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3 years ago

Three consecutive integers have a sum of 87. Find the integers.

Mathematics

2 answers:

ozzi3 years ago

8 0

Answer:

28, 29, 30

Step-by-step explanation:

Let the integers be x- 1, x and x +1, then:

x - 1 + x + x + 1 = 87
3x = 87
x = 29

The integers are 28, 29, 30

taurus [48]3 years ago

3 0

Answer:

Let the numbers be (x-1), x and (x+1)

According to the above problem,

$(x - 1) + x + (x + 1) = 87 \\ 3x = 87 \\ \boxed{x = 29}$

Therefore, the numbers are 28, 29 and 30.

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elena55 [62]

Answer:

That would be C, 9:25

Step-by-step explanation:

That is because you would dividing the number of boys over number of girls riding bikes. 45/125. Then in simplest form, the fraction will be 9/25, meaning in ratio it is 9:25

Hope it helps:)

6 0

3 years ago

(secx-tanx)(secx+tanx)=1 simplify

tigry1 [53]

Step-by-step explanation:

(secx-tanx)(secx+tanx)

=sec^2-tan^2

5 0

3 years ago

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The sum of Sasha’s and Natalie’s ages is 31. Twice Natalie’s age is 11 years more than Sasha’s age. Find each of their ages

ZanzabumX [31]

Answer:

Natalie's age is 14

Sasha's age is 17

Step-by-step explanation:

Let

Sasha's age be "s", and

Natalie's age be "n"

Sum of Sasha and Natalie is 31:

s + n = 31

Twice Natalie is 11 more than Sasha:

2n = s + 11

We ca solve this equation for s first:

s = 2n - 11

We put this into first equation and solve for n first:

s + n = 31

2n - 11 + n = 31

3n = 31 + 11

3n = 42

n = 42/3 = 14

Natalie's age is 14

Also, s = 2n - 11

s = 2(14) - 11

s = 28 - 11

s = 17

Sasha's age is 17

6 0

3 years ago

Base: z(x)=cosx Period:180 Maximum:5 Minimum: -4 What are the transformation? Domain and Range? Graph?

garik1379 [7]

Answer:

The transformations needed to obtain the new function are horizontal scaling, vertical scaling and vertical translation. The resultant function is $z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)$ .

The domain of the function is all real numbers and its range is between -4 and 5.

The graph is enclosed below as attachment.

Step-by-step explanation:

Let be $z (x) = \cos x$ the base formula, where $x$ is measured in sexagesimal degrees. This expression must be transformed by using the following data:

$T = 180^{\circ}$ (Period)

$z_{min} = -4$ (Minimum)

$z_{max} = 5$ (Maximum)

The cosine function is a periodic bounded function that lies between -1 and 1, that is, twice the unit amplitude, and periodicity of $2\pi$ radians. In addition, the following considerations must be taken into account for transformations:

1) $x$ must be replaced by $\frac{2\pi\cdot x}{180^{\circ}}$ . (Horizontal scaling)

2) The cosine function must be multiplied by a new amplitude (Vertical scaling), which is:

$\Delta z = \frac{z_{max}-z_{min}}{2}$

$\Delta z = \frac{5+4}{2}$

$\Delta z = \frac{9}{2}$

3) Midpoint value must be changed from zero to the midpoint between new minimum and maximum. (Vertical translation)

$z_{m} = \frac{z_{min}+z_{max}}{2}$

$z_{m} = \frac{1}{2}$

The new function is:

$z'(x) = z_{m} + \Delta z\cdot \cos \left(\frac{2\pi\cdot x}{T} \right)$

Given that $z_{m} = \frac{1}{2}$ , $\Delta z = \frac{9}{2}$ and $T = 180^{\circ}$ , the outcome is:

$z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)$

The domain of the function is all real numbers and its range is between -4 and 5. The graph is enclosed below as attachment.

8 0

3 years ago

Subtract 6 2/3 - 4 4/9

Orlov [11]

6 2/3 = 20/3 = 60/9

4 4/9 = 40/9

60/9 - 40/9 = 20/9 = 2 2/9

5 0

3 years ago

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