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3 years ago

What is the value of a in the diagram below?

Mathematics

1 answer:

adell [148]3 years ago

7 0

Answer:

a=8

Step-by-step explanation:

We can use ratios of similar triangles to solve

The smaller triangle has sides a and 12 and the larger triangle has sides a+a+4 and 12+18 which combine to 2a+4 and 30

a 2a +4

--------- = -----------

12 30

Using cross products

30a = 12(2a+4)

30a = 24a +48

Subtract 24a from each side

30a -24a = 24a-24a +48

6a = 48

Divide each sdie by 6

6a/6 =48/6

a =8

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How many sides does a pentagon have? A pentagon has number sides.

Anna007 [38]

Answer:

Step-by-step explanation:

A pentagon is a polygon that has 5 sides.

5 0

3 years ago

Read 2 more answers

Carter draws one side of equilateral △PQR on the coordinate plane at points P(-3,2) and Q(5,2). Which ordered pair is a possible

Law Incorporation [45]

Step-by-step explanation:

Hey, there!!!

Let me simply explain you about it.

We generally use the distance formula to get the points.

let the point R be (x,y)

As it an equilateral triangle it must have equal distance.

now,

let's find the distance of PQ,

we have, distance formulae is;

$pq = \sqrt{( {x2 - x1)}^{2} + ( {y2 - y1)}^{2} }$

$or \: \sqrt{( {5 + 3)}^{2} + ( {2 - 2)}^{2} }$

By simplifying it we get,

$8$

Now,

again finding the distance between PR,

$pr = \sqrt{( {x2 - x1}^{2} + ( {y2 - y1)}^{2} }$

or,

$\sqrt{( {x + 3)}^{2} + ( {y - 2)}^{2} }$

By simplifying it we get,

$= \sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13 }$

now, finding the distance of QR,

$qr = \sqrt{( {x - 5)}^{2} + ( {y - 2)}^{2} }$

or, by simplification we get,

$\sqrt{ {x}^{2} + {y}^{2} - 10x - 4y + 29 }$

now, equating PR and QR,

$\sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13} = \sqrt{ {x}^{2} + {y}^{2} - 10x - 4y + 29 }$

we cancelled the root ,

${x}^{2} + {y}^{2} + 6x - 4y + 13 = {x}^{2} + {y}^{2} -10x - 4y + 29$

or, cancelling all like terms, we get,

6x+13= -10x+29

16x=16

x=16/16

Therefore, x= 1.

now,

equating, PR and PQ,

$\sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13 } = 8}$

cancel the roots,

${x}^{2} + {y}^{2} + 6x - 4y + 13 = 8$

now,

(1)^2+ y^2+6×1-4y+13=8

or, 1+y^2+6-4y+13=8

y^2-4y+13+6+1=8

or, y(y-4)+20=8

or, y(y-4)= -12

either, or,

y= -12 y=8

Therefore, y= (8,-12)

by rounding off both values, we get,

x= 1

y=(8,-12)

So, i think it's (1,8) is your answer..

Hope it helps...

3 0

3 years ago

Please help n show work

notsponge [240]

x = time in minutes

y = distance remaining

Steve starts at home when the time is x = 0 minutes. The y value y = 40 pairs up with this x value. This is shown by the point (0,40) on the diagonal line, aka the y intercept. The y intercept is where the line crosses the y axis.

The y = 40 indicates that Steve has 40 miles remaining when he starts at home. In other words, the distance from home to work is 40 miles.

The x intercept is where the diagonal line crosses or touches the x axis. The x intercept is (45,0) which represents the idea that 45 minutes have passed by. The y = 0 means that he has 0 miles left go to. Steve has reached the office at this point.

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

Answers:

Steve's office is located 40 miles from home

It takes him 45 minutes to travel this distance

3 0

3 years ago

Write a function rule for the area of a rectangle whose length is 7

zzz [600]

Your answer should be A=98ft.

5 0

3 years ago

Solve for x. 144° 18 degrees 30 degrees 48 degrees 120 degrees

disa [49]

Answer:

Step-by-step explanation:

you have a rotation angle of 360 °, take out the known values (360 ° -90 ° -144 ° = 126), 144 ° is part of a flat angle of 180 °, from 180 ° remove 144 and you have 36 °, they are opposite angles therefore the same. therefore 360 - 144 - 90 - 36 - 36 = 54.

54 is 3x, so x = 18 ° (54 : 3 = 18)

7 0

2 years ago

What is the value of a in the diagram below?​

What is the value of a in the diagram below?