The length l of a rectangle is 4 inches greater than its width w. The area of the rectangle is 252 square inches.Using the method of completing the square, what are the length and width of the rectangle? Show your work.

Answers

Answer 1

l=w+4

lw=252, using l from above

(w+4)w=252

w^2+4w=252, now halve the linear coefficient, square it, then add that to both sides, ie (4/2)^2=4

w^2+4w+4=256

(w+2)^2=256

w+2=±16

w=-2±16

w=14 or 18, but since w<l

w=14in and l=18in

Related Questions

Find the equation of the linear function which passes through the points (-1, 3) and (4, -2). give your answer in y = mx + b form.

Answers

Hello : let A(-1,3) B(4,-2)
the slope is : (YB - YA)/(XB -XA)
(-2-3)/(4+1) = -1
an equation is : y=ax+b a is a slope

y = -x +b

the line through point B(4,-2) : -2 = -1(4)+b
b = 2
the equation is : y =-x+2

Solve the equation. 8d + 3d – 3d – 8 = 3d

Answers

the answer is

D = - 1.6

this is the answer simplified

Answer:

1.6

Step-by-step explanation:

Joey has a full 40 coins consisting of only quarters and nickels if the total value is $5.00 how many of each does joey have.

Answers

q + n = 40....q = 40 - n
0.25q + 0.05n = 5

0.25(40 - n) + 0.05n = 5
10 - 0.25n + 0.05n = 5
-0.25n + 0.05n = 5 - 10
- 0.20n = -5
n = -5 / -0.20
n = 25 <=== 25 nickels

q + n = 40
q + 25 = 40
q = 40 - 25
q = 15 <== 15 quarters

n=number of nickles
q=number of quarters

40 coins total so
n+q=40

total value is 500 cents
5n+25q=500
divide both sides by 5
n+5q=100

so we gots
n+q=40
n+5q=100

elimination
multily first equation by -1 and add to 2nd equation

-n-q=-40
n+5q=100 +
0n+4q=60

4q=60
divide both sides by 4
q=15

sub back
n+q=40
n+15=40
minus 15 both sides
n=25

25 nickles and 15 quarters

In pentagon ABCDE, angle A= 87, angle B=125, angle C= 63, angle D=169. Find angle E

Answers

sum of interior angle of pentagon = 540
m<E = 540 - (87+125+63+169)
m<E = 540 - 444
m<E = 96

answer
m<E = 96

Angle bisectors TX and UY triangle TUV meet at point I. Find all possible values of angleV if angleTIU = 109. As your answer, enter the number of degrees in angleV. If you find more than one possibility, list the possible values in increasing order, separated by commas.

Answers

Check the picture attached.

let m(VTI)= m(ITU)=a and let m(VUI)= m(IUT)=b

Then, in triangle TUV:

2a+2b+c=180°

2(a+b)+c=180°

c=180°-2(a+b)

In triangle TUI:

a+b+109°=180°

a+b=180°-109°=71°

substitute in c=180°-2(a+b):

c=180°-2(a+b)=180°-2*71°=180°-142°=38°

Aunt Mary is 6 times as old as Jane. If Aunt Mary is 72 years old, how old is Jane?

Answers

x = Jane's age
6x =Aunt Mary's age

6x = 72
x = 72/6
x = 12 years [Jane]

Jane is 12 years old.

Because if Mary is 6 times older than just divide her age by 6. Which is 12.

And you can check like this:
-Jane is 12
-Mary is 6 times that
-so Mary is 72

Find the dot product, a • b. a = 6i + 5j, b = -5i + 4j

Answers

If i is a normal variable: then it is -30i^2 - i*j + 20j^2

If i is the constant i, then it is 20j^2 -i*j + 30

Answer:

the answer is -10

A bicycle lock has a four-digit code. The possible digits, 0 through 9, cannot be repeated. What is the probability that the lock code will begin with the number 5? . What is the probability that the lock code will not contain the number 0? .

Answers

First let's find the number of the elements in the sample space, that is the total number of codes that can be produced.

The first digit is any of {0, 1, 2...,9}, that is 10 possibilities
the second digit is any of the remaining 9, after having picked one.
and so on...

so in total there are 10*9*8*7 = 5040 codes.

a. What is the probability that the lock code will begin with 5?

Lets fix the first number as 5. Then there are 9 possibilities for the second digit, 8 for the third on and 7 for the last digit.

Thus, there are 1*9*8*7=504 codes which start with 5.

so

P(first digit is five)=[tex] \frac{n(first -digit- is- 5)}{n(all-codes)}= \frac{1*9*8*7 }{10*9*8*7 }= \frac{1}{10}=0.1 [/tex]

b. What is the probability that the lock code will not contain the number 0?

from the set {0, 1, 2...., } we exclude 0, and we are left with {1, 2, ...9}

from which we can form in total 9*8*7*6 codes which do not contain 0.

P(codes without 0)=n(codes without 0)/n(all codes)=(9*8*7*6)/(10*9*8*7)=6/10=0.6

Answer:

0.1 ; 0.6

The probability that the lock code will begin with the number 5 is:

0.1

The probability that the lock code will not contain the number 0 is:

0.6

What is Probability?

This refers to the use of permutations to find the possible occurrence of events.

The total number of elements is 10

Hence, the total codes is 5040.

P(five)= n(first number)/n(all codes)= 1/10= 0.1

Next,

P(codes without zero)= n(codes without zero)/n(all codes)

(9*8*7*6)/(10*9*8*7)=6/10=0.6

=0.6

Read more about probability here:
https://brainly.com/question/24756209

If 3x² -6=y for all real numbers x, then x² - 2 =

Answers

3x² - 6 = 3(x² - 2)

If 3(x² - 2) = y, then
[tex] \frac{3(x^2-2)}{3}= \frac{y}{3} \\ \\ x^2-2 = \frac{y}{3} [/tex]

Answer:
x² - 2 = y/3

If 7 is added to twice a number and this sum is multiplied by 5 â, the result is the same as if the number is multiplied by 6 and 11 is added to the product. what is theâ number?

Answers

(2x+7)*5 = 6x+11

10x+35 = 6x+11

4x+35 =11

4x=-24

x=-6

the number is -6

What is the solution to this system of linear equations?

x + y = 4

x − y = 6

Answers

This is a simultaneous equation so you have to find the value of x or y. We can do this by adding the 2 equations. This would make 2x, and y + -y = nothing. 4 + 6 = 10. So we have the equation 2x = 10. Divide both sides by 2 and you get the value of x, which is 5. You then plug this into the orignal equation, either one will work. You get a value of -1 for y.
x = 5 when y = -1.

Answer:

x = 5 and y = -1

Step-by-step explanation:

[tex]x + y = 4[/tex]

[tex]x - y = 6[/tex]

To solve for x and y , we use elimination method

In the given equations, the co efficient of y are same with different coefficient

So we add both equations

[tex]x + y = 4[/tex]

[tex]x - y = 6[/tex]

--------------------------------

[tex]2x=10[/tex]

Divide both sides by 2

x= 5

now we plug in x value in first equation

[tex]5 + y = 4[/tex]

Subtract 5 on both sides

y= -1

In two or more complete sentences describe how to determine the appropriate model for the set of data, (0,2), (2,3), (5,4), (10,5).

Answers

The very first thing to do in every correlation activity is to plot the gathered data points in a scatter plot. It is better to use software tools like MS Excel because they have a feature there that uses linear regression like that one shown in the picture.

Once you plot the data points, make a trendline. You are given with options. If you want a linear function, then you will have a linear model with a function equation of y = 0.2907x + 2.2643. It has a correlation coefficient of 0.9595. That's a strong correlation already. The R² value tells how good your model fits the data points. If you want to increase the R², a better model would be a quadratic function with the equation, y = -0.0209x²+0.506x+2.0232. As you can see the R² increase even more to 0.9992.

Find the 6th term of a geometric sequence t3=444 t7=7104

Answers

Answer:

3552

Step-by-step explanation:

#27 how do I find x?

Answers

E to F is 6 F to G is x

and overall distance from e to g is 1.6x

so:

6+x = 1.6x

subtract x from each side

6 = 0.6x

now divide both sides by .6

x = 6/0.6 = 10

x = 10

What is the simplified form of the expression?

5(14 - 2)2 ÷ 2

Answers

I think you mean this:
[tex] \frac{5(14 - 2)^2}{2} = \frac{5(12)^2}{2}=\frac{5*144}{2}=5*72=360[/tex]

do 14-2 first and then you'd get 12
12 times 5 and get 60
2 divided by 2 is 1
so i broke it down for you, you should figure it out from here hope i helped

Find the measures of all of the angles in the parallelogram.

Answers

In a parallelogram, the opposite angles are equal so:
FED = DGF = 59x - 1
EDG = GFE = 121x + 1
And now since we know angles in a quadrilateral always add up to 360°, we can create an equation and solve for x:
2(59x - 1) + 2(121x + 1) = 360
118x - 2 + 242x + 2 = 360
360x = 360
x = 1
Now sub into our angle equations:
FED = DGF = 59(1) - 1 = 58°
EDG = GFE = 121(1) + 1 = 122°

The following is an arithmetic sequence.
-3, 3, -3, 3
true false

Answers

It's false, because arithmetic sequence should satisfy the following:
A(n)=a1 + d*(n-1)

So it should increase all the time linearly or decrease...

Answer: False

Rewrite using standard notation: 2.43 × 104

A: 24,300

B: 2,430

C: 2.43

D: 0.000243

Answers

24300 :) that's the answer

a basketball player has already scored 56 points in a game the team record for point a in a game is 72 which equation would allow you to find out how many more points the player needs to tie the record

Answers

One equation that would work is 56+x=72 where x is the number of points the player needs.

Answer: The player needs 16 more points to tie the record.

Step-by-step explanation:

Let the number of points the player needs to tie the record be 'x'.

Number of points that a basketball player has already scored = 56

Number of points a team need for record in a game = 72

According to question, it becomes,

[tex]x+56=72\\\\x=72-56\\\\x=16[/tex]

Hence, the player needs 16 more points to tie the record.

Using the given points, determine the slope.

(0, 32) and (100, 212)

Answers

Hi!

To find the slope of two given points, subtract the y values, and subtract the x values, or..

[tex] \frac{(y2 - y1)}{(x2 - x1)} [/tex]

[tex] \frac{(212 - 32)}{(100 - 0)} [/tex]

[tex] \frac{180}{100} [/tex]

The answer is 9/5 or 1.8.

Hope this helps! :)

The slope is the change in y divided by the change in x.

The slope is the ratio of rise to run.

so:

slope = (212-32) / (100-0) = 9/5 = 1.8

I need help with this problem

Answers

width is 11 meters and length is 22 meters

you would do 66 x 2 for how long she wants her garden fences

Rex weighed 80 pounds a year ago. Now he weighs 92 pounds. What is the percent increase in his weight?
(A)12%
(B)13%
(C)15%
(D)16%

Answers

(92-80)/80=.15
.15~15%
Answer is 15%

%change=100(final-initial)/initial

%change=100(92-80)/80

%change=1200/80

%change=15%

8. Find the congruence transformation that maps ∆ABC to ∆A’B’C’. Explain your reasoning

Answers

In this case, to flip any of the points to map up accurately to the other points, we would have to do a transformation of reflection about the y-axis. The reason behind this is that out of other transformation process, we can only achieve the image of triangle ∆A’B’C’ through reflection.

Dilation will not work since it only changes the size of the object. The shape and position will not affected.

A translation will not work because although the shape can move, it still needs to flip to achieve triangle ∆A’B’C’.

A rotation will also not work because when you rotate it, the shape will still not map over the new one.

Therefore the only answer to this question would be to reflect triangle ∆ABC about the y-axis.

Zeus Industries bought a computer for $2740. It is expected to depreciate at a rate of 24% per year. What will the value of the computer be in 3 years?

Round to the nearest penny. Do not type the "$" sign in your answer

Answers

The formula is
A=p (1-r)^t
A ?
P 2740
R 0.24
T 3years

A=2,740×(1−0.24)^(3)
A=2,740×(0.76)^(3)
A=1,202.8 round your answer to get
A=1203

What is the solution to this system of equations 2x-7=y y=2x+3

Answers

There is no solution to the system. They are parallel lines, so they never intersect.

Answer:

No solution

Step-by-step explanation:

[tex]2x-7=y[/tex]

[tex]y=2x+3[/tex]

To solve the system of equations, we use substitution method

Lets substitute the second equation y=2x+3 for y in the first equation and solve for x

[tex]2x-7=2x+3[/tex]

Lets solve for x

subtract 2x on both sides

[tex]2x-2x-7=2x-2x+3[/tex]

[tex]-7=+3[/tex] is false

So, no solution for this system of equations

Find the surface area of the figure below. Leave answer in terms of π.

A. 1060π in2
B. 1160π in2
C. 1260π in2
D. 1000π in2

Answers

The answer is D, 1000pi
Use SA=2πrh+2πr^2.
Plug in the numbers A=2π*10*40+2*π*10^2.
and you get 3141.59.
divide by Pi and you get 1000

Cylinder:
2Pi *r*h + Pi*r^2 = 2Pi*10*40 + 10^2 *Pi
= 800Pi + 100Pi = 900Pi
Cone:
Height = SQRT(26^2 - 10^2) = 24
=2Pi*r*h/3 = 160Pi
Total Surface Area is 1060Pi

A country population in 1993 was 94 million. In 1999 it was 99 million. Estimate the population in 2005 using the expoetential growth formula. Round your answer to the nearest million

Answers

First find the rate of growth
The formula is
P=Ae^rt
P 99 million
A 94 million
E constant
R rate of growth?
T time 1,999−1,993=6 years
Solve the formula for r
R=[log (p/A)÷log (e)]÷t
R=(log(99÷93)÷log(e))÷6
R=0.01

the population in 2005
P=Ae^rt
T time 2,005−1,993=12 years
P=93×e^(0.01×12)
P=105 million

10 POINTS AND BRAINLIST ANSWER TO FIRST CORRECT ANSWER

Answers

The correct answer is A

The correct answer is: [A]:
_________________________________________

Does anyone know how to do this problem? Thanks.

Answers

see picture for answer

If a and b are positive numbers such that 2b=3a, what's the value of ((a+b)/b)? I know you can plug in numbers for this, but i'm interested in solving this algebraically. Thanks.

Answers

[tex]\displaystyle 2b =3a \Rightarrow a= \frac{2b}{3} \\\\ \frac{a+b}{b}= \frac{ \frac{5b}{3} }{b} = \frac{5b}{3b} = \frac{5}{3} =1 \frac{2}{3} [/tex]

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