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hoa [83]
3 years ago
5

What is the scale factor solve of x

Mathematics
2 answers:
pav-90 [236]3 years ago
7 0
The scale factor is 1:2 and x is 11.5
Natasha_Volkova [10]3 years ago
3 0
The scale factor is 2

x = 11.5

14/7 = 2

23/x = 2

x = 11.5

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A person that is 5 feet tall casts a shadow 25 feet long. How long is the shadow of a tree that is 15 feet tall?
fiasKO [112]
The person and his shadow make a right triangle as well as the tree and it's shadow. they will be similar right triangles containing angles that are equal. I'm in similar triangles the angles are proportional so a ratio could be used to determine the shadow length. this ratio is:
25/5 = x/15
(Notice that both the height of the person and
the height of the tree height of the tree are on
the bottom because these would be similar
sides and the same for the shadows with both
on top. this could easily have been switched
with the shadows on bottom and heights on
top like:
5/25 = 15/x
however I noticed the 25/5 could easily be
reduced. this eliminated the need for cross
multiplication.)

The 25/5 can be reduced to 5:
5 = x/15
and then multiply both sides by 15 and you get:
x = 75
so the answer is 75 feet long.

this can be checked various ways. using trigonometry we have the opposite and adjacent sides so tangent could be used to find the angle between the shadow and the hypotenuse. this is:
tan (x) = opposite/adjacent
opposite = height
adjacent = shadow
so:
tan (x) = 5/25 for person
tan (x) = 15/75 for tree
these equations both reduce to:
tan (x) = 1/5
And of both equations are the same then the angLee are equal creating similar triangles and a correct answer
4 0
3 years ago
What is the equation in point-slope form of the line passing through (4, 0) and (2, 6)? (5 points) y = 4x − 2 y = 2x − 4 y = −3(
DIA [1.3K]

For this case we have that by definition, the point-slope equation of a line is given by:

y-y_ {0} = m (x-x_ {0})

We have the following points:

(x_ {1}, y_ {1}) :( 2,6)\\(x_ {2}, y_ {2}) :( 4,0)\\m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {0-6} {4-2} = \frac {-6} {2} = -3

We chose a point:

(x_ {0}, y_ {0}) :( 4,0)

Substituting in the equation we have:

y-0 = -3 (x-4)\\y = -3 (x-4)

Finally, the equation is: y = -3 (x-4)

Answer:

OPTION C

6 0
3 years ago
Read 2 more answers
7. Mr. Garcia bought 27 large boxes of chlorine tablets and 33 small boxes of chlorine tablets. Each
AVprozaik [17]

Answer:

$2,487.00

Step-by-step explanation:

27x53= 1431

33x32= 1056

1056 + 1431= 2487

4 0
3 years ago
Two points in the Cartesian plane are A(2.00 m, −4.00 m) and B(−3.00 m, 3.00 m). Find the distance between them and their polar
Brrunno [24]

The distance between the two points is d=8.6m

The polar coordinate of A is \left(4.47,296.57\right)

The polar coordinate of B is \left(4.24,135\right)

Explanation:

The two points are A(2,-4) and B(-3,3)

The distance between two points is given by,

d=\sqrt{(2+3)^{2}+(-4-3)^{2}}\\d=\sqrt{(5)^{2}+(-7)^{2}}\\d=\sqrt{25+49}\\d=8.6

Thus, the distance between the two points is d=8.6m

The polar coordinates of A can be written as (Distance, tan^{-1} \frac{y}{x} )

Distance = \sqrt{x^{2} +y^{2} }

Substituting A(2,-4), we get,

Distance = \sqrt{2^{2} +(-4)^{2} }=\sqrt{4+16 }=4.47

tan^{-1} \frac{y}{x} =tan^{-1} \frac{-4}{2}=-63.43

To make the angle positive, let us add 360,

\theta=360-63.43=296.57

The polar coordinate of A is \left(4.47,296.57\right)

Similarly, The polar coordinate of B can be written as (Distance, tan^{-1} \frac{y}{x} )

Distance = \sqrt{x^{2} +y^{2} }

Substituting B(-3,3), we get,

Distance = \sqrt{(3)^{2}+(3)^{2}}=4.24

tan^{-1} \frac{y}{x} =tan^{-1} \frac{3}{-3}=-45

To make the angle positive, let us add 360,

\theta=180-45=135^{\circ}

The polar coordinate of B is \left(4.24,135\right)

5 0
3 years ago
A recursive rule for a geometric sequence is a1=49;an=3an−1.
dalvyx [7]
I think it should be an= 49x3^(n-1)
3 0
3 years ago
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