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3 years ago

−4n−8=4(−3n+2) solve for n

Mathematics

1 answer:

IRINA_888 [86]3 years ago

5 0

-4n-8=-12n+8
-4n+12n=8+8
collect the like terms
8n=8+8 then you add 8+8
8n=16 divide both sides by 8
n=2

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Solving by the substitution method y=3x+7 y-5x+8

Sveta_85 [38]

3x+7-5x=8
-2x+7=8
-2x=1
X=-1/2
y=3(-1/2)+7
y=-1.5+7
y=5.5

6 0

3 years ago

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

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zvonat [6]

Answer:

1: male + female $\leq$ 30

2: 140 + 25x $\geq$ 550

Step-by-step explanation:

8 0

3 years ago

Question 2(Multiple Choice Worth 5 points) (04.01)The Boardman family walked two over five of a mile in two over seven of an hou

Zolol [24]

Answer:

The unit rate in miles per hour = 1.4 miles/hr

Step-by-step explanation:

Given that:

Distance walked by Boardman family = Two over five of a mile = $\frac{2}{5}\ miles$

Time taken by Boardman family = Two over seven of an hour = $\frac{2}{7}\ hour$

To find:

The unit rate in the miles per hour = ?

Solution:

Formula for the rate or the speed can be given as:

$Speed = \dfrac{Distance}{Time}$

Putting the values:

$\Rightarrow \dfrac{\frac{2}5}{\frac{2}7}\\\Rightarrow \dfrac{7}{5}\\\Rightarrow \bold{1.4\ miles/hr}$

So, the unit rate in miles per hour = 1.4 miles/hr

4 0

3 years ago

Use synthetic division to show that the number given to the right of the equation is a solution of the equation. Then solve the

AysviL [449]

Answer:

$x = 2 \: or \: x = - 2 \: or \: x = - \frac{1}{2}$

Step-by-step explanation:

The given polynomial equation is

$2 {x}^{3} + {x}^{2} - 8x - 4 = 0$

We perform the synthetic division as shown in the attachment by dividing by x-2.

This gives a remainder of 0 and a quotient of

$2 {x}^{2} + 5x + 2$

This means the polynomial equation becomes:

$(x - 2)(2 {x}^{2} + 5x + 2) = 0$

We factor the quadratic term by splitting the middle term;

$(x - 2)(2 {x}^{2} + 4x +x + 2) = 0$

$(x - 2)(2 x(x+ 2) +1(x + 2) )= 0$

Collect common factors again:

$(x - 2)((x+ 2)(2x + 1) = 0$

The solution is:

$x = 2 \: or \: x = - 2 \: or \: x = - \frac{1}{2}$

8 0

4 years ago