Answer:
(a) what is the sample space for this chance process?
If we toss a coin three times then there are total [tex]2^{3}=8[/tex] outcomes
The sample space associated with the given chance process is:
[tex]S= \left \{ HHH,HHT,HTH,HTT,THH,THT,TTH,TTT\right \}[/tex]
(b) what is the assignment of probabilities to outcomes in this sample space?
Since the given sample space has eight outcomes and we know that a fair coin is tosses three times. Therefore, the probability of all the events mentioned in the given sample space is same. Hence we have:
[tex]Probability = \frac{1}{8}[/tex]
When tossing a fair coin three times, the sample space includes all combinations of heads (H) and tails (T). With a fair coin, the probability of each possible outcome (HHH, HHT, HTH, THH, TTH, THT, HTT, TTT) is equal, at 0.125.
Explanation:When we're discussing the tossing of a fair coin three times, we're delving into the area of probability. (a) The sample space in this scenario is all the possible outcomes we could have. Those outcomes are: TTT, TTH, THT, THH, HTT, HTH, HHT, and HHH (Remember: H represents a head and T represents a tail).
(b) When we talk about the assignment of probabilities, we mean the likelihood of each potential outcome occurring. With a fair coin, it's equally likely to land on heads or tails - a 0.5 chance for each. Therefore, each of the eight possible outcomes has a 1/8 or 0.125 probability of occurring, granted that all outcomes are equally likely. So, for for instance, the probability of getting one head and two tails (HHT, HTH, THH) is 3/8 or 0.375, and similarly for all other cases.
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What is the distance between the points (–6, –10) and (2, 5)?
Answer:
17
Step-by-step explanation:
To find the distance between two points, we use the formula
d =sqrt( (x2-x1)^2 + (y2-y1)^2)
d= sqrt((2--6)^2+(5--10)^2 )
d= sqrt((2+6)^2+(5+10)^2 )
d = sqrt(8^2 + 15^2)
d = sqrt(64+225)
d =sqrt(289)
d =17
You jog 2 kilometers in 12 minutes ,at this rate how much will it take you to complete a 5 kilometers race
Calculate your speed per kilometer, by dividing the known time by the distance already ran:
12 minutes / 2 kilometers = 6 minutes per kilometer.
Now multiply the time for 1 by the total distance:
6 minutes per kilometer x 5 kilometers = 30 minutes total.
please include all steps
This is a pretty simple proof, actually.
A parallelogram's diagonal always bisects each other.
The given proves that both diagonals bisect each other at point N. So if they bisect each other, it is a parallelogram.
Write the quadratic equation whose roots are 6 and 3, and whose leading coefficient is 4
(Use the letter x to represent the variable)
If α and β are the Roots of a Quadratic Equation ax² + bx + c then :
✿ Sum of the Roots : α + β [tex]\mathsf{= \frac{-b}{a}}[/tex]
✿ Product of the Roots : αβ [tex]\mathsf{= \frac{c}{a}}[/tex]
Let the Quadratic Equation we need to find be : ax² + bx + c = 0
Given : The Roots of a Quadratic Equation are 6 and 3
⇒ α = 6 and β = 3
Given : The Leading Coefficient of the Quadratic Equation is 4
Leading Coefficient is the Coefficient written beside the Variable with Highest Degree. In a Quadratic Equation, Highest Degree is 2
Leading Coefficient of our Quadratic Equation is (a)
⇒ a = 4
⇒ Sum of the Roots [tex]\mathsf{: (6 + 3) = \frac{-b}{4}}[/tex]
⇒ -b = 9(4)
⇒ b = -36
⇒ Product of the Roots [tex]\mathsf{: (6 \times 3) = \frac{c}{4}}[/tex]
⇒ c = 18 × 4
⇒ c = 72
⇒ The Quadratic Equation is 4x² - 36x + 72 = 0
A company produces accessories for smart phones and tablets. The profit on each smart phone case is $2, and the profit on each tablet case is $3. The company made a profit of $1,200 on the cases last month. The equation 2x + 3y = 1,200 represents the company's profit from cases last month, where x is the number of smart phone cases sold and y is the number of tablet cases sold.
1. Change the equation into slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all of your work.
2. Describe how you would graph this line using the slope-intercept method. Be sure to write in complete sentences.
3. Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences.
4. Graph the function. On the graph, make sure to label the intercepts. o You may graph your equation by hand on a piece of paper and scan your work.
5. Suppose in the next month, the total profit on smart phone cases and tablet cases is $1,500. The profit amounts are the same, $2 for smart phone case and $3 for the tablet case. In a paragraph of at least three sentences, explain how the graphs of the functions for the two months are the same and how they are different. Be sure to use complete sentences.
6. Below is a graph that represents the total profits for a third month. Write the equation of the line that represents this graph.
Answer:
y= -2/3x(m) +400(b)
Step-by-step explanation:
1.2x + 3y = 1200
3y = -2x + 1200
y = (-2x/3)x + 1200/3
the slope is -2/3x the y intercept is 400
2.I would plot the ordered pair (0, 400) on the coordinate plane. Then to find the other ordered pair you would use the slope (-2, 3). You should go two spaces to the right of (0, 400) and then three spaces down. After this your slope look like (-2, 397)
3.the function t(x) gives the number of tablets, given that x smart-phones have been sold/produced
t(x) = (-2/3)x + 400
Suppose in the next month, the total profit on smart phone cases and tablet cases is $1,500. The profit amounts are the same, $2 for smart phone case and $3 for the tablet case. In a paragraph of at least three sentences, explain how the graphs of the functions for the two months are the same and how they are different. Be sure to use complete sentences.
They would be similar because the slope would stay the same. The slope would stay the same, because the prices remain the same. They would be different because their y intercept would change
4.F (x) = mx + b
F (x) = mx + 300
F (x) = 6/9x + 300
F (x) = 2/3x + 300
i dont really have clue about how to do next
Daryl earns $8 per hour working after school. He needs at least $352 for a stereo system. Write and solve an inequality to find the number of hours h Daryl must work to reach his goal.
Answer:
Step-by-step explanation:
First you need to divide by the amount he needs by the amount he gets, 352 divided by 8. That equals 44, so he will need to work 44 hours to reach his goal.
If lisa has 2,134 buttons that needed to be sorted equally into 12 jars.How many buttons will be in each jar.
In which expression is 13y a term?
a- 13y/4 −2y
b- 8+13y −yz
c- 4+ 13yz
d- 13+y
Answer:
Option b is the correct choice.
Step-by-step explanation:
We are asked to find the which of our given expressions has 13y as a term.
Since we know that a term can be a signed number, a variable, or a constant multiplied by a variable or variables as 2a or 5b. In term 2a, 2 is coefficient and a is a variable.
We can see that in 13y, 13 is coefficient and y is variable.
Let us see our given choices one by one.
a. [tex]\frac{13y}{4}-2y[/tex]
Let can write our 1st term as:
[tex]\frac{13}{4}y-2y[/tex]
We can see that both of our terms have y variable, but our 1st term has a coefficient 13/4 and 2nd term has a coefficient of -2. As none of these terms have 13 as a coefficient, therefore, option a is not a correct choice.
b. [tex]8+13y-yz[/tex]
We can see that 8 is a constant, while 13y and -yz are terms. Since our expression has 13y as a term, therefore, option b is the correct choice.
c. [tex]4+13yz[/tex]
We can see that 4 is a constant and 13yz is a term as it has variables yz. Since our given term has two variables, therefore, option c is not a correct choice as well.
d. [tex]13+y[/tex]
We can see that 13 is a constant and y is term of our given expression. Since our expression don't have 13 as coefficient, therefore, option d is not a correct choice.
b- 8+13y −yz. In the provided options, 13y is a standalone term in expression option b, which is 8+13y−yz. A term is part of an algebraic expression separated by plus or minus signs.
Explanation:The student is asking to identify in which expression 13y is a term. The correct answer is option b, which is 8+13y−yz. In this expression, 13y is a separate term that is being added to 8 and subtracted by yz.
It's important to recognize that in algebraic expressions a term is a single mathematical expression that can be a number, a variable, or the product of numbers and variables separated by a plus (+) or minus (−) sign. In the case of 13y, it is a term because it is separated by addition or subtraction in the expression. Other options include division or other variables combined with 'y', which do not present '13y' as a standalone term.
Spencer owns horses, and the nearest horse vet is 8 centimeters away from Spencers stable on a map. If the scale of the map is 1 centimeter = 7 kilometers, then what is the actual distance between Spencers stable and the vet?
Answer:
The actual distance is 56 km
Step-by-step explanation:
We can use ratio's to solve this problem
1 cm 8cm
---------- = -----------------
7 km x km
Using cross products
1 * x = 8 * 7
x = 56
x = 56 km
The sum of two numbers is 25 one number is twice the second number plus sevenwhat are the two numbers
Answer:
The two numbers are 6 and 19.
Step-by-step explanation:
To find these, we must first set the first number as x. Then we can set the second one in terms of x as 2x + 7.
Now that we have these values, we can add them together and set equal to 25.
x + 2x + 7 = 25
3x + 7 = 25
3x = 18
x = 6
With the first value being 6, we can solve for the second by using the equation built.
2x + 7
2(6) + 7
12 + 7
19
Solve the following equation; domain 0< x < 360; 3 cot x + sqrt 3 = 0
< is less than or equal too (I don't have the symbol on my keyboard. )
sqrt = square root.
Solve the equation 3 cot x + √3 = 0 by isolating cot x, and recognizing that tan x = -√3. The equation has solutions x = 120° and x = 300° in the given domain.
To solve the equation 3 cot x + √3 = 0 for the domain 0 ≤ x ≤ 360°, we can follow these steps:
Isolate cot x by moving √3 to the other side: 3 cot x = -√3.Divide both sides by 3: cot x = - (√3 / 3).Recall that cot x is the same as 1 / tan x, hence 1 / tan x = - (√3 / 3), which implies that tan x = -√3.Determine the angles where tan x = -√3. Tan x = -√3 at x = 120° and x = 300° within the specified domain.Thus, the solutions to the equation 3 cot x + √3 = 0 in the domain 0 ≤ x ≤ 360° are x = 120° and x = 300°.
Fluffy's tail was 1/3 of a meter long. Fireballs tail is 1/4 of a meter long . How much longer is fluffy's than Fireballs tail?
Answer:1/12
Step-by-step explanation:1/3-1/4=1/12
Find the arc length of a central angle of pi/6 in a circle whose radius is 10 inches.
Answer:
= 5/3 * pi inches
or approximately 5.235987756 inches
Step-by-step explanation:
The formula for arc length = r * theta where theta is in radians
arc length = 10 * pi/6
= 10/6 * pi
= 5/3 * pi
or approximately 5.235987756 inches
Answer: 5.23 inches
Step-by-step explanation:
Let the length of the arc intersected by a central angle x be l.
Given:- Central angle[tex]x=\frac{\pi}{6}\text{ radians}[/tex]
Radius r= 10 inches
We know that ,
[tex]l=x\ r\\\\\Rightarrow\ l=\frac{\pi}{6}\times10\\\\\Rightarrow\ l=\frac{3.14\times10}{6}= 5.2333333333\approx5.23\text{ inches}[/tex]
Thus, the length of the arc of a central angle [tex]\frac{\pi}{6}\text{ radians}[/tex] is 5.23 inches.
∆ABC is transformed with the center of dilation at the origin.
Pre-image: ∆ABC with vertices A(2, 5), B(6, 10), C(9, −1)
Image: ∆A'B'C' with vertices A' (0.5, 1.25), B' (1.5, 2.5), C' (2.25, −0.25)
What is the scale factor of the dilation that maps the pre-image to the image?
Answer:
1/4
Step-by-step explanation:
We are to find the scale factor of the dilation that maps the pre-image of triangle ABC with vertices A(2, 5), B(6, 10) and C(9, −1) to the image triangle A'B'C' with vertices A' (0.5, 1.25), B' (1.5, 2.5), C' (2.25, −0.25).
Center of dilation is at the origin.
To find the scale factor, we will divide the corresponding vertices of the image and pre-image.
A(2, 5) ---> A' (0.5, 1.25) = [tex]\frac{0.5}{2} , \frac{1.25}{5}=(\frac{1}{4} , \frac{1}{4})[/tex]
B(6, 10) ---> B' (1.5, 2.5) = [tex]\frac{1.5}{6} , \frac{2.5}{10}=(\frac{1}{4} , \frac{1}{4})[/tex]
C(9, −1) ---> C' (2.25, −0.25) = [tex]\frac{2.25}{9} , \frac{-0.25}{-1}=(\frac{1}{4} , \frac{1}{4})[/tex]
Therefore, the scale factor of the dilation is 1/4.
The scale factor of the dilation that maps triangle ABC to triangle A'B'C' is determined by calculating the ratio of the coordinates of corresponding vertices. The scale factor for this transformation is 0.25.
The student is asking how to find the scale factor of a dilation when given the coordinates of the vertices of a triangle before and after the transformation. To determine the scale factor, you need to compare the corresponding sides or coordinates of the pre-image and the image. Below is the step-by-step explanation:
Identify corresponding vertices between the pre-imageTherefore, the scale factor for the dilation that maps the pre-image to the image is 0.25.
For each of the following equations say whether it is a horizontal or vertical line and state the slope of the line.
1. x = - 2
2. y = -8
3. x = 15
4. y = -4
Answer:
1. vertical line. slope is undefined.
2. horizontal line. slope of 0
3. vertical line. slope is undefined.
4. horizontal line. slope of 0
Step-by-step explanation:
Joe gets paid 4 pounds to walk a dog. He wants to save 11 pound? How many times does he need to walk the dog.
Answer:
He needs to walk the dog 3 times as 3 times 4 = $12
Step-by-step explanation:
Cindy has 2 boxes of pencils. Patrice has 5 boxes of pencils. Each box has the same number of pencils in it.
Answer:
hey mate..
plzz add more to ur question soo that we can answer it...!
;)
The expression which represents the total number of pencils will be 7x where x is the number of pencils.
What is an expression?An expression is a combination of some mathematical symbol such that an arithmetic operator and variable such that all are constrained and create an equation.
In other meaning, expression is very useful to determine the end or root value of constraint.
As per the given,
Cindy has 2 boxes of pencils. Patrice has 5 boxes of pencils.
Suppose the number of pencils in each box is "x" as it is the same.
Total pencils in Cindy boxes = 2x
Total pencils in Patrice boxes = 5x
Total pencils = 2x + 5x = 7x
Hence "The expression which represents the total number of pencils will be 7x where x is the number of pencils".
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The complete question is below,
Find the constant of variation for the relationship shown in the following table:
x 1 2 3 4
y 5 10 15 20
1
2
5
10
Look at the picture below
John states that by ASA.
Mary states that by AAS.
Phillip states that the triangles are not congruent.
Which student is correct? why?
MY ANSWER:
Phillip is correct. XY=/ AC. (But i have another guess/answer)
No student is right, These triangles arent congruent but these triangles are to different triangles. We can see this with XY/AC. (But doesnt that just mean phillip is correct?) HELP!
Answer: Phillip is correct. The triangles are not congruent.
How do we know this? Because triangle ABC has the 15 inch side between the two angles 50 and 60 degrees. The other triangle must have the same set up (just with different letters XYZ). This isn't the case. The 15 inch side for triangle XYZ is between the 50 and 70 degree angle.
This mismatch means we cannot use the "S" in the ASA or AAS simply because we don't have a proper corresponding pair of sides. If we knew AB, BC, XZ or YZ, then we might be able to use ASA or AAS.
At this point, there isn't enough information. So that means John and Mary are incorrect, leaving Phillip to be correct by default.
Note: Phillip may be wrong and the triangles could be congruent, but again, we don't have enough info. If there was an answer choice simply saying "there isn't enough info to say either if the triangles are congruent or not", then this would be the best answer. Unfortunately, it looks like this answer is missing. So what I bolded above is the next best thing.
Answer:
Phillip states that the triangles are not congruent.
Step-by-step explanation:
Assume for a second the triangles are congruent.
Then the angles are equal
<A =< X
<B= <Y
<C = <Z
Then
Triangle ABC = Triangle XYZ
from this information
AB = XY
and BC = YZ
and CA = ZX
but the only other piece of information we have is CA = 15 and XY = 15
If this is true then CA = ZX = 15 and AB = XY = 15
That would make this an isosceles triangle (AB = AC)
so angles B and C would have to be equal, but they are not.
So these two triangles cannot be congruent.
There are 22456 pine trees in the park the park workers are going to plant 6478 more trees this year how many trees will there be when they are done
Answer:28934
Step-by-step explanation:
You add 22456 and 6478
After the park workers plant 6478 more trees in the park which currently has 22456 trees, the total number of trees would be 28934.
Explanation:This is a question of simple addition in mathematics. Currently, the park consists of 22456 pine trees. The park workers are planning to plant another 6478 trees. Therefore, to find out the total number of trees after they plant the new ones, we add together the current number of trees and the number of trees to be planted.
22456 (Current number of trees) + 6478 (Additional number of trees to be planted) = 28934
So, after planting the additional trees, there will be a total of 28934 trees in the park.
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The equation yˆ=−5.9x2+39x+2.2 approximates the average number of cars that pass through an intersection x hours after 3:00 p.m. What is the best estimate for the average number of cars that pass through the intersection at 4:30 p.m.?
Answer: 74
Step-by-step explanation:
x = 4:30 - 3:00
= 1:30
= 1.5 hours
y = -5.9x² + 39x + 2.2
= -5.9(1.5)² + 39(1.5) + 2.2
= -5.9(2.25) + 58.5 + 2.2
= 13.275 + 60.7
= 73.975
Answer: 47
Step-by-step explanation:
x = 4:30 - 3:00
= 1:30
= 1.5 hours
y = -5.9x² + 39x + 2.2
= -5.9(1.5)² + 39(1.5) + 2.2
= -5.9(2.25) + 58.5 + 2.2
= -13.275 + 60.7
= 47.425
What does the fundamental theorem of algebra state about the equation 2x^2-4x+16=0?
Answer: (A) degree of 2; 1 ± i√7
Step-by-step explanation:
Degree of the polynomial designates the number of roots.
x² - 2x + 8
a=1 b=-2 c=8
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]=\dfrac{-(-2)\pm\sqrt{(-2)^2-4(1)(8)}}{2(1)}[/tex]
[tex]=\dfrac{2\pm\sqrt{4-32}}{2}[/tex]
[tex]=\dfrac{2\pm\sqrt{-28}}{2}[/tex]
[tex]=\dfrac{2\pm2i\sqrt{7}}{2}[/tex]
[tex]=\dfrac{2(1\pm\\i\sqrt7)}{2}[/tex]
= 1 ± i√7
HELP PLEASE!! which of the following represents a function?
please explain too i don’t understand this.
Answer:
A is a function because if draw a line right down the middle no other dots will intercept
Step-by-step explanation:
A function is where one input has only one out put
As you can tell in the table(c) -3 is repeated that's what makes it not a function.same for B since there are more than one inputs it's not a function
Hope this helps!
What is the solution to the system of equations?
-3x-4y+z=-1
2x+y-z=-8
x+8y-z=23
A. (-3,4,6)
B. (4,-3,-1)
C. (-3,4,8)
D. (3,-4,-6)
Answer:
The answer is A (-3,4,6).
Step-by-step explanation:
1 Solve for z in -3x-4y+z=-1
z=3x-1+4y
2 Substitute z=3x-1+4y into 2x+y-z=-8
-x-3y+1=-8
3 Substitute z=3x-1+4y into x+8y-z=23
-2x+4y+1=23
4 Solve for x in -x-3y+1=-8
x=-3y+9
5 Substitute x=-3y+9 into z=3x-1+4y
z=-5y+26
6 Substitute x=-3y+9 into -2x+4y+1=23
10y-17=23
7 Solve for y in 10y-17=23
y=4
8 Substitute y=4 into z=-5y+26
z=6
9 Substitute y=4 into x=-3y+9
x=-3
10 Therefore,
x=-3
y=4
z=6
Graph the data in the table. Which kind of function best models the data? Right in equation to model the data.
A. Exponential y=2.5^x
B. Quadratic y=-2.5x^2
C. Quadratic y=2.5x^2
D. Linear y=2.5x
Answer:
c
Step-by-step explanation:
it is a parabola which has a standard equation of
y = x^2. option a is an exponentially positive curve. option b is a negative parabola. option d is a linear graph which isn't a parabola
The coordinates of the vertices of trapezoid ABCD are A (2,6), B (5,6), C (7,1), and D (-1,1). The coordinates of the vertices of trapezoid A'B'C'D' are A' (-6, -2),B' (-6, -5), C' (-1, -7), and D' (-1, 1). Which statement correctly describes the relationship between trapezoid ABCD and trapezoid A'B'C'D' ?
A. Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can reflect trapezoid ABCD across the x-axis and then across the y-axis.
B. Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can rotate trapezoid ABCD 180°about the origin and then translating it 4 units left.
C. Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can reflect trapezoid ABCD across the x-axis and then rotating it 90°clockwise.
Answer:
Correct answer is option C.
Step-by-step explanation:
Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can reflect trapezoid ABCD across the x-axis and then rotating it 90°clockwise.
Answer:
C. Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can reflect trapezoid ABCD across the x-axis and then rotating it 90°clockwise.
Step-by-step explanation:
Given : The coordinates of the vertices of trapezoid ABCD are A (2,6), B (5,6), C (7,1), and D (-1,1). The coordinates of the vertices of trapezoid A'B'C'D' are A' (-6, -2),B' (-6, -5), C' (-1, -7), and D' (-1, 1).
To find : Which statement correctly describes the relationship between trapezoid ABCD and trapezoid A'B'C'D'.
Solution : We have given that trapezoid ABCD.
Parent coordinates of A (2,6), B (5,6), C (7,1), and D (-1,1)
Translated coordinates A' (-6, -2),B' (-6, -5), C' (-1, -7), and D' (-1, 1).
By reflection rule : Reflection across x axis (x , y) →→( x , -y) and rotating it 90°clockwise (x , y) →→( -y, x).
Therefore, C. Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can reflect trapezoid ABCD across the x-axis and then rotating it 90°clockwise.
A rotation in the origin is shown. The angle of rotation appears to be A) 30°. B) 45°. C) 60°. D) 90°.
It looks like a 90º rotation
Answer:
90 egress
Step-by-step explanation:
Solve the system of equations using elimination.
8x + 7y = -16
10x + 7y = -6
A)
(3, 6)
B)
(8, 5)
C)
(7, 10)
D)
(5, -8)
Answer: D.(5, -8)
Step-by-step explanation:
(Multiply by -1)-8x-7y=16
10x+7y=-6
2x=10
X=5
(Subsitite 5 into one) 10(5)+7y=-6
50+7y=-6
7y=-56
Y=-8
Final answer:
To solve the system using elimination, subtract the first equation from the second to find x=5, then substitute x back into one of the original equations to find y=-8. The solution is (5, -8).
Explanation:
To solve the system of equations using elimination, we look at the given pairs:
8x + 7y = -1610x + 7y = -6We can eliminate the y-variable by subtracting the first equation from the second
(10x + 7y) - (8x + 7y) = -6 - (-16)10x - 8x + 7y - 7y = -6 + 162x = 10Divide both sides by 2:
x = 5Now that we have x, we can substitute it back into either of the original equations to find y. Let's use the first equation:
8(5) + 7y = -1640 + 7y = -167y = -16 - 407y = -56Divide both sides by 7:
y = -8Therefore, the solution to the system of equations is (5, -8), which corresponds with answer choice D.
Which expression helps you find the length x of a side of a rectangle that has a diagonal of 17 units and a width of 8 units?
To find the length of a rectangle given the diagonal and width, one can utilize the Pythagorean theorem. By treating the diagonal as the hypotenuse of a right triangle formed within the rectangle, we solve for 'x' (length) and get our desired result.
Explanation:To find the length (x) of the side of a rectangle given the diagonal (17 units) and the width (8 units), you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In the rectangle, the diagonal forms a right triangle with two sides.
In the context of this question, our hypotenuse is the diagonal, which is 17 units long. Let's denote the width as 'w' and the length we're trying to find as 'x'. With 'w' being 8 units, our scenario can be represented by the Pythagorean theorem like this: (17²) = (8²) + (x²)
In determining 'x', we can rearrange the equation to solve for 'x': x = sqrt[(17²) - (8²)]. So, when we subtract the square of 8 from the square of 17 then take the square root, we get the length of 'x'.
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Question:
1. What is the value of x? Show your work to justify your answer. (2 points)
2. What is the value of the exterior angle? Show your work to justify your answer. (2 points)
Answer:
1. [tex]x=56^o[/tex]
2. Exterior angle = [tex]116^o[/tex]
Step-by-step explanation:
1.
We can see from our given diagram that (2x+4) degrees is the measure of exterior angle of triangle PQR.
Since the measure of exterior angle of a triangle equals to the sum of the opposite interior angles. So measure of our given triangle's exterior angle will be equal to sum of measure of angle P and angle Q.
We can represent this information as:
[tex](2x+4)^o=60^o+x^o[/tex]
[tex]2x^o+4^o=60^o+x^o[/tex]
Let us subtract [tex]x^o[/tex] from both sides of our equation.
[tex]2x^o+4^o-x^o=60^o+x^o-x^o[/tex]
[tex]x^o+4^o=60^o[/tex]
Let us subtract [tex]4^o[/tex] from both sides of our equation.
[tex]x^o+4^o-4^o=60^o-4^o[/tex]
[tex]x=56^o[/tex]
Therefore, value of x is 56 degrees.
2. Since the measure of exterior angle of our given triangle is 2x+4, let us substitute x=56 in our expression to find the measure of exterior angle.
[tex]\text{Measure of exterior angle}=(2x+4)^o[/tex]
[tex]\text{Measure of exterior angle}=(2*56+4)^o[/tex]
[tex]\text{Measure of exterior angle}=(112+4)^o[/tex]
[tex]\text{Measure of exterior angle}=116^o[/tex]
Therefore, the measure of exterior angle of our given triangle is 116 degrees.