Solve 4x+8(x-3)=4+6x
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D. the final one, the one you currently have answered is the correct one, this is because a parallelogram, like this one, requires that the triangles on either side must be congruent in order for this to be true.

Triangles BPA and DPC are congruent, which implies that opposite sides AB and CD are parallel, thus making quadrilateral ABCD a parallelogram.

The statement Triangles BPA and DPC are congruent is used to prove that quadrilateral ABCD is a parallelogram.

Given that diagonals AC and BD bisect each other, we have:

[tex]$\angle BAP = \angle CDP$[/tex]  (vertically opposite angles)

[tex]$AP = CP$[/tex] and BP = DP  (given)

Therefore, triangles BPA and DPC are congruent by SAS (side-angle-side) congruence. This means that [tex]$\angle ABP = \angle CDP$[/tex] and [tex]\angle BPA = \angle DPC$.[/tex]

Since [tex]$\angle ABP$[/tex] and [tex]$\angle CDP$[/tex]  are alternate interior angles formed by transversal BD intersecting parallel lines AB and CD, we have:

AB \parallel CD

Similarly, since [tex]$\angle BPA$[/tex]  and [tex]$\angle DPC$[/tex] are alternate interior angles formed by transversal AC intersecting parallel lines AB and CD, we have:

AB \parallel CD

Therefore, quadrilateral ABCD is a parallelogram.

Proof:**

1. Given:[tex]$\angle BAP = \angle CDP$ and $AP = CP$ and $BP = DP$[/tex]

2. Prove:[tex]$AB \parallel CD$[/tex]

SAS Congruence**

1.[tex]$\triangle BAP \cong \triangle DPC$ (SAS)[/tex]

Alternate Interior Angles**

2. [tex]$\angle ABP = \angle CDP$[/tex](alternate interior angles)

3. [tex]$\angle BPA = \angle DPC$[/tex] (alternate interior angles)

Therefore, $AB \parallel CD.

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Answer:

7

Step-by-step explanation:

We know that since 6 ounces creates 6/7 of a serving, that basically says that 1/7 of a serving is created with 1 ounce of pasta. So if there were 7 ounces of pasta, that would make 7/7 servings and that would be 1 serving

B)

A= 8.6

B=8.66666...

C=8.25

D=7.33333...

Solution

In order to find  greatest to least number, we have to convert the given fractions into decimals.

3 [tex]\frac{1}{10}[/tex] % = 3 + 1/10 = 3 + 0.10 = 3.10%

3 [tex]\frac{2}{5}[/tex]% = 3 + 2/5 = 3 + 0.40 = 3.40%

3 [tex]\frac{1}{4}[/tex] %= 3 + 0.25 = 3.25%

3 [tex]\frac{1}{3}[/tex]% = 3 + 0.33 = 3.33%

Now we can easily, compare the numbers and write from greatest to least.

3.40%, 3.33%, 3.25%, 3.10%

Greatest to least  = 3 2/5%, 3 1/3%3, 3 1/4%,  1/10%,

Thank you :)

Answer:

3 2/5%, 3 1/3%, 3 1/4%, 3 1/10%

Step-by-step explanation:

Quick Answer: Yes

If you reduce both to their lowest terms each becomes 1/2

Divide the numerator and denominator by 7 for the first one

(7 ÷ 7)/(14 ÷ 7) = 1/2

And numerator and denominator by 3 for the second one

(3 ÷ 3)/ (6 ÷ 3) = 1/2

PEMDAS tells us to use multiplication and division before addition and subtraction.

-5(8) ÷ 10 - 14 ÷ 7 - (-2)(3)

-40  ÷ 10 -     2    -   -6

     -4       -    2     + 6    two negatives make a positive so - - 6  = + 6

            -6              +6

                      0

Answer: 0

Jenny's total earnings:

total earnings = (hours worked on design)*40 + (hours worked on maintenance)*35

average earnings = total earnings / hours worked

So far she has

total earnings = 18*40 + 20*35 = $1420

which is an average per hour = $1420/38hr = $37.37

How many more hours on webdesign: x

so that

($1420+x*$40)/(38+x)=38

Now solve for x - this I let you do. My results is x=12 (you can verify by plugging it iback into the equation).

The answer is Jenny needs to work 12 more hours to claim an average earnings of $38/hr. Lmk if you have questions.

Answer:  C looks like the best fit.

Answer:

C

Step-by-step explanation:

A scatterplot best fit line looks as thought the distance of the points above the line are the same as the points below the line in this case. See the comment under d for more.

A

All the points are above the line

B

Only a very few points come close to the line. Left right is more at work here rather than up and down.

C Answer

D

The average of those above the line might be the same as below the line, but the symmetry is a left right symmetry; all the downs are on the left and all the ups are on the right.. They might average out to be 0 but it is not what is meant. The x and y values both have something to do with the answer. D is the second best answer.

10:00 will show trhe corect tiem

2 two-thirds are in four-thirds because 4 divided by 2 is 2

Answer:

$290.50

Step-by-step explanation:

121.04 * 80% = 96.832

121.04 - 96.832 = 24.208

24.208 * 12 = 290.496 ~ 290.50

Answer:

Use the distance formula.  Result:  sqrt [ (a-c)^2 + (b-d)^2 ]

Step-by-step explanation:

distance = d = sqrt [ (a-c)^2 + (b-d)^2 ]

Answer:

[tex]d=\sqrt{(c-a)^2+(d-b)^2}[/tex]

Step-by-step explanation:

We are given two points (a, b) and (c, d)

We need to find the distance between two points.

It is coordinate of two points. Using coordinate formula of distance.

[tex]d=\sqtt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

where,

[tex]x_2\rightarrow c[/tex]

[tex]x_1\rightarrow a[/tex]

[tex]y_2\rightarrow d[/tex]

[tex]y_1\rightarrow b[/tex]

Substitute into formula

Distance between two points is

[tex]d=\sqrt{(c-a)^2+(d-b)^2}[/tex]

Hence, The formula of distance between two points  (a, b) and (c, d) is [tex]d=\sqrt{(c-a)^2+(d-b)^2}[/tex]

First

Multiply 20in. by 15in.

Second

Multiply 12 by 8

Third

Multiply the sum of 8 and 12 to 3

The answer would be yes because the sum of 12, 8, and 3 is 288 and 20 by 15 is 300 so you'd have some left over.

Yes, the rectangular piece of wrapping paper can cover the shirt gift box.

To determine if the rectangular piece of wrapping paper can cover the shirt gift box, we need to compare the dimensions of the paper to the dimensions of the box.

The dimensions of the paper are 20 in. by 15 in. The dimensions of the box are 12 in. long, 8 in. wide, and 3 in. deep.

To cover the box completely, the paper needs to have enough surface area to cover the top and all four sides of the box.

Since the dimensions of the paper are greater than or equal to the corresponding dimensions of the box, the rectangular piece of wrapping paper can cover the shirt gift box.

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Find the totals of both Angle s A and T by adding the 2 angles in each corner:

Angle A = 58 + 32 = 90 degrees

Angle T =  46 + 44 = 90 degrees.

Becuase both these angles are 90 degrees Lines AM and TH are parallel.

The correct evaluation for the expression 2⋅(36⋅3−5) under the order of operations is 206, which is not one of the provided options A: 2/3, B:3, C:6, D:18.

The subject is Mathematics and the question belongs to the Middle School grade. The problem given is to evaluate the expression: 2⋅(36⋅3−5). Here, we will use the order of operations, also known as BIDMAS or PEMDAS, which stands for Brackets, Indices (or exponents), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).

First, we evaluate the operation in the parentheses: 36 times 3 minus 5, which simplifies to 108-5 = 103. Next, this value is multiplied by 2 according to the expression, resulting in a final answer of 2*103= 206. Hence, the correct evaluation of the expression 2⋅(36⋅3−5) is 206. The options provided in the question A: 2/3, B:3, C:6, D:18 do not match the correct answer.

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He can play 4 rounds. If you find a common denominator, it would end up with 9/12 of an hour to play and then you subtract the 1/12 it took to set it up. this leaves you with 8/12. but, it takes 2/12 of an hour to play each round. so 8 divided by 2 is 4. Which is where the 4 rounds is from!

∠AKJ ≅ AIH  because they are corresponding angles

  60° = AIH   by substitution

ΔAIH

∠A + ∠I + ∠H = 180°   per the triangle angle sum theorem

 x  + 60 + 56 = 180    substituted known values

 x +       116     = 180   added like terms

                    x = 64     subtracted 116 from both sides  

Answer: 64°  

Answer:

280 adult tickets, 40 student tickets and 80 children tickets were sold.

Step-by-step explanation:

To solve this problem let's call:

x = number of tickets for adults

y = number of tickets for students

z = number of tickets for children

The income for the concert is $ 7840

Then we can raise the following equations according to the given conditions:

[tex]x+y+z = 400[/tex]   (i)

[tex]22x+15y +13.50z = 7840[/tex] (ii)

 There are 40 more children in the concert than students:

So:

[tex]z=40+y[/tex]  (iii)

We then have 3 equations and 3 unknowns:

To solve the system we multiply the equation (i) by -22 and add it to the equation (ii)

So:

[tex]-22x-22y-22z=-8800[/tex]

       +

[tex]22x+15y +13.5z =7840 [/tex]

[tex]-7y-8.5z = -960[/tex] (iv)

 Now we multiply (iii) by 7 and add it to (iv)

[tex]7y-7z = -280 [/tex]

   +

[tex]-7y-8.5z = -960[/tex]    

[tex]-15.5z = -1240 [/tex]

[tex]z = 80[/tex] (v)

We substitute (v) in (iv) and we have

[tex]y = 40[/tex] (vi)

We substitute (v) and (vi) into (i) and we have:

[tex]x =280[/tex]

280 adult tickets, 40 student tickets and 80 children tickets were sold.

54 x .50 = $27

54 x .25 = 13.5

50% = $27.00

25% = $13.50

it is an odd number. it is also a prime number . ie only divisible by one and  itself.

Let the smallest number = x

The next higher number would be x +1

The 3rd number would be x +2

The sum of the 3 numbers: x + x+1 + x+2

33 more than the smallest number is written as x+33

Now you have:

x + x+1 + x+2 = x+33

Simplify the left side:

3x +3 = x +33

Subtract 3 from each side:

3x = x +30

Subtract 1x from each side:

2x = 30

Divide both sides by 2:

X = 30/2

x = 15

The three numbers are 15, 16 and 17

We have two rules in case of rounding off digits,

Rule 1:

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. Example: 38 rounded to the nearest ten is 40.

Rule 2:

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

We are given the number 13_,644 which rounds off to 130,000.

Now as we can see the number is rounded down, so we can apply rule number 2 here.

If we place the digit 0, 1, 2, 3 or 4 then the number will round off to 130,000.

Answer: The possible digits that can go in thousands place are 0, 1, 2, 3 or 4.

Lets solve each one :

 If she is 9 :

9 times 2 = 18 + 9 = 27

If she is 11 :

11 times 2 = 22 + 11 = 33

If she is 20 :

20 times 2 = 40 + 20 = 60

If she is 10 :

10 times 2 = 20 + 10 = 30

You pick your answer :)

I hope this helped!

Have a great day!!!

The greatest age Raphael's sister can be is 10 years old.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =

Given that, Raphael is twice as old as his sister is. The sum of their ages is less than 30.

Let the age of Raphael's sister be x,

2x + x = 30

3x = 30

x = 10

Hence, The greatest age Raphael's sister can be is 10 years old.

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For this case we have:

Cost of manufactures of T-shirts [tex]C(x)=10.5x[/tex]

where x represents the number of T-shirts

Part A:

Substituting [tex]x = 8[/tex] in the total cost equation you have to:

[tex]C (8) = (10.5) (8)\\\\C (8) = 84\\[/tex]

Thus, the cost of 8 shirts will be [tex]C (8) = 84\\[/tex]

Part B:

If [tex]x = 12[/tex] then

[tex]C (12) = (10.5) (12)\\\\C (12) = 126\\[/tex]

Thus, the cost of 12 shirts will be [tex]C (12) = 126\\[/tex]

Answer:

[tex]C (8) = 84\\\\C (12) = 126\\\\[/tex]

The cost function c(x) = 10.5x, when applied for 8 and 12 t-shirts, indicates that 8 t-shirts will cost $84 and 12 t-shirts will cost $126.

The function c(x) = 10.5x represents the cost to manufacture t-shirts, where x is the number of t-shirts.

Part A: If a club needs 8 t-shirts, we substitute x=8 into the function. Therefore, c(8) = 10.5*8 = 84. Thus, it will cost $84 to manufacture 8 t-shirts.

Part B: If c(12), we substitute x=12 into the function. Therefore, c(12) = 10.5*12 = 126. This means that 12 t-shirts will cost $126.

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Ok so if the agent spend 1,500$ on advertising then thats -1,500 for his wallet eg.

WALLET:

-1,500$

Now if the house sells in 3 months that's 9,000 in wallet but since there is only a 40% chance then we need to work out 40% of 9000 we can do that by doing 9000 x 0.40 which = 3,600 so 3,600 in wallet on average

-1,500

+3,600

now if we combine these we get 2,100 so the answer is on average 2,100

Answer:

B edge

Step-by-step explanation:

The probability of drawing a red gumdrop is [tex]\( \frac{2}{5} \)[/tex] and butterscotch candy is [tex]\( \frac{3}{5} \)[/tex]. Combined, it's [tex]\( \frac{6}{25} \)[/tex]. Answer: A.

To find the probability that Craig will draw a red gumdrop and a piece of butterscotch candy, we need to find the probability of each event separately and then multiply them together because the events are independent.

1. Probability of drawing a red gumdrop:

[tex]\[ P(\text{red gumdrop}) = \frac{\text{number of red gumdrops}}{\text{total number of gumdrops}} \][/tex]

[tex]\[ P(\text{red gumdrop}) = \frac{2}{2 + 3} = \frac{2}{5} \][/tex]

2. Probability of drawing a piece of butterscotch candy:

[tex]\[ P(\text{butterscotch candy}) = \frac{\text{number of butterscotch candies}}{\text{total number of candies}} \][/tex]

[tex]\[ P(\text{butterscotch candy}) = \frac{3}{3 + 2} = \frac{3}{5} \][/tex]

Now, multiply the probabilities together:

[tex]\[ P(\text{red gumdrop and butterscotch candy}) = P(\text{red gumdrop}) \times P(\text{butterscotch candy}) \][/tex]

[tex]\[ P(\text{red gumdrop and butterscotch candy}) = \frac{2}{5} \times \frac{3}{5} \][/tex]

[tex]\[ P(\text{red gumdrop and butterscotch candy}) = \frac{6}{25} \][/tex]

So, the probability that Craig will get a red gumdrop and a piece of butterscotch candy is [tex]\(\frac{6}{25}\)[/tex], which corresponds to option A.

The correct question is:

Here are 2 red gumdrops and 3 green gumdrops in a small jar. Also, 3 pieces of butterscotch candy and 2 pieces of cinnamon candy are in another jar. If Craig draws one piece of candy from each jar without looking, what's the probability that he will get a red gumdrop and a piece of butterscotch candy? The Answer choices are

A. 6/25

B. 1/2

C. 4/25

D. 1/5

Hi the answer is:

y = IxI + 6