All categories

3 years ago

Amelia knits 1/10 of a scarf in 48 minutes. What fraction of a scarf can Amelia knit in 1 hour? Show work

Mathematics

1 answer:

satela [25.4K]3 years ago

3 0

That's

$\dfrac{60}{48} \times \dfrac{1}{10} = \dfrac{1}{8}$

Answer: 1/8

You might be interested in

On the blueprint of a house, 38 millimeters represents 6 meters. the length of the living room is 57 millimeters on the blueprin

Pie

For this case we can make the following rule of three:
38 milimeters ---------> 6 meters
57 milimeters ---------> x
Clearing x we have:
x = (57/38) * (6)
x = 9 meters
Answer:
the current length of the living room is:
x = 9 meters

3 0

3 years ago

sarah spent a total of 10 on oranges and apples at the supet market. if she spent 3 dollars less for oranges than she did on app

beks73 [17]

Let's write 2 equations from the two statements given.

Sarah spent 10 dollars on both oranges and apples

Let the price of oranges be "x" and price of apples be "y", thus we can write:

$x+y=10$

Oranges cost 3 less than apples, thus we can say:

$y-3=x$

We can substitute this into the first equation and solve for y:

$\begin{gathered} x+y=10 \\ y-3+y=10 \\ 2y=10+3 \\ 2y=13 \\ y=\frac{13}{2} \\ y=6.5 \end{gathered}$

Thus, let's solve for x now,

$\begin{gathered} x=y-3 \\ x=6.5-3 \\ x=3.5 \end{gathered}$

We want the price of oranges (x), thus,

Price of Oranges = $3.50

3 0

11 months ago

What are the solutions of the following equation?

noname [10]

Answer:

D. x = 7 and x = 14

Step-by-step explanation:

this is a quadratic equation, so use the quadratic formula: (-b+-√b^2-4ac) / 2a for ax^2+bx+c=0

7 0

3 years ago

Cos ( α ) = √ 6/ 6 and sin ( β ) = √ 2/4 . Find tan ( α − β )

Zina [86]

Answer:

$\purple{ \bold{ \tan( \alpha - \beta ) = 1.00701798}}$

Step-by-step explanation:

$\cos( \alpha ) = \frac{ \sqrt{6} }{6} = \frac{1}{ \sqrt{6} } \\ \\ \therefore \: \sin( \alpha ) = \sqrt{1 - { \cos}^{2} ( \alpha ) } \\ \\ = \sqrt{1 - \bigg( {\frac{1}{ \sqrt{6} } \bigg )}^{2} } \\ \\ = \sqrt{1 - {\frac{1}{ {6} }}} \\ \\ = \sqrt{ {\frac{6 - 1}{ {6} }}} \\ \\ \red{\sin( \alpha ) = \sqrt{ { \frac{5}{ {6} }}} } \\ \\ \tan( \alpha ) = \frac{\sin( \alpha ) }{\cos( \alpha ) } = \sqrt{5} \\ \\ \sin( \beta ) = \frac{ \sqrt{2} }{4} \\ \\ \implies \: \cos( \beta ) = \sqrt{ \frac{7}{8} } \\ \\ \tan( \beta ) = \frac{\sin( \beta ) }{\cos( \beta ) } = \frac{1}{ \sqrt{7} } \\ \\ \tan( \alpha - \beta ) = \frac{ \tan \alpha - \tan \beta }{1 + \tan \alpha . \tan \beta} \\ \\ = \frac{ \sqrt{5} - \frac{1}{ \sqrt{7} } }{1 + \sqrt{5} . \frac{1}{ \sqrt{7} } } \\ \\ = \frac{ \sqrt{35} - 1 }{ \sqrt{7} + \sqrt{5} } \\ \\ \purple{ \bold{ \tan( \alpha - \beta ) = 1.00701798}}$

8 0

3 years ago

-3x^{2}-21x-54 what are the zeros? (Solutions)

Irina-Kira [14]

The only way to solve if it is equal to something
assuming that the teacher wanted you to make it equal to zero do
0=-3x^2-21x-54

remember if we can do
xy=0 then assume x and y=0

so factor

0=-3x^2-21x-54
undistribute the -3
0=-3(x^2+7x+18)
remember 0 times anything=0 so
x^2+7x+18 must equal zero
use quadratice formula which is

if you have
ax^2+bx+c=0 then
x= $\frac{-b+/- \sqrt{b^{2}-4ac} }{2a}$

x^2+7x+18
a=1
b=7
c=18

x= $\frac{-7+/- \sqrt{7^{2}-4(1)(18)} }{2(1)}$
x= $\frac{-7+/- \sqrt{49-72} }{2}$
x= $\frac{-7+/- \sqrt{-23} }{2}$
i=√-1
x= $\frac{-7+/- i\sqrt{23} }{2}$

the zerose would be
x= $\frac{-7+ i\sqrt{23} }{2}$ or $\frac{-7- i\sqrt{23} }{2}$

4 0

3 years ago