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3 years ago

the sum of two numbers is 57. if the larger of the two numbers is 9 less than twice the smaller, find the two numbers

Mathematics

1 answer:

svp [43]3 years ago

7 0

Answer:

The answer is 35 and 22

Because:

U let the numbers(#) be x and y (x will be the larger number and y the smaller number

So:

x + y =57

x = 2*y - 9

Therefore,

{2*y - 9} + y = 57

Leaving the two numbers 35 and 22

I hope I could help

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Angle (theta) is in standard position. If (8,-15) is on the terminal ray of angle (theta), find the values of the trigonometric

mariarad [96]

Answer:

$\sin \theta =\frac{-15}{17}\\cos \theta =\frac{8}{17}\\\tan \theta =\frac{-15}{8}\\\csc \theta =\frac{-17}{15}\\\sec \theta =\frac{17}{8}\\\cot \theta =\frac{-8}{15}$

Step-by-step explanation:

Given: (8,-15) is on the terminal ray of angle

To find: All the trigonometric ratios

Solution:

Trigonometry is a branch of mathematics that explain relationship between the sides and angles of triangles.

If (x, y) lies on the terminal side of θ then $r=\sqrt{x^2+y^2}$

$r=\sqrt{(8)^2+(-15)^2}=\sqrt{64+225}=\sqrt{289}=17$ units

$\sin \theta =\frac{y}{r}=\frac{-15}{17}\\cos \theta =\frac{x}{r}=\frac{8}{17}\\\tan \theta =\frac{y}{x}=\frac{-15}{8}\\\csc \theta =\frac{1}{\sin \theta }=\frac{-17}{15}\\\sec \theta =\frac{1}{cos \theta}=\frac{17}{8}\\\cot \theta =\frac{1}{\tan \theta}=\frac{-8}{15}$

6 0

3 years ago

you are given numbers, {30 + n, n/3, square root n+16}. Find the smallest value of n so that all of the numbers in the set are n

Juli2301 [7.4K]

<h3>Answer: n = 9</h3>

========================================================

Explanation:

Let's assume that n is not negative. If we tried the smallest nonnegative value, n = 0, then we get

30+n = 30+0 = 30
n/3 = 0/3 = 0
sqrt(n+16) = sqrt(0+16) = 4

The middle result 0 isn't a natural number. The set of natural numbers is {1,2,3,4,...} which is the set of positive whole numbers.

So we can't use n = 0.

Through trial and error, you should find that n = 9 is the next value we can try such that sqrt(n+16) is a natural number, and so is n/3.

If n = 9, then,

30+n = 30+9 = 39
n/3 = 9/3 = 3
sqrt(n+16) = sqrt(9+16) = 5

We see that the middle result is now larger than 0 and it's a natural number. The same can be said for the last result as well.

7 0

3 years ago

What is the correct justification for the first step in solving this

Bas_tet [7]

The correct justification for the first step in solving the provided equation is that the first step should be distributive Property

<h3>What is the property of equality?</h3>

Property of equality says that by performing any mathematical operation, of both sides of a expression does not change the original value of the equation.

The equation given in the problem is,

$3(x - 4) + 1 = 12x$

To solve the above equation, we need to open the brackets of the equation. To do this, we need to use the distributive property of the equality.

This can be done by multiplying the number 3 inside the bracket (x-4). This operation simplify the equation, to solve it further. Therefore,

$3x - 3\times4 + 1 = 12x\\3x - 12 + 1 = 12x$

Hence, the correct justification for the first step in solving the provided equation is that the first step should be distributive Property.

Learn more about the property of equality here;

brainly.com/question/1601404

4 0

3 years ago

Read 2 more answers

Y = f(x) = 16x Find f(x) when x = 1/2

Alina [70]

Answer:

The answer depends on what the problem really is.

f(1/2) = 8

f(1/2) = 4

See below.