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Alinara [238K]
2 years ago
9

Two numbers differ by 5. Seven times the smaller plus four times the larger is 108. Find the number

Mathematics
1 answer:
ladessa [460]2 years ago
6 0

Answer:

<h3>8 and 13</h3>

Step-by-step explanation:

Let the two numbers be x and y

If the two numbers differs by 5, then;

y-x = 5 ...1

x is the smaller

y is the larger

If seven times the smaller plus four times the larger is 108, this is expressed as;

7x + 4y = 108 ... 2

From 1;

y = 5 + x .... 3

Substitute 3 into 2;

From 2;

7x + 4y = 108

7x + 4(5+x) = 108

7x + 20 + 4x = 108

11x + 20 = 108

11x = 108-20

11x = 88

x = 88/11

x = 8

Since y = 5+x

y = 5 + 8

y = 13

hence the numbers are 8 and 13

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4 0
3 years ago
The time it takes a student to walk from the dorm to the chemistry lab follows roughly a Normaldistribution with a mean of 20 mi
creativ13 [48]

Answer:

95.15%

Step-by-step explanation:

We have that the mean (m) is equal to 20, the standard deviation (sd) 3

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For this, the first thing is to calculate z, which is given by the following equation:

z = (x - m) / sd

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6 0
3 years ago
Help me please !<br> 4,5 and 6
andreev551 [17]

9514 1404 393

Answer:

  4a. ∠V≅∠Y

  4b. TU ≅ WX

  5. No; no applicable postulate

  6. see below

Step-by-step explanation:

<h3>4.</h3>

a. When you use the ASA postulate, you are claiming you have shown two angles and the side between them to be congruent. Here, you're given side TV and angle T are congruent to their counterparts, sides WY and angle W. The angle at the other end of segment TV is angle V. Its counterpart is the other end of segment WY from angle W. In order to use ASA, we must show ...

  ∠V≅∠Y

__

b. When you use the SAS postulate, you are claiming you have shown two sides and the angle between them are congruent. The angle T is between sides TV and TU. The angle congruent to that, ∠W, is between sides WY and WX. Then the missing congruence that must be shown is ...

  TU ≅ WX

__

<h3>5.</h3>

The marked congruences are for two sides and a non-included angle. There is no SSA postulate for proving congruence. (In fact, there are two different possible triangles that have the given dimensions. This can be seen in the fact that the given angle is opposite the shortest of the given sides.)

  "No, we cannot prove they are congruent because none of the five postulates or theorems can be used."

__

<h3>6.</h3>

The first statement/reason is always the list of "given" statements.

1. ∠A≅∠D, AC≅DC . . . . given

2. . . . . vertical angles are congruent

3. . . . . ASA postulate

4. . . . . CPCTC

8 0
3 years ago
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