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3 years ago

PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!! I NEED TO FINISH THESE QUESTIONS BEFORE MIDNIGHT TONIGHT.

Mathematics

1 answer:

Naily [24]3 years ago

4 0

Answer:

Step-by-step explanation:

Triangle HIJ is a right angle triangle.

From the given right angle triangle

IJ represents the hypotenuse of the right angle triangle.

With ∠J as the reference angle,

HJ represents the adjacent side of the right angle triangle.

HI represents the opposite side of the right angle triangle.

To determine IJ, we would apply Sine trigonometric ratio. It is expressed as

Sin θ = opposite side/hypotenuse. Therefore,

Sin 54 = 7/IJ

0.8090 = 7/IJ

IJ = 7/0.8090

IJ = 8.7 to the nearest tenth

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If wxyz is a square with wz=27, find each measure

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Step-by-step explanation:

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3 years ago

The length of a rectangle is 6 units and its width is 4 units. What is the approximate length of the diagonal of the rectangle?

ss7ja [257]

The correct answer is:  [D]:  " 7.2 units" .
_______________________________________________________
Explanation:
________________________________________________________
Use the Pythagorean theorem:

a² + b² = c² ;

in which:  "6 units" and "4 units" equal the lengths of the right angle (formed by the rectangle); and "c" is the length of the diagonal of the rectangle, or the "hypotenuse", of the right triangle formed by the rectangle; We wish to solve for "c" ;
_______________________________________________

6² + 4² = c² ; Solve for "c" ;

↔ c² = 6² + 4² ;

= (6*6) + (4*4) ;

= 36 + 16 ;

= 52 ;

c² = 52 ;

Take the "positive square root" of each side of the equation; to isolate "c" on one side of the equation; and to solve for "c" ;

  √(c²) = √52 ;

c = √52 ;

At this point, we know the 7² = 49 ; 8² = 64 ; so, the answer is somewhere between "7" and "8" ; yet closer to "7" ; so among the answer choices given;

The correct answer is: [D]: " 7.2 units" .
_________________________________________
However, let use a calculator:

c = √52 = 7.2111025509279786 ; which rounds to "7.2" ;
which corresponds to:
___________________________________________
Answer choice: [C]: " 7.2 units" .
___________________________________________

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3 years ago

Find the value of k so that 48x-ky=11 and (k+2)x+16y=-19 are perpendicular lines.

Rufina [12.5K]

Answer: k = -1 +/- √769

Step-by-step explanation:

48x - ky = 11

-48x -48x

-ky = -48x + 11

$\frac{-ky}{-k} = \frac{-48x}{-k} + \frac{11}{-k}$

$y =\frac{48x}{k} - \frac{11}{k}$

Slope: $\frac{48}{k}$

*************************************************************************

(k + 2)x + 16y = -19

- (k + 2)x -(k + 2)x

16y = -(k + 2)x - 19

$\frac{16y}{16} = -\frac{(k + 2)x}{16} - \frac{19}{16}$

$y = -\frac{(k + 2)x}{16} - \frac{19}{16}$

Slope: $-\frac{(k + 2)}{16}$

**********************************************************************************

$\frac{48}{k}$ and $-\frac{(k + 2)}{16}$ are perpendicular so they have opposite signs and are reciprocals of each other. When multiplied by its reciprocal, their product equals -1.

$-\frac{(k + 2)}{16}$ * $\frac{k}{48}$ = -1

$\frac{(k + 2)k}{16(48)}$ = 1

Cross multiply, then solve for the variable.

(k + 2)(k) = 16(48)

k² + 2k - 768 = 0

Use quadratic formula to solve:

k = -1 +/- √769

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3 years ago