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2 years 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]2 years 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]2 years 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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Answer:

$2278.846

Step-by-step explanation:

Given the following commision steps :

8% on first $1000;

12% next $2000;

20% on sales above $3000

Recorded sales for a week :

Monday $1500.00

Tuesday $3000.00

Wednesday $ 970.00

Thursday $4563.81

Friday $2760.42

This assu es that commision is calculated after weekly sales:

Total:

(1500 + 3000 + 970 + 4563.81 + 2760.42)

= $12794.23

8% on first $1000

0.08 × $1000 = $80

12% of $2000 = $240

20% of $(12794.23 - 3000)

= 0.2 × 9794.23

= 1958.846

Total commision for the week :

$(80 + 240 + 1958.846)

= $2278.846

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2 years ago

The harmonic motion of a particle is given by f(t) = 2 cos(3t) + 3 sin(2t), 0 ≤ t ≤ 8. (a) When is the position function decreas

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For the last part, you have to find where $f'(t)$ attains its maximum over $0\le t\le8$ . We have

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$3(\cos^3t-3\cos t\sin^2t)+4\sin t\cos t=0$

$\cos t(3\cos^2t-9\sin^2t+4\sin t)=0$

$\cos t(12\sin^2t-4\sin t-3)=0$

So either

$\cos t=0\implies t=\dfrac{(2n+1)\pi}2$

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where $n$ is any integer. We get 8 solutions over the given interval with $n=0,1,2$ from the first set of solutions, $n=0,1$ from the set of solutions where $\sin t=\dfrac{1+\sqrt{10}}6$ , and $n=1$ from the set of solutions where $\sin t=\dfrac{1-\sqrt{10}}6$ . They are approximately

$\dfrac\pi2\approx2$

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2 years ago

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Answer:

Step-by-step explanation:

Hello!

X₁: speed of a motorcycle at a certain intersection.

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n₂= 42 cars

X[bar]₂= 26.56 km/h

S₂= 2.45 km/h

Assuming

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and σ₁² = σ₂²

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The parameter of interest is μ₁-μ₂

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