All categories

1 month ago

What type of triangle has side lengths of 4√5, √145 and 19?

Mathematics

1 answer:

tester [12.3K]1 month ago

5 0

a, b, c - side lengths (a ≤ b ≤ c)

If $a^2+b^2 < c^2$ , it forms an Obtuse triangle.

If $a^2+b^2=c^2$ , it constitutes a Right triangle.

If $a^2+b^2 > c^2$ , it describes an Acute triangle.

$a=4\sqrt5,\ b=\sqrt{145},\ c=19\to a < b < c$

Verify that the sum of the lengths of the first two sides exceeds that of the third.

$a+b=4\sqrt5+\sqrt{145}\approx9+12=21 > 19=c\\\\CORRECT$

$a\neq b\neq c\neq a$ , thus identifying it as a Scalene triangle.

$a^2=(4\sqrt5)^2=4^2(\sqrt5)^2=16(5)=80\\\\b^2=(\sqrt{145})^2=145\\\\c^2=19^2=361\\\\a^2+b^2=80+145=225 < 361=c^2\\\\a^2+b^2 < c^2$

It qualifies as Obtuse triangle.

You might be interested in

Nik needs to estimate how many books will fit in a bin. Each book is 1 ft tall, 0.5 ft wide, and 0.1 ft thick. The bin is 5 feet

lawyer [12517]

Answer:

600 books

Step-by-step explanation:

The dimensions of the bin are

5 by 2 by 3

The volume of the bin is found by multiplying these three dimensions.

Volume of Bin = 5 * 2 * 3 = 30 cubic feet

To find the volume of each book, we use the same method. The dimensions of one book are:

1 by 0.5 by 0.1

Volume of 1 book = 1 * 0.5 * 0.1 = 0.05 cubic feet

The total number of books fitting into the bin is calculated by:

30/0.05 = 600 books

6 0

1 month ago

Frank has X stamps and Chris has 8 more than 7 times the number of stamps Frank has. How many stamps do Frank and Chris have in

zzz [12365]

I think the right answer is D. 8x+8;
This is because Frank possesses X stamps while Chris has 8 plus 7 times the number of stamps Frank holds, making the total 8 + 7x (which is 7 times Frank's amount), so when you add Frank's stamps (x) to 8 + 7x, it results in 8 + 8x.

I hope this was helpful!

5 0

1 month ago

A certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of awriting

tester [12383]

Answer:

a) Null hypothesis: $\mu \geq 10$

Alternative hypothesis: $\mu < 10$

b) $p_v =P(t_{17}$

Given that the p-value is lower than the significance threshold in this situation, we have sufficient grounds to reject the null hypothesis.

c) $p_v =P(t_{17}$

In this case, since the p-value exceeds the significance threshold, we have adequate evidence to FAIL to reject the null hypothesis.

d) $p_v =P(t_{17}$

Here again, with the p-value being less than the significance level, we can reject the null hypothesis.

Step-by-step explanation:

1) Provided data and references

$\bar X$ represents the average of the samples

$s$ denotes the standard deviation of the samples

$n=18$ indicates the number of samples

$\mu_o =10$ is the value we are examining

$\alpha$ defines the significance level for the test.

t represents the specific statistic of interest

$p_v$ indicates the p-value relevant to the test (the variable of concern)

Define the null and alternative hypotheses.

To assess if the true mean is at least 10 hours, we must set up a hypothesis:

Part a

Null hypothesis: $\mu \geq 10$

Alternative hypothesis: $\mu < 10$

If we consider the sample size being less than 30 and the population deviation unknown, it’s more appropriate to use a t-test to compare the actual mean with the reference value, calculated as:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Part b

In this scenario t=-2.3, $\alpha=0.05$

Initially, we need to calculate the degrees of freedom $df=n-1=18-1=17$

Since this is a left-tailed test, the p-value is determined by:

$p_v =P(t_{17}$

In this instance, with the p-value being less than the significance level, we have sufficient evidence to reject the null hypothesis.

Part c

For this situation t=-1.8, $\alpha=0.01$

We need to find the degrees of freedom $df=n-1=18-1=17$

For the left-tailed test, the p-value is given by:

$p_v =P(t_{17}$

In this case, since the p-value is above the significance level, we have enough grounds to FAIL to reject the null hypothesis.

Part d

For this case t=-3.6, $\alpha=0.05$

Firstly, we find the degrees of freedom $df=n-1=18-1=17$

Since we are conducting a left-tailed test, the p-value is calculated as:

$p_v =P(t_{17}$

Here, with the p-value being lower than the significance threshold, we can reject the null hypothesis.

5 0

1 month ago

A veterinarian surveys her clients and finds that 32 percent of the households have dogs, 25 percent have cats, and 11 percent h

babunello [11817]

Answer:

C and D

Step-by-step explanation:

6 0

1 month ago

Read 2 more answers

The graph of f(x) = |x – h| + k contains the points (–6, –2) and (0, –2). The graph has a vertex at (h, –5). Describe how to fin

lawyer [12517]

<span> The absolute value function exhibits symmetry. Given that the coordinates (–6, –2) and (0, –2) produce the same output, the points are equidistant from the line of symmetry. The value of –3 exists between –6 and 0. Therefore, the x-coordinate of the vertex must be –3, which is the value of </span>h<span>. This indicates that the graph of the parent function shifts 3 units to the left.</span>

5 0

15 days ago

Read 2 more answers