Simplify the polynomial expression. (1/2x +2)(1/2-2x)+(1/4x+7/2)

On solving the provided question, we can say that we have the equations as  y = 3x - 7 where x > 0. so let us assume x = 4 = > y = 5

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

here,

we have the equations as

y = 3x - 7 where x > 0

so let us assume x = 4

y = 5

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Answer:

$0.50/cm

Step-by-step explanation:

A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.

Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.

Denote this path as P. Let x be the vertex on path P that is closest to v.

By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.

Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.

Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

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The smallest to the largest side is SQ, RS, QR, the correct option is B.

A triangle is a polygon with three sides, angles, and vertices.

The triangle is classified into various types on the basis of the angle and on the basis of the equality of the length of the sides, as obtuse, acute and right-angled triangle and scalene, isosceles and equilateral triangle.

The measure of angle of the triangle is 56°, 83°, and 41°.

From the property of the triangle, the side opposite the bigger measure angle is the largest.

The measure of angle QRS is 41°, angle RQS is 56°, and angle QSR is 83°.

The smallest side will be the side opposite to QRS, i.e. SQ,

The largest side will be the side opposite to QSR, i.e. QR

The side in order from the smallest to the largest, SQ, RS, QR.

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Answer:

ring volume is 12cm3

Step-by-step explanation:

Lr ccm=volume of water and ring - Volume of water

ring cubic centimeters =x

x=9.2cm*4.5cm*7cm - 8.8cm*4.5cm*7cm

x=289.2cm3 - 277.2cm3

x=12cm3

Answer: False

Step-by-step explanation:

25% of the data is between Q1 and the median.

Answer:

884.4

Step-by-step explanation:

Answer:

The original price is 895.12$

I haven't done percent in ages, lmk if you get it right
kudos to any other answer besides this

Step-by-step explanation:

Answer:

Total Area = 84 feet

Step-by-step explanation:

Triangle = 1/2 (3 × 4) = 12/2 = 6 ft

Rectangle 1 = 7 × 4 = 28 ft

Rectangle 2 = 5 × 10 = 50 ft

Total Area = 6ft + 28ft + 50ft = 84ft

Then 1 - 3/5 = 2/5. This means that 2/5 of the frogs in that particular part of the rainforest are not poisonous. This fraction can also be expressed as 40/100 or 0.4 in decimal form.

In the given scenario, we know that 3/5 of the frogs in a particular part of the rainforest are poisonous. This means that the remaining fraction of the frogs are not poisonous.

To find this fraction, we need to subtract 3/5 from 1 (since the sum of the fractions of poisonous and non-poisonous frogs is equal to 1).

It's important to note that just because a frog is not poisonous, it doesn't mean it's safe to touch or handle them. It's always best to admire these beautiful creatures from a safe distance and leave them alone in their natural habitat.

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Answer:

f= 11

Explanation:

f= 2t-3 when t= 7 (just plug in 7 for the variable t!)

f= 2(7)-3

f= 14-3

f= 11

Answer:

f= 11

Step-by-step explanation:

Plug in 7, for the variable t. It will equal 14 because 2 times 7 is 14. Subtract 3 from 14, and the answer is 11.

Here is the work shown.

f= 2t - 3, t= 7

f= 2(7) - 3

f= 14 - 3

f= 11

I hope this helps. :)

answer:

10

step-by-step explanation:

easy: 100 ÷ 10 = 10. you need 10

explanation: you need 100 (on the left side) to equal the right side. each weight on the right side weighs 10, but you don't know how many you need. use x for the unknown amount. now, you have:

100 = 10x. solve by dividing each side by 10.

10 = x. verify by doing 10 x 10 = 100

Answer:

? = 92°

Step-by-step explanation:

the chord- chord angle ? is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is

? = \(\frac{1}{2}\) (LM + AK) = \(\frac{1}{2}\) (120 + 64)° = \(\frac{1}{2}\) × 184° = 92°

9514 1404 393

Answer:

  5)  (x, y) = (10, -1)

  6)  (x, y) = (5, 6)

Step-by-step explanation:

5) y coefficients are opposites, so y can be eliminated by adding the two equations.

  (x -y) +(2x +y) = (11) +(19)

  3x = 30 . . . . . simplify

  x = 10 . . . . . . . divide by 3

Using the second equation, we can find y:

  2(10) +y = 19

  y = -1 . . . . . subtract 20

The solution is (x, y) = (10, -1).

__

6) The x-coefficients are the same, so we can eliminate the x-term by subtracting the second equation from the first. We choose to do it that way so the y-coefficient ends up positive.

  (-6x +6y) -(-6x +3y) = (6) -(-12)

  3y = 18 . . . . . . simplify

  y = 6 . . . . . . . . divide by 6

Using the first equation to find x, we have ...

  -6x +6(6) = 6

  x -6 = -1 . . . . . . . divide by -6

  x = 5 . . . . . . . . . add 6

The solution is (x, y) = (5, 6).

Answer:

its the second one

Step-by-step explanation:

Each package has 18 granola bars.

This problem can be solved through a system of linear equations.

Let "x" be the total number of granola bars that each pack of granola has. Let "y" be the total amount of granola bars that each cafeteria has.

For cafeteria A: \(7x+12=y\)

For cafeteria B: \(3x+84=y\)

Since both equations are solved for y, we may take the argument at the left of the equal sign from both equations and equal them.

\(7x+12=3x+84\).

\(7x+12=3x+84\)

\(7x-3x=84-12\) --> Substract 3x and 12 from both sides.

\(4x=72\) --> Simplify by solving the substraction.

\(\frac{4x}{4} =\frac{72}{4}\)--> Divide both sides by 4.

\(x= 18\)

\(y=7(18)+12\\ \\y=138.\)

If a system of linear equations was created, where 2 equations that gave the number of granola bars that each cafeteria has, then the x value obtained when the system was solved, indicates the amount of granola bars that each cafeteria has in each package. Each package has 18 granola bars.

An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.

An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.

This function is one-to-one because for every element x in P, there is a unique element 2x in Q. It is onto because every element y in Q has a preimage x in P such that f(x) = y (e.g., y/2 = x).

Furthermore, this function preserves the group structure between P and Q, as it satisfies the properties of an isomorphism. In this case, the group structure is addition, and the function f preserves addition: f(x + y) = 2(x + y) = 2x + 2y = f(x) + f(y) for all x, y in P.

Therefore, the function f: P -> Q defined as f(x) = 2x is an example of a one-to-one function that is an isomorphism between sets P and Q.

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Answer:

  130

Step-by-step explanation:

Let h, t, e represent the number of inquiries in health, teaching, and electronics. The given relations are ...

  h = 2/3e

  t = e -50

  h + t + e = 430

Using the first two equations, we can substitute into the third equation:

  (2/3e) +(e -50) +e = 430

  8/3e = 480 . . . . . . . . . . . . . collect terms, add 50

  e = 180 . . . . . . . . . . . . . . multiply by 3/8

  h = 2/3(180) = 120

  t = 180 -50 = 130

130 inquiries were made about teaching.

_____

Additional comment

180 inquiries were made about electronics.

120 inquiries were made about health care.

Lines or points, are said to be coplanar when they line in the same plane.

Given the figure below:

Points A, B, C are coplanar points because they lie in one plane(plane x).

While noncoplanar points or lines do not lie in the same plane.

Given the figure below:

The points, A, B, C are noncoplanar because they do not lie in the same plane.

Answer:

36.5 is median Temperature for girls

Step-by-step explanation:

Let's first calculate the median Temperature for boys to show you how it is done;

Below are the Temperature, they are not in ascending order

37.0,36.1,37.1,37.3,36.3,36.4,36.7,36.7,36.7,35.8

Now let's arrange them in ascending order

35.8, 36.1, 36.3, 36.4, (36.7, 36.7, )36.7, 37.0, 37.1, 37.3

In the middle are 36.7 and 36.7 as seen in the bracket

to find median = 36.7+36.7/2

➟ 73.4/2

➟ 36.7

∴36.7 is median Temperature for boys

Now that I've shown you example with boys temperature let's go find the actual temperature which is girls

Below are temperature for girls

34.7,35.8,35.9,36.2,36.4,36.6,36.6,36.8,36.8,36.9

Let's arrange them in ascending order

34.7, 35.8, 35.9, 36.2,( 36.4, 36.6, )36.6, 36.8, 36.8, 36.9

In the middle are 36.4 and 36.6 as seen in the bracket

to find median = 36.4+36.6/2

➟ 73/2

➟ 36.5

∴36.5 is median Temperature for girls

The perimeter of the rectangle 48.48 inches and the expression of the new perimeter of the rectangle is 48.48 - (1.57/a) inches

In this question, we have

Area = 144 square inches

Length = 4 * Width

The area of a rectangle is represented as

A = lw

So, we have

A = (w + 4) * w

This gives

(w + 4) * w = 144

Expand

w² + 4w = 144

So, we have

w² + 4w - 144 = 0

Using a graphing calculator, we have

w = 10.12

Recall that

l = w + 4

So, we have

l = 10.12 + 4

Evaluate

l = 14.12

The perimeter is then calculated as

P = 2 * (l + w)

So, we have

P = 2 * (10.12 + 14.12)

Evaluate

P = 48.48

So, the perimeter is 48.48 inches

Here, we have

Value subtracted = (4/a) cm

Converted to inches

Value subtracted = (1.57/a) inches

So, we have

New perimeter = 48.48 - (1.57/a) inches

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Complete question

The length of a rectangle is four times its width. If the area of the rectangle is 144 square inches find its perimeter.

if the perimeter of the given rectangle is subtracted by (4/a)cm, what will be its new perimeter?;

Answer:

Based on the information given, we know that angles 3 and 4 are supplementary (they add up to 180 degrees) and angles 2 and 4 are vertical angles (they are congruent). Therefore, we can write:

m∠4 + m∠3 = 180 (since angles 3 and 4 are supplementary)

m∠4 = m∠2 (since angles 2 and 4 are vertical angles)

Substituting m∠4 = m∠2 into the first equation, we get:

m∠2 + m∠3 = 180

Now we can solve for m∠2 and m∠3:

m∠3 = 43 (given)

m∠2 = 180 - m∠3 = 180 - 43 = 137

Since angles 1 and 2 are also supplementary, we can find m∠1 by subtracting m∠2 from 180:

m∠1 = 180 - m∠2 = 180 - 137 = 43

Therefore, m∠1 = 43 degrees and m∠2 = 137 degrees.

\( \red{answer}\)

$-150

An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is C.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The expression that is equivalent to -(1/6)y + 1/3 is,

-(1/6)y + 1/3

Take 1/6 common from both first and the last term,

1/6 (-y + 2)

Hence, the correct option is C.

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Answer:

Greater than

Step-by-step explanation:

3/8 = 6/16

6<11

therefore, 11/16 is greater than 3/8

Answer:

\(y =\frac{x}{4}\)

Step-by-step explanation:

We are given several functions, and we want to figure out which one is linear.

A linear function has both of its variables (x and y) with a power of 1. Variables with other powers do not mean that the function is linear.

Let's go through the list.

Starting with \(y=\frac{3}{x} -7\), we can see that x is in the denominator. If this is the case, it means that the power of x is -1.

Even though y has a power of 1, this is NOT linear, because x has a power of -1.

Now, with y=√x-2, this is also not linear. This is because √x = \(x^\frac{1}{2}\), even though y has a power of 1.

For x² - 1 = y, we can clearly see that x has a power of 2, while y has a power of 1. This means that the function is not linear.

This leaves us with \(y = \frac{x}{4}\). x is in a fraction, however it is not in the denominator. This means that the power of x in this function is 1. We can also see that the power of y in this function is 1.

This means that \(y=\frac{x}{4}\) is linear.

Answer:

∠ ABC = 49°

Step-by-step explanation:

the chord- tangent angle ABC is half the measure of the intercepted arc AB

∠ ABC = \(\frac{1}{2}\) AB = \(\frac{1}{2}\) × 98° = 49°