Triangle ABC is an isosceles triangle. Find the measure of each base angle.

Answer:

7

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

9=x+1

5=10÷3

9=x+1

5=3.333°

Now you need to find scale factor (sf)

5÷3.333°=1.5

SF=1.5

9÷3.333=2.7

2.7-1=1.7

x=1.7

Answer:

  x = 5

Step-by-step explanation:

Given PQRS ~ UVWT and PQ = 5, RS = 9, UV = 10/3, WT = x+1, you want the value of x.

Corresponding side lengths of similar polygons are proportional. This means ...

  WT/UV = RS/PQ

  (x+1)/(10/3) = 9/5 . . . . . . . . . . . substitute given values

Multiplying by 10/3 gives ...

  x +1 = (10/3)(9/5) = 6

  x = 5 . . . . . . . . . subtract 1

The new co-ordinates of A' and B' will be A'(-6,15) and B'(-24,-3) respectively.

Coordination is the process of combining individual efforts for a common purpose. It involves the synchronization and integration of activities, resources, and decision-making to achieve a desired outcome. This process is essential for many activities, such as project management, team building, and problem solving. Coordination requires communication, collaboration, and understanding among all participants. It can involve the use of technology, such as project management software, to ensure everyone is on the same page. Coordination is an important part of any successful endeavor, as it ensures that all goals are met in a timely and efficient manner.

The distance between A' and B' will be the length of the line segment AB' which can be calculated by using the distance formula, i.e. distance = √((x2-x1)² + (y2-y1)²). Therefore, the distance of A'B' will be 30 units.

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Equation systems that have the same solution are referred to as comparable systems. The similar expressions are -3(-0.05 + 0.25p) and 0.15 - 0.75p.

Thus, conceptually speaking, an equation is composed of two expressions. The equal sign establishes the equality of the two sides of the equation as expressions. A mathematical phrase called an equation is used to illustrate the relationship between two or more variables and numbers.

As a result:

The expression is simplified to: = -3(0.15 - 0.2 + 0.25p)

A further simplification results in:

= 0.15 – 0.75p

The similar expressions are -3(-0.05 + 0.25p) and 0.15 - 0.75p.

Equation systems that have the same solution are referred to as comparable systems. A system of two equations can be made into an equivalent system by replacing one equation with the total of the two equations or by replacing an equation with a multiple of itself.

Therefore the correct answer is option B) 0.15 – 0.75p .

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Answer: 9/2

Step-by-step explanation:

Answer:

9:2

Step-by-step explanation:

Find the HCF of the numerator and denominator which is 6.

Divide the numerator and denominator by the HCF (54÷6)÷(12÷6)

The answer will be 9÷2 which is also 9:2

He can make 32 dozen Fasnacht with 8 pounds of butter.

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here, She has 8 pounds of butter and 1 cup of butter can make 2 dozen Fasnacht. Also, 1 pound of butter is 2 cups thus 8 pounds of butter is equivalent to 16 cups.

1 cup of butter to make 2 dozen Fasnacht

then 16 cups of butter can be used to make 16×2=32 dozen Fasnacht

Hence, he can make 32 dozen Fasnacht with 8 pounds of butter.

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The equation for the tangent to the graph of y = arcsin(x/2) at the origin is y = x. This means that for any given x-value, the corresponding y-value is equal to that x-value, creating a line with a slope of 1. This line is tangent to the graph of y = arcsin(x/2) at the origin, which is (0, 0).

To find the equation for the tangent to the graph of y = arcsin(x/2) at the origin, we must first find the slope at the origin. We can do this by taking the derivative of the function y = arcsin(x/2) with respect to x.

The derivative of

y = arcsin(x/2) with respect to x is y' = (1/2)cos(x/2).

At the origin, x = 0, so the slope of the tangent at the origin is

y' = (1/2)cos(0) = 1.

Therefore, the equation for the tangent to the graph of

y = arcsin(x/2) at the origin is y = x, which has a slope of 1.

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The initial value of A is 3, The initial value of B is 2.25 and club B has a greater rate of change.

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.

Given:

The graph of club A and the values of club B is given,

Calculate the initial value of A and B as shown below,

The initial value of A = 3,

The initial value of B = 2.25

Hence, A has a greater initial value,

Calculate the rate of change as shown below,

The rate of change for club A = 3.75 / 2.25

The rate of change for club A = 1.67

The rate of change for club B = 4 / 3

The rate of change for club B = 1.33

Thus, the rate of change is higher for club B.

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Here is a set of directions on how to walk from the schoolhouse to the grocery store: walk 5 units west and 12 units north.

To travel from the schoolhouse to the grocery store, find the distance between each point horizontally and vertically.

To find the horizontal distance between the schoolhouse and the grocery store on a coordinate plane, find the difference between the x-values of the two points.

x-distance = |4 - (-1)| = 5

Since the direction is from right to left, it should be 5 units west.

To find the vertical distance between the schoolhouse and the grocery store on a coordinate plane, find the difference between the y-values of the two points.

y-distance = |-5 - (7)| = |-12| = 12

Since the direction is upwards, it should be 12 units north.

Hence, one should walk 5 units west and 12 units north to get to the grocery store from the schoolhouse.

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The simplification of the expression using laws of exponents is 2 × 3³ × 5

Laws of exponents state that exponents of numbers or expressions are added when the numbers are multiplied, subtracted when the numbers are divided, and multiplied when raised by still another exponent e.tc. That is:

mᵃ × mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

(mᵃ)ᵇ = mᵃᵇ

Note: The bases must be the same e.g. mᵃ and mᵇ have the same base

Given: (2⁵ × 3⁴ × 25²) / (3 × 16 × 5⁴)  

(2⁵ × 3⁴ × 25²) / (3 × 16 × 5⁴)  = (2⁵ × 3⁴ × (5²)²) / (3¹ × 2⁴ × 5⁴)

                                               = (2⁵ × 3⁴ × 5⁴) / (3¹ × 2⁴ × 5⁴)

                                               = 2⁵⁻⁴ × 3⁴⁻¹ × 5⁴⁻⁴

                                               = 2¹ × 3³ × 5¹

                                               = 2 × 3³ × 5

Thus, the expression simplifies to 2 × 3³ × 5

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Answer:

a) 2

b) 93

Step-by-step explanation:

a) 4x - 2y

   4(3) - 2(5)

   12 - 10

   2

b) 2x^2 + 3y^2

   2(3)^2 + 3(5)^2

   2(9) + 3(25)

   18 + 75

   93

The 2nd relation is a function out of the given graph function.

The set of ordered pairs (x, y) where f(x)=y makes up a function's graph in mathematics. These pairs, which are Cartesian coordinates of points in two-dimensional space and thus constitute a subset of this plane in the typical case where x and f(x) are real numbers, are examples of real numbers.

Instead of the pairs ((x,y),z) as in the definition above, the graph in the context of functions of two variables, i.e. functions whose domain consists of pairs (x,y), typically refers to the set of ordered triples (x,y,z) where f(x,y)=z. For a continuous real-valued function of two real variables, this set is a surface. It is a subset of three-dimensional space.

Graphs are useful tools for a variety of tasks in science, engineering, technology, finance, and other fields.

A Set of points in a plane is the graph of a function if & only if no vertical line intersects the graph in more than one point

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The equivalent ratio between ounces and cups is given as follows:

230 ounces = 28.75 cups.

Conversion of units are made applying the proportions, which are a fraction giving the unit rates between two units.

These fractions are then combined with basic arithmetic operations, especially multiplication and division, to find the desired measures in the context of a problem.

The conversion rate from ounces to cups is given as follows:

1 ounce = 0.125 cups.

(a known conversion rate).

Hence the amount of cups equivalent to 230 ounces is calculated applying the proportion, which is the multiplication of 230 by 0.125, as follows:

230 x 0.125 = 28.75 cups.

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The total number of credit cards assigned at 2 locations are 44t + 25.

We can find the total number of credit cards opened at the two locations by adding the number of credit cards opened at each location. In this case, that means adding the functions a(t) and b(t).

The function for the number of credit cards opened at location a is a(t) = 15 * 3t

The function for the number of credit cards opened at location b is b(t) = 25 - t

So, to find the total number of credit cards opened at the two locations, we can add those two functions:

Total(t) = a(t) + b(t)

= (15 * 3t) + (25 - t)

= 45t + 25 - t

= (45 - 1)t + 25

= 44t + 25

This is the expression that can be used to determine the total amount of credit cards opened at the two locations.

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An expression that can be used to determine the total amount of credit cards opened at the two locations (a + b)(t) = 40 + 2t

In this question we have been given one location of the retail clothing store states that the number of credit cards, a, that are opened t months since january can be modeled by the function a(t) = 15 + 3t

And the number of credit cards opened at another location, b, is defined by the function b(t) = 25 − t

We need to find an expression that can be used to determine the total amount of credit cards opened at the two locations

Let the total number of credit cards that are opened at both the location together is nothing but the sum of functions a(t) and b(t)

So, the total number of credit cards

a(t) + b(t) =  (15 + 3t) + (25 - t)

(a + b)(t) = 15 + 3t + 25 - t

(a + b)(t) = 15 + 25 + 3t - t

(a + b)(t) = 40 + 2t

Therefore, the required expression is (a + b)(t) = 40 + 2t

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The triangle ΔABC is similar to the triangle ΔDEF. Then the value of the variable 'x' is 9 inches.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

In triangles ΔABC and ΔDEF, we have

∠B = ∠D    (Given)

∠C = ∠F    (Given)

Then the triangles ΔABC and ΔDEF will be similar to each other. Then the ratio of the corresponding sides will be constant. Then the equation is given as,

AC / DF = BC / EF

x / 12 = 6 / 8

x = 12 x 6 / 8

x = 72 / 8

x = 9 inches

The triangle ΔABC is similar to the triangle ΔDEF. Then the value of the variable 'x' is 9 inches.

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The dataset is quantitative and continuous.

Quantitative data is gathered by measuring and counting. Qualitative data is collected by interviewing and observing. Quantitative data is analyzed using statistical analysis, while qualitative data is analyzed by grouping it in terms of meaningful categories or themes. Quantitative data is anything that can be counted or measured; it refers to numerical data. Qualitative data is descriptive, referring to things that can be observed but not measured—such as colors or emotions.

Discrete data and continuous data are both types of quantitative data. The main difference between them is the type of information they represent. Discrete data typically only shows information for a particular event, while continuous data often shows trends in data over time. The type of data that has clear spaces between values is discrete data. Continuous information is information that falls into a continuous series. Discrete data is countable. Continuous data is measurable. There are distinct or different values in discrete data.

Given that the data set "Distance a baseball travels after being hit" has been provided.

Considering that numbers can be used to express it.

Therefore, the data set must be quantitative.

Since a baseball will move in an uninterrupted curve after being hit,

It would therefore be a continuous function.

Thus, the dataset is quantitative and continuous.

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Answer:

quantitative, continous

All the prime factors of 80 in ascending order will be;

⇒ 2, 2, 2, 2, 5

The numbers arrange in order to least to greatest number is called Ascending order.

Given that;

The number is,

⇒ 80

Now,

The number 80 is written as a product of prime factors as;

⇒ 80 = 2 × 2 × 2 × 2 × 5

Thus, The ascending order of prime factors of 80 are,

⇒ 2, 2, 2, 2, 5

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Answer:

Step-by-step explanation:

ME EITHER UGHHHHHHHH

Applying the slope formula calculated from the points, [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex] , The answer is undefined.

The slope of a line is a number that describes the steepness of the line and the direction in which it is sloping. It is often represented by the letter "m" and is calculated as the ratio of the change in the y-coordinate (rise) to the change in the x-coordinate (run) between two points on the line. The slope can be positive, negative, zero or undefined. A positive slope indicates that the line is rising from left to right, a negative slope indicates that the line is falling from left to right, a slope of zero indicates that the line is horizontal and an undefined slope indicates that the line is vertical.

The intercepts of a line are the points at which the line crosses the x-axis and y-axis. A line can have zero, one, or two intercepts, depending on its slope and the position of the line in the coordinate plane. The x-intercept of a line is the point at which the line crosses the x-axis. It is the point at which the y-coordinate is equal to zero. The y-intercept of a line is the point at which the line crosses the y-axis. It is the point at which the x-coordinate is equal to zero.

(x1,y1) = (6,-8)

(x2,y2) = (6,-3)

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

m=undefined (The points lie on vertical line.)

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After 9 minutes, the submarine will be at a depth of +91 feet below sea level.

Expression in math is a combination of numbers, symbols, and operations that represents a value or a mathematical relationship. It is written in a symbolic form, and can be evaluated to produce a numerical value or a logical result. Expressions are used to represent mathematical equations, and can range from simple equations like 2+2 to complex equations involving multiple operations, variables, and functions.

This is calculated by subtracting 9 from the initial depth of 370 feet and then adding the change of 13 feet per minute for 9 minutes. Therefore, the expression -370+13m = +91.

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d. dV/dt = -0.15V³ is a differential equation that could describe the relationship between the rate of change of the volume V with respect to time t of water leaking from a tank, and the cube of the volume.

A differential equation is an equation that relates a function and its derivatives. In this case, the function is the volume V of water in the tank, and the variable is time t. The problem states that the rate of change of the volume V with respect to time t is proportional to the cube of the volume. This means that the rate at which the volume is changing is directly proportional to the cube of the volume, and the proportionality constant is a negative number.

The differential equation that describes this relationship is dV/dt = -0.15V³, where dV/dt represents the rate of change of the volume with respect to time, and -0.15V³ represents the proportionality constant times the cube of the volume. The negative sign indicates that the volume is decreasing over time, as water is leaking out of the tank. This differential equation can be used to model the behavior of the water leaking from the tank, and can be used to determine the volume of water remaining in the tank at any given time.

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p > -19/2 is the solution for the given inequality.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given an inequality 19 + 2p >0

Solving the given inequality

19 + 2p >0

subtract 19 from both the sides

2p > -19

divide by 2 into both the sides

p > -19/2

Therefore, the solution for the inequality Given is p > -9.5.

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The three points that are in the solution set are E(3,0) F(5,-4)

Plotting graphs?

When plotting graphs, you typically use a set of Cartesian coordinates to specify the location of each point on the graph. The Cartesian coordinates, also known as rectangular coordinates, consist of an x-coordinate and a y-coordinate. The x-coordinate specifies the position of the point along the horizontal axis, also known as the x-axis, and the y-coordinate specifies the position of the point along the vertical axis, also known as the y-axis.

To determine which of the six points are a solution to the equation

2x + y = 6, we can substitute the x and y values of each point into the equation and see if it holds true.

The points are A (1, -6), B (7, -3), C (-1, 8), D (3, -5), E (3, 0), F (5, -4)

A = (1, -6), 2x+y = 21 + -6 = 6 , it is not a solution

B = (7,-3) , 2x+y = 27 + -3 = 6 , it's not a solution

C = (-1,8) , 2x+y = 2*-1 + 8 = 6 , it's not a solution

D = (3,-5) , 2x+y = 23 + -5 = 6 , it is not a solution

E = (3,0) , 2x+y = 23 + 0 = 6, it's a solution

F = (5,-4) , 2x+y = 2*5 + -4 = 6, it's a solution

So, the three points that are in the solution set are E(3,0) F(5,-4)

We can plot the points on a coordinate plane, with x on the horizontal axis and y on the vertical axis.

And connect all three points, which would result in a line.

You can label this line as 2x+y=6, and any point that lies on that line is a solution for the given equation.

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The vector pairs v, (22,15) and v₂ = (-2,4) are not orthogonal.

Vector algebra entails performing algebraic operations on vectors. Vector algebra performs algebraic operations on vector magnitude and vector direction. Many applications in physics and engineering use vector algebra to perform addition and multiplication operations on physical quantities represented as vectors in three-dimensional space.

Given that the vector pairs are v, (22,15) and v₂ = (-2,4). For the vectors to be orthogonal the dot product should be equal to zero.

Calculate the dot product for the given points,

V = ( 22i + 15j) . ( -2i + 4j )

V = -44 + 60  Here, (i.i =1 and j.j = 1)

V = 16

The dot product is not equal to zero. Hence, the vectors are not orthogonal.

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The cost of 2 specials and 2 glasses of milk is $16

The first step is to determine the price of a special and a glass of milk.

The elimination method would be used to solve the given system of equations :

4s + 2m = 28 equation 1

3s + 4m = 26.25 equation 2

Where:

Multiply equation 1 by 2

8s + 4m = 56 equation 3

Subtract equation 2 from equation 3:

5s = 29.75

Divide both sides of the equation by 5

s = 29.75 / 5

s = $5.95

Substitute for s in equation 1:

4(5.95) + 2m = 28

23.8 + 2m = 28

2m = 28 - 23.8

2m = 4.2

m = 4.2 / 2

m = $2.10

Cost of 2 specials and 2 glasses of milk = (2 x 2.10) + (2 x 5.95)

= $4.10 + 11.90 = $16

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The person's average speed during her commute is 33.75 mph.

The speed of an object can be obtained by comparing the distance covered to the traveling time needed.

speed = distance / time

Take a look at the problem. As the information given is time in minutes and speed in miles per hour (mph), then we have to convert the time into an hour unit.

Total time = 20 minutes = 20/60 hour = 1/3 hour

Break time = 5 minutes

Commuting time = 20 - 5 = 15 minutes

                                         = 15/60 hour = 1/4 hour

Given the speed = 45 mph, then the distance covered during commuting time is:

Distance = speed x time

              = 45 x 1/4

              = 11.25 miles

Then we can calculate the average time, by comparing the distance covered to the total time:

Average speed = distance / total time

                          = 11.25 / 1/3

                          = 33.75 mph

Thus the average speed during the commute is 33.75 mph.

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The vertical change in elevation is 1.06 miles.

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

From the right triangle formed, the adjacent side to the angle of elevation is 5 miles and the vertical change in elevation is the opposite side. From the trigonometric function, the tangent of an angle,

tan 12° = x / 5 miles

The value of x from the equation is 1.06 miles.

Thus, the vertical change in elevation is 1.06 miles.

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The vertical change in elevation from the point where the surveyor is standing to the point on the mountain = 1.06 miles

Here, angle of elevation θ = 12°

Let y be the the vertical change in elevation from the point where the surveyor is standing to the point on the mountain and x be the horizontal distance between the point on the mountain and the surveyor.

x = 5 miles

We need to find the value of y.

Consider tangent of angle of elevation θ

tan(θ) = y/x

tan(12°) = y/5

0.2126 = y/5

y = 0.2126 × 5

y = 1.06 miles

So, the vertical change in elevation = 1.06 miles

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Microsoft Access is NOT a relational database .

A relational database is a database that uses the relational model of data, which was first put forth by E. F. Codd in 1970. [1] A relational database management system is a program used to maintain relational databases (RDBMS). Many relational database systems offer the ability of querying and modifying the database using SQL (Structured Query Language).

An individual key identifies each row in a relational model, which groups data into one or more tables (or "relations") containing columns and rows. Records or tuples are other names for rows. [12] Attributes are another name for columns.

Each table or relation typically represents one "entity type" (such as customer or product). The columns indicate values associated with that instance, while the rows are instances of that sort of entity (such as "Lee" or "chair") (such as address or price).

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