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3 years ago

A cube in Emily's closet where she stores her jewelry has a side length of 1 1/4 feet.

Mathematics

2 answers:

sp2606 [1]3 years ago

4 0

Answer: $1\dfrac{61}{64}\text{ cubic feet}$

Step-by-step explanation:

Given : The side length of cube = $1\dfrac{1}{4}\text{ feet}$

We know that the volume of a cube is given by :-

$\text{Volume}=(\text{side})^3$

Thus, the volume of the given cube is given by :-

$\text{Volume}=(1\dfrac{1}{4})^3\\\\\Rightarrow\ \text{Volume}=(\dfrac{5}{4})^3\\\\\Rightarrow\ \text{Volume}=\dfrac{5^3}{4^3}\\\\\Rightarrow\ \text{Volume}=\dfrac{125}{64}=1\dfrac{61}{64}\text{ cubic feet}$

Hence, the volume of the cube is $1\dfrac{61}{64}\text{ cubic feet}$

Gnom [1K]3 years ago

3 0

Answer:

1.95 cubic feet

Step-by-step explanation:

We are given that Emily stores her jewelry in a cube and the cube has a side length of $1\frac{1}{4}$ feet.

$1\frac{1}{4}$ feet in an decimal form is 1.25 feet.

We know that,

volume of a cube = s $^{3}$

where s is the side length of the cube.

So substituting this value of side length of cube in the formula to get:

Volume of cube = $(1.25)^3$ = 1.95 feet

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Find an equation of the line through these points (15,2.2) (5,1.6). Write answer in a slope-intercept form

nadya68 [22]

Answer:

$y=\frac{\displaystyle 3}{\displaystyle 50}x+\frac{\displaystyle 13}{\displaystyle 10}$

Step-by-step explanation:

Hi there!

Slope-intercept form: $y=mx+b$ where $m$ is the slope and $b$ is the y-intercept (the value of y when x is 0)

1) Determine the slope (m)

$m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1}$ where two given points are $(x_1,y_1)$ and $(x_2,y_2)$

Plug in the given points (15,2.2) and (5,1.6):

$m=\frac{\displaystyle 1.6-2.2}{\displaystyle 5-15}\\\\m=\frac{\displaystyle -0.6}{\displaystyle -10}\\\\m=\frac{\displaystyle 0.6}{\displaystyle 10}\\\\m=\frac{\displaystyle 0.3}{\displaystyle 5}\\\\m=\frac{\displaystyle 3}{\displaystyle 50}$

Therefore, the slope of the line is $\frac{\displaystyle 3}{\displaystyle 50}$ . Plug this into $y=mx+b$ :

$y=\frac{\displaystyle 3}{\displaystyle 50}x+b$

2) Determine the y-intercept (b)

$y=\frac{\displaystyle 3}{\displaystyle 50}x+b$

Plug in a given point and solve for b:

$1.6=\frac{\displaystyle 3}{\displaystyle 50}(5)+b\\\\1.6=\frac{\displaystyle 3}{\displaystyle 10}+b\\\\1.6-\frac{\displaystyle 3}{\displaystyle 10}=\frac{\displaystyle 3}{\displaystyle 10}+b-\frac{\displaystyle 3}{\displaystyle 10}\\\\\frac{\displaystyle 13}{\displaystyle 10}=b$