Three students have proposed these ways to describe when two lines l and m are perpendicular: Read screenshot for info. Explain why each of these definitions is correct. What are some of the advantages and disadvantages with each?

Answer:

8b and 80

Step-by-step explanation:

Answer:

The expression that represents the area of this rectangle is 8b

When b = 10, the area of the rectangle is 80 square units.

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

f(4y) = -8y - 3

Step-by-step explanation:

Step 1: Define variables

f(x) = -2x - 3

f(4y) = x = 4y

Step 2: Plug in x = 4y

f(4y) = -2(4y) - 3

f(4y) = -8y - 3

Answer:

6

Step-by-step explanation:

1x2x3=6

Answer: It travels 100 miles

Step-by-step explanation:

If it drives 50 miles an hour it would drive 100 miles an hour if it were driving for 2 hours.

Based on the speed of the car and the amount of time it was travelling, the car travelled 100 miles in 2 hours.

The distance that the car travelled can be calculated by:

Distance = Speed x Time

Speed = 50 miles per hour

Time = 2 hours

Distance = 50 x 2

= 100 miles

In conclusion, the car would have gone 100 miles.

Find out more at https://brainly.com/question/22277265.

Answer:

172 kids and 160 adults

Step-by-step explanation:

We can create two equations with the information given.

1.5x + 4y = 898

x + y = 332

We can then bring the x in the second equation over to the other side.

y = 332 - x

We can now plug this equation into the one before.

1.5x + 4(332 - x) = 898

We now do the distributive property on the equation and result with

1.5x + 1328 - 4x = 898

Then we can combine like terms and add 1.5x and -4x together and bring 1328 over by subtracting it from 898.

-2.5x = -430

-430 / 2.5x = 172

x = 172

x is defining how many children when to the park.

Now we just need to figure out y by subtracting it from the total amount of people (aka plugging it into the second equation)

y = 332 - 172

y= 160

We end up with

x = 172

y = 160

172 children and 160 adults

Answer:

Inconsistent System of Equations

Explanation:

There is no solution for the system of equations that graphs as parallel lines.

Parallel lines never cross, therefore there is no intersection. This is an inconsistent system of equations.

Answer: Choice B  [tex]\{x | \ x \le 4.5\}[/tex]

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

Explanation:

The endpoint is at 4.5 and this endpoint is a filled in circle. So we'll have "or equal to" as part of the inequality sign. This is because we are including the endpoint as part of the shaded solution region.

The other part of the inequality sign is "less than" because the shading is to the left of the endpoint. Any point in the shaded region is less than 4.5, or it could be equal to 4.5

Put another way: x is either 4.5 or smaller

We write that as [tex]x \le 4.5[/tex] which is read out as "x is less than or equal to 4.5"

Surrounding this in curly braces tells the reader we're dealing with a set of values. The first part "x |" means "x such that"

All together we end up with the answer [tex]\{x| \ x \le 4.5\}[/tex] which translates to "x such that x is less than or equal to 4.5"

Answer:

B

Step-by-step explanation:

Given :

An automobile manufacturer introduces a new model that averages 27 miles per gallon in the city.

Standard deviation , S.D = 3 miles per gallon .

To Find :

The probability that the person will purchase a car that averages less than 20 miles per gallon for in-city driving.

Solution :

We have to find the probability , [tex]P(X\leq 20)[/tex] .

Here , we will use the excel function

So ,

[tex]P(X\leq 20)=NORMADIST( 20, 27 , 3 , 1 )=0.009815[/tex] .

Therefore , probability is 0.009815 .

Answer:

13(n-20)=322

Step-by-step explanation:

13 times n-20 equals 322

Answer:

11.2 feet

Step-by-step explanation:

The two furthest corners of the bed are at (8, 6) and (5, 10).  To determine which is the furthest from the origin, use the distance formula.

d = √((x₂ − x₁)² + (y₂ − y₁)²)

d = √((8 − 0)² + (6 − 0)²)

d = 10

d = √((x₂ − x₁)² + (y₂ − y₁)²)

d = √((5 − 0)² + (10 − 0)²)

d = 5√5

d ≈ 11.2

Therefore, the corner at (5, 10) is the furthest from the origin, about 11.2 feet away.

Answer:

  To write the equation y = ax + b in function notation, substitute f(x) for y

Step-by-step explanation:

The only true statement is the last one.

__

A function assigns exactly one output value to each input value.

The domain is the set of all input, or x-values.

The range is the set of all output, or y-values.

y=ax+b can be written in function notation by replacing y with f(x).

Answer:

The last one: To write the equation y = ax + b in function notation, substitute f(x) for y.

Step-by-step explanation:

A relation is a mapping from a set of input values, called the domain, to a set of output values, called the range. In a relation, each element in the domain can be assigned to one or more elements in the range.

A function is a relation where each input value is assigned to exactly one output value.

The domain of a function is the set of all input values, or x-values, for which the function is defined.

The range of a function is the set of all output values, or y-values, for which the function is defined.

To write the equation y = ax + b in function notation, substitute f(x) for y, resulting in the function f(x) = ax + b.

Answer:

In a room of just 23 people there's a 50-50 chance of at least two people having the same birthday. In a room of 75 there's a 99.9% chance of at least two people matching. Put down the calculator and pitchfork, I don't speak heresy.

Step-by-step explanation:

Step-by-step explanation:

1. Add all the different candies together

1/8 + 1/2 + 2/3=

2. Find the lowest common multiple of all the denominators

All the denominators can evenly multiply to 24 so 24 is the Lowest Common Denominator.

3. Multiply to make all the denominators 24

8x3=24 2x12=24 3x8=24

4. Whatever you did to the denominators, do the same thing to the numerators of that specific denominator.

1x3/8x3 1x12/2x12 2x8/3x8

5. Now that the denominators are the same for all the fractions, add all the numerators together.

3/24 + 12/24 + 16/24

3+12+16= 31

ANSWER: Natalie had 31/24 pounds of candy in all

Note: The decimal form is 1.292 pounds

Answer:

-96

Step-by-step explanation:

Assuming that the scores start at 0,

-12 x 8 = -96

Total of Jamies score in card game is -96

Given that;

Each turn score = -12

Number of turn = 8

Find:

Total of Jamies score

Computation:

Total of Jamies score = Each turn score × Number of turn

Total of Jamies score = -12 × 8

Total of Jamies score = -96

Learn more:

https://brainly.com/question/21512800?referrer=searchResults

Answer:

CE would be half of AD.

Step-by-step explanation:

A, E and D are all points on the circumference of the circle.  

AD is the diameter.  

CE is the radius.  

CE would be half of AD.

Answer:

dy/dx = (x + 1)(x-4)/(x-1)(x+4)[1/(x+1) + 1/(x-4) -1/(x-1) -1/(x+4)

Step-by-step explanation:

Here, we want to find the derivative using logarithmic differentiation.

What we will do here is to first take the natural logarithm of both sides, then we proceed to differentiate afterwards.

Please check attachment for complete solution and step by step explanation.

The correct answer is C. The hyphae absorb nutrition and detect when conditions are right to sprout a mushroom above ground.

Explanation:

Two key features of living organisms are energy processing and response to stimuli. These two features imply organisms require nutrients, which can be taken from the environment or created through a process such as photosynthesis and they sense their surroundings and respond to it.

Moreover, these two features are exemplified by mushroom (fungi) in the sentence "The hyphae absorb nutrition and detect when conditions are right to sprout a mushroom above ground" because the first section shows the developing mushroom takes nutrients from the soil or its environment and this is essential for growing and survival. Also, the second section of the sentence shows the developing mushroom can sense its environment and respond by developing only in appropriate conditions.

Answer:

C

Step-by-step explanation:

Got it right on edge 2020

Answer:

To find the perimeter of a triangle, you would need  first all three side lengths.  

9.7m-6.8m = 2.9, 6.6m+6.5p=7.1, 2.2p-6.4= -4.2. once I added all the sides it was 5.8.

2.

The domain of this function is 3≤x≤5 in interval notation that is [3,5]

The range is -3≤y≤3. In interval notation that is [-3,3]

4.

The domain of this function is -5≤x≤-1 in interval notation that is [-5,-1]

The range is 1≤y≤5. In interval notation that is [1,5]

:)

Answer:

it would be x=-4

hope i helped ya

Answer:

x = -4

Step-by-step explanation:

3x -2(6-x) = 7x +2(5+x) -6

Distribute -2 through the parentheses 3x -12 +2x = 7x +2(5+x) -6

Distribute 2 through the parentheses 3x -12 +2x = 7x +10 +2x -6

3x -12 +2x = 7x +10 +2x -6 cancel equal terms on both sides of the equation

3x -12 = 7x +10 -6 subtract the numbers 3x -12 = 7x +4

                           Move variable to the left left handed side and change its sign

3x -7x-12 = 4   -->   3x -7x = 4 + 12  -->  -4x = 4+12  --> -4x = 16

             Divide both sides of the equation by -4  -->  x = -4

2x - 1 < 4

First, let's add 1 to both sides.

2x < 5

Divide both sides by 2

x < 5/2 or (-∞, [tex]\frac{5}{2}[/tex])

-5x - 3 > -3

Add 3 to both sides.

-5x > 0

Divide both sides by -5

x < 0 or (-∞, 0)

The solution set of the given set of linear inequations 2x - 1 < 4 and -5x - 3 < -3 is [tex]\left ( -\infty , 0 \right )[/tex].

Algebraic expressions can be related to each other in many ways. When two expressions are equal to each other, they are called equations and are represented with an equal sign between them (=). When two expressions are not equal, they are called inequations and are represented by non-equal signs between them (>, <, ≥, ≤).

In the question, we are asked to solve the given inequations:

2x - 1 < 4 ... (i), and -5x -3 > -3 ... (ii).

First, we will solve (i), in the following ways:

2x - 1 < 4.

or, 2x - 1 + 1 < 4 + 1 (Adding 1 to both sides of the inequation)

or, 2x < 5 (Simplifying)

or, 2x/2 < 5/2 (Dividing both sides of the inequation by 2)

or, x < 5/2 (Simplifying)

or, x ∈ [tex]\left ( -\infty , \frac{5}{2} \right )[/tex] ...(iii)

Now, we will solve (ii), in the following ways:

-5x -3 > -3.

or, -5x - 3 + 3 > -3 + 3 (Adding 3 to both sides of the inequation)

or, -5x > 0 (Simplifying)

or, -5x/(-5) < 0/(-5) (Dividing both sides of the inequation by -5, sign of the inequality reverses as we are dividing by a negative number)

or, x < 0 (Simplifying)

or, x ∈ [tex]\left ( -\infty , 0 \right )[/tex] ...(iv)

For the solution set, we need the intersection of (iii) and (iv)

[tex]\left ( -\infty , \frac{5}{2} \right )[/tex] ∩ [tex]\left ( -\infty , 0 \right )[/tex]

= [tex]\left ( -\infty , 0 \right )[/tex]

∴ The solution set of the given set of linear inequations 2x - 1 < 4 and -5x - 3 < -3 is [tex]\left ( -\infty , 0 \right )[/tex].

Learn more about the linear inequations at

https://brainly.com/question/24242251

#SPJ2

Answer/Step-by-step explanation:

Recall: the ratio of the areas of two similar figures = the square of the ratio of the corresponding sides of the similar figures.

This will give us the scale factor.

The scale factor indicates how many times larger the second triangle is than the area of the first.

Let's find how many times larger is the area of the second triangle is to the first:

1. ∆ G And ∆ F

[tex] \frac{Area_{F}}{Area_{G}} = \frac{side_{F}^2}{side_{G}^2} [/tex]

[tex] \frac{Area_{F}}{Area_{G}} = \frac{6^2}{3^2} [/tex]

[tex] = \frac{36}{9} = 4 [/tex]

∆F is 4 times larger than ∆G

2. ∆ G And ∆ B

[tex] \frac{Area_{B}}{Area_{G}} = \frac{side_{B}^2}{side_{G}^2} [/tex]

[tex] \frac{Area_{B}}{Area_{G}} = \frac{2^2}{4^2} [/tex]

[tex] = \frac{4}{16} = 0.25 [/tex]

∆B is 0.25 times ∆G

3. ∆ B And ∆ F

[tex] \frac{Area_{G}}{Area_{B}} = \frac{side_{F}^2}{side_{B}^2} [/tex]

[tex] \frac{Area_{F}}{Area_{B}} = \frac{8^2}{2^2} [/tex]

[tex] = \frac{64}{4} = 4 [/tex]

∆F is 16 times larger than ∆B

4. ∆ F And ∆ H

[tex] \frac{Area_{H}}{Area_{F}} = \frac{side_{H}^2}{side_{F}^2}} [/tex]

[tex] \frac{Area_{H}}{Area_{F}} = \frac{2^2}{6^2} [/tex]

[tex] = \frac{4}{36} = \frac{1}{9} [/tex]

∆H is ⅑ times ∆F

5. ∆ G And ∆ H

[tex] \frac{Area_{H}}{Area_{G}} = \frac{side_{H}^2}{side_{G}^2} [/tex]

[tex] \frac{Area_{H}}{Area_{G}} = \frac{2^2}{3^2} [/tex]

[tex] = \frac{4}{9} [/tex]

∆G is 4/9 times ∆G

6. ∆ H And ∆ B

[tex] \frac{Area_{B}}{Area_{H}} = \frac{side_{B}^2}{side_{H}^2} [/tex]

[tex] \frac{Area_{B}}{Area_{H}} = \frac{1.5^2}{2^2} [/tex]

[tex] = \frac{2.25}{4} = 0.6 [/tex] (nearest tenth)

∆B is 0.6 times ∆H

Answer:

Yes

Step-by-step explanation:

If y is the total cost, then this would be correct.