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Vedmedyk [2.9K]
3 years ago
6

Identify the variation as direct, inverse, joint or combined. If the area of a rectangle stays constant, what is the relationshi

p between the base and the height?
Mathematics
2 answers:
Likurg_2 [28]3 years ago
7 0

Answer:

The Base and Height of a rectangle have an inverse relationship, as long as the Area of the rectangle remains constant.

Step-by-step explanation:

If the area of the rectangle remains constant, you have:

Area = Base * Height = K. Assuming K as a fixed real number, then:

Base = K / Height.

According to the previous expression, an increase in the value of the height of the rectangle generates a decrease in the value of the Base.

Conclusion: The Base and Height of a rectangle have an inverse relationship, as long as the Area of the rectangle remains constant.

kirill [66]3 years ago
4 0

Your answer is inverse.

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If y varies inversely as x, and y=10 when x=2, find y when x=8
dedylja [7]
\bf \qquad \qquad \textit{inverse proportional variation}\\\\
\textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad  y=\cfrac{k}{x}\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad  variation
\end{array}\\\\
-------------------------------\\\\
\textit{we also know that }
\begin{cases}
y=10\\
x=2
\end{cases}\implies 10=k2\implies \cfrac{10}{2}=k\implies 5=k
\\\\\\
therefore\qquad \boxed{y=\cfrac{5}{x}}
\\\\\\
\textit{when x = 8, what is \underline{y}?}\qquad y=\cfrac{5}{8}
4 0
3 years ago
Read 2 more answers
And can anyone do this?!!
Annette [7]

a. The interest earned will be $36.

b. The account balance will be $336.

Step-by-step Explanation:

Step 1:

The initial amount put into the account was $300.

This account has an interest rate of 4% every year. So we must calculate how much 4% of $300 is.

4% of $300 = \frac{4}{100} (300) = 0.04 (300) = 12.

Step 2:

So for every year, the interest of $12 is added into the account. To calculate total interest we multiply this interest amount and the number of years.

So after 3 years = 3(12) = 36.

So account balance after 3 years 300+36 = 336.

So the interest earned is $36 and the account balance is $336 after three years.

6 0
4 years ago
Janet has $120 . If she saves $20 per week, in how many days will she have $500?
Nata [24]
500-120= 380  380÷200= 19 so the answer is 19
6 0
4 years ago
Un triángulo rectángulo tiene un área de 84 pies2 y una hipotenusa de 25 pies de largo. ¿Cuáles son las longitudes de sus otros
jolli1 [7]

Answer:

7 feet and 24 feet

Step-by-step explanation:

In the right triangle, the hypotenuse is 25 feet long. The area of this triangle is 84 square feet.

Let x feet and y feet be the lengths of triangle's legs.

By the Pythagorean theorem,

x^2+y^2=25^2\\ \\x^2+y^2=625

The area of the right triangle is half the product of its legs, thus

84=\dfrac{1}{2}xy\\ \\xy=168

Solve the system of two equations:

\left\{\begin{array}{l}x^2+y^2=625\\ \\xy=168\end{array}\right.

From the second equation:

x=\dfrac{168}{y}

Substitute it into the first equation:

\left(\dfrac{168}{y}\right)^2+y^2=625\\ \\168^2+y^4=625y^2\\ \\y^4-625y^2+168^2=0\\ \\D=(-625)^2-4\cdot 168^2=(625-2\cdot 168)(625+2\cdot 168)=289\cdot 961=17^2\cdot 31\\ \\\sqrt{D}=17\cdot 31=527\\ \\y^2_{1,2}=\dfrac{-(-625)\pm 527}{2}=49,\ 576\\ \\y_1=7,\ y_2=-7,\ y_3=24,\ y_4=-24

The length of the leg cannot be negative, so

y_1=7\Rightarrow x_1=\dfrac{168}{7}=24\\ \\y_2=24\Rightarrow x_2=\dfrac{168}{24}=7

6 0
3 years ago
( 5x + 685 ) + ( 12x - 106 ) = 2500
uysha [10]

Answer:

            x  = 113

Step-by-step explanation:

( 5x + 685 ) + ( 12x - 106 ) = 2500                                          ( 685 - 106 =   579)

                       17x  +  579 = 2500

                             17x        = 2500 - 579

                                    17x =     1921

                                       x = 1921 / 17

                                      x  = 113

3 0
3 years ago
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