A student is building a parallelogram- shaped deck with a base of (4x + 3) feet and a height of (3x - 2) feet. Which polynomial represents the area of her deck in square feet? (A.108)
F (12x2 + x - 6) square feet
G (7x + 1) square feet
H (12x2 + x - 5) square feet
J (7x2 + x - 6) square feet​

Answer: 229,500 people to the nearest hundred

Step-by-step explanation:

Population decreases exponentially at 1.7% per year in a town that is currently 250,000 in number.

Population in 5 years = 250,000 * ( 1 - 1.7%) ⁵

= 250,000 * 0.917841286185143‬

= 229,460

= 229,500 people to the nearest hundred

The given statement "If A is n × n an orthogonal. Then for all X, Y ∈ Rₙ we have AX · AY = X · Y" is proved.

Given that A is a n * n order matrix.

And X, Y ∈ Rₙ so,

|X - Y|² = (X - Y) * (X - Y)

|X - Y|² = |X|² - 2 * X * Y + |Y|²

2 * X * Y = |X|² + |Y|² - |X - Y|²

Since A is orthogonal matrix so,

2 * (AX * AY) = |AX|² + |AY|² - |AX - AY|²

2 * (AX * AY) = |X|² + |Y|² - |X - Y|²

2 * (AX * AY) = 2 * X * Y

(AX * AY) =  X * Y

Hence the statement is proved.

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The question is incomplete. The complete question will be -

"Suppose that A is n × n an orthogonal. Then for all X, Y ∈ Rₙ we have

AX · AY = X · Y"

The volume of a rectangular prism with a length of 12 inches, width of 10 inches, and height of 2.5 inches is 300 cubic inches

Volume of a rectangular prism = length × width × height

= (12 × 10 × 2.5) inches

= 300 inches

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From the calculation based on the theory of the isosceles triangle, the value of x is 5.

We know that the base angles of the isosceles triangle are equal thus the length of the two sides of the isosceles triangle are equal. As such we would use this fact to try to find the value of x in the problem as it has been stated in the question.

We have the following from the question given;

2x + 3 = x + 8

2x - x = 8 - 3

x = 5

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Answer:

It is complementary.

Step-by-step explanation:

It is since the two angles add up to 90 degrees. If they were vertical angles they would be opposite and be made by intersecting lines. Complementary angles - Angles next to each other that add up to 90 degrees.     Supplementary angles : Angles that are next to each other adding up to 180 degrees.

Answer:

O (2.5, 5.5)

Step-by-step explanation:

for x = (x1+x2)/2 = (1+4)/2 = 5/2 =2.5
for y = (y1+y2)/2 = (4+7)/2 = 11/2 = 5.5


Hope it helps!
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The probability that the mean age of a sample of 36 vehicles is between 98 and 100 months is 15.71%.

For the given question;

The data for the vehicles registered in the united states is given as-

The formula for the z score is-

z = (x - μ)/(σ/√n)

Put the values.

√n = √36 = 6

For x = 98 months

z = (98 - 96)/(15/6)

z = 0.8

p(z < 0.8) = 0.7881

For x = 100 months

z = (100 - 96)/(15/6)

z = 1.6

p(z < 1.6) = 0.9452

P(0.8<x<1.6) = 0.9452 - 0.7881

P(0.8<x<1.6) = 0.1571

Thus, the probability that the mean age of a sample of 36 vehicles is between 98 and 100 months is 15.71%.

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Thus, the total length of lap covered to get the seven different obstacles is found as: 52 units.

the Pythagorean theorem is used to calculate the distance between two locations using the distance formula. The Pythagorean theorem can be rewritten as d = √((x2 - x1)²+(y2 - y1)²)  to calculate the separation between any two locations.

Given data:

Points on  y-axis and an x-axis are given,

M(-3,5), F(8,5), G(8,2), H(3,2), I(3,-5), J(-8,-5), K(-8,-2), and L(-3,-2).

Starting and ending point is F.

Points lies between the starting and ending are-

F ,G, H, I, J, K, L, M, F

Total length = sum of all length

d = √((x2 - x1)²+(y2 - y1)²)

FG =  √((8 - 8)²+(2 - 5)²)

FG =  √9

FG =  3

GH =  √((8 - 3)²+(2 - 2)²)

GH  =  √25

GH =  5

HI =  √((3 - 3)²+(2 + 5)²)

HI  =  √49

HI  =  7

IJ =  √((3 + 8)²+(-5 + 5)²)

IJ =  √121

IJ =  11

JK =  √((-8 + 8)²+(-2 - 5)²)

JK =  √9

JK =  3

KL =  √((-8 + 3)²+(-2 + 2)²)

KL =  √25

KL =  5

LM =  √((-3 + 3)²+(-2 - 5)²)

LM =  √49

LM =  7

MF =  √((8 + 3)²+(+5 - 5)²)

MF =  √121

MF =  11

Total length = 3 + 5 + 7 + 11 + 3 + 5 + 7 + 11

Total length = 52 units

Thus, the total length of the lap covered to get the seven different obstacles is found as: 52 units.

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Answer:

D. 44

Step-by-step explanation:

180 - 68 = 112

m∠1 = 112

112 + 24 = 136

180 - 136 = 44

Answer:

$420

Step-by-step explanation:

Calculate 3% of 3,500:

0.03*3500 = 105

105 per year for 4 years:

105*4 = 420

The ratio of John's money to Peter's money is 5/4. This means if John has a total amount of 5 then Peter will have a total of 4 as his amount.

Let's assume John has 'x' amount of  money, Peter has 'y' amount of money, The money John saved is 'p' and the money Peter saved is 'q'

So,

p = x - 80x/100                (equation 1)

q = y - 75y/100                (equation 2)

According to the given question, the amount John saved is equal to the amount Peter saved. Hence, we can equate equations 1 and 2.

p = q

x- 80x/100 = y - 75y/100

x - 0.8x = y - 0.75y

0.2x = 0.25y

x =  0.25y/0.2

x/y = 0.25/0.2

x/y = 25/20

x/y = 5/4

Hence, the ratio of John's money to Peter's money is 5/4.

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The best estimate of the elk population, to the nearest whole number, is 250.

To estimate the elk population, we can use the mark-recapture method. This method assumes that the ratio of marked individuals to the total population is equal to the ratio of marked individuals recaptured to the total number of individuals captured in the second sample.

Let's denote the total elk population as "P" and the number of marked elk in the first sample as "M1". We also know the number of marked elk recaptured in the second sample, which is "M2", and the total number of elk counted in the second sample, which is "N2".

According to the mark-recapture method, we can set up the following equation:

M1 / P = M2 / N2

Plugging in the given values, we have:

30 / P = 18 / 150

To solve for P, we can cross-multiply and then divide:

30 * 150 = 18 * P

4500 = 18P

Dividing both sides by 18:

P = 4500 / 18

P ≈ 250

Therefore, the best estimate of the elk population, to the nearest whole number, is 250.

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To gather information about the elk population, scientists marked 30 elk. Later, they flew over the area and counted 150 elk, 18 of which were marked. To the nearest whole number, what is the best estimate of the elk population ??

Answer:

zax is 31

Step-by-step explanation:

if his sister was 3 years older and born when the mom was 28 add 3 to 28 and you get 31 the age he was born thus this is the age he is today

Since w is not connected to u or v by a path, it must be connected to some other vertex in the graph. Let's call this vertex x. Since x is connected to w and not connected to u or v, the path from u to v must pass through x and w. this creates a cycle in the graph, which contradicts our assumption that the graph is circuit-free.



The graph is circuit-free, there is no cycle that includes both u and v. Therefore, the only way to reach vertex v from vertex u is to go through other vertices in the graph. Let's assume that the shortest path between u and v has length k.
Since the graph is simple and has n vertices, the maximum degree of any vertex in the graph is n-1. This means that there are at most n-1 vertices adjacent to vertex u.

Therefore, we have shown that if a graph is circuit-free, simple, and has n vertices and at least n-1 edges, then it must be connected.

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Answer:

4 weeks

Step-by-step explanation:

With the given coordinates it doesn't form a rectangle the correct set of the coordinates should be (2, 2), (1, 2), (1, -2), and (2,-2).

Answer:

The perimeter of the given rectangle that is formed by the given coordinates is 30miles.

Step-by-step explanation:

We are given the Rectangular coordinates such as

(2,2) , (1,2) ,(1,-2) (2,-2)

we will mark these  point on the cartesian planes to understand the rectangle

We can apply the distance formula or we can just look on the cartesian plane to simply get the distance between two points

we get

[(2,2) ,(1,2) ] and [(1,-2) ,(2,-2) ] are two units apart each pair as they are parallel so our width is

W = 2 units

similarly

we now need the length

(1,2) and (1,-2) are four units apart

so our length will be four units

L= 4 units

we need the perimeter

Perimeter of the rectangle = 2( L+W)

                                          = 2( 2 + 4)

                                          = 2* 6 = 12units

Now we are given that 1 unit is equal to 2.5 miles so 12 units will be  

             = 12* 2.5 = 30 miles

Therefore The perimeter of the given rectangle that is formed by the given coordinates is 30miles.

The value of a=17 cm and b=6 cm as FGHJ is a kite.

Kite has property their adjacent sides are equal. The top two sides of the kite are equal and the bottom two sides of the kite are equal.

Any quadrilateral with two sets of congruent successive sides is referred to as a kite (in contrast to a parallelogram where the opposite sides are congruent). Connecting points G and J, draw a section. Triangle GHJ and triangle GFJ are congruent. The information that GH = GF and FJ = HJ will be used.

FG=GH because of ∠F=∠H.

30=2a-4

2a=34

a=17 cm      

Similarly, ∠F=∠H

FJ=HJ

3b+6=24

3b=18

b=6 cm

Hence, The value of a=17 cm and b=6 cm

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Answer:

a=17 and b=6

Step-by-step explanation:

took the test

Answer:

C) 8

Step-by-step explanation:

5x=2x+24

5x-2x=24

3x=24

x=8

From the given numbers, the greatest number is 23 × 10^126

The first number = 23 × 10^126

The second number = 23 × 10^86

The third number = 23 × 10^66

The fourth number = 23 × 10^3

The scientific notation is defined as the easiest method to represents the very smallest or the largest number. The scientific notation consist of a whole number multiplied by the power of ten

Here, the whole number is same in all cases, only the power of the 10 is different . To find the largest number we have to find the number with largest power of 10

The number with largest power of 10 = 23 × 10^126

Hence, the greatest number is 23 × 10^126

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Answer:

  3/2

Step-by-step explanation:

Finding the slope of a line on a graph is easier if you can identify places where the line crosses grid intersections. We see two of those to be ...

  (4, 1) and (6, 4)

The second of these points is 4-1 = 3 grid squares higher than the first point. It is also 6 -4 = 2 grid squares to the right. The slope is the ratio of these values:

  slope = "rise"/"run" = 3/2

The slope of the graphed line is 3/2.

Answer:

Jesse's cards are 3, -5, 9, and -6. The problem is asking for the total, so you would add them up:

Step-by-step explanation:

Start at 0. Adding a positive integer is simple addition. Add 3 to get 3.

Adding a negative integer is like subtraction: 3 + (-5) = 3 - 5 = -2.

Add 9, taking 9 steps forward, on the number line, to get 7.

Add -6, by subtracting 6, to get 1.

Jesse's total score is 1.

---

As for part 2, Jesse getting two more cards, which don't affect his final score ...

Either he got two zeroes, or he got two cards with opposite signs, but equal magnitudes, such as 1 and -1.

The sign of a number is whether it is positive or negative. The magnitude (absolute value) of a number is how far that number is from zero. The magnitude of a number is NEVER negative.

The two cards do not affect Jesse's point total, because their effects cancel each other out. For example, a 1 would move him one step forward, on the number line, and a -1 would move him one step backward, on the number line.

Answer:

A and D

Step-by-step explanation:

so sorry im in school

x+y=4

 -y.  -y

x=4-y

4-y-y=2

4-2y=2

-4      -4

-2y= -2

/-2.   /-2

y=1

x+1=4

  -1 -1

x=3

so A and D is correct

The cost of one DVD to Hector is $11.8.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Hector spent $26.75 for 2 DVDs that cost the same amount.

The sales tax on his purchase was $4.15.

That means,

the cost of 2 DVDs = 26.75 - 4.15 = $22.6

Hector also used a coupon for $1.00 off his purchase.

That means,

the cost of 2 DVDs = $23.6

The cost of one DVD = 23.6 /2 = $11.8

Therefore, the cost of one DVD is $11.8.

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Answer:

-1 1/5

Hope this helped!

Also I would really appreciate it if you made me the brainliest! :D

The product of two rational numbers can always be written as a fraction. The Option D is correct.

The product of 2 rational numbers can not be written as either irrational or whole number. This is because it will be expressed as the ratio of two integers and the product of two ratios of integers will always result in another ratio of integers.

For example, if we multiply  3/5 & 2/7 (rational numbers), we get (3/5) x (2/7) = 6/35 which is also a rational number. Therefore, the product of two rational numbers will always be a rational number or a fraction.

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Applying the definition of congruent triangles:

1. QS = 57 units; TV = 57 units

2. m∠B = 3°; m∠Q = 3°

The triangles that are congruent to each other have corresponding parts that are congruent, that is their corresponding sides and angles are equal to each other.

1. Given that triangles QRS and TUV are congruent triangles, therefore:

QS = TV [corresponding congruent sides]

QS = 4v + 5

TV = 5v - 8

Therefore:

4v + 5 = 5v - 8

4v - 5v = -5 - 8

-v = -13

v = 13

QS = 4v + 5 = 4(13) + 5 = 57 units

TV = 5v - 8 = 5(13) - 8 = 57 units

2. Given that triangles ABC and PQR are congruent, therefore:

m∠B = m∠Q

m∠B = 2v + 1

m∠Q = 8v - 5

Therefore:

2v + 1 = 8v - 5

2v - 8v = -1 - 5

-6v = -6

v = -6/-6

v = 1

m∠B = 2v + 1 = 2(1) + 1 = 3°

m∠Q = 8v - 5 = 8(1) - 5 = 3°

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