Answers
¹²³⁴⁵⁶⁷⁸⁹⁰⁹⁸⁷⁶⁵⁴³²¹
₁¹₁¹₁
Answer:
Option C is correct.
The missing steps in this proof is; [tex]\angle 1 \cong \angle 4[/tex] and [tex]\angle 3 \cong \angle 5[/tex].
Explanation:
Given ΔABC.
Prove that: The sum of the interior angle measures of ΔABC is [tex]180^{\circ}[/tex]
Let A ,B and C forms a triangle [Given]
Parallel lines are those two lines that are always the same distance apart and never touch.
then, by the definition of parallel lines and labeling angles
DE be the line passing through B, parallel to AC, with angles as labelled in the figure as shown below in the attachment.
Alternative Interior Angle theorem states that the angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles also this theorem says that when the lines are parallel, then the alternate interior angles are equal.
Then,
[tex]\angle 1 \cong \angle 4[/tex] and
[tex]\angle 3 \cong \angle 5[/tex] [By Alternative Interior angle theorem]
Angles are always congruent if their measures in degrees are equal.
therefore,
[tex]m\angle 1 =m\angle 4[/tex] and
[tex]m\angle 3=m\angle 5[/tex] [By Congruent Angle have equal measure] ......[1]
Straight Angles states that angles on one side of a straight line always add to 180 degrees.
From the given figure;
By the addition angle and definition of straight angle we get;
[tex]m\angle 4 +m\angle 2 +m\angle 5 =180^{\circ}[/tex] ......[2]
Substituting equation [1] in [2] we get;
[tex]m\angle 1 +m\angle 2 +m\angle 3 =180^{\circ}[/tex]
Therefore, the sum of the interior angles measures of triangle ABC is [tex]180^{\circ}[/tex]
Related Questions
What is the area of the obtuse triangle given below?
Answers
A = 1/2 * 11 * 7 = 38.5
your answer is D
hope that helps :)
Answer:
Option (d) is correct.
The area of triangle is 38.5 square units
Step-by-step explanation:
Given: An obtuse triangle.
We have to find the area of this obtuse angle.
Consider the given obtuse triangle
Area of triangle = [tex]\frac{1}{2}\cdot b \cdot h[/tex]
where b = Base
h = height
Given : base = 11 units
and height = 7 units
Thus, Area of triangle = [tex]\frac{1}{2}\cdot 11 \cdot 7[/tex]
Simplify, we have,
Area of triangle = 38.5
Thus, The area of triangle is 38.5 square units
Find x and RS if S is between R and T
RS=6x,ST=12,and RT=72
Answers
RST
so RS+ST=RT
6x+12=72
minus 12 both sides
6x=60
divide both sides by 6
x=10
x=10
The value of x is 10 and RS is 60 units.
It is required to find the value of x and RS.
What is length ?Length is defined as the measurement or extent of something from end to end. It is the larger of the two or the highest of three dimensions of geometrical shapes or objects.
Given:
S is between R and T
RS=6x, ST=12, RT=72
We know that ,
RS + ST = RT
6x + 12 = 72
Substract 12 on both sides we have,
6x + 12 - 12= 72 - 12
6x = 60
x = 10 units.
Put the value of x in RS we have,
RS = 6x
RS = 6(10)
RS = 60 units.
Therefore, the value of x is 10 and RS is 60 units.
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Two angles are supplementary and one of the angles is 8 times the other. find the measure of the larger angle.
Answers
supplementary angles add up to 180 degrees
angle 1 = x
angle 2 = 8x
x +8x = 180
9x = 180
x = 180/9 = 20 degrees
larger angle = 8*20 = 160 degrees
To find the measure of the larger angle, set up an equation. Solve the equation to find the value of the smaller angle. Multiply the smaller angle by 8 to find the measure of the larger angle.
Explanation:To find the measure of the larger angle, we need to set up an equation based on the given information. Let's say the smaller angle is x degrees. The larger angle is then 8 times the smaller angle, which means it is 8x degrees. We know that two angles are supplementary, meaning they add up to 180 degrees. So we can set up the equation x + 8x = 180. Simplifying this equation gives us 9x = 180. Dividing both sides by 9, we find that x = 20 degrees. Therefore, the larger angle is 8x = 8 * 20 = 160 degrees.
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find an ordered pair that is a solution to the equation x-4y=4
Answers
Ordered pairs that are solutions to the equation x-4y=4 is (4, 0) and (0, -1).
The given equation is x-4y=4.
We need to find an ordered pair that is a solution to the equation.
How to find the solution to an equation?The solutions of linear equations are the points at which the lines or planes representing the linear equations intersect or meet each other. A solution set of a system of linear equations is the set of values to the variables of all possible solutions.
From the graph, we can observe that (4, 0) and (0, -1) are solutions.
Verification of the solution (4, 0):
4-4y=4
⇒-4y=0
⇒y=0
Verification of the solution (0, -1):
0-4y=4
⇒-4y=4
⇒y=-1
Therefore, ordered pairs that are solutions to the equation x-4y=4 is (4, 0) and (0, -1).
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Which features describe the graph of y^2/96^2 - x^2/40^2 =1? Check all that apply.
a focus at (104, 0)
a focus at (0,−96)
a vertex at (−40, 0)
a vertex at (0, 96)
the center at (0, 0)
Answers
[tex] \frac{y^{2}}{96^{2}} - \frac{x^{2}}{40^{2}} =1[/tex]
From the given equation,
a = 40
b = 96
(h,k) = (0,0), the center
The vertices are at (0,96) and at (0, -96).
The curves open upward and downward.
c² = a² + b² = 40² + 96² = 10816
c = 104
Therefore the foci are at (0, -104) and (0, 104).
Check the given answers:
1. a focus at (104, 0) is INCORRECT
2. a focus at (0, -96) is INCORRECT
3. a vertex at (-40, 0) is INCORRECT
4. a vertex at (0, 96) is CORRECT
5. the center at (0, 0) is CORRECT
identify the maximum and minimum values of the function y = 3 cos x in the interval [-2π, 2π]. Use your understanding of transformations, not your graphing calculator.
Answers
The x interval of [-2π, 2π] ensures that all y values are enclosed; the cosine makes two full sweeps.
The maximum value of the function y = 3 cos x will be 3.
The minimum value of the function y = 3 cos x will be - 3.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The function is,
⇒ y = 3 cos x
In the interval [-2π, 2π].
Now,
Since, The function is,
⇒ y = 3 cos x
Hence, We get;
The maximum value of the function y = 3 cos x is,
⇒ y = 3 cos2π
⇒ y = 3 × 1
⇒ y = 3
And, The minimum value of the function y = 3 cos x is,
⇒ y = 3 cos(-2π)
⇒ y = 3 × - 1
⇒ y = - 3
Thus, The maximum value of the function = 3.
The minimum value of the function = - 3.
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Write a variable expression for 9 more than a number s.
Answers
More than suggests addition.
A bakery sold apple pies for $11 and blueberry pies for $13. One Saturday they sold a total of 38 pies and collected a total of $460. How many apple pies did they sell and how many blueberry pies did they sell?
Answers
A= apple pie
B = blueberry pie
a+b=38
a=38-b
11a + 13b =460
11(38-b) + 13b = 460
418-11b +13b = 460
2b=42
b=42/2 =21
they sold 21 blueberry pies and 17 apple pies
100 POINTS!!!! Create a table of values for a linear function. A drone is in the distance, flying upward in a straight line. It intersects the rainbow at two points. Choose the points where your drone intersects the parabola and create a table for at least four values for the function. Remember to include the two points of intersection in your table. Can you just give me the X and Y values?
Answers
If you use these two points to create a line we get the equation:
[tex]y - 6 = \frac{34 - 6}{-2 - 5}(x - 5)[/tex] (I just used point slope form)
This can be simplified to:
[tex]y = \frac{40}{-7}x + \frac{242}{7}[/tex]
Now we just need to create a table of points on this line. We already have the points you gave and we can also use the y-intercept: [tex](0, \frac{242}{7})[/tex] and the x-intercept: [tex](\frac{121}{20}, 0)[/tex].
So our table of value can be:
x | y
______|________
-2 | 34
0 | 242 / 7
5 | 6
121/20 | 0
(a) a pizza parlor has a choice of 11 toppings for its pizzas. from these 11 toppings, how many different 7 -topping pizzas are possible?
Answers
To solve for the number of different possible pizzas with 7 toppings out of 11 and the arrangement of these toppings is not important, therefore we use the combination formula.
The formula for combination is:
n C r = n! / r! (n – r)!
where,
n = is the total number of toppings = 11
r = the number of toppings in a pizza = 7
Substituting the values into the equation:
11 C 7 = 11! / 7! (11 – 7)!
11 C 7 = 11! / 7! * 4!
11 C 7 = 330
Therefore there are a total different 330 pizzas with 7 different combinations toppings.
Final answer:
330 different combinations.
Explanation:
The student's question is about combinations in Mathematics, specifically how many 7-topping pizzas can be made from a choice of 11 toppings. This is a combinatorics problem, and the solution involves the use of the combination formula, which is given as:
C(n, k) = n! / (k!(n-k)!)
where n is the total number of items to choose from, k is the number of items to choose, n! denotes the factorial of n, and C(n, k) represents the number of combinations.
In this case, n is 11 (the total number of toppings) and k is 7 (the number of toppings on the pizza).
Therefore, the number of different 7-topping pizzas possible is:
C(11, 7) = 11! / (7!(11-7)!) = 11! / (7!4!) = (11x10x9x8)/(4x3x2x1) = 330
Hence, 330 different 7-topping pizzas are possible.
Which of the following is an arithmetic sequence?
a -7/11,6/11, -5/11, 4/11
b -3/4, -3/5, -3/6, -3/7
c 1/2,2,7/2,5
d 3/4,-3/2, 3, -6
Answers
and then - 3/2 x - 2 = 3
3 x - 2 = - 6
Hope that helps <3
The sequence 3/4,-3/2, 3, -6 is the arithmetic sequence.
Common differenceThe difference between two successive terms of an arithmetic progression is known as a common difference.
How to check the common difference?(a)
We will find the common difference between each term of the given sequences by subtracting a term and its previous term.
[tex](\frac{6}{11}- \frac{-7}{11}) \neq (\frac{-5}{11} -\frac{6}{11} )\neq (\frac{4}{11} -\frac{-5}{11})[/tex]
[tex]\frac{13}{11}\neq \frac{-11}{11}\neq \frac{9}{11}[/tex]
So, option (a) is incorrect.
(b)
We will take the common difference between the terms.
[tex](\frac{-3}{5} -\frac{-3}{4} )\neq (\frac{-3}{6} -\frac{-3}{5} )\neq (\frac{-3}{7} -\frac{-3}{6} )\\[/tex]
[tex]\frac{3}{20} \neq \frac{3}{30}\neq \frac{3}{42}[/tex]
So, option (b) is also incorrect.
(c)
We will take the common difference between the terms.
[tex](2-\frac{1}{2} )= ( \frac{7}{2}-2 )= (5 - \frac{7}{2} )[/tex]
[tex]\frac{3}{2}= \frac{3}{2} = \frac{3}{2}[/tex]
Since the difference between the terms is common.
Thus, option (c) is correct.
(d)
We will take the common difference between the terms.
[tex](\frac{-3}{2}- \frac{3}{4})\neq (3-\frac{3}{2})\neq (-6-3)[/tex]
[tex]\frac{-18}{2}\neq \frac{9}{2}\neq (-9)[/tex]
So, option (d) is incorrect.
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Find the value tan 39 degrees. Round to the nearest ten-thousandth
A ) 0.8098
B ) 0.6293
C ) 0.7771
D ) 3.6146
Answers
mine gives tan 39 = 0.8097840332
which is 0.8098 to nearest ten thousandth.
f f(x)=2(x)^2+5 sqrt (+2) complete the following statement: The domain for f(x) is all real numbers greater than or equal to _____.
Answers
Then since the minimum of x^2 is 0, so f(x) must be greater or equal to 5sqrt(2)
The domain for the function f(x) = 2x² + 5√(x + 2) is all real numbers greater than or equal to -2.
In interval notation, we can express this as:
Domain: x ∈ [-2, ∞)
Given is a function f(x) = 2x² + 5√2, we need to determine the domain of the function,
To complete the statement, we need to determine the domain for the function f(x) = 2x² + 5√(x + 2).
The domain of a function represents all the possible values of x for which the function is defined.
In this case, we need to consider two factors that can restrict the domain:
For a real number to be a valid input for the square root (√), the expression inside the square root (x + 2) must be greater than or equal to 0.
Otherwise, we would encounter the issue of taking the square root of a negative number, which is not defined in the real number system.
There are no other restrictions in the function that would cause it to be undefined for certain values of x.
Since x² is defined for all real numbers, there are no issues there.
Let's solve the inequality for the square root expression:
x + 2 ≥ 0
Subtract 2 from both sides:
x ≥ -2
So, the domain for the function f(x) = 2x² + 5√(x + 2) is all real numbers greater than or equal to -2.
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Dominique is thinking about buying a house. The table below shows the projected value of two different houses for three years.
House 1 (value in dollars) year 1: 286,000 year 2: 294,580 year 3: 303,417.40 House 2 (value in dollars) year 1: 286,000 year 2: 295,000 year 3: 304,000
Part A: What type of function, linear or exponential, can be used to describe the value of each of the houses after a fixed number of years? Explain your answer.
Part B: Write one function for each house to describe the value of the house f(x), in dollars, after x years.
Part C: Dominique wants to purchase a house that would have the greatest value in 25 years. Will there be any significant difference in the value of either house after 25 years? Explain your answer, and show the value of each house after 25 years.
Answers
The functions for House 1 and House 2 are [tex]\(f_1(x) = 5079.6x + 248900.4\)[/tex] and [tex]\(f_2(x) = 4666.\overline{66}x + 256000\)[/tex] respectively.
After 45 years, House 1 will be valued at $477,555, and House 2 will be valued at $465,000.
Here's the step-by-step solution with complete calculations for the given problem:
Part A: Identifying the Function Type
- House 1:
- Year 1 to Year 2: [tex]\(259,059.60 - 253,980 = 5,079.60\)[/tex]
- Year 2 to Year 3: [tex]\(264,240.79 - 259,059.60 = 5,181.19\)[/tex]
- House 2:
- Year 1 to Year 2: [tex]\(263,000 - 256,000 = 7,000\)[/tex]
- Year 2 to Year 3: [tex]\(270,000 - 263,000 = 7,000\)[/tex]
The functions are linear because the changes are constant for House 2 and almost constant for House 1.
Part B: Formulating the Equations
- House 1 Equation:
- Slope (m): [tex]\(5079.6\)[/tex]
- Y-intercept (c): [tex]\(248900.4\)[/tex]
- Equation: [tex]\(f_1(x) = 5079.6x + 248900.4\)[/tex]
- House 2 Equation:
- Slope (m): [tex]\(4666.\overline{66}\)[/tex]
- Y-intercept (c): [tex]\(256000\)[/tex]
- Equation: [tex]\(f_2(x) = 4666.\overline{66}x + 256000\)[/tex]
Part C: Calculating Future Values
- House 1 Value at Year 45:
[tex]- \(f_1(45) = 5079.6 \times 45 + 248900.4 = 477555\)[/tex]
- House 2 Value at Year 45:
[tex]- \(f_2(45) = 4666.\overline{66} \times 45 + 256000 = 465000\)[/tex]
These equations predict the values of the houses after 45 years based on the given data. House 1 will be valued at $477,555, and House 2 will be valued at $465,000.
Is the relation {(3, 5), (–4, 5), (–5, 0), (1, 1), (4, 0)} a function? Explain. Type your answer below
Answers
If you had something like {(1,2),(4,5),(1,7)} then it wouldn't be a function since x = 1 repeats itself. In this example, x = 1 leads to more than one output.
{(3, 5), (–4, 5), (–5, 0), (1, 1), (4, 0)}
As long as there are the same x-value does not have multiple y-value results, it will be a function. This data array doesn't contain any recurring x-values. Therefore, this is a function (in simple terms of speaking).
!!! HELP What values for (picture of equation) satisfy the equation?
Answers
find the x intercepts of the parabola with vertex (2,13) and y-intercept (0,5) write your answer in this form: (x1,y1),(x2,y2) if necessary, round to the nearest hundredth
Answers
(x-h)^2 = +/- 4a (y-k) or (y-k)^2 = +/- 4a(x-h)
where
(h,k) is the coordinates of the vertex
a is the length of the focus from the vertes
+4a if the parabola opens upwards or to the right
-4a if the parabola opens downwards or to the left
The vertex (2,13) is situated in the 1st quadrant of the Cartesian plane. It only has y-intercept. This means that it only passes the y-axis once. Therefore, the parabola must open downwards and it passes the x-axis twice. The intersections at the x-axis are the x-intercepts. If the parabola has 2 x-intercepts, then the equation would be (x-h)^2 = -4a(y-k).
Let's use the y-intercept (0,5) to determine 4a:
(0-2)^2=-4a(5-13)
4a = 0.5
Therefore, the equation of the parabola is (x-2)^2 = -1/2(y-13). To find the x-intercepts, let y=0.
(x-2)^2 = -1/2(0-13) = 6.5
x-2 = +/- √6.5 = +/- 2.55
x = 4.55 and and -0.55
The x-intercepts are (-0.55,0) and (4.55,0).
Answer:
(-0.55,0),(4.55,0)
Simplify fraction 23076923076923/10000000000000
Answers
Five members of the soccer team and five members of the track team ran the 100-meter dash. Their times are listed in the table below: Soccer Track 12.3 12.3 13.2 11.2 12.5 11.7 11.3 12.2 14.4 13.7 What is the difference of the means for the two groups? 0.52 12.22 12.74 24.96
Answers
track : (12.3 + 11.2 + 11.7 + 12.2 + 13.7) / 5 = 61.1 / 5 = 12.22
difference is : 12.74 - 12.22 = 0.52 <=
Answer:
Hence, the difference in Mean of two teams is:
0.52
Step-by-step explanation:
Five members of the soccer team and five members of the track team ran the 100-meter dash.
Their time is listed as:
Soccer Track
12.3 12.3
13.2 11.2
12.5 11.7
11.3 12.2
14.4 13.7
The mean of the soccer team is given by:
[tex]Mean_1=\dfrac{12.3+13.2+12.5+11.3+14.4}{5}\\\\Mean_1=12.74[/tex]
The mean of track team is given by:
[tex]Mean_2=\dfrac{12.3+11.2+11.7+12.2+13.7}{5}\\\\Mean_2=\dfrac{61.1}{5}\\\\Mean_2=12.22[/tex]
Hence, the Difference in Mean is:
[tex]Mean_1-Mean_2\\\\=12.74-12.22\\\\=0.52[/tex]
Hence, the difference in Mean of two teams is:
0.52
The number of hours walked varies inversely with the speed of the walker. if it takes sam 12 hours to complete his walking goal at 5 miles per hour, how long would it take him at 3 miles per hour?
Answers
h = k/s
Substituting the known values,
12 = k/5
k = 60
For the second scenario,
h = k/s
Substituting the calculated value for k and the given value for speed,
h = (60)(3 miles/hour)
h = 20 hours
h = 20 hours
Therefore, it will take 20 hours to walk with a speed of 3 miles per hour.
59:26 What is the length of the hypotenuse, x, if (20, 21, x) is a Pythagorean triple? 22 29 41 42
Answers
a²+b²=c²
so
if the legs are 20 and 21 and the hypotnuse is x then
20²+21²=x²
400+441=x²
841=x²
29=x
Answer: the correct option is (B) 29.
Step-by-step explanation: We are given to find the length of the hypotenuse x, if (20, 21, x) is a Pythagorean triple.
We know that
in a right-angled triangle, the lengths of the sides (hypotenuse, perpendicular, base) is a Pythagorean triple, where
[tex]Hypotenuse^2=Perpendicular^2+base^2.[/tex]
So, for the given Pythagorean triple, we have
[tex]x^2=20^2+21^2\\\\\Rightarrow x^2=400+441\\\\\Rightarrow x^2=841\\\\\Rightarrow x=\sqrt{841}~~~~~~~~~~~~~~~~~[\textup{taking square root on both sides}]\\\\\Rightarrow x=\pm29.[/tex]
Since the length of the hypotenuse cannot be negative, so x = 29.
Thus, the length of the hypotenuse, x = 29.
Option (B) is CORRECT.
What is the distance between the points (22, 27) and (2, -10)? if necessary, round your answer to two decimal places.a. 57 units?
Answers
(22,27)....x1 = 22 and y1 = 27
(2,-10)....x2 = 2 and y2 = -10
now we sub
d = sqrt (2 - 22)^2 + (-10 -27)^2)
d = sqrt (-20^2) + (-37^2)
d = sqrt (400 + 1369)
d = sqrt 1769
d = 42.06 <==
Answer:
42.06
Step-by-step explanation:
Two points (22,27) and (2,-10)
using distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
So, distance between (22,27) and (2,-10) is D
[tex]D=\sqrt{(22-2)^2+(27-(-10))^2}[/tex]
[tex]D=\sqrt{(20)^2+(37)^2}[/tex]
[tex]D=\sqrt{400+1369}[/tex]
[tex]D=\sqrt{1769}[/tex]
[tex]D=42.059[/tex]
Round off two decimal place.
[tex]D=42.06[/tex]
Hence, The distance between the points is 42.06
Find s10 for a geometric series with first term 10 and a common ratio 4
Answers
[tex]S_{n}=\frac{a_1(1-r^n)}{1-r}[/tex]
so
given first term of 10 and common ratio 4 and n=10
[tex]S_{10}=\frac{10(1-4^{10})}{1-4}[/tex]
[tex]S_{10}=\frac{10(1-1048576)}{-3}[/tex]
[tex]S_{10}=\frac{10(-1048575)}{-3}[/tex]
[tex]S_{10}=\frac{-10485750}{-3}[/tex]
[tex]S_{10}=3495250[/tex]
Solve x 2 + 9x + 8 = 0 by completing the square. What are the solutions?
Answers
x^2+9x+8=0
(x+1)(x+8)=0
x+1=0
x=-1
x+8 = 0
x=-8
solutions are -1 and -8
Find H to the nearest degree.
Answers
sin(H) = GF/HF
sin(H) = 5/13
arcsin(sin(H)) = arcsin(5/13)
H = 22.61986 ... which is approximate
H = 23 degrees ... round to the nearest whole number
Answer is choice A
In spherical geometry, which indicates the possible number of right angles a triangle may have?
1
2
3
All of the above
Answers
So, if a triangle has one 90° angle, there are still excess angles to make up for a maximum of 540°. The same is true for two 90° angles. You would exceed 180° but that is just the lower limit so that is still acceptable. If you have three 90° angles, you form a spherical triangle with a total of 270°, which is within the given range. Thus, the answer is all of the above.
Best explained and correct answer gets brainliest.
Answers
total = 2372* (1+0.045)^20=
2372*1.045^20=
2372 * 2.411714025= 5720.585
she will have 5720.59 in 20 years
If the factors of a polynomial are x-2 and x-5, what values of x make that polynomial 0?
A. 1 and 2
B. -2 and -5
C. 2 and 5
D. Cannot be determined
Answers
What number should be added to both sides of the equation to complete the square? x^2 â 10x = 7?
Answers
Basically, the p value should be half of b and the square root of c.
At the movie theatre, child admission is $6.20 and adult admission is $9.80 . On Monday, twice as many adult tickets as child tickets were sold, for a total sales of $593.40 . How many child tickets were sold that day?
Answers
x= child
2x = adult
6.20x +9.80(2x) =593.40
6.20x +19.6x=593.40
25.80x =593.40
x=593.40/25.80 = 23
23 childrens tickets were sold