How many sides does a polygon have if the sum of the interior angles is 900∘?
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Answer:

Option: 4

Step-by-step explanation:

It is in the form of ar^n-1.

For eg:

2nd term/1st term=3rd term/2nd term=4th term/3rd term

The equation is written as x + 25° + 25° = 90°. Then the value of the variable 'x' is 40°.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Adjacent angle - In math, two points are nearby in the event that they have a typical side and a typical vertex.

AB and BC are perpendicular lines. Then the equation is given as,

x + 25° + 25° = 90°

x + 50° = 90°

x = 90° - 50°

x = 40°

The equation is written as x + 25° + 25° = 90°. Then the value of the variable 'x' is 40°.

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The complete question is given below.

The required solution of the given differentiation is given as y'(2) = 135/16. Option A is correct.

The method of determining the derivative of an implicit function is by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol.

here,
y = [x - 1/x]³
y' = 3[x - 1/x]² × [1 + 1/x²]

put x = 2
y'(2) = 3 [2 - 1/2]² × [1 + 1/4]
y'(2) = 3[3/2]²[5/4]
y'(2) = 27/4 × 5/4
y'(2) = 135/16

Thus, the required solution of the given differentiation is given as y'(2) = 135/16.

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Answer:

b=8

Step-by-step explanation:

5(b-1)=30

5b-5=35

5b=40

b=8

The value for b is 7.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

Darryl had 5 boxes of books with b books in each box.

If one 1 book remove from each box then total number of books

= (b-1) +  (b-1) +  (b-1) +  (b-1) +  (b-1)

= 5(b-1)

and, After giving away 1 book from each box, he had 30 total books left.

Then, 5(b-1)= 30

b-1 = 6

b = 7

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Answer:

[tex]\displaystyle{x = \dfrac{\log 7}{\log 5}}[/tex]

Step-by-step explanation:

Given the equation:

[tex]\displaystyle{2\left(5^x\right)=14}[/tex]

Divide both sides by 2:

[tex]\displaystyle{\dfrac{2\left(5^x\right)}{2}=\dfrac{14}{2}}\\\\\displaystyle{5^x=7}[/tex]

Apply common logarithm both sides:

[tex]\displaystyle{\log 5^x = \log 7}[/tex]

From the property:

[tex]\displaystyle{\log a^n = n\log a}[/tex]

Thus:

[tex]\displaystyle{x\log 5 = \log 7}[/tex]

Divide both sides by log5:

[tex]\displaystyle{\dfrac{x\log 5}{\log 5} = \dfrac{\log 7}{\log 5}}\\\\\displaystyle{x = \dfrac{\log 7}{\log 5}}[/tex]

The fraction of their money remains for other expenses each month is 5/12.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given:

Williams spend 1/3 of their total monthly income for rent and 1/4 for food.

The fraction of their money remains for other expenses each month,

= 1 - 1/3 - 1/4

= 5/12

Therefore, 5/12 is the remaining money.

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The politician experience 16% of actual change and 47% relative change in his support.

Actual change refers to the simple difference between the ending and initial condition. In this case, actual change is the gap of the politician's support increase. The actual change of the politician's support is:

Actual change = Ending% - Initial %

Actual change = 50% - 34%

Actual change = 16%

Relative change is the percentage change between ending and initial condition based on the perspective of the initial condition. Relative change measures the gap between the ending and initial conditions compared to the initial condition. Relative change can be calculated by dividing the gap of 2 conditions with the initial condition.

The relative change of politician's support is:

Relative change = Ending% - Initial %

                                    Initial %

Relative change = 50% - 34%

                                    34%

Relative change = 47%

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Answer:

[tex]\displaystyle y=-\frac{3}{8}x+2[/tex]

Step-by-step explanation:

Perpendicular lines have opposite reciprocal slopes. So, we must first determine our slope of the original equation by converting to slope-intercept form:

[tex]-8x+3y=-6\\3y=8x-6\\y=\frac{8}{3}x-2[/tex]

Hence, because the slope of the original line is 8/3, then the slope of the perpendicular line is -3/8. We are not done, however, as we need to account for the point that the perpendicular line passes through by solving for the new y-intercept:

[tex]y=-\frac{3}{8}x+b\\ \\8=-\frac{3}{8}(-16)+b\\\\8=6+b\\\\2=b[/tex]

Thus, the perpendicular line equation is [tex]y=-\frac{3}{8}x+2[/tex]. See below for a graph.

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]-8x+3y=-6\implies 3y=8x-6\implies y=\cfrac{8x-6}{3} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{8}{3}}x-2\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{8}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{8}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{8} }}[/tex]

so we're really looking for the equation of a line whose slope is -3/8 and it passes through (-16 , 8)

[tex](\stackrel{x_1}{-16}~,~\stackrel{y_1}{8})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{3}{8} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{- \cfrac{3}{8}}(x-\stackrel{x_1}{(-16)}) \implies y -8= -\cfrac{3}{8} (x +16) \\\\\\ y-8=-\cfrac{3}{8}x-6\implies {\Large \begin{array}{llll} y=-\cfrac{3}{8}x+2 \end{array}}[/tex]

Algebraic Expression for the table of Nora, Nora's brother and Mother would be x, x-4 and 4x.

What is Algebraic Expression?

An algebraic expression is when we use numbers and words in solving a particular mathematical question.

Let x be Nora's age. Then Nora's brother is x - 4 years old, and Nora's mother is 4 * x years old.

The algebraic expression for the table is:

Nora: x

Nora's Brother: x - 4

Nora's Mother: 4x

Therefore, The Algebraic Expression for the table of Nora, Nora's brother and Mother would be x, x-4 and 4x.

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The value of x is 11 for the given condition that m||n.

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.

Numerous pairs of angles are created whenever any two parallel lines are intersected by a third line known as a transversal. The other angles are supplementary while some are congruent (equal).

Angles on a straight line sum up 180°

Let us take the line t as our straight line

(7x – 1)° + (9x + 5)° = 180°

(7x + 9x + 5 – 1) = 180

16x + 4 = 180

16x = 180 – 4

16x = 176

(16x)/16 = (176/16)

x = 11

Hence, the value of x is 11.

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The exponential grows at the same rate as the quadratic in the interval

0 ≤ x ≤ 1.

The average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing. In simple terms, an average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another.

The average rate of change of a function A = [tex](f(a) - f(b))/(b-a)[/tex]

Given an exponential function, say f(x), such that f(0) = 1 and f(1) = 2.

A quadratic function, say g(x), such that g(0) = 0 and g(1) = 1.

The rate of change of a function f(x) over an interval a ≤ x ≤ b is given by

[tex](f(a) - f(b))/(b-a)[/tex].

Thus, the rate of change (growth rate) of the exponential function, f(x) over the interval 0 ≤ x ≤ 1 is given by

 = (2-1)/1 = 1

Similarly, the rate of change (growth rate) of the quadratic function, g(x) over the interval 0 ≤ x ≤ 1 is given by

=(1 - 0)/1  = 1

Therefore, the exponential grows at the same rate as the quadratic in the interval 0 ≤ x ≤ 1.

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Answer:

B

Step-by-step explanation:

(-5, -3), in slope-intercept form, is parallel to the equation -3x - 7y = 10.

Therefore, we must first determine this's slope.

-3x - 7y = 10

To both sides, add three.

-7y = 3x + 10

Add -7 to both sides.

y = -3/7x - 10/7

Our slope is thus -3/7.

The slopes always remain the same when searching for a line that is parallel to something.

Remember that y = mx+b is the slope-intercept form as well.

Where b is the y-intercept and m is the slope.

Our y-intercept is -3 since the coordinates (-5,-3) are available.

The slope here is -3/7.

Put those numbers into the slope-intercept form equation, then, to solve.

y = mx + b

y = -3/7x - 3

(-5, -3), in slope-intercept form, is parallel to the equation -3x - 7y = 10.

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The equation of the line parallel to the given line is y = -3x/7 + 47/7

The equation of the perpendicular will be  y = 7x/3 -13/3

The formula for a straight line is y=mx+c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.

The slope of a line that is perpendicular to another line is equal to the negative reciprocal of that line's slope. The slope of the original line's perpendicular line is -2, which is the original line's negative reciprocal.

The equation of the line is 3x + 7y = 8

The slope of the line is = -3/7

so the equation of the line parallel to the given line is y = -3x/7 + c

the point given as (4,5)

The line is 5 = -3*4/7 + c

or, c = 5 + 12/7 = 47/7

the equation of the line parallel to the given line is y = -3x/7 + 47/7

The slope of the line perpendicular to the given line is 7/3

So, the equation of the line is y = 7x/3 + c

The intercept is 5 = 7*4/3 + c

or, c = 5 - 28/3 = -13/3

The equation of the perpendicular will be  y = 7x/3 -13/3

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The simplest form of the expression is -3x³ + 2x² + 13x -10

An algebraic expression in mathematics is an expression that is made up of letters and numbers, along with algebraic operations (addition, subtraction, multiplication, etc).

-(x − 2)(3x² + 4x − 5) can be expressed in simplest form as follows:

-(x − 2)(3x² + 4x − 5) = (-x +2)(3x² + 4x − 5)

                                 = -x(3x² + 4x − 5) + 2(3x² + 4x − 5)      

                                 = -3x³-4x²+5x + 6x²+8x-10

                                 = -3x³ + 2x² + 13x -10

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The length of the remaining sides is a = 57.50 and b = 61.93.

The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.

The side or unknown angle of an oblique triangle is found using the law of sine. Any triangle that is not a right triangle is referred to as an oblique triangle.

Given a triangle ABC, and ∠B = 90°

∠A = 68.2° and c = 23.0

so ∠C = 90 - ∠A

∠C = 90 - 68.2

∠C = 21.8°

according to the law of sines,

sinA/a = sinB/b = sinC/c

for a,

sinA/a = sinC/c

substitute the values

sin(68.2)/a = sin(21.8)/c

a = 23(sin68.2)/(sin21.8)

a = 57.50

and for b,

sinB/b = sinC/c

substitute the values

b = csinB/sinC

b = 23(sin90/sin21.8)

b = 61.93

Hence a = 57.50 and b = 61.93.

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The line could contain A'B' is 3x+2y=10, so correct option is (a).

It usually consists of variables, coefficients, and constants, connected by operations such as addition, subtraction, multiplication, and division. Equations are used to model relationships between different quantities and to solve problems in various fields such as physics, engineering, and economics. For example, the equation y = mx + b represents a straight line in two-dimensional space, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.

The line 2x + 3y = 5 contains AB, so AB lies on the line 2x + 3y = 5. To dilate triangle ABC to A'B'C, the center of dilation is a fixed point and the scale factor is a constant. Since AB lies on the line 2x + 3y = 5, the line containing A'B' after dilation must be parallel to the line 2x + 3y = 5, so the correct answer is (a) 3x + 2y = 10.

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Answer:

Slope is -2

Y-intercept is 8

Step-by-step explanation:

The given equation is in the form:

y = mx + b

It is called Slope-Intercept form of an equation. This is because you can look at the equation and automatically see/know the slope and the y-intercept.

The m is the slope, it is the number right next to the x. In your question it is -2. This is the slope -2/1 or 2/-1 (which are the same) It tells you how steep or flat a line is.

The b is the y-intercept, it is the number tacked on to the end of the equation. In your question it is the 8. It tells you where on the y-axis the line crosses.

Slope: m = -2

Y-int: b = 8

The total surface area painted black = 56.5 square feet to the nearest tenth.

A cone is a three-dimensional geometric form with a flat base and a smooth, tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that link the base's points to the apex, which is a common point on a plane that does not include the base.

Given that, three large cones hang from the ceiling in an office building in front of a bank of windows.

The height of each cone is 12 feet, and the circumference of the base of each cone is 8π feet.

The base and 40% of the lateral surface of each cone is painted red, and the rest of each cone is painted black.

Circumference of the base of the cone = 8π feet.

2πr = 8π

πr = 4π

The surface area of the cone = πr x slant height

Slant height = [tex]\sqrt{radius^2+height^2}[/tex]

= √12²+4² = 12.6 ft

The surface area of the cone = 12.6 x 4π

The surface area of the cone = 60π.

The lateral surface area painted black = 30% of 60π.

Therefore, The total surface area painted black = 56.5 square feet to the nearest tenth.

Hence, the required area is 56.5 square feet.

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Answer:

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

Since P is incenter, we have properties of incenter applicable to given questions:

Since JN is angle bisector of ∠J, set up equation:

Angle measures of the triangle are:

Then, according to triangle sum:

Then, find the missing angle:

Sides are equidistant from incenter:

Set up equation and solve or x:

Find one of equal segments:

Hence, MP = 38

ΔMPJ and ΔOPJ are congruent right triangles as MP = OP and JP is common hypotenuse, therefore JM and JO are congruent as corresponding sides:

Then JM is:

We know MP = NP = 22.

Find JP using Pythagorean:

Given that a, b, and c are all equal in a cube, we can calculate the length of each side of the cube by taking the square root of 192, which is 64, and multiplying it by three to get 8.

Add the areas of each of the six rectangular sides of a cuboid to determine its surface area. The cuboid's length, width, and height can also be labelled, and the surface area (SA) can be calculated using the formula SA=2lw+2lh+2hw.

Volume is a three-dimensional measurement that accounts for the sum of a figure's length, breadth, and height. Planes, polygons, and other two-dimensional figures have no volume because they lack a vertical dimension.

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The angle of least positive measure coterminal with -40 degrees is 320°

Coterminal angles are angles that share the same initial side and the same terminal side.

Since we have our initial angle as -40 degrees.

Let x be the angle of least positive measure coterminal with -40 degrees

We know that to get coterminal angles, we add or subtract 360° to the angle.

So, for a positive coterminal angle, we add 360° to it.

So, x = (-40°) + 360°

Which gives

x = -40° + 360°

x = 320°

So, tha angle is 320°

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The slope of the line represented by the graph of a linear function is  -5/2

The general equation of a straight line is -

y = mx + c

where -

m → slope of line

c → y - intercept of line

here, we have,

Given in a question a linear function that decreases from left to right passing through the coordinates A(0,3) and B(2, -2).

A linear function is a function of general equation → y = ax + b which is same as y = mx + c.

So, it represents a straight line.

The line passes through the points A (0,3) and  B (2, -2).

The Slope of the given line can be calculated using the following formula -

m = (y[2] - y[1]) / (x[2] - x[1])

m = (- 2 - 3) / (2 - 0)

m = -5/2

Therefore, the slope of the line represented by the graph of a linear function is  -5/2.

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Answer: 14

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Step-by-step explanation:

Answer:

A

Step-by-step explanation:

have great day

Answer: n= 4

Step-by-step explanation:

n+10=2(n+6) where n represents the number

you solve this.

n+10=2n+6

n+10-6=2n

n+4=2n

n=4

There's no need to turn it into a mixed number since 378/9 = 42 is entirely a whole number.

I suppose you could write  42  0/9 or 42 & 0/9 or [tex]42 \frac{0}{9}[/tex], but that isn't really necessary.

Answer:

192,753

Step-by-step explanation:

    194,753

 -     2,000

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

    192,753

194,753 - 2,000 = 192,753

The greatest possible number of pansies in each row is 9.

The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers. The GCF of two natural numbers x and y is the largest possible number that divides both x and y without leaving any remainder.

Given that, a gardener has 27 pansies and 36 daises.

Here, factors of 27 and 36 are

27 =3×3×3

36 =2×2×3×3

So, the GCF of 27 and 36 is 3×3 =9

Therefore, the greatest possible number of pansies in each row is 9.

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The first three terms for the sequence, which have x₁ = 3 and xₙ₊₁ = xₙ -5 are respectively,  3, -2, -7,

In the arithmetic sequence  the common difference remains constant between any two consecutive terms. In this sequence we can get the next term by adding one fixed value which is known as a common difference. It is also known as arithmetic progression(AP).

Formula for any nth term in AP,

T = a + nd

d = T₂-T₁

Where, a is first term , n is nth term and d is common difference

Given that,

The Sequence,

Having a relation,

x₁ = 3

And xₙ₊₁ = xₙ -5

Let,  n = 1

Then,

x₁₊₁ = x₁ - 5

x₂  =  x₁ - 5

x₂  =  3 - 5

x₂  =  - 2

x₂₊₁ = x₂ - 5

x₃   =  -2 -5

     =  -7

x₃₊₁ = x₃ - 5

x₄  =  -7 -5

     = - 12

Therefore, the first three terms are 3, -2, -7

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Answer:

5/2 or 2.5

Step-by-step explanation:

Divide both sides by 2.

The combined area of all the circles to the nearest hundredth would be = 14,519.36cm³

The formula for the area of a circle = πr²

The radius for one circle = 68/2 = 34cm

π = 3.14

The area of one circle = 3.14× 34²

= 3.14× 1156 = 3629.84

Therefore the combined area of the 4 circle = 4× 3629.84 = 14,519.36cm³.

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