What is the answer to the equation 13-3/2x=37?

The length of a rectangle is 4 inches more than its width, and its perimeter is 34 inches. Find the length and width of the

gizmo_the_mogwai [7]

Answer:

Width = 6.5 inches

Length = 10.5 inches

Step-by-step explanation:

Let

"l" be length of rectangle

and

"w" be width of rectangle

Since length of rectangle is 4 inches MORE THAN WIDTH, we can write:

l = 4 + w

The perimeter is sum of all sides, so

Perimeter = l + l + w + w = 2l + 2w

The perimeter is 34, so we can write:

2l + 2w = 34

Putting 1st equation in 2nd, we get equation in "w" and solve for this first:

$2l + 2w = 34\\2(4+w) + 2w = 34\\8+2w+2w=34\\4w=26\\w=\frac{26}{4}=6.5$

Width is 6.5 in

Now, l = 4 + w, so

l = 4 + 6.5 = 10.5

Length is 10.5 in

3 0

3 years ago

Which of these four sets of side lengths will form a right triangle? Set 1 4 cm, 5 cm, 6 cm Set 2 8 in., 12 in., 20 in. Set 3 10

Alenkasestr [34]

Answer: The correct option is (D) SET 4.

Step-by-step explanation: We are to select the correct set of side lengths that will form a right-angled triangle.

To form a right-angled triangle, we must have the following relation:

<em>Perpendicular² + Base² = Hypotenuse².</em>

<em>Hypotenuse is the length of the largest side; perpendicular and base are the two legs of the triangle.</em>

SET 1 : 14 cm, 5 cm, 6 cm.

We have

$5^2+6^2=25+36=61,\\\\14^2=196.$

Therefore,

<em>Perpendicular² + Base² ≠ Hypotenuse².</em>

So, this set will not form a right-angled triangle.

SET 2 : 8 in., 12 in., 20 in.

We have

$8^2+12^2=64+144=208,\\\\20^2=400.$

Therefore,

<em>Perpendicular² + Base² ≠ Hypotenuse².</em>

So, this set will not form a right-angled triangle.

SET 3 : 10 mm, 20 mm, 30 mm.

We have

$10^2+20^2=100+400=500,\\\\30^2=900.$

Therefore,

<em>Perpendicular² + Base² ≠ Hypotenuse².</em>

So, this set will not form a right-angled triangle.

SET 4 : 12 ft, 16 ft, 20 ft.

We have

$12^2+16^2=144+256=400,\\\\20^2=400.$

Therefore,

<em>Perpendicular² + Base² = Hypotenuse².</em>

So, this set will form a right-angled triangle.

Thus, the SET 4 will form a right-angles triangle.

Option (D) is correct.

5 0

3 years ago

Read 2 more answers

Emir made $182 in interest by placing $700 in a savings account with simple interest for 2 years. What was the interest rate?

Pavlova-9 [17]

Answer:

7.69230%

R=I/P×T

R=$182/$700×2

R=182/1400

R=91/700

=7.69230%

6 0

3 years ago

As Juan continued his hitting practice showing off his abilities, one of the balls flew over the center field stands and into th

WARRIOR [948]

Answer:

A. Find h(10) = 0 . . . (it is not)

B. h(5.235) = 0; hang time was about 5.235 seconds

Step-by-step explanation:

The hang time of the ball is the value of x in h(x) such that h(x) = 0.

__

Juan can show the hang time is 10 seconds by finding h(10) = 0. The value of h(10) is ...

h(10) = -16(10²) +83(10) +4 = -1600 +834 = -766 ≠ 0

Juan cannot prove the hang time was 10 seconds.

__

The hang time is the solution to ...

h(x) = 0

-16x² +83x +4 = 0 . . . . . use the given expression for h(x)

x² -5.1875x = 0.25 . . . . divide by -16

x² -5.1875x +6.7275390625 = 6.9775390625 . . . . add (5.1875/2)²

(x -2.59375)² = 6.9775390625 . . . . . . . . . . rewrite as a square

x = 2.59375 ±√6.9775390625 ≈ {-0.048, 5.235} . . . . square root, find x

The hang time of the ball was about 5.235 seconds.

__

We like a graphing calculator for finding a quick solution to questions like this.

4 0

2 years ago

Jill's weight is 92 kg 250 g. Jill's sister's weight is 8 kg 600 g less than Jill's weight. How much does the sister weigh?

hodyreva [135]

Answer:

S = 83 g and 650 kg.

Step-by-step explanation:

Gram (g)= 1000 kilograms (kg).

Jill (J)= 92000 + 250 kg.

J = 92250 kg

Sister (S) = J - (8000 + 600 kg)

S = 92250 - 8600 kg

S = 83650 kg.

S = 83 g and 650 kg.

4 0

2 years ago