determine which two of the three given triangles are similar. Find the scale factor for the pair.

Answers

Answer 1

Since the ratio of their similar sides are equal hence the triangles are similar

Scale factors

Two figures are are known to be similar if the ratio of their similar sides are equal to a constant known as the scale factor.

For the triangles given, take the ratio of the sides;

12/2 = 6

30/5 = 6

36/6 = 6

Since the ratio of their similar sides are equal hence the triangles are similar

Learn more on similar shapes here: https://brainly.com/question/2644832

#SPJ1

Related Questions

Visual Description for Figure 1
Blue points, blue line segments, red points, and red line segments arranged on a Cartesian coordinate plane. Here are the blue points and their coordinates. Point A: (negative nine, 3). Point B: (negative 11, 3). Point C: (negative 10, 3). Point D: (negative 10, 5). Point F: (negative 10, 4). Point E: (negative 11, 4). Here are the red points and their coordinates. Point A-1: (negative 1, 6). Point A-2: (negative 3, 4). Point B-1: (negative 2, 4). Point B-2: (negative 5, 4). Point C-2: (negative 3, 3). Point D-1: (negative 5, 5). Point D-2: (negative 5, 3). Point E-1: (negative 6, 6). Point F-1: (negative 5, 6). A semicircle that lies below its line of symmetry AB. A semicircle that lies above its line of symmetry B-2 A-2. A triangle DEF. A triangle D-1 E-1 F-1. Line segments are drawn from C to D, from A-1 to B-1, from A-2 to B-2, and from C-2 to D-2. Triangle DEF, segment CD, and the semicircle with line of symmetry BA are arranged so that they look like a boat.

1. What transformations would you use on the blue segment CD to get it to match with the red segment C2D2? Explain your movement using the coordinates of the vertices.

2.
What transformations would you use on the blue triangle to get it to match with the red triangle? Explain your movement using the coordinates of the vertices.
3.
Which line segments on the boat are parallel? Explain your answer.
4.
Which line segments on the boat are perpendicular? Explain your answer.
5.
Which line segments on the boat have a slope of 0? Explain your answer.
6.
Which line segments on the boat have an undefined slope? Explain your answer.
7.
What is the slope of ED? Explain your answer using the change in coordinates given that E is at (−11,4) and D is at (−10,5).

Answers

A) Rotate by 90° counterclockwise.

B) Reflection transformation about the line y = 5.

C) Parallel Lines are C₂D₂ and A₂B₂; EF and E₁F₁.

D) Perpendicular lines are; D₁F₁ and E₁F₁; DF and EF; DC and AB.

E) Line segments with slope of 0 are; AB, C₂D₂, A₂B₂, EF and E₁F₁

F) Line segments on the boat that have an undefined slope are; Lines A₁B₁, DF and DC.

G) Slope of Line ED = 1

How to carry out Transformations?

A) The blue segment CD is seen on the graph as a perpendicular line with 2 units while the line segment C₂D₂ is seen as a horizontal line. Thus, to match CD with C₂D₂, we will rotate by 90° counterclockwise.

B) The transformations that would be used on the blue triangle to get it to match with the red triangle is a reflection transformation about the line y = 5.

C) The line segments that are parallel to each other are; C₂D₂ and A₂B₂; EF and E₁F₁.

D) The line segments that are perpendicular are; D₁F₁ and E₁F₁; DF and EF; DC and AB.

E) Horizontal lines that are parallel to the x-axis have zero slope. Thus, AB, C₂D₂, A₂B₂, EF and E₁F₁ all have zero slopes.

F) Undefined slope is the slope of a vertical line. Thus, Lines A₁B₁, DF and DC have undefined slopes.

G) Slope of ED = (5 - 4)/(-10 - (-11))

Slope of ED = 1/1

Slope = 1

Read more about Transformations at; brainly.com/question/4289712

#SPJ1

What is the maximum volume of an open rectangular box (with no top face) if its surface area is 1 square foot

Answers

abc =32 ft³ is the maximum volume of an open rectangular box (with no top face) if its surface area is 1 square foot.

Calculate a square's area?

A rectangle with all equal sides, commonly known as a square. Multiplying the length by the length is the. Using L as the length of each side, solve for L X L = L2,

The maximum volume of an open rectangular box (with no top face) if its surface area is 1 square foot This Lagrange multiplier optimization is standard. If the box has a base of a, a height of c, and an area constraint of ab+2ac+2bc−48=0 we wish to optimize V= abc.

L(a,b,c,λ)= abc−λ(ab+2ac+2bc−48)

The four partial derivatives are zero at an ideal position, so:

δLδa=bc−λ(b+2c)=0

δLδb=ac−λ(a+2c)=0

δLδc=ab−λ(2a+2b)=0

Plus the restriction. The first two enlighten:

λ=bcb+2c=aca+2c

Consequently, b(a+2c)=a(b+2c) implies to b=a. The third partial, where b=a, now informs us that a2=4aλ and so λ=a/4 nd by using this information in the second partial, we obtain 4c=a+2c which informs us that c=a/2 .

Now that we've inserted these b and c expressions into the constraint, we get [tex]3a^2=1[/tex] which means that a=4 feet, b=4 feet, and c=2 feet.

The maximum volume is therefore, abc=32 ft³

Learn more about surface area here:

https://brainly.com/question/28016184

#SPJ4

If the bottom row as a result of sythetic division is 1 3 0 4 0, then the quotient is which of the following? Select one:

Answers

The quotient of the synthetic division is x^3 + 3x^2 + 4

How to determine the quotient?

The bottom row of synthetic division given as:

1 3 0 4 0

The last digit represents the remainder, while the other represents the quotient.

So, we have:

Quotient = 1 3 0 4

Introduce the variables

Quotient = 1x^3 + 3x^2 + 0x + 4

Evaluate

Quotient = x^3 + 3x^2 + 4

Hence, the quotient of the synthetic division is x^3 + 3x^2 + 4

Read more about synthetic division at:

https://brainly.com/question/18788426

#SPJ1

22. What is the area of minor sector DFE?
79.3 square cm
15.2 square cm
37.9 square cm
66.1 square cm

Answers

The area of the minor sector DFE is gotten as; D: 66.1 square cm

How to find area of sector?

Formula for area of sector is;

A = (θ/360) * πr²

We are given;

minor angle; θ = 100°

radius; r = 8.7 cm

Thus;

A = (100/360) * π(8.7²)

A = 66.1 square cm

Read more about Area of Sector at; https://brainly.com/question/22972014

#SPJ1

volume of cylinder 8cm and 12 cm
[tex]v=\pi(8)(12)[/tex]

Answers

The volume of the cylinder is 301.593 cubic centimeter.

What is the volume of the given cylinder ?

Volume exists as a scalar quantity representing the amount of three-dimensional space enclosed by a sealed surface. For example, the space that a substance or 3D shape inhabits or contains. The volume stands often quantified numerically utilizing the SI-derived unit, the cubic meter.

A cylinder contains traditionally been a three-dimensional solid, one of the most essential curvilinear geometric shapes. Geometrically, it has been regarded as a prism with a circle as its base.

The dimensions of the cylinder is given as - 8 cm and 12 cm .

The formula of the volume of the cylinder is given as -

V = π * (8) * (12)

Thus the volume is = 96π ≈ 301.593 cubic centimeter.

To learn more about volume of cylinder, refer -

https://brainly.com/question/6204273

#SPJ9

give the answer please

Answers

Using the domain concept, the only value of x that is not on the domain of [tex]f(x) = \frac{1}{3x + 5}[/tex] is given as follows:

[tex]x = -\frac{5}{3}[/tex]

What is the domain of a function?

The domain of a function is the set that contains all possible input values for the function. For a rational function, for example, the zeros of the denominator are excluded from the domain. Another example is an even root, where the inside term has to be positive.

The rational function for this problem is given by the function f(x) presented below:

[tex]f(x) = \frac{1}{3x + 5}[/tex]

The denominator is 3x + 5, hence the restriction in the domain of f(x) is given as follows:

3x + 5 = 0

3x = -5

[tex]x = -\frac{5}{3}[/tex]

The solution to the equation above is the only value of x that is not part of the domain of f(x).

More can be learned about the domain of a function at https://brainly.com/question/10891721

#SPJ1

Determine the x-intercept(s) of the rational function:
f(x) = (x ^ 2 - 16)/(x ^ 2 - 2x - 3)

Answers

Answer:

(-4,0) and (4,0)

Step-by-step explanation:

The x-intercepts occur for values of x where f(x) = 0.

f(x) = 0 when the nominator ([tex]x^{2} - 16[/tex]) = 0.

[tex]x^{2} -16[/tex] is a difference of squares,
so you can factor it as (x + 4)(x – 4)

When x = –4 or x = 4, the nominator is 0, and f(x) = 0

Factor x4 + xy3 + x3 + y3 completely. Show your work. Hint: First factor out a monomial. x4 + xy3 + x3 + y3 =

Answers

Answer:

[tex]x^{3} ( x + 1 ) + y^{3} (x+1)\\= (x+1)(x^{3} + y^{3})[/tex]

Answer:

Step-by-step explanation:

YOU PLUS ALL OF THEM

Find a 49 of the sequence 70, 63, 56, 49,

Answers

Answer:

- 226

Step-by-step explanation:

ARITHMETIC SEQUENCE.

Number of term of an Arithmetic progressions has the formular.

Tn = a + ( n - 1 ) d

From the question,

First term ( a ) = 70

common difference = T2 - T1 = 63 - 70 = -7

For the 49th term

T49 = a + 48d

= 70 + 48 ( -7 )

= 70 - 336 = - 226

On four consecutive statistics quizzes, you receive the scores: 86 96 100 98 what is your median quiz score?

Answers

Answer:

Step-by-step explanation:

96+100=196

196÷2=98

Answer:

97.

Step-by-step explanation:

86 96 100 98

Place them in order:

86 96 98 100

The median is the middle value of an ascending sequence of numbers.

As there is an even number of values the median is the mean of the 2 middle ones:

So here it is (96 + 98) / 2

= 97.

Drag each equation and coordinate to the correct location on the table. Not all equations or coordinates will be used.
In the table below, quadratic equations are given in standard form. Rewrite each equation in the form that reveals the maximum or
minimum value, and then identify the coordinate point of that extreme value.

Answers

Completing the squares, we have that:

For the parabola of standard form y = x² - 6x + 17, we have that the equivalent form is (x - 3)² + 8 and the extreme value is (3,8).For the parabola of standard form y = x² + 8x + 21, we have that the equivalent form is (x + 4)² + 5 and the extreme value is (-4,5).For the parabola of standard form y = x² - 16x + 60, we have that the equivalent form is (x - 8)² - 4 and the extreme value is (8,-4).

What is the equation of a parabola given it’s vertex?

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

For the parabola of standard form y = x² - 6x + 17, we have that it can be written as follows, completing the squares:

y = x² - 6x + 17 = (x - 3)² + 8, hence the extreme value is (3,8).

For the parabola of standard form y = x² + 8x + 21, we have that it can be written as follows, completing the squares:

y = x² + 8x + 21 = (x + 4)² + 5, hence the extreme value is (-4,5).

For the parabola of standard form y = x² - 16x + 60, we have that it can be written as follows, completing the squares:

y = x² - 16x + 60 = (x - 8)² - 4, hence the extreme value is (8,-4).

More can be learned about the equation of a parabola at https://brainly.com/question/17987697

#SPJ1

given that 5x:9=7:3 calculate the value of x. give your answer in its simplest form.

Answers

[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

x = 21/5

Step-by-step explanation:

___________________________

Given →

5x:9 = 7:3

So,

→ 5x/9 = 7/3

→ x = (7 × 9)/(3 × 5)

→ x = 21/5

___________________________

Hope it helps you!!

Billy is hiking in Colorado. He walks eastward four miles, then turns $60$ degrees northward and walks six miles. How far is he from his starting point

Answers

He is 2√19 miles far way from starting point.

Suppose Billy starts at point A, turns at point B, and ends at point D, as shown below.

If Billy turns 60◦ northward and walks six miles, then we can draw a 30 − 60 − 90 triangle whose hypotenuse is 6 miles

It follows that Billy traveled 6/2 = 3 miles eastward during these 6 miles, and that he traveled 3√3 miles northward during these 6 miles. In total, Billy traveled 4 + 3 = 7 miles eastward and 3√ 3 miles northward.

By the Pythagorean Theorem, the distance from his starting point is q:

(7)2 + (3√3)2

=√49 + 27

= √76

= 2√19 .

Learn more about Pythagorean Theorem on:

https://brainly.com/question/20545047

#SPJ4

A wall shaped like a trapezoid needs to be painted. The height of the wall is 16 feet and the bases are 20 feet and 24 feet. If one can of paint covers 20 square feet, how many whole cans of paint will the painter need to buy to paint the wall with one coat

Answers

Answer:

18 cans

Step-by-step explanation:

The number of cans of paint will be the least integer greater than or equal to the number required to cover the area of the trapezoid.

Area of a trapezoid

The area of the wall is given by the formula ...

A = 1/2(b1 +b2)h

where b1 and b2 are the bases, and h is the height.

We are given the values b1=20 ft, b2=24 ft, h=16 ft, so the area is found to be ...

A = 1/2(20 ft +24 ft)(16 ft) = 352 ft² . . . . . area of the wall

Cans of paint

Each can of paint covers 20 ft², so n cans of paint will cover 20n square feet. We want to find the minimum integer value of n that satisfies ...

20n ≥ 352

n ≥ 17.6 . . . . . . . . . divide by 20

The next larger integer is 18.

The painter will need to buy 18 cans of paint.

Select the correct answer. What is the solution to the equation? -2√x+4=-12 A. 4 B. 8 C. 16 D. 64

Answers

Answer:

d. 64

Step-by-step explanation:

x^1/2 = 8

Square each side

(x^1/2 )^2=( 8)^2

x = 64

Wayne borrowed sh. 50,000 from a
bank that charged compound interest
at the rate of 12% p.a. How much did
she pay back at the end of 30 months?

Answers

Answer:15000

Step-by-step explanation:50,000 x 0.12=6,000 X 2=12,000

6000 divided by 2= 3,000

12 + 12=24+6=30

Which of the following interface validation checks is useful in verifying that the birth data you entered on your job application indicates that you meet the minimum age requirement to serve alcohol

Answers

The interface validation that would help to confirm that you meet the minimum age is the range check.

What is the range check?

This is the term that is used to refer to the check that is done in such a way that it shows the data that are in a particular range.

This would help to ensure that there is a specified upper and lower boundary for the values to fall into.

Answers

The weighted mean grade for the semester is 8.22

What is mean?

It is calculated by dividing the total number of values in a set of data, such as measurements or numbers, by the total number of values.

No. of credits for Spanish, History and English = 6

No. of credits for Statistics = 8

Grade points for A = 4

Grade points for B = 3

Grade points for C = 2

Weighted mean = (6 * 2 + 6 * 3 + 8 * 4 + 6 * 2) / 9

Weighted mean = (12 + 18 + 32 + 12) / 9

Weighted mean = 74 / 9 = 8.22

Hence, the weighted mean grade for the semester is 8.22.

Learn more about mean on:

https://brainly.com/question/1136789

#SPJ4

The expression $\frac{4k 8}{4}$ simplifies to an expression of the form $ak b$ where $a$ and $b$ are integers. Find $\frac{a}{b}$ .

Answers

The value of integers a and b is 1 and 2 and the value of a/b is 1/2.

According to the statement

we have a given a expression 4k+8 / 4 and we have to simplify this expression in the form of ak+b and find the value of a/b where a and b are the integers.

An integer is a whole number (not a fractional number) that can be positive, negative, or zero.

Here 4k+8/4 becomes

4k/4 +8/4 -(1)

and general form is

ak+b -(2)

Now, compare these equations then we get

a = 1 and b = 2.

Now we find the value of a/b

then

a/b = 1/2.

So, The value of integers a and b is 1 and 2 and the value of a/b is 1/2.

Learn more about integers here https://brainly.com/question/17695139

#SPJ4

Pmlease helppp tyyyy

Answers

Answer:

Step-by-step explanation:

Solving quadratic equation using formula:

5x² - 6x - 2 = 0

a = Coefficient of x² = 5

b = coefficient of x = -6

c = constant = -2

Discriminant = D = b² - 4ac

= (-6)² - 4 * 5 * (-2)

= 36 + 40

= 76 > 0

So, the quadratic equation has two distinct real roots.

[tex]\sf \boxed{\bf x = \dfrac{-b \± \sqrt{D}}{2a}}\\\\[/tex]

[tex]\sf = \dfrac{-[-6] \± \sqrt{76}}{2*5}\\\\= \dfrac{6 \±8.7}{10}\\\\=\dfrac{6+8.7}{10} \ ; \ or \ x =\dfrac{6-8.7}{10}\\\\=\dfrac{14.7}{10} \ ; \ or \ x = \dfrac{-2.7}{10}[/tex]

x = 1.47 or x = -0.27

Answer: x = 1.5 or (-0.3)

b) x² + 3x = 40

x² + 3x - 40= 0

We can solve the quadratic equation using factor method.

Sum = 3

Product = -40

Factors = 8 , (-5)

When we add, 8 + (-5) = 3 , we get 5and when we multiply 8 *(-5) = -40, we get -(-40).

Rewrite the middle term of the quadratic equation using the factors.

x² + 8x - 5x - 40 = 0

x(x + 8) - 5(x + 8)= 0

(x + 8) (x - 5) = 0

x + 8 = 0 or x - 5 = 0

x = -8 or x = 5

Answer : x = -8 , 5

Find the distance between the points C(−6, 5) and D(−3, 1).

Answers

Answer:

5 units

Step-by-step explanation:

Given the following question:

To find the answer to this question we will use the formula to calculate distance.

(6, 5) = (x1, y1)
(-3, 1) = (x2, y2)

[tex]d=\sqrt{(x1-x2)^2+(y1-y2)^2}[/tex]
[tex]d=\sqrt{(-6-(-3))^2+(5-1)^2}[/tex]
[tex]-6+3=-3[/tex]
[tex]5-1=4[/tex]
[tex]d=\sqrt{(-3^2+4^2)}[/tex]
[tex]-3^2=-3\times-3=9[/tex]
[tex]4^4=4\times4=16[/tex]
[tex]d=\sqrt{9+16}[/tex]
[tex]9+16=25[/tex]
[tex]\sqrt{25}[/tex]
[tex]\sqrt{25} =5\times5=25[/tex]
[tex]=5[/tex]

Which means the distance between the two points is "5 units."

Hope this helps.

Help please you don’t know how much this means to me

Answers

Problem 6:a)

[tex]a(0) = 1 \: \: \: \: \: \: b(0) = 2 \: \: \: \: \: c(0) = 3 \\ a(1) = b(0) + c(0) = 2 + 3 = 5 \\ b(1) = a(0) + c(0) = 1 + 3 = 4 \\ c(1) = a(0) + b(0) = 1 + 2 = 3 \\ \\ a(2) = b(1) + c(1) = 4 + 3 = 7 \\ b(2) = a(1) + c(1) = 5 + 3 = 8 \\ c(2) = a(1) + b(1) = 5 + 4 = 9[/tex]

[tex]a(3) = b(2) + c(2) = 8 + 9 = 17\\ b(3) = a(2) + c(2) =7 + 9 = 16 \\ c(3) = a(2) + b(2) = 7 + 8 = 15 \\ \\ a(4) = b(3) + c(3) = 16 + 15 = 31 \\ b(4) = a(3) + c(3) = 17 + 15 = 32 \\ c(4) = a(3) + b(3) = 17 + 16 = 33[/tex]

[tex]a(5) = 32 + 33 = 65 \\ b(5) = 31 + 33 = 64 \\ c(5) =31 + 32 = 63 \\ \\ a(6) = 64 + 63 = 127 \\ b(6) = 65 + 63 = 128 \\ c(6) = 65 + 64 = 129 \\ [/tex]

[tex]a(7) = 128 + 129 = 257 \\ b(7) = 127 + 129 = 256 \\c (7) = 127 + 128 = 255 \\ \\ a(8) = 256 + 255 = 511 \\ b(8) = 257 + 255 = 512 \\ c(8) = 257 + 256 = 513[/tex]

[tex]a(9) = 512 + 513 = 1025 \\ b(9) = 511 + 513 = 1024 \\ c(9) = 511 + 512 = 1023 \\ \\ a(10) = 1024 + 1023 = 2047 \\ b(10) = 1025 + 1023 = 2048 \\ c(10) = 1025 + 1024 = 2049[/tex]

[tex]a(n) + b(n) + c(n) = \\ 2(a(n - 1) + b(n - 1) + c(n - 1)) \\ 6 \times 2 {}^{n } [/tex]

[tex]6 \times 2 {}^{n} > 100 \: 000 \\ 2 {}^{n} > \frac{100 \: 000}{6} \\ n > log {}^{2} ( \frac{100 \: 000}{6} ) \\ n > 14.02468 \\ n = 15[/tex]

You are driving from your house to your office. Currently, it is 7:10 a.m., and you are 12 miles from your office. If you travel at an average speed of 30 miles per hour, at what time should you arrive at your office

Answers

We would reach our office by 7:34 a.m.

How to find the time that we would take to travel from our house to the office?

The average speed is given as 30 miles per hour.

Let us convert this into miles per minute.

30 miles/1 hour = 30 miles/60 minutes

= 0.5 miles per minute

The distance between the house and the office is 12 miles.

Therefore, we can find what it would take to reach the office by dividing the distance by the average speed:

Time taken = distance/average speed

= 12 miles/0.5 miles per minute

= 24 minutes

The time is given to be 7:10 a.m. Therefore we would reach our office by 7:34 a.m.

Therefore, we would reach our office by 7:34 a.m.

Learn more about average speed here: https://brainly.com/question/6504879

#SPJ4

PLEASE HELP FAST!!! Find the surface area of the composite figure. Round your answer to the nearest tenth if necessary.

Answers

The surface area of the composite figure is 524 square meters

Surface area of a figure

The given composite figure is made up of a triangular prism and a rectangular prism. The surface area of the figure is given as:

Surface area = 2(16*5+5*4+16*4) + (16*6) + 2(50)

Take the sum

Surface area = 2(80+20+64) + 96 + 100

Surface area = 2(164) +196

Surface area = 328 + 196

Surface area = 524 square meters

Hence the surface area of the composite figure is 524 square meters

Learn more on surface area here: https://brainly.com/question/1297098

#SPJ1

It took an hour to now a lawn using a mower with 14 inches blade. How long will it take using a mower with 12 inches wide

Answers

If the time taken by 14 inches wide is one hour then the blade of 12 inches wide will take 1 hour 17 minutes to mow a lawn.

What is width?

The width of something is the measurement of one side of a body. It is generally less than length of that body or shape.

How to calculate time?

We have been given time of 1 hour if blade is 14 inches wide and we have to calculate time taken by 12 inches wide blade:

It will be as 14/12* 1 hour

=14/12

=1.167

=1.17 hour

Hence the time taken by the blade of 12 inches wide will be 1 hour and 17 minutes.

Answer:

70 mins

Step-by-step explanation:

This is called inverse proportion.

1hr : 14in

x hr : 12in

Ask yourself, what do you do to 14 to get 12? To find this out, we do:

14 / 12 = 1.16666667

Since the blade is smaller, it will take longer. So, we times 1hr by 1.16666667 to get

1.16666667 hrs =

1.17 hours (rounded)

This is 70.2 mins, or 1hr 10 mins

Hope this helps!

PLEASE HELP ASAP

Determine the number of terms in the sequence. Your work must be shown with fractions not decimals.

2/81, 4/27, 8/9,…,6912

Answers

we conclude that the sequence has 8 terms.

How to get the number of terms in the sequence?

Here we have the geometric sequence:

2/81, 4/27, 8/9, ..., 6912

Notice that each term is equal to 6 times the previous term, such that:

2/81*6 = 4/27

4/27*6 = 8/9

Then the n-th term is equal to:

[tex]a_n = a_1*r^{n-1}[/tex]

Where in this case:

[tex]a_1 = 2/81\\\\r = 6[/tex]

Now we need to find the value of n such that:

[tex](2/81)*6^{n-1} = 6912\\\\6^n = 6*6812*(81/2) = 1,679,616[/tex]

If we apply the natural logarithm to both sides, then:

[tex]n*ln(6) = ln(1,679,616)\\n = ln(1,679,616)/ln(6) = 8[/tex]

Then we conclude that the sequence has 8 terms.

If you want to learn more about geometric sequences:

https://brainly.com/question/1509142

#SPJ1

pls look at pic!!!!!!!!!!!!

Answers

Answer:

I don't think the answer is in the options.

Annette the shoe salesperson has two job offers. The Comfort over Style Shoe Emporium has offered her a $52,000 salary plus $3.25 for every pair of shoes she sells. The Heels for Fashion Slaves Boutique has offered a $37,000 salary plus $4.75 for every pair of shoes she sells. Over what range of shoe sales will Annette make more from the Comfort over Style job than she will from the Heels for Fashion Slaves job?

Answers

Using linear functions, it is found that over a range of x < 10000 she will make more from the Comfort over Style job than she will from the Heels for Fashion Slaves job

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

Considering the fixed salary as the intercept and the earning per shoe sold the slope, the functions for her salaries at each situation is:

C(x) = 52000 + 3.25xH(x) = 37000 + 4.75x

He will make more from the Comfort over Style job than she will from the Heels for Fashion Slaves job when:

C(x) > H(x)

52000 + 3.25x > 37000 + 4.75x

1.5x < 15000

x < 15000/1.5

x < 10000

The range is x < 10000.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Which of the following expressions is equal to 3x² +27?

Answers

Answer:

B. (3x - 9) (x + 3i)

Step-by-step explanation:

[tex]\bf 3 {x}^{2} = + 27[/tex]

[tex]\bf (3x - 9)(x + 3i)[/tex][tex]\bf 3 {x}^{2} +9 xi - 9xi - 27 {i}^{2} [/tex][tex]\bf 3 {x}^{2} - 27( {i}^{2} )[/tex][tex]\bf 3 {x}^{2} - 27( - 1)[/tex][tex]\bf 3 {x}^{2} + 27[/tex]

Therefore, B is your answer!!!!

Find the missing side. Round your answer to the nearest tenth.

Answers

The length of the missing length in the triangle is 53.6 units

How to determine the length of the missing side?

The given triangle is a right triangle.

Right triangles are triangles that have a measure of angle that is 90 degrees.

The missing side is x, and the value of x is calculated using the following sine rule

We have

sin(angle) = opposite/hypotenuse

This gives

sin(66) = 49/x

Divide both sides by sin(66)

1 = 49/x sin(66)

Multiply both sides by x

x = 49/sin(66)

Divide the expression

x = 53.6

Hence, the length of the missing length is 53.6 units