2x - (x + 1) = - 4 + 3(x-3)

The length of one side of the garage originally is 18.17 feet.

The length of one side of the garage now is 22.25 feet.

The percent increase is 22.4%.

A square is a quadrilateral with four sides of equal length. A square has two diagonals of equal length that intersect at right angles.

Given the area of a square, the length of one side can be determined by calculating the square root of the area.

Area of the square = length²

Length of one side of the square = √area

√330 = 18.17 ft

Area of the garage after it was increased : (1 + percentage increase) x initial area

(1 + 0.5) x 330

1.5 x 330 = 495 feet²

Length of the side of the garage after it is increased = √495 = 22.25 feet

The percentage increase = (22.25 / 18.17) - 1 = 0.224 = 22.4%

Here is the complete question:

Yossi used to have a square garage with 330ft of floor space. recently built an addition to it. The garage is still a​ square, but now it has​ 50% more floor space. What was the length of one side of the garage​ originally? What is the length of one side of the garage​ now? What was the percent increase in the length of one​ side?

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The amount that the students should charge for the wristbands will be at least $1.40.

From the information, the students want to buy 500 wristbands for just $0.90 each and they want to make at least $250.

Therefore, the amount that they should charge for each will be:

Total cost = 500 × $0.90 = $450

Therefore, the amount charged be:

500x - 450 >= 250

Collect like terms

500x >= 250 + 450

500x >= 700

x >= 700/500

x>= $1.4

They should charge at least $1.40.

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The rate of change of y with respect to x for given function is -0.2

We know that, the slope of a function is nothing but the rate of change of y with respect to x of a function.

In this question, we have been given a linear function passing through points (-3, 3.6) and (5, 2)

We need to find the slope of the line passing through points (-3, 3.6) and  (5, 2)

Let m be the slope.

By using the formula of the slope,

m = (2 - 3.6) / (5 - (-3))

m = -1.6 / 8

m = -0.2

Therefore, the rate of change of y with respect to x for given function is -0.2

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The answer include the following:

Step 1: 7x + 21 = 9x - 4x + 37 - distributive property.

Step 2: 7x+ 21 - 21 = 9x - 4x +37 - 21 - subtraction property

Step 3: 7x = 5x +16 - combine like terms.

Step 4: 7x - 5x = 5x - 5x +16 - subtraction property.

Step 5: 2x = 16 - combine like terms

Step 6: 2x ÷ 2 = 16 ÷ 2 - division property.

Step 7: x = 54 - simplification.

This is referred to as process in which a mathematical expression is replaced by another so as to ensure that it is simpler and shorter in other solve the problem and for better understanding.

In the case of 7(x + 3) = 9x - 4x − 35, distributive property is used to expand the bracket and collecting of like terms are also used for easier subtraction and addition process

This employs the use of different arithmetic operations such as division, etc and the steps above shoes the most appropriate justifications in this type of scenario.

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Using relations in a right triangle, the missing side lengths are given as follows:

1. D. [tex]x = 7\sqrt{2}, y = 7[/tex]

2. B. [tex]x = 3\sqrt{2}, y = 2[/tex].

3. C. x = 6, y = 3.

4. C. [tex]x = 2\sqrt{5}, y = \frac{2\sqrt{15}}{3}[/tex]

There are three relations in a right triangle, given as follows:

For the first triangle, we have that:

tan(45º) = 7/y

1 = 7/y

y = 7.

Applying the Pythagorean Theorem:

x² = 7² + 7²

x = sqrt(2 x 49)

[tex]x = 7\sqrt{2}[/tex]

Hence the correct option is:

D. [tex]x = 7\sqrt{2}, y = 7[/tex]

For the second triangle, we have that:

tan(45º) = y/3

1 = y/3

y = 3.

Applying the Pythagorean Theorem:

x² = 3² + 3²

x = sqrt(2 x 9)

[tex]x = 3\sqrt{2}[/tex]

Hence the correct option is:

B. [tex]x = 3\sqrt{2}, y = 2[/tex].

For the third triangle, we have that:

[tex]\tan{30^\circ} = \frac{y}{3\sqrt{3}}[/tex]

[tex]\frac{\sqrt{3}}{3} = \frac{y}{3\sqrt{3}}[/tex]

y = 3 x 3/3

y = 3.

Then:

[tex]\sin{30^\circ} = \frac{y}{x}[/tex]

0.5 = 3/x

x = 6.

Hence the correct option is:

C. x = 6, y = 3.

For the fourth triangle, we have that:

[tex]\sin{30^\circ} = \frac{y}{\frac{4\sqrt{15}}{3}}[/tex]

[tex]0.5 = \frac{y}{\frac{4\sqrt{15}}{3}}[/tex]

[tex]y = \frac{2\sqrt{15}}{3}[/tex]

[tex]\cos{30^\circ} = \frac{x}{\frac{4\sqrt{15}}{3}}[/tex]

[tex]\frac{\sqrt{3}}{{2}} = \frac{x}{\frac{4\sqrt{15}}{3}}[/tex]

[tex]x = 2\sqrt{5}[/tex]

Hence the correct option is:

C. [tex]x = 2\sqrt{5}, y = \frac{2\sqrt{15}}{3}[/tex]

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Bill Murray has 16 3/4 days in total of vacation per year.  Bill entitled to  8 1/6 days more vacation time.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Bill Murray has 16 3/4 days in total.

(16×4 + 3)/4 = 67/4 days.

Then;

1 3/4 = (1×4 + 3)/4 = 7/4 days

4 2/3 = (4×3 + 2)/3 = 14/3 days

2 1/6 = (2×6 + 1) = 13/6 days

To add and then subtract them directly, we need to bring all fractions to the same denominator.

we have to multiply each fraction by a fitting n/n factor to bring the denominators to 12

67/4 = 67/4 × 3/3 = 201/12

7/4 = 7/4 × 3/3 = 21/12

14/3 = 14/3 × 4/4 = 56/12

13/6 = 13/6 × 2/2 = 26/12

Thus the remaining vacation time will be

201/12 - 21/12 - 56/12 - 26/12 = 98/12 = 49/6

49/6 = 8 and remainder 1 = (8×6 + 1)/6 = 8 1/6 days

Hence, Bill Murray has 16 3/4 days in total of vacation per year.  Bill entitled to  8 1/6 days more vacation time.

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It should be noted that the value of t in the equation 2t = 80, t will be 40.

It should be noted that an equation is simony used to show the relationship between the variables or numbers that are given.

Therefore, it should be noted that solving the equation will be:

2t = 80

Divide through by 2

2t / 2 = 80 / 2

t = 40

Therefore, the value of t is 40.

Therefore, it should be noted that the value of t on the equation 2t = 80, t will be 40.

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The number of infected people will reach 568 in approximately 4 weeks

Exponential equations are inverse of logarithmic equation and are represented by the equation below:

y = ab^x

where

a is the base value and x is the exponent

Given the equation that shows the number of infected people from an outbreak of the measles as:

y = 4(6)^t

If the number of infected people reach 568, hence;

568 = 4(6)^t

568/4 = 4(6)^t/4

6^t = 568/4

6^t = 142

Take the natural logarithm of both sides

ln(6^t) = ln142

t = ln142/ln6

t = 4.37

Hence the number of infected people will reach 568 in approximately 4 weeks

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According to the solving the angular speed of the wheel in radius per minutes would be:

100.

The correct option is 3.

angular velocity is the rate at which an item rotates or revolves around an axis, or the pace that the angular displacement among two bodies varies. This displacement is shown in the diagram by the angle formed by a line with one body and a line on the opposite body.

Angular velocity is defined as the rate of change of an object's position angle with respect to time, therefore w = theta / t, where w denotes angular velocity, theta denotes position angle, and t denotes time.

The angular speed of a rotating object is a scalar measurement. The angular velocity of a rotating object is measured as a vector. Only the magnitude of angular speed is specified. The magnitude and direction of angular velocity are specified.

Radius of the wheel = 2ft

velocity of the wheel = 200 ft/min

We know that the formula of Angular velocity:

ω = ν/r

ω = output

ν = liner velocity

r = path radius

Substituting the value in the formula:

ω = ν/r

ω = 200/2

= 100

According to the solving the angular speed of the wheel in radius per minutes would be:

100.

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The value of x in the given object is 12.

The given shape is an equilateral triangle. A triangle is a three-sided polygon with three edges and vertices. The sum of angles in a triangle is equal to 180 degrees.

An equilateral triangle is a triangle in which the three angles are equal. This means that each angle in an equilateral triangle measures 60 degrees. Also, in an equilateral triangle the three sides are equal.

Since, all the three sides of an equilateral triangle is equal, the expressions for their sides can be equated to each other to determine the value of x

4x - 10 = 5x - 22

Combine similar terms: 22 - 10 = 5x - 4x

Add similar terms: 12 = x

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Let [tex]2n+1[/tex] be the smallest of these integers, so the next two are [tex]2n+3[/tex] and [tex]2n+5[/tex]. The sum of their squares is 83, so

[tex](2n+1)^2 + (2n+3)^2 + (2n+4)^2 = 83[/tex]

Let [tex]x=2n+3[/tex] be the middle number. By substitution, we rewrite the equation as

[tex](x-2)^2 + x^2 + (x+2)^2 = 83[/tex]

Solve for [tex]x[/tex]. Expand the left side.

[tex](x^2 - 4x + 4) + x^2 + (x^2 + 4x + 4) = 83[/tex]

[tex]3x^2 + 8 = 83[/tex]

[tex]3x^2 = 75[/tex]

[tex]x^2 = 25[/tex]

[tex]\implies \boxed{x=\pm5}[/tex]

Answer:

B = -24

Step-by-step explanation:

a + b = 23

Since a = 47

47 + b = 23

Subtract 47 from each side

47 - 47 + b = 23 - 47

Therefore:

B = -24

Answer:

b = -24

Step-by-step explanation:

a + b = 23

Substitute 47 for a.

47 + b = 23

Rearrange the equation.

23 - 47 = b

-24 = b

Check your answer by substituting the value you found for b into the equation.

47 + (-24) = 23

Answer

Two times a number plus seven

Step-by-step explanation:

Hope this helps!!!

Answer:

x=37

Step-by-step explanation:

If you stare at the picture long enough you can tell that you have six straight angles, which add up to [tex]180\°\times 6 = 1080\°[/tex]. You now need to take away the internal angles, that add up to [tex]180\° \times 6-360\° = 720\°[/tex]*

What you have left is two expression of the same quantity - the sum of the external angles. In one case is [tex]360\°[/tex] (the difference between the two values) and in the other is the sum of the various expressions containing x.[tex]2x +(x+10)+(x+18)+3x+(x-1)+x = 360\\9x = 360 - 27 \rightarrow 9x = 333\rightarrow x=37[/tex]

*Pick any point inside the polygon, and join it to the corners. You will create as many triangles as you have sides - in our case 6. Sum of angles will be 180 times the number of sides, minus a whole round angle - the one in the center.

Interval of convergence of the power series [tex]\frac{(x+3)^{n} }{n}[/tex] ; n = 1 is -5 < x < -1.

A power series is a special type of infinite series representing a mathematical function in the form of an infinite series that either converges or diverges.

The series is aₙ =  [tex]\frac{(x+3)^{n} }{n}[/tex]

To generate aₙ₊₁ term replace 'n' with 'n + 1'

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

Now plugging aₙ and aₙ₊₁ in the formula L = [tex]\lim_{n \to \infty} |\frac{an+1}{an}|[/tex]

L = [tex]\lim_{n \to \infty} |\frac{\frac{(x+3)^{n+1} }{n+1} }{\frac{(x+3)^{n} }{n} }|[/tex]

L = [tex]\lim_{n \to \infty} |{\frac{(x+3)^{n+1} }{n+1} }/{\frac{(x+3)^{n} }{n} }|[/tex]

L = [tex]\lim_{n \to \infty} |{\frac{(x+3)^{n+1} }{n+1} }*{\frac{n }{(x+3)^{n} }|[/tex]

L = [tex]\lim_{n \to \infty} |{\frac{(x+3) }{n+1} }*{n}|[/tex]

L = [tex](x+3)\lim_{n \to \infty} |{\frac{n}{n+1} }|[/tex]

L = [tex](x+3)\lim_{n \to \infty} |{\frac{n*(\frac{1}{n}) }{(n+1)*(\frac{1}{n}) } }|[/tex]

Since n = 1

L = [tex](x+3)\lim_{n \to \infty} |\frac{1}{1+1} |[/tex]

L = [tex](x+3)\lim_{n \to \infty} |\frac{1}{2} |[/tex]

L = [tex]\frac{1}{2} * |x+3|[/tex]

The ratio tells us that if L < 1 then the series will converge

[tex]\frac{1}{2}*(x+3) < 1[/tex]

[tex](x+3) < 2[/tex]

The interval of convergence will be

-2 < (x + 3) < 2

-5 < x < -1

The interval of convergence for the power series  [tex]\frac{(x+3)^{n} }{n}[/tex] is -5 < x < -1

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Answer:

c

Step-by-step explanation:

The average of -1 and 8 is 7/2, so the absolute value should equal 0 at 7/2.

The only option that satisfies this is c.

Answer:

  12

Step-by-step explanation:

Given a table of supply and demand at each price point, you are asked for the equilibrium price if the demand numbers are decreased by 0.5 million.

The equilibrium price is the price at which the quantity demanded is equal to the quantity supplied.

For the given table, we see that a price of $14 thousands will result in both demand and supply being 2.00 millions per year. That is the equilibrium price before any adjustment to the table is made.

The problem statement is telling you to use a table that has all of the demand values decreased by 0.5 million. That makes the demand column read ...

  2.25, 2.00, 1.75, 1.50, 1.25, 1.00, 0.75

This new column of reduced demand values matches the numbers in the supply column when they are both 1.75 million per year. That match occurs on the line with price $12 thousand.

The new equilibrium price is $12 thousand.

Answer: answer is 3

Step-by-step explanation: it is 3 because you do 1 d.p. plus a and b and you get 3

If 2XY = YZ then XY = 1/2YZ this is division property of equality.

Division property of equality, multiplication property of equality, subtraction property of equality and addition property of equality.

According to the given question we have to define each property that we used to solve or interpret if 2XY = YZ, then XY = 1/2YZ.

This is division property of equality.

2XY = YZ

Now if we divide both sides of the equality by 2 we'll get

XY = 1/2 YZ and we know diving by a same constant on both sides of the inequality doesn't change the equality relation.

If 2XY = YZ, then YZ = 12YZ is not the correct question,The correct question is If 2XY = YZ then XY = 1/2YZ.

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The simple interest, in two years at the rate of 1.2% is 880

In this case, we must calculate how much interest 2000 would earn compounded yearly over two years at a rate of 1.2.

I = 880 in interest earned

Annually, the system may be evaluated in terms of simple interest.

A = P(rt) for the first year, where r = 1.2 and t = 1.

Therefore;

A = 2000(1.2×1).

A = 2400.

As a result, the revised Principal amount for the second year is 2400.

As a result, A' = 2400 (1.21).

A' = 2880.

As a result, the sum owing after two years is 2880.

However, because the initial principal is $2,000,

The interest is defined as I = A' - P, or I = 2880 - 2000.

I = 880 as a result of interest.

Simple interest is computed as S.I. = P R T, where P = Principal, R = Annual Rate of Interest in %, and T = Time, commonly expressed as the number of years. The interest rate is expressed as a percentage r% and is written as r/100.

The principle is the money borrowed from the bank or invested at the outset. P represents the principal.

Rate: The rate of interest at which the principle amount is handed to someone for a specific period of time; the rate of interest can be 5%, 10%, or 13%, for example. R represents the interest rate.

Time is the length of time for which the primary amount is supplied to someone. T represents time.

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Answer:

0> 1/2

Step-by-step explanation:

a. The slope of the line parallel to y = 3/4x - 1 is: 3/4.

b. The slope of the line perpendicular to  y = 3/4x - 1 is: -4/3.

If two lines are parallel to each other, they will have the same slope value. On the other hand, if the two lines are perpendicular to each other, they will have slopes that are negative reciprocals of each other.

Thus, given the equation, y = 3/4x - 1, the slope of this line is 3/4.

The negative reciprocal of 3/4 is -4/3.

Therefore, we can conclude that:

a. The slope of the line parallel to y = 3/4x - 1 is: 3/4.

b. The slope of the line perpendicular to  y = 3/4x - 1 is: -4/3.

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Corresponding terms are those that appear in identical places in two similar situations.

Generate two numerical patterns given their rules. Understand that a term is a number in a pattern and corresponding terms are numbers in two patterns that show up in the same place in each pattern (e.g., the second term of each pattern are corresponding terms

.1) use the rule add 8 to find the cost of 6 t-shirts

 cost of 5 t-shirts to get the cost of 6 t-shirts.

the cost of 5 t-shirts plus $8 is $40+$8= $48

2) the second number is 4 times the first number.

one pattern starts at 0 and follows the rule add 2.

another pattern starts at 0 and follows the rule add5.

corresponding terms as ordered pairs

0,0

2,8

4,16

6,24

8.32

10,40

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Max is going to have more money than Shawn at the end of the seven weeks from the calculations

We would first have to define x to be the point where the money that they have would be equal

This is the week that is referred to as x

Sean would have $20 + $2x

Max would have $5x

When both amounts are equal, we would have sean = max

= $20 + $2x = $5x

Take like terms

20 = 5x - 2x

20 = 3x

divide through by 3

x = 20 / 3

= 6.6667

Remember

In 7 weeks sean = 20 + 2x 7 = 34

max = 5 x 7 = 75

Hence we can say that Max would have more money than Sean

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Based on this parallel lines cut by a transversal, the true statements include the following:

B. m∠1 + m∠3 = 180 because they form a straight angle.

C. ∠3 ≅ ∠6 because they are alternate interior angles.

D. ∠1 and ∠6 are supplementary because ∠3 ≅ ∠6 and m∠1 + m∠3 = 180.

Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

The Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.

A supplementary angle can be defined as two (2) angles or arc whose sum is equal to 180 degrees (180°).

In conclusion, ∠1 and ∠6 are supplementary angles because ∠3 is congruent to ∠6 and m∠1 + m∠3 = 180 degrees as shown in the image attached below.

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Complete Question:

Select all the true statements. Two parallel lines cut by a transversal. The transversal makes 4 angles with the top line. Angles 1 and 2 are above the line and angles 3 and 4 are between the lines. The transversal also makes 4 angles with the bottom line. Angles 5 and 6 are between the lines and angles 7 and 8 are below the bottom line. Between the lines, angles 3 and 6 are on opposite sides of the transversal and angles 4 and 5 are on opposite sides of the transversal.

A. ∠3 ≅ ∠2 because they are alternate interior angles.

B. m∠1 + m∠3 = 180 because they form a straight angle.

C. ∠3 ≅ ∠6 because they are alternate interior angles.

D. ∠1 and ∠6 are supplementary because ∠3 ≅ ∠6 and m∠1 + m∠3 = 180.

E. ∠1 ≅ ∠3 because they are vertical angles.

The inequality is 30 + 7.5v ≤ 135

The number of visits Emma could make to earn her first free movie ticket is 14

From the question, we are to write and solve an inequality which can be used to determine the number of visits Emma can make to earn her first fee movie ticket

From the given information,

"She receives 30 rewards points just for signing up"

and

"She earns 7.5 points for each visit to the movie theater"

If she visits the movie theater v number of times,

Then,

She would earn

30 + 7.5v points

Also,

She needs at least 135 points for a free movie ticket.

Thus,

The inequality that could be used to determine the number of visits, v, to earn a free movies ticket is

30 + 7.5v ≤ 135

Solving the inequality

30 + 7.5v ≤ 135

Subtract 30 from both sides

30 - 30 + 7.5v ≤ 135 - 30

7.5v ≤ 105

v ≤ 105/7.5

v ≤ 14

Hence, the number of visits Emma could make to earn her first free movie ticket is 14

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Answer:

m<a=45

m<b=90

m<c=45

m<d=45

m<e=90

m<g=130

m<h=50

m<i=130

m<k=85

m<l=95

m<n=95

Answer:

m=4/3

Step-by-step explanation:

slope=rise/run or y=mx+b

rise/run=8/6=4/3

Answer:

Step-by-step explanation:

Complete Question: You are building a shelf that fits in a corner in the figure the entire shelf is XYZ each unit in the coordinate plane represents one inch find the area of the shelf.

Answer:

112.5 units²

Step-by-step explanation:

Area of the shelf = ½*base*height.

The base is the distance between Z(0, 5) and Y(15, 5)

The height is the distance between X(15, 20) and Y(15, 5).

Therefore area of the shelf = ½*ZY*XY

Use the distance formula to find ZY and XY.

Distance between Z(0, 5) and Y(15, 5):

Let,

Distance between X(15, 20) and Y(15, 5):

Let,

Area of shelf = ½*15*15 = ½*225 = 112.5 units²