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1 year ago

Which value of x would make Triangle S U V Is-congruent-to Triangle T U M by HL?

Mathematics

2 answers:

Katarina [22]1 year ago

6 0

Answer:

$x=5$

Step-by-step explanation:

Actually, the complete question includes the expression of each hypothenuse, because the problem is about congruence between right triangle.

So, the hypothenuse for $\triangle SUV$ is: $2x+9$ .

The hypothenuse for $\triangle TUW$ is: $4x-1$ .

So, the postulate HL (Hypothenuse-Leg) states that both right triangles are equal if their hypothenuses and legs are equal. So, we have to make equal both hypothenuse expression and solve for $x$ :

$2x+9=4x-1\\9+1=4x-2x\\10=2x\\x=\frac{10}{2}=5$

Therefore, when $x=5$ these triangles are congruent.

Vaselesa [24]1 year ago

3 0

Answer:

Step-by-step explanation:

2x + 9 = 4x -1

1. substract the 2x from both sides so you end up with 4x - 2x = 2x

2. add the one to both sides so 9+1= 10

3. then divide 10 and 2x = 5

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A meter is 3.37 inches more than a yard swimmer a swims 100 meters and swimmer b swims 100 yeards how many more feet did swimmer

olga_2 [115]

Swimmer a swims 100 meters, which is 100 1-meters, which is 100
(1 yards +3.37 inches) = 100 yards + 337 inches.

1 yard is 3 feet, so 100 yards are 300 feet.

100 in is 8.33 feet so
337 in is (337*8.33)/100=28.07 feet

Swimmer b swims 100 yards, which is 300 feet

Swimmer a swam 28.07 feet.

4 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)$