Consider that ΔLMN is similar to ΔPQR and the measure of ∠P is 80°. What is the measure of ∠L?
A) 20°
B) 70°
C) 80°
D) 90°

supplementary angles add to equal 180. so x + 57 = 180. solve for x and you get 123.

Answer:

a) 1,440 ways

b) 59,280 or 64,000

Step-by-step explanation:

a) Aircraft boarding.

8 people, 2 in first class, boarding first, then 8 economy class.

The 2 people in first class board first, but they can board as AB or BA... so 2 ways here.

For the 6 economy class passengers, we have a permutation of 6 out of 6, so 720, as follows:

[tex]P(6,6) = \frac{6!}{(6 - 6)!} = 6! = 720[/tex]

Since the two are independent, we multiply them to have a global number of ways: 2 * 720 = 1,440 different ways for the 8 passengers to board that plane.

b) combination lock.

Here we do have a little problem... the question doesn't specify if the 3 numbers are different numbers of not.  So, we'll calculate both:

Numbers go from 1 to 40 inclusively... so 40 possibilities.

Normally, in a combination lock, the numbers are different, so let's start with that one:

First number: 40 options available

Second number: 39 options available (cannot take the first one again)

Third number: 38 different options (can't take First or Second number again)

Overall, we then have 40 * 39 * 38 = 59,280 different lock combinations.

If we can pick pick the same number twice:

First number: 40 options available

Second number: 40 options available

Third number: 40 options available

Overall 40 * 40 * 40 = 64,000 different lock combinations

Answer:

A and C

Step-by-step explanation:

Just plug in the point into the equations:

a) 14 = 2(4.5) + 5

14 = 9 + 5   14 = 14 A is correct

b) 14 = 3(4.5) + 1.5

14 = 13.5 + 1.5   14 ≠ 15 B is not correct

c) 14 = 4(4.5) - 4

14 = 18 - 4   14 = 14 C is correct

d) is not correct 12 is already to large and 10 is not a negative so it is far to large

Answer:

C

Step-by-step explanation:

Answer:

The measure of angle ERK is 55°

Step-by-step explanation:

step 1

Find the measure of arc EK

we know that

The diameter divide the circle into two equal parts

In this problem

EOR is a diameter

see the attached figure to better understand the problem

so

arc EK + arc RK=180°

substitute the given values

arc EK + 70°=180°

arc EK=180°-70°=110°

step 2

Find the measure of angle ERK

we know that

The inscribed angle is half that of the arc it comprises.

m∠ERK=(1/2)[arc EK]

substitute  

m∠ERK=(1/2)[110°]=55°

The measure of <ERK is 55 degrees

Given the following parameters

arcRK = 70 degrees

Determine the measure of arcEK
arcEK + arcRK + 180 = 360

arcEK + 70 + 180 = 360

arcEK + 250 = 360

arcEK = 110 degrees

<ERK = 1/2 arcEK

<ERK = 1/2(110)
<ERK = 55 degrees

Hence the measure of <ERK is 55 degrees

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ANSWER

$28

EXPLANATION

The profit function is given as:

[tex]p(x) = - 2 {(x - 9)}^{2} + 100[/tex]

where x is the price of the T-shirt in dollars.

To find the profit on a T-shirt whose price is $15, we substitute x=15 into the function and simplify.

[tex]p(15) = - 2 {(15 - 9)}^{2} + 100[/tex]

We simplify to get:

[tex]p(15) = - 2 {(6)}^{2} + 100[/tex]

[tex]p(15) = -72+ 100[/tex]

[tex]p(15) = 28[/tex]

Answer:

x >  2

Step-by-step explanation:

Given

- 8x + 2x - 16 < - 5x + 7x ← simplify both sides

- 6x - 16 < 2x ( subtract 2x from both sides )

- 8x - 16 < 0 ( add 16 to both sides )

- 8x < - 16 ( divide both sides by - 8 )

Remembering to reverse the symbol as a consequence of dividing by a negative value.

x > 2

Answer:

[tex]\large\boxed{y=\dfrac{1}{3}x+2\dfrac{1}{3}}[/tex]

Step-by-step explanation:

[tex]\text{Let}\ k:y=_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\============================\\\\\text{We have}\ y=-3x+1\to m_1=-3.\\\\\text{Therefore}\ m_2=-\dfrac{1}{-3}=\dfrac{1}{3}.\\\\\text{The equation of the searched line:}\ y=\dfrac{1}{3}x+b.\\\\\text{The line passes through }(2,\ 3).[/tex]

[tex]\text{Put the coordinates of the point to the equation.}\ x=2,\ y=3:\\\\3=\dfrac{1}{3}(2)+b\\\\3=\dfrac{2}{3}+b\qquad\text{subtract}\ \dfrac{2}{3}\ \text{from both sides}\\\\b=2\dfrac{1}{3}[/tex]

Answer:

  y = 1/3(x -2) +3

Step-by-step explanation:

The slope of the given line is the coefficient of x, -3. The slope of the perpendicular line will be the negative reciprocal of that: -1/-3 = 1/3. The line through a point (h, k) with slope m can be written in point-slope form as ...

  y = m(x -h) +k

For m=1/3, (h, k) = (2,3), the equation of the line is ...

  y = (1/3)(x -2) +3

In Bar Graphs;

- Bars have equal space

- One the y-axis, we have numbers & on the x-axis, we have data which can be anything.

In Histograms;

- Bars are fixed

- On the y-axis, we have numbers & and on the x-axis, we have data which in continuous & will always be number.

An easy way you can remember the difference is looking at the spaces of the bars.

A bar graph has gaps

A histogram has no gaps.

The area of the rectangular field given the dimensions of the field is 5000m^2.

a + b = 150 equation 1

a = 2b equation 2

Where:

a = length

b = width

Subsiture for b in equation 1 using equation 2

2b + b = 150

3b = 150

b = 50m

a = 2 x 50

q = 100m

Area = length x width

100 x 50 = 5000 m^2

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The rectangular field is found to be 5000 square meters. Option (1) 5000 m² is the correct answer.

To find the area of a rectangular field given its perimeter and that the length is twice the width, follow these steps:

Answer:

[tex]2.05\ miles[/tex]  or  [tex]2\frac{1}{20}\ miles[/tex]

Step-by-step explanation:

we know that

To calculate the total distance Barb walked, add the distance to her friend's house plus the distance to the library.

so

[tex]1.3+\frac{3}{4}[/tex]

Remember that

[tex]1.3=\frac{13}{10}[/tex]

substitute

[tex]\frac{13}{10}+\frac{3}{4}=\frac{13*2+5*3}{20}[/tex]

[tex]=\frac{41}{20}\ miles[/tex]

[tex]=2.05\ miles[/tex]

Convert to mixed number

[tex]\frac{41}{20}=\frac{40}{20}+\frac{1}{20}=2\frac{1}{20}\ miles[/tex]

Answer:

a)

x≥3

b)

[tex]t<-\frac{7}{3}[/tex]

c)

y < 28

d)

x > 5/2

Step-by-step explanation:

a)

We have been given the following inequality;

4x-3≥9

add 3 to both sides of the equation,

4x-3+3≥9+3

4x≥12

divide both sides by 4,

x≥3

b)

We have been given the following inequality;

3(t+4)<5

we open the brackets on the left hand side,

3t + 12 <5

subtract 12 on both sides of the equation,

3t + 12 -12 <5-12

3t < -7

divide both sides by 3,

[tex]t<-\frac{7}{3}[/tex]

c)

We have been given the following inequality;

[tex]\frac{2y}{7}<8[/tex]

multiply both sides by 7,

2y < 56

divide both sides by 2,

y < 28

d)

5x + 4 > -3(x-8)

we open the brackets on the right hand side,

5x + 4 > -3x + 24

add 3x to both sides of the inequality,

5x + 4 + 3x > -3x + 24 + 3x

8x + 4 > 24

subtract 4 on both sides,

8x + 4 - 4 > 24 - 4

8x > 20

divide by 8 on both sides,

x > 5/2

Exponential form, would be the number of times X gets multiplied by itself.

(x)(x)(x)(x)  there are 4 x's, so the exponential form would be x^4

(x)(x)(x)(x) in exponential form can be written as

[tex]\rm \bold{x^4}}[/tex]

According to the properties of exponent with same base number the powers/exponents of the number are added

This can be simply expressed in the form as formulated in equation (1)

[tex]\rm a ^x \times a^y = a ^{x +y} ............(1)[/tex]

here a = base  number

x and y are the exponents of number  a  

According to the  given question same number "x" is multiplied 4 times

let  the given expression be represented by a variable "y"  

[tex]\rm y = x\times x \times x \times x ...........(2)[/tex]

Equation (2)  can be simply written as follows

[tex]\rm y = x^1 \times x^1 \times x ^1 \times x^1 \\y = x ^{(1+1+1+1)} \\\bold{y = x ^4}[/tex]

So we can conclude that (x)(x)(x)(x) in exponential form can be written as

[tex]\rm \bold{x^4}}[/tex]

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Answer: 1/16

Step-by-step explanation:

1/2 would become 8/16 so 9-8 equals 1 and then just add the denominator so 1/16

Check the picture below, notice is simply a 12x36 rectangle = 432 cm².

Answer:

432 is correct as in this problem the cross section is identical in size and thus area to the face CDHG.

Step-by-step explanation:

ANSWER

1. No real roots

2. [tex] \frac{ 7\pm \: \sqrt{33} }{ - 4}[/tex]

3. The discriminant is negative.

EXPLANATION

1. The given equation is

[tex] - 2 {x}^{2} - 9x - 5 = 0[/tex]

We have a=-2,b=-9 and c=-5.

The discriminant is given by:

[tex]D= {b}^{2} - 4ac[/tex]

[tex]D= {( - 9)}^{2} - 4( - 2)( - 5)[/tex]

This simplifies to:

[tex]D= 36 - 40 = - 4[/tex]

Since the discriminant is less than zero, the quadratic equation has no real roots.

2. The given equation is:

[tex] - 2 {x}^{2} - 7x - 2= 0[/tex]

We have a =-2, b=-7 and c=-2.

The roots of this equation are given by;

[tex]x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

We plug in the values to get;

[tex]x = \frac{ - - 7\pm \: \sqrt{ {( - 7)}^{2} - 4( - 2)( - 2) } }{2( - 2)} [/tex]

[tex]x = \frac{ 7\pm \: \sqrt{33} }{ - 4} [/tex]

3. The given graph is hanging downwards. This means that it doesn't have x-intercepts.

Therefore the roots are complex or imaginary.

This implies that, the discriminant of the corresponding equation is negative.

Check the picture below.

L=4 and s=5 I’m to lazy to type it out

Answer:

L= 4

S= 5

Step-by-step explanation:

Given in the question, L+s = 9

So

L= 9-s

Substituting the value of L in the following equation

1.5L + 0.9s = 10.5

1.5 (9-s) + 0.9s = 10.5

13.5 - 1.5s +0.9s = 10.5

13.5 - 10.5 = 1.5s - 0.9s

3= 0.6s

s= 5

Now substituting the value of s in the equation L+s=9, we get the following

L= 9-5

L=4

let's firstly convert the mixed fractions to improper fractions and then divide.

[tex]\bf \stackrel{mixed}{-4\frac{3}{5}}\implies \cfrac{-4\cdot 5+3}{5}\implies \stackrel{improper}{\cfrac{-23}{5}}~\hfill \stackrel{mixed}{1\frac{1}{5}}\implies \cfrac{1\cdot 5+1}{5}\implies \stackrel{improper}{\cfrac{6}{5}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{-23}{5}\div \cfrac{6}{5}\implies \cfrac{-23}{\begin{matrix} 5 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\cdot \cfrac{\begin{matrix} 5 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}{6}\implies \cfrac{-23}{6}\implies -3\frac{5}{6}[/tex]

Okay I'm assuming this is a mixed fraction -4 ⅗ ÷ 11/5

First step get rid of the mixed fraction.

4 multiplied by 5 is 20 then you add 3 and you get 23

Next step cross cancel

-23     times    11     equals   -23

 5                    5                     11

improper fraction so convert to mixed number

answer is -2 1/11    

if you're still confused lemme know

Answer:

(5, -10)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

-9x - 6y = 15

9x - 10y = 145

Step 2: Solve for y

Elimination

Step 3: Solve for x

Step 4: Check

Graph the systems of equations to verify the algebraically solved solution set is the solution.

Where the 2 lines intersect is the solution set.

We see graphically that we get (5, -10).

∴ (5, -10) or x = 5 and y = -10 is the solution to our systems

Lets do the math together.

3.5/2 to find the weight loss per week= 1.75.

We know that every week the friend will reduce her goal by 1.75.

15/1.75= 8.6.

This means that in 8.6 weeks the friend will lose 15 pounds.

I hope this Helps! :)

Hello there! It should take her 8.6 weeks.

Well, the question doesn't specify whether it wants how long it'll take her in weeks, months, or days, so let's go with weeks. To do this, find the unit rate by dividing the amount she lost by the number of weeks it took.

3.5 pounds ÷ 2 weeks = 1.75 pounds lost a week.

Now, divide the total she wants to loose (15 pounds) by the 1.75 pounds a week to see how many she looses in total.

15/1.75 = 8.57142... Which is a little over 8.5 weeks, so we can round up to 8.6 weeks.

Answer:

x = 3

Step-by-step explanation:

Only one of the choices matches the given points:

x = 3

Answer:

a. 6km

b. 6.185 km

c. 18.37 km

Step-by-step explanation:

The question is on finding the distance of between two points

The general formulae is given by;

[tex]d= \sqrt{(X2-X1)^2+(Y2-Y1)^2}[/tex]

Where d is the distance

Given that;

1 unit on grid = 1.5 km

a. Finding distance between the library and Town A

A (-2,3)  and library (2,3)

[tex]d= \sqrt{(2- -2)^2  + (3-3)^2} \\\\= \sqrt{4^2} \\= 4[/tex]

Actual distance = 4 × 1.5 = 6 km

b. Distance between the library and Town B is

library (2,3)  and town B (1, -1)

[tex]d=\sqrt{(1-2)^2+ (-1-3)^2} \\\\\\d=\sqrt{-1^2 +-4^2}\\ \\\\d=\sqrt{1+16} \\\\\\d=\sqrt{17}  = 4.123[/tex]

Actual distance = 4.123×1.5 =6.185 km

c. First find the distance between Town B and Town C

Town B (1, -1) and Town C (-3,-2)

[tex]d=\sqrt{(-3-1)^2 + (-2--1)^2} \\\\d=\sqrt{-4^2 + -1^2} \\\\d=\sqrt{16+1} \\\\d=\sqrt{17} \\\\d=4.123[/tex]

Actual distance= 4.123×1.5 =6.185 km

Total distance traveled by Amelia = 6 +6.185 +6.185 =18.37 km

ANSWER

A. x-8

EXPLANATION

The given functions are:

[tex]f(x) = {x}^{2} - 11x + 24[/tex]

We factor this to get,

[tex]f(x) = (x - 8)(x - 3)[/tex]

and

[tex]g(x) = x - 3[/tex]

[tex]( \frac{f}{g} )(x) = \frac{f(x)}{g(x)} [/tex]

[tex]( \frac{f}{g} )(x) = \frac{ {x}^{2} - 11x + 24}{x - 3} \: for\: x \ne3[/tex]

[tex]( \frac{f}{g} )(x) = \frac{(x - 8)(x - 3)}{x - 3} [/tex]

Cancel the common factors to get,

[tex]( \frac{f}{g} )(x) = x - 8[/tex]

Answer: OPTION A

Step-by-step explanation:

You need to divide the function f(x) by the function g(x):

Then:

[tex](\frac{f}{g})(x)=\frac{x^2-11x+24}{x-3}[/tex]

Now, you need to simplify:

Factor the numerator. Find two numbers whose sum be -11 and whose product be 24. Theses numbers are -8 and -3. Then you get:

[tex](\frac{f}{g})(x)=\frac{(x-8)(x-3)}{x-3}[/tex]

Remember that:

[tex]\frac{a}{a}=1[/tex]

Then, you get that the expresson that is equal to  [tex](\frac{f}{g})(x)[/tex] is:

 [tex](\frac{f}{g})(x)=(x-8)[/tex]

Answer:

A motor-powered bike has wheels that travel a linear distance of approximately 62.8 inches in one

revolution. What is the central angle the bike wheels turn through, in degrees, when the bike travels 2

inches?​

Step-by-step explanation:

PLEASE HELP!!

A motor-powered bike has wheels that travel a linear distance of approximately 62.8 inches in one

revolution. What is the central angle the bike wheels turn through, in degrees, when the bike travels 2

inches?​

The central angle the bike wheels turn through, in degrees when the bike travels 2 inches will be 11.46°.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

Area of the circle = πr² and the perimeter of the circle = 2πr where r is the radius of the circle.

The linear distance in one revolution = perimeter of a circle or wheel

Perimeter = 2πR

R = 62.8/(2π)

R = 9.99 = 10 inches.

When L = 2 inches the center angle will be as,

Ф = L/R

Ф = 2/10 = 0.2 radian

In degree → 0.2 × 180/π = 11.46°

Hence "The central angle the bike wheels turn through, in degrees when the bike travels 2 inches will be 11.46°".

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Answer:

- 56 - 7k

Step-by-step explanation:

Given

- 7(8 + k)

Each term in the parenthesis is multiplied by - 7

= (- 7 × 8) + (- 7 × k)

= - 56 + (- 7k)

= - 56 - 7k

To solve the expression -7(8 + k), the distributive property is used. Multiplying -7 to each of the terms within the parentheses yields -56 - 7k. This is an example of product multiplying monomials.

The given expression is -7(8 + k). To find the product, you should use the distributive property. This property states that the multipliers of a sum or difference, multiplied separately by each addend or minuend, sum to the product. So -7 * 8 gives -56 and -7 * k gives -7k. Hence, the expression becomes -56 - 7k. This process is a demonstration of product multiplying monomials.

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Answer:

6x=90

Divide by 6 for 6x and 90

6x/6=90/6

x=15

Check answer by using substitution method

6x=90

6(15)=90

90=90

Answer is x=15

Answer:

Step-by-step explanation:

6x = 90                  Divide by 6

6x/6 = 90/6

x = 15

Answer:

What's your question?

If Tatiana ran the marathon with an average speed of 0.09 miles per minute. 5.4 was her speed to the nearest mile per hour

The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered.

Given,

Tatiana ran the marathon with an average speed of 0.09 miles per minute

We know that a hour has 60 minutes.

Speed to the nearest mile per hour we will calculate by multiplying 0.09 with 60

Zero point zero nine times of sixty.

0.09×60

Five point four miles per hour.

5.4 miles/hour

Hence 5.4 miles/hour is Tatiana speed to the nearest mile per hour

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Answer:

2.375 has the same value as 2 and 3/8.

19/8 also has the same value as 2 3/8.

If the parabola looks like an “n,” your vertex will be a maximum. If the parabola looks like a “u,” the vertex will be a minimum.

To determine if a vertex is a minimum or maximum, evaluate the behavior of the function at that point. If the function is increasing before the vertex and decreasing after, it is a minimum point. If the function is decreasing before the vertex and increasing after, it is a maximum point.

In mathematics, a vertex is a point where two or more lines, curves, or edges meet. When determining if a vertex is a minimum or maximum, we need to look at the behavior of the function or equation at that point.

If the function is increasing before the vertex and decreasing after the vertex, then the vertex is a minimum point. Conversely, if the function is decreasing before the vertex and increasing after the vertex, then the vertex is a maximum point.

For example, consider the parabola y = x^2. The vertex of this parabola is at (0, 0).

Since the parabola opens upwards and the function values increase on either side, the vertex is a minimum point.