Determine the number of solutions that exist to the equation?

The width of a rectangle is the length minus 3 units. The area of the rectangle is 54 units. What is the width, in units, of a r

saul85 [17]

Width of the rectangle is 9 units

Step-by-step explanation:

Step 1: Let the width of the rectangle be x. Then the length = x - 3. Find dimensions of the rectangle if its area = 54 sq. units

Area of the rectangle = length × width

54 = x (x - 3)

54 = x² - 3x

x² - 3x - 54 = 0

x² + 6x - 9x - 54 = 0 (Using Product Sum rule to factorize)

x(x + 6) - 9(x + 6) = 0

(x + 6)(x - 9) = 0

x = -6, 9 (negative value is neglected)

x = 9 units

4 0

3 years ago

Liz got home from school at 4:33. She decided to bake muffins as an after-school snack. It took Liz 55 minutes to prepare and ba

IgorC [24]

Answer:

The muffins were done at 5:28

Step-by-step explanation:

you add 4:33 to 55 minutes knowing well that 60mins makes one hour

4:33

55

5:28

6 0

2 years ago

What is the term, coefficient, constant, and factor of 1/2(base1 + base2)h? (Formula used to find area of trapezoid)

vovangra [49]

Answer:

i. Term = $\frac{b_{1}h }{2}$ + $\frac{b_{2}h }{2}$

ii. Coefficient = $\frac{1}{2}$

iii. Constant = $\frac{1}{2}$

iv. Factor = $\frac{h}{2}$

Step-by-step explanation:

A trapezoid is a quadrilateral which has its base parallel to the opposite side. It's area can be determined by;

Area of trapezium = $\frac{1}{2}$ ( $b_{1}$ + $b_{2}$ )h

Where $b_{1}$ is the measure of length of its fist base, $b_{2}$ is the measure of its second base and h is its height.

Considering the given question,

Term = $\frac{b_{1}h }{2}$ + $\frac{b_{2}h }{2}$

Coefficient = $\frac{1}{2}$

Constant = $\frac{1}{2}$

Factor = $\frac{h}{2}$

6 0

3 years ago

What was her speed?

harkovskaia [24]

0.1 mile per min

Step-by-step explanation:

lol i’m fye

8 0

3 years ago

Please asap<br>for 10 points!

kari74 [83]

<h3>Given:</h3><h3>Large cone:</h3>

r= 8 cm
h= 20 cm

<h3>Small cone:</h3>

r= 4 cm
h= 10cm

r: radius
h: height

The volume of the frustum of the given cone.

<h3>Solution:</h3>

Frustum is a part of a cone formed by cutting off the top by a parallel plane.

$\large\boxed{Formula: V= \frac{1}{3}\pi{r}^{2}h}$

Let's solve!

First, let's find the volume of the smaller cone.

Substitute the values according to the

formula.

$V= \frac{1}{3}×\pi×{4}^{2}×10$

$V= 167.5516082 \: {cm}^{3}$

Now, we can round off to the nearest hundredth.

The value in the thousandths place is smaller than 5 so we won't have to round up.

$\boxed{V= 167.55 \: {cm}^{3}}$

Next, let's find the volume of the bigger cone.

Substitute the values according to the formula.

$V= \frac{1}{3}×\pi×{8}^{2}×20$

$V= 1340.412866 \: {cm}^{3}$

Now, we can round off to the nearest hundredth.

The value in thousandths place is smaller than 5 so we won't have to round up.

$\boxed{V=1340.41 \: {cm}^{3}}$

Now, we can find the volume of the frustum.

We'll have to minus the volume of the smaller cone from the bigger cone.

$V= 1340.41-167.55$

$\large\boxed{V= 1172.86 \: {cm}^{3}}$

<u>Hence, the volume of the frustum is 1172.86 cubic centimeters.</u>

8 0

2 years ago