Which condition will not create a gap or an overlap at a vertex of polygons?

The sum of the measures of the angles is greater than 360°.

The sum of the measures of the angles is equal to 360°.

The sum of the measures of the angles is less than 360°.

Answer: 480

Step-by-step explanation: Since this is a triangle, we are using 1/2 * base * height. So since the height is 15, and the base is 64, that would equal 960. Then we are going to divide it by 2, which equals 480.

Answer: 14 miles and the donors will both owe $35 for a total of $70

Step-by-step explanation:

The mother is giving $35 and the grandmother is 2.50 per mile and at the end they both end up owing the same amount

grandmothers 2.50 per miles

you walk 14 miles

you multiply 2.50 and 14 to get $35

The mother and the grandmother both owe $35

so take $35x2= 70

By answering the above question, we may state that Shade the region to line the left of the open circle, since x is less than 4.

A line is a geometric object that is infinitely long and has no width, depth, or curvature. A line, which can also exist in two-, three-, and more-dimensional spaces, is therefore a one-dimensional object. A line is often used to refer to a line segment with two points as its endpoints. A line is a flat, one-dimensional object that may extend indefinitely in both directions and has no thickness. The terms "straight line" or "old correct line" are sometimes used to describe a line that has no "wobble" anywhere along its length.

plot the inequality 4x-22<-6 on a number line,

4x - 22 + 22 < -6 + 22

4x < 16

4x/4 < 16/4

x < 4

Plot an open circle at 4 on the number line to indicate that x is not included in the solution set.

Shade the region to the left of the open circle, since x is less than 4.

The resulting graph should look like this:

     ○----------------->

     |  |  |  |  |  |  |

   -∞  -5  -4  -3  -2  -1  0  1  2  3  4  5  6

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Answer: 941.33 inches squared

Step-by-step explanation:

You will find the area of each shape separately, then add them together.

The area of a square is s²

26² = 676

Area of a semicircle is 1/2(πr²)

1/2((3.14)(13)²)

1/2((3.14)(169))

1/2(530.66)

265.33

676 + 265.33 = 941.33 inches squared

Hope this helps!

Check the picture below.

The equation for the function shown in the given table is y = 4x + 2 OR 4x - y = -2. The graph of the equation is attached below

From the question, we are to determine the equation for the function

From the the given table,

When x = 0, y = 2

and when x = 1, y = 6

We can determine the equation for the function by using the formula,

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

From above

x₁ = 0

y₁ = 2

x₂ = 1

y₂ = 6

Thus,

(y - 2)/(x - 0) = (6 - 2)/(1 - 0)

(y - 2)/x = 4/1

1 × (y - 2) = 4 × x

y - 2 = 4x

y = 4x + 2

OR

4x - y = -2

Hence, the equation is y = 4x + 2

The graph of the equation is attached below

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Answer:

360 people pledged $25.

Step-by-step explanation:

You'll need to set up only one equation to solve this.

Let's use x for the number of people who pledged $50. Since twice as many people pledged $25, it would be 2x. Keep this in mind for later.

Multiply 2x by 25, and you should get 50x. Now, your equation is 50x + 50x = 18,000. Simplify this to 100x = 18,000.

Now, divide both sides by 100. After doing so, you should have x = 180. This is how many people pledged $50. To find how many pledged $25, plug the value of x into 2x. (In other words, multiply 180 by 2.) After doing so, you should get 360. This is how many people pledged $25.

Hope this helps!

Using the unitary method, we found that the equivalent amount of 750 US Dollars in Egyptian pounds is 1100 Egyptian pounds.

The unitary method is a strategy for problem-solving that involves first determining the value of a single unit and then multiplying that value to determine the required value. Therefore, the goal of this method is to establish values in relation to a single unit. Always write the things that need to be calculated on the right side and the things that are known on the left side to simplify things. The unitary approach must be applied whenever we need to determine the ratio of one quantity to another.

Given,

 The amount of money  in US dollars = 750 US Dollars

The conversion to Egyptian pounds can be done using the unitary method.

1 usd = 18.48 Egyptian pounds

The unitary method can be used to convert single units to multiple units.

So,

750 usd = 750 * 18.48 = 1110 Egyptian pounds.

Therefore using the unitary method, we found that the equivalent amount of 750 US Dollars in Egyptian pounds is 1100 Egyptian pounds.

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Anika has R283362.97 after 5 years of compound interest. She can use this money to start her bakery.

Anika invested, R180000 at 9.5% compound interest for 5 years. To find out how much money she has now, we need to use the formula for compound interest:

A = P(1 + r)^t

Where A is the final amount, P is the principal amount, r is the annual interest rate, and t is the number of years. Plugging in the values we have:
A = R180000(1 + 0.095)^5
A = R180000(1.095)^5
A = R180000(1.574)
A = R283362.97

So Anika has R283362.97 after 5 years of compound interest. She can use this money to start her bakery.

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Answer: We cannot solve this problem as there is a mistake in the equation you provided.

16 x 12 is not equal to 102. The correct answer is 192.

To find the weight of each cookie, we need to know the total weight of the box of cookies. Let's call the weight of the box "W".

Since there are 16 servings in the box and each serving contains 4 cookies, there are a total of 16 x 4 = 64 cookies in the box.

To find the weight of each cookie, we can divide the total weight of the box by the number of cookies:

Weight of each cookie = W / 64

Without knowing the weight of the box, we cannot determine the weight of each cookie.

Step-by-step explanation:

The solution set for the inequality 6x + 1 ≤ 4x + 1 is x ≤ -3/2 can be written in interval notation as (-∞, 0].

To solve the inequality 6x + 1 ≤ 4x + 1, we need to isolate the variable on one side of the inequality. Here are the steps to do so:

1. Subtract 4x from both sides of the inequality: 6x + 1 - 4x ≤ 4x + 1 - 4x
2. Simplify: 2x + 1 ≤ 1
3. Subtract 1 from both sides of the inequality: 2x + 1 - 1 ≤ 1 - 1
4. Simplify: 2x ≤ 0
5. Divide both sides of the inequality by 2: 2x/2 ≤ 0/2
6. Simplify: x ≤ 0

The solution set in interval notation is (-∞, 0]. This means that any value of x less than or equal to 0 will satisfy the inequality.

"

Prper question:

Solve the inequality. Write the solution set in interval notation.

6x + 1 ≤ 4x + 1

"

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Plotting the data and visually examining the connection between x and y equation is often the best method for identifying which equation best describes the line of best fit.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions.

Based on the above equations, y = x + 5 or y = x - 5 would be the most plausible contenders. Both of these equations have the typical slope for a linear connection, which is a straight line slope of 1.

While the y-intercept of the equation y = x + 15 has a significantly bigger value than would be predicted based on the other possibilities, the slope of the equation is 1. Similar to that, the slope of the equation y = 2x - 15 is 2.

Plotting the data and visually examining the connection between x and y is often the best method for identifying which equation best describes the line of best fit.

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The given function is (3x^(3)-2x^(2)+3)/(x-1). To express it in the form q(x)+(r(x))/(b(x)), we need to use polynomial long division.

First, divide the first term of the numerator, 3x^(3), by the first term of the denominator, x:

3x^(3)/x = 3x^(2)

Now, multiply this result by the denominator and subtract it from the numerator:

(3x^(3)-2x^(2)+3) - (3x^(2)(x-1)) = -2x^(2)+3x^(2)-3

Simplify:

x^(2)-3

Next, divide the first term of the new numerator, x^(2), by the first term of the denominator, x:

x^(2)/x = x

Multiply this result by the denominator and subtract it from the new numerator:

(x^(2)-3) - (x(x-1)) = -3+x

Simplify:

x-3

Since the degree of the new numerator is less than the degree of the denominator, we can stop here. The final result is:

q(x) = 3x^(2)+x

r(x) = x-3

b(x) = x-1

So, the function can be expressed as:

(3x^(3)-2x^(2)+3)/(x-1) = 3x^(2)+x + (x-3)/(x-1)

In HTML format, the answer would be:

<p>(3x^(3)-2x^(2)+3)/(x-1) = 3x^(2)+x + (x-3)/(x-1)</p>

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Answer:

The median is the middle value when a set of data is arranged in order from smallest to largest.

First, let's arrange the given shoe sizes in order:

5, 5.5, 6, 6.5, 6.5, 7, 7.5, 8, 8, 8.5

The median of this data set is 6.5 because it is the middle value.

Now, let's add a shoe size of 9 to the data set:

5, 5.5, 6, 6.5, 6.5, 7, 7.5, 8, 8, 8.5, 9

The new median of this data set is 7, which is greater than the previous median of 6.5.

Therefore, the answer is: The median increases to 7.

Answer: The median increases to 7.

Step-by-step explanation: I took the test and got a 100%

(a) The standard form of the equation of the given circle is (x + a/2)² + y² = (a/2)².

(b) The center point and radius of the circle is (-a/2, 0) and a/2, respectively.

(c) The center point and radius of the circle (-9/2, 0) and 9/2, respectively.

a) The equation for these circles in standard form is (x + a/2)² + y² = (a/2)². This is derived from the given equation by completing the square for the x term.

b) The center point of these circles is (-a/2, 0) and the radius is a/2. This can be seen from the standard form of the equation, where the center point is (h, k) and the radius is r in the equation (x - h)² + (y - k)² = r².

c) For the equation x² + y² + 9x = 0, the center point is (-9/2, 0) and the radius is 9/2. This is found by completing the square for the x term and comparing it to the standard form of the equation for a circle.

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A non-Abelian group is a group in which the order of the elements matters, meaning that the order that they are written in changes the outcome of the operation.

An automorphism is a transformation that preserves the group structure and is an isomorphism fromGto itself. SinceGis a non-Abelian group, its elements are not all the same, meaning that there is a difference between some elements.

This difference can then be used to generate an automorphism that is not the identity. For example, an automorphism in a groupGcould exchange two elements,g1andg2, and then evaluate the group operation on the exchange.

This automorphism does not leave the group unchanged, and therefore is not the identity. In conclusion, a non-Abelian groupGhas an automorphism that is not the identity because its elements are not all the same and can be exchanged to generate a new automorphism.

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Answer:

c. 3

Step-by-step explanation:

v=4 or v=-1.

The rational expression is undefined when the denominator is equal to 0. Therefore, we need to find the values of v that make the denominator 0.

v^(2)-3v-4=0

We can factor this equation to find the values of v:

(v-4)(v+1)=0

Therefore, the rational expression is undefined when v=4 or v=-1.

In conclusion, the rational expression (v^(2)+11)/(v^(2)-3v-4) is undefined when v=4 or v=-1.

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Answer: it is - 13

Step-by-step explanation: it is -13 because it either can be less or more

Answer:

The 6.5% compounded annually would get you the most money. This is because, when compounded annually, the interest is calculated on the original sum plus the interest already earned. Over the four year period, this would result in total interest earned being higher than if the interest was compounded daily, as the interest earned each day would be calculated on the original sum only. For example, with a 6.5% compounded annually rate, at the end of the fourth year you would have a total of $127.82, whereas with a 6.3% compounded daily rate, you would have a total of $126.56

Step-by-step explanation:

Hope this helps!  the screenshot is inserted and the explanation and answer are there

Surface area of the triangular prism which is a compound shape has an area of: 878mm².

The combined area of one or more circles and simple polygons is known as the area of the composite forms. The areas of every basic shape can be added together to determine the area of the composite shapes. Simply calculate each shape's area separately, then put them together to get the area of composite shapes.

Now in the question, we have 2 triangles with base, b =31mm and height, h = 14mm

Now area of both the triangles = 2 × 1/2 × b × h

= 2×1/2×14×31

=434mm²

Now we have three different rectangles.

In the first rectangle, length, l = 27mm and breadth, b = 6mm

Area of the rectangle as we know = l × b

= 27 × 6

= 162mm²

In the second rectangle, l = 16mm and b = 6mm

Area = 16 × 6

= 96mm²

In the final rectangle, l = 31mm and b = 6mm

Area = 31 × 6

= 186mm²

Therefore, the total surface area = 162 + 434 + 96 + 186 = 878mm².

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The linear function for the given values can be written as: f(x) = -x/2

The equation of a straight line is a relationship between x and y coordinates, The two point form of the equation of a straight line is:

y-y₁ = (y₂-y₁)/(x₂-x₁)*(x-x₁)

Given that,

f (-4)=2 and f (6)= -3

The linear function  = ?

we can consider input value as x and output value as y,

then the linear function can be estimated by using two point form of straight line.

y - 2 = (-3 - 2)/(6 - (-4))*(x - (-4))

y - 2 = -1/2 (x + 4)

y   =  - x/2 - 2 + 2

    =  - x/2

Hence, the linear function is f(x) = -x/2

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The three points that divide the line segment joining the given points into four equal parts are \((3.5, -1.25)\), \((4, -1.5)\), and \((4.5, -1.75)\)

To find the three points that divide the line segment joining the given points into four equal parts, we can use the Midpoint Formula repeatedly. The Midpoint Formula is given by:

\[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]

Let's first find the midpoint of the given line segment:

\[ \text{Midpoint} = \left( \frac{3 + 5}{2}, \frac{-1 + (-2)}{2} \right) = \left( 4, -1.5 \right) \]

Now we can use the Midpoint Formula again to find the two other points that divide the line segment into four equal parts. Let's first find the midpoint of the line segment joining the points \((3, -1)\) and \((4, -1.5)\):

\[ \text{Midpoint} = \left( \frac{3 + 4}{2}, \frac{-1 + (-1.5)}{2} \right) = \left( 3.5, -1.25 \right) \]

And then let's find the midpoint of the line segment joining the points \((4, -1.5)\) and \((5, -2)\):

\[ \text{Midpoint} = \left( \frac{4 + 5}{2}, \frac{-1.5 + (-2)}{2} \right) = \left( 4.5, -1.75 \right) \]

So the three points that divide the line segment joining the given points into four equal parts are \((3.5, -1.25)\), \((4, -1.5)\), and \((4.5, -1.75)\).

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The true statement is 'The value 36 represents the initial water level before it began to recede.

First of all, understand the word problem,  

Given that The water level of a river recedes at a constant rate each day it implies the water level is decreasing at a constant rate. The expression 36 - 0.25x represents the water level after 'x' days.

Here we have

The expression 36 - 0.25x represents the water level after 'x' days

Let x = 0 which implies the water level is not begin to recede

Then the Initial water level = 36 - 0.25(0) = 36  

Hence, we can conclude that the initial water level is 36

Therefore,

The true statement is 'The value 36 represents the initial water level before it began to recede.

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The Complete Question is attached below

Answer:

x=0

Step by step explanation:

cos (a+b) = cos(a) cos(b) -sin (a) sin (b)

Same identity forms in question.

L.H.S -cos (x+60)

Now write it in the form of sin .

sin [90-(60+x)]

Equal to RHS

R.H.S - 30

90-(60+x)=30

30-x=30

x=0

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The answer to the equation cos195°cos285° is -1/4.

An equation is a mathematical statement that asserts the equality of two expressions. Equations are used to describe relationships between different quantities and can be used to solve for unknown values. Equations are typically written as symbols, but can also be written in words. Simple equations might involve addition, subtraction, multiplication, and division, while more complex equations may involve exponents, logarithms, and trigonometric functions. Equations can be used to model and understand real-world phenomena, such as calculating projectile motion, or predicting the behavior of a chemical reaction.

This is derived from the trigonometric identity cos{60°−x}cosx – sin(60°−x)sinx. This identity states that the cosine of the sum of two angles is equal to the product of the cosines of each angle minus the product of the sines of each angle.

By substituting the angles 195° and 285° into the identity, we get cos{60°−195°}cos195° – sin(60°−195°)sinx. When we use the values of the angles, we get cos{-135°}cos195° – sin(135°)sinx. We can then simplify this to -1/4cos195° – 0sinx. As the sine of the angle is 0, this simplifies to –1/4cos195°. As the cosine of 195° is -1/4, the answer to the equation cos195°cos285° is -1/4.

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The solution to the set of equations is (x, y) = (8, 17).

What is system of linear equations?

A system of linear equations is a set of two or more equations with two or more variables that are to be solved simultaneously. Each equation in the system is linear, meaning it can be written in the form of ax + by + cz + ... = d, where a, b, c, and d are constants and x, y, z, and other variables are unknowns.

The goal of solving a system of linear equations is to find the values of the variables that satisfy all of the equations in the system. The solution of a system of linear equations is a set of values for the variables that make all of the equations true.

There are different methods to solve systems of linear equations, such as substitution method, elimination method, and matrix method. These methods involve manipulating the equations in the system to isolate one variable, substitute its value into another equation, and eventually find the values of all the variables.

Systems of linear equations are used in many areas of mathematics, science, engineering, and economics to model real-world situations and solve practical problems.

To find the solution to the set of equations, we need to determine the values of x and y that satisfy both equations simultaneously. One way to do this is to use substitution or elimination methods.

However, the given answer choices do not seem to be the steps of a solution process. We need to use both equations to find a solution. Here is one possible way to do it:

Equation S: y = x + 9

Equation T: y = 2x + 1

Since both equations equal to y, we can set them equal to each other:

x + 9 = 2x + 1

Simplifying this equation, we get:

x = 8

Now that we know the value of x, we can substitute it into either Equation S or Equation T to find the value of y. Let's use Equation S:

y = x + 9

y = 8 + 9

y = 17

Therefore, the solution to the set of equations is (x, y) = (8, 17).

None of the given answer choices matches this solution process.

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Its means that either statement p is false or statement q is true

The symbolic statement that needs to be translated into words is not provided in the question. However, I will provide an example of how to translate a symbolic statement involving the statements p and q into words.

Example: p ∧ q

This symbolic statement can be translated into words as follows: "You mowed the lawn and you left the room a mess." The symbol ∧ represents the logical conjunction "and", which means that both statements p and q are true.

Another example: ¬p ∨ q

This symbolic statement can be translated into words as follows: "You did not mow the lawn or you left the room a mess." The symbol ¬ represents the logical negation "not", and the symbol ∨ represents the logical disjunction "or", which means that either statement p is false or statement q is true.

I hope this helps! If you have a specific symbolic statement that you need help translating, please provide it in the question and I will be happy to help.

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Answer:30.69230769 in decimal form

399/13 in percent form

30 9/13 in fraction form

These are all the means in different forms.

Step-by-step explanation: