Statement Reason
∠1 = ∠2, WX = ZY Given
WP = ZP converse of isosceles triangle theorem
△WXP ≅ △ZYP SAS
XP = YP CPCT
∠3 = ∠4 Isosceles triangle teorem
What is the isosceles triangle?
A triangle's corresponding angles are congruent if its two sides are.
Given that ∠1 = ∠2, WX = ZY.
Statement 1 is given.
According to the converse of the isosceles triangle theorem:
WP = ZP
SAS rule: If the two sides and an included angle of one triangle match the two sides and an included angle of the other, then two triangles are said to be congruent. This is referred to as SAS congruency.
In triangles △WXP and △ZYP:
∠1 = ∠2
WX = ZY.
WP = ZP
According to SAS rule, △WXP ≅ △ZYP
By CPCT, XP = YP
Again the isosceles triangle theorem ∠3 = ∠4.
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3. Which statement about parallel lines cut by a transversal is NOT true?
When two parallel lines are cut by a single transversal, 8 angles are created.
A transversal cuts through a set of parallel lines.
Parallel lines have identical slope values. A transversal will have a different slope value.
Parallel lines and their transversal all have equal slopes.
Answer:
Parallel lines and their transversal all have equal slopes.
Step-by-step explanation:
I say this is wrong because the slope of parallel lines is equal but the transversal has a different slope.
1. Assume you are on an island inhabited only by knights and knaves, where knights always tell the truth and knaves always lie. You encounter two people, A and B. Determine, if possible, what A and B are if they address you in the ways described. a. A says "The two of us are both knights" and B says "A is a knave." b. A says "At least one of us is a knave" and B says nothing.
a. If A says "The two of us are both knights" and B says "A is a knave," then we know that one of them must be lying, and thus that one of them is a knave. However, we cannot determine from this information alone which of them is the knave and which is the knight.
b. If A says "At least one of us is a knave" and B says nothing, then we know that one of them is a knave, but we cannot determine from this information alone which of them is the knave and which is the knight.
POSSIBILITY SCENARIOIn the first scenario, person A claims that both he and person B are knights, which is a true statement if A is a knight. However, person B says that A is a knave, which means that A is a liar. These statements contradict each other, so we know that one of them is not telling the truth and is therefore a knave. But we cannot determine which one of them is the knave, because we don't have enough information.
In the second scenario, person A says that at least one of them is a knave, and person B remains silent. This means that A could be telling the truth, or could be lying. If A is a knight, then he is telling the truth and at least one of them, B, is a knave. But if A is a knave, then he could be lying and both of them could be knights. So we don't have enough information to know who is a knave and who is a knight.
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Which graph correctly shows the solution to the inequality
7- 3> 8-2003 Show or explain
your reasoning.
The given inequality can be correctly shown in the graph containing all the numbers greater than or equal to 3. The correct option is (D).
What is a number line?A number line is a graphical representation of numbers on a line.
The number line has one convention that the positive numbers are always on the right side of the origin and the negative numbers are on the left side.
The inequality is given as below,
[tex]\frac{7x-3}{9} \geq 8 - 2x[/tex]
It can be solved as follows,
[tex]\frac{7x-3}{9} \geq 8 - 2x[/tex]
Multiply both sides by 9 to get,
⇒ 7x - 3 ≥ 9(8 - 2x)
⇒ 25x ≥ 75
⇒ x ≥ 3
It implies that the solution is the set of numbers greater than or equal to 3.
Hence, the solution of inequality is obtained as number line satisfying x ≥ 3.
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I know where u stay;)
Answer:
ok
Step-by-step explanation:
Whats the answer for this
the value of the Perpendicular distance of F from Chord AB is 10.
What is the right-angle triangle?A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.
Given a circle, Where F makes a right angle triangle with the chord CD and also with Chord AB.
We know that,
Equal chords of a circle are equidistant from the center of a circle.
Here,
Chords AB and CD are equal to 18.
So, Chords AB and CD are equidistant from F(center of the circle).
Thus, x = 10
therefore, the value of the Perpendicular distance of F from Chord AB is 10.
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If A(2,3),B(4,6),C(7,4) and D(a,b) are vertices of quadrilateral
It can be concluded that the given coordinates of A(2,3), B(4,6), C(7,4) and D(a,b) can be used to determine the length of the sides as well as the angles of the quadrilateral ABCD.
What is quadrilateral?A quadrilateral is a four-sided polygon with four angles. It is a two-dimensional shape that is bounded by four line segments, each of which is called a side. The sum of the angles of a quadrilateral is 360 degrees. Types of quadrilaterals include rectangles, squares, trapezoids, parallelograms, and kites.
First of all, ABCD is a quadrilateral, which means it has four sides and four vertices. A, B, C and D are the vertices of this quadrilateral. It can be seen that A(2,3), B(4,6), C(7,4) and D(a,b) given in the question are coordinates of the vertices. Therefore, from these coordinates, we can conclude that A, B, C and D are the vertices of the quadrilateral ABCD.
Moreover, these coordinates can also be used to determine the length of the sides of the quadrilateral. The distance between A and B can be calculated by using the Pythagorean theorem. Similarly, the lengths of other sides can also be calculated by using the same theorem. Furthermore, the coordinates will also help us to calculate the angles formed by the sides of the quadrilateral ABCD.
Therefore, it can be concluded that the given coordinates of A(2,3), B(4,6), C(7,4) and D(a,b) can be used to determine the length of the sides as well as the angles of the quadrilateral ABCD.
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complete questions as follows-
If A(2,3),B(4,6),C(7,4) and D(a,b) are vertices of quadrilateral prove its true.
8 dm to 3.2 dm
pls helppp
Answer:
8 dm decreased 60%
Step-by-step explanation:
8-3.2=4.8
4.8/8=0.6
0.6=60%
Hallie and Mattie donated blue jeans to the clothing drive. Hallie donated 3 pairs of blue jeans. Mattie donated 6 pairs of blue jeans. Write a ratio to represent the relationship between Hallie's donation of jeans and Mattie's donation of jeans.
3:15
3 over 9
1:2
6 to 18
The ratio to represent the relationship between hallies donation of jeans and Mattie’s donations of jeans is C 1:2.
What is the ratio to represent the relationship?The ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
In this situation, Hallie donated 3 pairs of blue jeans. Mattie donated 6 pairs of blue jeans.
The ratio to represent the relationship between hallies donation of jeans and Mattie’s donations of jeans will be:
= 3/6
= 1/2
= 1:2
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Answer:
c
Step-by-step explanation:
I got right on the quiz
A dog kennel charges $30 per night to board your dog and $6 for each hour of playtime. The amount of money you spend is given by 30x+6y=180, where x is the number of nights and y is the number of hours of playtime. Graph the equation and interpret the intercepts. Keyboard Instructions Initial graph state The horizontal axis goes from -0.9 to 10.4 with ticks spaced every 1 unit(s). The vertical axis goes from -3.9 to 34.4 with ticks spaced every 5 unit(s).
The graph of the equation 30x+6y=180 will be a line in the xy-plane.
What is equation?An equation is a mathematical statement that expresses the equality of two expressions. It is composed of one or more terms and an equal sign, and can contain constants, variables, and operators. Equations are used to represent relationships between different values, quantities, and objects, and to solve for unknowns. Equations are a fundamental tool of mathematics and can be used to describe physical processes as well as abstract concepts.
The line will pass through the origin, since the equation is satisfied when both x and y are 0. The intercepts of the line on the x-axis and y-axis represent the values of x and y that will make the equation true, regardless of the values of the other variable.
For this equation, the y-intercept is 30, since when x=0, the equation becomes 30(0)+6y=180, and so y=30. This means that if you do not board your dog, you would need to play with it for 30 hours in order to meet the requirement of spending a total of 180 dollars.
The x-intercept is 6 since when y=0, the equation becomes 30x+6(0)=180, and so x=6. This means that if you do not play with your dog, you would need to board it for 6 nights in order to meet the requirement of spending a total of 180 dollars.
Therefore, the graph of the equation 30x+6y=180 shows that it is possible to meet the requirement of spending a total of 180 dollars either by boarding your dog for 6 nights or by playing with it for 30 hours, regardless of the values of the other variable.
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PLS HELP WILL MARK BRAINIEST
The given figure is a polygon, a quadrilateral and a trapezoid.
What is a polygon?A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.
Given is a figure,
The figure is a polygon, a quadrilateral and a trapezoid.
It can not be a parallelogram, rhombus or a rectangle, because none of their properties are shown in the figure.
Hence, the given figure is a polygon, a quadrilateral and a trapezoid.
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Identify the focus and directrix of the parabola represented by the equation (y-3)^2=-4(x 3)
The focus is at (3,3+1/4) and the directrix is the equation of a line is 2.75.
A parabola is defined as the set of all points that are equidistant to the focus (F) and the directrix (d).
In the case of this parabola represented by the equation (y-3)² = 4(x-3), the vertex is located at the point (3,3) which means that this parabola opens horizontally to the left. Since the coefficient of x² is positive the parabola opens up.
The focus is located at the point (3,3+1/4) which is (3,3.25) and the directrix is the line x = 2.75. These two elements are crucial in understanding the shape and behavior of the parabola, The focus is where the parabola bends, and the directrix is where it opens.
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The owner of a movie theater was counting the money from I day's ticket sales. He knew that a total of 150 tickets were sold. Adult tickets cost $7 each and children's tickets cost $4 each. II the total receipts for the day were $855, how many of each kind of ticket were sold?
The solution to the system of equations are
The number of adult tickets x = 85
The number of children's ticket y = 65
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first equation be represented as A
Let the number of adult tickets be = x
Let the number of children's tickets be = y
A total of 150 tickets were sold
Substituting the values in the equation , we get
x + y = 150 be equation (1)
And , Adult tickets cost $7 each and children's tickets cost $4 each
So , 7x + 4y = 855 be equation (2)
Multiply equation (1) by 7 , we get
7x + 7y = 1050 be equation (3)
Subtracting equation (2) from equation (3) , we get
3y = 1050 - 855
3y = 195
Divide by 3 on both sides of the equation , we get
y = 65
Substitute the value of y in the equation (1) , we get
x + 65 = 150
Subtracting 65 on both sides of the equation , we get
x = 150 - 65
x = 85
Hence , the number of adult tickets x is 85 and the number of children's ticket y is 65
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What is the measure of ∠a? ° what is the measure of ∠b? °
Angle a is 18 degrees.
The Mesure of ∠b ⇒∠B=180∘−120∘=60∘
Answer:
A = 72
B = 108
Step-by-step explanation:
5y - 3 = 3y + 27
5y - 3y = 27 + 3
2y = 30
y = 30/2 = 15
A = 5y - 3 = 5(15) - 3 = 72
B = 180 - 72 = 108
Find the value of x
Answer:
2x + 1 = 79 (being alternate angel )
2x = 79-1
2x = 78
x = 78/2
x = 39
For which list of ordered pairs is y a function of x?
A.(7,-7), (-7,-5), (-7,-3), (-7,-1)
B.(-3, 9), (0, 0), (0, 9), (3, 12)
C. (6, 8), (10, 8), (15,-7), (16, 0)
D. (11, -2), (12, 1), (13,-4), (13, 9)
The option (A) (7,-7), (-7,-5), (-7,-3), (-7,-1) ordered pair is y a function of x.
What is a function?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.
In a mathematical relation, for a given value of x, there can only be one unique value of y.
It is a requirement that a function must follow.
In option A, the x values are all different, so y is a function of x
In option B, there are two (0,0) and (0,9) which means for x=0 there are two possible values of y, thus y is not a function of x.
In option C, there is a repetition of the x-value, 15, so y is not a function of x
In option D, there is a repetition of the x-value, 13, so y is not a function of x.
So, the correct option is A (7,-7), (-7,-5), (-7,-3), (-7,-1)
Hence, the option (A) (7,-7), (-7,-5), (-7,-3), (-7,-1) ordered pair is y a function of x.
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Alex’s school is selling tickets to their spring musical. Each student ticket costs $10, and each senior citizen ticket costs $5. If the school sold 55 total tickets for $425 on their first day of sales, how many student tickets (x) and senior citizen tickets (y) were sold?
Natalia spent an eighth of the money in her
account on a shopping spree plus an
additional $20 on gas. If she spent $320, how
much did she originally have in her account?
Answer:
2420
Step-by-step explanation:
since it’s an eighth, you need to multiply 300 by 8 but not 320 since it’s separate. so you get 2400 but then add the 20 and get 2420
Wich of this relations is a function?
Pls Help
The relations depicted in graph 1 is a function as every input value has exactly one output value.
What are functions?A relation called a function is one in which every potential input value results in exactly one possible output value. They are set of ordered pairs.
What are relations?Relations indicate the relationship between the indicated input and output value.
Graph 1:
In graph 1 each input value has exactly one output hence relations in graph 1 is a function.
Graph 2:
Graph 2 represents a circle, in this each input value does not have exactly one output value and hence it is not a function.
Graph3:
In graph 3, each input value does not have exactly one output value and hence it is not a function.
Graph 4:
In graph 4, each input value does not have exactly one output value and hence it is not a function.
Hence, relations in graph 1 is a function.
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Solve for y 6x+2y=10
On solving the provided question, we can say that - the value of the following equations is 6(0) + 2y = 10y = 5
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
here,
6x + 2y = 10
so, x = 0;
6(0) + 2y = 10
y = 5
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100pts and Brainiest
Jabez worked at Wendy's and earned $11.50 per hour. If he worked a full work week, what would be his gross pay?
Question 5 options:
$400
$455
$465
$460
A minor league baseball stadium offers general admission seats and premier seats. During the season opener, the stadium sold 1,348 tickets and had $12,748.30. The price of a premiere seat was 30% more than the $8.50 general admission seat. How many premiere seats and how many general admission seats were sold for the season opener?
The number of general admission seat sold is 842 and the number of premiere seat sold is 506.
How many of each seats were sold?The system of equations that represent the information provided in the question are:
a + b = 1348 equation 1
8.5a + (1.30 x 8.5)b = 12,748.30
8.5a + 11.05b = 12,748.30 equation 2
Where:
b = number of premiere seat solda = number of general admission seat soldThe elimination method would be used to solve these equations
Multiply equation 1 by 8.5
8.5a + 8.5b = 11,458 equation 3
Subtract equation 3 from equation 2
1290.30 = 2.55b
b = 1290.30 / 2.55
b = 506
Substitute for b in equation 1 :
a + 506 = 1348
a = 1348 - 506
a = 842
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Solve the equation.
20=r+11
r=?
Answer:
9
Step-by-step explanation:
The answer is 9
Answer: 8
Step-by-step explanation:
20=r+11
-11 -11
8=r
When a rational number and an
irrational number are multiplied, the
product is always ___.
Answer: irrational number
Step-by-step explanation:
Explain how to solve: 3(9+4a)−19=32
step by step
Answer:
First, distribute the 3 on the left side of the equation: 3 * 9 + 3 * 4a - 19 = 32
Next, combine like terms on the left side of the equation: 27 + 12a - 19 = 32
Add 19 to both sides of the equation to isolate the variable term: 27 + 12a = 51
Subtract 27 from both sides of the equation to isolate the variable term: 12a = 24
Divide both sides of the equation by 12 to solve for the value of "a": a = 2
So the solution to the equation is "a = 2".
Step-by-step explanation:
rika gives away samples of a new fragrance and a new scented hand lotion to customers. she must hand out a total of 114 samples during her shift she has already handed out 36 samples which represent 1/3 the number of fragrances samples and 1/4 the number of hand lotion samples she must hand out, write a system of equations for this problem situation.
Answer:
Let F be the number of fragrance samples and L be the number of hand lotion samples.
We know that F + L = 114, since Rika must hand out a total of 114 samples.
We also know that F = (1/3)L and L = (1/4)F, since the number of fragrance samples is 1/3 of the number of hand lotion samples, and the number of hand lotion samples is 1/4 of the number of fragrance samples.
Substituting the second equation into the first equation, we get:
F + (1/4)F = 114
Combining like terms, we get:
(5/4)F = 114
Dividing both sides by (5/4), we get:
F = 92
Substituting this value back into the second equation, we get:
L = (1/4)(92) = 23
Therefore, the system of equations is:
F + L = 114
F = (1/3)L
L = (1/4)F
The solution to this system is F = 92 and L = 23
Find length of third side help please
Length of third side = 10 units.
What is Pythagorean theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.
Here, given that,
Height = 7 units
Base = √51 units
And, we have, it is a right angle triangle
and we have to find the hypotenuse.
By Pythagorean theorem we get,
Hypotenuse = √7²+ 51
=√100
=10 units.
Hence, Length of third side = 10 units.
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. Which theorem can be used to determine whether a function f(x) has any zeros in a given interval? O A. Rolle's Theorem OB. Intermediate value theorem O C. Extreme value theorem OD. Mean value theorem
The correct answer is the Intermediate value theorem (Option B).
The Intermediate Value Theorem states that if a function is continuous on a closed interval [a, b], then for any value y between the minimum and maximum values of the function on that interval, there exists at least one x-value in the interval such that f(x) = y. In other words, if f(x) is a continuous function on a closed interval, then for any value y between the minimum and maximum values of the function on that interval, there exists at least one x-value in the interval such that f(x) = y, or in other words if a function is continuous in an interval [a,b], any zero of the function must be in that interval.
Therefore, The correct answer is the Intermediate value theorem (Option B)
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If x:y = 1/2:1/3 and y:z = 1/5:1/6, find x:y:z
The value of the ratio x : y : z is 1/2 : /3 : 5/18
How to determine the ratioFrom the question, we have the following parameters that can be used in our computation:
x:y = 1/2:1/3 and y:z = 1/5:1/6
Express the ratio properly
So, we have the following representation
x : y = 1/2 : 1/3 and y : z = 1/5 : 1/6
Multiply the ratio y : z = 1/5 : 1/6 by 5/3
So, we have
y : z = 1/3 : 5/18
So, we have
x : y : y : z = 1/2 : 1/3 : 1/3 : 5/18
Remove the repetition
This gives
x : y : z = 1/2 : /3 : 5/18
Hence, the ratio is 1/2 : /3 : 5/18
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A sequence is defined by the term-to-term rule
U(n+1) = U₁² +3
Given that u0= 1,
a) find u₁
b) find u₂
c) find u3
The terms of sequences are u₁ = 4, u₂ = 19 and u₃ = 364.
What is a sequence?An ordered list of things is a sequence (or events). Similar to a set, it has members (also called elements, or terms). The length of the sequence is the number of ordered items (potentially infinite).
Given:
A sequence is defined by the term-to-term rule
uₙ₊₁ = u₁² + 3
And u₀ = 1,
a). The second term
u₁ = u₀² + 3
u₁ = (1)² + 3
u₁ = 4
b). The third term
u₂ = u₁² + 3
u₂= (4)² + 3
u₂ = 19
c). The fourth term
u₃ = u₂² + 3
u₃ = (19)² + 3
u₃ = 364
Therefore, The values, u₁ = 4, u₂ = 19 and u₃ = 364.
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The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. Find the ratio of the volume of the balloon in both the cases.