A) Work out the value of 23 + 52

Find the area of the shaded region. (Plz show work)

Kamila [148]

Answer:

Area of shaded region ≈ 192.42

Step-by-step explanation:

21/2 = radius

radius = 10.5 m

A = πr squared

Area of shaded region≈346.36

10.5 - 3.5 = 7

Area of unshaded region ≈ 153.94

346.36 - 153.94 = 192.42

8 0

3 years ago

Find the equation of the line that is parallel to the given line and passes through the given point

Sati [7]

Answer:

$\huge\boxed{y=-\dfrac{1}{4}x-1\to x+4y=-4}$

Step-by-step explanation:

$\text{Let}\ k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\l\ ||\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\==========================\\\\\text{We have}\ x+4y=-6.\\\text{Convert to the slope-intercept form:}\\\\x+4y=-6\qquad\text{subtract}\ x\ \text{from both sides}\\\\4y=-x-6\qquad\text{divide both sides by 4}\\\\y=\dfrac{-x}{4}-\dfrac{6}{4}\\\\y=-\dfrac{1}{4}x-\dfrac{3}{2}\to m_1=-\dfrac{1}{4}$

$\text{Lines are to be parallel. Therefore}\ m_2=-\dfrac{1}{4}.\\\\\text{We initially have the form equation}\ y=-\dfrac{1}{4}x+b.\\\\\text{The line passes through the point}\ (9,\ -3).\\\\\text{Substitute the coordinates of the point to the equation of a line:}\\\\x=9,\ y=-3\\\\-3=-\dfrac{1}{4}(9)+b\\\\-3=-\dfrac{9}{4}+b\qquad\text{add}\ \dfrac{9}{4}\ \text{to both sides}\\\\-\dfrac{12}{4}+\dfrac{9}{4}=b\to b=-\dfrac{3}{4}$

$\text{Lines are to be parallel. Therefore}\ m_2=-\dfrac{1}{4}.\\\\\text{We initially have the form equation}\ y=-\dfrac{1}{4}x+b.\\\\\text{The line passes through the point}\ (8,\ -3).\\\\\text{Substitute the coordinates of the point to the equation of a line:}$

$x=8,\ y=-3\\\\-3=-\dfrac{1}{4}(8)+b\\\\-3=-2+b\qquad\text{add 2 to both sides}\\\\-1=b\to b=-1$

$\text{Therefore the equation is:}\ y=-\dfrac{1}{4}x-1.\\\\\text{Convert to the standard form}\ Ax+By=C:\\\\y=-\dfrac{1}{4}x-1\qquad\text{multiply both sides by 4}\\\\4y=-x-4\qquad\text{add}\ x\ \text{to both sides}\\\\x+4y=-4$

5 0

3 years ago

105 people must be split into 3 equal groups. How many people in each group?

Allisa [31]

Answer:

35 people in each

Step-by-step explanation:

105÷3=35

6 0

2 years ago

What does (f(x)) mean in math for a input and output graph?

shtirl [24]

In maths, f (x) means as a special relationship where every single input has one output.

<u>Step-by-step explanation:</u>

In mathematics, a function is any expression that gives exactly one answer for each particular number. Input is the number provided in the expression, and output is the number obtained from the search or calculation.

In an ordered pair, input’s first number corresponds to the horizontal axis, and output’s second number in the vertical axis. These ordered pairs can then be plotted. Some data on the costs associated with this are called relationships. For example,

$f(x)=x^{2}$

It is often written as "f (x)" where x is the input value and $x^{2}$ is the output value.

3 0

3 years ago

i need help on math

dolphi86 [110]

X=2
2x-3=-x+3

add three to both sides
add 1x to each side
should be left with 3x=6
divide both sides by 3 to get x alone
your answer then is x=2

7 0

3 years ago