Explain the Pythagorean Theorem and triples using the side lengths 3,4,5.

Answer:

Step-by-step explanation:

It's a simple question as we know:

y-y1=m(x-x1)

y-20=12(x-3)

y=12x-36+20

y=12x-16

Now, your line is in slope intercept form you can compare it with

y=mx+c

m=12 and c=16. You can also put your point to verify your answer.

Answer:

7 / 15= 0.47

Step-by-step explanation:

Answer:

(4, 10)

Step-by-step explanation:

Hope this helps

The solution to the system of equations is the ordered pair in option B. (4, 10).

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Population growth of two towns over a period of five years is represented by the system of equations :

y = x + 6

y = 2x + 2

Here y represents the population growth and x represents the number of years.

Solution of the system of equations is the point where the graph of both equations intersect.

Intersecting point is (4, 10).

Algebraically, we can solve this as,

We have y =  x + 6 and y = 2x + 2.

x + 6 = 2x + 2

x - 2x = 2 - 6

x = 4

y = x + 6 = 4 + 6 = 10

So (x, y) = (4, 10)

Hence the solution to the system of equations  y =  x + 6 and y = 2x + 2 is the point (4, 10).

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Answer:

D

Step-by-step explanation:

Because pi never ends.

Hence, D (π) is a irrational number.

Answer:

a) h = 15

b) x = 4

Step-by-step explanation:

a) set up a proportion:

  5 = h

   8     24

cross-multiply:

8h = 120

h = 15

b) x + 5 = x + 5 + 15

   5x + 1    5x + 1 + 35

cross-multiply:

(x + 5)(5x + 36) = (5x + 1)(x + 20)

5[tex]x^{2}[/tex] + 61x + 180 = 5[tex]x^{2}[/tex] + 101x + 20

180 = 40x + 20

160 = 40x

x = 4

Answer:

$267.5

Step-by-step explanation:

7% of 250=17.5. 250+17.5=267.5

Answer:

267.5

Step-by-step explanation:

250+7%=267.5

Hope this helps :)

Answer:

5.25x + 55 is greater than or equal to 399

Step-by-step explanation:

55 is a fixed amount of money that Amelia already has so that will be added to the part of the eqaution: 5.25x.

Her total should be greater than or equal to $399

Answer:

<XWY= 180-23

Step-by-step explanation:

angles on a straight line add up to 180!

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Answer:

A. 35°C.

Step-by-step explanation:

35 C (Celsius), converted to F (Fahrenheit), would be 95. Which would make it a hot day.

So, you answer is 35°c.

Answer:

9 years ( approximately)

Step-by-step explanation:

900(1.03)^t = 1200

(1.03)^t= 1.33

( 1.03)^t= ( 1.03)^9

So, t= 9

Answer:

3/10 shade 3 in

Step-by-step explanation:

Answer:

-2/x

Step-by-step explanation:

simplified is y = -x/2 - 6

Perpendicular slopes are just reciprocals of the original slope, so just flipp the original slope around to be the complete opposite.

Example if slope= -2, the reciprocal= -1/2

Just flip the numerator with the denominator for perpendicular slope

did you get ittttt???

please help me out

Answer:

Quotient : 3x² + 5x + 1

Step-by-step explanation:

Answer:

52 students or 51

Step-by-step explanation:

9514 1404 393

Answer:

  4)  6x

  5)  2x +3

Step-by-step explanation:

We can work both these problems at once by finding an applicable rule.

  [tex]\text{For $f(x)=ax^n$}\\\\\lim\limits_{h\to 0}\dfrac{f(x+h)-f(x)}{h}=\lim\limits_{h\to 0}\dfrac{a(x+h)^n-ax^n}{h}\\\\=\lim\limits_{h\to 0}\dfrac{ax^n+anx^{n-1}h+O(h^2)-ax^n}{h}=\boxed{anx^{n-1}}[/tex]

where O(h²) is the series of terms involving h² and higher powers. When divided by h, each term has h as a multiplier, so the series sums to zero when h approaches zero. Of course, if n < 2, there are no O(h²) terms in the expansion, so that can be ignored.

This can be referred to as the power rule.

Note that for the quadratic f(x) = ax^2 +bx +c, the limit of the sum is the sum of the limits, so this applies to the terms individually:

  lim[h→0](f(x+h)-f(x))/h = 2ax +b

__

4. The gradient of 3x^2 is 3(2)x^(2-1) = 6x.

5. The gradient of x^2 +3x +1 is 2x +3.

__

If you need to "show work" for these problems individually, use the appropriate values for 'a' and 'n' in the above derivation of the power rule.

Answer:

x = 41

Step-by-step explanation

9^2 + 40^2 = x^2

81 + 1600 = 1682

square root of 1681 = 41

x = 41

9514 1404 393

Answer:

  x = 10√3

Step-by-step explanation:

The Pythagorean theorem tells you ...

  FB^2 = BC^2 +CF^2

  FA^2 = FB^2 +BA^2

Substituting for FB^2, we have ...

  FA^2 = BC^2 +CF^2 +BA^2 = x^2 +x^2 +x^2

  FA^2 = 3x^2

  FA = x√3 = 30 . . . . take the square root and substitute for FA

  x = 30/√3

  x = 10√3

Answer:

a. 311 hours

b. i. $3,100 in receipts  

   ii. $2,799 in expenses.

Step-by-step explanation:

a. The company is making $10 per hour and spending $9 an hour. Their profit is therefore:

= 10 - 9

= $1 per hour

Since they spent $311 on the new equipment, the amount of time it would take for them to make this back is:

= 311 / 1

= 311 hours

b. In 311 hours, the total receipts would be:

= 311 * 10

= $3,110

The expenses would be:

= 311 * 9

= $2,799

Answer:

C

Step-by-step explanation:

AE = 14.6 I think. If I'm wrong, use whatever number it is.

Sin(x) = 5/14.6

Sin(x) = 0.3425

x = Sin-1 (0.3425)

x =20.03

Now the other larger triangle has an acute angle of 90 -20.03 =  69.97

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

Cos(69.97) = 13.1/DE

DE = 13.1/cos(69.97)

DE = 38.25

Answer:

Solving the inequality: [tex]x - 2 > 2x + 12[/tex] we found the value of x: [tex]\mathbf{x<-14}[/tex]

Option D is correct option.

Step-by-step explanation:

We need to solve the inequality: [tex]x - 2 > 2x + 12[/tex] and find value of x

Solving the inequality

[tex]x - 2 > 2x + 12[/tex]

First of all, we will add 2 on both sides

[tex]x - 2+2 > 2x +12 +2\\x>2x+14[/tex]

Now, add -2x on both sides of inequality

[tex]x-2x>2x+14-2x\\-x>14[/tex]

Now, multiply both sides by -1, when multiplying by negative number, the inequality is reversed i.e. > will become <

[tex]-1*-x<14*-1\\x<-14[/tex]

So, solving the inequality: [tex]x - 2 > 2x + 12[/tex] we found the value of x: [tex]\mathbf{x<-14}[/tex]

Option D is correct option.

The expression to represent the net yardage is 30.5x+12.9y.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Given that, gain 25x yards, gain 0.9y yards lose 12y yards and lose 5.2x yards.

Now, net yardage

= 25x+0.9y+12y+5.5x

= 30.5x+12.9y

Therefore, the expression to represent the net yardage is 30.5x+12.9y.

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Answer: It number 4

Step-by-step explanation:

Answer:

[tex]\displaystyle y = x^{-\frac{2}{3}}[/tex]

Step-by-step explanation:

Logarithms

Some properties of logarithms will be useful to solve this problem:

1. [tex]\log(pq)=\log p+\log q[/tex]

2. [tex]\displaystyle \log_pq=\frac{1}{\log_qp}[/tex]

3. [tex]\displaystyle \log p^q=q\log p[/tex]

We are given the equation:

[tex]\displaystyle \log_{2}(x) = \frac{3}{ \log_{xy}(2) }[/tex]

Applying the second property:

[tex]\displaystyle \log_{xy}(2)=\frac{1}{ \log_{2}(xy)}[/tex]

Substituting:

[tex]\displaystyle \log_{2}(x) = 3\log_{2}(xy)[/tex]

Applying the first property:

[tex]\displaystyle \log_{2}(x) = 3(\log_{2}(x)+\log_{2}(y))[/tex]

Operating:

[tex]\displaystyle \log_{2}(x) = 3\log_{2}(x)+3\log_{2}(y)[/tex]

Rearranging:

[tex]\displaystyle \log_{2}(x) - 3\log_{2}(x)=3\log_{2}(y)[/tex]

Simplifying:

[tex]\displaystyle -2\log_{2}(x) =3\log_{2}(y)[/tex]

Dividing by 3:

[tex]\displaystyle \log_{2}(y)=\frac{-2\log_{2}(x)}{3}[/tex]

Applying the third property:

[tex]\displaystyle \log_{2}(y)=\log_{2}\left(x^{-\frac{2}{3}}\right)[/tex]

Applying inverse logs:

[tex]\boxed{y = x^{-\frac{2}{3}}}[/tex]

Answer:

2*2=4

Step-by-step explanation: