Madeline is standing 2x- 4 feet from the base of a tree. The height of the tree is 5x + 6 feet. Find the equation that shows
the straight-line distance from Madeline's feet to the top of the tree in terms of x.
Provide your answer below:

Answer:

Clockwise rotation of 90 degrees with the center of rotation being the origin or anti-clockwise rotation of 270 degrees with the center of rotation being the origin.

Step-by-step explanation:

Rotation is one of the examples of linear transformations in which a point or a group of points move at a given angle with the fixed length. This means that the initial points (pre-images) move along the arc of the circle. They can be transformed at any angle. The resultant of any transformation is called the image. The trapezoid 2 is the pre-image and the trapezoid 6 is the image. It can be clearly sensed that the trapezoid 2 is being rotated clockwise at the angle of 90 degrees with the center of rotation being the origin. However, further inspections show that trapezoid 2 can also be mapped/transformed on trapezoid 6 by the anti-clockwise rotation of 270 degrees, center of rotation being the origin. Rest of the trapezoids are either reflections or rotations of different angles!!!

Answer:

Rotation I think.

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:

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:

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:

Part 1) False

Part 2) False

Step-by-step explanation:

we know that

The equation of the circle in standard form is equal to

[tex](x-h)^{2} +(y-k)^{2}=r^{2}[/tex]

where

(h,k) is the center and r is the radius

In this problem the distance between the center and a point on the circle is equal to the radius

The formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Part 1) given the center of the circle (-3,4) and a point on the circle (-6,2), (10,4) is on the circle.

true or false

substitute the center of the circle in the equation in standard form

[tex](x+3)^{2} +(y-4)^{2}=r^{2}[/tex]

Find the distance (radius) between the center (-3,4) and (-6,2)

substitute in the formula of distance

[tex]r=\sqrt{(2-4)^{2}+(-6+3)^{2}}[/tex]

[tex]r=\sqrt{(-2)^{2}+(-3)^{2}}[/tex]

[tex]r=\sqrt{13}\ units[/tex]

The equation of the circle is equal to

[tex](x+3)^{2} +(y-4)^{2}=(\sqrt{13}){2}[/tex]

[tex](x+3)^{2} +(y-4)^{2}=13[/tex]

Verify if the point (10,4) is on the circle

we know that

If a ordered pair is on the circle, then the ordered pair must satisfy the equation of the circle

For x=10,y=4

substitute

[tex](10+3)^{2} +(4-4)^{2}=13[/tex]

[tex](13)^{2} +(0)^{2}=13[/tex]

[tex]169=13[/tex] -----> is not true

therefore

The point is not on the circle

The statement is false

Part 2) given the center of the circle (1,3) and a point on the circle (2,6), (11,5) is on the circle.

true or false

substitute the center of the circle in the equation in standard form

[tex](x-1)^{2} +(y-3)^{2}=r^{2}[/tex]

Find the distance (radius) between the center (1,3) and (2,6)

substitute in the formula of distance

[tex]r=\sqrt{(6-3)^{2}+(2-1)^{2}}[/tex]

[tex]r=\sqrt{(3)^{2}+(1)^{2}}[/tex]

[tex]r=\sqrt{10}\ units[/tex]

The equation of the circle is equal to

[tex](x-1)^{2} +(y-3)^{2}=(\sqrt{10}){2}[/tex]

[tex](x-1)^{2} +(y-3)^{2}=10[/tex]

Verify if the point (11,5) is on the circle

we know that

If a ordered pair is on the circle, then the ordered pair must satisfy the equation of the circle

For x=11,y=5

substitute

[tex](11-1)^{2} +(5-3)^{2}=10[/tex]

[tex](10)^{2} +(2)^{2}=10[/tex]

[tex]104=10[/tex] -----> is not true

therefore

The point is not on the circle

The statement is false

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:

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:

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:

[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:

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:

4th option

Step-by-step explanation:

i have answered ur question

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

Answer:

The value of x is 4

Step-by-step explanation:

we know that

The Intersecting Secants Theorem states that  When two secant lines intersect each other outside a circle, the products of their segments are equal

so

[tex](x-1+5)(5)=(x+2+4)(4)\\ (x+4)5=(x+6)4\\5x+20=4x+24\\5x-4x=24-20\\x=4[/tex]

Answer:

y=2

Step-by-step explanation:

If I interpreted what you wrote correctly, the equations were 5x-4y=7 and x=5-y. Given these equations, we can substitute the x=5-y into the other equation due to it quite literally being equal to x. When you substitute the x-equation in, it reads 5(5-y)-4y=7. Distribute the 5 into the (5-y) to get 25-5y-4y=7. Combine like terms to get 25-9y=7. Next, subtract the 25 from each side to isolate the -9y. This leaves yoy with -9y= -18. Divide by -9 on each side to isolate and find y. This leaves you with y=2. You can check your work by substituting the y=2 into the second equation to find x and then use the x and y to check your solution in the first equation. :)

Answer:

36/23

Step-by-step explanation:

Answer:

B - 0.18B

0.82B

Step-by-step explanation:

If B is the price of the board game, then the discount will be:

B * 18/100

= B * 0.18

= 0.18B

The expression for the cost Bo will pay for the game is:

B - 0.18B => Original price - discount

The expression can also be written as: (after solving)

0.82B ..

Answer:

A=0.82B

E=B−0.18B

hope this helps

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:

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:

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:

C

Step-by-step explanation:

The general rule for the quadratic function is

[tex]y=ax^2+bx+c[/tex]

From the graph you can see that the curve passes through the points (2,4), (1,7) and (3,7), so

[tex]y(2)=4\Rightarrow 4=a\cdot 2^2+b\cdot 2+c\\ \\y(1)=7\Rightarrow 7=a\cdot 1^2+b\cdot 1+c\\ \\y(3)=7\Rightarrow 7=a\cdot 3^2+b\cdot 3+c[/tex]

We get the system of three equations:

[tex]\left\{\begin{array}{l}4a+2b+c=4\\ \\a+b+c=7\\ \\9a+3b+c=7\end{array}\right.[/tex]

Subtract these equations:

[tex]\left\{\begin{array}{l}4a+2b+c-a-b-c=4-7\\ \\9a+3b+c-a-b-c=7-7\end{array}\right.\Rightarrow \left\{\begin{array}{l}3a+b=-3\\ \\8a+2b=0\end{array}\right.[/tex]

From the second equation:

[tex]b=-4a[/tex]

Substitute it into the first equation:

[tex]3a-4a=-3\\ \\a=3[/tex]

So,

[tex]b=-4\cdot 3=-12[/tex]

and

[tex]3+(-12)+c=7\\ \\c=7+9=16[/tex]

The quadratic function is

[tex]y=3\cdot x^2-12x+16[/tex]

[tex]a_1=-3\\r=7\\a_n=a_{n-1}\cdot r\\\\ \boxed{a_n=7a_{n-1}}[/tex]

[tex]a_{n+1} =7a_{n}[/tex].

If we know the term [tex]n^{th}[/tex] and the common relation, r, of a geometric sequence, you can find the term [tex](n+1)^{th}[/tex] using the recursive formula [tex]a_{n+1} =a_{n}.r[/tex].

The first term of the geometric sequence is a₁ = -3.

The common relation we have to find the relationship between a term and the term that precedes it.

[tex]r=\frac{-21}{-3} = 7[/tex]

The recursive formula is:

[tex]a_{1} =-3[/tex]

[tex]a_{n+1} =7a_{n}[/tex]

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.

Learn more about graphs here:

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[tex]\bf y = \stackrel{\stackrel{monthly~fee}{\downarrow} }{10}~~\stackrel{\stackrel{month}{\downarrow }}{x}+\underset{y-intercept}{\stackrel{\stackrel{registration~fee}{\downarrow }}{30}}~\hfill \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Answer: a. The y-intercept is 30. This is the cost of registration.

Step-by-step explanation:

The standard equation of line in intercept form is given by  :-

[tex]y=mx+c\ \ \ \ \ \ \ (i)[/tex], where m is the slope of the line and c is the y-intercept.

Given : Sara plotted the data and determined that the average gym costs consist of a one-time registration fee and a monthly fee modeled by the equation :-

[tex]y = 10x + 30[/tex]

By comparing it to the equation (i), we have

c=30 and m=10

i.e. The y-intercept is 30.

Also, y-intercept of any function shows the starting value of the function when x=0.

Thus, This is the cost of registration ( starting fee).

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.

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:

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:

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!

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:

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:

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