The area of a trapezoid is 30 cm. If

On a bicycle, Jack can travel 20 miles in 4 hours. How many miles did he travel in one hours?

abruzzese [7]

Answer:

Jack traveled 5 miles in 1 hour

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

How much is the interest on my loan?

kirill [66]

Answer: The interest is: " $ 64 .00 " .

_____________

Step-by-step explanation:

_____________

Take note of the formula:

" Ⅰ = Prt " ;

→ that is:

_____________

→ " Ⅰ = P * r * t " ;

_____________

In which:

_____________

" Ⅰ = the interest " ;

" P = the Principal amount of money " ;

" r = rate " (expressed as the "decimal form" of the percentage) ;

" t = time " (in years) ;

_____________

We are given:

_____________

P = $400 ;

r = 0.08 ;

{<u>Note of interest</u>: That is " 8% " ; since "8 % " = "(8/100)" ;

= "(8 ÷ 100)"

= " 0.08 ".}.

t = 2 ; {that would represent: " 2 (two) years".}.

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We are to solve for "Ⅰ" ; the amount of "Ⅰnterest" :

→ To solve for "Ⅰ " ; we plug in our given values; and calculate:

_____________

→ Ⅰ = P * r * t ;

= 400 * 0.08 * 2 ;

= 64 .

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→ Ⅰ = $ 64.00 .

_____________

Hope this is helpful to you!

Best wishes!

_____________

4 0

3 years ago

A card is drawn from a stands 52 card deck what is the probability that the card is a red card, or that it is a ten of clubs or

marusya05 [52]

Answer:

d. 15/26

Step-by-step explanation:

5 0

3 years ago

You have 100 cm of string which can be cut in one place (or not cut at all) and then formed into a circle and a square (or just

Ne4ueva [31]

Answer:

44cm for minimum area and 0 for maximum area (circle)

Step-by-step explanation:

Let's C be the circumference of the circle and S be the circumference of the square. If we cut the string into 2 pieces the total circumferences would be the string length 100cm.

S + C = 100 or S = 100 - C

The side of square is S/4 and radius of the circle is $\frac{C}{2\pi}$

So the area of the square is

$A_S = \frac{S^2}{4^2} = \frac{S^2}{16}$

$A_C = \pi\frac{C^2}{(2\pi)^2} = \frac{C^2}{4\pi}$

Therefore the total area is

$A = A_S + A_C = \frac{S^2}{16} + \frac{C^2}{4\pi}$

We can substitute 100 - C for S

$A = \frac{(100 - C)^2}{16} + \frac{C^2}{4\pi}$

$A = \frac{100^2 - 200C + C^2}{16} + \frac{C^2}{4\pi}$

$A = 625 -12.5C + \frac{C^2}{16} + \frac{C^2}{4\pi}$

$A = 625 -12.5C + C^2(\frac{1}{16} + \frac{1}{4\pi})$

To find the maximum and minimum of this, we can take the first derivative and set that to 0

$A^{'} = -12.5 + 2C(\frac{1}{16} + \frac{1}{4\pi}) = 0$

$C(\frac{1}{8} + \frac{1}{2\pi}) = 12.5$

$C \approx 44 cm$

If we take the 2nd derivative:

$A^{''} = \frac{1}{8} + \frac{1}{2\pi} > 0$

We can see that this is positive, so our cut at 44 cm would yield the minimum area.

The maximum area would be where you not cut anything and use the total string length to use for either square or circle

if C = 100 then $A_C = \frac{C^2}{4\pi} = \frac{100^2}{4\pi} = 795.77 cm^2$

if S = 100 then $A_S = \frac{S^2}{16} = \frac{100^2}{16} = 625 cm^2$

So to yield maximum area, you should not cut at all and use the whole string to form a circle

4 0

3 years ago

find the slope of the lines that pass through each pair of points. (-1,4) and (5,1); (-3,4) and (0, 10), m1= and m2=

Amiraneli [1.4K]

For these equations, we are going to use the slope formula, as defined below ( $m$ is slope and $(x_1, y_1)$ and $(x_2, y_2)$ are coordinate points):

$m = \dfrac{y_2 - y_1}{x_2 - x_1}$

We can simply "plug in" the coordinates we are given:

$m_1 = \dfrac{1 - 4}{5 - (-1)} = \dfrac{1-4}{5+1} = - \dfrac{3}{6} = - \dfrac{1}{2}$

$m_2 = \dfrac{10 - 4}{0 - (-3)} = \dfrac{10-4}{3} = \dfrac{6}{3} = 2$

Our answers are:

$\boxed{m_1 = - \dfrac{1}{2}}$

$\boxed{m_2 = 2}$

7 0

3 years ago