Given a quadrilateral with vertices ????(0, 5), ????(6, 5), ????(4, 0), and H(−2, 0):

Fill in the blanks to rewrite the following statement with variables: Given any positive real number, there is a positive real n

sveticcg [70]

Answer:

a) there is s such that r>s and s is positive

b) For any r>0 , there exists s>0 such that s<r

Step-by-step explanation:

a) We are given a positive real number r. We need to wite that there is a positive real number that is smaller. Call that number s. Then r>s (this is equivalent to s<r, s is smaller than r) and s is positive (or s>0 if you prefer). We fill in the blanks using the bold words.

b) The last part claims that s<r, that is, s is smaller than r. We know that this must happen for all posirive real numbers r, that is, for any r>0, there is some positive s such that s<r. In other words, there exists s>0 such that s<r.

3 0

3 years ago

Suppose there are two circles where the radius of one circle is twice the radius of the other circle. Each circle has an arc whe

Artemon [7]

Answer:

$L=2l$ where $l,L$ denote arc lengths of two circles

Step-by-step explanation:

Let $l,L$ denote arc lengths of two circles, $r,R$ denote corresponding radii and

$\alpha _1\,,\alpha _2$ denote the corresponding central angles.

So,

$l=r\alpha _1$ and $L=R\alpha _2$

This implies $\alpha _1=\frac{l}{r}$ and $\alpha _2=\frac{L}{R}$

As each circle has an arc where the measures of the corresponding central angles are the same, $\alpha _1=\alpha _2$

$\frac{l}{r}=\frac{L}{R}$

As radius of one circle is twice the radius of the other circle,

$R=2r$

$\frac{l}{r}=\frac{L}{2r}\\\frac{l}{1} =\frac{L}{2}\\L=2l$

7 0

3 years ago

A recipe takes 90 minutes to make 25% of the time he spent preparing the ingredients how many minutes are spent preparing

gizmo_the_mogwai [7]

25% * 90 minutes is 22.5 22.5 minutes

5 0

3 years ago

George observes that for every increase of 1 in the value of x, there is a increase of 60 in the corresponding value of y. He cl

Brums [2.3K]

Hi there!

FACTS :

To see if multiple ratios are proportional, you can write them as fractions, reduce them, and compare them. If the reduced fractions are all the same, then you have proportionnal ratios. You can also write them as fractions and divide the numerator (top number) by its denominator (bottom number), and compare the decimal numbers the same way you would compare the fractions (I personnaly find this method easier because you don't need to simplify the fractions).

STEPS TO ANSWER:

x = 1 ; y = 90 → $\frac{1}{90} =$ 1 ÷ 90 = 0.01111111...

x = 2 ; y = 150 → $\frac{2}{150} =$ 2 ÷ 150 = 0.0133333...

x = 3 ; y = 210 → $\frac{3}{210} =$ 3 ÷ 210 = 0.01428571

x = 4 ; y = 270 → $\frac{4}{270} =$ 4 ÷ 270 = 0.0148148...

x = 5 ; y = 330 → $\frac{5}{330} =$ 5 ÷ 330 = 0.01515152

** You didn't really need to calculate them all because even the first two decimal numbers weren't equivalent, but I wanted to show you the whole process so I calculated them all.

⇒ If you compare all the decimals you got, you can easily see that they are not the same, which means that the ratios between the values of "x" and the values of "y" are not proportional. Therefore, George's reasoning wasn't good.

There you go! I really hope this helped, if there's anything just let me know! :)

5 0

3 years ago

Eric bought 21 pounds of sugar for $12 . how many dollars did he pay per pound of sugar?

Stels [109]

$1.75 per pound of sugar

8 0

3 years ago