A rectangular pool measures 5 yd by 6 yd. A concrete deck of uniform width is constructed around the pool. The deck and pool together cover an area of 72. How wide is the deck?

Answer:

1) For [tex]a = 1[/tex]: [tex]b = 6[/tex] and [tex]k = 6[/tex], 2) For [tex]a = 3[/tex]: [tex]b = 4[/tex] and [tex]k = 12[/tex]

Step-by-step explanation:

The polynomial [tex]y = x^{2} - 7\cdot x + k[/tex] is a second-order polynomial of the form [tex](x-a)\cdot (x-b) = x^{2}-(a+b)\cdot x + a\cdot b[/tex]. By direct comparison, we construct the following system of equations:

[tex]a + b = 7[/tex] (1)

[tex]a\cdot b = k[/tex] (2)

By (1) we know that there are a family of pairs such that the system of equations is satisfied. Let suppose that both [tex]a[/tex] and [tex]b[/tex] are integers. We assume two arbitrary integers for [tex]a[/tex]:

1) [tex]a = 1[/tex]

[tex]b = 7 - a[/tex]

[tex]b = 6[/tex]

[tex]a\cdot b = k[/tex]

[tex]k = (6)\cdot (1)[/tex]

[tex]k = 6[/tex]

2) [tex]a = 3[/tex]

[tex]b = 7 - a[/tex]

[tex]b = 4[/tex]

[tex]a\cdot b = k[/tex]

[tex]k = (3)\cdot (4)[/tex]

[tex]k = 12[/tex]

Answer:

Step-by-step explanation:

¿A qué se llamó feudalismo? ¿Dónde y cuándo se desarrolló?

Answer:C the students were amounting to almost nothing in theater a

Step-by-step explanation:

Answer:

36 miles

Step-by-step explanation:

18 + 18 = 36

I didn't get a lot of information so my apologies if wrong.

Answer:

Joan<18

Step-by-step explanation:

These symbols indicate the following:

< less than

> greater than

= equal to

If Joan ran less than 18 miles, you must write the inequality just as you would say it. Therefore, Joan < 18 is the correct inequality.

Answer: The probability of it is 1/6

Step-by-step explanation:

Answer:

I think its 2/2 or 1????

Answer:

96 i think

Step-by-step explanation:

I think its 96. just multiply all the sides

Answer:

The equation is y=6x

Y

Step-by-step explanation:

Answer:

37

Step-by-step explanation:

the equation is /a^2 + b^2 =c

so 12^2=144 and 35^2=1225

144+1225=1413

the square root of 1413 is equal to 37

Answer:

Supplementary!

Answer:

Complementary I believe.

correct me if I’m wrong

if not adjacent

Answer:

Step-by-step explanation:

Answer:

The object is moving at a constant speed

Step-by-step explanation:

Answer: 0.001

Step-by-step explanation:

Given

The lock has 3 dials, each with the number 0 through 9.

The first place can be filled in 10 ways and the probability of selecting number '4' out of the 10 is  [tex]\frac{1}{10}[/tex]

Similarly for selecting '3' and '9' is also [tex]\frac{1}{10}[/tex]

Therefore the probability of getting a combination of 4-3-9 is

[tex]\Rightarrow P=\dfrac{1}{10}\times \dfrac{1}{10}\times\dfrac{1}{10}\\\\\Rightarrow P=\dfrac{1}{1000}\\\\\Rightarrow P=0.001[/tex]

Answer:

The equation is [tex](x - 2)^2 + (y + 7)^2 = 9[/tex]

Step-by-step explanation:

Answer:

The total weight is 5kg

Step-by-step explanation:

Given

See attachment for box plot

Required

Determine the total weight of the kitten

First, we represent the plot in the following table where the number of dots represent the frequency.

So, we have:

[tex]Weight \to Frequency[/tex]

[tex]\frac{1}{2} \to 3[/tex]

[tex]1 \to 2[/tex]

[tex]1\frac{1}{2} \to 1[/tex]

[tex]2 \to 0[/tex]

[tex]2\frac{1}{2} \to 0[/tex]

Multiply the weight by the frequency, then add up the result

So, we have:

[tex]Total = \frac{1}{2} * 3 + 1 * 2 + 1\frac{1}{2} * 1 + 2 * 0 + 2\frac{1}{2} * 0[/tex]

[tex]Total = 1\frac{1}{2} + 2 + 1\frac{1}{2} + 0 + 0[/tex]

[tex]Total = 1\frac{1}{2} + 2 + 1\frac{1}{2}[/tex]

Express as improper fraction

[tex]Total = \frac{3}{2} + 2 + \frac{3}{2}[/tex]

Take LCM

[tex]Total = \frac{3+4+3}{2}[/tex]

[tex]Total = \frac{10}{2}[/tex]

[tex]Total = 5kg[/tex]

Answer:

x= 17/5

Step-by-step explanation:

Answer:

17/5

Step-by-step explanation:

hope this helps with the work

Answer:

A, B, and C. Not D.

Step-by-step explanation:

He wants all four colors to have equal share on the quilt which means each color needs to have 4 squares each to make up equal share of the quilt. D is the only one that doesn't follow this rule so it is the only one that is incorrect and would not work as a design.

Answer:

∠P = 21

Step-by-step explanation:

angle P is an inscribed angle and arc RQ is the arc it intercepts

The measure of an inscribed angle is equal to half the measure of the arc it intercepts.

Hence, ∠P = [tex]\frac{1}{2}[/tex] ( arc RQ )

So if arc RQ = 42°

Then ∠P = 42/2

42 / 2 = 21

Hence, ∠P = 21°

Answer:

7.1 meters

Step-by-step explanation:

Use the pythagorean theory:

10 would be the hypotenuse

7 would be one of the legs

and x (or whatever variable you'd like) would be the other leg.

7^2+x^2=10^2

49+x^2=100

subtract 49 from both sides

x^2=51

take the square root on both sides

x is approximately 7.1

Answer:

See the matching below

Step-by-step explanation:

Given data

We have two expressions to match

3 * 9 and 2x3x9

3 * 9= 9*3

3 * 9=3*(4+5)

2x3x9= (2*3)*9

2x3x9= 9*3*2

Answer:

1⅕

Step-by-step explanation:

it shows a whole box filled so that means it's a whole

the next box only has one out of five filled so it's ⅕

1⅕

Answer:

60°

Step-by-step explanation:

if you look on a unit circle the coordinates correspond to (cos, sin) so at 60° they are (1/2, √3/2)

Answer:

x=2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

➜-2x+4=0

➜-2x=-4

➜2x=4

➜x=4/2

➜x=2

Answer:

[tex]f(x) = -2x^3 -5x^2 +4x -2\\option 1 : x+2 \\f(-2) = -2(-2)^3 -5(-2)^2 +4(-2)-2 = 16 -20-8-2= -14\\\\\\option 2: x+3\\f(-3) = -2(-3)^3 -5(-3)^2 +4(-3) - 2 = 54 -45 -12-2 = -5\\\\option 3: x-2\\f(2) = -2(2)^3-5(2)^2-4(2)-2=-16 -20-8-2=-46\\\\option4 :x-3\\f(3) = -2(3)^3 - 5(3)^2-4(3)-2 = -54-45-12-2=-113\\[/tex]

option 1: x + 2

Answer: (−1,−812)

How to: Rewrite in vertex form and use this form to find the vertex ( h , k ) .

Have a great day and stay safe !

Answer:

An obtuse isosceles triangle

Step-by-step explanation:

Obtuse triangles always have one large angle that is bigger than 90 degrees and two smaller angles.

An isosceles triangle always has two sides that are the same length.

Answer:

obtuse isosceles triangle

Step-by-step explanation:

trust me bro