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irina [24]
2 years ago
10

Points X and Z are on a number line, and point Y partitions

Mathematics
1 answer:
abruzzese [7]2 years ago
6 0

Answer:

The coordinate of Z is 13.36.

Step-by-step explanation:

According to the statement, we have the following information:

\frac{XY}{XZ} = \frac{5}{12} (1)

\frac{YZ}{XZ} = \frac{7}{12} (2)

X = 0.4 (3)

Y = 5.8 (4)

From (2), we have the following expression:

YZ = \frac{7}{12}\cdot XZ

Y-Z =\frac{7}{12}\cdot (X-Z)

Y - Z = \frac{7}{12}\cdot X -\frac{7}{12}\cdot Z

Y-\frac{7}{12}\cdot X = Z-\frac{7}{12}\cdot Z

\frac{5}{12}\cdot Z = Y-\frac{7}{12}\cdot X

5\cdot Z = 12\cdot Y-7\cdot X

Z = \frac{12}{5}\cdot Y-\frac{7}{5}\cdot X (5)

If we know that Y = 5.8 and X = 0.4, then the coordinate of Z is:

Z = \frac{12}{5}\cdot (5.8)-\frac{7}{5}\cdot (0.4)

Z = 13.36

The coordinate of Z is 13.36.

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\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
&({{ 6}}\quad ,&{{ -4}})\quad 
%  (c,d)
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\end{array}\qquad 
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d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
d=\sqrt{[2-6]^2+[-7-(-4)]^2}\implies d=\sqrt{(2-6)^2+(-7+4)^2}
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3 years ago
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The total amount of water a tank can hold is 14 1/2 gallons. Raul wants to find out how many 1 1/4 gallon buckets of water can b
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Step-by-step explanation: Let me know if you need an explanation.

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A car has a gasoline
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Answer:

Yes, look at the explanation:

Step-by-step explanation:

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8 0
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Carmen wants to join a gym. Gym A costs $26.76 plus an additional $4 for each visit. Gym B has no initial fee but costs $12.92 f
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Answer:

After 3 visits both plans will cost the same.

Step-by-step explanation:

Gym A costs $26.76 plus an additional $4 for each visit.

Gym B has no initial fee but costs $12.92 for each visist.

The cost for gym A can be written as

C= $26.76 + 4(x)  where x is the number of visits to the gym A

The cost for gym B can be written as

C= $12.92 (x)  where x is the number of visits to the gym B

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after 3 visits both plans will cost the same.

Check

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12.92*3= 26.76 +12

38.76= 38.76

3 0
2 years ago
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