determine if the sequence is arithmetic. if it is find the common difference and the next 3 terms in the sequence 35, 32, 29, 26

The triangle is Isosceles and Acute.

From the given data, the coordinates of the three points of the triangle are, A(2, 3), B(8, 3), and C(5, 6).

applying the distance formula, D = √((x2-x1)²+(y2-y1)²) the distance AC and BC are obtained as 3√2 and the distance AB as 2√3.

From this, it can be concluded that AC=BC≠AB.

thus since two of the sides, AC and BC are equal and the third side AB is not equal to AC and BC hence the given triangle is an isosceles triangle.

To check whether the given triangle is right, acute.

A right triangle is a triangle with one of its angles equal to 90 degrees.

An acute triangle is a triangle with all three of its angles less than 90 degrees.

An obtuse triangle is a triangle with at least one of its angles greater than 90 degrees.

To check whether the given triangle is right, acute, or obtuse we use the law of cosines.

To find the angle of a triangle given 3 of its sides, let the angle between the sides AB and AC be A then,

cos(A) =  (AC² + AB² − BC²)÷(2×AB×AC).

cos(A) = (3√2² + 2√3² - 3√2²)÷(2×2√3×3√2) =2÷√6

[tex]cos^{-1}[/tex](2÷√6) = 39.182.

Let the angle between the sides AB and BC be B then,

cos(B) =  (BC² + AB² − AC²)÷(2×AB×BC).

cos(B) = (3√2² + 2√3² - 3√2²)÷(2×2√3×3√2) =2÷√6

[tex]cos^{-1}[/tex](2÷√6) = 39.182.

Let the angle between the sides AC and BC be then,

cos(C) =  (AC² + BC² − AB²)÷(2×AC×BC).

cos(C) = (3√2² + 3√2² - 2√3²)÷(2×3√2×3√2) =2÷3

[tex]cos^{-1}[/tex](2÷3) = 53.544.

Since all the angles A, B, and C is less than 90 degrees the triangle is acute.

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The ratios, 1 : 4 and 2 :6 are not equivalent.

Ratio shows the relationship that exist between two or more numbers. Ratio is used to compare two or more numbers. It shows the number of times that one value is contained within other value(s).

In order to determine if the ratios are equivalent, express 2 : 6 in its simplest form. To do this, divide 2 and 6 by 2, a common  multiple of both numbers.

2 :6 in its simplest form is 1 : 3

Since, 1 : 3 is different from 1 : 4, the ratios are not equivalent.

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The exponential function which shows the exponential growth rate of graduating women is: A(t) = A₀e∧(0.037t).

The following equation can be used to calculate an exponential function again for number of women graduating from four-year colleges in t years after 1930:

A(t) = A₀e∧(rt)

In which A₀ is the starting point and r is the exponential growth rate expressed as a decimal.

In 1930, 48780 women received a bachelor's degree.

This implies that;

A₀ = 48780

In 2004, approximately 756000  people

The year 2003 is 73 years after 1930, that also means

Using the equation as an example:

A(t) = A₀e∧(rt)

Put the values;

756000 = 48780 e∧(73r)

e∧(73r) = 756000/ 48780

e∧(73r) = 15.49

Taking log both side;

73r = ㏑ 15.49

r = 2.7/7

r = 0.037

The function becomes;

A(t) = A₀e∧(0.037t)

Thus, the exponential function which shows the exponential growth rate of graduating women is: A(t) = A₀e∧(0.037t).

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The line on the graph is a function

The given parameter is the graph

From the graph, we can see that the curve or the line is a quadratic function

As a general rule, all lines represented by a quadratic function are functions

This implies that the line is a function

It should be noted that:

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

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Step-by-step explanation:

we can find the number of students passed in both subject by following method.

Solution;

Answer:

The total of all calories in a coffee with milk and sugar, is somewhere between 120 and 180. A couple of cups per day could easily add a lot of calories to the 2 000 calories needed per day.

Step-by-step explanation:

Answer:

A standard coffee with whole milk and sugar contains around 140 calories. This number can increase depending on the type of milk used, as well as the amount of sugar added.

Triangle A is right angled triangle

Triangle B is right angled triangle

Triangle C is obtuse angled triangle

Triangle D is acute angled triangle

In right angled triangle one of the three angles in the triangle is 90 degrees

In acute angled triangle all the angels in the triangle is less than 90 degrees

In obtuse angled triangle one of the three angles in the triangle is greater than 90 degrees

In triangle A one of the angle is 90 degrees, then the triangles is right angled triangle

In triangle B one of the angle is 90 degrees, then the triangles is right angled triangle

In triangle C one of the angle is greater than 90 degrees, then the triangle is obtuse angled triangle

In triangle D all the angles are less than 90 degrees, then the triangle is acute angled triangle

Hence, Triangle A is right angled triangle

Triangle B is right angled triangle

Triangle C is obtuse angled triangle

Triangle D is acute angled triangle

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Answer:

x = 40

Step-by-step explanation:

We just have to manipulate the terms, putting each term that has the variable "x" on one side of the equation like this:

5x + 8 = 7x - 72​

5x - 7x = - 72 - 8​

-2x = -80

x = -80/--2

x = 40

Answer:

x = 40

Step-by-step explanation:

Given equation:

[tex]5x+8=7x-72[/tex]

Add 72 to both sides:

[tex]\implies 5x+8+72=7x-72+72[/tex]

[tex]\implies 5x+80=7x[/tex]

Subtract 5x from both sides:

[tex]\implies 5x+80-5x=7x-5x[/tex]

[tex]\implies 80=2x[/tex]

Divide both sides by 2:

[tex]\implies \dfrac{80}{2}=\dfrac{2x}{2}[/tex]

[tex]\implies 40=x[/tex]

Therefore, the solution to the given equation is x = 40.

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:slope(m) = \dfrac{5}{2} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Slope (m) of a line can be calculated by using this formulae :

[tex]\qquad \tt \rightarrow \: m = \dfrac{rise}{run} [/tex]

Considering two points [ (60 , 0) and (80 , 50) ]

[tex]\qquad \tt \rightarrow \: m = \dfrac{y2 - y1}{x2 - x1} [/tex]

[tex]\qquad \tt \rightarrow \: m = \dfrac{50 - 0}{80 - 60} [/tex]

[tex]\qquad \tt \rightarrow \: m = \dfrac{50}{20} [/tex]

[tex]\qquad \tt \rightarrow \: m = \dfrac{5}{2} [/tex]

So, slope of given line is 5/2

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

An ordered stem-and-leaf plot has the following results:

0=4 counts

1=7 counts

2=6 counts

3=4 counts

4=1 count

The shape of the distribution is skewed to the right

Part 1

An ordered stem-and-leaf plot:

                              Total Counts          

0 | 3 4 5 7             | 4

1 | 2 2 4 4 5 7 7    | 7

2 | 0 3 4 4 5 8      | 6

3 | 3 4 7 9             | 4

4 | 1                       | 1

Part 2

Shape of distribution

When the data in the stem-and-leaf plot given above is plotted in graph, the tail of the plot will be on the right. Hence, the shape of the distribution is skewed to the right

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Answer:

-1.5 goes in between -2 and -1

3/2 goes in between 2 and 1 but closer to 1

-2/3 goes in between 0 and -1 but closer to 0

I’m not very sure about -4/3 but I think it goes in between -2 and -1 but closer to -1 than 3/2

Step-by-step explanation:

23

Explanation

Complementary angles are pair angles with the sum of 90 degrees, so we can say that

are complementary angles, therefore

Step 1

so,we need to equals to 90 and solve for x

so, the answer is

23

I hope this helps you

Answer:

78, 3, 28, 42

Step-by-step explanation:

This appears to be a repeating sequence of four numbers:

72, 3, 28, 42

so the missing 4 numbers must be as above

Answer:

16!

Step-by-step explanation:

The sequence shows that from left to right, the numbers are being divided by two (or multiplied by 1/2). So, for that reason I think that the answer must be 16.

Answer:

A

Step-by-step explanation:

it reflects over the y axis

The most appropriate choice for fraction will be given by

Fraction of banana bread will be donated to the homeless is [tex]\frac{1}{4}[/tex]

What is a fraction?

Suppose there is a collection of objects and some part of the objects are taken from the collection. The part which has been taken is called fraction. In other words, part of a whole is called fraction.

The upper part of the fraction is called numerator and the lower part of the fraction is called denominator.

Here,

Total number of banana breads 16

Number of adults who got banana bread = 6

Number of Children who got banana bread = 6

Total number of children and adult who got banana bread = 6 + 6 = 12

Number of banana breads given to the homeless = 16 - 12 = 4

Fraction of banana bread given to the homeless = [tex]\frac{4}{16}[/tex]

                                                                                 = [tex]\frac{1}{4}[/tex]

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The values of the radical expressions are [tex]\frac{5x^4z^3}{7y}[/tex] and [tex]2x^2y\sqrt{5z}[/tex]

Expressions are mathematical statements that are represented by variables, coefficients and operators

Expression 1

Here, we have

[tex]\sqrt{\frac{25x^8z^6}{49y^2}}[/tex]

Take the square roots of 25 and 49

So, we have

[tex]\frac{5}{7}\sqrt{\frac{x^8z^6}{y^2}}[/tex]

Next, we apply the law of indices in simplifying the radical expressions

This gives

[tex]\frac{5}{7}\frac{x^{(8/2)}z^{(6/2)}}{y^{(2/2)}}[/tex]

Evaluate

[tex]\frac{5}{7}\frac{x^4z^3}{y}[/tex]

Rewrite as

[tex]\frac{5x^4z^3}{7y}[/tex]

Expression 2

Here, we have

[tex]\frac{\sqrt{100x^4y^2z}}{\sqrt 5}}[/tex]

Take the square roots of 100

So, we have

[tex]10\frac{\sqrt{x^4y^2z}}{\sqrt 5}}[/tex]

Rationalize

[tex]10\frac{\sqrt{5x^4y^2z}}{5}[/tex]

Next, we apply the law of indices in simplifying the radical expressions

This gives

[tex]10\frac{\sqrt{5z}x^{4/2}y^{2/2}}{5}[/tex]

Evaluate

[tex]2\sqrt{5z}x^2y[/tex]

Rewrite as

[tex]2x^2y\sqrt{5z}[/tex]

Hence, the solution is  [tex]2x^2y\sqrt{5z}[/tex]

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The total surface area of the pyramid (a) is  624.32 cm² , and of pyramid (b) is 265.6 m²  .

The Total Surface Area of the Pyramid with pentagon base can be calculated using the formula

TSA = 5/2*b(a+s) ,

where b is the base length (side of pentagon)

s is the slant height ,

a is the apothem

and the Total Surface Area of the Pyramid with square base can be calculated using the formula .

TSA = b² + 2bs

where , b is the base and

s is the slant height .

Pyramid (a)

we can see from the figure that ,the pyramid has a pentagon base ,

So, the TSA will be 5/2*b(a+s) ,

in the figure , given that height =12 cm , apothem = 7.8cm

we find the slant height by Pythagoras theorem

(slant height)²=(height)²+(apothem)²

(slant height)² = 12² + 7.8²

(slant height) = √(12² + 7.8²)

(slant height) = √(144+60.84)

(slant height) = 14.3 cm

Substituting in TSA formula , TSA = 5/2*b(a+s)

we get ,

TSA = 5/2*11.3(7.8+14.3)

= 2.5*11.3(22.1)

= 28.25*22.1

=624.32 cm²

Pyramid (b)

we can see from the figure that ,the pyramid has a square base ,

So, the TSA will be b² + 2bs,

in the figure , given that height =12 m , apothem = 4 m

we find the slant height by Pythagoras theorem

(slant height)²=(height)²+(apothem)²

(slant height)² = 12² + 4²

(slant height) = √(12² + 4²)

(slant height) = √(144+16)

(slant height) = 12.6 m

Substituting in TSA formula , TSA = b² + 2bs

we get ,

TSA = 8² + 2*8*12.6

= 64 + 16*12.6

= 64 + 201.6

= 265.6 m²

Therefore , the total surface area of the pyramid (a) is 624.32 cm²  , and of pyramid (b) is 265.6 m² .

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By using a translation rule, the coordinates of C' are (- 1, - 2). (Correct choice: E)

Triangles are defined by the locations of its three vertices on Cartesian plane and we must find the locations of the images of the three vertices after applying a translation rule. In this case, we must translate each vertex  2 units upward and 4 units to the right. The general translation formula is described below:

P'(x, y) = P(x, y) + T(x, y)

Where:

If we know that C(x, y) = (- 5, - 4) and T(x, y) = (4, 2), then the location of the image of point C is:

C'(x, y) = (- 5, - 4) + (4, 2)

C'(x, y) = (- 1, - 2)

The coordinates of C' are (- 1, 2).

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This polynomial have 5 degree , 4 terms and one connstant

Algebraic expressions called polynomials only have non-negative integer powers for their variables. A polynomial is, for instance, Expressions with one or more terms that have a non-zero coefficient are called polynomials. The terminology include constants, exponents, and variables. The "leading term" refers to the first term of the polynomial in standard form. A standard polynomial is one in which the first term, which has the highest degree, is followed by succeeding terms that are organized in descending order of the exponents or powers of the variables, then by constant values. A "coefficient" is a number that has been multiplied by a variable.

Given that : [tex]9m^{5}+3n^{2} +2q^{2} +1[/tex]

[tex]9m^{5}+3n^{2} +2q^{2} +1[/tex]

This polynomial have 5 degree , 4 terms and one connstant

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a)The expression for the total cost for all four classes can be given as 32s + 200. b) the rational expression for the cost per student is 2(4s+25)/s c) if each class has 20 students then the cost per student is equal to $10.50.

a) Total cost expression can be determined as follows:

total fees of admission + fees of bus = total cost

total cost = (4s × 8) + 200

total cost = 32s + 200

b) A rational expression to determine the cost per student can be calculated as follows:

cost per student = total cost ÷ the total number of students

cost per student = 32s + 200 ÷ 4s

We now factor the numerator by using its GCF;

cost per student = 4 × 2 (4s + 25) / 4×s

cost per student =2 (4s + 25) / s

c) Now using this expression we can find the cost per student if each class has 20 students;

cost per student = 2 (4s + 25) / s

cost per student = 2 ( 4×20 + 25)/ 20

cost per student = 2 ( 80 + 25) / 20

cost per student = 2 (105) / 20

cost per student = 210 / 20 = $10.50

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Answer:

x < 0.5

Step-by-step explanation:

2(1 - x) > 2x ( divide both sides by 2 )

1 - x > x ( add x to both sides )

1 > 2x ( divide both sides by 2 )

0.5 > x , that is

x < 0.5

The coordinates of the vertices of triangle A'B'C' after a reflection over the y-axis to triangle ABC are: C. A' = (3, -3), B' = (6, -3), C' = (5, -6), D' = (0, -6).

A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

In Geometry, a reflection over the y-axis (y = x) is given by this transformation rule (x, y) → (x, y).

By applying a reflection over the y-axis to triangle ABC, the coordinates of the vertices of the image triangle A'B'C' include the following:

(x, y)                    →            (x, y)

Point A = (3, -3)   →  Point A' = (3, -3)

Point B = (6, -3)   →    Point B' = (6, -3)

Point C = (5, -6)   →     Point C' = (5, -6)

Point D = (0, -6)   →     Point D' = (0, -6)

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The hiking trail that has the least change in elevation, related to sea level, is:

Southern Moon.

The change in altitude of each trail is calculated as the subtraction of the highest altitude by the lowest altitude, that is:

Change in elevation = highest altitude - lowest altitude.

For Eastern Point, the change is given as follows:

Change = 78 - (-85) = 78 + 85 = 163 feet.

(subtracting by a negative is the same as adding to the positive of the number).

For Northern Star, the change is given as follows:

Change = 34 - (-150) = 34 + 150 = 184 feet.

For Southern Moon, the change is calculated as follows:

Change = 48 - (-62) = 48 + 62 = 110 feet.

The smallest amount is of 110, hence Southern Moon has the least change in elevation relative to sea level.

The table is shown by the image at the end of the answer.

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Answer:

x < -4 or x > -2

Step-by-step explanation:

[tex]2 |x + 3| + 1 > 3[/tex]

[tex]2 |x + 3| > 2[/tex]

[tex] |x + 3| > 1[/tex]

x + 3 > 1 or x + 3 < -1

x > -2 or x < -4

Answer:

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

assuming everyone takes their own car, 9.75+17.75 * 7 = 192 I don’t know the state tax, because each state is different but 192 gives about $3 worth of room for tax. If the tax is higher in your state maybe I’d answer with 6 people. Hope this helped!

The expression can be rewritten as:

2*(n - 3)

This is twice an integer number, so this is an even number

Here we know that n is an integer larger than 1, and we have the expression:

n² - (n - 2)² - 2

Now, remember that for any integer m, 2m is always an even number.

Expanding the term in the middle of the expression we get:

n² - (n - 2)² - 2

n² - (n² - 4n + 4) - 2

4n - 4 - 2 = 4n - 6 = 2*(n - 3)

Integer numbers are closed under addition, then n - 3 is an integer, so we have:

2*(n - 3)

This is twice an integer, so this is an even number.

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To transform A to A', B to B' and C to C' rotate the triangle ABC clock- wise 90° about the A.

Simple polygons with three sides and three internal angles make up triangles.

It is one of the fundamental geometric shapes in which the three vertices are connected to one another.

Triangles come in 4 different varieties.

1. Equilateral: Equilateral triangles have three equal sides and three identical 60-degree angles.

2. Isosceles: Isosceles triangles have equal sides and angles on both of their two sides.

3. Right-angled: In right-angled triangles, one of the angles is a right angle (90°).

4. Scalene: Triangles with this property do not have equal sides or angles.

To transform A to A', B to B' and C to C' rotate the Triangle ABC 90° clock- wise about the A.

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Answer:

x = 11°

Step-by-step explanation:

Hello!

These angles are called vertical angles or angles opposite to each other during the intersection of two lines.

Vertical angles are equal to each other, so we can set the expressions equal to each other and solve for x.

The value of x is 11°.

Answer:

[tex]x=\boxed{11}[/tex]

Step-by-step explanation:

Vertical Angle Theorem

The opposite vertical angles of two straight intersecting lines are congruent.

Therefore, equate the expressions and solve for x:

[tex]\boxed{\begin{aligned}(9x-4)^{\circ}&=(8x+7)^{\circ}\\9x-4&=8x+7\\9x-4-8x&=8x+7-8x\\x-4&=7\\x-4+4&=7+4\\x&=11\end{aligned}}[/tex]

Therefore:

[tex]x=\boxed{11}[/tex]