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mr Goodwill
1 day ago
6

Malcolm is driving 1,373 miles from Wichita to Charleston for a family Reunion. He drives 468 miles the first day and 434 miles

the second day. Round each distance to the nearest ten and Estimate about how many miles Malcolm has left to drive. A) 500 miles B) 400 miles C) 480 miles D) 470 miles
Mathematics
1 answer:
zzz [9K]1 day ago
8 0
Malcolm's remaining distance is roughly
   1370 - 470 - 430 = 470

This coincides with selection...
   D) 470 miles
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Triangles ΔABC ≅ ΔBAD so that C and D lie in the opposite semi-planes of segment AB. Prove that segment CD bisects segment AD.
Zina [9171]

Answer:

Review the explanation

Step-by-step explanation:

The triangles ΔABC and ΔBAD are congruent, establishing:

  • AB ≅ BA;
  • AC ≅ BD;
  • BC ≅ AD;
  • ∠ABC ≅ ∠BAD;
  • ∠BCA ≅ ∠ADB;
  • ∠CAB ≅ ∠DBA.

Now, consider triangles AEC and BED. In these triangles, we have:

  • AC ≅ BD;
  • ∠EAC ≅ ∠EBD (due to ∠CBA ≅ ∠BAD);
  • ∠AEC ≅ ∠BED (being vertical angles).

Therefore, ΔAEC ≅ ΔBED, which leads to the conclusion that:

AE ≅ EB.

This indicates that line segment CD bisects segment AD.

6 0
21 day ago
Kathleen and Arnob both run from the park entrance along a loop. Kathleen starts walking from the park entrance and gets a 5-mil
zzz [9080]

In this scenario, the first step is to assign variables.

We define:

x: time measured in minutes

y: distance covered.

The equations formulated are as follows:

For Kathleen:

y = (\frac{1}{15}) x + 5

For Arnob:

y = (\frac{2}{15}) x

At the moment Arnob meets Kathleen, we have:

(\frac{1}{15}) x + 5 = (\frac{2}{15}) x

Next, we isolate x.

We now have:

(\frac{2}{15}) x - (\frac{1}{15}) x = 5

(\frac{1}{15}) x = 5\\x = (15) * (5)\\x = 75 min

Answer:

Arnob takes a total of 75 minutes to catch up to Kathleen:

d. 75

5 0
27 days ago
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A​ 0.8-liter bottle of Mexican wine costs 101 pesos. At that​price, how much would a​ half-gallon jug of the same wine cost in​d
AnnZ [9099]

Answer:

$12.18

Step-by-step explanation:

Provided:

The price of a 0.8 liter bottle of Mexican wine amounts to 101 pesos.

Consequently,

The price for 1 liter of Mexican wine can be determined as \frac{\textup{101}}{\textup{0.8}} pesos.

Additionally,

Converting, 1 Mexican peso equates to 0.051 dollars.

As a result, the equivalent cost of 1 liter of Mexican wine is \frac{\textup{101}}{\textup{0.8}}\times0.051 dollars.

Moreover,

Knowing that 1 gallon equals 3.78541 liters;

Thus, half a gallon equals \frac{\textup{3.78541}}{\textup{2}} = 1.892705 liters.

Therefore, the cost for a half-gallon jug would be \frac{\textup{101}}{\textup{0.8}}\times0.051\times1.892705 dollars.

In conclusion, the price for a half-gallon of this wine is $12.18.

3 0
1 month ago
What is the product? StartFraction 3 k Over k + 1 EndFraction times StartFraction k squared minus 1 Over 3 k cubed EndFraction S
PIT_PIT [9117]

Answer:

StartFraction negative 1 Over k cubed EndFraction

Detailed breakdown:

3k / (k + 1) × (k² - 1) / 3k³

= 3k(k² - 1) / (k + 1)(3k³)

= 3k³ - 3k / 3k⁴ + 3k³

= -3k / 3k⁴

= -1/k³

StartFraction k + 1 Over k squared EndFraction

(k + 1) / k²

StartFraction k minus 1 Over k squared EndFraction

(k - 1)/k²

StartFraction negative 1 Over k cubed EndFraction

= -1/k³

StartFraction 1 Over k EndFraction

= 1/k

4 0
17 days ago
Brian pays £475.29 a year on his car insurance. The insurance company reduces the price by 2.1%.
zzz [9080]

Response:

470.12??? not certain!!!!

Step-by-step explanation:

3 0
10 days ago
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