Find the measure of angle 3.

statuscvo [17]

First differences are ... 0-7 = -7, -1-0 = -1, 4-(-1) = 5, 15-4 = 11, 32-15 = 17.

Second differences are -1-(-7) = 6, 5-(-1) = 6, 11-5 = 6, 17-11 = 6.

The second differences are constant at 6, so the table values would be best fit by a function that is ...

quadratic

_____

The degree of the polynomial function corresponds to the level of differences that are constant (when the x-values are evenly spaced).

The quadratic function that matches these values is

... y = 3x² +2x -1

... y = (3x-1)(x+1) . . . . in factored form

7 0

3 years ago

What is the solution to log 2 (2x^3 -8 )-2log 2 x=log 2x

Fantom [35]

Answer:

x=9

Step-by-step explanation:

8 0

3 years ago

Solve the system of equations.

emmainna [20.7K]

$x = \frac{ 419 }{ 113 } ~,~y = -\frac{ 208 }{ 113 } ~,~z = \frac{ 21 }{ 113 }$

<h2>Explanation:</h2>

We have the following system of three linear equations:

$\begin{array}{ cccc }2~ x&+~~4~ y&+~~32~ z&~=~6\\5~ x&+~~8~ y&+~~~~ z&~=~4\\4~ x&+~~5~ y&+~~2~ z&~=~6\end{array}$

Let's use elimination method in order to get the solution of this system of equation, so let's solve this step by step.

Step 1: Multiply first equation by $-5/2$ and add the result to the second equation. So we get:

$\begin{array}{ cccc }2~ x&+~~4~ y&+~~32~ z&~=~6\\&-~~~2~ y&-~~~79~ z&~=~-11\\4~ x&+~~5~ y&+~~2~ z&~=~6\end{array}$

Step 2: Multiply first equation by −2 and add the result to the third equation. So we get:

$\begin{array}{ cccc }2~ x&+~~4~ y&+~~32~ z&~=~6\\&-~~~2~ y&-~~~79~ z&~=~-11\\&-~~~3~ y&-~~~62~ z&~=~-6\end{array}$

Step 3: Multiply second equation by −32 and add the result to the third equation. So we get:

$\begin{array}{ cccc }2~ x&+~~4~ y&+~~32~ z&~=~6\\&-~~~2~ y&-~~~79~ z&~=~-11\\&&+~~\frac{ 113 }{ 2 }~ z&~=~\frac{ 21 }{ 2 }\end{array}$

Step 4: solve for z.

$\begin{aligned} \frac{ 113 }{ 2 } ~ z & = \frac{ 21 }{ 2 } \\ z & = \frac{ 21 }{ 113 } \end{aligned}$

Step 5: solve for y.

$\begin{aligned}-2y-79z &= -11\\-2y-79\cdot \frac{ 21 }{ 113 } &= -11\\y &= -\frac{ 208 }{ 113 } \end{aligned}$

Step 6: solve for x by substituting $y=-\frac{208}{113}$ and $z = \frac{21}{113}$ into the first equation:

$2x+4(-\frac{208}{113})+32(\frac{21}{113})=6 \\ \\ 2x-\frac{832}{113}+\frac{672}{113}=6 \\ \\ 2x=6+\frac{832}{113}-\frac{672}{113} \\ \\ 2x=\frac{838}{113} \\ \\ x=\frac{319}{113}$

Finally:

$x = \frac{ 419 }{ 113 } ~,~y = -\frac{ 208 }{ 113 } ~,~z = \frac{ 21 }{ 113 }$

<h2>Learn more:</h2>

Solving System of Equations: brainly.com/question/13121177

#LearnWithBrainly

7 0

4 years ago

eva is working two summer jobs, making $9 per hour landscaping and $14 per hour clearing tables. Last week eva earned a total of

Mariulka [41]

so she makes $23 each hour because 9+14=23
last week she earned a total of $74? and worked as twice as many hours..ok so she worked about 3 hours last week

4 0

3 years ago

What is the value of r? 3/5(r−7)=1 Enter your answer in the box.

Andrew [12]

try 5.5 or 5 1/2 I hope this helps!

3 0

4 years ago

Find the measure of angle 3.​

Find the measure of angle 3.