Explain why three angle measures do not determine a unique triangle. How many triangles are determined by three angles measures?

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.

To know more about the arithmetic progression, here

https://brainly.com/question/24989563

#SPJ4

The baseball field mark up its organic hotdogs from $2.00 to $6.50 each by 225%.

The markup on cost is defined as the amount added to the original cost of a product or service to arrive at the new selling price. It can also be a percentage of the original cost.

mark up = selling price - original price

If organic hotdogs at the grocery store cost $2.00 each and at a major league baseball game, an organic hotdog cost $6.50, then the mark up price is the difference between the two.

mark up = selling price - original price

mark up = $6.50 - $2.00

mark up = $4.50

To get the percentage of the mark up from the original price, divide the mark up price by the original selling price and multiply by 100%.

percent mark up = (mark up price/original price) x 100%

percent mark up = ($4.50/$2.00) x 100%

percent mark up = 2.25 x 100%

percent mark up = 225%

Learn about mark up price here: https://brainly.com/question/1153322

#SPJ4

Answer:

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

Step-by-step explanation:

Yes, the opposite of the reciprocal of 5 is same as the reciprocal of the opposite of 5  ,both are equals to (-1/5).

As given in the question,

Given number is 5

Case 1 : First find reciprocal of 5

Reciprocal of 5 =1/5

Then, opposite of the reciprocal of 5 =(-1/5)

Case 2. First find the opposite of 5

Opposite of 5 =-5

Reciprocal of the opposite of 5 =(1/ -5)

                                                =(1/-5) × (-1/-1)

                                                =(-1/5)

Therefore, the opposite of the reciprocal of 5 is same as the reciprocal of the opposite of 5  ,both are equals to (-1/5).

Learn more about reciprocal here

brainly.com/question/18634761

#SPJ4

Answer: r=-3

Step-by-step explanation:

12-6r=2r+36

12=8r+36

-24=8r

r=-3

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 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.

Find out more information about equation here:

https://brainly.com/question/17139602

#SPJ4

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

Learn more about calories on:

brainly.com/question/1178789

#SPJ1

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

Answer: M(-4.75,-6.25)

Step-by-step explanation:

C(-3,-8)    D(-6.5,-4,5)

Let the midpoint of C(-3,-8) and D(-6.5, -4.5) is M(x,y)

[tex]\displaystyle\\M(x,y)=(\frac{-3+(-6.5)}{2} ,\frac{-8+(-4.5)}{y} )\\\\M(x,y)=(\frac{-9.5}{2},\frac{-12.5}{2})\\\\M(x,y)=(-4.75,-6.25)\\\\Thus, \ M(-4.75,-6.25)[/tex]

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.

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]

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

Learn more about functions here:

https://brainly.com/question/2328150

#SPJ1

Answer:

-1/10 - 7i/24

Step-by-step explanation:

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]

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.

To learn more about escalators. Click, https://brainly.com/question/13063850

#SPJ4

Answer: v= root[3]  {12}=2.2894

Step-by-step explanation:

Answer:Your answer is V=4

Step-by-step explanation:Need brainliest award

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

To know more about probability refer to the link https://brainly.com/question/11234923?referrer=searchResults.

#SPJ4

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)

Learn more about coordinates

brainly.com/question/27749090

#SPJ9

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

To know more about Midpoint - https://brainly.com/question/28224145

#SPJ1

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.

Learn more about absolute value inequality here:

https://brainly.com/question/25275758

#SPJ9

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

Find out more on percentages at https://brainly.com/question/843074

#SPJ1

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

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?

To learn more about summation, refer:

https://brainly.com/question/542712

#SPJ4

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.

To know more about Pythagoras theorem visit:

https://brainly.com/question/343682

#SPJ9

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

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!