Mathematics High School

A rectangular deck
is 12 ft by 14 ft. When the length and width are increased by the same amount very becomes 280 squares ft. By how much were the dimensions increased ?

Answers

Answer 1
Both dimensions were increased by 127.

The other response seems more complex so probably ignore mine. I probably misinterpreted the question.

Answer 2
Original length: 14 ft. New length x + 14.
Original width: 12 ft. New width x + 12.

New area:

[tex] A = LW [/tex]  or [tex] LW = A [/tex]

[tex] (x + 14)(x + 12) = 280 [/tex]

[tex] x^2 + 14x + 12x + 168 = 280 [/tex]

[tex] x^2 + 26x - 112 = 0 [/tex]

[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]

[tex] x = \dfrac{-26 \pm \sqrt{26^2 - 4(1)(-112)}}{2(1)} [/tex]

[tex] x = \dfrac{-26 \pm \sqrt{676 + 448}}{2} [/tex]

[tex] x = \dfrac{-26 \pm \sqrt{1124}}{2} [/tex]

[tex] x = \dfrac{-26 \pm 2\sqrt{281}}{2} [/tex]

[tex] x = -13 \pm \sqrt{281} [/tex]

[tex] x \approx -29.76 [/tex]   or   [tex] x \approx 3.76 [/tex]

We discard the negative answer.

Answer:

Exact:
[tex] (-13 + \sqrt{281})~ ft [/tex]

Approximate:
[tex] 3.76 ~ft [/tex]

Related Questions

Simplify: 8x + 4 - 5

Answers

To simplify that expression you'll join like terms.

8x + 4 - 5
8x - 1
 8x + 4 -5

Calculate the sum or difference. 

Keep the sign of the number with the larger absolute value and subtract the smaller absolute value from the larger.

- ( 5 - 4 )

Subtract the numbers. 

-1

8x - 1

PLS HELP!!!!! Medal!


Joey has a beach ball with a radius of 20 cm. What volume of air will it hold when fully inflated? (Round to nearest tenth.)

A) 83.8 cm^3
B) 251.4 cm^3
C) 1676.2 cm^3
D) 33,493.3 cm^3,

Answers

The volume V of a sphere is four-thirds times pi times the radius cubed. V=4/3*Pi*Radius^3 Hence the answer is D) 33,493.3 cm^3 V = 4/3 * Pi * 20^3 = 33,493.3 cm^3

how would you do this problem

Answers

If line BC is congruent to line BD then angles C and D are also congruent
so you would set up the problem to find x as:
5x-19=2x+14
   +19      +19
____________
5x=2x+33
-2   -2
_____________
3/3x=33/3
____________
x=11
Just pug in x to the equations to solve the rest

What is the value of x?
4/5 x- 1/10= 3/10

A. 1/4
B. 8/25
C. 2/5
D.1/2

Answers

the answer is D. 1/2

a factory worker can make 14 products in 45 minutes. what is the worker's unit rate?

Answers

Divide the number of products by the time.

unit rate = (14 products)/(45 minutes) = 0.311 products/minute

Since there are 60 minutes in an hour, if you want the unit rate in products per hour, just multiply what we got above by 60.

unit rate = 18.667 products/hour
3.2 minutes per products

divide 14 by 45.0 = 3.2 r 30

hope this helps

Given the equation 2x +4 = 4x -2, select the reasoning that correctly solves for x.
A.add 2, subtract 2x, then divide by 2
B.add 2, subtract 4x, then divide by -2
C.subtract 4, subtract 2x, then divide by -2
D.subtract 4, subtracts 4x, then divide by 2.,

Answers

The correct answer is A, as you add two to both sides, giving 2x +6=4x, then subtract 2x from both sides, giving 6=2x, and then divide both sides by 2, giving 3=x.

A is the correct answer.

2x+4=4x-22x+4+2=4x-2+22x+6=4x2x-2x+6=4x-2x6/2=2x/23=x

If AB < AC < CB in triangle ABC then which of the following is true?

Angle A < Angle B < Angle C
Angle C < Angle A < Angle B
Angle C < Angle B < Angle A
Angle A < Angle C < Angle B,

Answers

 The answer would be the third option where angle C is the smallest while angle A is the largest. For example, in a 30-60-90 triangle the hypotenuse (2x) uses angles 30 and 60 which are smaller than 90. Then the smaller leg (x) uses angles 60 and 90 while the larger leg (x [tex] \sqrt{3} [/tex]) uses angles 30 and 90. I hope this helped!
Angle C < Angle B < Angle A

For this problem, the sides opposite each angle is proportional to the sine of the angle. Larger side = larger angle. So we've been given AB < AC < CB.
Side AB is opposite angle C

Side AC is opposite angle B
Side CB is opposite angle A
So
C < B < A

Now looking at the options, the third options matches, which is
Angle C < Angle B < Angle A

The other 3 options don't match and therefore are wrong.

given that an intercepted arc has length 6pi inches and a central angle is pi/3, find the radius

Answers

[tex]\bf \textit{arc's length}\\\\ s=r\theta \quad \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ ------\\ s=6\pi \\ \theta =\frac{\pi }{3} \end{cases}\implies 6\pi =r\left( \frac{\pi }{3} \right)\implies \cfrac{6\pi }{\frac{\pi }{3}}=r \\\\\\ \cfrac{6\pi }{1}\cdot \cfrac{3}{\pi }=r\implies 18=r[/tex]

Water is flowing into a 50-gallon bathtub at a rate of 2.3 gallons per minute (gpm). To the nearest minute, how long will it take to completely fill the bathtub?

A. 48 minutes
B. 22 minutes
C. 26 minutes
D. 115 minutes

Answers

It would be b. If you divide the 2

Determine how many, what type, and find the roots for f(x) = x4 + 21x2 − 100.

Answers

Answer:

Step-by-step explanation:

We will make a substitution to make our work easier (when we get there).  We also need to know that

[tex]i^2=-1[/tex]

We will use that as another substitution.  First, let's make the job of factoring a bit easier.  Here's the first substitution.  We will let

[tex]x^4=u^2[/tex]

Therefore,

[tex]x^2=u[/tex]

Now we will write the polynomial in terms of u instead of x:

[tex]f(x)=u^2+21u-100[/tex]

Solve for the values of u by setting the polynomial equal to 0 and factoring.  When you factor, you will get:

[tex](u+25)(u-4)[/tex]

But don't forget that

[tex]x^2=u[/tex]

so we have to put those back in now:

[tex](x^2+25)(x^2-4)=0[/tex]

By the Zero Product Property, either

[tex]x^2+25=0[/tex] or

[tex]x^2-4=0[/tex]

We will factor the first term.  Solving for x-squared gives us:

[tex]x^2=-25[/tex] and

x = ±√-25

which simplifies down to

x = ±√-1 × 25

we can sub in an i-squared for the -1:

x = ±√[tex]i^2*25[/tex]

The square root of i-squared is "i" and the square root of 25 is 5, so

x = ±5i

The next one is a bit easier.  If

[tex]x^2=4[/tex], then

x = ±2

You can see you have 4 solutions.  But you knew that already, since this is a 4th degree polynomial.  The types of solutions are:  2 real, 2 imaginary

Your friend wants to borrow $1,137.45 from you to pay off a credit card that charges a 14.7% APR. You agree to the loan but require your friend to pay you interest of 3.6% APR on the loan and your friend agrees.
Your friend pays you $200.00 at the end of the first month. How much goes toward the principal?

Answers

$196.59  
Let's start by calculating the interest on the first month. 1137.45 * (0.036/12) = 1137.45 * 0.003 = 3.41235 
 So at the end of the 1st month, the amount owed will be 1137.45 + 3.41 = 1140.86 
 And after the 200 payment is done, the new balance will be:
 1140.86 - 200 = 940.86 
 Meaning that the principle reduced is: 1137.45 - 940.86 = 196.59 
 We could have also gotten the amount going towards the principle by subtracting the interest from the paying like: 200 - 3.41 = 196.59

The amount that goes into the principal when friend pays you $200.00 at the end of the first month is $296.56.

How to calculate the amount?

The first interest will be:

= 1137.45 × (0.036/12)

= 3.41

The amount owed at the month end will be:

= 1137.45 + 3.41

= 1140.86

The new balance after 200 payment will be:

= 1140.86 - 200

= 940.86

Therefore, the reduction in principal will be:

= 1137.45 - 940.86

= 196.59

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(40 POINTS!)
What is the center of the circle that has a diameter whose endpoints are (-3, -5) and (-11, -7)

A. (-8, -1)
B. (-7, -6)
C. (-4, -6)

Answers

Hello there!

The center of any circle is the midpoint of the diameter.
Let's use the midpoint formula to find the midpoint of the diameter.

The midpoint of a line segments with endpoints [tex](x_1, y_2)[/tex] and [tex](x_2, y_2)[/tex] will have a midpoint of [tex]( \dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})[/tex]

Midpoint of the diameter:

[tex]( \dfrac{-3-11}{2}, \dfrac{-5-7}{2})[/tex]

[tex]=(-7, -6)[/tex]

Your answer is B. Hope this helps!

Identify the 35th term of an arithmetic sequence where a1 = -7 and a18 = 95. (2 points)
Question 1 options:

1) 203

2) 197

3) 168

4) 163,

Answers

Arithmetic sequences have the same value added repeatedly. There are 17 increments between a1 and a18 and the value changes a total of 102 (95 - -7). 102 divided by 17 shows that the value of 6 is being added each time. The 35th term is then given by a1+(35-1)*6 = -7 + 34*6 = -7 + 204 = 197.

Answer: 197

Step-by-step explanation: I took the test :)))

.Wind is related to the movement of warm and cold air masses. Which kind of heat transfer does this represent? ANSWERS: A. radiation


B. conduction


C. convection


D. absorption

Answers

C. Convection 
Explanation: Convection heat transfer creates wind because hotter, less dense air rises, while colder, more dense air moves downward. This movement of heated and cooled air is wind.

Answer:

Convection

Step-by-step explanation:

Please answer this and thank you

If DF=78, DE=5x-9, and EF=2x+10, find EF.

Answers

DE + EF = DF
5x - 9 + 2x + 10 = 78
7x+ 1 = 78
7x = 77
x = 77/7 = 11

EF = 2x + 10
EF = 2*11 + 10
EF = 22 + 10
EF = 32

Question

If DF = 78, DE = 5x-9, and EF = 2x+10, find EF.

Answer

EF = 32

MEDAL AND FAN!!


A bike was originally $240.00. The price was marked up 15%. What is the new price of the bike?,

Answers

Origina Price = $240 
Mark Up percentage = 15%
(15/100)*240
= $36
new price = $240 + $36
= $276
this is the answer
hope it helps :
first you should find that how much 15% of 240 is:
[tex] \frac{15}{100} = \frac{x}{240} \\ x = \frac{240 \times 15}{100} = \frac{3600}{100} = 36 [/tex]
15% of 240 is 36. then:
[tex]240 + 36 = 276[/tex]
the new price of the bike is $276

Question 1.1. Suppose a normal distribution has a mean of 20 and a standard deviation of 4.

A value of 26 is how many standard deviations away from the mean?
(Points : 1)
1.5

0.5

0.5

1.5



Question 2.2. Suppose a normal distribution has a mean of 20 and a standard deviation of 4.

What is the z-score of a value that is 0.52 standard deviations less than the mean?
(Points : 1)
0.52

0.13

0.13

0.52,

Answers

Answer: Question 1.1: It is 1.5 standard deviations away from the mean.

Our value of 26 is 6 units about the mean of 20. If each standard deviation is 4, we just divide 6 by 4. This gives us the number of standard deviations.

Question 2.2 The correct answer is -0.52

If we are 0.52 standard deviations below the mean, then our z-score is simply -0.52. The definition of a z-score is the number of standard deviations from the mean.

A person invested $7,200 in an account growing rate allowing money to double every 8 years. How much money would be in the account after 19 years, to the nearest dollar?

Answers

273600 in his bank account

After 19 years, the final amount is $29,936.93, to the nearest dollar.

What is the formula for exponential growth?

The formula for exponential growth:

[tex]final amount = initial amount * (rate)^(number of time periods)[/tex]

In this case, the initial amount is $7,200, the rate is 2 (since the money doubles every 8 years), and the number of time periods is 19/8=2.375 (since 19 years is 2.375 times the 8-year doubling period). Plugging these values into the formula, we get:

final amount = $7,200 * 2^2.375

The final amount is $29,936.93, to the nearest dollar.

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You've randomly surveyed some students in your science class to find the number of hours per week they study. what is the mean, based on your sample?
a.4.75 hours
b.5.05 hours
c.5.25 hours
d.5.45 hours

Answers

d. 5.45 hrs based on your sample

Answer:

D) 5.45 hours

Step-by-step explanation:

I got it correct on USATP.

Hope this helps!

From: Aug1e

Which is the graph of f(x)= square root of x

Answers

The bottom graph is the graph for the sqrt(x)!
f (x) = root (x)
 For this case what you must do is build a table with the values that the function takes when inserting a value of x.
 We have then:
 x f (x)
 1    1
 4    2
 16  4
 25  5
 36  6
 When you get a sufficient number of points, graph each orderly and see the behavior of the graph.
 Answer:
 The graph looks like in the attached image.

emily is converting 9 feet per hour into inches per minute. which conversion factor should she use

Answers

[tex] 9 \dfrac{ft}{hr} \times \dfrac{12~in}{ft} \times \dfrac{hr}{60~min} = [/tex]

[tex] = 9 \dfrac{ft}{hr} \times \dfrac{12~in \times hr}{60~ft \times min} [/tex]

[tex] = 9 \dfrac{ft}{hr} \times \dfrac{1~in \times hr}{5~ft \times min} [/tex]

The conversion factor is 1/5.



Which are the roots of the quadratic function f(b) = b2 – 75? Check all that apply.Which are the roots of the quadratic function f(b) = b2 – 75?

Answers

For this case, what we must do is equal the function to zero:
 b ^ 2 - 75 = 0
 From here, we clear the value of b. We have then:
 b = + / - root (75)
 We rewrite:
 b = + / - root (3 * 25)
 b = + / - 5 * root (3)
 So, the roots are:
 b1 = 5 * root (3)
 b2 = -5 * root (3)
 Answer:
 The roots of the quadratic function are: 
 b1 = 5 * root (3)
 b2 = -5 * root (3)

What is n -7_> 2. ( p.s. that’s a greater than equal to sign_>)

Answers

n - 7 ≥ 2
add 7 to both sides
n ≥ 2 + 7
n ≥ 9

ANSWER: n ≥ 9

Hope this helps! :)

It takes Susan 3 hours to fix 2 broken cars and it takes Joseph 4 hours to fix 3 broken cars. If they work together how long will it take them to fix 17 broken cars?

Answers

combined rates

Susan = 2 car / 3 hr
= 2/3

Joe = 3 car / 4 hr
= 3/4

add the rates to get the new combined rate as 17 cars in "t" hours.

2/3 + 3/4 = 17/t

Need common denominator

2/3(4/4) + 3/4(3/3) = 17/t

8/12 + 9/12 = 17/t

17/12 = 17/t

see that "t" is 12 hours
Final answer:

Susan and Joseph can fix 17 broken cars together in 12 hours.

Explanation:

To calculate the time it takes for Susan and Joseph to fix 17 broken cars together, we can calculate their individual rates of work.



Susan takes 3 hours to fix 2 cars, so her rate is 2/3 cars per hour.



Joseph takes 4 hours to fix 3 cars, so his rate is 3/4 cars per hour.



When they work together, their rates are additive. So their combined rate is (2/3 + 3/4) cars per hour. This is equal to (8/12 + 9/12) cars per hour, which simplifies to 17/12 cars per hour.



To find the time it takes to fix 17 cars, we can divide the number of cars by the combined rate: 17 cars / (17/12 cars per hour) = 12 hours.

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The population of wild horses on a wildlife refuge decreased from 110 to 99 in a year. If this trend were to continue, what exponential equation could be used to predict the horse population in the future?
y = 110(1.1)^x
y = 99(0.9)^x
y = 99(1.1)^x
y = 110(0.9)^x,

Answers

The exponential equation for this situation is y = 110(0.9) ^x. This is because 110 is the principal or the initial number of horses and y is the resultant population after a certain number of years X with a rate of 0.9.  Note that the rate is less than 1 which means that the population is decreasing as time goes by.

Answer:

The person is right.

Step-by-step explanation:

Look at his profile.

Simplify each expression. Use positive exponents.
m^3 n^-6 p^0

Answers

m^3 is the first one
1/n^6 is the second one
1 is the third answer

The infinite sequence 1, 6, 15, 28, 45, ... exhibits which pattern? multiply the term number by 2, subtract 1 from the result, multiply by the term number, and divide the result by 2. multiply the term number by 2, multiply the result by the term number, subtract 1, and divide the result by 2. multiply the term number by 2, subtract 1 from the result, multiply by 2 times the term number, and divide the result by 2. multiply the term number by 2, multiply the result by 2 times the term number, subtract 1, and divide the result by 2.

Answers

the correct response is ;
multiply the term number by 2, subtract 1 from the result, multiply by 2 times the term number, and divide the result by 2.
if term number is x,
the number in the pattern for xth term is ;
multiply term number by 2 - 2x
subtract 1 - 2x - 1
multiply by 2 times the term number - (2x-1) * 2x
divide by 2 - ((2x-1) * 2x)/2
so first term x=1
((2*1-1) * 2*1)/2
2/2 = 1
second term x = 2
((2*2-1) * 2*2)/2
(3*4)/2 = 6
third term x = 3
((2*3-1) * 2*3)/2
5*6/2 = 15
fourth term  x= 4
((2*4-1) * 2*4)/2
56/2 = 28
Therefore the above response shows the correct pattern
These are so-called  Hexagonal numbers. The general formula for the n-th hexagonal number is:
[tex]h_n=2n^2-n [/tex]
[tex] h_n=\frac{2n(2n-1)}{2}[/tex]
Let's compute a couple of them:
[tex]h_1=2(1)^2-1=1\\ h_2=2(2)^2-2=8-2=6\\ h_3=2(3)^2-3=18-3=15\\ h_4=2(4)^2-4=32-4=28\\ h_5=2(5)^2-5=50-5=45\\ [/tex]
Indeed this is our pattern.
The answer is:
multiply the term number by 2, subtract 1 from the result, multiply by 2 times the term number, and divide the result by 2.

What are the coordinates for this graph!

Answers

the correct answer is (2,4)
(2,4)? It has to be because 2 is on the x-axis and 4 is on the y-axis

I need help with this question

Answers

The area of each triangular face is
.. A = (1/2)*b*h
.. Aside = (1/2)*(6 cm)*(5 cm) = 15 cm^2

The area of the triangular base is
.. Abase = ((√3)/4)*s^2 = (√3)/4*(6 cm)^2 = 9√3 cm^2

The total surface area is the base area plus the area of the three sides.
.. Atotal = Abase + 3*Aside
.. = 9√3 cm^2 +3*15 cm^2
.. = (45 +9√3) cm^2
.. ≈ 60.6 cm^2


Actually, there's an error in the picture. The height of the side should be 4, and the length of the edge should be 5. Making that adjustment, the total area is 51.6 cm^2.

It is hard to tell what is intended. Not all answers are showing, so we can't "reverse-engineer" the problem from the answers.

HURRY!!! PLEASE
Which equation represents a direct variation?

y = 2x
y = x + 4
y =1/2x
y = 3/x

Answers

The answer is y = x + 4 because both x and y are being multiplied by the same thing.  They both have a coefficient of 1.  When ever the same number is being multiplied or divided by both x and y, it is considered a direct variation.  This means the coefficients would be the same.

Answer:

A. [tex]y=2x[/tex]

Step-by-step explanation:

We are asked to find the equation that represents a direct variation.

We know that a direct variation is in form [tex]y=kx[/tex], where y is directly proportional to x and k is constant of variation.

Upon looking at our given choices, we can see that equation [tex]y=2x[/tex] represents direct variation, where [tex]k=2[/tex].

Therefore, option A is the correct choice.

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