If a spacecraft was parked on Venus and needed to make a flight to Jupiter, how far would it need to travel? (Assume both planets are aligned with the sun and are on the same side of the sun.) in scientific notation.

Step-by-step explanation:

The radius of the circle = 10

The central angle of the arc = 3[tex]\frac{\pi }{2}[/tex]

By formula, S = rΘ

where S is the lenth of the arc

r is the radius of the circle

Θ is the central angle of the arc

substituting the values in the formula, we get

S = rΘ = 10 (3[tex]\frac{\pi }{2}[/tex]) = 15[tex]\pi[/tex] = 47.1

Answer:

No, not exactly. But they do cross the same point

Step-by-step explanation:

Basically, the axis of symmetry is a line that runs through the vertex,

The vertex is a single point on the line,

They both mark the graphs turning point though!

Using the Pythagorean theorem, it is determined that the paths between the three cities, given their distances of 200 km, 300 km, and 400 km, do not form a right triangle because the sum of the squares of the shorter distances does not equal the square of the longest distance.

To determine if the paths between the three cities form a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

The equation is a² + b² = c².

According to the provided distances, one city is 200 kilometers (a) from a third city, and the other city is 300 kilometers (b) from the third city.

The two original cities are 400 kilometers (c) apart.

Plugging these numbers into the Pythagorean theorem:

Since a² + b² does not equal c² (130000 ≠ 160000), the paths do not form a right triangle.

Answer:

D

Step-by-step explanation:

Because when you half answer D it will give you Matrix A.

Answer:

660

Step-by-step explanation:

20 * 8 = 160

25,000 * 2% = 500

500 + 160 = 660

Therefore your answer is 660

Answer:

The width is 2 cm and the length is 7 cm.

Step-by-step explanation:

Hope this helps!

Answer:

27 gallons, 2 quarts

Step-by-step explanation:

The measurements are given in gallons and quarts. Lets convert everything to quarts.

We know:

4 quarts = 1 gallons

So,

Rain Barrel Capacity = 47*4  + 1 = 189 quarts

Jiko uses 12 gallon  2 quart to water flower garden = 12*4  + 2 = 50 quarts

Jiko uses 7 gallons 1 quarts to water trees = 7*4  + 1 = 29 quarts

He used up = 50 + 29 = 79 quarts

Remaining Water in Rain Barrel = 189 - 79 = 110 quarts

In gallons and quarts:

27 * 4 = 108 quarts

So, water left = 27 gallons, 2 quarts

A set of symbols that expresses a mathematical rule is called a formula.

A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.

Given is a definition as -

"A set of symbols that expresses a mathematical rule is called a ?".

Therefore, a set of symbols that expresses a mathematical rule is called a formula.

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Final answer:

A set of symbols expressing a mathematical rule is called a mathematical model or equation, using variables and relationships to define concepts such as a set or a group in group theory.

Explanation:

A set of symbols that expresses a mathematical rule is often referred to as a mathematical model or equation. These models are essential for describing phenomena in a precise and universal language that transcends natural language, allowing for consistent replication and understanding across various fields of study. In mathematics, we use variables like x, y, or n and symbols to create equations which express relationships or rules. For example, to define a set of all even numbers, we could write the rule as the set of all real numbers x such that x/2 is an integer. This uses the structure of the equation to convey the membership rule for the set, which in this context would be described by the notation '{x : x/2 is an integer}' where the colon represents 'such that'.

Furthermore, when these symbols and rules are organized into a specific system with defined properties, such as closure, identity, inverses, and associativity, they can form a group, which is a fundamental concept in group theory.

Answer:She would need 144 liters of soda

Step-by-step explanation:

Answer:

12 liters

Step-by-step explanation:

Since she needs three liters for every 12 guests, and there are 48 guests, we should see how many times 12 goes into 48:

48/12 = 4

Therefore, you need to multiply the amount needed for 12 guests by four:

3 x 4 = 12

You need 12 liters.

Answer:

[tex]3 {x}^{2} (2 {x}^{5} ) = 6 {x}^{7} [/tex]

Answer:

answer is b (max y + min y)/2

Step-by-step explanation:

Answer:

(max y + min y)/2

Step-by-step explanation:

k=4

Answer:

both rates of change equal the slope of the line (3/4)

Step-by-step explanation:

Part a)

We calculate the rate of change using the formula:

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

for the first interval [0,6], we calculate the y-values at x=0 and x=6;

at x=0 : [tex]y=\frac{3}{2} (0)+2=2[/tex]

at x=6 : [tex]y=\frac{3}{2} (6)+2=11[/tex]

therefore, the rate of change in this interval is: [tex]\frac{y_2-y_1}{x_2-x_1}=\frac{11-2}{6-0}=\frac{9}{6} =\frac{3}{2}[/tex]

For the second interval [-4,4], we calculate the y-values at x=-4 and x=4;

at x=-4 : [tex]y=\frac{3}{2} (-4)+2=-4[/tex]

at x=4 : [tex]y=\frac{3}{2} (4)+2=8[/tex]

therefore, the rate of change in this interval is: [tex]\frac{y_2-y_1}{x_2-x_1}=\frac{8-(-4)}{4-(-4)}=\frac{12}{8} =\frac{3}{2}[/tex]

Part b):

Notice that both rates of change equal the value of the slope of the linear function (3/2)

Answer:

0.4

Step-by-step explanation:

10 divided by 25

Answer: Tan O= 5/12

Step-by-step explanation:

Cot O=12/5

Looking at the pythagoras theory

Cot= 1/tan

So

Cot O=1/tango

Cross multiply

CotO tan O=1

Make tan the subject of formula

TanO= 1/Cot O

Cot O=12/5

Substitute for cot O

Tan O= 1/12/5

Tan O= 5/12

Based on the table of values, the slope of the points is equal to: B. 2.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

[tex]Slope(m)=\frac{y_2-y_1}{x_2-x_1}[/tex]

Based on the information provided, we can logically deduce that some of the points are as follows;

Points = (3, 3) and (4, 5)

By substituting the given data points (3, 3) and (4, 5) into the formula for the slope of a line, we have the following:

Slope (m) = (5 - 3)/(4 - 3)

Slope (m) = 2

In conclusion, we can logically deduce that the slope of the points is equal to 2 based on the table of values.

Complete Question:

Use the table to find the slope.

-2

2

1/2

-1/2

Answer:

you could just add a negative if that makes since to you

Step-by-step explanation:

Adjust the sign on the integer to be subtracted to subtract integers. When all signs are positive, then the answer is positive. If both signs are negative, then the answer is negative. When the signs vary, deduct the lesser absolute value from the greater absolute value.

Answer:

-(-7)=7

Step-by-step explanation:

the opposite of the Justine score (-7) = Meghan  score  (7)

-(-7)=7

Final answer:

The correct representation of Meagan's score as the opposite of Justine's is -(-7) = 7, which is option D, where the double negative results in a positive score.

Explanation:

The trivia game scenario presents a situation where Justine and Meagan end up with opposite scores, with Justine losing 7 points and Meagan gaining the opposite. To express this numerically, if Justine's score change is represented as -7, then Meagan's score, being the opposite, is the negation of Justine's score, which is -(-7). This negation flips the sign of Justine's score change, resulting in a positive 7 for Meagan. Therefore, the correct way to represent that “the opposite of Justine’s score was equal to Meagan’s score” is -(-7) = 7.

Answer:

28.46

Step-by-step explanation:

Use a^2+b^2=c^2 to find height

Then use the area formula bh/2 to find area :))

Answer: 44.1

Step-by-step explanation:

Answer:

decrease, increase.

Step-by-step explanation:

Answer:

14.4 lb

Step-by-step explanation:

In a see-saw in equilibrium, the torque generated by one side needs to be the same generated in the other side. The torque is calculated by the product between the mass and the distance to the center of the see-saw.

The torque generated by the child is:

T1 = 60 * 3 = 180 lb*feet

So, the torque generated by the weight needs to be higher than T1 in order to lift the child.

The lowest mass is calculated when the mass is in the maximum distance, that is, 12.5 feet from the center.

So, we have that:

T2 = 180 = mass * 12.5

mass = 180/12.5 = 14.4 lb

So the lowest weight is 14.4 lb

The concept of leverage acting through a see-saw requires a balancing of forces on either side of the fulcrum. By calculating the torque from the child's weight and distance from the fulcrum, we can estimate the minimal weight needed on the other side to lift the child. The answer is approximately 14.4 lbs when placed 12.5 feet from the fulcrum.

The concept being explored here is leverage, specifically in the context of a see-saw. The see-saw operates on the principle of a basic lever where the two sides are balanced around a pivot point known as the fulcrum.

The input force, or effort, is defined by the weight of the child and the distance from the fulcrum they are sitting, while the output force, or resistance, is the weight needed on the other side to lift the child off the ground.

Here's how you calculate it: the child's weight of 60 lbs is 3ft from the fulcrum. So, the torque, or turning force, created by the child is 60lbs x 3ft = 180 lb-ft. Since we're looking for balance, the weight needed to lift the child would produce the same amount of torque. Technically, that could be achieved with a number of combinations of weight and distance, but given that the question asks for the smallest weight, the weight needs to be placed at the furthest available distance from the fulcrum, which would be half the length of the see-saw (12.5 feet). So, the weight would be 180 lb-ft / 12.5 ft = 14.4 lbs.

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Answer:

2677

Step-by-step explanation:

Let's make this easier first of all:

a^2-y^3(a-y^2)y^2

a^2-y^5(a-y^2)

a^2-ay^5+y^7

(-2)^2-(-2)(3)^5+3^7

4-(-2*243)+2187

4-(-486)+2187

4+486+2187

490+2187

2677

Answer:

2677

Step-by-step explanation:

a² - y⁵(a - y)²

(-2)² - (3⁵)(-2 - 3²)

4 - (243)(-11)

2677

Answer:

cells bacteria enzymes

Step-by-step explanation:

Answer:

Step-by-step explanation:

You can observe a representation of the problem in the image attached.

Notice that angle ABD and DBC are congruent.

Also, those angles are complementary, which means

[tex]\angle ABD + \angle DBC = 90\°[/tex]

And we know that [tex]\angle ABD = \angle DBC = x[/tex]

So,

[tex]x+x=90\°\\2x=90\°\\x=\frac{90\°}{2}\\ x=45\°[/tex]

Which means that [tex]\angle DBC = 45\°[/tex]

Therefore, the measure of angle DBC is 45°.

Answer:

< DBC is [tex]45^{0}[/tex]

Step-by-step explanation:

The line segment AB perpendicular to CB implies that a right angle is formed at point B. So that, AB and CB meets at B at [tex]90^{0}[/tex] to each other. Since the ray BD bisects <ABC, i.e it divides <ABC into two equal parts.

Thus,  

           [tex]\frac{90^{0} }{2}[/tex]  = [tex]45^{0}[/tex]

Therefore, < DBC = [tex]45^{0}[/tex]

and                  < DBC =  < ABD = [tex]45^{0}[/tex]

These two angles are said to be complementary angles. Complementary angles are set of two or more angles that add up to [tex]90^{0}[/tex].

Answer:

k = 4

Step-by-step explanation:

f(x)=5x+k

Let x =2

f(2) = 5*2 +k

f(2) = 10+k

We know f(2) = 14

14 = 10+k

Subtract 10 from each side

14-10 = 10+k-10

4 =k

We are given the function f(x) = 5x + k when k is a constant, x equals 2, and f(x) equals 14

Steps to solve:

14 = 5x + k; x = 2

~Substitute

14 = 5(2) + k

~Simplify

14 = 10 + k

~Subtract 10 to both sides

14 - 10 = 10 - 10 + k

~Simplfy

4 = k

Best of Luck!

Answer: Y=8

Step-by-step explanation:

Final answer:

To find the new value of y when x = 2 and knowing that y varies inversely with x, we first calculate the constant of variation k with the given values and then apply it to find the new y value, resulting in y = 8.

Explanation:

To solve the problem where y varies inversely with x, we use the inverse variation formula, which is y = k/x, where k is the constant of variation. First, we will find the value of k using the given values of y and x when y = 4 and x = 4.

Using the formula and substituting the known values:

k = xy = 4 × 4 = 16

Now, using k and solving for y when x = 2:

y = k/x = 16/2 = 8

Therefore, when x = 2, y = 8.

Answer: 35

Step-by-step explanation: It's an arith metic sequence that can be represented throigh the equation y= 65-5x where 5 is the amount of hous since 4pm and if you insert 6 for x you get 35

The mathematics problem involves subtraction, where the temperature drops 5 degrees per hour from 4pm to 10pm. The equation to represent this would be 65 - 5*6 = T. After performing the calculation, we find the temperature at 10pm is 35 degrees Fahrenheit.

In this problem, you are dealing with a decline in temperature over time, which is considered as a subtraction problem. Since the temperature drops by 5 degrees every hour from 4pm to 10pm, that's a total of six hours (10pm - 4pm = 6 hours), so you'll subtract 5 degrees 6 times from the initial temperature of 65 degrees.

The equation to represent this problem is:

65 - 5*6 = T

This means you are subtracting 5 degrees six times from the initial temperature of 65 Fahrenheit to get the temperature (T) at 10pm. So, the calculation would be:

65 - (5*6) = 65 - 30 = 35

So, the temperature at 10pm is 35 degrees Fahrenheit.

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Answer:

There is no graph

Step-by-step explanation:

Answer: ben

Step-by-step explanation:b

e

n

ben

Answer:

30 times one for every 5 hours she baby sits

Answer:

B. [tex]y = 6x[/tex]

Step-by-step explanation:

Step 1: Divide 30 by 5

[tex]\frac{30}{5}\\\\=30 \div 5\\\\= 6[/tex]

Therefore, the answer closest to that is B. y = 6x.