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2 years ago

12

Can you tell which of the following triangles are right and explain your answer? The numbers represent the lengths of the sides:

5,6,7

1 answer:

abruzzese [7]2 years ago

5 0

….? Where are the triangles…?

….? Where are the options…?

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The temperature in the Arctic Circle at 9:00am was 22.8° below zero. By 6:00pm on the same day, the temperature had decreased by

rosijanka [135]

4.65 is the new temperature.

8 0

3 years ago

It is hard to calculate the volume of a mountain but several estimates put the volume of Mount Everest at around 2,413 cubic kil

scoray [572]

Answer:

About 609,000 Cowboy stadiums could fit inside of Mount Everest

Step-by-step explanation:

we have

The estimate volume of Mount Everest is at around $2,413\ km^{3}$

The Dallas Cowboys Stadium has a volume of $140,000,000\ ft^{3}$

step 1

Convert ft³ to km³

we know that

1 km=3,280.84 ft

so

$140,000,000\ ft^{3}=140,000,000*(1/3,280.84)^{3}=0.003964\ km^{3}$

step 2

To find how many Cowboy stadiums could fit inside of Mount Everest, divide the volume of Mount Everest by the volume of the Dallas Cowboys Stadium

$2,413/0.003964=608,729$

Round to the nearest Thousands

$608,729=609,000$

The volume of Mount Everest is about 609,000 times greater than the volume of the Dallas Cowboys Stadium

8 0

3 years ago

What is the number that has the same absolute value as 81

LenaWriter [7]

The absolute value of -81 has the same absolute value as that of 81 because they both have the same distance to 0.

4 0

3 years ago

At which x value will f(x)=3x+3 exceed g(x)=3x+10

Anvisha [2.4K]

We write an inequality:

$f(x) > g(x)$

$3^x + 3 > 3x + 10$

$3^x > 3x + 7$

This equation cannot be solved using trivial methods found in high-school classes, so we resort to graphical examination. $3x+7$ is a linear function while $3^x$ is an exponential one (with limit zero as $x$ approaches $- \infty$ ). We see that $3^x = 3x+7$ at approximately $x=2.4$ and $x=-2.3$ .

Indeed, using a computer algebra system such as the ones on modern TI calculators and on many internet sites gives equality at $x=2.42, -2.31$ . By observing our graph, we see that $f(x) > g(x)$ when $x > 2.42$ or $x < -2.31$ .

3 0

2 years ago

Read 2 more answers

When the effective interest rate is 9% per annum, what is the present value of a series of 50 annual payments that start at $100

ser-zykov [4K]

Answer:

$1,109.62

Step-by-step explanation:

Let's first compute the <em>future value FV.</em>

In order to see the rule of formation, let's see the value (in $) for the first few years

<u>End of year 0</u>

1,000

<u>End of year 1(capital + interest + new deposit)</u>

1,000*(1.09)+10

<u>End of year 2 (capital + interest + new deposit)</u>

(1,000*(1.09)+10)*1.09 +10 =

$\bf 1,000*(1.09)^2+10(1+1.09)$

<u>End of year 3 (capital + interest + new deposit)</u>

$\bf (1,000*(1.09)^2+10(1+1.09))(1.09)+10=\\1,000*(1.09)^3+10(1+1.09+1.09^2)$

and we can see that at the end of year 50, the future value is

$\bf FV=1,000*(1.09)^{50}+10(1+1.09+(1.09)^2+...+(1.09)^{49}$

The sum

$\bf 1+1.09+(1.09)^2+...+(1.09)^{49}$

is the <em>sum of a geometric sequence </em>with common ratio 1.09 and is equal to

$\bf \frac{(1.09)^{50}-1}{1.09-1}=815.08356$

and the future value is then

$\bf FV=1,000*(1.09)^{50}+10*815.08356=82,508.35564$

The <em>present value PV</em> is

$\bf PV=\frac{FV}{(1.09)^{50}}=\frac{82508.35564}{74.35572}=1,109.616829\approx \$1,109.62$

rounded to the nearest hundredth.

5 0

3 years ago