Mathematics College

A square pyramid has a base with an area of 20 square meters, and its lateral faces have a slant height of x meters. Sydney is constructing a second square pyramid with the same size base, but the lateral faces of her pyramid have a slant height twice as long, 2x. Which statement best describes how the surface area of Sydney’s pyramid compares to the surface area of the original pyramid?

1. Sydney’s pyramid will have the same surface area because the .5 in the expression for the area of the triangular faces will make up for the slant height being doubled.
2. Sydney’s pyramid will have the same surface area because the slant height is not used when finding surface area.
3. Sydney’s pyramid will have a surface area that is exactly double the original pyramid’s because the slant height is used when finding the area of every lateral face.
4. Sydney’s pyramid will have a surface area that is greater than the original pyramid’s but not double the area because the slant height is not used when finding the area of the base.


30 POINTS

Answers

Answer 1
the surface area of a square pyramid with base length b and slant height x is
[tex]A=b^2+2bx[/tex]

note that b²=base area

so, if we say that her original pyramid's surface area is [tex]A_1=b^2+2bx[/tex], then the new one has a slant height of twice that, ie, we replace x with 2x and see what happens
[tex]A_2=b^2+2b(2x)[/tex]
[tex]A_2=b^2+4bx[/tex]
if we try to work [tex]A_1[/tex] back into there
[tex]A_2=b^2+2bx+2bx[/tex]
[tex]A_2=(b^2+2bx)+2bx[/tex]
[tex]A_2=A_1+2bx[/tex]



see our options
option 1 is wrong since the surface area increased by 2bx

option 2 is wrong since the surface area increased by 2bx, also we do use the slant height when finding surface area

option 3 is wrong because we got [tex]A_2=A_1+2bx[/tex] and not [tex]A_2=2(A_1)[/tex]

option 4 is correct since the new surface area is greater than the original by 2bx


answer is option 4
Answer 2

Answer:

Sydney’s pyramid will have a surface area that is greater than the original pyramid’s but not double the area because the slant height is not used when finding the area of the base.

Step-by-step explanation:

Related Questions

To win at lotto in a certain state, one must correctly select 6 numbers from a collection of 50 numbers (one through 50). the order in which the selections is made does not matter. how many different selections are possible?

Answers

Asked and answered elsewhere.
https://brainly.com/question/10013755

We have been given that the order doesn't matter in the selection procedure. Hence, the case is of combination.

The formula for the combination is given by

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Now, in order to win at lotto, one must correctly select 6 numbers from a collection of 50 numbers. Thus, the required ways should be

[tex]^{50}C_6[/tex]

Using the above formula, the number of different selections are

[tex]^{50}C_6=\frac{50!}{6!(50-6)!}\\ \\ =\frac{50!}{6!44!}\\ \\ =\frac{44!\times 45\times 46\times 47 \times 48\times 49\times 50}{6!44!}\\ \\ =15890700[/tex]

Therefore, 15890700 different selections are possible.

fully expand the logarithm: log(x^3/z^5)

Answers

to expand this logarithm, we have to apply the rules. These rules are;

Log(A/B) = logA - LogB and Alogx=log(x∧A)

Log (x³/z∧5) = log (x³) - log z∧5
                    =3log x - 5log z
Using the following properties we can expand the given expression:

1) Quotient Rule of Logs:
Log(A/B) = Log A - Log B

2) Power Rule of Logs: 
[tex]Log(a)^{b}=b*Log(a) [/tex]

[tex]log( \frac{ x^{3} }{ z^{5} } ) \\ \\ =log( x^{3})-log( z^{5}) \\ \\ =3logx-5logz[/tex]

Given: KLMN is a trapezoid, KF =10 MF ║ LK AKLMF = AFMN Find: KN

Answers

The trapezoid is shown in the picture attached.

We know:
LK // MF
KF = 10
A(KLMF) = A(FMN)

Since LM // KF (because they are bases of the trapezoid) and LK // MF because is given in the hypothesis, KLMF is a parallelogram.
The area of a parallelogram is given by the base times the height.
A(KLMF) = b × h
               = 10 × h

The area of a triangle is given by the formula:
A(FMN) = (b × h) / 2
             = (FN × h) / 2

We know that the two areas are congruent, therefore:
A(KLMF) = A(FMN)
10 × h = FN × h / 2

The two "h" cancel out because they are the same and we can solve for FN:
10 = FN / 2
FN = 20

Now we can calculate:
KN = KF + FN = 10 + 20 = 30

Hence, KN is 30 units long.
Final answer:

In a trapezoid with parallel sides, if a pair of opposite sides are equal, then the other pair of opposite sides are also equal. Therefore, in the given trapezoid KLMN, KN is equal to AN + 10.

Explanation:

In the given trapezoid KLMN, the sides KF and LM are parallel. We are given that KF = 10 and AFMN = AKLMF. We need to find KN.

Since KF and LM are parallel, KF = LM. Therefore, LM = 10.

Since AFMN = AKLMF, we can say that AN = KL. So, AN + LM = KL + KF. Substituting the given values, we get AN + 10 = KL + 10. Therefore, AN = KL.

Hence, KN = KL + LM = AN + LM = AN + 10.

Therefore, KN = AN + 10.

Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time period. What interest rate did she earn? Use the formula I=Prt to find your answer, where I is interest, P is principal, r is rate and t is time. Enter your solution in decimal form rounded to the nearest hundredth. For example, if your solution is 12%, you would enter 0.12.

Answers

[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\to &\$450\\ P=\textit{original amount deposited}\to& \$3000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to &3 \end{cases} \\\\\\ 450=(3000)(r)(3)\implies \cfrac{450}{(3000)(3)}=r\implies \cfrac{1}{20}=r \\\\\\ 0.05=r\implies r\%=0.05\cdot 100\implies r=\stackrel{\%}{5}[/tex]

What is the number of social security credits a worker needs to earn over his or her working lifetime to collect Social security benefits?

Answers

According to the Social Security Administration website, the number of work credits you need to get benefits depends on when you were born.  If you were born in 1929 or afterward, you need 40 credits.  If you were born before 1929, you don't need 40: 39 credits are required if you were born in 1928, 38 credits if you were born in 1927, etc.

The graph of y=|x| is transformed as shown in the graph below. Which equation represents the transformed function?

Answers

The vertex of the graph y=|x| is at (0,0)

After transformation the vertex becomes at (-3,-2)
Apply axes transformation from (0,0) to (h,k)
So, the transformation rule is (x,y) → (x-h, y-k)
(h,k) will be equal (-3,-2)


∴ y=|x| ⇒ (y-(-2)) = |x-(-3)|
∴(y+2) = |x+3|
∴ y = |x+3|-2


So, the correct answer is option 2

we have that

the original function [tex]y=\left|x\right|[/tex] has the vertex at point [tex](0,0)[/tex]

The transformed function has the vertex at point [tex](-3,-2)[/tex]

so

the rule of the translation is equal to

[tex](x,y)------> (x-3,y-2)[/tex]

That means

The translation is [tex]3[/tex] units to the left and [tex]2[/tex] units down

therefore

the answer is

the transformed function is [tex]y=\left|x+3\right|-2[/tex]



function that has the same domain as y=2√x

Answers

The rest of the question;
A.y= [tex] \sqrt{2x} [/tex]
B.y=[tex] \sqrt[3]{ x^{2} } [/tex]
C.y=[tex] \sqrt{x-2} [/tex]
D.y=[tex] \sqrt[3]{x-2} [/tex]
====================================================

We are given the function
y = 2 √x

The domain for the given function is this
{ x | x ≥ 0 }

The answer is A. y = √2x

In general any function that has a domain of x that is equal to or greater than 0. Some examples:
f(x) = √x  -  2
f(x) = 5 √x



Answer:

The answer is A. y = √2x

Step-by-step explanation:

Ben buys a car for $50,000. The value of the car decreases at a rate of 4% per year. How much will the car be worth in 3 years? A. $48,000 B. $44,237 C. $45,082 D. $43,270

Answers

Given that the value of $50000 car decreases by 4%  per year, the value after 3 years will be given by exponential form:
y=abˣ
where:
a=initial value
b=decreasing rate
x=time in years
from the information:
a=50000, b=0.96, x=3
thus
y=50000(0.96)³
simplifying we get:
y=$44, 236.8
~$44237

Answer:
B. $44,237

Solve the equation 3x+5y=4
for y

Answers

Answer:

y = (4 -3x)/5

Step-by-step explanation:

Find the terms containing y. If they are all on one side of the equation (it is), then identify the terms not containing y. Subtract those. Then, divide by the coefficient of y.

3x +5y = 4

5y = 4 - 3x . . . . . non-y term subtracted

y = (4 -3x)/5 . . . . divide by the coefficient of y

_____

If you like, you can rearrange this to slope-intercept form:

... y = -3/5x +4/5

The net asset value of stock in a mutual fund had increased by $20 per share when an investor decided to redeem them. The investor had purchased 100 shares of the stock for $2,316 and redeemed them for $4,301. What can you conclude about the fund? a. The fund is a no-load fund. b. The offer price of the fund was $0.15 less than the net asset value when purchased. c. The offer price of the fund was $0.15 more than the net asset value when purchased. d. The offer price of the fund was $0.15 more than the net asset value when sold.

Answers

The correct answer is letter c. The offer price of the fund was $0.15 more than the net asset value when purchased.


Formula for calculating NAV:

Net Asset Value (NAV) = (Assets - Debts) / (Number of Outstanding Units)

The Net Asset Value (NAV) is the price in which you pay to buy a unit of mutual fund scheme when you invest.

Which ordered pair is the vertex of y = [x - 3]+ 2?

A.(2, –3)

B.(–3, 2)

C.(3, 2)

D.(2, 3)

Answers

An absolute value function without transformations, [tex]y = |x|[/tex], has a vertex at (0, 0).  The transformations here are to shift the function right 3 and up 2.  The vertex would then be at (3, 2).  Your answer should be C.

on a game show that are 10 keys in the bag and three of the key start a car and contest in randomly choosing the key it doesn't not start the car she returned to the bag the host mixed up the back she randomly selects another key this key does not start the car either what is the probability of this no start no start outcome

Answers

What are the answers

y = x3 - 3x On which intervals is this function increasing?

Answers

The function is increasing on the intervals
  x ∈ (-∞, -1) ∪ (1, ∞)

hey can you please help me posted picture of question

Answers

G(x) = x² is the parent square function.

It has its vertex at origin and opens upwards.

The given graph is obtained by shifting the graph of x² 2 units vertically down. This vertically translation can be expressed by subtracting 2 from the parent function.

So,

F(x) = G(x) - 2

F(x) = x² - 2

Thus the correct option is A

What is the equivalent of pi over 3 radians in degrees?

Answers

(π/3)x(180/π)=60 degrees

[tex] \frac{ \pi }{3} [/tex] is equivalent to 60°


A line has a slope of 2 and a y intercept of (0,-4) what is the value of y when x=6

Answers

First we set up an equation with the givens (slope and y intercept):
y = 2x -4
next plug in 6 for x.
y = (2x6) - 4
y = 12 - 4

And this will give us the value of y: 8.
Final answer:

The question is about finding the y-value of a line when the x-value is given, knowing the slope and the y-intercept. By plugging the given slope, y-intercept and the provided x-value into the formula y = mx + b, we find that y equals 8 when x equals 6.

Explanation:

If we know the slope (m) of a line and the y-intercept (b), we can use the formula y = mx + b to calculate the y-value for any x-value. In the given question, the slope (m) is 2 and the y-intercept (b) is -4. If we want to find the y-value when x = 6, we can substitute these values into the formula:

y = 2*6 - 4

So, y = 12 - 4 = 8. Therefore, when x = 6, the value of y is 8.

Learn more about Line equation here:

https://brainly.com/question/21511618

#SPJ2

This is incredibly frustrating. PLEASE HELP ME

Answers

The correct option is: Option (C)

Explanation:
Given expression:
[tex]\sum_{i=1}^{25} 2^{2i}[/tex]

When i = 1: The answer is [tex]2^{2*1}[/tex] = 4
When i = 2: The answer is [tex]2^{2*2}[/tex] = 16
When i = 3: The answer is [tex]2^{2*3}[/tex] = 64
.
.
When i = 25: The answer is [tex]2^{2*25}[/tex] = [tex]2^{50}[/tex]

Which is the series mentioned in Option C

What is the vertex of the quadratic function f(x) = (x - 8)(x - 2)

Answers

good day ~_~ /////////////

Answer: (5, -9)

What is the vertex of the quadratic function f(x) = (x – 8)(x – 2)?

hey can you please help me posted picture of question

Answers

The correct answer is D. Graph D

Find the Vertex of   y = 3x2+7x+2

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 3 , is positive (greater than zero). 

 Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions. 

 Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex. 

 For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is  -1.1667  

 Plugging into the parabola formula  -1.1667  for  x  we can calculate the  y -coordinate : 
  y = 3.0 * -1.17 * -1.17 + 7.0 * -1.17 + 2.0 
or   y = -2.083
Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = 3x2+7x+2
Axis of Symmetry (dashed)  {x}={-1.17} 
Vertex at  {x,y} = {-1.17,-2.08}  
 x -Intercepts (Roots) :
Root 1 at  {x,y} = {-2.00, 0.00} 
Root 2 at  {x,y} = {-0.33, 0.00} 

We can find the roots of the given equation to determine its graph.

3x²+7x+2=0

Solving using factorization.

3x²+6x+x+2=0

3x(x+2)+1(x+2)=0

(3x+1)(x+2)=0

This means the roots of the equation are x = -2 and x = -1/3

Now from the graphs determine which one has the roots at  these two points. We can observe that Graph D has the roots at x=-2 and x=-1/3

So the answer to this question is option D

ln(x+2)-ln(4x+3)=ln(1/2*x)

Answers

ln(x+2)-ln(4x+3)=ln(1/2*x)

Using properties of  logarithms

[tex] \frac{ln(x+2)}{ln(4x+3)} = ln \frac{x}{2} \\ \\ \frac{x+2}{4x+3} = \frac{x}{2} \\ \\2(x+2)=x(4x+3) 2x+4=4x^2+3x \\ \\ 4 x^{2} +x-4=0 \\ \\ x= \frac{-b+/- \sqrt{b^{2}-4ac} }{2a} \\ \\ x= \frac{ -1+/-\sqrt{1+64} }{8} \\ \\ x_{1} = \frac{-1+ \sqrt{65} }{8} \\ \\ x_{2} = \frac{-1- \sqrt{65} }{8} Check: When you substitute x_{2} into \\ \\ ln(4x+3)=ln(4* \frac{-1- \sqrt{65} }{8} ) =ln( \frac{-1- \sqrt{65} }{2} ) you will get negative number under ln, that is impossible , [/tex]

so x2 is not a solution of this logarithmic equation.

Only x1 is a solution.


Instructions:Select the correct answer from each drop-down menu. The range of all real numbers x such that 2x − 5 < 7 and 4x + 10 > 6 is . The range of all real numbers x such that 2x − 5 < 7 or 4x + 10 > 6 is

Answers

In order to find the rang, solve for the first inequality:

2x - 5< 7

2x <12

x < 6

Solve for the second inequality:

4x +10 > 6
4x > -4 
x > -1

Graph these two inequalities on a number line to see that their union is the complete number line. Note that for any number of x can either be greater than negative 1 or less than 6 and can be both.

so the answer is:

range of negative infinity to infinity. required to use parenthesis

(-∞, ∞)

The circle belowis centered at the point (-2 ,1) and has a radiusof length 3

Answers

Answer:
Option A, (x + 2)² + (y - 1) = 9

Explanation:
The equation form of a circle is (x - h)² + (y - k)² = r², where the center is ordered pair (h, k) and r represents the radius.

From the given information, the center is point (-2, 1) and the radius (r) is 3 units. With this, we can plug the information in and simplify:
(x - (-2))² + (y - (1))² = (3)²
(x + 2)² + (y - 1)² = 9

The equation for the given circle is (x + 2)² + (y - 1)² = 9

which transformations are needed to change the parent some function to the sine function below?

Answers

Beginning with the function y = sin x, which would have range from -1 to 1 and period of 2pi:
Vertical compression of 1/2 compresses the range from -1/2 to 1/2
Phase shift of pi/2 to the left
Horizontal stretch to a period of 4pi, as the crests are at -4pi, 0, 4pi
Vertical shift of 1 unit up moves the range to 1/2 to 3/2
So the first choice looks like a good answer.
The first choice is the answer:

Solution:
the function y = sin x, which would have range from -1 to 1 and period of 2pi:

So the answer would be:Vertical compression of 1/2 compresses the range from -1/2 to 1/2Phase shift of pi/2 to the leftHorizontal stretch to a period of 4pi, as the crests are at -4pi, 0, 4piVertical shift of 1 unit up moves the range to 1/2 to 3/2

Factor \2x^2-11x+5=0

Answers

2x² - 11x + 5
2x² - x - 10x + 5
x(2x - 1) - 5(2x - 1)

(2x - 1)(x- 5) is your answer. 
Final answer:

The quadratic equation [tex]2x^2[/tex]-11x+5=0 is factored into (2x - 1)(x - 5), and it has solutions x = 0.5 and x = 5.

Explanation:

The question asks us to factor the quadratic equation[tex]2x^2[/tex]-11x+5=0. To do this, we need to find two numbers that multiply to give ac (where a is the coefficient of x^2 and c is the constant term) and add to give b (the coefficient of x). Here, ac is (2)(5)=10, and b is -11. The two numbers that satisfy this are -10 and -1 because -10 * -1 = 10 and -10 + -1 = -11.

We rewrite the middle term using these two numbers and then group the terms to factor by grouping:

[tex]2x^2[/tex]- 10x - x + 5 = 0
([tex]2x^2[/tex]- 10x) - (x - 5) = 0
2x(x - 5) - 1(x - 5) = 0
(2x - 1)(x - 5) = 0

The factored form of the quadratic equation is (2x - 1)(x - 5). Therefore, the solutions to the equation are x = 0.5 and x = 5, found by setting each factor equal to zero.

A ball is thrown into the air with an upward velocity of 32 ft/s. Its height h in feet after t seconds is given by the function h = –16t2 + 32t + 6. a. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. b. What is the ball’s maximum height? 1 s; 54 ft 2 s; 6 ft 2 s; 22 ft 1 s; 22 ft

Answers

For this case we have the following equation:
 h = -16t2 + 32t + 6
 Deriving we have:
 h '= -32t + 32
 Equaling to zero:
 -32t + 32 = 0
 We clear the time:
 t = 32/32
 t = 1 s
 We are now looking for the maximum height:
 h (1) = -16 * (1) ^ 2 + 32 * (1) + 6
 h (1) = 22 feet
 Answer:
 The ball reaches its maximum height in:
 t = 1 s
 The ball's maximum height is:
 h (1) = 22 feet
 option: 22 ft, 1 s

Answer: 22 ft, 1 s

Step-by-step explanation:

PLz help!

Write the equation of the line that passes through (3, −2) and has a slope of 4 in point-slope form. (2 points)


1 y + 2 = 4(x − 3)

2 y − 3 = 4(x + 2)

3 x − 3 = 4(y + 2)

4 x + 2 = 4(y − 3)

Answers

[tex]y+2=4(x-3)[/tex]

It's the first answer.
[tex]\text{Slope} = \dfrac{Y_2 - Y_1}{X_2 - X_1} [/tex]

Given that the slope = 4 and the coordinate is (3, -2),

[tex]4 = \dfrac{y + 2}{x + 3} [/tex]

[tex] y + 2 = 4(x - 3) [/tex]

Answer : y + 2 = 4(x - 3)  (Answer A)

Chloe puts 4 soaps and two bottles of lotion in each gift basket. She has 127 soaps and 85 bottles of lotion. How many gift baskets can Chloe complete?

Answers

127/4 = 31.75 = 31
85/2 = 42.5 = 43

She can only make 31 full gift baskets with the amount of soap she has.

Therefore, Chloe can make 31 gift baskets.

graph of this ellipse

x^2 + y^2 =1
_ _
4 16

Answers

check the picture below.

Q # 15 in the diagrams a || b a. Use the fiagrama o answer the question(diagrama not to scale.)

Answers

The interior angel to ∠7 is the angel ∠4

because ∠7 + ∠4 = 180°

The correct choice is number 1
I’m pretty sure its <4 angle four...
///EAGLEPAW

Two thirds of the families in smithville own their own homes. The total number of home owning families there is 480. How many families live in smithville?

Answers

x- the total number of families in Smithville.
(2/3)x  - the number of home owning families.
At the same time,  the number of home owning families is 480.

(2/3)x=480
x=480*3/2=720.

720 families live in Smithville.
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Cicero and Seneca introduced ideas of a successful government, including popular sovereignty, which means: Find the new concentration of a solution if 25.0 mL of water is added to 125.0 mL of 0.150 M NaCl solution. What is the final volume? mL The _____ proposes that the emotion we experience is influenced by feedback from facial muscles or skin. facial network proposal feedback principle physiological-feedback initiative facial feedback hypothesis Seventeen years after this vote and this article, Japan attacked the united states at pearl harbor. is there a possible connection between the immigration quota act of 1924 and pearl harbor? What are three reasons children may experience speech difficulties? Which box plot represents the data? 30, 35, 25, 5, 5, 25, 40, 45, 50, 10, 15, 40 The endpoints of a line segments are at the coordinates (-6,3,4) and (4,-1,2) what is the midpoint of the segment Measuring the Orbital Speeds of PlanetsIntroductionA Boeing 747 can fly 624 miles per hour. Thats pretty fast! Right now, Earth and other objects in thesolar system are orbiting the Sun, but how fast are these objects moving? In this assignment, you willcalculate the orbital speeds of objects in our solar system.Part A: Planetary PeriodsIn the 1600s, Johannes Kepler discovered three laws that govern the motion of objects around the sun.Keplers first law explains that objects travel in an elliptical, or oval-shaped, path around the sun.Keplers second law explains that an object travels faster in its orbit when it is closer to the Sun andslower in its orbit when it is farther away. In this activity, you will investigate Keplers third law: therelationship between an objects distance from the sun and the time it takes the object to complete anorbit around the sun.Access the Gizmo from within today's lesson. The exploration guide found within this simulation willhelp you work through the Gizmo. Click on the Lesson Materials link, which appears on the top leftcorner of the screen once you enter the simulation, to access the student exploration sheet. Use it asyou work through Activity C and answer all parts.Part B: Calculating Orbital SpeedEvery object moves at a different average speed in its orbit around the Sun. In this activity, you will usedata collected from Part A to calculate the average orbital speeds of each planet and of Pluto.1. Recall that the path an object takes around the Sun is an ellipse, and not a circle. However, toapproximate the circumference, or length, of each orbit, you will treat the orbits as circles. Goback to your notes in your student exploration sheet from Part A. Using the mean orbital radius(R) that you recorded, calculate the circumference of each planets orbit and record it in thetable below. Use the following formula to calculate the circumference:Circumference 2 = r2. Using the periods you recorded in your student exploration sheet and the circumference of orbitthat you just calculated, calculate the average orbital speed of each planet and record it in thetable below. Use the following formula to calculate speed:Distance Circumference Average Orbital Speed Time Period = =The units of your answer will be in AU/year.3. To give you a better perspective of how fast these orbital speeds really are, convert the orbitalspeeds you just calculated from AU/year to miles/hour. 1 AU/year = 10,604 miles/hour. Recordyour answers in the table below.TableObjectMeanorbitalradius (AU)(copy from#6 in part A)Circumference ofOrbit (AU)Period(EarthYears)(copyfrom #6in partA)Orbital Speed(AU/year)Orbital Speed(miles/hour)MercuryVenusEarthMarsJupiterSaturnUranusNeptunePlutoDrawing Conclusions4. Which planet takes the longest amount of time to travel once around its orbit? Which planettakes the shortest amount of time?5. How does an increase in orbital radius affect average orbital speed?ExtensionperihelionIn astronomy, the term refers to the point in the orbit of an asteroid, comet, or planet atwhich it is closest to the sun. Aphelion refers to the point at which the object is furthest away from thesun. Research facts about the dwarf planet Ceres. Calculate the average orbital speed of Ceres inmiles/hour when it is closest to the sun and when it is farthest away. The equilibrium constant for the reaction sr(s) + mg2+(aq) sr2+(aq) + mg(s) is 3.69 1017 at 25c. calculate e o for a cell made up of sr / sr2+ and mg / mg2+ half-cells. How did a move toward mercantilism strengthen royal power?a. by increasing the amount of a nations importsb. by allowing nobles to control taxationc. by creating colonies that supported the kingd. by ensuring more economic prosperity for the merchant and middle classes According to abraham maslow, people are motivated by: question 3 options:a.optimal arousal.b.drive reduction.c.a hierarchy of needs. and) instincts. Without the skeletal system, the body could not fight off infection. Please select the best answer from the choices provided. T F During the 1950's, the typical suburban male was all of the following except white, young, blue-collar, or married with children? What layer of the rainforest do gliding leaf frogs live in? Francesca is in junior high, and her parents have decided to divorce, due to a high-conflict marriage. despite the difficulty of adjusting, francesca may be better off because children in high-conflict intact families ____________ than children in divorced families. ) a pair of fair dice is rolled. what is the probability that the sum of the top faces is a number 10 or greater? Explain how the difference of a fraction or a rational number and its additive inverse is equal to zero. Encryption and decryption algorithms are known as ________________. How does the chef justify the theft of the professors briefcase and identity? which visual aid is best for showing comparative data? A. photograph B. video clip C. chart D. diagram