Solve the equation for all real values of x.

a.pi/6
b.pi k,pi/6
c. pik
d.pi/6+pik

[tex]\bf \begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} {-2}~~\ast&{4}~~\ast\\ 0&2\\ 1&1\\ {3}~~\ast&{-1}~~\ast\\ \cline{1-2} \end{array}~\hspace{10em} (\stackrel{x_1}{-2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-4}{3-(-2)}\implies \cfrac{-5}{3+2}\implies \cfrac{-5}{5}\implies -1[/tex]

The slope of this line is -1.

The slope formula is useful:

m = (y2 -y1)/(x2 -x1)

where:

m is the slope of the line

y1 and y2 are the y-coordinates of two points on the line

x1 and x2 are the x-coordinates of the two points on the line

 m = (2 -4)/(0 -(-2)) = -2/2 = -1

The slope of this line is -1.

The points on the line drop 1 unit for each 1 unit to the right.

 m = rise/run = -1/1 = -1

Answer:

circle area = PI * radius^2

circle area = 11^2 * PI

circle area = 121 * PI

That would be the area for the ENTIRE area but the circle but we are only dealing with 135 degrees of a circle so the area equals

121 * (135 / 360) * PI

= 45.375 PI

Answer is C

Step-by-step explanation:

Answer:

y = - 7

Step-by-step explanation:

The y- intercept is the point on the y- axis that the line passes through.

The line passes through the y- axis at (0, - 7), hence

the y- intercept is - 7

Slope-intercept form: y = mx + b   [m is the slope, b is the y-intercept or the y value when x = 0 ---> (0 , y)]

Since you know m = -3, you can plug that into the equation

y = mx + b

y = -3x + b       To find b, plug in the point they gave you into x and y, but since x = 0, your y-intercept is -7

Answer:

[tex]\large\boxed{\bold{one\ solution}\ (1,\ -4)\to x=1,\ y=-4}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=2x-6\\y=-x-3\end{array}\right\\\\\text{These are linear functions. We only need two points to draw a graph.}\\\\\text{Choice two values of x, substitute to the equation,}\\\text{and calculate the values of y.}\\\\y=2x-6\\for\ x=0\to y=2(0)-6=0-6=-6\to(0,\ -6)\\for\ x=3\to y=2(3)-6=6-6=0\to(3,\ 0)\\\\y=-x-3\\for\ x=0\to y=-0-3=0-3=-3\to(0,\ -3)\\for\ x=-3\to y=-(-3)-3=3-3=0\to(-3,\ 0)\\\\\text{Look at the picture}[/tex]

[tex]\text{The intersection of the line is the solution of the system of equations:}\\\\(1,\ -4)\to x=1,\ y=-4[/tex]

Answer:

The correct answer is option A.  5 units

Step-by-step explanation:

Points to remember

Distance formula

Length of a line segment with end points (x1, y1) and (x2, y2) is given by,

Distance = √[(x2 - x1)² + (y2 - y1)²]

It is given that, two points are

(5, –2) and (5, 3)

To find the distance

(x1, y1) = (5, -2)  and (x2, y2) = (5, 3)

Distance = √[(x2 - x1)² + (y2 - y1)²]

 = √[(5 - 5)² + (3 - -2)²]

 = √[(5)²  = 5

Therefore the correct option is Option A  5 units

if the diameter is 6 units, then the radius is half that, or 3.

[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} r=3 \end{cases}\implies A=\pi 3^2\implies A=9\pi \implies A\approx 28.27[/tex]

Final answer:

To calculate the area of a circle with a 6-inch diameter, use the radius (3 inches) in the area formula πr² to get an approximate area of 28.274 square inches.

Explanation:

To find the area of a circle with a diameter of 6 inches, we use the formula for the area of a circle, which is πr², where r is the radius of the circle. Since the diameter is 6 inches, we divide by two to find the radius (r = diameter / 2 = 6 / 2 = 3 inches).

Substituting the radius into the formula gives us π(3²) = π(9), and using the approximation π ≈ 3.14159, we find the area to be approximately 28.274 square inches.

Answer:

3 left

Step-by-step explanation:

If she starts out with 73 and drops 5 she is left with 68, an you cannot evenly divide 68 and 13 so you divide it as much as you can evenly which is five containers leaving 3 extra cupcakes.

For this case we have that initially there are 73 cupcakes, if Leda dropped 5 then we are left with:

[tex]73-5 = 68[/tex]

Now, you must equally divide the 68 cupcakes into 13 containers:

putting 5 cupcakes in each of the 13 containers we have;

[tex]13 * 5 = 65[/tex]

[tex]68-65=3[/tex]

So, we have 3 cupcakes left.

Answer:

3 cupcakes

Answer: 9

Step-by-step explanation: 4.5=.5xZ. 4.5/.5=9=z

Answer: 4

Step-by-step explanation:

The degree is the highest exponent , in which in this problem it is 4. The 3x counts as an exponent of 1 because the variable x is 1, and the 2 counts as an exponent of zero. Which means the degree is 4.

Answer:

-3

Step-by-step explanation:

We have

y = F(x) = x + 3

so

x = y  - 3

so

F⁻¹(y) = y - 3

which we can write

F⁻¹(x) = x - 3

We solve

0 = F⁻¹(x) = x - 3

x = 3

Answer: 3

Answer:

D

Step-by-step explanation:

If y = log x is the basic function, let's see the transformation rule(s):

Then,

1. y = log (x-a) is the original shifted a units to the right.

2. y = log x + b is the original shifted b units up

Hence, from the equation, we can say that this graph is:

** 2 units shifted right (with respect to original), and

** 10 units shifted up (with respect to original)

only, left or right shift affects vertical asymptotes.

Since, the graph of y = log x has x = 0 as the vertical asymptote and the transformed graph is shifted 2 units right (to x = 2), x = 2 is the new vertical asymptote.

Answer choice D is right.

see if u understand, note that the degree is 90

The height of the kite is 9 feet.

Trigonometric ratio is used to show the relationship between the sides of a triangle and its angles.

Let h represent the height of the kite. Hence, using trigonometric ratios:

sin(30) = h / 18

h = 9 feet

Therefore the height of the kite is 9 feet.

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Answer:

8

Step-by-step explanation:

The number is a, another number is b.

a = b + 18 So, b=a - 18

(a+b) + ab

= a + a - 18 + a (a - 18)

= 2a - 18 + a^2 - 18a

{ ax^2 + bx + c }

= a^2 -1 6a - 18 {a = 1b = -16 }

When a = b/-2a = -16/-2*1 = 8

the a^2 - 1ba - 18 is minimum,

So the number is 8

Answer:

a ≈ 14 or 6

Step-by-step explanation:

264 = π × a × (20 - a)

a(20 - a) = [tex]\frac{264}{Pi}[/tex] ≈ 84 (rounded off to nearest whole number)

Opening the brackets we get;

a² - 20a + 84 = 0

Applying the quadratic formula we get:

a ≈ 14 or 6

Answer:

A. [tex]h=\dfrac{2A}{b}[/tex]

Step-by-step explanation:

You are given formula

[tex]A=\dfrac{1}{2}bh[/tex]

Multiply this equation by 2 to get rid of fraction:

[tex]2A=bh[/tex]

Divide this equation by b to find h in terms of A and b:

[tex]h=\dfrac{2A}{b}[/tex]

Answer:

D

Step-by-step explanation:

Using the midpoint formula

midpoint of 2 points (x₁, y₁ ) and (x₂, y₂ ) is

[ [tex]\frac{1}{2}[/tex](x₁ + x₂), [tex]\frac{1}{2}[/tex](y₁ + y₂ ) ]

let (x₁, y₁ ) = (- 1, 5) and (x₂, y₂ ) = (5, 5), then midpoint is

[ [tex]\frac{1}{2}[/tex](- 1 + 5), [tex]\frac{1}{2}[/tex](5 + 5) ]

= (2, 5) → D

The midpoint of the segment is (2,5).

To find the midpoint of a line segment with endpoints [tex]\((-1, 5)\) and \((5, 5)\)[/tex], we can use the midpoint formula:

[tex]\[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]

Given the endpoints:

[tex]\( x_1 = -1 \), \( y_1 = 5 \)[/tex] (coordinates of the first point)

[tex]\( x_2 = 5 \), \( y_2 = 5 \)[/tex] (coordinates of the second point)

Now, let's plug these values into the midpoint formula:

[tex]\[ \text{Midpoint} = \left( \frac{-1 + 5}{2}, \frac{5 + 5}{2} \right) \][/tex]

[tex]\[ = \left( \frac{4}{2}, \frac{10}{2} \right) \][/tex]

[tex]\[ = \left( 2, 5 \right) \][/tex]

Therefore, the midpoint of the segment is (2, 5)

Among the given options, the correct one is option D: (2, 5).

Check the picture below.

so then, the perimeter of that hexagon will  just be the sum of all its 6 sides, or namely 3⅖ + 3⅖ + 3⅖ + 3⅖ + 3⅖ + 3⅖, or just 6( 3⅖ ).

[tex]\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap~~ \begin{cases} a=apothem\\ p=perimeter\\[-0.5em] \hrulefill\\ a=3\\ p=6\left(3\frac{2}{5} \right) \end{cases}\implies A=\cfrac{1}{2}(3)\left[ 6\left(3\frac{2}{5} \right) \right]\implies A=\cfrac{1}{2}(3)\left[ 6\left(\cfrac{17}{5} \right) \right] \\\\\\ A=\cfrac{1}{2}(3)\left(\cfrac{102}{5} \right)\implies A=\cfrac{1}{2}\left( \cfrac{306}{5} \right)\implies A=\cfrac{153}{5}\implies A=30\frac{3}{5}[/tex]

Answer:

It's option 2.

Step-by-step explanation:

- 1/2x > 6

Divide both sides by -1/2:

x < -12   (Note the inequality sign flips when we divide by a negative value).

Answer: {x |x ∈ R, x < -12}

Step-by-step explanation:

Given the following inequality:

[tex]-\frac{1}{2}x>6[/tex]

You can find the solution set by solving for the variable "x".

Then, to solve for the variable "x" you need to multiply both sides of the inequality:

[tex](-\frac{1}{2}x)(2)>(6)(2)[/tex]

[tex]-x>12[/tex]

And finally, you must multiply both sides of the inequality by (-1). Notice that the direction of the symbol of the inequality will change:

[tex](-x)(-1)>(12)(-1)[/tex]

[tex]x<-12[/tex]

Therefore, the solution set is: {x |x ∈ R, x < -12}

Check the picture below.

Answer:

Step-by-step explanation:

z score= x - mean/standard deviation

1.20= x -100/15

18= x -100

118=x

z score= x - mean/standard deviation

0.5=x-73/4

2=x-73

75= x

The area of the rectangle is decreased by 75%, when the dimensions of a rectangle are decreased by 50%.

The area of the rectangle is the multiplication of length and width.

Area = l × b

It is given that:  length and breadth is by 50%

New Length = l × (1-50/100)

                   = l × (1-1/2)

                  = l/2

New Width = b × (1-50/100)

                  = b × (1-1/2)

                 = b/2

New area = new length × new width

               = (l/2) x (b/2)

              = lb/4

Change percent =[tex]\frac{Final Area\;-\; Initial Area}{Initial Area} * 100[/tex]

                        = [tex]\frac{(lb/4)\;-\; lb}{lb} * 100[/tex]

                        = (- 3lb)/4× 100

                        = (-3)/4 × 100

                        =  -75%

Hence, the area decreased by 75 %.

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Final answer:

Decreasing the dimensions of a rectangle by 50% results in a new area that is 25% of the original, equating to a decrease of 75% in the area.

Explanation:

When the dimensions of a rectangle are decreased by 50%, each dimension (length and width) becomes 50% of the original. To determine the effect on the area, you can use the formula for the area of a rectangle, which is Area = length tmes width.

Let's consider the original length to be L and the original width to be W. The original area is L times W. When both dimensions are decreased by 50%, the new length is 0.5L and the new width is 0.5W. Therefore, the new area is (0.5L) times (0.5W), which is 0.25 times (L times W). This means the new area is 25% of the original area, representing a 75% decrease.

Answer:

203 minutes

Step-by-step explanation:

This can be expressed as an arithmetic sequence, that is

20, 23, 26, 29,...

With first term a = 20 and common difference d = 3

The sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a + (n - 1)d ], hence

[tex]S_{7}[/tex] = [tex]\frac{7}{2}[/tex] [ (2 × 20) + (6 × 3) ]

                        = 3.5 ( 40 + 18) = 3.5 × 58 = 203

It might have come from

9/n  =  10/m

Answer: Hi, in the equation 9*m = 10*n the proportion is 9 to 10, which means that 9 times the number m is equal to 10 times the number n.

So n is proportional to m in the way that n= (9/10)*m

and m is proportional to n in the way that m= (10/9)*n

This means that the proportion can be written as 9 to 10, or 9:10.

Answer:

Other division expression that have the same value as 61.12 divided by 3.2 are

122.24 divided by 6.4 AND

183.36 divided by 9.6

Step-by-step explanation:

61.12/3.2 = 19.1

Other division expression that have the same value as this:

122.24/6.4 = 19.1

183.36/9.6 = 19.1

The volume is 12 770.05 cubic centimeters (cm3)

12 770.50 cubic centimeters

Answer:

The value 1.8 represent the club's total number of members today or the present number of members

Step-by-step explanation:

Given an exponential function;

[tex]y=ab^{x}[/tex]

b is the base or the growth factor

a is the initial value, that is the value of y when x = 0

We have been given the exponential function;

[tex]y=1.8(1.02)^{12t}[/tex]

The value 1.8 simply represents the initial value of y. Plug in t = 0 in the equation;

[tex]y=1.8(1.02)^{12(0)}=1.8[/tex]

Therefore, the value 1.8 represent the club's total number of members today or the present number of members.

Answer:

The correct answer option is 0.2.

Step-by-step explanation:

We are given that there are 3 red marbles and 3 green marbles in an opaque bag.

If two marbles are chosen one after one without replacement, we are to find the probability of getting both green marbles.

P (1st green marble) = [tex] \frac { 3 } { 6 } [/tex]

P (2nd green marble) = [tex] \frac { 2 } { 5 } [/tex]

P (both green marbles) = [tex] \frac { 3 } { 6 } \times \frac { 2 } { 5 } [/tex] = 0.2

Answer:

i think its forty

Step-by-step explanation:

im sorry if its wrong

I think it is bottom right because it goes through the most points.

Answer:

300π ft^3

Step-by-step explanation:

let's use the volume of a cylinder formula:

π*r^2*h

π=3.14

r=5

h=12

since we need to solve in terms of pi, do not plug the value of pi into the formula

π*5^2*12= 300π

300π

Answer:

a

Step-by-step explanation:

Answer:

Option (A) and (D) are not trigonometric identities.

Step-by-step explanation:

Option (A )  tan²x + sec²x = 1

Since [tex]tanx =\frac{sinx}{cosx}[/tex] and [tex]secx =\frac{1}{cosx}[/tex]

put these in left hand side of tan²x + sec²x = 1

[tex](\frac{sinx}{cosx})^{2}[/tex] + [tex](\frac{1}{cosx})^{2}[/tex]

[tex](\frac{sin^{2}x}{cos^{2}x})[/tex] + [tex](\frac{1}{cos^{2}x})[/tex]

Take L.C.M of above expression,

[tex](\frac{sin^{2}x + 1}{cos^{2}x})[/tex]

since, sin²x  = 1 - cos²x

[tex](\frac{1-cos^{2}x+1}{cos^{2}x})[/tex]

[tex](\frac{2-cos^{2}x}{cos^{2}x})[/tex]

we are not getting 1

so, this is not a trigonometric identity.

Option (A) is correct option

Option (B)  sin²x + cos²x = 1

This is an trigonometric identity

Option (C)  sec²x - tan²x = 1

Divide the trigonometric identity sin²x + cos²x = 1 both the sides by cos²x so, we get

[tex]\frac{sin^{2}x}{cos^{2}x}+\frac{cos^{2}x}{cos^{2}x}\,=\,\frac{1}{cos^{2}x}[/tex]

[tex]tan^{2}x}+1\,=\,sec^{2}x}[/tex]

subtract both the sides by tan²x in above expression

[tex]tan^{2}x}+1\,-tan^{2}x=\,sec^{2}x-tan^{2}x[/tex]

[tex]1=\,sec^{2}x}-tan^{2}x[/tex]

Hence, this is the trigonometric identity.

Option (D)  sec²x + cosec²x = 1

Since [tex]secx =\frac{1}{cosx}[/tex] and [tex]cosecx =\frac{1}{sinx}[/tex]

put these in left hand side of sec²x + cosec²x = 1

[tex](\frac{1}{cosx})^{2}+(\frac{1}{sinx})^{2}[/tex]

[tex]\frac{1}{cos^{2}x}+\frac{1}{sin^{2}x}[/tex]

we are not getting 1

so, this is not a trigonometric identity.

Option (D) is correct option.

Hence, Option (A) and (D) are not trigonometric identities.