the words at the bottom go into the boxes (statements and reasons)

The scale factor of the dilation of the square is (b) 18 : 1

To find the scale factor, we need to determine how many times the length of the original square was multiplied to obtain the length of the new square.

The length of the original square is 4.5 meters, and the length of the new square is 81 meters.

Therefore, we need to divide the length of the new square by the length of the original square to find the scale factor:

81 meters ÷ 4.5 meters = 18

So the scale factor is 18:1.

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Answer:

  x = 3√2

Step-by-step explanation:

You want the length x of the hypotenuse of an isosceles right triangle with sides of length 3.

The two legs of an isosceles right triangle are congruent. The length of the hypotenuse can be found from the Pythagorean theorem:

  x² = 3² +3²

  x² = 3²·2

  x = √(3²·2) = 3√2

The length of side x is 3√2.

__

Additional comment

A isosceles right triangle is one of two "special" right triangles. The ratios of its side lengths are 1 : 1 : √2. This tells you the hypotenuse is √2 times the side length, as we found above.

The other "special" right triangle is the 30°-60°-90° triangle. Its side lengths have the ratios 1 : √3 : 2. Both of these are seen often in algebra, trig, and geometry problems.

Answer:

To make 10 liters of 20% alcohol solution, RSM would need to use a combination of the 18% and 40% alcohol solutions. Let's call the amount of 18% solution used "x" and the amount of 40% solution used "y".

To set up the equation, we'll use the fact that the amount of pure alcohol in the final solution must be equal to 20% of the total volume.

So:

0.18x + 0.40y = 0.20(10)

Simplifying:

0.18x + 0.40y = 2

We have one equation with two unknowns, which means we need another equation. Fortunately, we know that RSM is making a total of 10 liters of solution. So:

x + y = 10

We now have two equations with two unknowns, which we can solve simultaneously. One way to do this is to solve one equation for one variable, then substitute that expression into the other equation, like so:

x = 10 - y (from the second equation)

0.18(10-y) + 0.40y = 2 (substituting into the first equation)

1.8 - 0.18y + 0.40y = 2

0.22y = 0.2

y = 0.91

So RSM would need to use approximately 0.91 liters (or 910 milliliters) of the 40% solution, and the rest (9.09 liters or 9090 milliliters) of the 18% solution, to make 10 liters of 20% alcohol solution.

The vertices οf the given inequalities are (2,0);(-6,0); (0,-1);(0,-3);(-2,-2)

In mathematics, inequality is  a statement οf an οrder relatiοnship that is a relatiοnship between twο values that are nοt equal,—greater than, greater than οr equal tο, less than, οr less than οr equal tο—between twο numbers οr algebraic expressiοns. Such as 7<9 οr 5>3 etc.

The given system οf inequalities are:

2y-x≥ -2

2y+x≥ -6

y≤0

x≤0

Tο find the vertices we must cοnvert the inequality intο an equatiοn.

Sο the equatiοns are:

2y - x= -2-----------------(1)

2y + x= -6----------------(2)

y=0-----------------(3)

x=0 -----------------(4)

Putting the value οf equatiοn (3) in equatiοn (1) and (2) we get,

x=2 and x= -6

Again putting the value οf equatiοn (4) in equatiοn (1) and (2) we get,

y=-1 and y=-3

Sο frοm these the vertices can be written as (2,0);(-6,0) and (0,-1);(0,-3)

Nοw , subtracting equatiοn (2) frοm equatiοn (1) we get,

( 2y - x )-(2y+x)= -2-(-6)

⇒ -2x= 4

⇒x= -2

Putting this value x=-2 in equatiοn (1) we get,

2y-(-2)=-2

⇒2y+2=-2

⇒2y=-4

⇒ y= -2

Hence the vertices οf the given inequalities are (2,0);(-6,0); (0,-1);(0,-3);(-2,-2)

A graph fοr the inequalities is attached belοw.

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It would take the giant tortoise approximately 21.43 hours to travel 3 miles at a rate of 0.14 miles per hour.

What is distance?

Distance is the measure of how far apart two objects or locations are from each other. It is usually measured in units such as meters, kilometers, miles, or feet. Distance is a scalar quantity, meaning it has only magnitude and no direction.

We can use the formula:

time = distance ÷ speed

where "distance" is the total distance to be traveled and "speed" is the rate of travel.

In this case, the distance is 3 miles and the speed is 0.14 miles per hour. So we can substitute these values into the formula and solve for "time":

time = 3 miles ÷ 0.14 miles per hour

time ≈ 21.43 hours

Therefore, it would take the giant tortoise approximately 21.43 hours to travel 3 miles at a rate of 0.14 miles per hour.

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Answer:

  (a)  y = 1.5x² -4.5x -6

Step-by-step explanation:

You want the standard form of the quadratic with roots 4 and -1, and passing through the point (1, -9).

For roots p and q, the standard form can be found from the factored form:

  (x -p)(x -q) = x² -(p+q)x +pq

For the given roots, the product pq will be ...

  (4)(-1) = -4

The sum p+q is 4+(-1) = 3. The x-coefficient is the opposite of this.

The parent quadratic (before vertical scaling) will be ...

  (x -4)(x +1) = x² -3x -4

The coefficients of the last two terms have the same sign. (Eliminates the 2nd and 4th answer choices.)

The given point has an x-value (1) between the given roots (-1, 4):

  -1 < 1 < 4

The y-value at that point is negative. This means the vertex of the parabola will be below the x-axis, so the parabola opens upward and the leading coefficient is positive. (Eliminates the last two answer choices.)

The answer choices tell us the leading coefficient is 1.5, so the equation is ...

  y = 1.5(x² -3x -4)

  y = 1.5x² -4.5x -6 . . . . . . matches the first choice

__

Additional comment

We could find the value of the leading coefficient 'a' by evaluating ...

  y = a(x -4)(x +1)

for x = 1. We would get ...

  -9 = a(1 -4)(1 +1) = -6a   ⇒   a = -9/-6 = 1.5

As we saw above, this isn't necessary. We only need to know that its sign is positive. The answer choices tell us the value.

If the x-value of the given point is not between the roots, then we know the sign of the y-value is the sign of the leading coefficient.

For multiple-choice questions, you only need to work enough of the problem to determine which answer choice is correct. You don't necessarily need to work the problem all the way to an answer.

Amount of money that he have left over monthly to put into savings is $585.

Subtraction can be done for any numbers or algebraic expressions. It is the process of taking out certain value from a given amount of number.

The process of subtraction can also be termed as finding difference.

Given that,

Hourly rate of Mr. Smith = $20

If he works full time, then the number of working hours in a week is 40 hours.

So the number of working hours in a month = 40 × 4 = 160 hours

Rate for a month = 160 × $20 = $3200

Tax percent from the income = 25%

Income after tax = 3200 - (25% × 3200)  = 3200 - 800 = $2400

Total budget of Mr. Smith = $1,410 + $405 = $1815

Income after the monthly budget = $2400 - $1815 = $585

Hence the money that is left is $585 for the savings.

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The complete question is given below :

Mr. Smith makes $20 an hour working full time. He gets about 25% of his income taken out for taxes. He came up with the following monthly budget.

Household:

Rent: $700

Cable: $85

Cell Phone: $175

Electric: $100

Food: $350

Total: 1,410

Automobile

Car: $200

Car Insurance: $100

Gas: $90

Maintenance: $15

Total: $405

How much money does he have left over monthly to put into savings?​

The value of x is approximately 4.83 centimeters.

Answer: B (03)

The value of x, we need to add up all the side lengths of the figure and set it equal to the given perimeter of 33 cm.
The top and bottom sides have length [tex]2x-3[/tex] cm each, and the left and right sides have length [tex]x+5 cm[/tex] each.
So, we can write the equation:
[tex]2(2x-3) + 2(x+5) = 33 [/tex]
Simplifying and solving for x:
[tex]4x - 6 + 2x + 10 = 33 [/tex]
[tex]6x + 4 = 33 [/tex]
[tex]6x = 29 [/tex]
[tex]x = 29/6 [/tex]
[tex]x ≈ 4.83 [/tex]
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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 2.7\%\to \frac{2.7}{100}\dotfill &0.027\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{\underline{semi-annually}, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &10 \end{cases}[/tex]

[tex]A = 4000\left(1+\frac{0.027}{2}\right)^{2\cdot 10}\implies A=4000(1.0135)^{20} \implies \boxed{A \approx 5230.40} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \textit{Annual Percent Yield Formula} \\\\ ~~~~~~~~~~~~ \left(1+\frac{r}{n}\right)^{n}-1 ~\hfill \begin{cases} r=rate\to 2.7\%\to \frac{2.7}{100}\dotfill &0.027\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{\underline{semi-annually}, thus twice} \end{array}\dotfill &2 \end{cases} \\\\\\ \left(1+\frac{0.027}{2}\right)^{2}-1\implies 1.0135^2-1\approx 0.02718 ~~ \approx ~~ \stackrel{ 0.02718\times 100 }{\boxed{2.718~\%}}[/tex]

Step-by-step explanation:

To create a rectangle with vertices located at (-5, 3), (-5, -7), and (5, -7), we need to find the fourth vertex that completes the rectangle. Since opposite sides of a rectangle are parallel and congruent, we can determine the missing vertex by finding the midpoint of either of the two given sides and then moving in the direction perpendicular to that side by the length of the other side.

The given sides are:

Side 1: (-5, 3) to (-5, -7), which has length 3 - (-7) = 10

Side 2: (-5, -7) to (5, -7), which has length 5 - (-5) = 10

Since the sides are congruent, we can find the midpoint of Side 1 as:

Midpoint of Side 1 = [(-5 + (-5))/2, (3 + (-7))/2] = [-5, -2]

To find the missing vertex, we need to move from (-5, -2) in the direction perpendicular to Side 1 by a distance of 10 units (the length of Side 2). Since Side 2 is horizontal, we need to move vertically. We can do this by adding or subtracting 10 from the y-coordinate of the midpoint of Side 1, depending on whether we want to move up or down. In this case, we want to move down, so we subtract 10:

Missing vertex = [-5, -2 - 10] = [-5, -12]

Therefore, the fourth vertex needed to create a rectangle with vertices located at (-5, 3), (-5, -7), and (5, -7) is (-5, -12).

The volume of each shape (A right triangular prism and the trapezoidal prism are):

A right triangular prism is a three-dimensional shape that has a triangular base and three rectangular faces. It is a prism because its two bases are identical and parallel. The formula for finding the volume of a right triangular prism is V = (1/2) * base * height * length.

A trapezoidal prism is a three-dimensional shape with trapezoidal bases and four rectangular faces. It is also a prism because its two bases are identical and parallel. The formula for finding the volume of a trapezoidal prism is V = ((b1 + b2) / 2) * height * length, where b1 and b2 are the lengths of the two parallel sides of the trapezoidal base.

Recall that the formula for the volume of a trapezoidal prism is:

V = (1/2)h(b1+b2)L

where:

Hence, substituting the given values, we have:

V = (1/2)(20 + 19)(7) 4

V = (1/2)(39)(7) 4

V = (273/2) 4

V = 546ft³

Therefore, the volume of the trapezoidal prism is 546ft³

2) Recall that the formula for the volume of a right triangular prism is:

V = (1/2) * b * h * L

Where:

b is the length of the base of the triangle

h is the height of the triangle

L is the length of the prism (the distance between the triangular faces)

The factor of (1/2) is included since the base of the prism is a triangle.

Given the forumla above:

b = 9ft

h = 7ft

L = 4ft


Plugging in the values given:

V = (1/2) * 9ft * 7ft * 4ft

V = 126ft³

Therefore, the volume of the right triangular prism is 126ft³

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Answer:

Detra's rule: Output = 3 x Input. This means that for every input value, the output value is three times greater. Detra likely arrived at this solution by noticing a pattern in the input-output values and determining that the output values were always three times greater than the input values.

Trinh's rule: Output = Input + 3. This means that for every input value, the output value is the input value plus three. Trinh likely arrived at this solution by noticing a pattern in the input-output values and determining that the output values were always three more than the input values.

Step-by-step explanation:

Answer:

x = 8°

Step-by-step explanation:

∠GJL = ∠WJZ = 90° - 18° = 72° (cross angles)

(9x)° = 72° / : 9

x = 8°

Answer:

x = 8

Step-by-step explanation:

Find the measure of angle WJZ.

Since angles on a straight line sum to 180°:

⇒ m∠GJH + m∠HJW + m∠WJZ = 180°

⇒ 90° + 18° + m∠WJZ = 180°

⇒ 108° + m∠WJZ = 180°

⇒ 108° + m∠WJZ - 108° = 180° - 108°

⇒ m∠WJZ = 72°

According to the Vertical Angles Theorem, when two straight lines intersect, the opposite vertical angles are congruent.

Since line GJZ and line LJW intersect, then ∠GJL and ∠WJZ are vertical angles and therefore congruent:

⇒ m∠GJL = m∠WJZ

⇒ (9x)° = 72°

⇒ 9x = 72

⇒ 9x ÷ 9 = 72 ÷ 9

⇒ x = 8

Therefore, the value of x is 8.

Answer:

Yes the Triangle are similar by A.A.A Axiom

Answer:

yes, they two triangles are similar

Step-by-step explanation:

.........

Problem: Imagine a person, John, facing a scheduling conflict due to overlapping appointments.

John had a dentist appointment at 2 PM, which he expected to last an hour, but he also had a meeting scheduled with his colleague at 3 PM.

Why it was difficult: The scheduling conflict made it difficult for John to manage both appointments without disappointing either party.
Math used to solve the problem: John decided to calculate the time it would take him to travel from the dentist's office to the meeting location, considering the appointment duration and travel time.
Dentist appointment: 2 PM - 3 PM

Travel time (calculated using distance and speed): 30 minutes
Meeting time: 3 PM
John realized he would be 30 minutes late for the meeting if he attended the dentist appointment.
Outcome: John decided to reschedule his dentist appointment to an earlier time or another day to avoid the conflict.
Approaching the problem differently next time:

In the future, John could consider using a calendar app to keep track of his appointments and avoid scheduling conflicts.

Additionally, he could factor in the duration of events and travel times when scheduling appointments to ensure he has enough time between engagements.

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Answer:

  step 1

Step-by-step explanation:

You want to know which step in Marta's simplification of 4·log₅(x) +log₅(2x) -log₅(3x) contains an error in application of properties of logarithms.

  log(a^b) = b·log(a)

  log(ab) = log(a) +log(b)

  log(a/b) = log(a) -log(b)

  [tex]4\log_5(x)+\log_5(2x)-\log_5(3x)\\\\=\log_5(x^4)+\log_5(2x)-\log_5(3x)\qquad\text{Step 1. Mistake: $4x$ instead of $x^4$}\\\\\log_5(x^4\cdot2x)-\log_5(3x)=\log_5\left(\dfrac{2x^5}{3x}\right)\\\\=\boxed{\log_5\left(\dfrac{2x^4}{3}\right)}[/tex]

The two are similar because both use a percentage as a decimal to get a new price.

According to the question the expected net gain for a player on a $1 straight bet is -$0.60.

Simply multiply each value of the discrete random variable X by its probability and add the products to get the expected value, E(X), or mean. The formula is as follows: E (X) =  ∑ x P (x)

The possible outcomes for X are winning with a probability of 1/1000 and net gain of $399, and losing with a probability of 999/1000 and net gain of -$1. Therefore, we can calculate the expected value of X as follows:

E(X) = (1/1000)($399) + (999/1000)(-$1)

E(X) = $0.399 - $0.999

E(X) = -$0.60

Therefore, the expected net gain for a player on a $1 straight bet is -$0.60. This means that, on average, a player will lose $0.60 for each $1 bet they place on this game.

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Answer:

-0.60

Step-by-step explanation:

Khan Academy

Answer:

A disadvantage to using equations for solving problems might be that it can be difficult to remember what an equation means without a diagram, graph, or table (Option A).

Step-by-step explanation:

The gas company would charge $154.48 for using 200 hundred cubic feet of natural gas during the month.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can include numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division.

The equation that represents the gas company's monthly charges in dollars for using x hundred cubic feet of natural gas is:

y = 0.6924x + 16

Where:

x is the number of hundred cubic feet of natural gas used during the month

0.6924 is the cost per hundred cubic feet of natural gas used

16 is the fixed monthly service fee charged by the gas company.

To calculate the monthly charges for a given amount of natural gas used, we can substitute the value of x into this equation and simplify. For example, if x = 200, then:

y = 0.6924(200) + 16

y = 138.48 + 16

y = 154.48

Therefore, the gas company would charge $154.48 for using 200 hundred cubic feet of natural gas during the month.

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The prοbability that in a sample οf 12 custοmers, nοne οf the 12 will οrder a nοnalcοhοlic beverage is 0.0042.

Binοmial prοbability is a type οf prοbability that deals with the number οf successes in a fixed number οf independent trials, where each trial has οnly twο pοssible οutcοmes, cοmmοnly referred tο as success οr failure. It is calculated using the binοmial prοbability fοrmula.

This is a binοmial prοbability prοblem, where the prοbability οf success (οrdering a nοnalcοhοlic beverage) is 0.53, and the number οf trials is 12.

The prοbability οf nο custοmers οrdering a nοn-alcοhοlic beverage can be fοund using the binοmial prοbability fοrmula:

[tex]P(X = k) = (n choose k) * p^k * (1-p)^{(n-k)[/tex]

where:

n = number of trials

k = number of successes (in this case, 0)

p = probability of success (ordering a non-alcoholic beverage)

Plugging in the values, we get:

[tex]P(X = 0) = (12 choose 0) * 0.53^0 * (1 - 0.53)^{(12 - 0)[/tex]

[tex]= 1 * 1 * 0.47^{12}[/tex]

= 0.0042 (rounded to 4 decimal places)

Therefοre, the prοbability that in a sample οf 12 custοmers, nοne οf the 12 will οrder a nοnalcοhοlic beverage is 0.0042.

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Answer:

Step-by-step explanation:

Start by substituting the first equation into the second equation to eliminate y:

2x^2 = -3x - 1

Move all terms to one side:

2x^2 + 3x + 1 = 0

Factor the quadratic equation:

(2x + 1)(x + 1) = 0

Solve for x by setting each factor to zero:

2x + 1 = 0 or x + 1 = 0

x = -1/2 or x = -1

Plug in the values of x to find the corresponding values of y:

For x = -1/2:

y = 2(-1/2)^2 = 1/2

For x = -1:

y = 2(-1)^2 = 2

The solutions to the system are (-1/2, 1/2) and (-1, 2).

Answer:

0.5

Step-by-step explanation:

We want to get an equation with only one variable for it to be able to be solved.

To do this, we will solve the first equation for y.

[tex]x+y=2\\y=2-x[/tex]

Now, we can plug this value of y into the second equation

[tex]7x-y=2\\7x-(2-x)=2\\[/tex]

Finally, we have just one variable, and we can solve for x.

[tex]7x-(2-x)=2\\7x-2+x=2\\8x=4\\x=0.5[/tex]

Answer:

74.43 pounds

Step-by-step explanation:

To find the amount of oxygen needed in the outer tank, we need to first find the volume of the space between the two tanks. This space is a rectangular prism with length 20 feet, width 8 feet, and height 6 feet, but with a rectangular prism removed from the center. The removed prism has length 5 feet, width 4 feet, and height 3 feet.

The volume of the rectangular prism between the two tanks is:

V = (20 x 8 x 6) - (5 x 4 x 3)

V = 960 - 60

V = 900 cubic feet

To find the amount of oxygen needed to fill this space with a density of 0.0827 pounds per cubic foot, we can multiply the volume by the density:

m = V x d

m = 900 x 0.0827

m ≈ 74.43 pounds

Therefore, approximately 74.43 pounds of oxygen is required to meet the density requirement.

Answer: 74 pounds

Step-by-step explanation:

(20*8*6) - (5*4*3)

960-60

v=900 ft3

density=0.0827

mass=0.0827*900

Mass is 74 pounds

A subtraction expression for each length OB and AB is  [tex]OBX = \sqrt (x - 4)^2 + (y - 2)^2] + 2 \sqrt (1 - x)^2 + 16] - y.[/tex]

Let r be the radius of the circle. Then we have:

r = distance(O, B)

We can use the distance formula to find the distance between two points:

distance(P, Q) = √[(x2 - x1)² + (y2 - y1)²]

where P = (x1, y1) and Q = (x2, y2)

Substituting O = (4, 2) and B = (x, y), we get:

r = distance(O, B) = √[(x - 4)² + (y - 2)²]

Now, let's consider the subtraction expression:

OBX-2 AB-y+h

We can simplify this expression as follows:

[tex]OBX = r + 2 AB = \sqrt{[(x - 4)^2 + (y - 2)^2] } + \sqrt[2]{[(1 - x)^2 + (6 - y)^2]}[/tex]

We don't need to include the variables y and h in the expression since they were not defined in the problem. So the final subtraction expression for OBX is:

[tex]OBX = \sqrt{ [(x - 4)^2 + (y - 2)^2]} + \sqrt[2]{[(1 - x)^2 + 6]-y} .[/tex]

Therefore, the expression is OBX [tex]= \sqrt(x - 4)^2 + (y - 2)^2] + 2 \sqrt(1 - x)^2 + 16] - y.[/tex]

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Answer:

13

Step-by-step explanation:

Given

7u - 4 = 3 ( add 4 to both sides )

7u = 7 ( divide both sides by 7 )

u = 1

Then

9u + 4 = 9(1) + 4 = 9 + 4 =13

Answer:   [tex]\frac{3}{4}[/tex]c

Step-by-step explanation:

       If one pound of chicken costs c dollars, and we are writing an expression for 3/4 a pound of chicken, our expression will be the price (c) multiplied by how much chicken there is (3/4):

               3/4c

- In mathematics, an expression is a combination of numbers, variables (represented by letters), symbols, and operators, arranged in a way that represents some meaningful mathematical relationship or calculation.

- Expressions can be simple, like 3x or 4 + 5, or complex, like (3x + 4y) / (2x - 5y). Expressions are not equations or inequalities, as they do not contain an equal sign, but they can be used to build equations or inequalities.

The price of 1 pound of chicken is c dollars. To find the price of 3/4 pound of chicken, we can multiply the price of 1 pound by 3/4:

[tex]\begin{aligned}\sf Price\: of\: \dfrac{3}{4}\: pound\: of\: chicken& =\sf \dfrac{3}{4} \times c \\&=\boxed{\bold{\:\dfrac{3}{4}c\:}}\end{aligned}[/tex]

Therefore, the expression for the price of 3/4 pound of chicken is 3/4c.

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