Solve the following word problem
The width of a rectangular parking lot is 20 meters less than the length. The perimeter is 200
meters. Find the length and the width.

Answer:

The nth term for the given sequence can be written as:

[tex]a_n=6\,n+1[/tex]

Step-by-step explanation:

Notice that this arithmetic sequence is created by adding to each term a common difference of 6 units:

7 + 6 = 13

13 + 6 = 19

19 + 6 = 25

Then, using the general expression for the nth term of an arithmetic sequence of first term "[tex]a_1[/tex]"  and common difference "d" we can write the nth term as:

[tex]a_n=a_1+(n-1)\,d[/tex]

which in this case translates as:

[tex]a_n=a_1+(n-1)\,d= 7\,+(n-1)\,6=7+6\,n-6=6\,n+1[/tex]

Answer:

Step-by-step explanation:

7,  13,  19,   25, .......

Arithmetic sequence.

First term = a = 7

Common difference = d = second term -  first term

            d = 13 - 7 = 6

nth term [tex]a_{n}=a+(n-1)d\\[/tex]

[tex]a_{n} = 7 +(n-1)*6\\\\\\a_{n}=7 + 6n - 6\\\\\\a_{n} = 1 + 6n[/tex]

1)Option B is the correct option.

231

2)Option A is the correct option.

6336

3)Option B is the correct option.

307 (not sure)

Answer:

3

Step-by-step explanation:

[tex]3+11t-9u\\\\\rightarrow\boxed{t = 9; u = 11}\\\\3+11(9)-9(11)\\\\3+99-99\\\\102-99\\\\\boxed{3}[/tex]

Hope this helps.

Answer: a. y=5

b. RS = 37 ,  ST =16 and RT = 53 .

Step-by-step explanation:

Given: On number line we have,

RS = 7y + 2, ST = 2y +6, and RT = 13y - 12.

a. Since its on number line so we have

RT = RS+ ST

i.e. 13y - 12 = (7y + 2) + ( 2y +6)

⇒ 13y - 12 = 7y + 2 + 2y +6

⇒  13y-12 = 9y+8

⇒    13y-9y = 8+ 12   [Subtract 9y from both sides and add 12 in both sides]

⇒    4y = 20

⇒  y= 5  [Divide both sides by 4 ]

b. Now ,  RS = 7(5) + 2 = 35+2= 37,

ST = 2y +6 = 2 (5)+6 = 10+6 =16,

and RT = 13y - 12  = 13 (5)-12 = 65-12 = 53.

Hence, RS = 37 ,  ST =16 and RT = 53 .

Answer:

2 < x < 3

Step-by-step explanation:

4x - 4 < 8    AND    9x + 5 > 23

4x < 12  AND   9x > 18

x < 3 AND x > 2 so the answer is 2 < x < 3.

  Solve  :    9x-28 = 0

Add  28  to both sides of the equation :

                     9x = 28

Divide both sides of the equation by 9:

                    x = 28/9 = 3.111

Answer:

Quadrant I

Step-by-step explanation:

Reflection is a type of solid transformation in which an object or a point is flipped with respect to a reference point or plane to produce its image. It changes the orientation of an object, but not its shape and size.

Reflecting the point X across x-axis produces an image in quadrant II. Now, reflecting it across the y-axis would fix its image now in quadrant I.

Therefore, reflecting point X across the x-axis and then y-axis would produce its image in quadrant I.

Correct Question : The sum of squares of two consecutive positive odd numbers is 514. Find the numbers.

[tex]\rule{130}1[/tex]

Solution :

Let the two consecutive positive odd numbers be x and (x + 2)

[tex]\rule{130}1[/tex]

☯ [tex]\underline{\boldsymbol{According\: to \:the\: Question\:now :}}[/tex]

[tex]:\implies\sf x^2 + (x + 2)^{2} = 514 \\\\\\:\implies\sf x^2 + x^2 + 4x + 4 = 514\\\\\\:\implies\sf 2x^2 + 4x + 4 = 514 \\\\\\:\implies\sf 2x^2 + 4x = 514 - 4\\\\\\:\implies\sf 2x^2 + 4x = 510 \\\\\\:\implies\sf 2x^2 + 4x - 510 = 0\\\\\\:\implies\sf x^2 + 2x - 255 = 0 \:\:\:\:\:\Bigg\lgroup \bf{Dividing\:by\:2}\Bigg\rgroup\\\\\\:\implies\sf x^2 + 17x - 15x - 255 = 0\\\\\\:\implies\sf x(x + 17) - 15(x + 17) = 0\\\\\\:\implies\sf (x + 17) (x - 15)\\\\\\:\implies\sf x = - 17\:or\:x = 15\\\\\\:\implies\underline{\boxed {\sf x = 15}}\:\:\:\:\:\Bigg\lgroup \bf{Positive\:odd\: number}\Bigg\rgroup[/tex]

When,

[tex]\bullet\: \textsf {x = } \textbf {15} [/tex]

[tex]\bullet\: \sf x + 2 = 15 + 2 =\textbf{ 17} [/tex]

[tex]\therefore\:\underline{\textsf{The required positive integer is \textbf{15 and 17}}}.[/tex]

Step-by-step explanation:

According to rules of Proportionality :

[tex]a = k \frac{b}{ {c}^{2} } [/tex]

(A) When (a = 10, b = 8, c = 2)

K = 5

(B) When (b = 20, c = 5)

[tex]a = 5 \times \frac{20}{25} = 4[/tex]

Answer:

It would be 5.

Step-by-step explanation:

3 - 5 is -2, because it goes like this:

-5  -4  -3  -2  -1  0  1  2  3  4  5 (just count down)

Answer:

-10

Step-by-step explanation:

imma be honest all i do is put in different numbers until it is right. But the way to do it is subract 2 by puting it under the negative 3 and you get -5. then multiply the 2 by putting it under the -5. you get -10. and the answer will read r = -10. Therefore r is -10

Answer:

I’m sorry I thought I saw a positive 3, The correct answer would be -10.

Answer:

-30x +20

Step-by-step explanation:

-5(6x-4)

Distribute

-5*6x -5*-4

-30x +20

Answer:

-30x + 20

Step-by-step explanation:

I think you need to expand the brackets

you will need to times -5 with 6x

then times -5 with -4

Answer:

A.) 16.75

Step-by-step explanation:

First, find the volume of each mold:

[tex]Cylinder_{volume}[/tex] = πr²h

Where,

π = 3.14

r = 2 in

h = 4 in

[tex]Cylinder_{volume} = 3.14*2^2*4 = 50.24 in^3[/tex]

[tex]Sphere_{volume}[/tex] = ⁴/3πr³

Where,

π = 3.14

r = 2 in

[tex]Sphere_{volume} = \frac{4}{3}*3.14*2^3 = 33.49 in^2[/tex]

Approximate difference in the amount of wax needed = 50.24 - 33.49 = 16.75 in^3

Answer:

A

Step-by-step explanation:

"Former" means "past", more or less. So he used to be a camper.

Antonym means the opposite.

I would say "future" is more opposite than "past", but "current" works as well too.

Answer:

it's A

Step-by-step explanation:

[tex]6x-3y=36\\\\-3y=36-6x\\\\y=\frac{36-6x}{-3} \\\\y=\frac{36}{-3}-\frac{6x}{-3}\\\\ y=-12 +2x \\ OR\\y=2x-12[/tex]

Answer:

Rational

Step-by-step explanation:

A surd is an irrational number. An irrational number refers to any number that can not be written in the form a/b where a and b are integers.

Given √3600, which can be written as √36 × √100 = 6 ×10 = 60.

Hence √3600 is a rational number.

Answer: Length of RS = 13

Step-by-step explanation: Segment is a line connecting two points.

Length or Distance of a segment is the distance between these two points and is calculated as:

[tex]d=\sqrt{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}}[/tex]

For the line RS:

[tex]d=\sqrt{[1-(-4)]^{2}+[9-(-3)]^{2}}[/tex]

[tex]d=\sqrt{(1+4)^{2}+(9+3)^{2}}[/tex]

[tex]d=\sqrt{(5)^{2}+(12)^{2}}[/tex]

[tex]d=\sqrt{25+144}[/tex]

[tex]d=\sqrt{169}[/tex]

d = 13

The length of segment RS is 13 units.

Answer:

^ Answer is C

Step-by-step explanation:

Answer:

45% male teachers

55% female teachers

Step-by-step explanation:

multiply the number of teachers with 100 and divide it by the total number of teachers

Answer:

√29

Step-by-step explanation:

We have points (3,4) and (5,9), so the distance:

Answer:

x'5/3.y1/3 is the correct answer

Answer:

y = 14 [tex](6)^{x}[/tex]

Step-by-step explanation:

For an exponential function of the form y = a[tex]b^{x}[/tex]

Use the given points to find a and b

Using (0, 14 ), then

14 = a[tex]b^{0}[/tex] ( [tex]b^{0}[/tex] = 1 ) , thus

a = 14

y = 14[tex]b^{x}[/tex]

Using (3, 3024 ) , then

3024 = 14 b³ ( divide both sides by 14 )

216 = b³ ( take the cube root of both sides )

b = [tex]\sqrt[3]{216}[/tex] = 6 , thus

y = 14 × [tex]6^{x}[/tex] ← exponential function

Answer:

Step-by-step explanation:

present value | $741.37 (US dollars)

Answer:

Step-by-step explanation:

We need to add the measurements together to get the answer.

___________________________________________________________

[tex]\frac{4}{5} + \frac{1}{4} + \frac{1}{4} + \frac{3}{5}[/tex]

___________________________________________________________

Since [tex]\frac{1}{4}[/tex] and

___________________________________________________________

[tex]\frac{3}{5} + \frac{4}{5}[/tex] = [tex]\frac{7}{5}[/tex] and [tex]\frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2}[/tex]

7/5 + 1/2 (we need to find a common denominator to add these)

14/10 + 5/10 = 19/10 or 1 9/10 hours

___________________________________________________________

Answer:

19/10 hours or 1 [tex]\frac{9}{10}[/tex] hours.

Step-by-step explanation:

jog = 4/5 hours

lifting = 1/4 hours

stretching = 1/4 hours

cycling = 3/5 hours

total hours for that week = 4/5 + 1/4 + 1/4 + 3/5 = 19/10 hours or 1 [tex]\frac{9}{10}[/tex] hours.

Answer:

2

Step-by-step explanation:

√4 = 2

Answer:

18 quarters

Step-by-step explanation:

4.50/.25=18

Answer:

He has 18 quarters

Step-by-step explanation:

Each dollar is equivalent to 4 quarters, and max has $4. Therefore max has 16 quarters. Then you add the 50 cents, which is equivalent to 2 quarters. Now you add the 16to the 2 and you get 18. Max has 18 quarters.

Answer:

7) a = 60; b = 100

8) c = 20

9) d = 45

Step-by-step explanation:

7)

a + 120 = 180

a = 60

b + 80 = 180

b = 100

8)

5c + 4c = 180

9c = 180

c = 20

9)

3d + d = 180

4d = 180

d = 45

Answer:

3x-15

Step-by-step explanation:

> First start off by rewriting with each term that has the same variable beside each other

5x+ x -3x+xy+2xy-3xy-4-2-9

> Start to combine like terms

3x + 0xy - 15

> Rewrite

3x-15

Answer:

r= square root of A /π

Step-by-step explanation:

to find the radius with the area

use the formula square root of area/pi

Answer:

$35 per ticket

Step-by-step explanation:

1120 divided by 32 is 35, I used a calculator. If you divide the cost by the quantity you will get the cost for one quantity

Answer:

x=8

Step-by-step explanation:

A= x+3

B= x+2

C= x+1

A+B+C=30

[tex]x+3+x+2+x+1=30\\3x+6=30\\3x=30-6\\3x=24\\x=\frac{24}{3}\\x=8[/tex]

ANS: X=8