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3 years ago

How are improper fractions and mixed numbers different from proper fractions?

Mathematics

1 answer:

madreJ [45]3 years ago

4 0

Improper fractions and mixed numbers are always greater than or equal to 1, while proper fractions are less than 1 and greater than 0. Improper fractions have a numerator that's bigger than it's denominator, while proper fractions have a numerator that's smaller than it's denominator.

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A cleaner recommends mixing 1 1/2 cup of cleaner for every 12 cups of water. What is the ratio of cleaner to water.

Anna007 [38]

Answer: $\frac{1}{8}$ or $1:8$

Step-by-step explanation:

First, you can convert the mixed number $1\ \frac{1}{2}$ into a decimal number. To do this, you need to divide the numerator (which is 1) by the denominator (which is 2) of the fraction:

$\frac{1}{2}=0.5$

Now you must add 0.5 to the whole number part. Then:

$1+0.5=1.5$

In order to find the ratio of cleaner to water, you must divide 1.5 cups of cleaner by 12 cups of water.

Therefore, the ratio is:

$ratio=\frac{1.5}{12}=\frac{1}{8}$ or $1:8$

6 0

3 years ago

Which proportional statements are true of the

Nuetrik [128]

Answer: number 1 2 and four are correct

Step-by-step explanation:

I DID THE SAME THING

4 0

3 years ago

We are interested in the dimensions of a certain rectangle. this rectangle has length twice the side of the square and width thr

Mila [183]

Area of square = s^2
Area of Rectangle = lw
l = 2s

w+3 = s
solve for w, w=s-3
Now we have l and w.
Plug both into area of rectangle formula so: (2s)(s-3)
Since both areas are equal set both equations equal to each other:
(2s)(s-3)=s^2
Now simplify
2s^2-6s=s^2
s^2-6s=0, Solve for s.
Factor polynomial. s(s-6)=0 , s can be equal to 0 or 6. HOWEVER, you cannot have a side length of 0 therefore the side length has to be 6.
Now plug in s for the length formula for the rectangle:
l = 2s so... l = 2(6) so length of rectangle = 12.
Now plug in s for the width formula for the rectangle:
w+3=s so... w+3=6 so width of rectangle = 3.
Now the dimensions of the rectangle are 12 by 3. 12 being length and 3 width.
To CHECK:
Find area of rectangle:
A=lw so A=3 times 12 so A=36
Find area of square:
We know the side is equal to 6 so
A=s^2 so 6^2 = 36
The areas are equal that verifies the answer of 12 by 3.

8 0

3 years ago

Find sin 2a and cot 2a:

geniusboy [140]

Answer:

$sin(2\alpha )=2(\frac{5}{12})(\frac{12}{13})=\frac{10}{13}\\cot(2\alpha ) = \frac{16511}{18720}$

Step-by-step explanation:

$\text{if } cos(\alpha)=\frac{12}{13}\\\text{That must mean we have a triangle with base 12, and hypotenuse 13.}\\\text{Using Pythagoras, we can determine the base of the triangle must be 5.}\\a^2+b^2=c^2 \text{, where c is the hypotenuse and a, b are the two other sides.}\\c^2-b^2=a^2\\\sqrt{c^2-b^2}=a\\\sqrt{13^2-12^2}=\sqrt{169-144}=\sqrt{25}=5\\\text{Therefore, }sin(\alpha) = \frac{5}{12}\\sin(2\alpha)=2sin(\alpha )cos(\alpha)\\\text{(From double angle formulae identities)}\\$

$sin(2\alpha )=2(\frac{5}{12})(\frac{12}{13})=\frac{10}{13}\\cos(2\alpha )=cos^2(\alpha)-sin^2(\alpha)\\cos(2\alpha )=(\frac{12}{13})^2-(\frac{5}{12})^2=\frac{16511}{24336}\\cot(2\alpha)=\frac{cos(2\alpha)}{sin(2\alpha)}=\frac{\frac{16511}{24336}}{\frac{10}{13}}=\frac{16511}{18720}$

8 0

3 years ago

On a trip, you had to change your money from dollars to British pounds.

irga5000 [103]

Answer:

560/800 = 0.7 pounds per dollar

6 0

3 years ago

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