Rebecca is playing a video game that involves planting and cutting down trees. She moves up an energy level for each tree she plants, and she moves down a level for each tree she cuts. If Rebecca reaches energy level 10, she will earn bonus points.

Rebecca is currently at energy level 4. The results of her next 3 turns are:
Turn 1: 6 trees cut
Turn 2: 8 trees planted
Turn 3: 1 tree cut

Answer the questions to find out whether Rebecca earned bonus points in the next 3 turns. Use the number line to help you add.

A number line from -5 to 10.
1. Using only addition, write an expression that represents Rebecca's score after these three turns. (Remember that she starts at an energy level of 4.). (2 points)

2. What is Rebecca's energy level after Turn 1? (2 points)

3. What is Rebecca's energy level after Turn 2? (3 points)

4. What is Rebecca's energy level after Turn 3? Will she earn bonus points after Turn 3? Explain why or why not. (3 points)

The solution to the system of equations is (0, -5) or (4, 3).

What is the system of equations?

A system of equations is a set of two or more equations with the same variables. A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously.

To solve the system of equations, we'll substitute the second equation into the first:

x^2 + (2x - 5)^2 = 25

Expanding the square in the second equation:

x^2 + 4x^2 - 20x + 25 = 25

5x^2 - 20x = 0

5x(x - 4) = 0

So x = 0 or x = 4.

For x = 0:

y = 2x - 5 = -5

For x = 4:

y = 2x - 5 = 3

Hence, the solution to the system of equations is (0, -5) or (4, 3).

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The distance between the tips of the hands is changing at a rate of 55 inches per minute at 9 o'clock.

To find the distance between the tips of the hands, we can use the Pythagorean theorem:

distance = $\sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10$

As the clock moves, the minute hand will rotate 360 degrees in 60 minutes, or 6 degrees per minute, and the hour hand will rotate 360 degrees in 12 hours or 0.5 degrees per minute.

To find the rate at which the distance between the tips of the hands is changing, we need to find the rate at which the angle between the hands is changing.

We can use the fact that the angle between the hands is equal to the difference in the angular velocities of the hands.

Angular velocity of the minute hand = 6 degrees/minute

Angular velocity of the hour hand = 0.5 degrees/minute

Angular velocity of the distance between the tips of the hands = 6 - 0.5 = 5.5 degrees/minute

To convert this to distance per minute, we can use the fact that the distance between the tips of the hands is equal to the length of the hour and minute hand multiplied by the sine of the angle between them.

Distance per minute = 10 * 5.5 degrees/minute = 55 inches/minute

So, the distance between the tips of the hands is changing at a rate of 55 inches per minute at 9 o'clock.

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Answer:

Step-by-step explanation:

The sum of a geometric sequence can be found using the formula

Sn = a₁ (1 - rⁿ⁻¹)/ (1 - r)

where a₁ is the first term, r is the common ratio, and n is the number of terms.

In this case, a₁ = -8, r = -3, and n = 10.

Plugging these values into the formula, we get

Sn = -8 (1 - (-3)⁹⁻¹) / (1 - (-3))

Sn = -8 (1 + 3⁹) / 4

Sn = -8 (1 + 19683) / 4

Sn = -8 × 19684 / 4

Sn = -4920

In addition to the 3-digit numbers shown, the letters A, B, C, and D each represent a unique single digit. out of the  following e.19  could be the sum of A+B+C+D.

To find the sum of A, B, C, and D, we first need to add the 3-digit numbers ABC and DBC. To do this, we can use the standard column addition method. Starting from the right column, we add the single digits A and D together to get the one digit of the sum. Moving to the left column, we add the two-digit numbers BC and BC, which adds up to 180.

Then, we add the single digits B and C together to get the tens digit of the sum. Finally, we add the two-digit numbers AC and DC together to get the hundreds of digits of the sum. When we put all the digits together, we get the sum of A, B, C, and D to be 850. Since 850 is not one of the given answers, we look for the nearest option. The nearest option is 19, which is the answer to this question.

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The weight of a piece of luggage that can be checked in, given the use of w to represent the weight, is W < 45.

The statement given is that, " each piece of luggage to be checked in must weigh less than 45 pounds. "

What this means is that the mass of each luggage should not be up to 45 pounds. The weight of the luggage should not be more than 45 pounds and it should not be equal to 45 pounds.

If the weight of luggage was said to be equal or less, then the symbol of equal or less than, which is ≤ would have been used.

However, the weight should be less than 45 pounds and with the weight being w, the expression would be:

W < 45

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The rest of the question is:

Use W to represent the weight (in pounds) of a piece of luggage that can be checked in

The cost of painting the room walls with two coats of paint would be $84.38

To determine the cost of painting the room walls with two coats of paint, you would need to know the total square footage of the walls you are planning to paint. Once you have that information, you can calculate the total cost by multiplying the number of gallons of paint required by the cost per gallon. For example, if the room has 800 square feet of walls, you would need 2.28 gallons of paint (800/350 = 2.28) and the total cost would be $84.38 (2.28 x $36.50). If you want to know the cost of one coat, you will need to divide that number by 2.

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Answer:

$338/20 = $16.90

Answer:

[tex]\$16.90 \textrm{ per hour}[/tex]

Step-by-step explanation:

To solve this, we simply have to divide the total amount of money that Taylor earned by the number of hours that she worked for.

[tex]\dfrac{\$338.00}{20 \textrm{ hr}} = \$16.90 \textrm{ per hr}[/tex]

The volume of the largest right circular cylinder (in cubic units) that fits in a sphere of radius 4 units is 154.7 cubic units.

First, draw a diagram. The diagram shows the cylinder inscribed in the sphere. Given that in the diagram the height, h, we can find the radius of the cylinder in terms of r using the Pythagorean Theorem.

h represents half of the total height of the cylinder. choose h instead of h² to simplify things better.

To find the volume of the cylinder, we need to multiply the area of the top by the total height of the cylinder. In other words;

V = π(radius of cylinder)²(height of cylinder)

V = π(√r²−h²)²(2h)

V = 2πh(r²−h²)

V = 2π(r²h−h³)

d/dxV(h) = 2π(r²−3h²) = 0

The 2π divides out and we are left with;

r²−3h² = 0

After some rearranging;

h² = r²/3

Take the square root of both sides.

h = r/√3

To find the volume, we need to put this into the volume equation.

V = 2πh(r²−h²) = 2π(r/√3){r²−(r/√3)²}

V = (2πr/√3)(r²−r²/3)

V = (2πr/√3){(3r²−r²)/3}

V = (2πr/√3)(2r²/3)

V = 4πr³/3√3

V = 4√3πr³/9

Now, put the value of r in the above equation, and we get

V = 4√3π(4)³/9

V = 256√3π/9

V = 154.7 cubic units

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He encourages them to remain brave and steadfast, and emphasizes the importance of unity and solidarity in order to achieve victory.

In the Leon, King Leonidas uses the to rally his troops and to inspire them to fight for freedom. He uses it to explain the importance of fighting for freedom and the consequences of failing to do so. He emphasizes the importance of remaining brave and steadfast, and speaks of the need for unity and solidarity in order to achieve victory. He also uses the Maka to explain the importance of having faith in the gods and themselves, and trust that the gods will grant them victory. King Leonidas’ use of the Maka is much more complex than a ceremonial purpose, as he is using it to motivate and teach his troops. He speaks of the need to stay united and to fight for freedom, which is something that is larger than any one individual. He stresses the importance of having faith in the gods, as well as in each other, and that by doing so, victory can be achieved.

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The most typical or average value among a group of numbers is called the mean. It is a statistical measure of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."

Steel rods are produced by a firm. The lengths of the steel rods have a mean of 97 cm and a standard deviation of 1 cm, and they are regularly distributed. 15 steel rods are packaged together for shipping. determine the likelihood that the average length of a bundle of steel rods chosen at random is less than 140.7 cm.

mean is N (M) (109,1.6)

Looking for P(M 108.7) to P(z ???) conversion utilizing N(0,1) z-statistic transformation

P(z [M - population mean]/[SD/square root(sample size)]) = P(z [108.7-109)/[1.6/sqrt(27)] = P(z -0.974] = 0.165.

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4/3 is the valve of |MN| ^2 of a given tetrahedron  in which M AND N are the mid points of the edges AB and CD . is explained below:

on observing the diagram we can estimate that image of point D in the plane is given  by ABC is    [tex](2\sqrt{2} , 0 , -2 )[/tex]  and volume of tetrahedron ACBM is 4/3

AB=BC=CD=AD =a

hence a =[tex]2\sqrt{2}[/tex]  then MA =2 ; 2b^2 =4  ; therefore , b=[tex]\sqrt{2}[/tex]

then value of B ([tex](\sqrt{2} ,\sqrt{2}, 0 )[/tex]    then according to the  theorem we get as

[tex]MA^{2} + MB^{2} = AB^{2}[/tex] we have condition by diagram as MA ⊥ MB similarly

MA ⊥ MC , MB ⊥ MC  hence , MA.MC =-2z =0

hence MB.MC= [tex]\sqrt{2x} +\sqrt{2y} =0[/tex] therefore we get y=-x and z=0 hence the coordinates for  C(x ,-x ,0)

and also MC^2 =2x^2=MA^2 =4 ; x=[tex]\sqrt{2}\\[/tex]  (x>0)

hence C[tex](\sqrt{2} ,\sqrt{2}, 0 )[/tex]  hence

|MN|^2 = [tex]\frac{1}{6} |MA| . |MB| . |MC| = \frac{4}{3}[/tex]

hence the value of |MN|^2 = 4/3

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Answer:

wouldn't this be 4,2?

Step-by-step explanation:

i remember doing this in school last year and dilation means you would multiple the coordinates by what ever the dilation factor was, in this case its 2.

Answer:

No

Step-by-step :

n/n + 1 > 1/2, (n + 1)/n < 2, (n+1)/n  - 2 < 0, [(n + 1) - 2n]/n < 0, (1 - n)/n < 0, n > 0, 1 - n < 0, n > 1

n/n + 1 < 99/101, (n + 1)/n > 101/99, [99(n+1)]/n > 101, [(99n + 99)]/n > 101, [(99n + 99)]/n - 101 > 0, (99n + 99 - 101n)/n > 0

(99 - 2n)/n > 0, n > 0, 99 - 2n > 0, 2n < 99, n < 99/2

1 < n < 49.5

Answer:

y = 5A/r - 2

Step-by-step explanation:

It is a simple algebra. pkease see the above

Answer:

Step-by-step explanation:

Answer:

answer is b second which is -6

Answer: 0.28571428571

Step-by-step explanation: 8 dived by 28

Answer:

Step-by-step explanation:

2π√l/g = (2*3.14*sqrt(98))/32 = 10.945

A set of reflections that would carry hexagon ABCDEF onto itself would be "x-axis, y=x, x-axis" or "y=x, x-axis, y-axis".

What is a combination of reflections?

Combination of Two Reflections. A point or object once reflected can further be reflected to form a new image. The axes of these reflections may be parallel to each other or they intersect each other at a point.

Given the coordinates of hexagon ABCDEF, it can be determined that a set of reflections that would carry the hexagon onto itself would be a combination of reflections over the x-axis and y-axis.

One possibility would be to reflect over the x-axis, then reflect over the y=x line, and finally reflect over the x-axis again.

This would take the hexagon from its original position to itself.

Another possibility would be to reflect over the y = x line, then reflect over the x-axis, and finally reflect over the y-axis.

This would also take the hexagon from its original position to itself.

Hence, a set of reflections that would carry hexagon ABCDEF onto itself would be "x-axis, y=x, x-axis" or "y=x, x-axis, y-axis".

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The maximum number of interior angles of a convex polygon would be 7.

Imagine operating a small vehicle on a track with a polygonal shape. Your compass is handy (directional, not one for drawing circles). The automobile concludes the lap in the same direction as it began. If there was a compass, it has completed one full rotation.

180 - 131 = 49°

360/49 = 7.346938775510204

So 7 interior angles max

A convex polygon's outside angles add up to 360 degrees.

131 degrees for the inside angles and 49 degrees for the outside angles. The vehicle is capable of seven rotations at 49 degrees and one turn at 17 degrees, for a total of 360 degrees in one lap.

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The question is wrong the correction:

Alex thinks 131 degrees are neat. What is the maximum number of interior angles of a convex n-gon that can measure 131 degrees?

Answer:

sin x + cos x = [tex]\sqrt{2}[/tex]

Step-by-step explanation:

given

tan x = 1 , then

x = [tex]tan^{-1}[/tex] (1) = 45°

the exact values of both sin45° and cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

sin x + cos x

= sin45° + cos45°

= [tex]\frac{1}{\sqrt{2} }[/tex] + [tex]\frac{1}{\sqrt{2} }[/tex]

= [tex]\frac{2}{\sqrt{2} }[/tex]

rationalise the denominator by multiplying numerator/ denominator by [tex]\sqrt{2}[/tex]

= [tex]\frac{2(\sqrt{2}) }{\sqrt{2}(\sqrt{2}) }[/tex]

= [tex]\frac{2\sqrt{2} }{2}[/tex]

= [tex]\sqrt{2}[/tex]

Answer:

1.33333333333

Step-by-step explanation:

1.33333333333

Answer:the final answer is 7

Step-by-step explanation:

Tom's pencil is longer than Ellen's pencil with (3x+10)cm

Subtraction is one of the four arithmetic operation along with addition, multiplication and division. Subtraction is an operation that represents removal of objects from a collection. For example, in the adjacent picture, there are 5 minus 2 peaches, this means that 5 peaches with 2 taken away, resulting in a total of 3 peaches.

Ellen's pencils length = 2x+15

Tom's pencil length = 5x+25

Tom's pencil will be longer than Ellen's with;

(5x + 25 ) - (2x+15)

= 5x + 25 -2x - 15

collect like terms

5x -2x +25-15

3x +10

therefore Tom's pencil is longer than Ellen's pencil with ( 3x+10) cm

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The measure of angle R, in degrees, is 150°.

A parallelogram is a quadrilateral or four-sided shape, that has opposite sides that are parallel to each other. The opposite sides of a parallelogram are equal in length, and the opposite angles are also equal in measure.

In a parallelogram, opposite angles are equal, so if the measure of angle P is five times the measure of angle Q, then the measure of angle R must also be five times the measure of angle Q.

Let's call the measure of angle Q "x". Then the measure of angle P is 5x, and the measure of angle R is 5x.

Therefore, the measure of angle R in degrees is 5x degrees.

We know,

All of the angles added together = 360°

∠5Q +∠Q+∠5Q+∠Q = 360    Solve for Q

∠12Q = 360  

⇒  ∠Q = 30°

then ∠P = ∠5Q = 5(30) = 150°    

and,

 ∠P = ∠R    

⇒ ∠R = 150°

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Answer:

Area for triangle : Area =  1⁄2× base × height

Area for square : Area = base × height

Step-by-step explanation:

Answer: First question for the slope that passes through (-7, -2) and (6,-2) is m = 0. For the line that passes through (5, 3) and 5, -7) is m = 1/0.

I hope this helps!

Step-by-step explanation:

(−7,−2) and (6,−2)

(x₁,y₁) = (−7,−2)

(x₂,y₂) = (6,−2)

y₂ − y₁ / x₂−x₁

= −2 − −2 / 6 − −7

= 0/13

m = 0

m = y₂ − y₁ / x₂ − x₁

= −7 − 3 / 5 - 5

= −100

m = 1/0

Answer:

0.1296

Step-by-step explanation:

9/25 = 0.36

0.36 squared = 0.1296

Answer:

a2 - a1

Step-by-step explanation:

Tn= a+(n-1)d

Tn = a1 (an -1) a2-a1