One interior angle of a convex polygon (a convex polygon is a polygon where all angles
are less than 180 degrees) is 120 degrees. All the other angles are 130 degrees. How many sides
does the polygon have?

Answer:

159

Step-by-step explanation:

Median = When ordered least to greatest, the number in the middle

140, 141, 146, 148, 151, 156, 159, 159, 160, 167, 170, 173, 174

The the average age of the remaining 4 students is 9.5 years.

The average may be calculated by dividing the total number of values by the sum of all the numbers. An average of the values in a sample of data may be used to determine a mean. In other words, the arithmetic mean is another name for an average. A mean is a term used to describe the average.

The average age of 5 students is 10 years.

∴  Sum of age of 6 students =5 × 10 = 66

⇒  When two more students of age 5 and 1 added to 4 students then, total students will become 8

⇒  Sum of age of 6 students =66 + 6 + 4 = 76

∴  Required average =

76 / 8  = 9.5

=9.5 years

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Answer:

True

Step-by-step explanation:

True

Answer:

5%

Step-by-step explanation:

105=100

110=x

*cross multiply*

=100x110/105

=104.76

=100-105

=5%

subtract the answer gotten with the 100 %

Answer:

a)  See below.

b)  Geometric sequence

[tex]\textsf{c)} \quad a_n=7.5(0.5)^{n-1}[/tex]

Step-by-step explanation:

From inspection of the given table, t(n) halves each time n increases by 1.

Therefore:

[tex]\implies a_4=1.875 \div 2 = 0.9375[/tex]

[tex]\implies a_5=0.9375 \div 2 =0.46875[/tex]

Completed table:

[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} n&t(n) \\\cline{1-2} \vphantom{\dfrac12} 1& 7.5\\\cline{1-2} \vphantom{\dfrac12} 2& 3.75\\\cline{1-2} \vphantom{\dfrac12} 3&1.875 \\\cline{1-2} \vphantom{\dfrac12} 4& 0.9375\\\cline{1-2} \vphantom{\dfrac12} 5& 0.46875\\\cline{1-2} \end{array}[/tex]

As the given sequence has a constant ratio of 0.5, it is a geometric sequence.

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

The first term of the sequence is 7.5.  Therefore,:

The common ratio is 0.5. Therefore:

Therefore, to write an equation for the given geometric sequence, substitute the found values of a and r into the formula:

In linear equation, 16 is represent The speed at which Serena is cycling from the dance class to her home

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                    Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

6x + y = 16

6x = 16 - y

x = 8/3 - y/6

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Answer:

  a)  93 cm²

  b)  98 cm²

Step-by-step explanation:

You want the areas of the squares shown in each of the figures.

The Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the other two sides of a right triangle.

The square of the hypotenuse is 17² = 289.

The sum of the squares of the other two sides is ...

  shaded square + (14)² = 17²

  shaded square + 196 = 289

  shaded square = 289 -196 = 93 . . . . cm²

Sabcd = 93 cm².

The square of the diagonal is the sum of the squares of the sides. Each of those squares is the area of interest:

  14² = (shaded square) + (shaded square)

  196 = 2(shaded square)

  98 = shaded square

Sabcd = 98 cm².

__

Additional comment

Perhaps you have seen the attached figure. It is intended to show the squares on each of the legs of the right triangle, and to illustrate that the sum of the areas of the green and purple squares is the area of the red square. This figure compares to the one for part (a) of the problem.

  a² +b² = c²   ⇒   a² = c² -b²

Therefore , the solution of the given problem of unitary method comes out to be $ 4 for garry  and $ 1.33 for peter.

To accomplish a task through using unitary procedure, multiply the number of a tiny slice by two after first determining its size. The unit technique, to put it simply, is used to isolated a programmed object from either a specific set or set of sets. For illustration, 40 pens would cost 400 pounds ($1.01), or Rs. It's feasible that one nation will have complete control over the technique used to do this. Almost all living things have a unique characteristic. It can integrate and reciprocate in equal measure (mathematics, algebra).

Here,

Given :

Garry charges for one carrot for  :

=> 12/3

=> $ 4

Peter charges for one carrot :

=> 20/15

=>  4/3

=> $ 1.33

Therefore , the solution of the given problem of unitary method comes out to be $ 4 for garry  and $ 1.33 for peter.

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The value of X is 7.625 while the two sides are 38.125 and 27.875.

Perimeter = 2(L+B)

112 = 2(5x + 3x + 5)

112 = 2(8x + 5)

Dividing both sides by 2

56 = 8x + 5

56 + 5 = 8x

61 = 8x

x = 61/8

x = 7.625

The sides are;

5x = 5(7.625)

5x = 38.125

3x + 5 = 3(7.625) + 5

3x + 5 = 22.875 + 5

3x + 5 = 27.875

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Answer:

x intercepts (-2,0) and (-4,0)

y intercept: (0,8)

Vertex: (-3,-1)

Axis of symmetry x = -3

Step-by-step explanation:

Answer:

[tex]\frac{19}{18}=1\frac{1}{18}[/tex]

Step-by-step explanation:

[tex]3\frac{1}{6}\div3=\frac{19}{6}\div3=\frac{19}{6}*\frac{1}{3}=\frac{19}{18}=1\frac{1}{18}[/tex]

Therefore , the solution of the given problem of expression comes out to be 4x² +1 cannot equal 0 and thus (4x²≥0+1) has no Real factors.

Verifying an algebraic expression requires substituting a number for each variable and performing arithmetic operations. Given that 6 + 6 equals 12, the answer variable in the example above is equivalent to 6. If we are aware of the values of the variables, we can substitute those values for the original ones, which will allow us to evaluate the expression.

Here,

It is important to note that now the ratio of a coefficient of the terms 

The coefficient ratio of the words

8x³ and 2x is 8:2 = 4:1, and the coefficient ratio of the phrases 12x² and 3 is 12:3 = 4:1.

This suggests that we should categorize the original statement as follows: 

This suggests that we should combine the original expression, which is written as

=> (8x³+2x)(12x²+3)=2x(4x²+1))3(4x²+1),

before determining the common component (4x2+1)=(2x³)(4x2+1).

The fact that 4x²≥0 for x ∈ R means that

4x² +1 cannot equal 0 and thus (4x²≥0+1) has no Real factors.

Therefore , the solution of the given problem of expression comes out to be 4x² +1 cannot equal 0 and thus (4x²≥0+1) has no Real factors.

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Answer:2

Step-by-step explanation:1+1=2

Answer: 2

Step-by-step explanation:

1

+

1

____

2

Reason:

Point C is located at (3,3)

Triple each coordinate since the scale factor is 3. That's how we go from (3,3) to (9,9)

If the scale factor was 5 for instance, then we'd go from (3,3) to (15,15)

This trick works only if the center of dilation is the origin.

Answer:

C' = (-3, 4)

Step-by-step explanation:

When a shape is dilated by a factor of 3, the size of the shape is multiplied by 3 in both the x and y directions. To find the new coordinates of point C' after a dilation by a factor of 3, we can multiply the original coordinates of point C by 3.

The original coordinates of point C are (-2, -10). When we multiply these coordinates by 3, we get (-6, -30) for the new coordinates of C' after the dilation. So the answer is (-6, -30)

Luis genera $13680 al mess, sir se incremental un 14% ell valor de sub seldom actual.

De actedron con las condictiones dadas, planter=12000*(14% + 1)

Calculary loss dos primero's terminus =12000*1.14

Calculary loss dos primero's terminus =13680

get the result=13680

Explication paso a paso:

multiplicate ell 14% de 12.000= 1.680

le sulfas ese 1.680 a 12.000 y tee da ell resulted de 13.680

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the total area will be covered in the paint will be 2143.9cm²

What is cylinder?

Two parallel, identical bases connected by a curving surface form a 3D solid shape known as a cylinder. Similar to a disc in shape, these bases. The axis of the cylinder shape is a line drawn through the middle of, or connecting, two circular bases. Perpendicular distance is the measurement separating the two bases, and it is denoted by the letter "h," which stands for height. The distance between the two circular bases' centers and outer edges is known as the cylinder's radius and is denoted by the letter "r". A rectangle and two circles combine to form the cylinder.

A cylinder with base radius of 4 cm and a height of 7 cm is removed from the cuboid.

Volume of cuboid is = 16*15*24 = 5760 cm³

Volume of the cylinder = π r² h = π* 4² *7 = 351.85 cm³

So the surface area of the cylinder = 2π r h = 2*π*4*7 = 175.9 cm²

Total area of the cuboid = 2(240+360+384) = 1968

Toatl area = 1968+175.9 = 2143.9cm²

So the total area will be covered in the paint will be 2143.9cm²

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a) To evaluate loga 15, we can use the property of logarithms that states logab = loga + logb. Since 15 = 3 * 5, we can use this property to find that loga 15 = loga 3 + loga 5. Since loga 3 = 0.56 and loga 5 = 0.83, we can add these values to find that loga 15 = 0.56 + 0.83 = 1.39.

The power to which a number must be increased in order to obtain additional values is referred to as a logarithm. The easiest approach to express enormous numbers is this manner.

Numerous significant characteristics of a logarithm demonstrate that addition and subtraction logarithms may also be represented as multiplication and division of logarithms.

b) To evaluate loga(2/5), we can use the property of logarithms that states log(a/b) = loga - logb. Since 2/5 = 2*(1/5) we can use this property to find that loga(2/5) = loga2 - loga(1/5). Since loga2 = 0.36 and loga(1/5) = -loga5, we can subtract these values to find that loga(2/5) = 0.36 - 0.83 = -0.47

c) To evaluate loga (8a^4), we can use the property of logarithms that states log (a^n) = nloga. We get, loga (8a^4)=loga 8 + log (a^4)

=> loga 8 + loga (a^4)

=>3loga 2 + 4 loga a

=>3loga 2 + 4

=>3 * 0.36 + 4

=5.08

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The value of dy when x changes from -1 to -1.1 for equation y = 4x² is 0.84.

Here we are given an equation y = 4x²

In an equation, dy/dx, implies the change in y due to a change in x.

Now here we already have given that x changes from -1 to -1.1.

Hence, here we need to find the values of y when x = -1 and when x = -1.1

Then we need to subtract the value of y when x = -1.1 and when x = -1

We are given y = 4x²

Hence when x = -1,

y = 4 X 1

= 4

When x = -1.1

y = 4 X 1.21

= 4.84

Hence dy = 4.84 - 4

= 0.84

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The equivalent function of the form J(t)= ab^t is J(t) = 448(16)^(t)

Equivalent functions are functions that work the same even though they look different. If two exponential functions are equivalent, then the two functions will have the same value when we substitute the same value(s) for the variable(s).

We can write the given function, (t)=28(4)^(2t+2) as:

J(t) = 28(4)^(2t+2)

J(t) = 28(4²)^(t) × 4²

J(t) = 28(16)^(t) × 16

J(t) = 448(16)^(t)

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The polynomial's zeros must be located using a method of your choice, and the linear expressions that produce those zeros must then be combined in order to describe the polynomial as a product of linear factors.

The term "triple zero" or "zero with multiplicity 3" is used to describe this. The power p governs the behaviour close to the x-intercept if a polynomial has a factor of the type (xh)p. A zero of multiplicity p is defined as x=h. The x-axis will be touched at zeros with even multiplicities on a polynomial function's graph.

A real number is multiplied by an imaginary unit, I whose feature i2 = 1 defines it as an imaginary number. Bi is an imaginary number, while b2 is its square. For instance, the square of the fictitious integer 5i is 25. Zero is regarded as both real and fictitious by definition.

You must first determine the polynomial's zeros using the method of your choice, and then combine the linear equations that result in those zeros. If you factor, you will arrive at the third degree polynomial, which must then be sorted through.

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The best estimate willl 20

Step-by-step explanation:I

By using the given relation, we can perform a change of units to get:

$2525 = 108,072.25 Ars.

Here we want to do a change of units, from US dollars to Argentine pesos.

We know the relation:

$0.023364 = 1 Ars.

Here we want to convert $2525 to argentine pesos, then we just need to divide by $0.023364

$2525 = ($2525/$0.023364) ars = 108,072.25 Ars.

That is the equivalent amount in Argentine pesos.

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In the graphic below, assuming the lines are parallel, the value of x is 15.

Parallel lines are coplanar infinite straight lines that do not cross at any point in geometry. Parallel planes are planes that never intersect in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance. Parallel lines in geometry are two lines in the same plane that are at equal distance from each other but never intersect. They can be both horizontal and vertical in orientation. Parallel lines can be found in everyday life, such as zebra crossings, notepad lines, and railway tracks.

Here,

6x+3=7x-12

x=15

The value of x in the figure below assuming that the lines are parallel is 15.

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Joe made a mistake in his calculations by multiplying 28 quarts by 4.

To know the mistake that Joe made and the possible correction, we shall convert 28 quart to gallon.

Recall that 4 quart = 1 gallon

Therefore, 28 quart will be:

= 28 quart × 1 gallon / 4 quart

28 quart = 7 gallon

Therefore, 28 quarts is equivalent to 7 gallons.

Hence, Joe made a mistake in his calculations by multiplying 28 quarts by 4 instead of dividing 28 quart by 4.

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The area of the irregular polygon is 24 square inches. Hence option A is the correct option.

What is an irregular polygon?

An irregular polygon does not have all of its sides equal, nor are all of its angles equal in size. Scalene triangles, right triangles, isosceles triangles, rectangles, parallelograms, irregular pentagons, irregular hexagons, and so on are examples of irregular polygons.

The length of DE is 5 in and HI is 5in.

The length of AL is 12in.

The length of AD + EH + IL = AL - (DE+HI) = 12 - (5+5) = 2 in

The length of AB = DC = EF = HG = IJ = LK = 7in.

The sum area of the rectangles ABCD, EFGH, and IJKL is

AB×AD + EF×EH + IJ×IL

= 7×AD + 7×EH +7×IL

= 7(AD + EH + IL)

= 7×2

= 14 square inches

The length of DW = EX = HY = IZ = 7 - 6 = 1in.

The area of DWXE is DW×WX = 1×5 = 5 square inches

The area of HYZI is HY×YZ = 1×5 = 5 square inches

The area of the irregular polygon is

14  + 5 + 5 square inches

= 24 square inches

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Answer:

she had here eyes open for 12.4 more hours than she had them closed

Step-by-step explanation:

1/10 eyes closed = 9/10 eyes open

9/10 is 90% is 0.9

1/10 is 10% is 0.1

15 1/2 is 15.5

15.5 x 0.9 = 13.95

15.5 x 0.1 = 1.55

13.95-1.55 = 12.4

Brooke's yard is a square with a side length of 22 meters.

Perimeter is the total distance around the outside edge of a two-dimensional shape. Perimeter is a measure of the length of the boundary of a shape and is typically expressed in units of length, such as feet or meters. Calculating the perimeter of a shape can help you measure the size of a yard, garden, or other outdoor area.

Since the perimeter of the part covered in gravel is 22 meters, we can use the formula for the perimeter of a square (4s) to find the length of one side of the square. Therefore, the side length of the part covered in grass is 4s = 22, or s = 5.5 meters.

Using the formula for the area of a square (A = s²), we can calculate the area of the grass section of Brooke's yard. The area of the grass section of Brooke's yard is A = s²= 5.5²= 30.25 square meters.

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Answer:

-------------------------------

Slope- intercept form:

Use two points on the line:

The first point is the y- intercept:

The slope is:

The line is: