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sasho [114]
3 years ago
10

Two consecutive odd integers have a sum of 48 . find the integers. ,

Mathematics
1 answer:
AlladinOne [14]3 years ago
5 0
Two consecutive odd integers have a sum of 48 . find the integers.

Two consecutive odd integers:
2x+1, 2x+3

Two consecutive odd integers have a sum of 48
2x+1+2x+3=48

find the integers:
Solve for x

2x+1+2x+3=48
4x+4=48
4x+4-4=48-4
4x=44
4/4x=44/4
x=11

sub in x=11

2x+1, 2x+3
2(11)+1, 2(11)+3
22+1, 22+3
23,25

Check: 23+25=48

23 and 25 are two consecutive odd numbers that have a sum of 48
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suter [353]

Answer:

FALSE, (2, 9) is not a solution to the set of inequalities given.

Step-by-step explanation:

Simply replace x by 2 and y by 9 in the inequalities and see if the inequality is true or not:

irst inequality:

y\geq 4x\\9\geq 4\,(2)\\9\geq 8

so thi inequality is verified as true since 9 is larger or equal than 8

Now the second inequality:

y

This is FALSE since 9 is larger than 4 (not smaller)

Therefore the answer to the question is FALSE, (2, 9) is not a solution to the set of inequalities given.

6 0
3 years ago
Find the length of the leg(s) of a right triangle, to the nearest hundredth, if both legs are equal and the hypotenuse is 10.
charle [14.2K]

Answer:

7.07 units

Step-by-step explanation:

Use the Pythagorean theorem for the right triangle:

\text{hypotenuse}^2=\text{leg}_1^2+\text{leg}_2^2,\\ \\c^2=a^2+b^2.

If a = x, b = x, and c = 10, then

10^2=x^2+x^2,\\ \\100=2x^2,\\ \\x^2=50,\\ \\x=\sqrt{50}=5\sqrt{2}\approx 7.07\ units.

7 0
3 years ago
A triangle has side lengths of 9 in, 13 in, and 20 in. What is the measurement of this triangle's largest angle?
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1. Given any triangle ABC with sides BC=a, AC=b and AB=c, the following are true :

     i) the larger the angle, the larger the side in front of it, and the other way around as well. (Sine Law) Let a=20 in, then the largest angle is angle A.

      ii) Given the measures of the sides of a triangle. Then the cosines of any of the angles can be found by the following formula:

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2.

20^{2}=9 ^{2}+13 ^{2}-2*9*13(cosA)

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cosA=150/-234= -0.641

3. m(A) = Arccos(-0.641)≈130°,

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