I need some help with my math please: Triangles ABD and ACE are similar right triangles. Which ratio best explains why the slope of AB is the same as the slope of AC?

[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-9}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{7}~,~\stackrel{y_2}{4}) ~\hfill AB=\sqrt{(~~ 7- (-9)~~)^2 + (~~ 4- 4~~)^2} \\\\\\ ~\hfill AB=\sqrt{( 16)^2 + ( 0)^2}\implies \boxed{AB=16} \\\\\\ B(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad C(\stackrel{x_2}{7}~,~\stackrel{y_2}{-8}) ~\hfill BC=\sqrt{(~~ 7- 7~~)^2 + (~~ -8- 4~~)^2}[/tex]

[tex]~\hfill BC=\sqrt{( 0)^2 + ( -12)^2}\implies \boxed{BC=12} \\\\\\ C(\stackrel{x_1}{7}~,~\stackrel{y_1}{-8})\qquad A(\stackrel{x_2}{-9}~,~\stackrel{y_2}{4}) ~\hfill CA=\sqrt{(~~ -9- 7~~)^2 + (~~ 4- (-8)~~)^2} \\\\\\ ~\hfill CA=\sqrt{( -16)^2 + (12)^2}\implies CA=\sqrt{400}\implies \boxed{CA=20} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{Perimeter}{16~~ + ~~12~~ + ~~20\implies \text{\LARGE 48}}[/tex]

The expression for m from the given equation is m = E/o^2

The subject of formula is a way of representing a variable with another variable

Given the equation

E = mo^2

We are to make m the subject of the formula. To do that, we will divide both sides of the equation by o^2 to have:

E/o^2 = mo^2/o^2

E/o^2 = m

Swap

m = E/o^2

Hence the expression for m from the given equation is m = E/o^2

Learn more on subject of formula here: https://brainly.com/question/657646

#SPJ1

1/3 is the probability of rolling either a 5 or a 6 using a normal six-sided die.

Probability can be defined as the ratio between the number of favorable outcomes and the total number of outcomes of an event.

Given:

Six-sided dice rolled once

Let n be the number of outcomes

let x be the number of favorable outcomes

We know that,

[tex]Probability=\frac{x}{n}[/tex]

When the six-sided dice roll, The possible outcomes are,

[tex]\{1,\;2,\;3,\;4,\;5,\;6\}[/tex]

Therefore,

[tex]Number\;of\;outcomes,\;n=6[/tex]

[tex]Probability\;rolling\;5\;is\;\frac{1}{6}[/tex]

[tex]Probability\;rolling\;6\;is\;\frac{1}{6}[/tex]

Therefore, Probability of rolling either 5 or 6 is,

[tex]P(5\;or\;6)=\frac{1}{6} +\frac{1}{6}[/tex]

[tex]P(5\;or\;6)=\frac{2}{6}[/tex]

[tex]P(5\;or\;6)=\frac{1}{3}[/tex]

To learn more about Probability, visit:

https://brainly.com/question/11234923

#SPJ4

Answer:

AP = 29,37,45,...

d= t2-t1

=37-29

=8

n=59

t59=?

tn=a+(n-1)d

t59=29+(59-1)8

t59=28+58×8

t59=28 + 464

t59=492

Step-by-step explanation:

please mark it brainliest and thank it please  

Harry's speed on the freeway is 67 miles per hour

Time Harry drove on freeway = 3 hours

Time Harry drove on country road = 6 hours

Total distance covered by him = 483 miles

Let his speed be x miles per hour

Formula to be used:

Speed*Time = Distance

Therefore, the distance covered by him on the freeway  = 3x -----(1)

Distance covered by him on country road = 6(x - 20)------(2)

Formulating the equations using (1) and (2)

3x + 6(x-20) = 483

3x + 6x - 120 = 483

9x = 603

x = 67 miles per hour

So, his speed on the freeway is 67 miles per hour and on the country road it is 47 miles per hour

Learn more about algebra:

https://brainly.com/question/19245500

#SPJ4

Answer:

16

Step-by-step explanation:

Given that the total number of seats in an auditorium is modeled by the following equation:where x represents the number of rows of seats.We are to find the number of rows are there in the auditorium with a total of 416 seats.So, we are to find the value of x if f(x) = 416.

Since the number of rows cannot be negative, so the required number of rows in the auditorium is 16.Thus, the number f rows is 16.

Answer:

30 pieces

540 inches of ribbon in total

Step-by-step explanation:

1 foot = 12 inches

9 feet of ribbon = (9x12) 108 inches of ribbon (1 roll)

5 x 108 = 540 inches of ribbon (in total)

540 / 18 = 30

30 pieces of ribbon

Answer:

64,100

Step-by-step explanation:

64,100are the values that are perfect square

Mark me as brainlist

Answer:

F(x) = -6x - 3

F(x) = -6(-8) - 3

F(x) = 48 - 3

F(x) = 45

By unitary method we can say that number of stacks of papers Lashona will pass back  from 140 if each stack conatins 28 papers is 5.

According to the given question.

Total number of papers Lashonna passed back = 140

And one stack is made up of 28 papers.

As we know that, the unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Therefore,

By unitary method number of stacks of papers would be made from 140 if each stack conatins 28 papers

= 140/28

= 5

Hence, by unitary method we can say that number of stacks of papers Lashona will pass back  from 140 if each stack conatins 28 papers is 5.

Find out more information about unitary method here:

https://brainly.com/question/22056199

#SPJ4

Answer:

-1 yard per play

play 6 - play 3=0

play 2 - play 4=0

play 1 - play 5 = -6

hope it helped

The independent variable x ,represents minutes and dependent variable is the number of candies eating by Levi because the eating of candies depends on the minutes.

A function relating these variable is Z(x)=4x

So Z(7)=28 meaning In 7 minutes Levi ate 28 candies and number of candies left in the bag is 22.

As given,

Independent variable=x

Dependent variable=Z(x)

Function Z(x)=4x

So, Z(7)=4×7

            =28

Candies left in bag =50 -28

                              =22

Therefore, function relating independent variable x with Z(x)=4x  and Z(7)=28 represents number of candies ate by Levi in 7 minutes ,number of candies left in the bag is 22.

Learn more about  independent variable here

brainly.com/question/1479694

#SPJ1

The value of the constant of variation is 130

Constant of variation can be defined as the ratio between two variables in  an inverse variation on a direct variation.

From the information given, we have that;

The number of hours is x

The temperature is y

x α 1/ y

x = k/y

k = xy

Substitute the values

k = 2 × 65

k= 130

Thus, the value of the constant of variation is 130

Learn more about constant of variation here:

https://brainly.com/question/18087321

#SPJ4

The complete question:

the number of hours it takes for a block of ice to melt varies inversely as the temperature. If it takes 2 hours for a square inch of ice to melt at 65 degrees find the constant of variation

The tax on the product will be $1.964.

It should be noted that from the information, the sales tax is 6% and the price of the product is $32.74.

Therefore, the value of the tax will be:.

Tax percentage × Price

= 6% × $32.74

= 0.06 × $32.74

= $1.9643

Therefore, the tax on the product will be $1.964.

Learn more about tax on:

brainly.com/question/25783927

#SPJ1

Answer:

Step-by-step explanation:

jeans           $42.95

sweater    + $36.99

total          = $69.94

tax             + 5% ($3.497 round to nearest hundredth ($3.50))

total with tax = 73.44

hope this helped!!!! let me know if you need anymore help with this :) have a good day!

Answer:

1.6

Step-by-step explanation:

| -1.6 | = 1.6

The expression that gives the distance, d, between the ships after t hours is d = 25t

From the question, we are to write an expression that gives the distance, d, between the ships after t hours

First, we will determine the distance the ships have traveled after t hours

Using the formula,

Distance = Speed × Time

Thus,

The first ship would have traveled

20 × t miles

= 20t miles

The second ship would have traveled

15 × t miles

= 15t miles

Using the Pythagorean theorem,

The distance, d, between the ships after t hours is

d² = (20t)² + (15t)²

d² = 400t² + 225t²

d² = 625t²

d = √(625t²)

d = 25t miles

Hence, the expression that gives the distance, d, between the ships after t hours is d = 25t

Learn more on Calculating Distance here: https://brainly.com/question/10428039

#SPJ1

The probability that:

Probability refers to the possibility of the occurrence of an event.

P(E) = probability of occurrence of an event E = [tex]\frac{Number Of Favourable Outcomes}{Total Number Of Outcomes}[/tex]

Now,

(a) Total number of books = 5 + 3 + 1 = 9

Probability of getting a dictionary = [tex]\frac{1}{9}[/tex]

(b) Number of ways to select 3 books out of 9 books = [tex]\binom{9}{3}[/tex] =  [tex]\frac{9!}{3!(6!)} = \frac{9\times\ 8 \times 7}{6}[/tex] = 84

Number of ways to select 1 out of 3 books of poems = [tex]\binom{3}{1} = \frac{3!}{2!}[/tex] = 3

Number of ways to select 2 out of 5 novels = [tex]\binom{5}{2} = \frac{5!}{2! 3!} = \frac{5\times 4}{2} = 10[/tex]

Thus, the probability of getting 2 novels and 1 book of poem = [tex]\frac{3\times10}{84} = \frac{10}{28} = \frac{5}{14}[/tex]

To learn more about probability, refer to the link: https://brainly.com/question/25870256

#SPJ4

(COMPLETE QUESTION:

If three books are picked at random from a shelf containing 5 novels, 3 books of poems, and a dictionary, what is the probability that (a) a dictionary is selected? (b) 2 novels and 1 book of poems are selected?)

Answer:

It's rational, because it can be converted into a reasonable fraction.

➯ Hope this helps!

Answer: x= 33

Step-by-step explanation: hope this helps!!!

Answer:

x can be -3, or +3

Step-by-step explanation:

The equation would be

5[tex]x^{2}[/tex] = 45

Divide both sides by 5

[tex]x^{2}[/tex] = 9

Take the square root of both sides

x = ± 3

The two numbers by setting up a linear equation are 56 and 32

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

Let the two numbers be x and y

Where

y = 4 + 1/2x

So, we have

x + y = 88

Substitute y = 4 + 1/2x in x + y = 88

x + 4 + 1/2x = 88

Evaluate

1.5x = 84

Divide by 1.5

x = 56

Substitute x = 56 in y = 4 + 1/2x

y = 4 + 1/2 * 56

Evaluate

y = 32

Hence, the two numbers by setting up a linear equation are 56 and 32

Read more about linear equations at:

https://brainly.com/question/14323743

#SPJ1

7.86 liters  of purple paint in each container.

volume of red paint is 8.54 liters.

volume of blue paint is 8.31 liters.

Number of container taken is 2 container.

Paint left after equally poured in 2 container.

and we have to find how many liters of paint are in each container.

Volume of RED Paint + Volume of BLUE Paint =  Volume of PURPLE Paint

8.54 liters + 8.31 liters = 16.85 liters.

(16.85/2) - (1.13/2) = 15.72/2

                            =7.86 liters

7.86 liters of purple paint in each container.

To know more about Alligation or Mixture concept, visit:https://brainly.in/question/9802683

#SPJ9

[tex]Answer:\ -55.102^0F\leq t^0\leq 595.958^0F[/tex]

Step-by-step explanation:

[tex]\displaystyle\\C^0=\frac{5}{9} (F^0-32^0)\\[/tex]

Let's multiply both parts of the equation by 9/5:

[tex]\displaystyle\\\frac{9}{5} C^0=F^0-32^0\\\\\frac{9}{5} C^0+32^0=F^0-32^0+32^0\\\\\frac{9}{5} C^0+32^0=F^0\\\\Thus,\\\\F^0=1.8C^0+32^0[/tex]

[tex]t=-48.39^0C\\Hence,\\t^0(F)=1.8(-48.39^0)+32^0\\t^0(F)=-87.102^0+32^0\\t^0(F)=-55.102^0[/tex]

[tex]t=313,31^0C\\Hence,\\t^0(F)=1.8(313,31^0)+32^0\\t^0(F)=563.958^0+32^0\\t^0(F)=595.958^0[/tex]

[tex]Thus,\\-55.102^0F\leq t^0\leq 595.958^0F[/tex]

Answer:

122 degrees

Step-by-step explanation:

43 + 15 = 58 - 180 = 122

The Associative property is not  displayed by any of the given equations.

The associative property of several binary operations in mathematics states that the outcome will not change if the parenthesis in an expression are rearranged.

The order in which the operations are carried out within an expression that has two or more instances of the same associative operator in a row doesn't matter as long as the order of the operands is left untouched.

Examples of associative property :

[tex]{\displaystyle {\begin{aligned}(7+8)+1&=7+(8+1)=9\,\\5\times (3\times 7)&=(5\times 3)\times 7=24.\end{aligned}}}[/tex]

The parentheses were rearranged on each line, but the expression values were left alone. It can be argued that "addition and multiplication of real numbers are associative operations" because this is true for addition and multiplication of all real numbers.

Here 8=8+0 displays additive identity property.

10×1=10 displays multiplicative identity

5+0=5 displays displays additive identity property.

[tex]5\times \frac{1}{5}=1[/tex]  displays multiplicative inverse property.

[tex]3+\frac{3}{4} =3+\frac{3}{4}[/tex]  displays reflexive property.

Hence no equation displays associative property.

To learn more about associative property visit:

https://brainly.com/question/5637942

#SPJ9

Answer:

ssdf

Step-by-step explanation:

dbd beddbees sveveusbs wie eje edidjebebe djebejdjebe ejd s

a)

Solution,

Given,

Cost for 1 pen = $ 1.50

= 1.50×100 cents

= 150 cents

Cost for 1 ruler = 80 cents

No. of Pens needed to be bought = x

No. of rulers needed to be bought = x+10

Now,

Cost for x pens = x×150 cents

= 150x cents

Cost for (x+10) rulers = (x+10)×80 cents

= 80x cents+800 cents

Then,

Total cost = 150x cents+(80x cents+800 cents)

= 150x cents+80x cents+800 cents

= 230x cents+800 cents

= $(230x ÷ 100)+$(800 ÷ 100)

= $2.3x + $8

Therefore,Louise spent $2.3x and $8 as total amount

b)

Sorry,I dont know inequality

Answer:

Step-by-step explanation:

20 divided by 5x20+10=90

Answer:

90

Step-by-step explanation:

this is easiest if you know your order of operations PEMDAS so there are no parenthesis or exponents so next is multiplication and division. so 20/5= 4 then 4*20 is 80 and 80+10=90.

here's an easy way to remember PEMDAS

Please Excuse My Dear Aunt Sally