Which one of the following expressions represents the perimeter of a rectangle whose length is 18 meter and whose width is 9 meter

Answer:

The equation in y = mx+b form is  y = (4/3)x - 20/3

The equation in Ax+By = C form is  4x - 3y = 20

There are other ways to express the second equation.

==============================================================

Explanation:

First we must complete the square for x and y.

This will get the equation into (x-h)^2+(y-k)^2 = r^2 form so we can determine the center.

x^2+y^2 - 8x-14y + 40 = 0

(x^2-8x) + (y^2-14y) + 40 = 0

(x^2-8x+16 - 16) + (y^2-14y+49-49) + 40 = 0

(x^2-8x+16) + (y^2-14y+49) + (-16-49+40) = 0

(x-4)^2 + (y-7)^2 = 25

(x-4)^2 + (y-7)^2 = 5^2

This circle is centered at (h,k) = (4,7) and it has radius r = 5.

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

Next, we need to find the slope of line AB such that

A = (4,7) = center of the circle

B = (8,4) = point on the circle, which is the point of tangency

m = slope

m = (y2-y1)/(x2-x1)

m = (4-7)/(8-4)

m = -3/4

The slope of line AB is -3/4. Any perpendicular slope will have us do two things:

that would get us from -3/4 to +4/3 or just 4/3.

The perpendicular slope is 4/3.

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

So we must find the equation of the line with slope m = 4/3 and it goes through (x,y) = (8,4)

That means,

y = mx+b

4 = (4/3)*8 + b

4 = 32/3 + b

4 - 32/3 = b

12/3 - 32/3 = b

(12-32)/3 = b

-20/3 = b

b = -20/3

Therefore, the equation of the tangent line is y = (4/3)x - 20/3

Optionally, we can get this equation into standard form like so

y = (4/3)x - 20/3

3y = 4x - 20 ... multiply everything by 3

3y-4x = -20

-4x+3y = -20

4x - 3y = 20

The diagram is shown below.

Answer:

The first option

Step-by-step explanation:

If you check the first one we can verify that WX and ZY are perpendicular as shown with the 90 degree mark then we can see that WX is parallel with AB.

Answer:

4x + 6 = 94 could be used to solve the problem

The answer you are looking for is DXCVI.

D=500.

X=10.

C=100.

V=5.

I=1

Solution:

So,

500+(100-10)+5+1

500+90+5+1

596

Therefore, DXCVI=596.

Answer:

596 in Roman Numerals should be DXCVI

Answer:

I don't knowwwwwwwwwwwww

Answer:

00000000000000000000000000

Step-by-step explanation:

00000000000000000

Answer:

[tex]4m + 5 - 3m \\ = 4m - 3m + 5 \\ = 1m + 5 \\ = (m + 5)[/tex]

Given the expression:

[tex] \displaystyle \large{4m + 5 - 3m}[/tex]

To simplify the expression, notice that 4m and 3m have the same term.

These are called like terms. Let's see some examples of like terms.

Then we also have the example of non-like term

In conclusion,

And that brings us to this topic, to evaluate or simplify the expression with two like terms and one non-like term.

Note that only like terms can evaluate. Let's see some examples:

How about a subtraction?

But what if it's non-like terms? Simple, we keep it like that!

So to simplify the expression in the question, we evaluate like terms first!

Since 4m and 3m both are like terms. We can do 4m-3m.

[tex] \displaystyle \large{4m + 5 - 3m} \\ \displaystyle \large{4m - 3m + 5} [/tex]

Evaluate 4m-3m

[tex] \displaystyle \large{1m + 5} [/tex]

We don't usually write 1m so we keep as m instead.

[tex] \displaystyle \large{m + 5} [/tex]

Now, can we evaluate m+5? No, because m and 5 are not like terms so we keep like this.

Hence, the answer is m+5

It looks like the differential equation is

[tex]y'-\dfrac y{x+1}=2[/tex]

Multiply both sides by 1/(x + 1) :

[tex]\dfrac{y'}{x+1}-\dfrac y{(x+1)^2} = \dfrac2{x+1}[/tex]

The left side is now a derivative of a product,

[tex]\left(\dfrac y{x+1}\right)' = \dfrac2{x+1}[/tex]

Integrate both sides with respect to x :

[tex]\dfrac y{x+1} = 2\ln|x+1|+C[/tex]

Solve for y :

[tex]y = 2(x+1)\ln|x+1| + C(x+1)[/tex]

Answer:

is there a picture that go with the problem

Step-by-step explanation:

Answer:

x = 95

y = 147

z = 128

Step-by-step explanation:

x can be found by using the exterior angle triangle theorem, where, when you add the two opposite angles, it equals the measure of the exterior angle.  In this case, 50 + 45 = 95.

The same theorem can be used to solve for y.  95 + 52 = 147

We see that angle z is composed of a linear pair, and we have one of the angle values, so just do 180 - 52 and you get 128.

Answer:

[tex]ab + 2 - 1 = ab + 1 \\ a = 3 \\ b = 4 \\ then \: 3 \times 4 + 1 \\ = 12 + 1 = 13 \\ thank \: you[/tex]

Answer:

550 mi. !!!!

Step-by-step explanation:

Answer: 550 miles

Work Shown:

1 in = 100 mi

5.5*(1 in) = 5.5*(100 mi) ..... multiply both sides by 5.5

5.5 in = 550 mi

Answer:

?

Step-by-step explanation:

So first, you need to multiply 7 by four to get the quarterly part of it, which will be 28. Then, multiply 9% (.9) by your 28 to get 25.2. Finally, multiply that by 7,000 to get 176,400...

Answer:

0= x

Step-by-step explanation:

8= 8 + 4x +5x

Combine like terms

8 = 8+9x

Subtract 8 from each side

8-8 =8+9x-8

0 = 9x

Divide by 9

0/9 = 9x/9

0= x

Answer:

the answer of this question is rs99

Answer:

33 - C

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

each angle measurement has to equal 180°

Answer:

SOH-CAH-TOA

Tan(angle) = Opposite side length/adjacent side lenght

Tan(49 deg) = h/900

Multiply both sides by 900:

900* tan(49deg) = h

Throw it into a calculator

h ≈ 1035.331566

Step-by-step explanation:

If your car is traveling 65 miles per hour, then it is also going 343,200 feet (65 × 5,280 = 343,200) per hour. Then, you can divide the total feet per hour by 60, and you know that your car is traveling 5,720 feet per minute.

Answer:

r = -3

Step-by-step explanation:

3r + 2 - r = -4

2r + 2 = -4

2r = -6

r = -3

Answer:

r = -3

Step-by-step explanation:

3r + 2 - r = -4         (Given)

2r + 2 = -4             (Simplify)

2r + 2 - 2 = -4 - 2  (Subtract 2 on both sides)

2r = -6                   (Simplify)

2r/2 = -6/2            (Divide 2 on both sides)

r = -3                     (Simplify)

Answer:

2.   12

5.   30

Step-by-step explanation:

Put 3 instead of x

2.   [tex]\frac{36}{x}[/tex]

    = [tex]\frac{36}{3}[/tex]

    = 12

5. 10x

   = 10 × 3

   = 30

Answer:

No because she added 2 instead of 2398. She thought the 2 was separate because of the comma separating the 2 thousand. She also made a mistake by thinking she could add easily by adding 2 to 2398 to make 2400.

The addition of the given numbers is 7,758.

Use the concept of addition defined as:

In mathematics, addition is an arithmetic operation that combines two or more numbers to produce a sum.

It is a fundamental operation used to calculate the total or the result of combining quantities. When adding numbers, you start with the first number, and then incrementally add subsequent numbers to obtain a final sum. The order in which numbers are added does not affect the result, thanks to the commutative property of addition.

This fundamental concept of addition forms the basis for more advanced mathematical operations and problem-solving techniques.

The given numbers are:

5,356+2,398

Now simply add these numbers:

 5 3 5 6

+2 3 9 8  

 7 7 5 4  

Hence,

The addition of the given numbers is 7,758.

To learn more about the addition visit:

https://brainly.com/question/25421984

#SPJ3

Answer:

d= 7.81

r= 3.905

Step-by-step explanation:

Answer:

Step-by-step explanation:

New Balance = 110 + 110*2/100

New Balance = 110 + 2.20

New Balance = 112.20

Answer:

9 miles

Step-by-step explanation:

I have to ask here too: are you sure you have this description right ? because cm and miles are usually not used in combination.

but fine.

1 cm <-> 4.5 miles

2 cm <-> ? miles

remember questions like "if 1 apple costs $1.10, how much are 2 apples or 5 or 10 apples ?"

you remember what you had to do ?

pretty common sense : you multiplied the price by the same number that you multiplied the unit count number with. so, in my example, by 2, by 5 and by 10. and you got $2.20, $5.50 and $11.00 as prices.

so, what do you think we need to do to calculate the miles that are residents by 2 cm on the map ?

right ! we need to multiply by 2 - because 2×1 = 2.

so, 4.5 × 2 = 9 miles

yes, if 1 cm on the map stands for 4.5 actual miles, then 2 cm stand for 2×4.5 = 9 actual miles.

Answer:

f+g = (x-2)+(x²-x)

= x²-2

(f+g)(-3) = -3(x²-2)

-3x²+6

Step-by-step explanation:

follow the expression (f+g)(-3)

What you want to do at the beginning is to "Keep-Change-Flip" the fractions. You're going to keep the first fraction the same, change the divide sign to a multiply sign, and flip the second fraction.

Next, you'll have to factor, and then you can cancel out common components.

Answer:

A. 0.4

Step-by-step explanation:

Write 12 of 30 as a fraction:

12/30

Convert this to be a fraction over 100 by setting up an equation:

Variable x = proportional answer to 12/30

12/30 = x/100

Cross multiply:

12 × 100 = 30 × x

1200 = 30x

40 = x

40/100

Convert this number into a decimal by adding a zero and decimal point before the "4" in 40:

0.40

Simplify:

0.40 = 0.4

I converted it into a decimal through the use of fractions, but you can also find the answer by doing long division: 12 ÷ 30. However, showing work for long division over a message is too complex so I solved the problem this way instead.

Step-by-step explanation:

Supplement= 180°- 13°

167° Answer

Answer:

167°

Step-by-step explanation:

Supplementary angles, by definition, when combined will give a total angle measurement of 180°.

One of the given angle measurements is 13°. Subtract 13 from the total, 180:

180 - 13 = 167°

167° is the supplement angle.

~