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max2010maxim [7]

3 years ago

6

Expand the brackets 7x+5-3(x-4)

1 answer:

aleksklad [387]3 years ago

8 0

Answer:

7x+5-3x+12

7x-3x+12+5

4x+17

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Assume that the terminal side of thetaθ passes through the point (negative 12 comma 5 )(−12,5) and find the values of trigonomet

zmey [24]

Answer:

$\sin \theta = \dfrac{5}{13}$ and $\sec \theta = -\dfrac{13}{12}$

Step-by-step explanation:

Assume that the terminal side of thetaθ passes through the point (−12,5).

In ordered pair (-12,5), x-intercept is negative and y-intercept is positive. It means the point lies in 2nd quadrant.

Using Pythagoras theorem:

$hypotenuse^2=perpendicular^2+base^2$

$hypotenuse^2=(5)^2+(12)^2$

$hypotenuse^2=25+144$

$hypotenuse^2=169$

Taking square root on both sides.

$hypotenuse=13$

In a right angled triangle

$\sin \theta = \dfrac{opposite}{hypotenuse}$

$\sin \theta = \dfrac{5}{13}$

$\sec \theta = \dfrac{hypotenuse}{adjacent}$

$\sec \theta = \dfrac{13}{12}$

In second quadrant only sine and cosecant are positive.

$\sin \theta = \dfrac{5}{13}$ and $\sec \theta = -\dfrac{13}{12}$

6 0

3 years ago

SOLVING EACH SYSTEM BY ELIMINATION <br><br><br> x+3y=5 x=-6y+14<br><br><br> HELP

nata0808 [166]

Answer:

$\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}$

$x=-4,\:y=3$

Step-by-step explanation:

Given the system of the equations

$x+3y=5;\:x=-6y+14$

solving by elimination method

$\begin{bmatrix}x+3y=5\\ x=-6y+14\end{bmatrix}$

$\mathrm{Arrange\:equation\:variables\:for\:elimination}$

$\begin{bmatrix}x+3y=5\\ x+6y=14\end{bmatrix}$

$x+6y=14$

$-$

$\underline{x+3y=5}$

$3y=9$

$\begin{bmatrix}x+3y=5\\ 3y=9\end{bmatrix}$

solve $3y=9$ for $y$ :

$3y=9$

$\frac{3y}{3}=\frac{9}{3}$

$y=3$

$\mathrm{For\:}x+3y=5\mathrm{\:plug\:in\:}y=3$

Solve $x+3\cdot \:3=5$ for x:

$x+3\cdot \:3=5$

$x+9=5$

$x=-4$

Therefore,

$\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}$

$x=-4,\:y=3$

6 0

2 years ago

Solve the proportion: 35/8 = 105/x

dangina [55]

Answer:

x=24

Step-by-step explanation:

6 0

2 years ago

6.875 rounded to the nearest gram

zhenek [66]

Answer: 6.9

Step-by-step explanation: Find the number in the tenth place 8

and look one place to the right for the rounding digit 7. Round up if this number is greater than or equal to 5 and round down if it is less than 5.

6.9

7 0

2 years ago

What is the 103rd term of the arithmetic sequence

UNO [17]

Answer:

option B: 31/4

Step-by-step explanation:

Given

-3/4, -2/3 , -7/12, -1/2...........

General formula for arithmeti sequence to find nth term is

a_n = a_1 + (n-1) d

first term a_1 = -3/4

We find out common difference 'd'

Lets find the difference of first two terms

$\frac{-2}{3} -\frac{-3}{4} = \frac{-8}{12} +\frac{9}{12} =\frac{1}{12}$

common difference is 1/12

now we need to find 103rd term

$a_n = a_1 + (n-1) d$

First term is -3/4, d= 1/12

$a_{103} = \frac{-3}{4}+(103-1)\frac{1}{12}$

$a_{103} = \frac{-3}{4}+(102)\frac{1}{12}$

$a_{103} = \frac{-3}{4}+\frac{34}{4}$

$a_{103} = \frac{-3+34}{4}$

$a_{103} = \frac{31}{4}$

5 0

2 years ago

Read 2 more answers