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1 year ago

The sum of three consecutive numbers is equal to 4 times the largest number minus 29. What is the smallest of the three numbers?

Mathematics

1 answer:

gulaghasi [49]1 year ago

5 0

The smallest of the three consecutive integers is 24.

<h3>How to solve algebraic word problems?</h3>

Let the 3 consecutive integers be;

x, y and z

Thus;

y = x + 1

z = x + 2

Now, we are told that their sum is equal to 4 times the largest number minus 29. Thus;

x + x + 1 + x + 2 = 4(x + 2) - 29

3x + 3 = 4x + 8 - 29

4x - 3x = 3 + 21

x = 24

Thus, we can conclude that the smallest of the three consecutive integers is 24.

Read more about algebra word problems at; brainly.com/question/13818690

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SVETLANKA909090 [29]

Answer:

Option (3)

Step-by-step explanation:

w = $\frac{\sqrt{2}}{2}[\text{cos}(225) + i\text{sin}(225)]$

Since, cos(225) = cos(180 + 45)

= -cos(45) [Since, cos(180 + θ) = -cosθ]

= - $\frac{\sqrt{2}}{2}$

sin(225) = sin(180 + 45)

= -sin(45)

= - $\frac{\sqrt{2}}{2}$

Therefore, w = $\frac{\sqrt{2}}{2}[-\frac{\sqrt{2}}{2}+i(-\frac{\sqrt{2}}{2})]$

= $-\frac{2}{4}(1+i)$

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z = 1[cos(60) + i(sin(60)]

= $[\frac{1}{2}+i(\frac{\sqrt{3}}{2})$

= $\frac{1}{2}(1+i\sqrt{3})$

Now (w + z) = $-\frac{1}{2}(1+i)+\frac{1}{2}(1+i\sqrt{3})$

= $-\frac{1}{2}-\frac{i}{2}+\frac{1}{2}+i\frac{\sqrt{3}}{2}$

= $\frac{(i\sqrt{3}-i)}{2}$

= $\frac{(\sqrt{3}-1)i}{2}$

Therefore, Option (3) will be the correct option.

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2 years ago

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djyliett [7]

Answer:

A) -7/9

Step-by-step explanation:

-4(x + 4x) = 2(2 - x) + 10

-4x - 16x = 4 - 2x + 10

-4x - 16x + 2x - 4 - 14 = 0

-18x -14 = 0

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x = - 7/9

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2 years ago

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Ket [755]

Answer:

Step-by-step explanation:

Let's test these values using the Pythagorean Theorem.

a^2+b^2=c^2

where a and b are the legs and c is the hypotenuse.

a and b are the legs, or the shorter sides. 5 and 12 are the shorter sides, so they are a and b.

c is the hypotenuse, or the longest side. 14 is the longest side, so it is c.

5^2+12^2=14^2

Evaluate all the exponents

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Add 25 and 144

169=196

169 $\neq$ 196

169 is not equal to 196, so 5, 12 and 14 cannot be a Pythagorean Triple

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2 years ago

The number of runs scored by the home team at a base ball game is represented by (x + 7). The number of runs scored by the visit

jok3333 [9.3K]

Given :

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An expression to find how many more runs the home team scored than the visiting team. Then evaluate the expression if the value of x is 6.

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Let, number of more runs the home team scored than the visiting team is R.

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Now, putting value of x = 6 in above equation, we get :

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