Answer: m∠R=30° m∠N=30°

If ΔRST is congruent to ΔNPQ, then we can infer that m∠R is congruent to m∠N

m∠R=-7x+9

m∠N=-10x

If both angles are congruent, we can solve for x...

-7x+9=-10x
add 7x to both sides
9=-3x
divide both sides by -3
-3=x

Now that we know the value of x, we can solve for the measure of the angles.

m∠R=-7x+9
m∠R=-7(-3)+9
m∠R=21+9
m∠R=30°

m∠N=-10x
m∠N=-10(-3)
m∠N=30°

6 0

3 years ago

The length of a standard jewel case is 3 cm more than its width. The area of the rectangular top of the case is 304 cm squared.

valentina_108 [34]

Answer:

width = 16 cm

length = 19 cm

Step-by-step explanation:

Let the width be x cm.

Given that length is 3 cm more than width then

length = x+3 cm

area of rectangle = 304 square cm. -----1

area of rectangle is given by

area =length * width

substituting from equation 1 and length and width in terms of x we have

304 = x(x+3)

$=> 304 = x^2+3x\\\\=> 304 -304= x^2+3x -304\\=> 0= x^2+3x -304\\=> x^2+3x -304 = 0\\=> x^2+19x - 16x -304 = 0\\=> x(x+19 ) -16(x+19) = 0\\=> (x-16) (x+19 )= 0\\x-16 = 0 \ or \ x+19 = 0\\ x= 16 \or \ x = -19$

As length cannot be negative hence x = 16

Thus width = x = 16 cm

length = x+3 = 16+3 = 19 cm

6 0

4 years ago

Hugh bought some magazines that cost $ 3.95 each and some books that cost $ 8.95 each. I have spent a total of $ 47.65. If Hugh

Alexxandr [17]

For how many books he got : 4

This is but adding up 3 of $3.95 to get the total of $11.85

You then want to subtract that from $47.65 to get $34.80

You subtract that by the $8.95 4 times so you see he bought 4 books

After you talk about how many books did he buy after that sentence I’m not sure what your saying

5 0

3 years ago