Look at the parallelogram ABCD shown below: The table below shows the steps to prove that if the quadrilateral ABCD is a parallelogram, then its opposite sides are congruent:
Statement Reasons 1 AB is parallel to DC and AD is parallel to BC Definition of parallelogram 2
angle 1 = angle 2, angle 3 = angle 4 If two parallel lines are cut by a transversal then the _______________ are congruent 3
BD = BD Reflexive Property 4
triangles ADB and CBD are congruent If two angles and the included side of a triangle are congruent to the corresponding angles and side of another triangle then the triangles are congruent by ASA postulate 5
AB = DC, AD = BC Corresponding parts of congruent triangles are congruent
Which choice completes the missing information for reason 2 in the chart?
alternate interior angles
corresponding angles
same-side interior angles
vertical angles

Answer:

1. [tex]a_{n}=\frac{1}{3} a_{n-1}[/tex] where [tex]a_{1} =27[/tex]

2. [tex]2^{x+1}[/tex]

3. The domain is {-12,-8,0,1}. The range is {0,12,8}.

Step-by-step explanation:

1. The recursive formula is defined as an implicit way of writing the rule of a function or pattern. It is implicit because it uses previous terms to find the next term in the pattern. We multiply, add, subtract or divide a previous term by a constant value or expression to find the next. In this case, 27 becomes 9 through division by 3 or multiplication by 1/3. The pattern continues 9(1/3)=3 and so forth.

2. The function f(x) is an exponential and has a general form of [tex]y=ab^x[/tex]. We know f(x) is [tex]2^x[/tex]. The points of g(x) all changed from f(x) by shifting over to the left. This transformation occurred by [tex]2^{x+1}[/tex].

3. Domain is defined as the set of all x-values. Range is defined as the set of all y-values. The domain is {-12,-8,0,1}. The range is {0,12,8}.

ΔABC ≅ ΔDEF

I find it easier to see the congruencies if I write them underneath each other:

∠A ≅ ∠D           [tex]\overline{AB}[/tex] ≅ [tex]\overline{DE}[/tex]

∠B ≅ ∠E            [tex]\overline{BC}[/tex] ≅ [tex]\overline{EF}[/tex]

∠C ≅ ∠F            [tex]\overline{AC}[/tex] ≅ [tex]\overline{DF}[/tex]

w - width

6w - length

486 in² - area of the rectangle

(w)(6w) = 6w² - area of the rectangle

The equation:

6w² = 486     divide both sides by 6

w² = 81 → w = √81

w = 9 in

l = 6w → l = (6)(9) → l = 54 in

The perimeter: P = 2l + 2w

P = 2(54) + 2(9) = 108 + 18 = 126 in

Final answer:

The rectangle with an area of 486 square inches has a width of 9 inches and a length of 54 inches, leading to a perimeter of 126 inches.

Explanation:

To find the perimeter of a rectangle when given the area and the relationship between length and width, first, set up an equation where length (L) is equal to six times the width (W), so L = 6W. The area of a rectangle is found by multiplying the length by width, so we have the equation Area = L × W. With the given area of 486 square inches, we can substitute L with 6W to get 486 = 6W × W.

Solving this equation, W2 = 486/6 leads to W2 = 81. Taking the square root, we find that W = 9 inches. Since the length is six times the width, L = 6 × 9 = 54 inches.

The perimeter (P) of a rectangle is the sum of twice the length plus twice the width, so the equation P = 2L + 2W can be used. Substituting the values we found, P = 2(54) + 2(9) leads to P = 108 + 18, so the perimeter equals 126 inches.

Answer:

[tex]\displaystyle m=\frac{-5}{6}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point (8, 8)

Point (20, -2)

Step 2: Find slope m

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

Answer:

x = -9, -3

Step-by-step explanation:

x^2 + 12x + 27 = 0

We need 2 numbers whose product is  + 27 and whose sum is + 12. These are 3 and 9. So the factors are:-

(x + 3)(x + 9)  and this = 0

So (x + 3) = 0  or x + 9 = 0

x = -3 , -9

Answer:

-5 and 7

Step-by-step explanation:

we need to find numbers a and b such that a+b=-2 and ab=-35.

a=5 and b=-7 satisfy both conditions, so our equation can be re-written:

(x + 5)(x-7) = 0

According to the zero-product property, we know that

x+5=0 or x-7=0, which means

x=-5x or x=7

Please mark brainliest and thank! Thank you!

Answer:

The Constant of Proportionality is 4.

Step-by-step explanation:

This is because in the table provided,

The correct answer to the question is 4.

I did the quiz and got an A on it.

Hope it helps, I'm on K12 OHVA aswell.

Answer:

The more 'chocolatey' chocolate milk is the one prepared by Nell's mom.

Step-by-step explanation:

This problem can be solved by establishing the ratio of chocolate syrup for one ounce of milk in each beverage.

For mom's chocolate milk:

[tex]\frac{30mL}{2ounces} = 15\frac{mL}{ounce}[/tex]

For dad's chocolate milk:

[tex]\frac{65mL}{5ounces} = 13\frac{mL}{ounce}[/tex]

We know that:

15 > 13

So we can conclude that mom's chocolate milk is more 'chocolatey'.

Answer:

The correct option is b. 15

Explanation:

We are given that a freight train travels at an average speed of 60 mph.

Also we are given that the average speed of passenger train is 72 mph.

We are also given that the freight train leaves 3 hours before passenger train. So the number of miles covered by freight train in 3 hours is:

[tex]3 \times 60 = 180[/tex] miles.

Let X be the number of hours it takes the passenger train to catch up the freight train.

Therefore, we have:

[tex]180 + 60 \times X = 72 \times X[/tex]

[tex]72X-60X = 180[/tex]

[tex]12X=180[/tex]

[tex]X=\frac{180}{12}[/tex]

[tex]X=15[/tex]

Therefore, the passenger train will take 15 hours to catch up the freight train.

Answer:

sorry im answering late but the answer is C. 18

Step-by-step explanation:

60 x 18 = 1,080

72 started 3 hours later so that means you subtract 3 from 18 which equals 15 and 72 x 15 = 1,080

ur answer is 18

Answer:

A) about 1 pet

Step-by-step explanation:

Total the products of number of pets and their probability.

... 0×0.4 +1×0.3 +2×0.25 +3×0.05

... = 0 +0.3 +0.5 +0.15 = 0.95 . . . . . about 1

___

We assume that "3 or more" will be closer to 3 than to 15, a number that would raise the expected value to more than 1.5.

Answer:

110 Walnuts

Step-by-step explanation:

Firstly, there are 6 bags and 330 walnuts. You divide 330 by 6 and you get 55. 330/6. Now, you multiply 55 by 2 and you get your answer. So basically in each bag there are 55 walnuts and if you multiply that by 6 you get 330 again. Hope this helped!

Answer:

110 walnuts

Step-by-step explanation:

330÷6 is 55

55•2 is 110

Answer: D/3f^2 = e

Step-by-step explanation:

D = 3ef^2

Divide by 3f^2 on both sides.

D/3f^2=e, the first option.

Answer:

0.33

Step-by-step explanation:

Answer:

option B

Step-by-step explanation:

[tex]2x^2-4x+16=0[/tex]

We need to solve this equation using quadratic formula

[tex]x= \frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]

a=2, b= -4, c=16

Plug in the values in the formula

[tex]x= \frac{-(-4)+-\sqrt{(-4)^2-4(2)(16}}{2(2)}[/tex]

[tex]x= \frac{4+-\sqrt{16-128}}{4}[/tex]

[tex]x= \frac{4+-\sqrt{-112}}{4}[/tex]

Simplify the square root. the value of square root (-1) = 'i'

[tex]x= \frac{4+-4i\sqrt{7}}{4}[/tex]

Now we divide by 4

[tex]x= 1+-i\sqrt{7}[/tex]

So there are two complex roots. since the degree of polynomial is 2

Answer:

B

Step-by-step explanation:

I took the test :)

Answer:

The midpoint is (-6,-4)

Step-by-step explanation:

The formula for the midpoint is

midpoint = (x1+x2)/2, (y1+y2)/2

Substituting what we know

               = (-8+-4)/2, (-1+-7)/2

                = -12/2, -8/2

                  = -6, -4

Final answer:

The midpoint M of the line segment joining points S = (-8, -1) and T = (-4, -7) is calculated using the midpoint formula and is found to be M = (-6, -4).

Explanation:

The midpoint M of the line segment joining the points S and T can be found using the midpoint formula. To find the midpoint M between the points S = (-8, -1) and T = (-4, -7), you need to take the average of the x-coordinates and the y-coordinates separately.

The midpoint M's x-coordinate is the average of the x-coordinates of S and T: ((-8 + (-4)) / 2 = -6. Similarly, the midpoint M's y-coordinate is the average of the y-coordinates of S and T: ((-1 + (-7)) / 2 = -4.

Therefore, the midpoint M is located at (-6, -4).

Answer:

There may be a correlation between eating blueberries and a lower cholesterol level.

Step-by-step explanation:

cause correlation does not cause causation.

The greatest number he can spend on is $5 since he has $10 he will have $5 reamining.

Answer:

Correct choice is B

Step-by-step explanation:

The function [tex]f(x)=20x[/tex] represents the situation, where x is the number of sold video games and f(x) is the total cost of sold games.

Jason  must sell a minimum of 5 games, this means that [tex]x\ge 5.[/tex] He has 30 video games he can sell, then [tex]x\le 30.[/tex] Thus, the domain of the function is [tex]5\le x\le 30.[/tex]

The range of the function f(x) is

[tex]20\cdot 5\le f(x)\le 20\cdot 30,\\ \\100\le f(x)\le 600.[/tex]

Answer: SAS congruence (choice C)

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

Explanation:

Let's go through the various answer choices. I'll say whether or not they are used

A) This is used because angle WXZ = angle WYZ and angle WZX = angle ZWY are the two pairs of angles. The pair of sides are WZ = WZ which overlap (aka shared) between the two triangles. Note how the sides are not between the angled mentioned. Eg: for the triangle on the left, WZ is not between angle WXZ and angle WZX. So we can cross choice A off the list. Note: AAS is slightly different from ASA. Make sure not to confuse the two.

B) We use this to prove that the right angles (WXZ and WYZ) are congruent to each other. Both are 90 degrees. This will then feed in to choice A above, to help use AAS. We can cross choice B off the list.

C) We do not use SAS because we use AAS instead. We only have info about one pair of sides (WZ = WZ). We do not have info about another pair of sides. Therefore, this is the answer.

D) We use this fact to help set up that angle WZX = angle ZWY. The segments WY and XZ are parallel. I like to think of them as train tracks. On the inside of the train tracks are the angles WZX and ZWY, and they are on opposite sides of the transversal segment WZ, so this is why the pair of angles are alternate interior angles. They are congruent as long as WY is parallel to XZ. Like with choice B, this helps feed into choice A. We can cross choice D off the list.

Among the listed reasons, the Alternate Interior Angles Theorem would typically not appear in a proof proving that segment WY is congruent to segment ZX, unless the diagram involved parallel lines cut by a transversal. Other postulates might be used if angle and side measurements are congruent.

In proving that segment WY ≅ segment ZX, some postulates or theorems may not appear in the proof depending on the given diagram. The Angel-Angle-Side (AAS) Congruence Theorem, the Side-Angle-Side (SAS) Congruence Postulate, and the Right Angles Congruence Theorem could all potentially appear in the proof if relevant angle and side measurements are given in the diagram.

However, the Alternate Interior Angles Theorem would typically not appear in this proof. This theorem is related to the indication that two lines are parallel when they are cut by a transversal and the alternate interior angles are congruent. This theorem does not directly involve proving the congruity of sides (or segments) as would be necessary for proving segment WY ≅ segment ZX. Unless the diagram specifically involved parallel lines cut by a transversal, this theorem would not be used.

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Answer:

12x

Step-by-step explanation:

number 1 is 12x bcuz two x plues ten equals 12x although i did it another way i still got it right just letting you no im working on the second one

The outside angle is equal to the sum of the two opposite inside angles.

So you have:

X + 82 = 2X+10

Subtract 1 X from each side:

82 = X+10

Subtract 10 from each side:

x = 72

Now you can calculate the exterior angle by replacing x with 72:

2x+10 = 2(72) +10 = 144+10 = 154

Answer:

(2,1)

Step-by-step explanation:

You are only asking that the graph be drawn and that the minimum be stated. You are not asking how the minimum was obtained (by completing the square).

The graph (using Desmos) shows that the min is at (2,1)

Graphing is a mighty powerful tool, wouldn't you say? It tells you the answer before you have to do one bit of algebra.

Final answer:

Ms. Keller will grade 17.5 projects in seven hours at her current rate of 2.5 projects per hour.

Explanation:

The student's question is about determining at what rate Ms. Keller is grading projects and how many projects she will grade in seven hours based on her current pace. Since Ms. Keller has graded five projects in two hours, her grading rate is 5 projects / 2 hours, which simplifies to 2.5 projects per hour. To find out how many projects Ms. Keller will grade in seven hours at this rate, we multiply 2.5 projects/hour by 7 hours, resulting in 17.5 projects.

Therefore, Ms. Keller will grade 17.5 projects in seven hours at a rate of 2.5 projects per hour.

Answer:

48

Step-by-step explanation:

you need 4 one-fourth cups to make one cup. multiply 12 by 4 and you get 48

By dividing the total amount of soup (12 cups) by the amount of soup per bowl (1/4 cup), we find that Joe can fill 48 bowls.

The student poses a question related to division and unit conversion. To address the student's question, we should calculate how many bowls Joe can fill by dividing the total amount of soup by the amount used for each bowl. Joe has 12 cups of soup and uses 1/4 cup of soup for each bowl. The calculation would be:

Number of bowls = Total cups of soup / Cups of soup per bowl

Number of bowls = 12 cups / 1/4 cup per bowl

Number of bowls = 12 / 0.25

Number of bowls = 48

Therefore, Joe will use 48 bowls to serve the 12 cups of soup, with 1/4 cup of soup in each bowl.

Answer:

(x^2 +6)/2

or  1/2 x^2 +3

Step-by-step explanation:

f(x)= sqrt(2x-6)

y =sqrt(2x-6)

To find the inverse function, we interchange the x and y and solve for y

x = sqrt(2y-6)

Square each side

x^2 = sqrt(2y-6)^2

x^2 = 2y-6

Add 6 to each to each side

x^2 +6 = 2y-6+6

x^2 +6 = 2y

Divide each side by 2

(x^2 +6)/2 = 2y/2

(x^2 +6)/2 = y

The inverse function is

(x^2 +6)/2

or  1/2 x^2 +3

Two functions f(x) and g(x) are inverses if:

f(g(x)) = x = g(f(x))

The solution is:

[tex]g(x) = \frac{1}{2} x^{2} + 3[/tex]

Now we want to find the inverse function to:

[tex]f(x) = \sqrt{2x - 6}[/tex]

Because this is a square root function, we know that the inverse must be a quadratic function, so let's try with something like:

[tex]g(x) = a*x^2 + c[/tex]

Now we can use the first property to get:

[tex]g(f(x)) = a*f(x)^2 + c = x\\\\ = a*\sqrt{2x - 6}^2 + c = x\\\\= a*(2x - 6) + c = x\\\\2*a*x -6*a + c = x[/tex]

Then we must have:

2*a  =1

a = 1/2

And:

-6*a + c = 0

-6*(1/2) + c = 0

-3 + c = 0

c = 4

Then the inverse function is:

[tex]g(x) = \frac{1}{2} x^{2} + 3[/tex]

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Option: C is the correct answer.

                 C.   Vector d

Vector--

We know that the vector is used to represent a quantity which have both magnitude as well as direction.

The vector is represented in a diagram with the help of a line segment with an arrow.

We know that the negative of a vector reverses the direction of the original vector i.e. it directs to the opposite direction of the original vector.

i.e. both have the same starting point but the direction changes.

Here by looking at the figure we observe that the negative of the vector v is the vector d.

[tex]\text{Use}\\\\(ab)^n=a^nb^n\\\\(a^n)^m=a^{n\cdot m}\\------------------\\\left(2m^3n^2\right)^5=2^5(m^3)^5(n^2)^5=32m^{3\cdot5}n^{2\cdot5}=32m^{15}n^{10}[/tex]

Answer:

b

Step-by-step explanation:

Looking at the graph, as  x gets more and more negative, y gets larger and larger.

x→-∞  y →∞

As x approaches negative infinity, y approaches infinity

As x gets larger and larger, y gets more and more negative

x→∞, y→-∞

As x approaches infinity, y approaches negative infinity

The correct answer is B) "As x approaches infinity, f(x) approaches negative infinity; as x approaches negative infinity, f(x) approaches infinity."

"As x approaches infinity, function f(x) approaches negative infinity": When x becomes very large (positive infinity), the term (3/17)x dominates the function. Since the coefficient 3/17 is positive, as x increases towards infinity, (3/17)x also increases without bound, causing f(x) to approach negative infinity.

"As x approaches negative infinity, function f(x) approaches infinity": Similarly, as x becomes very large in the negative direction (negative infinity), the term (3/17)x becomes very negative. Again, since the coefficient 3/17 is positive, f(x) increases without bound (but in the positive direction) as x approaches negative infinity.

In summary, the end behavior of the graph is such that as x goes to positive infinity, f(x) goes to negative infinity, and as x goes to negative infinity, f(x) goes to positive infinity, which corresponds to option B.

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Answer:

The amount of their mortgage loan is $108000

Step-by-step explanation:

we are given

total purchasing amount =$123000

down payment amount = $15000

we know that

Mortgage loan amount =  (total purchasing amount)-(down payment amount)

now, we can plug value

Mortgage loan amount = $123000-$15000

Mortgage loan amount =$108000

Patti Green and her husband need a mortgage loan of $108,000 for their condominium purchase.

The student has asked for the amount of the mortgage loan that Patti Green and her husband would need for purchasing a condominium. To find this, we would subtract their down payment from the total cost of the condominium. Since the condominium costs $123,000 and they have a $15,000 down payment, we do the following calculation:

Total cost of the condominium = $123,000
Down payment = $15,000
Mortgage loan needed = Total cost of the condominium - Down payment
Mortgage loan needed = $123,000 - $15,000
Mortgage loan needed = $108,000

Therefore, the amount of the mortgage loan that Patti Green and her husband would need is $108,000.