The interior angle measure of a regular polygon is given. Identify the polygon.
108

Answer:

[tex]\textsf{1.} \quad x^2-2x-1[/tex]

[tex]\textsf{2.} \quad -3x^4-5x^3+14x^2+20x-8[/tex]

[tex]\textsf{3.} \quad -\dfrac{5}{2}[/tex]

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x) = x^2 - 4\\g(x) = x + 2\\h(x) = -3x + 1\end{cases}[/tex]

Question 1

The composite function (f + g - h)(x) means to add functions f(x) and g(x) then subtract function h(x):

[tex]\begin{aligned}(f+g-h)(x) & = f(x)+g(x)-h(x)\\& = (x^2-4)+(x+2)-(-3x+1)\\& = x^2-4+x+2+3x-1\\& = x^2+3x+x-4+2-1\\& = x^2+4x-3\end{aligned}[/tex]

Question 2

The composite function (fgh)(x) means to multiply functions f(x), g(x) and h(x):

[tex]\begin{aligned}(fgh)(x) & = f(x)\cdot g(x) \cdot h(x)\\& = (x^2-4)(x+2)(-3x+1)\\& = (x^2-4)(-3x^2-5x+2)\\& = -3x^4-5x^3+2x^2+12x^2+20x-8\\& = -3x^4-5x^3+14x^2+20x-8\end{aligned}[/tex]

Question 3

The composite function (f/g)(h)(1/2) means to substitute the value of function h(x) when x = 1/2 into function f(x) and function g(x) and divide the former by the latter:

[tex]\begin{aligned}\left(\dfrac{f}{g}\right)(h)\left(\dfrac{1}{2}\right) & = \dfrac{f\left(h\left(\dfrac{1}{2}\right)\right)}{g\left(h\left(\dfrac{1}{2}\right)\right)}\\\\& = \dfrac{f\left(-3\left(\dfrac{1}{2}\right)+1\right)}{g\left(-3\left(\dfrac{1}{2}\right)+1\right)}\\\\& = \dfrac{f\left(-\dfrac{1}{2}\right)}{g\left(-\dfrac{1}{2}\right)}\\\\& = \dfrac{\left(-\dfrac{1}{2}\right)^2-4}{\left(-\dfrac{1}{2}\right)+2}\\\\& = \dfrac{-\dfrac{15}{4}}{\dfrac{3}{2}}\\\\& = -\dfrac{5}{2}\end{aligned}[/tex]

1,200 is not a viable solution to this problem as B.

No; 1,200 will cause her to exceed 1,500

It should be noted that Luna has consumed 900 calories so far today and has also burned 500 calories in dance class.

Therefore, the amount left will be:

= 1500 - (900 - 500)

= 1500 - 400

= 1100

Therefore, 1,200 is not a viable solution to this problem

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The probability that the number spun is a 3 given that it was less than 4 is 1/6.

Let A is the event of a number less than 4.

P(A) is the probability of getting a number less than 4.

The total number less than 4 is 3

Here, the total numbers in the game are 6.

By the Formula for the probability of an event E can be observed as:

P(A)= no of favorable cases/total no. of cases  = 3/6 = 1/2

B is the event of getting the number  3

P(B) be the probability of getting 3

The total  possible cases  is 1

Therefore , P(B)= 1/6

Now, P(B/A) is the probability of getting 3 which is an odd number.

P(B/A)= P(A ∩ B) / P(A)

          =1/6 / 1/2

   = 1/3

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Coordinates of point G is ( 10 , 2) in this equation.

What do mathematical point coordinates mean?

M is the mid points of FG.

coordinates of M is ( 8,5)

coordinates of F is ( 6,8 )

Let coordinates of G point is ( x₂, y₂)

[tex]x = \frac{x_{1} + y_{1} }{2} , y = \frac{x_{2}+ y_{2} }{2}[/tex]

[tex]8 = \frac{6 + x_{2} }{2} , 5 = \frac{8 + y_{2} }{2}[/tex]

[tex]16 = 6 + x_{2} , 10 = 8 + y_{2}[/tex]

x₂ = 10  ,  y₂ = 2

So, coordinates of point G is ( 10 , 2)

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The length of the unknown leg is 8 yd in the given right triangle.

The Pythagoras theorem states that a right-angled triangle's hypotenuse square (90 degrees) equals the sum of the squares of its other two sides.

Let the three legs of the right triangle be a, b and c where a is the altitude, b is the base and c is hypotenuse of the given right angled triangle.

Here, a = [tex]\sqrt{23}[/tex] yd, b = ? and c = [tex]\sqrt{87}[/tex]

According to the Pythagoras theorem,

Hypotenuse² = Base² + Altitude²

c² = b² + a²

[tex](\sqrt{87})^{2}[/tex] = b² + [tex](\sqrt{23})^{2}[/tex]

87 = b² + 23

Subtracting 23 from both sides of the equation.

87 - 23 = b²

b² = 64

Taking square root of the both sides.

b = ± 8

Since the value of length can't be negative so the value of b = - 8 is rejected.

Therefore, the value of b = 8 yd.

As we have calculated above, the length of the unknown leg is 8 yd.

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Answer:

x = 21, -21

Step-by-step explanation:

Let's solve the problem,

→ |x/7| = 3

→ x/7 = 3 ll -x/7 = 3

→ x = 3 × 7 ll -x = 3 × 7

→ [ x = 21 ] ll [ x = -21 ]

So, the value of x is 21, -21.

The climbing steps have parallel planes for the treads. Although each step may appear to be a line, it is actually a plane.

Considering it as a staircase; a moving stairway that transports people between levels of a building or structure is known as an escalator. It is made up of a motor-driven chain of individually connected steps on a track that cycles along a pair of tracks that maintain them horizontal.

The climbing stair treads are parallel planes. Each step appears to be a line, but it is actually a plane.

The top two steps of the inclination are on the same plane. They are parallel.

These tires are twisted. They are neither parallel, nor do they share the same plane.

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Answer:

r=2

Step-by-step explanation:

To find the slope, we take the difference in the y values over the difference in the x values

m = ( y2-y1)/(x2-x1)

2 = ( 9-3)/ (5-r)

2 = (6)/(5-r)

Multiply each side by (5-r)

2 ( 5-r) = 6

Divide each side by 2

5-r = 6/2

5-r = 3

Subtract 5 from each side

5-r-5 = 3-5

-r = -2

r = 2

Answer:

r = 2

Step-by-step explanation:

To solve this problem, we have to use the following formula for slope:

[tex]\boxed{m= \frac{y_2 - y_1}{x_2 - x_1}}[/tex],

where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are the coordinates of two points.

We are given the coordinates [tex](r, 3)[/tex] and [tex](5, 9)[/tex], and told that [tex]m = 2[/tex]. To find the value of r, we have to substitute the given values into the formula and then solve for r :

[tex]2 = \frac{9 - 3}{5-r}[/tex]

⇒ [tex]2 = \frac{6}{5-r}[/tex]

⇒ [tex]2\times (5-r) = \frac{6}{5-r} \times (5 - r)[/tex]         [Multiplying both sides by (5 - r)

⇒ [tex]2(5-r) = 6[/tex]

⇒ [tex]\frac{2}{2}(5-r) = \frac{6}{2}[/tex]                                [Dividing both sides by 2]

⇒ [tex]5- r = 3[/tex]

⇒ [tex]5 - r - 5 = 3 - 5[/tex]                         [Subtracting 5 from both sides]

⇒ [tex]-r = -2[/tex]

⇒ [tex]\frac{-r}{-1}= \frac{-2}{-1}[/tex]                                       [Dividing both sides by -1]

⇒ [tex]r = \bf 2[/tex]

What is the value of Σ⁵n=1 (2 n-3) ? 15

             [tex]\sum_{n=1}^{5} (2 n-3)\\\\ (2 (1)-3)+ (2 (2)-3)+ (2 (3)-3)+ (2 (4)-3)+ (2 (5)-3)\\\\ -1+1+3+5+7=15[/tex]

The sum of the given expression is 15

What is summation?

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The set notation will be S ∈ { 14, 16, 18, 20, 22, 24, 26, 28}.

When we have to represent set having defined specific number, we do my writing the number in curly bracket. When we have to represent the set having collection of continuous number between two specific defined number, we do by writing first and last number in small bracket.

As the terms given for the set is 14, 16, 18, 20, 22, 24, 26, 28 which are defined and specific terms so it will be represented by writing it in curly brackets

i.e. S ∈ { 14, 16, 18, 20, 22, 24, 26, 28}

Final answer,  the set will be S ∈ { 14, 16, 18, 20, 22, 24, 26, 28}

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Answer:

5X2 + 2X + 3 orr 10x + 2

Step-by-step explanation:

Step-by-step explanation:

[tex]x_{1,\:2}=\frac{-6\pm \sqrt{6^2-4\cdot \:1\cdot \left(-16\right)}}{2\cdot \:1}\\\sqrt{6^2-4\cdot \:1\cdot \left(-16\right)}\\\sqrt{6^2+64}\\\sqrt{36+64}\\\sqrt{100}\\\sqrt{10^2}\\=10\\x_1=\frac{-6+10}{2\cdot \:1},\:x_2=\frac{-6-10}{2\cdot \:1}\\\\\bold{x_1:2}\\\frac{-6+10}{2\cdot \:1}\\\frac{4}{2\cdot \:1}\\\frac{4}{2}\\=2\\\\\bold{x_2:-8}\\\frac{-6-10}{2\cdot \:1}\\\frac{-16}{2\cdot \:1}\\\frac{-16}{2}\\-\frac{16}{2}\\=-8[/tex]

Answer:

x₁ = 2

x₂ = -8

Answer: v= root[3]  {12}=2.2894

Step-by-step explanation:

Answer:Your answer is V=4

Step-by-step explanation:Need brainliest award

Answer: a) y=x²+6x+2   b) x=-3-√7, -3+√7

Step-by-step explanation:

(0,2)    (-6,2)     (-3,-7)

a)

y=ax²+bx+c

(0,2)

x=0   y=2

⇒ 2=a(0²)+b(0)+c

⇒ 2=0+0+c

⇒ 2=c

(-6,2)

x=-6   y=2

⇒ 2=a(-6)²+b(-6)+2

⇒ 2=36a-6b+2

⇒ 2-2=36a-6b+2-2

⇒ 0=36a-6b

⇒ 0+6b=36a-6b+6b

⇒ 6b=36a

Divide both parts of the equation by 6:

b=6

(-3,-7)

⇒ -7=a(-3)²+6(-3)+2

⇒ -7=9a-18+2

⇒ -7=9a-16

⇒ -7+16=9a-16+16

⇒ 9=9a

Divide both parts of the equation by 9:

1=a

Hence,

y=x²+6x+2

b)

x²+6x+2=0

D=(-6)²-4*1*2

D=36-8

D=28

√D=√28

√D=√(4*7)

√D=2√7

x=(-6±2√7)/2

x=-3-√7

x=-3+√7

The events are independent. The probability of getting 5 each dice after rolling the dice 2 times is 1/36.

As we are rolling two different die simultaneously, the events are independent.

The probability of getting a 5 in the first die = 1/6

The probability of getting a 5 in the second die = 1/6

Hence, as the events are independent, we can write :-

The probability of getting 5 each dice after rolling the dice 2 times =

probability of getting a 5 in the first die * probability of getting a 5 in the second die = (1/6)*(1/6) = 1/36

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The line segment FG can be represented as expression 4x whose midpoint is N

We are provided with that Point N is the midpoint of FG and FN = 2x and We need to find expression that  represents FG

As N is the midpoint of line segment FG than FN = NG

Also it could be written as FG = FN + NG because FG is the broken into two different line segment FN and NG because of the midpoint N

Therefore, FN = 2x which means FN= NG=2x

So, we can write an expression that could represent FG

FG = FN + NG

FG = 2x + 2x

FG = 4x

Hence, The line segment FG can be represented as expression 4x

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Answer:

True

Step-by-step explanation:

Its true because the absolute value of integers is either its positive side or negative side. For example -4 turn into 4 and -5 turn into 5. Hope this helps!

Answer: r=-3

Step-by-step explanation:

12-6r=2r+36

12=8r+36

-24=8r

r=-3

If you are looking to solve the inequality for y:

_____________________________________

Inequality Form:

[tex]-12 < y < -6[/tex]

Interval Notation:

[tex](-12, -6)[/tex]

Hope this helps!

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

By Pythagoras theorem :

[tex]\qquad \sf  \dashrightarrow \: hypotenuse = \sqrt{(perpendicular) {}^{2} + (base) {}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: h= \sqrt{15 {}^{2} + {8}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: h = \sqrt{225 + 64} [/tex]

[tex]\qquad \sf  \dashrightarrow \: = \sqrt{289} [/tex]

[tex]\qquad \sf  \dashrightarrow \: h = 17 \: \: units[/tex]

Now, we know ~

[tex]\qquad \sf  \dashrightarrow \: \sin(A) = \dfrac{opposite \: \: side}{hypotenuse} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sin(A) = \dfrac{8}{17} [/tex]

The average rate of change between the given values of the variable is 21

A function can be defined as an expression or rule showing the relationship between a dependent and an independent variable.

Given the function;

h(t) = 2t^{2}[/tex] − t

For t =2

Substitute the value of t as 2 in the function, we have;

h(2) = 2 (2)² - (2)

Find the square

h(2) = 2(4) - 2

h(2) = 8 - 2

h(2) = 6

For t = 9

Substitute the value of t as 9 in the function, we have;

h(9) = 2(9)² - 9

Find the square

h(9) = 2(81) - 9

h(9) = 153

The average change = 153 - 6 = 147/ 9 -2 = 147/ 7 = 21

Thus, the average rate of change between the given values of the variable is 21

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The given pattern 5/7, 8/7, 11/7, 2, ....... is in the form of the arithmetic progression AP. The next 3 terms are  17/7, 20/7, 23/7.

An arithmetic progression is a sequence whose terms continue to increase and otherwise decrease by a constant number. The common difference is the set amount through which they either increase or decrease.

The following arithmetic progression formulas are frequently utilized to solve various AP problems for the initial term 'a' of an AP and the common difference 'd'-

Now, as per the stated question;

The AP given as; 5/7, 8/7, 11/7, 2, ...........

The series consists of four given terms.

Consider the initial term be 'a₁' = 5/7.

Then, the second term be 'a₂' = 8/7.

And, the third term be 'a₃' = 11/7.

And, the fourth term is 'a₄' = 2.

The AP have the same common difference. so,

d = a₃ - a₂

Substitute the values.

d = 11/7 - 8/7

d = 3/7

Thus, the common difference is 3/7.

or d = a₄ - a₃ (Put the values)

d = 2 - 11/7

d = 3/7

As, a₃ - a₂ = a₄ - a₃

Thus, we can conclude that the given sequence is in AP.

The fifth term will be; a₅ = a₄ + d = 2 + 3/7

a₅ = 17/7

Now, the 6th term will be; a₆ = a₅ + d = 17/7 + 3/7

a₆ = 20/7

Similarly, the 7th term will be; a₇ = a₆ + d = 20/7 + 3/7

a₇ = 23/7

Therefore, it can be said that the given sequence is in AP next three terms be 17/7, 20/7, 23/7.

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Answer:

Pencils = 35

Notebooks = 15

Step-by-step explanation:

15 cents = 15/100 = $0.15

85 cents = 85/100 = $0.85

p + n = 50                    Eq. 1

0.15p + 0.85n = 18       Eq. 2

p = number of pencils

n = number of notebooks

From Eq. 1

p = 50 - n               Eq. 3

Replacing Eq. 3 in Eq. 2:

0.15(50-n) + 0.85n = 18

(0.15*50 + 0.15*-n) + 0.85n = 18

(7.5 - 0.15n) + 0.85n = 18

7.5 + 0.7n = 18

0.7n = 18 - 7.5

0.7n = 10.5

n = 10.5 / 0.7

n = 15

From Eq. 3:

p = 50 - n

p = 50 - 15

p = 35

Check:

From Eq. 2

0.15p + 0.85n = 18

0.15*35 + 0.85*15 = 18

5.25 + 12.75 = 18

e

Answer:

{y|y≥0}

Step-by-step explanation:

The parent absolute value function is

This is a V-shaped function whose vertex is at the origin.

This means that, the least y-value is 0 and there is no highest y-value.

The range refers to all y-values for which the function exists.

Therefore the range is

Or

{y|y≥0}

Answer:

{y | y is a real number}

Step-by-step explanation:

because yxy=y=2

The solution of the given linear equation is y = 80.

According to the given question.

We have an equation.

-y + 13 = -67

Since, we have to solve the above linear equation in variable.

As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Thereofre, the solution of the linear equation in one variable -y + 13 = -67 is given by

-y + 13 = -67

⇒ - y = -67 -13 (subtractting 13 from both the sides)

⇒ -y = -80

⇒ y = 80

Hence, the solution of the given linear equation is y = 80.

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Based on the number of votes that the two finalists received, the number of votes that Luke received was 2,875 votes

Assuming that the number of Sean's votes could be shown as x, the expression for the votes would be:

x + (x + 25%) = 5,175

2.25x = 5,175

x = 5,175 / 2.25

= 2,300 votes

Luke's votes were:

= 2,300 x (1 + 25%)

= 2,875 votes

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We get the absolute value inequality as | x - 88 | > 38.

We are given that:

Hypoglycemia (low blood sugar) and hyperglycemia (high blood sugar) are potentially dangerous and can occur when a person's blood sugar fluctuates by more than 38 mg from the normal blood sugar level of 88mg. We need to write an inequality for it.

We know that the blood sugar level should not be less than:

88 mg - 38 mg = 50 mg

Also, the blood sugar level should not be higher than:

88 mg + 38 mg = 126 mg

The inequality then will become:

50 mg ≤ Blood sugar level ≤ 126 mg.

The absolute value inequality will be:

| x - 88 | > 38

Therefore, we get the absolute value inequality as | x - 88 | > 38.

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Answer: 95%

Step-by-step explanation:

To find the percentage, we divide the number of students who chose red by the total number of students and then multiply by 100.

[tex]\frac{285}{300} \times 100=95[/tex]