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Ksivusya [100]
3 years ago
15

Find the unknown side length x. ​

Mathematics
1 answer:
Ganezh [65]3 years ago
6 0

Answer:

x = \sqrt{65}

Step-by-step explanation:

The altitude of the triangle must equal 4 because it is a right triangle with another leg of 3 and a hypotenuse of 5 (reason is due to the pythagorean theorem)

Therefore, the triangle on the right has legs of 4 and 7 and, again, use the phythagorean theorem to find 'x' (the hypotenuse)

4^{2} + 7^{2} = x^{2}

16 + 49 = x^{2}

65 = x^{2}

x = sq rt 65

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What color does blue and pink make
Flauer [41]
The color magenta! Or purple
8 0
3 years ago
Read 2 more answers
What are the approximate values of the minimum and maximum points of f(x) = x5 − 10x3 + 9x on [-3,3]? A. maximum point: (–2.4, 3
slava [35]

Answer:

(-2.4, 37.014)

Step-by-step explanation:

We are not told how to approach this problem.  

One way would be to graph f(x) = x^5 − 10x^3 + 9x on [-3,3] and then to estimate the max and min of this function on this interval visually.  A good graph done on a graphing calculator would be sufficient info for this estimation.  My graph, on my TI83 calculator, shows that the relative minimum value of f(x) on this interval is between x=2 and x=3 and is approx. -37; the relative maximum value is between x= -3 and x = -2 and is approx. +37.  

Thus, we choose Answer A as closest approx. values of the min and max points on [-3,3].  In Answer A, the max is at (-2.4, 37.014) and the min at (2.4, -37.014.

Optional:  Another approach would be to use calculus:  we'd differentiate f(x) = x^5 − 10x^3 + 9x, set the resulting derivative = to 0 and solve the resulting equation for x.  There would be four x-values, which we'd call "critical values."

3 0
3 years ago
Read 2 more answers
6 1/2 chocolate chips and 5/2 cups of flour how many more cups of chocolate chips use than cups of flours
PIT_PIT [208]

Answer: 4

Step-by-step explanation:

Amount of chocolate chips = 6 1/2

Amount of cups of flour = 5/2

The cups of flour should be changes to a mixed fraction and this will be 5/2 = 2 1/2

The question simply means we should find the difference between the fractions given and this will be:

= 6 1/2 - 2 1/2

= 4

8 0
2 years ago
The doubling period of a bacterial population is 20 20 minutes. At time t = 100 t=100 minutes, the bacterial population was 9000
Nuetrik [128]

Answer:

The initial population was 2810

The bacterial population after 5 hours will be 92335548

Step-by-step explanation:

The bacterial population growth formula is:

P = P_0 \times e^{rt}

where P is the population after time t, P_0 is the starting population, i.e. when t = 0, r is the rate of growth in % and t is time in hours

Data: The doubling period of a bacterial population is 20 minutes (1/3 hour). Replacing this information in the formula we get:

2 P_0 = P_0 \times e^{r 1/3}

2 = e^{r \; 1/3}

ln 2 = r \; 1/3

ln 2 \times 3 = r

2.08 \% = r

Data: At time t = 100 minutes (5/3 hours), the bacterial population was 90000. Replacing this information in the formula we get:

90000 = P_0 \times e^{2.08 \; 5/3}

\frac{9000}{e^{2.08 \; 5/3}} = P_0

2810 = P_0

Data: the initial population got above and t = 5 hours. Replacing this information in the formula we get:

P = 2810 \times e^{2.08 \; 5}

P = 92335548

3 0
3 years ago
Which of the following behaviors would best describe someone who is listening and paying attention? a) Leaning toward the speake
nataly862011 [7]

Answer:

D

Step-by-step explanation:

If you ask questions while their speaking it shows that you are paying attention to them. Avoiding eye contact could mean your thinking about something else or you aren't interested. Interrupting them is just being disrespectful. Leaning towards them doesn't really do anything other than you moving.

7 0
3 years ago
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