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Dominik [7]
2 years ago
6

Henry ran five races, each of which was a different positive integer number of

Mathematics
1 answer:
dolphi86 [110]2 years ago
7 0

Answer:

10 miles.

Step-by-step explanation:

Let x be the number of miles on Henry's longest race.

We have been given that Henry ran five races, each of which was a different positive integer number of  miles.

We can set an equation for the average of races as:

\frac{\text{The sum distances of 5 races}}{5}=4

As distance covered in each race is a different positive integer, so let his first four races be 1, 2, 3, 4.

Now let us substitute the distances of 5 races as:

\frac{1+2+3+4+x}{5}=4

\frac{10+x}{5}=4

Let us multiply both sides of our equation by 5.

\frac{10+x}{5}*5=4*5

10+x=20

Let us subtract 10 from both sides of our equation.

10-10+x=20-10

x=10

Therefore, the maximum possible distance of Henry's longest race is 10 miles.

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Answer:

4

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7 0
2 years ago
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tensa zangetsu [6.8K]

Answer:

(a) AH < HC is No

(b) AH < AC is Yes

(c) △AHC ≅ △AHB is Yes

Step-by-step explanation:

Given

See attachment for triangle

Solving (a): AH < HC

Line AH divides the triangle into two equal right-angled triangles which are: ABH and ACH (both right-angled at H).

To get the lengths of AH and HC, we need to first determine the measure of angles HAC and ACH. The largest of those angles will determine the longest of AH and HC. Since the measure of the angles are unknown, then we can not say for sure that AH < HC because the possible relationship between both lines are: AH < HC, AH = HC and AH > HC

Hence: AH < HC is No

Solving (b): AH < AC

Length AC represents the hypotenuse of triangle ACH, hence it is the longest length of ACH.

This means that:

AH < AC is Yes

Solving (c): △AHC ≅ △AHB

This has been addresed in (a);

Hence:

△AHC ≅ △AHB is Yes

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Answer: B

Step-by-step explanation:

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3 years ago
Pherris is graphing the function f(x) = 2(3)x. He begins with the point (1, 6). Which could be the next point on his graph?
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Answer: (2, 18)

Step-by-step explanation:

When x=2, f(2)=2(3)^{2}=18.

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Option (4)

Step-by-step explanation:

Domain of a function is defined by the x-values or input values of the function.

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From the graph attached,

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Option (4) will be the answer.

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