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mihalych1998 [28]
3 years ago
5

Find the first of three consecutive even integers if the sum of the first and second is 15 less than 3 times the third.

Mathematics
1 answer:
lilavasa [31]3 years ago
4 0

Answer:

<em>First even integer: 6</em>

Step-by-step explanation:

<u>Inequalities</u>

Assume x is the first even integer. The next integer is x+2, and the last integer ix x+4.

The condition states that the sum of the first and the second number is 15 less than three times the third. This takes us to the inequality:

x+x+2

Operating:

2x+2

Subtracting 2 and 2x:

0

Simplifying:

0

Solving:

x>5

There are infinitely many solutions. For example, for x=6 (first even number into the solution interval):

First integer: 6

Second integer: 8

Third integer: 10

There are other solutions, like 20,22,24 but the first set is 6,8,10.

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Convert the decimal into a reduce fraction.
Ivanshal [37]

Answer:

hey i dont really know, but look up calculator soup, it has a ton of different calculators and may be able to help u

Step-by-step explanation:

/

7 0
2 years ago
Place these numbers in order from greatest to least. 19/5, 1.62, –14/3, –0.5​
max2010maxim [7]

Answer:

See below:

Step-by-step explanation:

Hello my name is Galaxy and I'll be helping you today. I hope you are having a nice day!

Simplification

To figure out how we can order them, we can first simplify the problems so that we can easily determine its place. We can put the fractions into decimal form so that they are are in one form and will be easy for us to comprehend.

\frac{19}{5}=3\frac{4}{5}=3.80

We know that \frac{1}{5} is equal to 0.20 because we know that 1.00 will be equal to 100 in this case and we can divide that by five to get 20 which will be divided back to get to 0.20.

As I've explained how I've simplified the first one, simplifying the others should be a quite similar process, feel free to comment below if you need any assistance with this.

\frac{19}{5}=3.80\\1.62=1.62\\\frac{-14}{3}=-4.6667\\  -0.5=-0.5

(Everything simplified to decimal form.)

We can now proceed to ordering them.

Ordering

Ordering decimals doesn't have to be as hard as it looks, we know that as per the number line a number that is more negative (e.g. -37) will be less than (e.g. -5) as it is closer to the number 0.

Now that we know how to order the negative numbers, we can order them into order, and for ordering the positive numbers, we should already know how to do that.

So, now, in order from Greatest to Least. We can order them by what I said above.

3.80>1.62>-0.5>-4.666

We can convert the numbers back into their original form by looking at how we converted them in the Simplification section.

Final Answer

After converting them into a way that we can comprehend, we get our final answer in terms of greatest to least as:

\frac{19}{5}>1.62>-0.5>\frac{-14}{3}

Cheers!

6 0
2 years ago
Questions (no partial grades if you don't show your work) 1. In a group of 6 boys and 4 girls, four children are to be selected.
mariarad [96]

Answer:

Total number of ways will be 209

Step-by-step explanation:

There are 6 boys and 4 girls in a group and 4 children are to be selected.

We have to find the number of ways that 4 children can be selected if at least one boy must be in the group of 4.

So the groups can be arranged as

(1 Boy + 3 girls), (2 Boy + 2 girls), (3 Boys + 1 girl), (4 boys)

Now we will find the combinations in which these arrangements can be done.

1 Boy and 3 girls = ^{6}C_{1}\times^{4}C_{3}=6\times4=24

2 Boy and 2 girls=^{6}C_{2}\times^{4}C_{2}=\frac{6!}{4!\times2!}\times\frac{4!}{2!\times2!}=15\times6=90

3 Boys and 1 girl = ^{6}C_{3}\times^{4}C_{1}=\frac{6!}{4!\times2!}\times\frac{4!}{3!}=\frac{6\times5\times4}{3 \times2} \times4=80

4 Boys = ^{6}C_{4}=\frac{6!}{4!\times2!} =\frac{6\times 5}{2\times1}=15

Now total number of ways = 24 + 90 + 80 + 15 = 209

7 0
3 years ago
Talia has a daily budget of $94 for a car rental. Write and solve an inequality to find the greatest distance Talia can drive ea
MariettaO [177]

Answer:

Step-by-step explanation:

Distance traveled by Talia = x

Cost for travelling 'x' miles = x * 0.20 = 0.2x

Daily budget = $94

Inequality,

30 + 0.2x ≤ 94

Solution:

0.2x ≤ 94 - 30      

0.2x ≤ 64        {Divide both sides by 0.2

   x ≤ 64/0.2

 x ≤ 320

4 0
2 years ago
Read 2 more answers
The base of a pyramid is a rectangle with a width of 4.6cm and a length of 9cm.What is the height,in centimeters of the pyramid
den301095 [7]

Answer:

Step-by-step explanation:

The formula for determining the the volume of a rectangular base pyramid is expressed as

Volume = 1/3 × base area × height

From the information given,

Length of base = 9 cm

Width of base = 4.6 cm

Area of base = 9 × 4.6 = 41.4 cm²

Volume of pyramid = 82.8cm³

Therefore

82.8 = 1/3 × 41.4 × height

82.8 = 13.8 × height

Dividing both sides of the equation by 13.8, it becomes

height = 82/13.8

Height = 5.94 8 cm

4 0
3 years ago
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