circle O has a circumference of 36tt cm. what is length of the radius r

Final answer:

To solve the system of equations, use the method of substitution to find the values of x, y, and z.

Explanation:

To find the solution to the system, we can use the method of elimination or substitution. Let's use the method of substitution to solve this system.

From the first equation, we can isolate y in terms of x and z: y = 2x + 6z - 1.

Substitute this expression for y in the other two equations to eliminate the variable y. This will give you an equation with variables x and z.

Solve the resulting equation to find the values of x and z.

Substitute these values back into any of the original equations to solve for the remaining variable, y.

The solution to the system -2x + y + 6z = 1, 3x + 2y + 5z = 16, and 7x + 3y - 4z = 11 is x = 1, y = 2, and z = 3.

Answer:

139 dollars a month.

Final answer:

To save $2500 for a down payment on a car in a year and a half with an interest rate of 6.2%, you would need to deposit approximately $136.92 each month.

Explanation:

To calculate the monthly deposit needed, we can use the formula for the future value of a series of deposits: FV = P ×  [((1 + r)ⁿ - 1) / r], where FV is the future value (in this case, $2500), P is the monthly deposit, r is the interest rate (6.2% or 0.062), and n is the number of periods (18 months).

Plugging in the values, we have $2500 = P ×  [((1 + 0.062)¹⁸ - 1) / 0.062]. Solving for P:

$2500 = P ×  [(1.062¹⁸ - 1) / 0.062]

Doing the calculations, we find that P = $136.92. Therefore, you would need to deposit approximately $136.92 each month to save $2500 for a down payment on a car in a year and a half.

Answer:

They traveled 800 km by train.

Step-by-step explanation:

We assign variables and write two equations. Then we solve the system of 2 equations in 2 unknowns.

Assign variables:

let x = kilometers traveled by bus

let y = kilometers traveled by train

Write first equation:

"they traveled a total of 1450 km"

x + y = 1450

Write second equation:

"riding on the train 150 more kilometers than on the bus"

The distance on the train, y, is 150 km greater than the distance on the bus, x.

y = x + 150

We have a system of 2 equations:

x + y = 1450

y = x + 150

Since the second equation is already solved for y, we can use the substitution method. Substitute y of the first equation with x + 150.

x + y = 1450

x + x + 150 = 1450

2x + 150 = 1450

2x = 1300

x = 650

y = x + 150

y = 650 + 150

y = 800

They traveled 800 km by train.

Triangle GDO is the correct answer.

Although Triangle DOG seems like the exact same triangle, it's not (Ok, well technically it is, but when showing two congruent triangles, the points on the triangle should correspond to eachother).

Answer:

To find the pythargoeren(sorry I do not know how to spell this word at all:) you can use the formula a^2+b^2=c^2.

Step-by-step explanation:

If you recieve the numbers for the longest side and a shorter side then here is how you would set it up:  7^2+b^2=12^2 that was an example.

And if you recieve the numbers for the two shortest sides the set it up like this: 7^2+4^2=c^2

Just so you know these are for example and I am not actually sure if they equal a right triangle or if they are true

Good luck.

Answer:

x=-1 vertical

y=4 horizontal

Step-by-step explanation:

The vertical asymptote if it exist will be the x's such that it makes your fraction undefined.  You cannot divide by 0.  So 2/(x+1) will be undefined when x=-1.

x=-1 is your vertical asymptote.

Now a fraction will only be 0 when the top is 0. 2/(x+1) will therefore never be 0 because the numerator will never be 0.

So since 2/(x+1) is never 0, you have 2/(x+1)   + 4 is never 4.

So the horizontal asymptote is y=4.

Answer:

B. 30.47.

Step-by-step explanation:

E(X) = 23*0.16 + 25*0.09 + 26*0.18 + 31*0.12+ 34*0.24+38*0.21

=  30.47.

Answer:

B. 30.47

Step-by-step explanation:

The mean for a discrete random variable when the probability distribution is given is calculated by the formula:

E(X) = ∑(x_i)*P(x_i)

So, from the values given in the table

[tex]E(X) = (23)(0.16) + (25)(0.09)+(26)(0.18)+(31)(0.12)+(34)(0.24)+(38)(0.21)\\= 3.68+2.25+4.68+3.72+8.16+7.98\\= 30.47[/tex]

Hence, the correct answer is:

B. 30.47 ..

Answer:

y+4=-6(x+8)  point-slope form

y=-6x-52 slope-intercept form

6x+y=-52 standard form

Step-by-step explanation:

Slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.

Lines that are perpendicular have opposite reciprocal slopes.

So the slope of y=(1/6)x+3 is 1/6.

The opposite reciprocal of (1/6) is -6.

So the equation for the line we are looking for is in the form:

y=-6x+b         (Since the slope of our new line is -6)

Now we want our line to go through (-8,-4).

So plug that in:

-4=-6(-8)+b

-4=48+b

Subtract 48 on both sides:

-52=b

The equation for the line we are looking for is

y=-6x-52.

Now you could do other forms.

Another one is point-slope form.

We already know it goes through (-8,-4) and a slope of -6.

Point slope form is: y-y1=m(x-x1) where m is the slope and (x1,y1) is a point on the line.

Plug in the information to get:

y-(-4)=-6(x-(-8))

y+4=-6(x+8)

I'm going to do one more form.

Standard form is ax+by=c where a,b,c are integers.

y=-6x-52

Add 6x on both sides:

6x+y=-52

Answer:

minimum (3,7)

Step-by-step explanation:

y = x^2 - 6x + 16

Take the coefficient of the x term  -6

Divide it by 2   -6/2 =-3

Then square it  ( -3)^2 =9

Add that to the equation (remember if we add it we must subtract it)

y = x^2 - 6x +9  -9+ 16

y = (x^2 - 6x +9)  -9+ 16

The term inside the parentheses is x+b/2 which is x+ -3  or x-3 quantity squared

y = (x-3)^2 +7

This is in vertex form

y = a(x-h)^2 +k  where (h,k) is the vertex

(3,7) is the vertex

Since a=1, it is positive, so it opens upward and the vertex is a minimum

Final answer:-

The quadratic equation y = x ²- 6x 16 can be rewritten in vertex form as y = ( x- 3) ² 7, with the vertex at the point( 3, 7), which is a minimum.

Explanation:-

To complete the square and rewrite the quadratic equation y = x2- 6x 16 in vertex form, we need to produce a perfect square trinomial on the right- hand side. The measure of x is-6, so we take half of that, which is-3, and square it to get 9. Adding and abating this inside the equation gives us y = ( x2- 6x 9)- 9 16.

Factoring the trinomial we also have y = ( x- 3) 2 7. This is the vertex form, where the vertex is the point( 3, 7). Since the measure of the x2 term is positive, the parabola opens overhead, which means the vertex represents a minimum.

The answer is 6 only.

The roots of the equation y^2 - 12y = -36 can be found by rewriting the equation as y^2 - 12y + 36 = 0 to make it quadratic.

By factoring this quadratic equation, we get (y - 6)(y - 6) = 0, resulting in one repeated root at y = 6.

Therefore, the correct answer is b. 6 only.

Answer:

5

Step-by-step explanation:

f(x)= 3х^2

g(x) = 4х^3 + 1

(f•g)(x) = (3x^2) * (4x^3+1)

           = 12x^(2+3) + 3x^3

          = 12 x^5 + 3x^2

The degree is the highest power of x, which is 5

Answer:

B

Step-by-step explanation:

The sequence is as follows:

7,19,31,43,55

Here:

a_1=7

d= 12

The standard formula for arithmetic sequence is:

[tex]a_n=a_1+(n-1)d\\a_n=7+(n-1)12[/tex]

By looking at the options we can see that

option B is correct ..

Answer: B a(n)=7+(n-1)*12

Step-by-step explanation:

A P E X

Answer:

Step-by-step explanation:

To build a picture graph, collect your data, decide what each picture will symbolize, and create a graph with horizontal and vertical axes. The horizontal axis labels the categories while the vertical axis accounts for the quantities. Graphs are a useful tool in displaying data visually but they can convey different meanings based on various elements.

To create a picture graph, you must first collect your data and decide what each picture will represent. For instance, if you are depicting the favorite fruit of students in your class, a single picture could represent one student's vote.

Next, we draw a set of horizontal and vertical axes. The horizontal axis is where you label the different categories, in this case, the types of fruit. The vertical axis would represent the number of students who chose each type of fruit. For every student who prefers a particular fruit, you add one picture onto that fruit's stack on the graph.

Graphs are a way to express equations visually and also to display statistics or data. They provide a single visual perspective on a subject. But remember, graphs can leave different impressions based on what data is included, how it's grouped, and the scale of the axes.

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Answer:

Step-by-step explanation:

We only need two points to draw a graph of each equation.

2x + y = 6

Convert to the slope-intercept form y = mx + b:

2x + y = 6          subtract 2x from both sides

y = -2x + 6

for x = 0 → y = -2(0) + 6 = 0 + 6 = 6 → (0, 6)

for x = 3 → y = -2(3) + 6 = -6 + 6 = 0 → (3, 0)

6x + 3y = 12

Convert to the slope-intercept form:

6x + 3y = 12            subtract 6x from both sides

3y = -6x + 12          divide both sides by 3

y = -2x + 4

for x = 0 → y= -2(0) + 4 = 0 + 4 = 4 → (0, 4)

for x = 2 → y = -2(2) + 4 = -4 + 4 = 0 → (2, 0)

Mark given points in the coordinate system.

Draw the lines passing through these points.

Look at the picture.

The lines are parallel. The intersection of the line is not exist. Therefore the system of equations has no solution.

The graph of the given equation is Attached below.

An important math tool is graphing. It can be a straightforward method for introducing more general concepts like most and least, greater than, or less than. It can also be a great way to get your child interested in math and get them excited about it. Using graphs and charts, you can break down a lot of information into easy-to-understand formats that quickly and clearly convey key points.

Given equation 2x + y = 6 we can drive from this equation that at x = 0 y will be 6 and y =0 x will be 3 hence we have two points of the line (0,6) and (3,0)

From the Given equation (2) 6X + 3Y = 12 we can drive from this equation that at x = 0 y will be 4 and y =0 x will be 2 hence we have two points of the line (0,4) and (2,0).

Hence, we have two coordinates from both lines which is enough to draw a  line on an XY cartesian plan.

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Answer:

B

Step-by-step explanation:

150/100=2/3

2/3 of 100 = 66 2/3

A 100-pound person will burn 66 2/3 calories while sitting still for 1 hour.

To find out how many calories a 100-pound person will burn while sitting still for 1 hour, we can use the given ratio of 150-pound person: 100 calories = 1 hour. Since the ratio is constant, we can set up a proportion to solve for the unknown value:

150 pounds : 100 calories = 100 pounds : x calories

Coss-multiplying, we get:

150 pounds * x calories = 100 pounds * 100 calories

Simplifying, we have:

x = (100 pounds * 100 calories) / 150 pounds

Calculating the value of x, we find that a 100-pound person will burn 66 2/3 calories while sitting still for 1 hour.

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Answer:

D

Step-by-step explanation:

Trust me I did t on edge

The vertex form of the given parabola is  [tex]f(x) = 3(x + 4)^2 - 6[/tex], option A is correct.

The vertex form of a quadratic function is given by [tex]f(x) = a(x - h)^2 + k[/tex] where (h, k) represents the vertex of the parabola.

We have a = 3, which determines the steepness or "stretching" factor of the parabola.

If a is positive, the parabola opens upwards, and if a is negative, it opens downwards.

The vertex form tells us that the vertex of the parabola is at the point (-4, -6).

The value -4 represents the horizontal shift of the parabola, moving it 4 units to the left, while -6 represents the vertical shift, moving it 6 units downwards.

The vertex form is [tex]f(x) = 3(x + 4)^2 - 6[/tex].

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Answer:

[tex]A=54\sqrt{3}[/tex]

Step-by-step explanation:

here we are going to use the formula which is

Area=[tex]\frac{1}{2} \times P \times A[/tex]

Where P is perimeter and A is apothem

Please refer to the image attached with this :

In a Hexagon , there are six equilateral triangle being formed by the three diagonals which meet at point O.

Consider one of them , 0PQ  with side a

As Apothem is the Altitude from point of intersection of diagonals to one of the side. Hence it divides the side in two equal parts . hence

[tex]PR = \frac{a}{2}[/tex]

Also OP= a

Using Pythagoras theorem ,

[tex]OP^2=PR^2+OR^2[/tex]

[tex]a^2=(\frac{a}{2})^2+(\3sqrt{3})^2[/tex]

[tex]a^2=\frac{a^2}{4}+27[/tex]

Subtracting both sides by [tex]\frac{a^2}{4}[/tex]

[tex]a^2-\frac{a^2}{4}=27[/tex]

[tex]\frac{4a^2-a^2}{4}=27[/tex]

[tex]\frac{3a^2}{4}=27[/tex]

[tex]a^2=\frac{4 \times 27}{3}[/tex]

[tex]a^2=4 \times 9[/tex]

[tex]a^2=36[/tex]

taking square roots on both sides we get

[tex]a=6[/tex]

Now we have one side as 6 mm

Hence the perimeter is

[tex]P=6 \times 6[/tex]

[tex]P=36[/tex] mm

Apothem = [tex]3\sqrt{3}[/tex]

Now we put them in the main formula

Area = [tex]\frac{1}{2} \times 36 \times 3\sqrt{3}[/tex]

Area=[tex]18 \times 3\sqrt{3}[/tex]

Area=[tex]54\sqrt{3}[/tex]

Answer:

A. 94 in^2

Step-by-step explanation:

Answer:

The distance between Point S and Point T is 6.1 unit.

Step-by-step explanation:

Given : The coordinates of Point S are [tex](\frac{2}{5} , 9\frac{1}{8} )[/tex]. The coordinates of Point T are [tex](-5\frac{7}{10},9\frac{1}{8})[/tex].

To find : What is the distance between Point S and Point T?​

Solution :

The distance formula between two point is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The point S is [tex](x_1,y_1)=(\frac{2}{5} , 9\frac{1}{8} )=(\frac{2}{5} ,\frac{73}{8} )[/tex]

The point T is [tex](x_2,y_2)=(-5\frac{7}{10},9\frac{1}{8})=(-\frac{57}{10},\frac{73}{8})[/tex]

Substitute the value,

[tex]d=\sqrt{(-\frac{57}{10}-\frac{2}{5})^2+(\frac{73}{8}-\frac{73}{8})^2}[/tex]

[tex]d=\sqrt{(\frac{-57-4}{10})^2+(0)^2}[/tex]

[tex]d=\sqrt{(\frac{-61}{10})^2+0}[/tex]

[tex]d=\frac{61}{10}[/tex]

[tex]d=6.1[/tex]

Therefore, the distance between Point S and Point T is 6.1 unit.

Final answer:

The distance between Point S (2/5, 9 1/8) and Point T (-5 7/10, 9 1/8) is 6.1 units.

Explanation:

The distance between two points in a Cartesian coordinate system is calculated using the distance formula, which is derived from the Pythagorean theorem.

In this case, the y-coordinates of Points S and T are the same, so the distance is simply the difference in the x-coordinates.

To find the distance, subtract the x-coordinate of Point S from the x-coordinate of Point T and take the absolute value:

Distance = |(2/5) - (-5 7/10)|

To simplify, first convert -5 7/10 to an improper fraction: -5 7/10 = -57/10

Distance = |(2/5) - (-57/10)|

Next, find a common denominator and subtract the fractions:

Distance = |(4/10) - (-57/10)|

Distance = |61/10|

Distance = 6 1/10 or 6.1 units

The distance between Point S and Point T is 6.1 units.

Answer:

The average power use in watts is 806.

Step-by-step explanation:

The month of May has 31 days and 1 day  is 24 hours. So May has:

31*24=744 hours

Now, we divide 600 kW-hr by the number of hours in the month (744 hrs) to get average power use:

600/744 = 0.80645161. kW. Since 1000 Watts = 1 kW, we multiply this by 1000 to get the answer in Watts:

0.80645161 * 1000 = 806 Watts

"The average power use is 806 watts."

Answer:

An anti-clockwise rotation of 180 degrees about the origin.

Step-by-step explanation:

We can draw a straight line between A and A' going through (0, 0). Same with the other points. We also see that A'B'C'D' faces the opposite way  to ABCD which is characteristic of a rotation of 180 degrees.

Answer:

D. 8

Step-by-step explanation:

The given diagram is a trapezium. We know that the consective sides of a trapezium are equal. so,

Putting the values of consecutive sides equal:

So, KI will be equal to LI

3x-7 = x+3

[tex]3x-7-x=x+3-x\\2x-7=3\\2x-7+7=3+7\\2x=10\\x=5[/tex]

Putting the value of x in the equation of KI

3x-7

=3(5)-7

=15-7

=8

Hence, the correct answer is D. 8 ..

Answer:

40

Step-by-step explanation:

a+b=c

a=girls

b= boys

c= total

the statement tell us:

4/5 of a class is girls:

a=(4/5)*c

boys=b=8

c=a+b

so we have:

c=(4/5)*c + 8

c-(4/5)*c=8

(5c-4c)/5 = 8

c/5=8

c=8*5

c=40

total=40

Answer:

the volume is 0.8 × 0.3 × 1.3 = 0.312 units cubed.

Step-by-step explanation:

After scaling down 1/10:

Length = 8 ÷ 10 = 0.8

Width = 3 ÷ 10 = 0.3

Height = 13 ÷ 10 = 1.3

Answer:

He should turn 60° to head straight towards island B.

Step-by-step explanation:

Let us assume a Triangle ABC. Where side AB is the distance of the island A and island B and is 210 miles. AC is the wrong Course that a ship took and is 230 miles. CB is the course straight towards island B from C and equals 180 miles.

Finding angle C:

Now that the three sides of the triangle are known, we can find the angle that the ship should turn to using the law of cosines:

Cos C = (a²+b²-c²)/2ab   where c = AB, b = AC, a = BC

Cos C = (180² + 230² - 210²)/2*180*230

C = cos⁻¹ (41200/82800)

C = cos⁻¹ (0.4976)

angle C = 60.15

angle C = 60° approx

Answer:

119.84

Step-by-step explanation:

Side a = 180

Side b = 230

Side c = 210

Angle ∠A = 48.03° = 48°1'49" = 0.83829 rad

Angle ∠B = 71.81° = 71°48'36" = 1.25332 rad

Angle ∠C = 60.16° = 60°9'35" = 1.04998 rad

180-60.16=119.84

Answer:

see explanation

Step-by-step explanation:

Given that x = - [tex]\frac{4}{3}[/tex] is a solution of the equation, then

Substitute this value into the equation and solve for b

21 (- [tex]\frac{4}{3}[/tex] )² + b (- [tex]\frac{4}{3}[/tex] ) - 4 = 0

21 × [tex]\frac{16}{9}[/tex] - [tex]\frac{4}{3}[/tex] b - 4 = 0

[tex]\frac{112}{3}[/tex] - [tex]\frac{4}{3}[/tex] b - 4 = 0

Multiply through by 3

112 - 4b - 12 = 0

100 - 4b = 0 ( subtract 100 from both sides )

- 4b = - 100 ( divide both sides by - 4 )

b = 25 ← value of b

The equation can now be written as

21x² + 25x - 4 = 0 ← in standard form

with a = 21, b = 25, c = - 4

Use the quadratic formula to solve for x

x = ( - 25 ± [tex]\sqrt{25^2-(4(21)(-4)}[/tex] ) / 42

  = ( - 25 ± [tex]\sqrt{961}[/tex] ) / 42

  = ( - 25 ± 31 ) / 42

x = [tex]\frac{-25-31}{42}[/tex] = [tex]\frac{-56}{42}[/tex] = - [tex]\frac{4}{3}[/tex]

or x = [tex]\frac{-25+31}{42}[/tex] =  [tex]\frac{6}{42}[/tex] = [tex]\frac{1}{7}[/tex]

The other solution is x = [tex]\frac{1}{7}[/tex]

Answer:

E. 36 is the answer.

Step-by-step explanation:

27 is a multiple of 9. 9 is 1/3 of 27. Add 9 with 27 to get 36. 9/36 is equal to 1/4. To prove it, multiply 9 with 4 to get 36.

I hope this was clear!

Answer:

11.33 in.  to the nearest hundredth.

Step-by-step explanation:

The perimeter of the shaded area =   length of the 2 straight lines + the length of the 2 arcs = 4 + length of the 2 arcs.

Calculate the length of the outer arc:

This equals (30 / 360) * perimeter of the largest circle

= 1/12 * 2 π * 8

= 4/3 π in.

The inner circle has a radius of  8 - 2 = 6 ins

so the length of the inner arc

= 1/12 * π * 2 * 6

= π in.

So the perimeter of the shaded region = 4 + 4/3 π + π

= 4 + 7π/3

=  11.33 in.

Answer:

Fourth graph

Step-by-step explanation:

First:  some important housekeeping:

Please use " ^ " to denote exponentiation:  f(x) = (1/4)(4)^x, and enclose fractional coefficients such as 1/4 inside parentheses:  (1/4).

f(x) = (1/4)(4)^x is an exponential growth function; we know that because the base is greater than 1.  The graph is vertically compressed by a factor of 1/4.

You have four graphs from which to choose.

Eliminate the first and second graphs; they are of expo decay functions.

Evaluate f(x) = (1/4)(4)^x at x = 0 to find the y-intercept:

f(0) = (1/4)(4)^0 = 1/4

Both the 3rd and the 4th graphs go through (0, 1/4).  Good.

The 3rd graph shows the curve going through (3, 2).  Let's determine whether or not this point lies on f(x) = (1/4)(4)^x:

f(3) = (1/4)(4)^2  =  (1/4)(16) = 4.  No.

The 4th graph shows the curve going through (1, 1).  Does this point satisfy f(x) = (1/4)(4)^x?  f(1) = (1/4)(4)^1 = 1.  Yes.

The fourth graph is the correct choice.

The graph of the function is given below.

The graph will have the coordinates: (1, 1) and (2, 4).

Option D is the correct answer.

We have,

The graph of the function f(x) = [tex](1/4)4^x[/tex] is an exponential function.

The base of the exponential function is 4, and the function is raised to the power of x.

The coefficient (1/4) affects the rate of growth or decay of the function.

Here are some characteristics of the graph:

- As x approaches negative infinity, the function approaches 0, but it never reaches exactly 0.

- As x approaches positive infinity, the function grows without bound, becoming larger and larger.

- The graph is always positive, as the base 4 raised to any power is positive.

And,

When x = 1, f(x) = 1/4 x [tex]4^1[/tex] = 1/4 x 4 = 1

When x = 2, f(x) = 1/4 x 4² = 1/4 x 16 = 4

Thus,

The graph of the function is given below.

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Answer:

it would be 30

Step-by-step explanation:

Answer:

b=2

Step-by-step explanation:

1.1     Pull out like factors :

  4b - 8  =   4 • (b - 2)

Equation at the end of step  1  :

Step  2  :

Equations which are never true :

2.1      Solve :    4   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

2.2      Solve  :    b-2 = 0

Add  2  to both sides of the equation :

                     b = 2

One solution was found :

                  b = 2

Answer:

b = 2

Step-by-step explanation:

Equation: 4b - 2 = 6

Step 1: Use the addition property of equality by adding 2 on both sides to put x on one side. Now we have the equation 4b = 8.

Step 2: Use the division property of equality by dividing 4 on both sides to isolate x. Now we have the equation b = 2.

Step 3: Verify your answer by substituting 2 into the equation 4b - 2 = 6. Now we have 4(2) - 2 = 6, which is the same as 8 - 2 = 6. After simplifying, we get 6 = 6, which is a true statement. Therefore, the answer is b = 2