A two-column method be that can used to prove that segment QR is parallel to segment PS is presented as follows;
Statement \({}\) Reasons
1. \(\overline{QP}\) ≅ \(\overline{RS}\) 1. Given
2. \(\overline{QP}\) ║ \(\overline{RS}\) \({}\) 2. Given
3. ∠PRQ ≅ ∠RPS \({}\) 3. Alt. int. angles theorem
∠QPR ≅ ∠PRS \({}\)
4. ∠PRQ = ∠RPS \({}\) 4. Definition of congruency
∠QPR = ∠PRS
5. ∠QRS = ∠PRQ + ∠PRS \({}\) 5. Angle addition postulate
∠QPS = ∠QPR + ∠RPS
6. ∠PRQ + ∠PRS = ∠QPR + ∠RPS \({}\) 6. Substitution property
7. ∠QRP = ∠QPS \({}\) 7. Transitive property
8. \(\overline{PR}\) ≅ \(\overline{PR}\) \({}\) \({}\) 8. Reflexive property
9. ΔQRP ≅ ΔSPR \({}\) 9. ASA congruency rule
10. ∠PQR ≅ ∠PSR \({}\) 10. CPCTC
11. ∠PQR = ∠PSR \({}\) 11. Definition of congruency
12. QRSP is a parallelogram \({}\) 12. Parallelogram opp. int. ∠s theorem
13. \(\overline{QR}\) ║ \(\overline{PS}\) \({}\) 13. Properties of a parallelogram
What is a parallelogram?A parallelogram is a quadrilateral that has opposite parallel sides.
The details of the reasons used to prove that the segment \(\overline{QR}\) is parallel to segment \(\overline{PS}\) are as follows;
Alt. int. angles theorem
The alternate interior angles theorem states that the alternate interior angles formed between two parallel lines and their common transversal are congruent
Definition of congruency
Two geometric figures are congruent if they have the same measurements.
Angle addition postulate
The angle addition postulate states that the measure of an angle ∠A, which is formed by two adjacent angles ∠B and ∠C, is the same as the sum of the measures of the two angles, ∠A = ∠B + ∠C
Substitution property
The substitution property of equality states that if a variable, a = another variable, b, a = b, then b can be plugged into expressions and equations to substitute for a and the values of the expressions and sides of equations remain the same.
Transitive property
The transitive property of equality states that if a = b, and b = c, then a = c
Reflexive property
The reflexive property of congruency states that a geometric figure is congruent to its self
ASA congruency rule
The Angle-Side-Angle congruency rule states that if two angles and the included side of one triangle are congruent to the two angles and included side of another triangle, then the two triangles are congruent.
CPCTC
CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent
Parallelogram opp. int. ∠s theorem
The parallelogram opposite interior angles theorem states that the opposite interior angles of a parallelogram are congruent.
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Classify the decimal expansion of each fraction as a terminating decimal or a repeating decimal.
DESPERATE WILL GIVE BRAINLIST AND THANKS
Drag and drop the fractions into the boxes to correctly complete the table.
Terminating Decimal Repeating Decimal
Options: 56/72 12/30 15/40 12/37
Answer:
repeating-- terminating-- terminating-- repeating.
Step-by-step explanation:
PLS HELP ASAP! GIVING BRAINLIST!
Answer:
I think it is 8, i did not learn this in school
Step-by-step explanation:
2(3x^2+5)
6x^2+10
create an infinite geometric series to represent the decimal 0.44444... use this information to find the fraction to which this infinite geometric series converges.
Therefore, the infinite geometric series representing the decimal 0.44444... converges to the fraction 4/9.
To represent the decimal 0.44444... as an infinite geometric series, we can start by noticing that this decimal can be written as 4/10 + 4/100 + 4/1000 + ...
The pattern here is that each term is 4 divided by a power of 10, with the exponent increasing by 1 for each subsequent term.
So, we can express this as an infinite geometric series with the first term (a) equal to 4/10 and the common ratio (r) equal to 1/10.
The infinite geometric series can be written as:
0.44444... = (4/10) + (4/10)(1/10) + (4/10)(1/10)^2 + ...
To find the fraction to which this series converges, we can use the formula for the sum of an infinite geometric series:
S = a / (1 - r)
Plugging in the values, we have:
S = (4/10) / (1 - 1/10)
= (4/10) / (9/10)
= (4/10) * (10/9)
= 4/9
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Agatha made a five-digit number with 0.3.5.8 and 9. The number is
bigger than 39 and smaller than 53. The thousandths digit is 3 times the
tenths digit. What number did Agatha make?
help pls
Answer:
92
Step-by-step explanation:
Use the distributive property to multiply, combine like terms & find the equations
34(x + 5) - 2(x+5)
Answer:
32+160
Step-by-step explanation:
Which complex number has an absolute value of 5?
–3 + 4i
2 + 3i
7 – 2i
9 + 4
Answer:
Step-by-step explanation:
-3 + 4i
value = square( (-3)^2 + (4i)^2 ) = sqr(9 + 16) = sqr(25) = 5
The absolute value is like the Pythagoras theorem
9 in
11 in
5 ft
19 in
12 in
Surface
Surface Area =
9)
3)
I need the surface area some please help
Answer:
730 in cubed
Step-by-step explanation:
hope this helps
have a good day
Briefly define product possibility curve with a suitable illustration.
The Production Possibility Curve is a graphical representation that illustrates the different combinations of two goods that can be produced within an economy using available resources and technology.
It demonstrates the concept of trade-offs and opportunity costs that arise when resources are allocated between the production of different goods.
The PPC is typically shown as a curve on a graph with one good plotted on the x-axis and the other on the y-axis. The curve represents the maximum attainable production levels of both goods given the available resources, technology, and efficiency. The shape of the curve is concave, indicating increasing opportunity costs.
The PPC demonstrates the fundamental economic principle of scarcity, as it shows the limited nature of resources and the need to make choices. Points on the curve represent efficient allocation of resources, while points inside the curve represent underutilization of resources, and points outside the curve are unattainable with the given resources.
The PPC helps economists analyze production efficiency, resource allocation, and the potential for economic growth by understanding the trade-offs between different goods or services.
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when the angle of an incline with a block resting on it increases the normal support force? A) decreases B) increases C) stays the same
Answer:
normal force decreases
Step-by-step explanation:
N=mgcosθ, and cosine decreases as theta increases
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Answer:
A) decreases
Step-by-step explanation:
As the angle of the incline increases, the normal force decreases, which decreases the frictional force. The incline can be raised until the object just begins to slide.
Make a parabola that is 3 units to the right from the original one. It should have the same shape and size as the red one except have a vertex of (3, 0).
90 girls and boys have planned for an educational tour. They are in a ratio of 3 girls 6 to boys. How many girls are there?
Answer:
30 girls 60 boys
Step-by-step explanation:
Two angles of a triangle measure 12 degrees and 40 degrees. What is the measurement of the third angle of the triangle
Answer:
128
Step-by-step explanation:
A triangle's angles must add up to 180 degrees, so 180 = 40 + 12 + x which is the same as 180 - 40 - 12 = x
x = 128
Answer: 128 degrees
Step-by-step explanation:
ANSWER IMMEDIATELY
Which of the following best describes the number of solutions to the system of equations shown below?
2x+y=3
-4x-2y=-6
Answer:
2*1/2+2=3
-4x-2y=-6 is x=−1/2y+3/2
Step-by-step explanation:
9x-y=17 and 5x+4y=-27 solve by substitution
Answer:
(1, -8)
Step-by-step explanation:
Solve by Substitution
9x − y = 17 and 5x + 4y = −27
Solve for y in the first equation.
y = −17 + 9x 5x + 4y = −27
Replace all occurrences of y with −17 + 9x in each equation.
Replace all occurrences of y in 5x + 4y = −27 with −17 + 9x. 5x + 4 (−17 + 9x) = −27
y = −17 + 9x
Simplify 5x + 4 (−17 + 9x).
41x − 68 = −27 y = −17 + 9x
Solve for x in the first equation.
Move all terms not containing x to the right side of the equation.
41x = 41
y = −17 + 9x
Divide each term by 41 and simplify.
x = 1
y = −17 + 9x
Replace all occurrences of x with 1 in each equation.
Replace all occurrences of x in y = −17 + 9x with 1. y = −17 + 9 (1)
x = 1
Simplify −17 + 9 (1).
y = −8
x = 1
The solution to the system is the complete set of ordered pairs that are valid solutions.
(1, −8)
The result can be shown in multiple forms.
Point Form:
(1, −8)
Equation Form:
x = 1, y = −8
please help!!/!/!/&///8:&2
Use graphing to find the x-coordinate of the solution to each system.
y=-x+4
y=-6x-6
A) -3
B) 2
C) -2
D) Infinite number of solutions
Answer:
-2
Step-by-step explanation:
plug both equations in desmos graphing calculator website
and you can see that the solution (where both equations intersect)
is (-2,6)
solutions are (x,y)
so the x coordinate of the solution is -2
3
Select the correct answer.
Which statement best describes the solution to this system of equations?
3x + y= 17
x+2y= 49
OA.
It has no solution.
B.
It has infinite solutions.
O c.
It has a single solution: x = 15, y= 17.
OD
It has a single solution: x= -3, y = 26.
Answer:
X= –3, y=26
Step-by-step explanation:
3X+Y=17====> –2(3X+Y)=–34===> –6X–2Y=–34
X+2Y=49
Aight so let's head to the sum
–5X=15===> X=–3
–3+2Y=49===> 2Y=52===> Y=26
Which relation is displayed in the table?
A: {(-2, -3), (1, -1), (2, -2), (3, 3)}
B: {(-3, -2), (-1, 1), (2, -2), (3, 3)}
C: {(-2, -3), (-1, 1), (-2, 2), (3, 3)}
D: {(-2, -3), (-1, 1), (-2, -2), (3, 3)}
The relation displayed in the table is
B: {(-3, -2), (-1, 1), (2, -2), (3, 3)}How to find the relation in the tableThe relation in the table is compared by identifying how a coordinate point are expressed as ordered pair and how they are expressed as a table
For instance, say (b, c) is represented in a table as
x y
a b
Using this instance and writing out the values in the table we have
(3, 3), (-1, 1), (2, -2), and (-3, 2)
This is similar to option B making option B the appropriate option
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Karla está haciendo volar su cometa. Ha soltado ya 53 m de hilo y sabe que el ángulo que forma la cuerda de la cometa con la horizontal es de 48º. Supuesto que la cometa está atada al suelo, ¿a qué altura se encuentra la cometa?
The comet is located at a height of around 40.32 metres above the ground. We may use trigonometry and the seno and coseno trigonometric functions to solve this problem.
We may use trigonometry and the seno and coseno trigonometric functions to solve this problem. First, we drew a diagram that illustrates the situation:
perl A \s /| \s / | \s / | h \s / | \s / θ | \s / | \s / | \s / | \s /_______| \s d
Donde:
C is the comet's position in the atmosphere, and K is Karla's position on the ground.
The horizontal distance between Karla's position and the comet is equal to x.
h is the height of the comet above the ground.
is the angle that joins the comet's horn to the horizontal.
Using trigonometric functions, the following can be written:
Cos() = x / 53m = x = 53m * cos() Sen() = h / 53m = h = 53m * sen()
substituting the known values:
53m * Sen(48o) = 40.32 m, 53m * Cos(48o) = 35.78 m, and 53m * X = 35.78 m
Hence, the comet is located at a height of around 40.32 metres above the ground.
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A 19 ft rope is tied from the top of a tent pole to a stake 11 ft away. To the nearest degree, what is the angle of elevation from the stake up to the tent pole?
The angle of elevation from the stake up to the tent pole is, 54.55°.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecen/hypotenuse and
tan = opposite/adjacent.
Given, A 19 ft rope is tied from the top of a tent pole, It is the hypotenuse length.
Also, The state is 11 feet away and it is the adjacent length.
We know, cos = adjacent/hypotenuse.
cos = 11/19.
Ф = cos⁻¹(0.58).
Ф = 54.55°.
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What is the answer to this question? There is 10 points available.
Answer:
0.20
Step-by-step explanation:
.....
A batch of 500 machined parts contains 10 that do not conform to customer requirements.Parts are selected succesively, without replacement, until a nonconforming part is obtained. Determine the range (possible values) of the random variable giving the number of parts selected.
The range (possible values) of the random variable giving the number of parts selected is from 1 to 10.
The random variable X represents the number of parts selected until a nonconforming part is obtained. X can take values from 1 to 11, since if the first part selected is nonconforming, X=1 and if the 10th part selected is the first nonconforming part, then X=10.
To see this, we can consider the following cases:
If the first part selected is nonconforming, then X=1.
If the first part selected is conforming and the second part selected is nonconforming, then X=2.
If the first two parts selected are conforming and the third part selected is nonconforming, then X=3.
Similarly, we can continue this process until we select the 10th part, which is the first nonconforming part.
Therefore, the range of the random variable X is 1 to 10, inclusive.
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determine the intercepts of line.
do not round answers.
The y-intercept is (0, -20) and the x-intercept is (20, 0).
what is an algebraic expression?
An algebraic expression is a mathematical phrase consisting of variables, numbers, and mathematical operations. It can include variables (such as x, y, or z), constants (such as 2, 3, or 4), and operators (such as +, -, *, or /) that combine these elements.
For example, 2x + 3y - 4 is an algebraic expression that contains the variables x and y, the constants 2, 3, and 4, and the operators + and -. It does not contain an equal sign and does not represent an equation, but it can be simplified or evaluated for specific values of the variables. Algebraic expressions are commonly used in algebra and other branches of mathematics to represent mathematical relationships and solve problems.
The given equation is y = -32 + 12.
To find the y-intercept, we set x = 0 and solve for y:
y = -32 + 12
y = -20
So the y-intercept is (0, -20).To find the x-intercept, we set y = 0 and solve for x:
0 = -32 + 12
20 = x
So the x-intercept is (20, 0).
Therefore, the y-intercept is (0, -20) and the x-intercept is (20, 0).
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Find the measure of the angle x. Round to the nearest tenth if necessary?
Answer:
x = 28.1°
Step-by-step explanation:
Cos = adjacent side/hypotenuse
cos x = 15/17
x = arccos (15/17)
= 28.1°
Note: If you memorize all the definitions of the trig functions, then these kinds of problems are much easier. OK?
Evaluate the indefinite integral. Use a capital " C " for any constant term. ∫(3ex+4x5−x34+1)dx= TIP Enter your answer as an expression. Example: 3x∧2+1,x/5,(a+b)/c Be sure your variables match those in the question
The equatiion where C is the constant of integration.To evaluate the indefinite integral ∫(3e^x + 4x^5 - x^3/4 + 1)dx, we can integrate each term separately.
∫3e^x dx = 3∫e^x dx = 3e^x + C₁
∫4x^5 dx = 4∫x^5 dx = 4 * (1/6)x^6 + C₂ = (2/3)x^6 + C₂
∫-x^3/4 dx = (-1/4)∫x^3 dx = (-1/4) * (1/4)x^4 + C₃ = (-1/16)x^4 + C₃
∫1 dx = x + C₄
Now, we can combine these results to obtain the final answer:
∫(3e^x + 4x^5 - x^3/4 + 1)dx = 3e^x + (2/3)x^6 - (1/16)x^4 + x + C
Therefore, the indefinite integral of (3e^x + 4x^5 - x^3/4 + 1)dx is:
∫(3e^x + 4x^5 - x^3/4 + 1)dx = 3e^x + (2/3)x^6 - (1/16)x^4 + x + C
where C is the constant of integration.
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the perimeter of a curch window is 60 inches if the window is in the shape of a regular pentagon, what is the lengh of each side of the window
Answer:
12 in
Step-by-step explanation:
A regular pentagon has 5 sides of equal length.
Length of one side = total perimeter ÷ number of sides
= 60 ÷ 5 = 12
Therefore, the length of each side of the window is 12 in
A right triangle has a base of 14.3 cm, a slant height of 21.75 cm, and a height of 15 cm. What is the area of the triangle?
Answer:
107.25cm²
Step-by-step explanation:
Area of triangle = 0.5 * base * height
Base = 14.3 cm
Height = 15 cm
Hence, Area of triangle :
Area = 0.5 * 14.3 * 15
Area = 107.25cm²
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A
Find the values of x and y.
B
vo
xo
47°
D
C
Drawing not to scale
The angle measures in this problem are given as follows:
x = 43º.y = 66.5º.What are the angle measures?The sum of the measures of the internal angles of a triangle is of:
180º.
The internal angles of isosceles triangle ABC are given as follows:
Two measures of 47º, as the equivalent sides on the isosceles triangle have angle measures of 47º.One measure of 2y, as y is the angle of the bisection AD of angle 2y, dividing the angle 2y into two angles of equal measure.Hence the value of y is obtained as follows, applying the sum of the internal angles of the triangle.
2y + 2 x 47 = 180
2y = 180 - 94
y = (180 - 94)/2
y = 43º.
The bisection forms a right angle, hence the value of x is given as follows:
x = 90º.
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A pair of jeans at a local retail store has a cost of $32.00. If the sales tax is 5.3%, what is the total amount paid for the jeans?
The total amount that a customer will pay for the jeans is $33.696.
How to calculate the value?From the information given, pair of jeans at a local retail store has a cost of $32.00. If the sales tax is 5.3%,
The value of the sales tax will be:
= Sales percentage × Amount
= 5.3% × $32
= $1.696
The total amount paid will be:
= Cost + Tax
= $32 + $1.696
= $33.696
The amount is $33.696.
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please help me with this Pythagoras theorum
Step-by-step explanation:
18 m = hypotenuse = c
5 m = b
a² + b² = c²
a² + (5)² = (18)²
a² + 25 = 324
a² = 324 - 25
a² = 299
a = √299
a = 17.29 or 17.3 m
perimeter = a + b + c
= 17.3 + 18 + 5
= 40.3 m
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