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3 years ago

What is the base of a triangle with a height of 14 cm and an area of 42 square cm?

Mathematics

2 answers:

sasho [114]3 years ago

5 0

Answer:

$6cm$

Step-by-step explanation:

$area = \frac{1}{2} \times base \times height \\ 42 = \frac{1}{2} \times b \times 14 \\ 42 = \frac{14b}{2} \\ 42 = 7b \\ \frac{42}{7} = \frac{7b}{7} \\ base = 6cm$

<em>hope</em><em> </em><em>this</em><em> </em><em>helps</em>

Naily [24]3 years ago

4 0

Answer:

Step-by-step explanation:

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3 years ago

A population of bees is decreasing. The population in a particular region this year is 1,250. After 1 year, it is estimated tha

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To model this situation, we are going to use the decay formula: $A=Pe^{rt}$
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$A$ is the final pupolation
$P$ is the initial population
$e$ is the Euler's constant
$r$ is the decay rate
$t$ is the time in years

A. We know for our problem that the initial population is 1,250, so $P=1250$ ; we also know that after a year the population is 1000, so $A=1000$ and $t=1$ . Lets replace those values in our formula to find $r$ :
$A=Pe^{rt}$
$1000=1250e^{r}$
$e^{r}= \frac{1000}{1250}$
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Now that we have $r$ , we can write a function to model this scenario:
$A(t)=1250e^{-0.2231t}$ .

B. Here we are going to use a graphing utility to graph the function we derived in the previous point. Please check the attached image.

C.
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- The function doe snot have a x-intercept
- The function has a y-intercept at (0,1250)
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$A_{0}=1250e^{0}$
$A_{0}=1250$
- Over the interval [0,10], the function will have a minimum at t=10:
$A(10)=1250e^{(-0.2231)(10)$
$A_{10}=134.28$

D. To find the rate of change of the function over the interval [0,10], we are going to use the formula: $m= \frac{A(0)-A(10)}{10-0}$
where
$m$ is the rate of change
$A(10)$ is the function evaluated at 10
$A(0)$ is the function evaluated at 0
We know from previous calculations that $A(10)=134.28$ and $A(0)=1250$ , so lets replace those values in our formula to find $m$ :
$m= \frac{134.28-1250}{10-0}$
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3 years ago

Solve the proportions:

IRINA_888 [86]

<u>Answer:</u>

6. 6.75
7. 27
8. 92/17
9. 49

<u>Step-by-step explanation:</u>

<u>- Question 6 -</u>

9/16 = x/12
=> 16x = 12 x 9
=> 16x = 108
=> x = 6.75

Hence, <u>the value of x in this proportion is 6.75.</u>

<u>- Question 7 -</u>

-3 + x/18 = 12/9
=> -3/18 + x/18 = 4/3
=> x/18 = 4/3 + 1/6
=> x/18 = 8/6 + 1/6
=> x/18 = 9/6
=> x = 9/6 x 18
=> x = 27

Hence, <u>the value of x is 27</u>

<u>- Question 8 -</u>

17/15 = 10/2x - 2

=> 17(2x - 2) = 150

=> 34x - 34 = 150

=> 34x = 184

=> x = 184/34

=> x = 92/17

Hence, <u>the value of x is 92/17</u>

<u>- Question 9 -</u>

x - 16/x + 6 = 3/5
=> 5(x - 16) = 3(x + 6)
=> 5x - 80 = 3x + 18
=> 2x = 98
=> x = 49

Hence, <u>the value of x is 49.</u>

Hoped this helped.

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3 years ago