 ft
8 ft
10 ft

Answers

Answer 1
To solve this problem you must apply the proccedure shown below:

 1. You have the following information given in the problem above:

 - The rectangular deck has the following dimensions: 12 ft by 14 ft.
 - When the length and width are increased by the same amount, the area becomes 288 ft².

 2. Therefore, you have:

 A=bxh

 288=(12x)(14x)
 288=168x²

 3. When you clear the x, you obtain:

 x=√288/168
 x=(2√21)/7≈1.31
 
Answer 2

Answer:

4 ft option (c)

Step-by-step explanation:

Length of a rectangular deck = 12 ft.

width of rectangular deck= 14 ft.

let the length and width are increased by the x ft.

New length = (12 + x) ft  

New width = (14+ x) ft.

area of rectangular width = length × width

according to the question

(12+x)(14+x) = 288

168+[tex]x^{2}[/tex]=+14x+12x = 288

[tex]x^{2}[/tex]+26x = 228-168

[tex]x^{2}[/tex]+26x-120=0

[tex]x^{2}[/tex]+ 30x-4x-120=0

x(x+30)-4x(x+30)

x=4 or x=-30

x=-30 is rejected

Hence, the length and width are increased by the 4 ft.

Related Questions

Name all numbers between 67 and 113 that are a multiple of 4, 9 and 12.

Answers

There are only 2 possbile answers: 72 and 108.
Hello!

I believe that there are 2 number that are in between the given numbers and are multiples of 4, 9, and 12. The numbers are...
72 and 108.

You can find these numbers by counting by the given one digit numbers
For example...

9, 18, 27, 36, 45, 54, 63, 72
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30..., 68, 70, 72

You can do the same for 108 as well

9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72..., 104, 108
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30..., 100, 102, 104, 106, 108

I hope this helps!

In the equation 6x − 2 = −4x + 2, Spencer claims that the first step is to add 4x to both sides. Jeremiah claims that the first step is to subtract 6x from both sides. Who is correct? Explain

Answers

6x - 2 = -4x + 2
Spencer: 6x - 2 = -4x + 2       /+4x6x - 2 + 4x = -4x + 2 + 4x10x - 2 = 2
Jeremiah:6x - 2 = -4x + 2      /-6x6x - 2 - 6x = -4x + 2 - 6x-2 = -10x + 2
They both are correct. But in Jeremiah's version of solving the equation, we would have to multiply equation by -1, which we don't have to do in the Spencer's version.
Source: Brainly.com 

Sample Response: Both are correct. As long as inverse operations and the properties of equality are used properly, both methods will generate the same solution. They both isolate the variable on one side of the equation.

perimeter and circumference 9-1

Answers

Not sure what you mean by that?

The length of the major axis of the ellipse below is 14, and the length of the red line segment is 3. how long is the blue line segment?

Answers

Apex the answer is 11.

The length of the blue line segment is 11 units.

What is relation between sum of the distance of a point from the focus of ellipse and the length of major axis?

For any point P on an ellipse, the sum of the distances from P to the two foci is equal to the length of the major axis of the ellipse. This is known as the "distance property" of an ellipse.

To see why this is true, consider an ellipse with foci F₁ and F₂ and major axis length 2a. Let P be any point on the ellipse, and let D₁ and D₂ be the distances from P to F₁ and F₂, respectively. Then, by definition of an ellipse, we know that:

D₁+ D₂ = 2a

Given that,

Two line segments

Red segments of length = 3 unit

So from the definition we know that,

The sum of segments = the length of major axis

The length of major axis  =  2a

2a  = D₁+ D₂

14=  3 + D₂

D₂ =  11

Therefore, the length of the blue line segment is 11 units.

To know more about ellipse here:

brainly.com/question/19507943.

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Sally bought a car for 35000 in 2017. If the car loses 5.5% semiannually, what will the value of the value of the car be at the end of 2025

Answers

The value of the year at the end of 2025 will be given by:
A=P(1+r/100)^n
where:
A=future value
P=principle
r=rate
n=number of terms
hence for the data given;
p=35000
R=5.5
n=(2025-2017)*2=16
Thus
A=35000(1+5.5/100)^16
A=$82, 434. 20

9(T - 1) = 6(T + 2) - T

T = ?

Answers

9(T-1)=6(T+2)-T
9T-9=6T+12-T
9T-9=5T+12
4T-9=12
4T=21
T=5.25
but the equation is wrong 
i think that answer is T=5.25

a + 5=5a +5
[tex]a + 5 = 5a + 5 = [/tex]

Answers

First, let's isolate the a on the left side by subtracting both sides by 5:
a = 5a
Now subtract both  sides by a:
4a = 0
a = 0

find the circumference of a circle with an area of 254.47 square inches

Answers

circumference is 56.55in

A circle with an area of 254.47 square inches is given.

We have to determine the circumference of the circle.

Since, Area of circle = [tex] \Pi r^{2} [/tex] where r is the radius of the circle.

[tex] \Pi r^{2}=254.47 [/tex]

[tex] \frac{22}{7} \times r^{2}=254.47 [/tex]

[tex] r^{2}=\frac{254.47 \times 7}{22} [/tex]

[tex] r^{2}=80.97 [/tex]

[tex] r=\sqrt{80.97} [/tex]

r = 8.99

Therefore, r = 9 inches (approximately)

Circumference of a circle = [tex] 2\Pi r [/tex]

= [tex] 2 \times \frac{22}{7} \times 9 [/tex]

= 56.57 inches

= 56.6 inches (approximately).

Therefore, the circumference of the circle is 56.6 inches.

A store sells 48 count packages of Snickers candy bars for $27.50 per package, and 36 count packages of KitKat bars for $21.50 per package. Mrs. Sweettooth bought total of 204 Snickers and KitKat bars in the store and paid $119.50. How many of each candy bars did she buy?

Answers

Final answer:

To find out how many Snickers and KitKat bars Mrs. Sweettooth bought, we can solve a system of equations using the count and cost information.

Explanation:

Let's assume that Mrs. Sweettooth bought x packages of Snickers and y packages of KitKat bars.

From the given information, we can set up two equations:

48x + 36y = 204 (equation 1) - representing the total count of candy bars27.50x + 21.50y = 119.50 (equation 2) - representing the total cost of the candy bars

To solve this system of equations, we can use a method called substitution:

Rearrange equation 1 to solve for x: x = (204 - 36y)/48Substitute the value of x in equation 2: 27.50[(204 - 36y)/48] + 21.50y = 119.50Simplify and solve for yOnce y is found, substitute its value back into equation 1 to find the value of x

By solving this system of equations, we can determine the number of Snickers and KitKat bars that Mrs. Sweettooth bought.

Suppose a1=2,an+1=12(an+2an). assuming an has a limit, find limn→∞an= . hint: let a=limn→∞. then, since an+1=12(an+2an), we have a=12(a+2a). now solve for
a.

Answers

Looks like the sequence might be

[tex]a_{n+1}=\dfrac{a_n+\frac2{a_n}}2[/tex]

Assume that [tex]\displaystyle\lim_{n\to\infty}a_n=L[/tex]. Then taking the limit of both sides, we have

[tex]L=\dfrac{L+\frac2L}2\implies L=\pm\sqrt2[/tex]

But in order for the sequence to converge, only one of these values must be true. Since [tex]a(1)=2>0[/tex], each successive number will also be positive, so the limit must be [tex]L=\sqrt2[/tex].
Final answer:

The limit of the sequence defined by an+1=1/2*(an+2an), as n approaches infinity, is 0. This is determined by setting a = limn→∞an and solving for 'a' in the equation a=1/2*(a+2a).

Explanation:

This question is about calculating the limit of a sequence, where the sequence, denoted as {an}, is defined recursively with a given formula, an+1=1/2*(an+2an).

To calculate the limit as n approaches infinity (limn→∞an), we first suppose a is this limit. This means as n grows very large, the values of an and an+1 converge to 'a'. Hence we can write the recursive formula of the sequence in terms of 'a': a=1/2*(a+2a).

By simplifying the equation, we get: a = 1/2 * (3a). This implies that 2a = 3a, and thus 'a' must be 0.

Therefore, the limit of the sequence as n tends to infinity is 0.

Learn more about Limit of a sequence here:

https://brainly.com/question/34548995

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I need yo help B, on dis question

Answers

For this case we can use the law of the sine to solve the problem.
 We have then:
 [tex]5 / sine (68) = 5 / sine (x) [/tex]
 From here, we clear the value of x.
 We have then:
 [tex]sine (x) = (5/5) * (sine (68)) [/tex]
 Rewriting we have:
 [tex]sine (x) = (1) * (sine (68)) sine (x) = sine (68) x = arcsine (sine (68)) x = 68[/tex]
 Answer:
 The angle R is given by:
 x = 68 degrees
 option B

Answer:

b

Step-by-step explanation:

PLZ HELP ASAP TANGENTS OF CIRCLES WORD PROBLEMS

Answers

AC and AB are tangents to circle O, meaning that the angles C and B are right angles of 90 degrees. Since a quadrilateral's internal angles must sum up to 360 degrees, this means that A + B + C + O = 360
70 + 90 + 90 + O = 360
O = 110 degrees.

At one​ store, Julia saved ​$10 with a coupon for 40​% off her total purchase. At another​ store, the ​$29 she spent on books is 58​% of her total bill. How much did Julia spend in all at the two​ stores?

Answers

Let "a" and "b" represent the values of the first and second purchases, respectively.
  0.40*(original price of "a") = $10
  (original price of "a") = $10/0.40 = $25.00 . . . . divide by 0.40 and evaluate
  a = (original price of "a") - $10 . . . . . . Julia paid the price after the discount
  a = $25.00 -10.00 = $15.00

At the other store,
  $29 = 0.58b
  $29/0.58 = b = $50 . . . . . . . divide by the coefficient of b and evaluate

Then Julia's total spending is
  a + b = $15.00 +50.00 = $65.00

Julia spent $65 in all at the two stores.

Hey can you please help me posted picture of question

Answers

Answer: Option B. 1/2
A simple event is the one which has only one possible outcomes, hence such an event does not involve addition or multiplication of probabilites.

The option B gives only such a probability which can represent a simple event. The rest of the options belong to the compound events as they are sum or product of probabilities.

So, the correct answer is option B

Q #6 in the figure A B || C D Find the measure ГGEB

Answers

Angle GEB is correspondent with the angle of 50°, and since the lines AB and CD are parallels, these angles must be congrunets, then
Answer: Second option 50°

the answer is b hoped i helped

how much interest is earned on 2,700 in one year if it is invested at 3%?
a. $8.10
b.$81.00
c.$810.00

Answers

It is $81.00, $2700 * .03 = 81

Suppose the entering freshmen at a certain college have a mean combined application test score of 1225​, with a standard deviation of 120. in the first​ semester, these students attained a mean gpa of 2.64​, with a standard deviation of 0.58. a scatterplot showed the association to be reasonable​ linear, and the correlation between application test score and gpa was 0.44. what combined test score would you predict for a freshmen who attained a​ first-semester gpa of 2.9​?suppose the entering freshmen at a certain college have a mean combined application test score of 1225​, with a standard deviation of 120. in the first​ semester, these students attained a mean gpa of 2.64​, with a standard deviation of 0.58. a scatterplot showed the association to be reasonable​ linear, and the correlation between application test score and gpa was 0.44. what combined test score would you predict for a freshmen who attained a​ first-semester gpa of 2.9​?

Answers

The enrollees of a particular university have an average application test score of 1225 with a standard deviation of 120. In the first semester, the average number of students was 2.64, the standard deviation was 0.58. The scatter plot showed that it was rational linear and the correlation between application test score and gpa was 0.44. Predictive test score for freshmen who achieved the first sem

Using the correlation coefficient, mean test scores, and mean GPA, we can predict that a freshman with a GPA of 2.9 would have an approximate combined test score of 1260.71.

Since we know the mean combined application test score is 1225, the standard deviation is 120, the mean GPA is 2.64, and the standard deviation for GPA is 0.58, we can use this information to predict scores.

First, we will use the correlation coefficient (r), which in this case is 0.44, to calculate the slope (b) of the best-fit line. The slope (b) is calculated by dividing the product of the standard deviations by the mean test score, and then multiplying by the correlation coefficient.

b = r * (Sy / Sx)
b = 0.44 * (0.58 / 120)
b = 0.44 * 0.0048333
b ≈ 0.0021

Next, we need to find the intercept (a) of the best-fit line, which can be calculated using the means of the two variables (mean test score and mean GPA).

a = mean of GPA - b * mean of test scores
a = 2.64 - 0.0021 * 1225
a ≈ 0.10

With the slope (b) and the intercept (a), we can now predict the combined test score for a student with a GPA of 2.9.

Predicted Test Score = a + b * GPA
Predicted Test Score = 0.10 + 0.0021 * 2.9
Predicted Test Score ≈ 1260.71

Thus, for a freshman with a first-semester GPA of 2.9, the predicted combined test score would be approximately 1260.71.

Distributive Property: 2(5c-7)=1

Answers

The formula for distributive property is:

a(b + c) = ab + ac

Steps:

so, 2(5c - 7) = 1

1.) 2(5c) - 2(7) = 1

10c - 14 = 1

2.) Add 14 to both sides:

10c - 14 + 14 = 1 + 14

3.) Simplify:

10c = 15

4.) Then, divide both sides by 10:

10c/10 = 15/10

5.) Simplify:

c = 3/2  
is the answer.



Hope this helped you solve this question!!!

~Shane

Good Luck! Hope this helps! <3

find the product of 9x^2+2x-7

Answers

To solve the problem you must apply the proccedure shown below:

 1. You have the following quadratic equation given in the problem:

 9x^2+2x-7=0

 2. When you factor it, you obtain:

 (9x-7)(x+1)=0

 3. Then, you have that the roots of the quadratic equation are:

 (9x-7)(x+1)=0
 x1=7/9
 x2=-1
 

Suppose that a test is standardized (normally distributed) with a mean of 75 and a standard deviation of 11. what is the probability that an individual will have a test score greater than 80

Answers

p(x > 80) ≈ 32.47%

A suitable calculator can help you figure this.

if the leg of a right triangle are 3 ft and the 4ft the length of the hypotenuse is

Answers

Since the triangle is a right triangle, you can use the Pythagorean Theorem to find the length of the hypotenuse.
The Pythagorean Theorem: a² + b² = c², where c is the hypotenuse of the triangle.

Plug in the leg lengths and solve.

    a² + b² = c²
    3² + 4² = c²
    9 + 16 = c²
          25 = c²
            5 = c

Answer:
The length of the hypotenuse is 5 ft.
The hypotenuse would be 5 because it is one of the Pythagoream Theorem triplets. 

The number of cartoons watched on saturday mornings by students in mrs. kelly's first grade class is shown below. number of cartoons watched x 0 1 2 3 4 5 probability p(x) 0.15 0.20 0.30 0.10 0.20 0.05 what is the mean of the data?
a.1.37
b.2.15
c.1.89
d.1.18

Answers

The mean is the sum of the products of x and p(x). That is
     [tex]\mu =\sum \left(x\cdot p\left(x\right)\right)[/tex]

     [tex]\mu =0\left(0.15\right)+1\left(0.20\right)+2\left(0.30\right)+3\left(0.10\right)+4\left(0.20\right)+5\left(0.05\right)[/tex]

     [tex]\mu =2.15[/tex]

The mean is 2.15.

How can I derive the first equation to get the second equation?

Answers

keeping in mind that "R" and "r" are constants whilst "s" is a variable and θ is a function in terms of "s", thus

[tex]\bf s^2=R^2+r^2-2Rrcos(\theta )\implies 2s^1=0+0-2Rr\left[ \stackrel{chain~rule}{-sin(\theta )\cfrac{d\theta }{ds}} \right] \\\\\\ 2s=2Rrsin(\theta )\cfrac{d\theta }{ds}\implies 2s=\cfrac{2Rrsin(\theta )d\theta }{ds}\implies \cfrac{2s\cdot ds}{2Rr}=sin(\theta )d\theta \\\\\\ \cfrac{s\cdot ds}{Rr}=sin(\theta )d\theta[/tex]
Final answer:

To derive the second equation from the first equation, you can substitute the expression for the unknown in terms of the other known variables. This reduces the equation to one unknown.

Explanation:

To derive the second equation from the first equation, you need to substitute the expression for T₂ in terms of T₁. This will reduce the unknowns in the equation to one. Here are the steps:

Start with the equilibrium equation for the problem.Substitute the expression for T₂ in terms of T₁ into the equation.This will eliminate one unknown and result in a new equation with only one unknown left.

Find the length of each hypotenuse such that KMN = LMN

Answers

If triangle KMN is congruent with triangle LMN, then:
1) KM must be congruent with LM→KM=LM→
x+2y=3x-y→x+2y-x-2y=3x-y-x-2y→0=2x-3y→2x-3y=0   (1)

2) KN must be congruent with LN→KN=LN→
5x+3y=8x-7→5x+3y-5x-3y+7=8x-7-5x-3y+7→7=3x-3y→3x-3y=7  (1)

We have a system of two equations and two unkowns:
(1) 2x-3y=0
(2) 3x-3y=7

Subtracting equation (1) from equation (2)
(3x-3y)-(2x-3y)=7-0
3x-3y-2x+3y=7
x=7

Replacing x=7 in equation (1)
(1) 2x-3y=0→2(7)-3y=0→14-3y=0→
14-3y+3y=0+3y→14=3y→14/3=3y/3→14/3=y→y=14/3

The length of the hypotenuse is:
KN=5x+3y=5(7)+3(14/3)=35+14→KN=49
or
LN=8x-7=8(7)-7=56-7→LN=49

Answer: Option C. 49


hey can you please help me posted picture of question

Answers

When a number is added to or subtracted from a function it moves it vertically up or down.

G(x) is obtained by subtracting 3 from F(x). This means G(x) is obtained by vertical translation of F(x). Since 3 is subtracted from F(x), the vertical translation is downwards.

So, we can say: G(x) is obtained by moving F(x) 3 units vertically down.

Therefore, the correct answer is option D

The access code for a car's security system consists of four digits. the first digit cannot be zero or one and the last digit must be even. how many different codes are available?

Answers

There are a total of 10,000 four-digit combinations using the numbers 0 to 9, assuming that 0 is allowed as the first digit and repetition of digits is allowed. So if you must remove 1 and 0 being the first and only even for the last digit then there are

what has to be added to the sum of 2/3 & 3/2 to get 3? give answer as whole number or fraction <question 10 in the image>

Answers

Be x that has to be added to the sum of 2/3 and 3/2
(2/3+3/2)+x=3

Solving for x:
(2*2+3*3)/6+x=3
(4+9)/6+x=3
13/6+x=3
13/6+x-13/6=3-13/6
x=(6*3-13)/6
x=(18-13)/6
x=5/6

Answer: 5/6 has to be added to the sum of 2/3 and 3/2 to get 3

20 points! plz help me

Answers

2a + 3 + a = 180
      - 3           - 3

2a + a = 177

3a = 177
----    ----   =   59
 3       3

59 is a.

What is the volume of a rectangular prism with the dimensions: L = 1 in, W = 3/4 in, and H = 1/2in. V = LWH.

Answers

The volume of a rectangular prism is the product of the length, width, and height.

V = LWH

V = (1 in.)(3/4 in.)(1/2 in.) = 3/8 in.^3 = 0.375 in.^3

Hey can you please help me posted picture of question

Answers

c because there are 7 days in a week and Monday is one of them
It should be C). 1/7. Because there are 7 days in a week and if all the days were equally just as likely to have the solstice happen, Monday is 1 day out of a 7-day week, hence, 1/7!
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