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3 years ago

Find the height, round to the nearest hundredthArea is 72units squared

Mathematics

1 answer:

salantis [7]3 years ago

4 0

Answer:

$\large\boxed{h=10\dfrac{2}{7}}$

Step-by-step explanation:

The formula of an area of a triangle:

$A=\dfrac{bh}{2}$

We ahve b = 14 and A = 72. Substitute:

$72=\dfrac{14h}{2}$ multiply both sides by 2

$144=14h$ divide both sides by 14

$h=\dfrac{144}{14}\\\\h=\dfrac{144:2}{14:2}\\\\h=\dfrac{72}{7}\\\\h=10\dfrac{2}{7}$

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A cube with sides 5 inches, and a pyramid with base edges 5 inches. What is the height, so that the volume of the cube and the p

Ostrovityanka [42]

15 inches is the height of the pyramid

Step-by-step explanation:

The volume of a cube is a³

Given a = 5 inches

→ Volume = a³

= 5³

= 5×5×5

= 125 in²

The volume of a pyramid is $\frac{1}{3} {a}^{2}h$

Given a = 5 inches , h = height of pyramid

$= > \frac{1}{3} {a}^{2} h$

$= > \frac{1}{3}(5)^{2}h$

$= > \frac{1}{3} \times 25 \times h$

$= > \frac{25}{3}h$

then,

$125 = \frac{25h}{3}$

$= > 25h = 125 \times 3$

$= > 25h = 375$

$= > h = \frac{375}{25}$

$= > h = 15$

Hence, the height of pyramid is 15 inches

7 0

2 years ago

Antonia bought a set of dishes, a towel, and a candle at a housewares store. The set of dishes cost $35.02, the towel cost $21.4

vekshin1

Answer:

Antonia saved $5.39

Step-by-step explanation:

Candle:

$9.59 - $0.50 (coupon) = $9.09

Towel:

$21.43 - $2.75 (coupon) = $18.68

Dishes:

$21.43 x 10% = 2.143

$21.43 - $2.143 = $19.287, rounded to the nearest cent and it’s $19.29.

Calculate the amount of money saved by adding 0.50 + 2.75 + 2.143, which is 5.393. Round to the nearest cent and it will be $5.39.

4 0

2 years ago

Account A and Account B both have a principal of $2,000 and an annual interest rate of 2%. No additional deposits or withdrawals

GuDViN [60]

Answer:

Account B earns more interest.

After 20 years, account B will have earned $171.89 more.

Step-by-step explanation:

Let's calculate the total for each account.

Account A:

Account A earns simple interest. We know that the principal value is $2000 and the interest rate is 2% or 0.02. We can use the simple interest formula:

$A=P(1+rt)$

Where A is the future value, P is the principal, r is the rate, and t is the time in years.

So, let's substitute 2000 for P, 0.02 for r, and 20 for t. This yields:

$A=2000(1+0.02(20))$

Multiply and add:

$A=2000(1+0.4)=2000(1.4)$

Multiply. So, the total amount of money in Account A after 20 years is:

$A=\$2800$

Since we initially deposited $2000 and our total is now $2800, this means that we earned an interest of $2800-2000=\$ 800$

Account B:

Account B earns compound interest. Like Account A, Account B has a principal value of $2000 and the interest rate is 2% or 0.02. We also know that it's compounded annually, so once per year. We can use the compound interest formula:

$B=P(1+\frac{r}{n}})^{nt}$

Where B is the future value, P is the principal, r is the rate, n is the times compounded per year, and t is the time in years.

So, let's substitute 2000 for P, 0.02 for r, n for 1 (since it's compounded annually), and t for 20. This yields:

$B=2000(1+\frac{0.02}{1})^{(1)(20)}$

Simplify this to acquire:

$B=2000(1.02)^{20}$

Evaluate. Use a calculator. So, after 20 years, the amount of money in Account B is:

$B\approx\$2971.89$

Since our principal was $2000, this means that we earned an interest of approximately $2971.89-2000=\$ 971.89$ .

So, Account A earned an interest of $800 and Account B earned an approximate interest of $971.89.

So, Account B earned more interest.

And it earned $971.89-800=\$ 171.89$ more than Account A.

And we're done!

5 0

3 years ago

Answer These Questions and show your work to be brainliest

Andre45 [30]

1. 20 of 40 is 50% 20/40 = 1/2 1/2 = 50%

2. It is 20% because 600 is 20% of 3000

3. 40% of 30 = 12 50 = 15 10% = 3 (get it)

4, 40% of 65 = 26 50%= 32.5 (get it)

3 0

3 years ago

Write an equation of the hyperbola given that the center is at (2, -3), the vertices are at (2, 3) and (2, - 9), and the foci ar

zavuch27 [327]

Check the picture below.

so, the hyperbola looks like so, clearly a = 6 from the traverse axis, and the "c" distance from the center to a focus has to be from -3±c, as aforementioned above, the tell-tale is that part, therefore, we can see that c = 2√(10).

because the hyperbola opens vertically, the fraction with the positive sign will be the one with the "y" in it, like you see it in the picture, so without further adieu,

$\bf \textit{hyperbolas, vertical traverse axis }
\\\\
\cfrac{(y- k)^2}{ a^2}-\cfrac{(x- h)^2}{ b^2}=1
\qquad 
\begin{cases}
center\ ( h, k)\\
vertices\ ( h, k\pm a)\\
c=\textit{distance from}\\
\qquad \textit{center to foci}\\
\qquad \sqrt{ a ^2 + b ^2}\\
asymptotes\quad y= k\pm \cfrac{a}{b}(x- h)
\end{cases}\\\\
-------------------------------$

$\bf \begin{cases}
h=2\\
k=-3\\
a=6\\
c=2\sqrt{10}
\end{cases}\implies \cfrac{[y- (-3)]^2}{ 6^2}-\cfrac{(x- 2)^2}{ b^2}=1
\\\\\\
\cfrac{(y+3)^2}{ 36}-\cfrac{(x- 2)^2}{ b^2}=1
\\\\\\
c^2=a^2+b^2\implies (2\sqrt{10})^2=6^2+b^2\implies 2^2(\sqrt{10})^2=36+b^2
\\\\\\
4(10)=36+b^2\implies 40=36+b^2\implies 4=b^2
\\\\\\
\sqrt{4}=b\implies 2=b\\\\
-------------------------------\\\\
\cfrac{(y+3)^2}{ 36}-\cfrac{(x- 2)^2}{ 2^2}=1\implies \cfrac{(y+3)^2}{ 36}-\cfrac{(x- 2)^2}{ 4}=1$

3 0

3 years ago

Find the height, round to the nearest hundredthArea is 72units squared ​

Find the height, round to the nearest hundredthArea is 72units squared