George is afraid of falling off his roof, but he needs to measure to measure his roof so he can re-shingle it.

What is the measure of AB?​

Answer:

- Inverse Variation

- Equation: [tex]XY = 12[/tex]

Step-by-step explanation:

Given

X-> 2 | 4 | 8 | 12

Y-> 6 | 3 | 3/2 | 1

Required

- State the type of variation the table represents

- Determine the equation to model the data

To check for type of variation; we'll make use of trial by error method.

To start with; We'll check for direct variation.

This is done using the following expression;

[tex]Y = kX[/tex]where k is the constant of variation

Make k the subject of formula

[tex]k = \frac{Y}{X}[/tex]

When Y = 6, X= 2

[tex]K = \frac{6}{2} = 3[/tex]

When Y = 3, X = 4

[tex]K = \frac{3}{4}[/tex]

There's no need to check further as both values of k are not equal

To check for inverse variation;

[tex]Y = \frac{k}{X}[/tex]

Make k the subject of formula

[tex]k = YX[/tex]

When Y = 6, X= 2

[tex]K = 6 * 2 = 12[/tex]

When Y = 3, X = 4

[tex]K = 3 * 4 = 12[/tex]

When Y = 3/2; X = 8

[tex]K = \frac{3}{2} * 8 = \frac{24}{2} = 12[/tex]

When Y = 1, X = 12

[tex]K = !2 * 1 = 12[/tex]

Note that for all values of X and Y, K remains constant;

Hence, the table represents an inverse direction

To determine the equation;

We make use of  [tex]k = YX[/tex]

Substitute 12 for k

So, the equation becomes

[tex]12 = XY[/tex]

Reorder

[tex]XY = 12[/tex]

Hence, the equation is [tex]XY = 12[/tex]

Answer:

4.5

Step-by-step explanation:

Let the number be x

6x-14 = 40

Add 14

6x = 40+14

6x = 54

Divide by 6

6x/6 = 54/6

x = 9

We want 1/2 of the number

1/2 of 9 is 4.5

Answer:

a) 78°

b) 39°

Step-by-step explanation:

In circle with center O, DE is tangent at point A and AC is chord (or secant if extended both sides).

Therefore by tangent secant theorem.

[tex] m\angle CAE = \frac{1}{2} \times m\widehat{(AC)} \\\\

\therefore 39\degree = \frac{1}{2} \times m\widehat{(AC)} \\\\

\therefore m\widehat{(AC)} = 39\degree\times 2\\

\red{\bold{\therefore m\widehat{(AC)} = 78\degree}}\\[/tex]

Since, measure of central angle of a circle is equal to the measure of its corresponding minor arc.

[tex] \therefore m\angle AOC = m\widehat{(AC)}\\

\huge \purple {\boxed {\therefore m\angle AOC = 78\degree}} \\[/tex]

Next, by inscribed angle theorem:

[tex] m\angle CBA = \frac{1}{2}\times m\widehat{(AC)}\\\\

\therefore m\angle CBA = \frac{1}{2}\times 78\degree \\\\

\therefore m\angle CBA =39\degree \\\\

\huge \orange{\boxed {\therefore m\angle OBA = 39\degree}}\\... (\because C-O-B) \\[/tex]

Answer:

its wht u r searching for...

Answer:

Solution,

Principal=$1200

Rate=3%=3/100=0.03

Interest=$108

Time=?

Now,

[tex]t = \frac{i}{p \times r} [/tex]

[tex] = \frac{108}{1200 \times 0.03} \\ = \frac{108}{36} \\ = 3 \: years[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

38

Step-by-step explanation:

The most occuring number is the mode, which in this case is 38.

Answer: 38

Step-by-step explanation:

The mode of a data set is the number that shows up the most, in this case 38, which shows up 7 times.

Hope it helps <3

Answer:

in this expression, -2 is the coefficient.

Step-by-step explanation:

We know that, a coefficient is the number or value placed before a variable in an algebraic expression. here, the only variable is x, so, the coefficient is -2.

in other words, we can say that -2 is the coefficient of x.

Answer: -2

Step-by-step explanation:

Answer:

y= 2x +12

Step-by-step explanation:

Given:

The line parallel to the given has the same slope of 2, let's find the intercept using the given point:

So the equation is:

Answer: A

Slope = -6

Step-by-step explanation:

Given that the column of the table are:

Column X (-2,-1,0,1,2) and

Column Y (8,2,-4,-10,-16) 

Since the table represent a linear function, the equation of the function will obey the general linear equation

Y = MX + C

Where M = slope

M = ( Y2 - Y1 ) / ( X2 - X1 )

Let Y1 = 8, Y2 = 2 and X1 = -2 and X2 = -1

Substitutes all the parameters into the formula

M = ( 2 - 8 )/( -1 - - 2 )

M = ( 2 - 8 ) / ( -1 + 2 )

M = -6/1

M = -6

Therefore, the slope of the function is -6

Answer:

6

Step-by-step explanation:

4x-8=16

4x=16+8

4x=24

x=24÷4

x=6

if there are 54 in total, and 32 are women, that means 22 are men, we get this by subtracting 32 from 54 (54-32).

then if 18 of the 41 are male, who are right handed, subtract 18 from 41  (41-18) to get 23. that means there are 23 right handed women.

then we do 32-23 to get 9, this is how many left handed women there are.

then we do 22-18 which is 4. there are 4 left handed males

Answer:

X is a missing number . Find the missing number then multiply for example that 8 to the x then what the x is it’s the same number for all

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given,

Radius ( r ) = 1 m

Height (h) = 10 m

Surface area of cylinder= ?

Now,

Surface area of cylinder :

[tex]2\pi \: {r}^{2} + 2\pi \: r \: h[/tex]

[tex] = 2\pi \: r \: (r + h)[/tex]

[tex] = 2\pi \: \times 1(1 + 10)[/tex]

[tex] = 2\pi \: \times 1 \: \times 11[/tex]

[tex] = 22\pi[/tex]

[tex] = 22 \: \times 3.14[/tex]

[tex] = 69.08 \: {m}^{2} [/tex]

Hope this helps...

Good luck on your assignment..

Answer: I think it is “the y-value is always positive” because none of the y-values are below the x-axis, which would make them negative. Hope I helped!

Step-by-step explanation:

Slope intercept form of the equation 8x+2y=0 is y= -4x

Slope intercept form gives the graph of a straight line and is represented in the form of y=mx + c

Given,

8x+2y=0

2y =-8x

y=-4x

Hence, the Slope intercept form of the equation 8x+2y=0 is y= -4x

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Answers:

minor arc RP = 125 degrees

minor arc QS = 125 degrees

============================================================

Explanation

Definition: A minor arc is a piece of a circle such that it is smaller than a semi-circle with the same radius. In other words, it's measure is always less than 180 degrees.

Based on this definition, a minor arc is where we take the shortest path between any two points on a circle. For minor arc RP, we start at R then go to the right and take the shortest path to P. We do not go left when we start at R because that's the longer path and it is the major arc.

Minor arc RP is subtended by central angle ROP = 120 degrees. This central angle is equal to the arc measure in question. This isn't really a theorem, but more a definition if anything.

Central angle QOS is equal to angle ROP through the vertical angles theorem. Any pair of vertical angles are always congruent. Since QOS is 125 degrees, so is minor arc QS.

Answer:

Arc RP is 125, Arc QS is 125, Arc QR is 55, and arc SP is 55

Step-by-step explanation:

We know Arc QS is 125 degrees because angle QOS is a vertical angle with Angle ROS, so Arc QS is 125, and ARC RP is 125. We can figure out the other two arcs using the knowledge that ARC QR is equal to arc PS because angle QOR an SOP are vertical angles and all the degrees have to add up to 360. From this we get 2x + 125 + 125 = 360. From here we simplify and get 2x + 250 = 360; 2x = 110; x = 55, so arc QR and ARC SP are both 55.

Hope this helps :)

Answer:

A. T, U

Step-by-step explanation:

T and U are stretched across the paper. the others seem a bit close or smaller to the size of X and Y, but when you look at T and U they seem longer than X an Y

Hope this helps!!!  :)

Answer:

B)140

Step-by-step explanation:

So a line is=180 and the interior angles of a triangle= 180, so I did some manipulations

1. 100 + (5x+5) + <ECD = 180. But we also know that (21x-7) + <ECD=180. With some manipulation we can find that <ECD= 180 - (21x-7), so we can plug that into the other equation

2. Now: 100 + (5x+5) + (180- (21x-7))= 180

3. Solve:

105+5x+180-21x+7=180

112-16x=0

112=16x

x=7

4. Plug x=7 into 21x-7= 140

Answer:

mRP = 125°

mQS = 125°

mPQR = 235°

mRPQ = 305°

Step-by-step explanation:

Given that

Then:

Given that

Then:

Given that

Then:

Given that

Then:

mQOS + mROP + mQOR + mSOP = 360°

250° + 2mQOR = 360°

mQOR = (360°- 250°)/2

mQOR = mSOP = 55°

And (QOR and SOP are central angles):

Finally:

measure of arc PQR, mPQR = mQOR + mSOP + mQOS = 55° + 55° + 125° = 235°

measure of arc RPQ, mRPQ = mROP + mSOP + mQOS = 125° + 55° + 125° = 305°

Answer:

[tex]P(Male) = \frac{1}{3}[/tex]

Step-by-step explanation:

Given

[tex]Male = 4[/tex]

[tex]Female = 8[/tex]

Required

Probability of selecting a male

First, we need to get the total population;

[tex]Total = Male + Female[/tex]

[tex]Total = 4 + 8[/tex]

[tex]Total = 12[/tex]

Let P(Male) represent Probability of Male

Let n(Male) represent number of Male

[tex]P(Male) = \frac{n(Male)}{Total}[/tex]

[tex]P(Male) = \frac{4}{12}[/tex]

Simplify fraction by dividing the numerator and denominator by 4

[tex]P(Male) = \frac{1}{3}[/tex]

Hence, the probability of selecting a male is 1/3

Answer:

Option D

Step-by-step explanation:

Collect all like terms and Calculate

-10x-7x= -17x

20-54= -34

Divide

-17x < -34

x>2

Answer:

B 2 ≤x

Step-by-step explanation:

54 - 10x ≤20 +7x

Add 10x to each side

54 - 10x+ 10x ≤20 +7x+10x

54 ≤20 + 17x

Subtract 20 from each side

54-20 ≤20+17x-20

34 ≤17x

Divide by 17

34/17 ≤17x/17

2 ≤x

Graph of function is attached below.

Option D is correct.

To understand more, check below explanation.

We have to draw the graph of function,

                    [tex]f(x)=\left \{ {x, {x < 1} \atop {1, x\geq 1}} \right.[/tex]

The graph of above function is attached below,

For domain [tex]x > 1, f(x)=x[/tex]

For domain, [tex]x\geq 1, f(x)=1[/tex]

After observing attached graph, option D is correct.

Learn more about the graph of function here:

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The function is plotted and is attached , Option D is the correct graph similar to one in the image.

It is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (dependent).

It is given in the question that

f(x) =

x if x <1

1 if x>_ 1

The graph of above function is attached below,

For domain x > 1, f(x)=x

For domain, x≥ 1, f(x)=1

When we see the graph that have been plotted on the basis of domain, Option D is the correct graph similar to one in the image attached.

To know more about Function

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Explanation:

Focus on one point, such as A = (1,2). Note how it moves to point A ' = (-1, -2). Both x and y coordinates have been flipped from positive to negative. The rule therefore is [tex](x,y) \to (-x,-y)[/tex]. This describes a 180 degree rotation (either clockwise or counterclockwise, it doesn't matter). Points B and C follow the same idea.

Side note: Lines AA', BB' and CC' all go through the origin (0,0).

Answer:

x° = 62

Step-by-step explanation:

The vertical angle to 28 degrees is 28 degrees in size.

The vertical angle to 90 degrees is 90 degrees in size.

Angles in a circle add up to 360 degrees.

x + 28 + 152 + 28 + 90 = 360

x + 298 = 360

x = 360 - 298

x = 62

Angle x is 62 degrees in size.

Step-by-step explanation:

i think the answer is -3 only

Answer:

A

Step-by-step explanation:

Let me know If you want me to explain it.

Answer:

A. h = V/(pi * r^2)

Step-by-step explanation:

V = pi r^2 h

Divide both sides by pi r^2.

V/(pi r^2) = h

The h variable is isolated now.

Answer: f⁻¹(x)=4x-56

Step-by-step explanation:

f⁻¹(x) is the inverse of f(x). To find the inverse, we replace the y with x, and x with y. Once we do that, we solve for y.

[tex]x=\frac{1}{4}y+14[/tex]                 [subtract 14 on both sides]

[tex]x-14=\frac{1}{4}y[/tex]                 [multiply both sides by 4]

[tex]4(x-14)=y[/tex]               [distribute 4]

[tex]4x-56=y[/tex]

[tex]f^-^1(x)=4x-56[/tex]

Solution:

x + y = 11, -x = -y - 9

~Isolate x in [ x + y = 11 ]

x = 11 - y

~Substitute x in the other equation

-(11 - y) = -y - 9

~Simplify

-11 + y = -y - 9

y = -y + 2

2y = 2

y = 1

~Substitute y in the first equation

x + 1 = 11

~Simplify

x = 10

Therefore, the solution to the system of equations is (10, 1)

Best of Luck!

Answer:

A) Point C

B) Point E

Step-by-step explanation:

There are 3 vowels in the word square, and there are six total letters in the word square.

Square

There is a half chance of picking a letter that is a vowel in the word "square". (Three is half of six.)  

Point C would be the most accurate spot for question 'a'.

The word square does not have a 'T'. It is certain that a letter that is not 'T' would be picked.

Point E would be the most accurate spot for question 'b'.

Answer:

a)  c  b) e

Step-by-step explanation:

There are 3 vowels out of 6 total cards, and c lands at 3/6->1/2.

There is no letter T, so it is a 1/1 chance of not getting a T. E lands at 1.

You're welcome.

Answer:

D) "No, because for the 12 months in the year each date is not equally likely."

Step-by-step explanation:

For example, february does not have 31 days as well as april so it would not be a fair representation.

Answer:

The third option, or initial value:2, rate of change:1.

Step-by-step explanation:

The initial value is where the y-intercept is on the y-axis. For this problem it falls on the 2.

Your rate of change is your slope. I like to think of it as rise/run. Your slope in this graph is 1/1. Or just 1.

let me know if your need further explanation!