Ash and Bea are engravers. Ash charges a flat fee of $\$1.50$ for the first $21$ letters engraved, and $8$ cents per letter thereafter. Bea charges a flat fee of $\$1.60$ for the first $15$ letters engraved, and $7$ cents per letter thereafter. For what nonzero number of letters will Ash and Bea's engraving prices be the same?

Answer:

y = 2x+ 3

Step-by-step explanation:

Answer: v = 100

Step-by-step explanation:

v+15 = v-37 + v-48

v + 15 = 2v - 85

85 + 15 = 2v - v

100 = v

You can rearrange terms in an expression using the commutative and associative qualities to arrange compatible numbers next to one another and in groups.

According to the associative property, numbers can be added to or multiplied while still maintaining the same result. According to the commutative property, even if the numbers are added or multiplied, the solution will remain the same.

Explain:

[tex]\frac{4}{5}[/tex] ×(20×17/8)

20×17/8

340÷8

[tex]\frac{4}{5}[/tex]×[tex]\frac{340}{8}[/tex]

= [tex]\frac{64}{2}[/tex]

= 32

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The polynomial in intercept form so that P(x)=0 has the given roots is, x^2 - √3x - 2x + 2√3 = 0.

What is polynomial?

A polynomial is an expression in mathematics that only uses the operations of addition, subtraction, multiplication, and powers of positive-integer variables. It consists of indeterminates and coefficients. The polynomial x^2 4x + 7 is an illustration of one with a single indeterminate x.

We have to find the polynomial in intercept form so that P(x)=0 has the roots 2 and √3.

Let 2 and √3 are the roots of the polynomial so,

x = 2,  x = √3

⇒ x - 2 = 0,  x - √3 = 0

⇒ (x - 2)(x - √3) = 0

x^2 - √3x - 2x + 2√3 = 0

Hence, the polynomial in intercept form so that P(x)=0 has the given roots is, x^2 - √3x - 2x + 2√3 = 0.

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The cost of soda as calculated from the data given is found to be as 0.9 cents.

the price of 1 burger = x

the price of 1 soda =y

Therefore, the equation for Uri and Gen becomes,

2x + y = $2.10

x+ 2y = $2.40

On solving these two equations we will get the value of x and y which represents their cost.

on multiplying equation 2 with 2 , we will get ,

2x + 4y = 4.80

Therefore , on subtracting equation 1 and 2 ,

 2x + y = $2.10

- 2x + 4y = 4.80

=> -3y = - 2.7

=> y = 0.9

Therefore x will be ,

x+ 2y = $2.40

x+ 2(0.9) = $2.40

x + 1.8 = $2.40

x = 2.40 - 1.8

  = 0.60

Therefore, cost of soda is 0.9 cents.

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Answer: 88

Step-by-step explanation:

Answer: 88

Step-by-step explanation: 5x5=25 + 9x7=63 ----> 25+63= 88

On solving the provided question we cans ay thatVertical Angles: TZU, XZW Adjacent Angles: TZU, UZV are Vertical angle and adjacent angle.

What is Vertical angle and adjacent angle,?

Vertical angles are two angles that share the same vertex and are formed by two intersecting lines. They are congruent (i.e. have the same measure) and are opposite each other

Adjacent angles are two angles that share a common vertex and side, but do not overlap. They are also called "next to" or "sharing an arm" angles.

Fig 1:

Vertical Angles: NMJ, LMK

Adjacent Angles: NMJ, JMK

Fig 2:

Vertical Angles: DEA, CEB

Adjacent Angles: DEA, AEB

Fig 3:

Vertical Angles: LQM, PQN

Adjacent Angles: LQM, MQN

Fig 4:

Vertical Angles: TZU, XZW

Adjacent Angles: TZU, UZV

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280t + 320t = 1,000 is distance equation can be used to solve for t, the time it takes the planes to be 1,000 miles apart.

What does distance mean in a nutshell?

Distance is the overall movement of an object without consideration of direction.

                      Regardless of an object's starting or ending point, distance can be defined as the amount of ground it has traveled.

At 10:00 a.m. two planes leave an airport. If the northbound plane flies at 280 mph and the southbound at 320 mph

Let 't' be the time taken when they are 1000 miles apart

the northbound plane flies at 280 mph

Distance  = speed * time

distance covered by northbound plane D1= 280 * t= 280t

the southbound at 320 mph

distance covered by southbound plane D2=320 t

Distance is 1000 miles apart

D1 + D2= 1000

280t + 320t = 1,000

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The area of the garden whose length and width as given in the task content is; 30 (x + 2) square units.

It follows from the task content that the expression which represents the area of the garden plot whose dimensions are as given.

Recall that Area, A = length × width.

Therefore, since length = 6 (√(x + 2)) units

The width = (5 √(x + 2) ) units

Hence, the area of the garden plot as required in the task content is; 6 (√(x + 2)) × ( 5 √(x + 2) )

= 30 (x + 2) square units

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The amount of snow on Peyton's lawn after 2 hours is 4 inches

amount of snow after t hours y = 8 - t

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

definition of variable to suit the problem

y = output variable = amount of snow remaking

m = slope = 1 inch per hour

x = input variable = number of hours

c = y intercept = 8 inches of snow on Peyton's lawn

The equation as described in the problem is represented using linear function as as follows

y = 8 - x

in 2 hours x = 2

y =8 - 2 = 4 inches

The quantity of snow after t hours

x = t

y = 8 - t

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Developer has 627264 square feet land available.

The minimum permissible quantity of an asset that is accepted for purchasing.

How many lots the developer has as per question?

A developer wants to develop 18-acre property = 784080 square feet area

he notices that street and common area will take up about 20% of total area.

hence, the remaining area for developing works = 80%

the amount of land rest for the developer = 784080 ×80 /100

                                                                    = 627264 square feet.

there is a rule that minimum lot size is to be 10000 square feet for developing works,

the above amount 627264 square feet lot can the developer have on this property that is higher than the minimum lot value.

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Answer:

[tex]x=\dfrac{\log 6}{\log 23}[/tex]

Step-by-step explanation:

Given exponential equation:

[tex]23^x=6[/tex]

[tex]\textsf{Apply the log law}: \quad a^c=b \iff \log_ab=c[/tex]

[tex]\implies\log_{23}6=x[/tex]

[tex]\textsf{Given change of base formula}: \quad \log_by=\dfrac{\log y}{\log b}}[/tex]

Apply the given change of base formula:

[tex]\implies x=\dfrac{\log 6}{\log 23}[/tex]

Answer:

41,500 people

Step-by-step explanation:

First you find 3% of 36,000= 1,080

Then you do 1080 x 5= 4,500

Then finally do 36,000 + 4,500= 41,500

Answer:

There is one unique solution (-3, 6)

Step-by-step explanation:

Desmos graphing calculator helps a lot with this stuff

Answer: b) there is only one unique solution (-3, 6)

Step-by-step explanation:

Answer: It is a straight line

Step-by-step explanation:

The depiction of numbers as an equilateral triangle organized in a series is known as a triangular number sequence. These numerals follow a 1, 3, 6 order.

A number that may be expressed as the sum of the initial n positive integers is referred to as a triangular number.

Thus, the first three triangular numbers 1, 3, 6.

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Answer: Toni invested in pounds= $1350

Step-by-step explanation:rate of compound interest=4%

Step-by-step explanation:

Toni invests money into an account which pays a fixed rate of compound interest each year. The total value, £V, of her investment after t years is given by the formula:  

Given equation is in the form of

where P is the amount invested

'r' is the rate of interest

t is the time taken

P= 1350 is the initial amount invested

1+r= 1.04  (subtract 1 from both sides)

multiply it by 100 to get percentage

r= 4%

I just search it bc my brain dosent work any more

The three combinations of pennies and quarters are:

A. 1,560 Pennies and 124 Quarters

B. 2,600 Pennies and 49 Quarters

C. 3,120 Pennies and 24 Quarters

The total value of the pennies and quarters is $62.00. This can be achieved with either 1,560 pennies and 124 quarters (1,560 x 0.01 + 124 x 0.25 = 62.00), 2,600 pennies and 49 quarters (2,600 x 0.01 + 49 x 0.25 = 62.00) or 3,120 pennies and 24 quarters (3,120 x 0.01 + 24 x 0.25 = 62.00).

To find the combinations of pennies and quarters that are worth $62.00, begin by finding the number of pennies that equal $

62.00. 62.00/0.01 = 6,200 pennies.

Next, subtract the value of the pennies from the total to find the value of the quarters.

62.00 - (6,200 x 0.01) = 24.00.

Divide the value of the quarters by 0.25 to find the number of quarters. 24.00/0.25 = 96 quarters.

To arrive at the three combinations

, 1,560 pennies and 124 quarters

(1,560 + 96 = 1,656, 1,656 x 0.01 + 124 x 0.25 = 62.00),

2,600 pennies and 49 quarters

(2,600 + 49 = 2,649, 2,649 x 0.01 + 49 x 0.25 = 62.00)

and

3,120 pennies and 24 quarters

(3,120 + 24 = 3,144, 3,144 x 0.01 + 24 x 0.25 = 62.00).

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Answer: 40

Step-by-step explanation:

   We will substitute x = 8 and simplify the given expression.

 Given:

6x-x

 Substitute:

6(8) - 8

 Multiply:

48 - 8

 Subtract:

40

Answer: 4

Explanation:

In Algebra a term is either a single number or variable, or numbers and variables multiplied together.

Terms are separated by + or − signs, or sometimes by divide.

1. The best geometric model for the rail road is C. Line

2. Two straight lines cannot go through any two points. It is false.

3. The length of the cake is A. 5.5 inches.

4. The vertical angles are AHC and GHE.

The best geometric model for a set of railroad tracks would likely be a line, as it represents the linear path that the tracks follow. A point would not be appropriate as it does not represent the length or direction of the tracks, and a plane would not be necessary as the tracks are linear and exist in a three-dimensional space.

It should be noted that two straight lines cannot go through any two points. Only one line can. The length of the cake will be:

= 6.0 - 0.5

= 5.5

It should be noted that vertical angles are equal. This was Illustrated as AHC and GHE.

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Answer: You need to drew , this arrow , to each point  K,L,M,N,

Drawing must be parallel to , this arrow, AND , exactly the same length, as the arrow .

step 2.  when you drew it , then at the end are your new points, K",L",M",N".

Ok?

step 3.

Then you just read  the  coordinates.  of new  points .

I would gladly drew it ,  but I do not knew how to put picture  in  this , jet .

Step-by-step explanation:

The percentage of ounce Dariu has left of his port drink is 55%.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

It is given that Dariu ha a 40-ounce port drink.

He drank 18-ounce port drink.

First calculate what percentage of port drink Dariu drank.

The equation is -

= (18/40) × 100

= 45%

So, Dariu drank 45% of the port Drink.

Now, subtract the percentage Dariu drank from the 100% (40 Ounce) drink Dariu had -

100 - 45 = 55

Therefore, Dariu has 55% drink left.

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Using the concept of fraction, the percentage edited on the video is 62.5 percent.

What is Percentage

Percentage is a standard mathematical concept used to express a portion of a whole number in terms of a hundred. It is denoted by the symbol “%” and is often expressed as a fraction or a decimal. For example, 25% can be expressed as 0.25 or 1/4.

In this problem, Thorton has done a 2.5 hours work. The percentage he has edited can be calculated using fraction or ratio as;

percentage edited = (2.5 / 4) × 100

Percentage = 0.625 × 100

Percentage = 62.5 %

From the above, Thorton has edited 62,5 percent of the video for his school project.

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Answer:

------------------------------------

There is no indication that the given triangles are congruent.

We can see one angle of each triangle is marked as congruent and that is is. No more evidences of congruence and therefore we state the triangles are not congruent.

This is a choice C.

Answer:

12.

Step-by-step explanation:

right!!

Answer: 3

Step-by-step explanation:You can't start at station 0 or 1, as there is not enough gas to travel to the next station.

Let's start at station 2 and fill up with 4 unit of gas. Your tank = 0 + 4 = 4

Travel to station 0. Your tank = 4 - 3 + 2 = 3

Travel to station 1. Your tank = 3 - 3 + 3 = 3

You cannot travel back to station 2, as it requires 4 unit of gas but you only have 3.

Therefore, you can't travel around the circuit once no matter where you start.

The description of isometry and transformations is as follows,

isometry mean A distance-preserving transformation between metric spaces is known as isometry, congruence, or congruent transformation.

The transformation, or f, is a function that maps to itself: X  X. Following the transformation, the pre-image X transforms into the image X. Any or all of the operations like translation, rotation, reflection, and dilation can be used in this transformation. A function is translated by moving it in a particular direction, rotated by spinning it about a point, reflection by reflecting the function, and dilation by scaling it.

Isometry: If two distinct points, a and b, were to be mapped to the same point, then the coincidence axiom of the metric d would be violated. This proof is similar to the proof that an order embedding exists between partially ordered sets. Clearly, a topological embedding exists for each and every isometry between metric spaces.

A bijective isometry is a global isometry, isometric isomorphism, or congruence mapping. A global isometry, like any other bijection, has a function inverse. A global isometry is also the inverse of a global isometry.

Types of transformations;

Transformation of Reflection: The term "reflection" refers to the kind of transformation that takes place when every point in the shape is reflected over a line. The image is on the opposite side of the line from the pre-image but at the same distance from the line when the points are reflected over it. An image point (q,p) is reflected from each point (p,q).

Transformation of Rotation: Rotation is the transformation that rotates each point of the shape by a predetermined number of degrees around that point. When the number of degrees is positive, the shape rotates counterclockwise, and when the number of degrees is negative, the shape rotates clockwise.

Transformation of Translation:  Sliding occurs when a 2-d shape is translated. Let's look at how the vertices of the blue and red figures are positioned in relation to one another in order to describe their relative positions. By comparing its position to the positions of A, B, and C, we must determine their positions.

Hence the basic description of transformation is as follows.

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