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Ilya [14]
3 years ago
8

The sum of two numbers is 31. twice the smaller number is 11 more than the larger number. the positive difference between the nu

mbers is
Mathematics
1 answer:
Artist 52 [7]3 years ago
4 0
(x+y=31)2
2x-y=11
2x+2y=62
- 2x -y=11
3y=51
y=17
x+17=31
x=14
y-x=3
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There are 416 students who are enrolled in an introductory geology course. if there are seven boys to every six girls, how many
Alenkinab [10]

\text{Let the number of boys be x and number of girls be y.}\\
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\text{and there are total 416 students enrolled in the course. so we have}\\
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x+y=416 \ \ \ \ \ \ \ \ \ \ ......(i)\\
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\text{also given that there are seven boys to every six girls, that is}\\
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\frac{x}{y}=\frac{7}{6}

\Rightarrow 6x=7y\\
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\Rightarrow y=\frac{6x}{7}\\
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\text{substitute this value of y in (i), we get}\\
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x+\frac{6x}{7}=416\\
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\Rightarrow \frac{7x+6x}{7}=416\\
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\Rightarrow \frac{13x}{7}=416\\
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\Rightarrow x=\frac{416\times 7}{13}\\
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\Rightarrow x=224

Hence the number of boys in the course are: 224

4 0
3 years ago
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TiliK225 [7]

Answer:

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Step-by-step explanation:

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3 0
3 years ago
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Simplify by using order of operations: 4 + (9∙2) ÷ (4 - 1) - 4
Stella [2.4K]

Answer:

20

Step-by-step explanation:

Use <u>PEMDAS</u>

P = parenthesis

E = Exponents

M = Multiplication*

D = Division*

A = Addition**

S = Subtraction**

*either can come first, it just depends which comes first in the equation.

**either can come first, it just depends which comes first in the equation.

<em>Step 1 : Write equation</em>   4( 9 × 2 ) ÷ ( 4 -1 ) - 4

<em>Step 2: Solve in parenthesis   </em>4(18) ÷ (3) - 4

<em>Step 3: Solve multiplication   </em> 72 ÷ 3 - 4

<em>Step 4: Solve division               </em>24 - 4

<em>Step 5 : Solve subtraction</em>         20

3 0
3 years ago
Read 2 more answers
(a) A survey of the adults in a town shows that 8% have liver problems. Of these, it is also found that 25% are heavy drinkers,
jekas [21]

Answer:

The probability that the selected adult has liver problems is 0.08

Step-by-step explanation:

In this question, from the data given, we want to calculate the probability that an adult selected at random has liver problems.

Let E(L) be the event that an adult has liver problems.

The probability is directly obtainable from the question and it is given as 8%

Thus, the probability that the selected adult has liver problems; P(L) = 8% = 8/100 = 0.08

3 0
3 years ago
There is a triangle with a perimeter of 63 cm, one side of which is 21 cm. Also, one of the medians is perpendicular to one of t
NemiM [27]

Answer:

21cm; 28cm; 14cm

Step-by-step explanation:

There is no info in the problem/s  text which one of the triangle's  side is 21 cm. That is why we have to try all possible variants.

Let the triangle is ABC . Let the AK is the angle A bisector and BM is median.

Let O is AK and BM cross point.

Have a look to triangle ABM.  AO is the bisector and AOB=AOM=90 degrees (means that AO is as bisector as altitude)

=> triangle ABM is isosceles => AB=AM  (1)

1. Let AC=21   So AM=21/2=10.5 cm

So AB=10.5 cm as well.  So BC= P-AB-AC=63-21-10.5=31.5 cm

Such triangle doesn' t exist ( is impossible), because the triangle's inequality doesn't fulfill.  AB+AC>BC ( We have 21+10.5=31.5 => AB+AC=BC)

2. Let AB=21 So AM=21 and AC=42 .So  BC= P-AB-AC=63-21-42=0 cm- such triangle doesn't exist.

3. Finally let BC=21 cm. So AB+AC= 63-21=42 cm

We know (1) that AB=AM so AC=2*AB.  So AB+AC=AB+2*AB=3*AB

=>3*AB=42=> AB=14 cm => AC=2*14=28 cm.

Let check if this triangle exists ( if the triangle's inequality fulfills).

BC+AB>AC    21+14>28 - correct=> the triangle with the sides' length 21cm,14 cm, 28cm exists.

This variant is the only possible solution of the given problem.

6 0
3 years ago
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