A non-regular octagon has seven interior angle measures of: 103, 175, 155, 158, 169, 157,
55. What is the sum of all interior angles and what is the measure of the eighth interior
angle?
Sum of Interior Angles =
Eighth interior Angle =

angle RQS = 101 degrees

angle TQS = 79 degrees

===================================================

Explanation:

A straight angle has a measure of 180 degrees. It's another way of saying "straight line".

The two angles shown add to 180.

We'll use this fact to solve for x.

(angleRQS) + (angleTQS) = angle RQT

(9x+2) + (7x+2) = 180

16x+4 = 180

16x = 180-4

16x = 176

x = 176/16

x = 11

Use this x value to determine the angles we're after.

Check:

(angleRQS) + (angleTQS) = 101+79 = 180 which confirms the answer is correct.

The axis of symmetry is the line x=3.

As y  is a linear term and x is quadratic, this means we’re dealing with either an ‘n-shaped’ parabola or a ‘u-shaped’ parabola.

As the coefficients of  x² and y have the same sign they’re both positive, which means we have a ‘u-shaped’ parabola.

One can express a parabola in the vertex form,  y=a(x−p)²+q, which tells us that the vertex is the point  (p,q)  and the axis of symmetry is the line x=p.

So, let’s apply this format to your parabola.

y=(x−3)²=(x−3)²+0

From this, it’s clear that:

The vertex is the point (3,0)

The axis of symmetry is the line x=3

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To the nearest tenth of a kilogram, m = 0.6 kg.

What is ttemperature rate ?

With increase in temperature, the rate of the reaction and the rate constant increases. As a generalization, the rate of the reaction (and the rate constant) becomes almost double for every ten degree rise in temperature. This is also called temperature coefficient.

the heat Q required to raise the temperature of water varies jointly as the mass m of the water and the amount of temperature change T, and Q = 20,930 J when m = 1 kg and T = 5°C.

So, write an equation for Q as:

Q = k * m * T

where k is a constant of proportionality.

Substituting the known values, we can find k:

20930 = k * 1 * 5

k = 20930 / (1 * 5) = 4186

Now that we have k, use it to find m when Q = 8349 J and T = 3°C:

8349 = 4186 * m * 3

m = 8349 / (4186 * 3)

To the nearest tenth of a kilogram, m = 0.6 kg.

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The mass of the water m is 0.7 kg.

Since Q varies jointly as m and T, we know that Q = k * m * T where k is a constant of proportionality. Using the given information, we can find the value of k:

Q = 20,930 J when m = 1 kg and T = 5° C

k = Q / (m * T) = 20,930 / (1 * 5) = 4186

Now that we have found k, we can use it to find m when Q = 8,349 J and T = 3°C:

Q = k * m * T

8,349 = 4186 * m * 3

m = 8,349 / (4186 * 3) = 8,349 / 12,558

m = 0.67 kg

To the nearest tenth of a kilogram, m = 0.7 kg.

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Hey there,

We have,

f(x) = x² + 11x + 30g(x) = x + 6

Now,

(f.g)(x) = f(g(x))

Substituting...

g(x) = x + 6f(g(x)) = f(x + 6)

Now,

f(x + 6)= (x + 6)² + 11(x + 6) + 30= x² + 12x + 36 + 11x + 66 + 30= x² + 23x + 132

So,The value is x² + 23x + 132

Answer:

70.80

Step-by-step explanation:

40.00 increased by 77% is 70.80. The increase is 30.80.

Answer:

$70.80

Step-by-step explanation:

The dress was $40 to add the 77% increase, you would multiply 40 x .77= 30.80, then you would add the 30.80 to the original 40, giving you a total of $70.80

D) The quadratic equation's roots, 2x2 4x + 3 = 0, are imaginary in nature.

The quadratic formula, using square roots, factoring, and completing the square are the four ways to solve a quadratic problem.

Given a quadratic equation, it is 2x 2 + 4x + 3= 0.

∴ a=2,b=4,c=3

As a result, the discriminant of this equation is given by D=b 2 4ac.

∴D=(4) \s2 \s −4(2)(3) (3)

∴D=16−24

∴D=−8<0

The equation's roots are therefore fictitious.

The quadratic equation has the general form ax2 + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable. An example of a quadratic equation is x2 + 2x + 1.

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Full Question = The nature of the roots of the quadratic equation 2x ^2 + 4x + 3= 0 are

A. Real & Distinct

B. Real & Equal

C. No Real Roots

D. Imaginary

Answer:

125

Step-by-step explanation:

5x + 20 + 3x - 8 = 180

8x + 12 = 180

8x = 168

x = 21

5(21) + 20

= 105 + 20

= 125

Answer:

I believe the answer is Graph A

Answer:

6xˆ2 - x - 2 = 0

D = 1 + 1*2*6*4=49=7ˆ2;

using formula of discriminant you get

x1= -1/2

x2= 2/3

answer = x1, x2

The amount of peanuts Maggie puts in each container is 1/9 pounds per container.

Number of pounds of peanut Maggie has = 2/3 pounds

Number of containers = 6

Number of peanuts in each container = Number of pounds of peanut Maggie has / Number of containers

= 2/3 ÷ 6

multiply by the reciprocal of 6

= 2/3 × 1/6

= 2/18

= 1/9 pounds per container

Hence, there are 1/9 pounds of peanuts in each container if Maggie puts an equal amount.

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No, the number 52 is not a perfect square. Because the square root of 52 is an irrational number.

An irrational number is a real number that cannot be expressed as a ratio of two integers, or in other words, as a fraction. Irrational numbers include numbers such as pi (π), the square root of 2, and the square root of 3, which are not terminating or repeating decimals. They cannot be written as a finite decimal or a fraction of integers. Irrational numbers have an infinite number of decimal places, which means they cannot be represented exactly as a decimal.

They are also non-repeating and non-terminating decimals. Irrational numbers have many important properties and applications in mathematics, such as in geometry, where they are used to calculate the lengths of curves and the areas of circles. They also appear in trigonometry and calculus. Irrational numbers are also important in physics and engineering as well as other branches of science and technology. They are often used to express the precise measurements and calculations that are essential in these fields.vb

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The degree of the polynomial p(x) = 3x²y³ - 4xy⁴ + x⁶ + y⁵ is 6.

A degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 2x^3 + 4x^2 - 5x + 7, the degree is 3 (the highest power of x is x^3). A polynomial of degree 0 is a constant polynomial and a polynomial of degree 1 is a linear polynomial.

To find the degree of a polynomial, you can do the following:

→ Write the polynomial in standard form, with the terms arranged in descending order of exponents.

→ Take the exponent of the term with the highest exponent. This exponent is the degree of the polynomial.

Given,

p(x) = 3x²y³ - 4xy⁴ + x⁶ + y⁵

Here,

Degree of polynomial is 6

As, 6 is highest of all the exponent given in p(x)

Hence, the degree of the polynomial p(x) = 3x²y³ - 4xy⁴ + x⁶ + y⁵ is 6.

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The number of atoms that can be laid end-to-end on a meter stick is equivalent to 10^8 atoms.

A meter is equivalent to 100 centimeters (cm), and an atom is about 10^-8 centimeters in length. So, when we divide the length of a meter stick (100 cm) by the length of one atom (10^-8 cm).

we are essentially dividing 100 by a decimal number on the order of 0.00000001.

This is the same as multiplying 100 by a number on the order of 100,000,000. In other words, we are multiplying 100 by 10^8.

So, 100 cm / (1*10^-8 cm) = 10^8 atoms

This means that the number of atoms that can be laid end-to-end on a meter stick is equivalent to 10^8 atoms which is a very big number, this is why we use scientific notation to represent it.

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Kweku age is 21 years and his brother kofi is 14 years

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

To solve this problem, we have to state the equation using the information of the problem:

Lets call Kweku's age as (x)

Sofi's age will be 2/3x

If both are 35 then the equation is as follow:

x + 2/3x = 35

Clearing the variable we have:

(3x+2x) /3 = 35

5x = 35*3

5x = 105

x = 105/5

x = 21

Kweku's age is 21 years

Sofi's age is 2/3x = 2/3*21 = 14 years

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On that particular night, there were 144 student tickets and 432 non-student tickets sold.

Let x be the number of student tickets sold that night

y be the number of non-student tickets sold that night

On that night, there were three times as many student as there were non-students. Hence, we can write that as an algebraic expression such that

3x = y

If tickets cost $5 for students and $9 for non-students, and on that night, they sold $4,608 in tickets, then we can express that as

$5x + $9y = $4608

5x + 9y = 4608

Substitute the value of y from the first expression to the second and solve for x.

5x + 9y = 4608

5x + 9(3x) = 4608

5x + 27x = 4608

32x = 4608

x = 144

Plug in the value of x into the first expression and solve for y.

y = 3x

y = 3(144)

y = 432

Hence, the number of tickets sold on that night to students and non-students were 144 and 432, respectively.

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Given that the polynomial is 12xy - 9x - 8y + 6, we must determine its fully factored form.

There are two variables in the given polynomial.

12xy - 9x - 8y - 6 = 3x(4y - 3) Now, 12xy - 9x - 8y - 6 = 3x(4y - 3) - 2(4y - 3) = (3x - 2)(4y - 3) The polynomial's fully factored form is (3x - 2)(4y - 3)

(3x - 2)(4y - 3) is the fully factored form of 12xy - 9x - 8y + 6.

One approach to factoring expressions is factoring by grouping. If the expression can be broken down into its component parts, this approach is helpful. On the other hand, we can employ additional strategies.

A polynomial is an expression made up of variables, constants, and exponents that are added, subtracted, multiplied, and divided using mathematical operations (no division by a variable).

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Full Question = What is the completely factored form of 12xy - 9x - 8y + 6?

To calculate the composition of two functions, "F" and "G", represented by the notation "FG", you first need to have a specific input value, usually represented as "x".The first step is to apply the function "G" to the input "x", resulting in G(x).

The next step is to take the output of the function G, which is G(x), and use it as the input for the function F.

The final step is to apply the function F to the output of G(x) resulting in F(G(x)), which is the composition of the two functions F and G.

In other words, you apply the function G to the input x, and then you apply the function F to the result of G(x). The final result is the function F(G(x)), which is the composition of the functions F and G.

It's important to note that the order of the functions in composition matters and can change the result of composition. The notation "FG)(x)" is different from "GF)(x)" which means that the order of the functions matter in composition.

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The polynomial function with zeroes at -2, 0, and 3√2 is (x+2)(x-0)(x-3√2) = [tex](x+2)*(x-3\sqrt{2}) = x^3 - 3x\sqrt{2x} - 2x^2.[/tex]

The polynomial function with zeroes at -1, 3, and 2i is (x+1)(x-3)(x-2i) = [tex](x+1)(x-3)(x^2+4) = x^3 +x^2 - 11x -12[/tex]

A polynomial function is a function of the form f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0, where n is the degree of the polynomial and the a_i are constants. To find a polynomial function with zeroes at -2, 0, and 3√2, we can use the fact that if a polynomial function has a zero at x=c, then (x-c) is a factor of the polynomial. Therefore, we can write the polynomial function as [tex](x+2)(x-0)(x-3\sqrt{2}) = (x+2)x(x-3√2) = x^3 - 3x\sqrt{2x} - 2x^2[/tex].

In this case, we can see that x = -2, x = 0, x = 3√2 are the zeroes, so we know that (x+2), x and (x-3√2) are the factors of the polynomial.

Similarly, to find a polynomial function with zeroes at -1, 3, and 2i, we can use the fact that if a polynomial function has a zero at x=c, then (x-c) is a factor of the polynomial. Therefore, we can write the polynomial function as [tex](x+1)(x-3)(x-2i) = (x+1)(x-3)(x^2+4) = x^3 +x^2 - 11x -12[/tex]

In this case, we can see that x = -1, x = 3, x = 2i are the zeroes, so we know that [tex](x+1), (x-3), (x^2+4)[/tex]are the factors of the polynomial.

It is worth noting that (x-2i) is a zero of the polynomial, so (x-2i)(x+2i) = [tex]x^2[/tex]+4 is a factor of the polynomial and it is included in the polynomial..

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Answer:

cp=(SP * 100 ) / ( 100 – percentage loss)

6786*100/100-13

7800

The relation's graph can be seen in the graphic at the bottom, where it is clear that it is   function.

The actual function can be specified using this "mapping" notation. Writing f:(x,y)x+y would allow us to define the above f(x, y). Real numbers are referred to as scalars to distinguish them from vectors. Each input is translated into a single output in a relation known as a function (input, output).

The horizontal axis is used for inputs, and the vertical axis is used for outputs. Here, we have the relationship shown below:

(-5,-1), (-4,1), (-3,3), (-1,5), (1,7) (1,7)

The figure below shows the graph of these points. Since there are no two points on the same vertical line, the relation is a function, as you can see.

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Answer:

X = 20

Step-by-step explanation:

The two quadrilaterals are similar to each other. So the ratio of  each side of the larger quadrilateral to the corresponding side of the smaller quadrilateral must be the same.

Examining the two figures we see the side which has  68° and 128° pf the smaller quadrilateral has length 2

The corresponding side of the larger quadrilateral on the right is 6

So each side of the larger quadrilateral =6/2 = 3 times each side of the smaller one

Side which has length 10 pf the smaller quadrilateral corresponds to the side with length x+10 of the larger one. This ratio must also be 1:3

So

[tex]\dfrac{10 + x}{10}= 3\\\\[/tex]

Cross-multiplying we get
10 + x = 10 x 3

10 + x = 30

x = 30-10

x =20

ANSWER

Answer: 11

Step-by-step explanation: (8/2.56) x 3.52 = 11 ounces

Answer: 83r^2 - 59 + 60

Step-by-step explanation:

R^2 - 59R - 82r^2 + 60

= 83r^2 - 59 + 60

The standard deviation is 4 The variance is equal to 16.

In information, the standard deviation is a degree of the quantity of variation or dispersion of a fixed of values. A low standard deviation indicates that the values tend to be near the implied (additionally called the predicted price) of the set, whilst an excessive preferred deviation suggests that the values are spread out over a wider variety.

Popular deviation can be abbreviated SD, and is maximum commonly represented in mathematical texts and equations by means of the decrease case Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample general deviation.

The standard deviation of a random variable, pattern, statistical population, statistics set, or possibility distribution is the square root of its variance. it's miles algebraically easier, even though in exercise less sturdy, than the common absolute deviation.

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If there were 18 students in each group and they were asked to form six equal groups, then there would be a total of 108 students.

i.e. (18 students x 6 groups = 108 students)

When a group of students are asked to form a certain number of equal groups, the total number of students can be determined by multiplying the number of students in each group by the number of groups.

In this case, the students were asked to form six equal groups and there were 18 students in each group.

To find the total number of students, we simply multiply 18 by 6.

Therefore, there were 108 students in total.

This is because when you have x number of groups and y number of students in each group, the total number of students is xy.

In this case x=6 and y=18, so the total number of students is 6*18 = 108.

Question:

"In gym class, students were asked to form ix equal group. If there were 18 students in each group, then how many total students were there?"

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Answer: 2:7

Step-by-step explanation:

Vanilla icecream = 4

Chocolate icecream = 14

4:14=2:7

2X2=4

7X2=14

Step-by-step explanation:

a ratio is simply relating 2 (or more) groups and their sizes.

in our case here the ratio is

4/14 = 2/7

this is often written as

4:14 = 2:7

it means that for every 2 people liking (I assume "preferring") vanilla ice cream there are 7 people liking (preferring) chocolate ice cream.

FYI

in total, a ratio also tells us about the size of the sample for the observation or analysis. 4/14 tells us there are 18 (4+14) people in the survey. and the simplified form 2/7 tells us that we can split the whole survey group into units of 9 (2+7) people with the same behavior as the total group.

a ratio is a fraction (incl. all the calculation and comparison rules) with a special meaning.

so, don't mix the ratio up with e.g. the fractions of the different behaviors in the group :

4/18 = 2/9 of the whole group prefer vanilla.

14/18 = 7/9 of the whole group prefer chocolate.

the ratio is now the relative size relationship between both : 2/9 / 7/9 = 2/7

Answer:

To solve for g in terms of T, L, we can manipulate the formula T = 2π √(L/g) as follows:

First, we divide both sides by 2π:

T/2π = √(L/g)

Then, we square both sides:

(T/2π)² = (L/g)

Then, we multiply both sides by g^2 :

(T^2/4π^2) = L

Finally, we divide both sides by L:

(T^2/4π^2 * L) = g

So the formula for g in terms of T, L is g = (T^2/4π^2 * L)

Please note that this formula is only valid for simple pendulum and not for any complex pendulum, and also the result is in terms of acceleration due to gravity g.

9 11 13 15 17

first term (a) = 9

diffrence (d) = 11-9 = 13-11 = 2

we know

a + (n-1)d

9+(n-1)2

9+2n-2

7+2n

2n + 7

2n + 7 is the sequences of 9 11 13 15 17 for nth term

The required value of the x in a similar triangle by the ratio of proportionality of sides is given as 12.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,
In the figure, Similar triangles is shown,
Applying the property of proportional sides in the triangles

30/18 = 20/x
x = 18 / 30 × 20
x = 12

Thus, the required value of the x in a similar triangle by the ratio of proportionality of sides is given as 12.

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