Eric bought a few marbles and divided equally among four of his friends and his brother, Imer. Eric lost 2 marbles and has only 7 marbles left. How many marbles did Eric buy in all.

The proof that shows that AB∥CD in the diagram given is:

1. E is the midpoint of AD --> Given

2. [tex]\overline{AE} \cong \overline{ED}[/tex] ---> Definition of midpoint

3. E is the midpoint of BC --> Given

4. [tex]\overline{BE} \cong \overline{EC}[/tex] ---> Definition of midpoint

5. ∠AEB ≅ ∠CED --> Vertical Angles Theorem

6. ΔABE ≅ ΔDCE ---> SAS Congruence Theorem

7. AB∥CD ---> CPCTC Theorem.

The given figure showing ΔABE ≅ ΔDCE is in the image attached below.

We know that:

E is the midpoint of AD. Therefore, AE ≅ ED by the definition of midpoint.

E is the midpoint of BC. Therefore, BE ≅ EC by the definition of midpoint.

∠AEB and ∠CED are vertical angles, therefore, ∠AEB ≅ ∠CED by the vertical angles theorem.

This means that ΔAEB and ΔDEC have:

two pairs of congruent sides - AE ≅ ED and BE ≅ EC

one pair of congruent included side -  ∠AEB ≅ ∠CED

Hence, ΔABE ≅ ΔDCE by the SAS Congruence Theorem.

If both triangles are congruent, it implies that all corresponding sides and angles of ΔAEB will be congruent to that of ΔDEC.

Therefore, AB∥CD by the CPCTC Theorem.

Thus, the proof that shows that AB∥CD in the diagram given is:

1. E is the midpoint of AD --> Given

2. [tex]\overline{AE} \cong \overline{ED}[/tex] ---> Definition of midpoint

3. E is the midpoint of BC --> Given

4. [tex]\overline{BE} \cong \overline{EC}[/tex] ---> Definition of midpoint

5. ∠AEB ≅ ∠CED --> Vertical Angles Theorem

6. ΔABE ≅ ΔDCE ---> SAS Congruence Theorem

7. AB∥CD ---> CPCTC Theorem.

Learn more about the CPCTC Theorem on:

https://brainly.com/question/14706064

The corresponding answers for each student plan are:

plan A: 15 years

plan B: 5 years

plan C: 10 years

plan D: 9 years

Thus, first, the graph corresponding to each of the plans must be analyzed. The Y-axis corresponds to money and the x-axis corresponds to the time in years.

Thus, in-plane A, it can be observed that to reach the desired value, the graph will be projected in exponential, so it will be close to 15 years. In plan B, this projection will be reached around 5 years. In plans C and D, this projection will be 10 years and 9 years respectively.

Learn more: brainly.com/question/14355665

Answer:

1) The profit made is $560.

2) Don't know sorry!!

3) A student will pay $1134 for a calculator.

Step-by-step explanation:

Answer:

[tex]y=\frac{4}{5}x-\frac{18}{5}[/tex]

Step-by-step explanation:

Hi there!

We want to find the equation of the line that passes through the point (-3, -6) and (2, -2)

There are 3 ways to write the equation of the line:

The easiest way would either be slope-intercept or point-slope form, but let's write the equation in slope-intercept form, since it's the most common way

So we'll need to find the slope

The formula for the slope calculated from 2 points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

We have everything needed to find the slope, let's just label the values of the points to avoid any confusion:

[tex]x_1=-3\\y_1=-6\\x_2=2\\y_2=-2[/tex]

Now substitute these values into the formula. Remember that m is the value of the slope:

m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m=[tex]\frac{-2--6}{2--3}[/tex]

Simplify the fraction:

m=[tex]\frac{-2+6}{2+3}[/tex]

Add the numbers together:

m=[tex]\frac{4}{5}[/tex]

So the slope of the line is 4/5

Let's plug it into the formula y=mx+b, since we now know the value of m

y=[tex]\frac{4}{5}[/tex]x+b

Now let's find b

As the equation passes through both (-3, -6) and (2, -2), we can use either point to help solve for b

Either point works, but let's take (2, -2) for instance

Substitute 2 as x and -2 as y

-2=4/5(2)+b

Multiply

-2=8/5+b

subtract 8/5 from both sides

-18/5=b

Now substitute -18/5 as b into the equation:

[tex]y=\frac{4}{5}x-\frac{18}{5}[/tex]

Hope this helps!

Answer:

y = 2x-1

Step-by-step explanation:

I'm guessing gradient of 2 means slope of 2

if line passes through (2,3) and has a slope of 2, we can use the slope intercept equation

slope-intercept (y=mx+b)

m is the slope and b is the y-intercept (which we are trying to find)

so far, we have a point and a slope so we can fill in x,y, and m

(3) = (2)(2) + b

3 = 4 + b

3-4 = 4-4 + b (to undo addition, you use subtraction so I minus 4 from each side)

-1 = b

we found b so we just take the (2,3) out of the equation substitute the x,y back into the equation

y = 2x - 1

Answer:

$27.45 for 3 pizzas

In my opinion

Answer:

$32.48 for 7 pizzas

Step-by-step explanation:

25 divided by 5 = $5

32.48 divided by 7 = $4.64

27.45 divided by 3 = $9.15

28.74 divided by 4 = $7.185

Answer: 6+3 = 9

Step-by-step explanation:

-3-6 is equivalent to 6-(-3). Subtracting a negative number is the same as adding a positive number, so 6-(-3) is the same as 6+3. 6+3 = 9.

Answer:

1/3 or 0.33

Step-by-step explanation:

Hope it helps

LMK if it does and weather it is wrong or right

Answer:

2(n-8) = 5

Step-by-step explanation:

I'm assuming that its supposed to say "a number and 8"

Answer:

x=10.5

Step-by-step explanation:

x will be a number

2(x-8)=5 --> I'm assuming your question is " twice the difference of a number and 8 equals 5.

Solving

2(x-8)=5

2x-16=5 --> distrubute the 2--> 2*x = 2x and 2*-8 = 16

2x=16+5--> add 16 to other side of x

2x=21--> add like terms

2x / 2 =21 / 2--> single out x

x=10.5 --> 21/2 --> just divide

Answer:

6,543

Step-by-step explanation:

This is my guess ONLY.

Answer:

[tex]7\frac{5}{3}[/tex]

Step-by-step explanation:

[tex]2\frac{3}{5}[/tex] × [tex]3\frac{1}{3}[/tex]

First make these two fractions as improper fractions.

[tex]\frac{13}{5}[/tex] × [tex]\frac{10}{3}[/tex]

Now multiply the fractions

[tex]\frac{130}{15}[/tex]

You can divide both sides by 5 to simplify the fraction.

[tex]\frac{26}{3}[/tex]

Now make it as a mixed number.

[tex]7\frac{5}{3}[/tex]

Hope this helps you.

Let me know if you have any other questions :-)

Hello there! (:

[tex]2\frac{3}{5} *3\frac{1}{3}[/tex]

Follow these steps to multiply mixed numbers:

Now, how do we convert a mixed number into an improper fraction?

Here are the steps:

Step 1:

2*5=10

10+3=13

[tex]\frac{13}{5}[/tex]

Now, we do the same to the second fraction:

[tex]\frac{10}{3}[/tex]

[tex]\frac{13}{5} *\frac{10}{3}[/tex]

Step 2. Multiply the numerator times the numerator and the denominator times the denominator:

[tex]\frac{26}{3}[/tex]

Now, let's convert this fraction into a mixed number:

[tex]7\frac{5}{3}[/tex]

Hope it helps you!

If you have any queries, feel free to ask me! (:

~A smiley teen who adores helping others

[tex]MagicalNature[/tex] here to help

Answer:

A and D

Step-by-step explanation:

A is 2 times 6 to the 2nd which is just 24 and D is 16 times 9 which is 144 both are prime factors of 144.

Answer:

A

Step-by-step explanation:

Answer:

conversion from gram to kilogram

u divide the gram by 1000

which is 722/ 1000

=0.722kilograms

i.e answer is A

Answer:

I may not know his balance but I think he's not making a good financial decision because he already has - $60 in his account and he's spending more making him more liable to burn money and it's not advisable

Answer:

x = 6

Step-by-step explanation:

6x - 3y = -21 => 6x = 3y - 21

4x = 3y - 9 => 4x = 3y - 9

-2x =  -12

-2x/-2 = -12/-2

x = 6

Hope this works

Answer:

its b

Step-by-step explanation:

Answer:

a₅ = 160

Step-by-step explanation:

Using the recursive rule and a₁ = 10 , then

a₂ = 2a₁ = 2 × 10 = 20

a₃ = 2a₂ = 2 × 20 = 40

a₄ = 2a₃ = 2 × 40 = 80

a₅ = 2a₄ = 2 × 80 = 160

Answer:

the reciprocal of 1 6/7 is 7/15, so 7/15 and 7/13 have a difference of two in their denominators.

Step-by-step explanation:

hope I helped you! :D

Answer:

2

Step-by-step explanation:

Step-by-step explanation:

Answer:

d - $36

Step-by-step explanation:

I=Prt

(interest=principle*rate*time in years)

I=1200*.03*1

I=1200*.03

I=36

Answer:

-60m/s²

Step-by-step explanation:

The first thing to do is know the equation:

(Final velocity - initial (original) velocity) / time (seconds)

Next you check the units:

10 minutes = 600 seconds

Then you use the equation to solve the problem:

(4000 - 40000) = -36000

-36000 / 600 = -60

Units for acceleration = m/s²

Answer = -60m/s²

The value is negative because the satellite's velocity has decreased

Hope this helps.

Answer:

(−2, 3), (−5, 3) lie on a horizontal line.  The y value is 3 for both values of x.  The line runs parallel to the x axis and 2 steps above.

Step-by-step explanation:

Answer:

B and D

Step-by-step explanation:

opposite rays 180° to each other

here B and D are opposite rays

Answer:

B and D

Step-by-step explanation:

Each opposite ray need 180 degree.

Answer:

0.01

Step-by-step explanation:

your welcome :D have a good day pls mark me with the crown (whatever its called lol)

Answer:

Step-by-step explanation:

Volume of prism:

Substitute dimensions:

Answer:

h(x) = - 2x² + 3

Step-by-step explanation:

Given f(x) then f(x) + c is a vertical translation of f(x)

• If c > 0 then a shift up of c units

• If c < 0 then a shift down of c units

Here the shift is 7 units up , then

h(x) = f(x) + 7 = - 2x² - 4 + 7 = - 2x² + 3

Answer:

y=-2x+8

Step-by-step explanation:

Hi there!

We want to find the equation of the line that passes through the point (8, -8) and has a slope of -2

We can write this equation in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

Since we already know the slope of the line, we can immediately plug it into the equation as m:

y=-2x+b

Now we need to find b

As the equation of the line passes through the point (8, -8), we can use it to help solve for b, since (8, -8) is a solution to the equation, meaning that it will yield a true statement when plugged into the equation

So substitute 8 as x and -8 as y:

-8=-2(8)+b

Multiply

-8=-16+b

Add 16 to both sides

8=b

Now substitute 8 as b into the equation:

y=-2x+8

Hope this helps!

.Equation of line in point slope form

[tex]\\ \sf\longmapsto y-y_1=m(x-x_1)[/tex]

[tex]\\ \sf\longmapsto y+8=-2(x-8)[/tex]

[tex]\\ \sf\longmapsto y+8=-2x+16[/tex]

[tex]\\ \sf\longmapsto 2x+y+8-16=0[/tex]

[tex]\\ \sf\longmapsto 2x+y-8=0[/tex]

Answer:

Hello!

After reviewing the question you have provided, I came up with the correct answer:

C) 2

Step-by-step explanation:

Firstly:

As the question states, you need to round each number to the nearest whole number and then choose the closest estimate to what the nearest solution could be.

When you round the two numbers you should come up with "3-1= ____".

This is because you round up with a number has .5 or higher, and you round down when any number has .4 or lower.

So 3.2 rounds to 3

And 1.4 rounds to 1.

With the new equation you can then solve "3-1= 2"!

Hope this helps!

Answer:

0

Step-by-step explanation:

Absolute values can't have negatives as answer. Useful tip, If there is a negative as an answer for absolute value, there is no solution, if it has 0 as an answer, there is 1 solution, and if it has a positive as answer, then it will have 2 solutions.