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3 years ago

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Four times a number added to 3 times a larger number is 31. Seven subtracted from the larger number is equal to twice the smalle

r number. Let x represent the smaller number and y represent the larger number. Which equations represent this situation?

2 answers:

aev [14]3 years ago

5 0

Let the smaller number be x.
Let the bigger number be y.

$\begin{cases} &4x + 3y = 31 \tex{ ----- (1) } \\ &y- 7 = 2x \tex{ ----- (2) } \end{cases}$

Rearrange equation (2):
$\begin{cases} &4x + 3y = 31 \tex{ ----- (1) } \\ &y = 2x + 7 \tex{ ----- (2) } \end{cases}
$

Sub (2) into (1):

$4x + 3(2x + 7 ) = 31$
$4x + 6x + 21 = 31$
$10x + 21 = 31$
$10x = 10$
$x = 1$

Sub x = 1 into (2):

$y = 2x + 7$
$y = 2(1) + 7$
$y= 9$

Answer: The two numbers are 1 and 9.

Gelneren [198K]3 years ago

3 0

4x+3y=31

y-7=2x

(y-7)/2=x

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Write each expression as an algebraic (nontrigonometric) expression in u, u > 0.

max2010maxim [7]

Answer:

$\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0$

Step-by-step explanation:

We want to write the trignometric expression:

$\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)\text{ where } u>0$

As an algebraic equation.

First, we can focus on the inner expression. Let θ equal the expression:

$\displaystyle \theta=\sec^{-1}\left(\frac{u}{10}\right)$

Take the secant of both sides:

$\displaystyle \sec(\theta)=\frac{u}{10}$

Since secant is the ratio of the hypotenuse side to the adjacent side, this means that the opposite side is:

$\displaystyle o=\sqrt{u^2-10^2}=\sqrt{u^2-100}$

By substitutition:

$\displaystyle= \sin(2\theta)$

Using an double-angle identity:

$=2\sin(\theta)\cos(\theta)$

We know that the opposite side is √(u² -100), the adjacent side is 10, and the hypotenuse is u. Therefore:

$\displaystyle =2\left(\frac{\sqrt{u^2-100}}{u}\right)\left(\frac{10}{u}\right)$

Simplify. Therefore:

$\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0$

4 0

3 years ago

Help please and thanks! I always give brainliest! (Explain too please)

qwelly [4]

Answer:

A. 2/3

Opposite Sides of a Parallelogram

The two pairs of sides in a parallelogram are parallel to each other.

Parallel lines have the same slope.

The slope of the opposite sides of a parallelogram are congruent (equal in measure).

Given:

Slope of PQ = 2/3

Slope of QR = -1/2

For PQRS to be a parallelogram, the slope of SR must be same as the slope of PQ.

This implies that: Slope of SR = Slope of PQ = 2/3.

Therefore, based on the properties of a parallelogram, the slope of SR for PQRS to be a parallelogram would be: 2/3.

4 0

3 years ago

The sum of an infinite geometric series is 450, while the common ratio of the series is 4/ 5 . What is the first term of the ser

pogonyaev

Answer:

answer is 90 for first term

Step-by-step explanation:

Let the terms be

First term x

We will use the formula s∞=x/1−r to find the sum of an infinite geometric series, where −1<r<1.

We know the sum and the common ratio, so we'll be solving for x where r =4/5

s∞=x/1−r

450=x/1−4/5

450=x/1/5

450=5x

x=90

this is the first term x1 = 90

we know that common ratio is 4/5, so multiplying the first term by factor 4/5 to get the second term

90 x 4/5= 72 second term

7 0

4 years ago

Read 2 more answers

45% of $360 is what as a quantity

Bess [88]

I'm assuming you want to know what 45% of 360 is.....

so you multiply 360 by 0.45 (since 45 is a percent, and to revert it back, you must move the decimal 2 times to the left) and you have your answer...

5 0

4 years ago

What would the answer be???

Korolek [52]

Answer:

The solution is obtained by adding the two equations.

The solution is: (x, y) = ( $- \frac{2}{3}$ , $- \frac{7}{3}$ )

Step-by-step explanation:

We are given two equations with two variables. The strategy is to eliminate one variable and solve for both the variables.

The two equations are:

$7x + y = - 7 \hspace{15mm} \hdots (1)$

$2x - y = 1 \hspace{15mm} \hdots (2)$

Adding both the equations, we get:

$7x + 2x + y - y = - 7 + 1$

$\implies 9x = - 6$

$\implies x = - \frac{2}{3}$

Substituting the value of 'x', we get the value of y.

We substitute in (2). [Can be substituted in any equation].

We get: y = 2x - 1

$\imples y = 2\bigg(\frac{-2}{3}\bigg) - 1$

$\implies -\frac{4}{3} - 1$

$\implies y = -\frac{7}{3}$

So, we get the corresponding values of x and y which is the solution of the two equations.

4 0

3 years ago