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2 years ago

N the diagram, the ratios of two pairs of corresponding sides are equal.

Mathematics

2 answers:

Mrrafil [7]2 years ago

4 0

Answer:

Correct answer: A

Step-by-step explanation:

MaRussiya [10]2 years ago

3 0

Answer:

$\angle N\cong \angle Z$

Step-by-step explanation:

Given:

In ΔLMN and ΔXYZ, $MN=3\,,\,LN=2\,,\,YZ=9\,,\,XZ=6$

To find: criteria that needs to be shown to prove ΔLMN $\sim$ ΔXYZ using SAS similarity theorem

Solution:

According to SAS Similarity Theorem, if two sides in one triangle are proportional to two sides in another triangle and the included angle between the sides are congruent, then the two triangles are said to be similar.

In ΔLMN and ΔXYZ,

$\frac{LN}{XZ}=\frac{2}{6}=\frac{1}{3}\\\frac{MN}{YZ}=\frac{3}{9}=\frac{1}{3}\\\therefore \frac{LN}{XZ}=\frac{MN}{YZ}$

So, ΔLMN $\sim$ ΔXYZ by SAS similarity theorem if $\angle N\cong \angle Z$

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Cindy’s parking garage charges $3.50 for weekday parking, and weekends are half price. If Cindy parked in the garage 20 times pe

Pachacha [2.7K]

Answer: $\$64.75$

Step-by-step explanation:

You know that for weekdays parking the price is $3.50 and weekends are half price. Then for weekends, the price is the following:

$\frac{\$3.50}{2}=\$1.75$

You know that Cindy parked in the garage 20 times per month, and three of these days were weekend days. This means that she parked 17 times in week days and 3 times in weekends days.

Therefore, the total amount of money she would spend on parking per month can be calculated with:

$Total\ per\ month=17(\$3.50)+3(\$1.75)\\\\Total\ per\ month=\$59.5+\$5.25\\\\Total\ per\ month=\$64.75$

6 0

2 years ago

A deck of playing cards has four suits, with thirteen cards in each suit consisting of the numbers 2 through 10, a jack, a queen

Rudik [331]

A. True. There are 52 cards total and you only pick 5. Order doesn't matter.

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B. False. Order doesn't matter so you use a combination (instead of a permutation) as choice A shows.

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C. False. The answer is roughly 0.000858 as shown by the calculation below

(13/52)*(12/51)*(13/50)*(12/49)*(11/48) = 0.000858

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D. False. See calculation below

(13/52)*(12/51)*(11/50)*(10/49)*(9/48) = 0.000495

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

E. True. See calculation below

(13/52)*(12/51)*(11/50)*(10/49)*(9/48) = 0.000495
this value rounds to roughly 0.0005

6 0

2 years ago

Read 2 more answers

The fuel cost per hour for running a ship is approximately one half the cube of the speed (measured in knots) plus additional fi

andrezito [222]

Answer:

6 knots

Step-by-step explanation:

Let the speed be v knots

then time taken to cover 500 M = 500 / v hrs

fuel consumption /hr = 216 + 0.5v^3

let F be the fuel consumption for trip

= [500/v][216 + 0.5v^3]

= 500[216/v + 0.5v^2]

dF/dv = 500[ - 216/v^2 + v]

d^2F/d^2v = 500[432/v^3 + 1] , i.e. +ve

so setting dF/dv will give a minima

500[ -216/v^2 + v] = 0

or v = 216/v^2

or v^3 = 216

solving, we get v = [216]^(1/3) = 6 knots

7 0

2 years ago

Annie is creating a stencil for her artwork using a coordinate plane. The beginning of the left edge of the stencil falls at (2,

taurus [48]

Answer:

(A)(12, 9)

Step-by-step explanation:

Given:

The beginning of the left edge of the stencil falls at (2, −1).

A point, say Q on the stencil is at (4, 1).

Point Q divides the stencil into the ratio 1:4.

We are required to find the end of the stencil.

Mathematically, Point Q divides the stencil internally in the ratio 1:4.

For internal division of a line with beginning point $(x_1,y_1)$ and end point $(x_2,y_2)$ in the ratio m:n, we use the formula

$Q(x,y)=(\dfrac{mx_2+nx_1}{m+n} ,\dfrac{my_2+ny_1}{m+n} )$

$(x_1,y_1)=(2, -1)$ , $(x_2,y_2)=?$ , Q(x,y)=(4,1), m:n=1:4

Therefore:

$(4,1)=(\dfrac{1x_2+4*2}{1+4} ,\dfrac{1y_2+4*-1}{1+4} )\\(4,1)=(\dfrac{x_2+8}{5} ,\dfrac{y_2-4}{5} )\\$Therefore:\\\dfrac{x_2+8}{5}=4\\x_2+8=4X5\\x_2=20-8=12\\$Similarly\\\dfrac{y_2-4}{5}=1\\y_2-4=5\\y_2=4+5=9\\(x_2,y_2)=(12,9)$

The correct option is A.

6 0

2 years ago

Read 2 more answers

A graph represents the perimeter ,y, in units for an equilateral triangle with the side lengths x units. The slope of the line i

kicyunya [14]

Answer:

see the explanation

The graph in the attached figure

Step-by-step explanation:

The correct question is

Explain what the slope and intercept mean in each situation.

A graph represents the perimeter,y, in units, for an equilateral triangle with side length x units. The slope of the line is 3 and the y-intercept is 0

we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope

b is the y-intercept

In this problem

y is the perimeter in units

x is the side length of a equilateral triangle

we have

$m=3\\b=0$

substitute

The linear equation is

$y=3x$ ---> Is a proportional relationship because the line passes through the origin

see the attached figure to better understand the problem

Explanation

The slope is ---> $m=\frac{3}{1}\frac{units}{unit}$

That means

The ratio of perimeter of triangle to side length of triangle is 3:1

The y-intercept is 0

Remember that

The y-intercept is the value of y when the value of x is equal to zero

In this context

The y-intercept is the value of the perimeter when the value of the side length is equal to zero

The value of the perimeter is 0 when the value of side length is 0

3 0

2 years ago