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2 years ago

What is the purpose and structure of a proof in Geometry?

1 answer:

6 0

Answer: A geometric proof involves writing reasoned, logical explanations that use definitions, axioms, postulates, and previously proved theorems to arrive at a conclusion about a geometric statement.

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MZRSK = x + 53, m KST = x + 109, and mZRST = 156º Find x.

Dahasolnce [82]

Answer:

$-3 = x$

Step-by-step explanation:

Since we are not given a midpoint, we use the Angle Addition Postulate:

156 = [x + 109] + [x + 53]

156 = 162 + 2x

-162 - 162

_______________

−6 = 2x

___ ___

2 2

−3 = x

[−3 + 53] + [−3 + 109] = 156

50 106

156 = 156 ☑

Therefore, $-3 = x$ is a genuine statement.

I am joyous to assist you anytime.

4 0

3 years ago

After driving 152 km, 4/5 of a trip is completed. How long is the total trip? How many more kilometers must be driven to compl

nikitadnepr [17]

Answer:

1. Total Trip Distance = 190 kilometers

2. To complete the trip, 38 more kilometers left

Step-by-step explanation:

Let total trip be x kilometers.

So we can say

"152 is $\frac{4}{5}$ of total" --- this into equation is:

$152=\frac{4}{5}x\\x=\frac{152}{\frac{4}{5}}\\x=190$

Total trip is 190 km.

Since already driven 152, to complete 190, you have to drive $190-152=38$ kilometers more.

So, 38 more kilometers to complete the trip.

7 0

3 years ago

Read 2 more answers

A farmer needs to ship 71 pumpkins to a grocery store if each crates can hold 19 pumpkins how many crates Will the farmer need ?

Lesechka [4]

Answer:

The farmer will need 7 crates.

Step-by-step explanation:

It is given that there are 71 pumpkins in total.

And each crate holds 19 pumpkins.

Let the number of crates required be "n".

The total number of pumpkins can be calculated by multiplying number of pumpkins in each crate with total number of crates.

Thus, the equation is

$19(n) = 71$

$n = \frac{71}{19} = 7$

Thus, the farmer needs 7 crates to hold total of 71 pumpkins.

3 0

3 years ago

calcula el área lateral de un prisma cuya base es un pentagono de 10cm de arista, 16.88 cm de apotema y 15 cm de altura

Romashka-Z-Leto [24]

Answer:

Lateral surface area of pentagonal prism = 750 cm²

Step-by-step explanation:

Given information:

Height of pentagonal prism = 15 cm

Length of edge = 10 cm

Length of apothem = 16.8 cm

Find:

Lateral surface area of pentagonal prism

Computation:

Lateral surface area of pentagonal prism = 5(a)(h)

Lateral surface area of pentagonal prism = 5(10)(15)

Lateral surface area of pentagonal prism = 750 cm²

5 0

2 years ago

In a manufacturing process a random sample of 9 bolts manufactured has a mean length of 3 inches with a standard deviation of .3

Serggg [28]

Answer:

The correct option is (C) (2.769, 3.231).

Step-by-step explanation:

The confidence interval for mean when the standard deviation is not known is:

$CI=\bar x\pm t_{\alpha/2, (n-1)}\frac{s}{\sqrt{n}}$

Given:

$\bar x = 3\\s=0.3\\n=9\\\alpha =1-0.95=0.05$

Compute the critical value as follows:

$t_{\alpha/2, (n-1)}=t_{0.05/2, (9-1)}=t_{0.025, 8}=2.31$

**Use a t-table.

The 95% confidence interval for true mean length of the bolt is:

$CI=\bar x\pm t_{\alpha/2, (n-1)}\frac{s}{\sqrt{n}}\\=3\pm 2.31\times \frac{0.30}{\sqrt{9}}\\ =3\pm 0.231\\=(2.769, 3.231)$

Thus, the 95% confidence interval for true mean length of the bolt is (2.769, 3.231).

The correct option is (C).

7 0

2 years ago