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3 years ago

What is the slope? First, determine the slope. (200,14) (225,16)

Mathematics

1 answer:

Maksim231197 [3]3 years ago

7 0

Answer:

$\displaystyle m=\frac{2}{25}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Slope Formula: $\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

Step-by-step explanation:

Step 1: Define

Point (200, 14)

Point (225, 16)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Substitute in points [SF]: $\displaystyle m=\frac{16-14}{225-200}$
[Fraction] Subtract: $\displaystyle m=\frac{2}{25}$

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Barbara found that 35 of the 60 people she surveyed had pets. About what percent of the students she surveyed had pets?

Sergio [31]

Answer:

35/60 = 0.583333333

= 0.58

0.58 * 100 = 58

58%

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3 years ago

Read 2 more answers

There are 40 people at Drake's sweet sixteen party. Drake's only rule is that everyone in the party must meet and shake each oth

nikdorinn [45]

1) This is a combination, so use ⁴⁰C₂.
⁴⁰C₂ = 780
There are 780 handshakes in total.

2) I got my solution by using the combinations formula. Or another way you could do this is to add up... 39 + 38 + 37 + 36 + 35 + 34 + 33 + 32 + 31... +1. You will end up with 780 (I did this to double check my work).

3) The quickest way to figure this out if Drake invited 1,000 people is to use the natural numbers formula = n(n+ 1)/2.
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3 years ago

Read 2 more answers

Not sure what to do here can someone please help

kumpel [21]

Answer:

x = 2

Step-by-step explanation:

These equations are solved easily using a graphing calculator. The attachment shows the one solution is x=2.

<h3>Squaring</h3>

The usual way to solve these algebraically is to isolate radicals and square the equation until the radicals go away. Then solve the resulting polynomial. Here, that results in a quadratic with two solutions. One of those is extraneous, as is often the case when this solution method is used.

$\sqrt{x+2}+1=\sqrt{3x+3}\qquad\text{given}\\\\(x+2)+2\sqrt{x+2}+1=3x+3\qquad\text{square both sides}\\\\2\sqrt{x+2}=(3x+3)-(x+3)=2x\qquad\text{isolate the root term}\\\\x+2=x^2\qquad\text{divide by 2, square both sides}\\\\x^2-x-2=0\qquad\text{write in standard form}\\\\(x-2)(x+1)=0\qquad\text{factor}$

The solutions to this equation are the values of x that make the factors zero: x=2 and x=-1. When we check these in the original equation, we find that x=-1 does not work. It is an extraneous solution.

x = -1: √(-1+2) +1 = √(3(-1)+3) ⇒ 1+1 = 0 . . . . not true

x = 2: √(2+2) +1 = √(3(2) +3) ⇒ 2 +1 = 3 . . . . true . . . x = 2 is the solution

<h3>Substitution</h3>

Another way to solve this is using substitution for one of the radicals. We choose ...

$u=\sqrt{x+2}\qquad\text{requires $u\ge0$}\\\\u^2-2=x\qquad\text{solve for x}\\\\u+1=\sqrt{3(u^2-2)+3}\qquad\text{substitute for x in the original equation}\\\\(u+1)^2=3u^2-3\qquad\text{square both sides, simplify a little}\\\\2u^2-2u-4=0\qquad\text{subtract $(u+1)^2$}\\\\2(u-2)(u+1)=0\qquad\text{factor}$

Solutions to this equation are ...

u = 2, u = -1 . . . . . . the above restriction on u mean u=-1 is not a solution

The value of x is ...

x = u² -2 = 2² -2

x = 2 . . . . the solution to the equation

_____

Additional comment

Using substitution may be a little more work, as you have to solve for x in terms of the substituted variable. It still requires two squarings: one to find the value of x in terms of u, and another to eliminate the remaining radical. The advantage seems to be that the extraneous solution is made more obvious by the restriction on the value of u.

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2 years ago

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mars1129 [50]

Step-by-step explanation:

There are 2 questions in one.

Roberta is 20 years older than Julian. In 4 years, Roberta's age will be twice Julian's age:

r = j + 20
r + 4 = 2j

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

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r = 2d
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Correct choice is A

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3 years ago

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matrenka [14]

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