What is the definition of similarity? *
A. If two figures have the same angles, then they are similar.
B. If two figures have proportional side lengths, then they are similar.
C. If there is a sequence of transformations taking one figure to another, then they are similar.
D. If there is a sequence of rigid transformations and dilations, that take one figure to the other, then they are similar.

Answer:

The GCF of 3x^4, 15x^3 and 21x is 3x^2

Step-by-step explanation:

3x^2(x^2), 3x^2(5x) , 3x^2(7)

Answer:

3

Step-by-step explanation:

3*4=12

15*3=45

21x= 7*3*x

Answer:

2 hours

Step-by-step explanation:

30 miles/x hours = 15 miles/1 hour

30 = 15x

x = 2 hours

To find the time it took to get to the store, divide the distance traveled (30 miles) by the average speed (15 mph), which results in 2 hours. Thus, the trip took 2 hours.

To calculate the time it took to get to the store, we can use the formula time = distance ÷ speed. In this case, the vehicle traveled 30 miles at an average speed of 15 miles per hour. Therefore, the time can be calculated as follows:

Time = 30 miles ÷ 15 miles per hour = 2 hours.

So, it took 2 hours to get to the store.

Answer:36 units2

Step-by-step explanation:

Took the testc

The sum of the areas of the two shaded sectors is 36 π units²

A sector is said to be a part of a circle made of the arc of the circle along with its two radii.

Given that a circle, with central angle 80° and the radius is 9 units

So, area of a sector = θ/360° x π x radius², where θ = central angle

Since, both the sectors are vertically opposite to each other so will same areas,

Therefore, the area of the two shaded sectors,

= 2θ/360° x π x radius²

= 2·80/360 × π × 9²

= 4/9 × π × 81

= 36π

Hence, the sum of the areas of the two shaded sectors is 36 π units²

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The complete question is attached

Answer:

660

Step-by-step explanation:

20 * 8 = 160

25,000 * 2% = 500

500 + 160 = 660

Therefore your answer is 660

Answer:

0.4

Step-by-step explanation:

10 divided by 25

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:

-(-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:

3.600

Step-by-step explanation:

0.25(x+1.6)+5x=18

Open the bracket first

0.25x+0.72+5x=18

Collect like terms

0.25x+5x=18-0.72

5.25x=18.72

Divide both sides by 5.25

x=3.566~3.600(nearest hundredth)

Answer:

x ≈ 3.2

Step-by-step explanation:

0.45(x + 1.6) + 5x = 18

45/100(x + 16/10) + 5x = 18

¹⁰⁾45x/100 + 720/1000 + ¹⁰⁰⁰⁾5x = ¹⁰⁰⁰⁾18

450x + 720 + 5000x = 18000

5450x = 18000 - 720

5450x = 17280

x = 17280/5450

x = 3.17

x ≈ 3.2

Answer:

decrease, increase.

Step-by-step explanation:

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!

Answer:

it should equal 68 degrees.

Step-by-step explanation:

if you are looking for the value of m<1, you would first need to find the value of the missing angle on the left triangle. the angles in triangles are equal to 180 degrees, so the equation would be 180 = 50 + 80 + x, and x = 50.

Then move to the middle triangle. The angle you solved for has an angle "connected" to it, its vertical pair, which also equals 50. Then you solve for the last angle, the angle on the right. 180 = 50 + 62 + x, and x = 68.

m<1 is equal to its vertical angle, which is the angle you just solved for. its value should be 68 degrees.

if that wasn't what you were looking for, sorry. hope this helped :)

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.

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.

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:

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)

The answer for this question is C

Answer:

I believe the answer is 12 hours long all year seen a diagram of the earths axis over all the  year

Step-by-step explanation:

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:

D

Step-by-step explanation:

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

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:

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: 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:

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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Huh, alright?

The equation would be (n - 14) / 3 = -8

Hope that helps! :)

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

Answer:

4+36x

Step-by-step explanation:

Use the distributive property to multiply the equation. 1 times 4 is 4. 9 times 4 is 36 and you must leave the x as a variable.