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3 years ago

11

What is the length of the missing leg in this right triangle?18 mm 24 mm 26 mm 32 mm

2 answers:

topjm [15]3 years ago

8 0

Answer:

24 mm

Step-by-step explanation:

25^2 - 7^2

625 - 49

= 576

missing side = √576 = 24

solmaris [256]3 years ago

5 0

Answer:

24 mm

Step-by-step explanation:

We use the Pythagorean theorem to solve this. In the theorem, a and b are the legs of the triangle and c is the hypotenuse:

a² + b² = c²

a² + 7² = 25²

a² + 49 = 625

Subtract 49 from each side:

a² + 49 - 49 = 625 - 49

a² = 576

Take the square root of each side:

√(a²) = √576

a = 24

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Circle P is described by the equation (x−1)2+(y+6)2=9 and circle Q is described by the equation (x+4)2+(y+14)2=4. Select from th

xeze [42]

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(a) Circle Q is 9.4 units to the center of circle P

(b) Circle Q has a smaller radius

Step-by-step explanation:

Given

$P:(x - 1)^2 + (y + 6)^2 = 9$

$Q:(x + 4)^2 + (y + 14)^2 = 4$

Solving (a): The distance between both

The equation of a circle is:

$(x - h)^2 + (y - k)^2 = r^2$

Where

$Center: (h,k)$

$Radius:r$

P and Q can be rewritten as:

$P:(x - 1)^2 + (y + 6)^2 = 3^2$

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So, for P:

$Center = (1,-6)$

$r = 3$

For Q:

$Center = (-4,-14)$

$r = 2$

The distance between them is:

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2$

Where:

$Center = (1,-6)$ --- $(x_1,y_1)$

$Center = (-4,-14)$ --- $(x_2,y_2)$

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$d = \sqrt{(1 - -4)^2 + (-6 - -14)^2$

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$d = \sqrt{25 + 64$

$d = \sqrt{89$

$d = 9.4$

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In (a), we have:

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$r = 2$ --- circle Q

By comparison

$2 < 3$

<em>Hence, circle Q has a smaller radius</em>

4 0

2 years ago

Complete the following statements to prove that ∠IKL and ∠JLD are supplementary angles. It is given that ∠EIJ ≅ ∠GJI. Also, ∠EIJ

baherus [9]

Answer:

1st blank: substitution property of equality

2nd blank: linear pair theorem

3rd blank: substitution property of equality

Step-by-step explanation:

<u>1st blank</u>

∠EIJ ≅ ∠GJI (eq. 1)

∠EIJ ≅ ∠IKL (eq. 2)

∠GJI ≅ ∠JLK (eq. 3)

Substituting eq. 3 into eq. 1:

∠EIJ ≅ ∠JLK

and then, substituting eq. 2:

∠IKL ≅ ∠JLK

which means that m∠IKL = m∠JLK

<u>2nd blank</u>

The Linear Pair Theorem states that two angles that form a linear pair are supplementary

<u>3rd blank</u>

m∠JLK + m∠JLD = 180°

Substituting with the previous result:

m∠IKL + m∠JLD = 180°

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2 years ago