Two parallelograms will be congruent only when all four corresponding sides are equal in length & one corresponding internal angle is equal.
What is mean by congruency?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
If two line segments are the same length, they are said to be congruent.If two angles have the same measure, they are said to be congruent.If two circles have the same diameter, they are congruent.If and only if two angles have equal measurements, they are said to be congruent. If and only if two segments have equal amounts of each, they are congruent. If and only if all of the corresponding angles and sides are congruent, two triangles are said to be congruent.
Two parallelograms will be congruent only when all four corresponding sides are equal in length & one corresponding internal angle is equal.Two rectangles are congruent if both of them have the opposite sides are equal. Two squares are congruent if both of them have the same edges.To learn more about congruency refer to:
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Because of friction and air resistance, each swing of a pendulum is a little shorter than the previous one. The lengths of the swings form a geometric sequence. Suppose the first swing of a pendulum has a length of 100 cm and the return swing is 99 cm .
b. What is the total distance traveled by the pendulum when it comes to rest?
The total distance traveled by the pendulum when it comes to rest is 10,000 cm.
Because of friction and air resistance, each swing of a pendulum is a little shorter than the previous one. The lengths of the swings form a geometric sequence. Suppose the first swing of a pendulum has a length of 100 cm and the return swing is 99 cm .
Now,
Given,
On the first swing, the distance traveled is 100, and on the second swing, the distance is 99.
The first term of the geometric sequence is, a1 = 100
The second term of the sequence is, a2 = 99
The common ratio r = 99/100
Therefore, the expression for the n-t h term of the sequence is:
a_n = 100*(99/100)^(n-1)
Theoretically, using this formula, it would take an infinite number of trips to come to rest.
Hence we need to find the sum of the series a_n = 100*(99/100)^(n-1) from n=1 to n=infinity.
The sum of an infinite series is given by S = a/(1-r) where a=the first term and r=the common ratio.
Therefore,
the total distance traveled is S = 100/(1-(99/100) = 100/0.01 = 10,000 cm
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You want to join a new pool. Beckett Pool charges a $90 membership fee and $25 per month. Lakota Hills Pool charges a $45 membership fee and $40 per month. After how many months is the total cost the same at both pools?
Answer:
3
Step-by-step explanation:
if m is the number of months
Beckett: 90 + 25m
Lakota Hills 45 + 40m
so 90 + 25m = 45 + 40m
40m - 25 = 90 - 45
15m = 45
m = 45/15 = 3
Pleas help I need to pass
Answer:
?
Step-by-step explanation:
Maths
m solving/reasoning
The length of each side of a regular hexagon is 4.7cm to 1 decimal place
Write the error interval for the perimeter, P
27.9 cm≤ perimeter ≤28.5cm
The length of the regular hexagon is 4.7cm to 1 decimal place, i.e.,
4.65≤ length≤4.75
As we know the number of sides of a regular hexagon is 6
So the perimeter for the upper bound of length = 6×4.65
= 27.9cm
The lower bound of length perimeter = 6× 4.75
= 28.5cm
Therefore the interval of the perimeter of a regular hexagon is:
27.9cm ≤ perimeter ≤ 28.5cm
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Find the eighth term of each geometric sequence. 2/3, 4/9, 8/27 . . . . .
The eighth term of the given geometric sequence is 256/6561.
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Given: 2/3, 4/9, 8/27...
As we can observe, each successive term of the geometric sequence is 2/3 of the previous one.
Thus, r = 2/3 and a₁ = 2/3.
The formula used to find the nth term of a geometric sequence is given by: [tex]a_n=a_1(r^{n-1})[/tex]
For n = 8, [tex]a_8=\frac{2}{3}(\frac{2}{3})^7=\frac{2}{3}^8=\frac{256}{6561}[/tex]
Thus, the eighth term of the given geometric sequence is 256/6561.
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Explain why classifying an equiangular triangle as an acute equiangular triangle is unnecessary.
Classifying an equiangular triangle as an acute equiangular triangle is unnecessary because by definition, all angles are 60°
What is an equiangular triangle?An equiangular triangle is one with three equal sides and three equal angles, all of which are measured at 60 degrees. Given that the characteristics of both triangles are the same, an equiangular triangle can also be referred to as an equilateral triangle.
This triangle is regarded as a regular polygon because its sides and angles are both equal. Equiangular refers to angles that are all equal.
All triangles have 3 angles that together total 180 degrees. Because an equilateral triangle has equal sides, its angles can only be 60 degrees. This entails that all angles must be acute. It is not required to write that it is intense because of this.
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An architectural drawing has a scale of 2 in: 5 ft. If the living room is 15ft by 18ft in real life, what is the area in the drawing?
Answer: 7.5
Step-by-step explanation: 15 ft * 2 in/ft = 30 in18 ft * 2 in/ft = 36 inso area on plan = 30*36 = 1080 in^2on the real size area = 15*18 = 270 ft^2well to compare them change in^2 to ft^2there are 12 in /ftso 144 in^2 per ft^2so1080 in^2 *1 ft^2/144 in^2 = 7.5 ft^2or you could say30 in = 30/12 ft36 in = 3 ftarea = 90/12 ft^2 = 7.5 ft^2 luckily :)
Helpppp it is due at 11:59
Answer: x<1
Step-by-step explanation:
add 12 to both sides, divide by 2 on both sides.
Kahoe says he is thinking of a four-digit number in which all digits are the same. The value of the digit in the hundreds place is 600. what is the numnber?
Answer:
6,666
Step-by-step explanation:
A four-digit number: 1,234
All digits are the same: 1111, 2222, 3333...
Value in the hundreds place: 0,600
Answer: 6,666
Which lines are parallel to the graph of 4x – y = 6? Check all that apply.
x – 4y = –12
y – 2 = –4(x + 1)
y + 1 = 4(x – 2)
y = 4x + 11
y = x – 3
8x – 2y = 6
Answer: Options 3, 4, 6
Step-by-step explanation:
[tex]4x-y=6 \\\\-4x+y=-6\\\\y=4x-6[/tex]
This means are looking for lines with a slope of 4 (since parallel lines have the same slope).
x – 4y = –12: This rearranges to y=0.25x+3, so the slope is 1/4.y – 2 = –4(x + 1): This has a slope of -4.y + 1 = 4(x – 2): This has a slope of 4.y = 4x + 11: This has a slope of 4.y = x – 3: This has a slope of 1.8x – 2y = 6: This rearranges to y=4x-3, so the slope is 4.Answer:
Which lines are parallel to the graph of 4x – y = 6? Check all that apply.x – 4y = –12y – 2 = –4(x + 1)y + 1 = 4(x – 2)y = 4x + 11y = x – 38x – 2y = 6
Step-by-step explanation:
Which lines are parallel to the graph of 4x – y = 6? Check all that apply.x – 4y = –12y – 2 = –4(x + 1)y + 1 = 4(x – 2)y = 4x + 11y = x – 38x – 2y = 6
The history book cause 850
Given p(x)=−3(x−4)2+14, what is the value of p(2)?
PS you cant leave out exponents when typing questions without the attached photo. multiplying by 2 is not the dame as a exponent of 2. Use ^2 to show that a number is to the power of 2.
the value of p(2) in this equation is 2.
Answer:
p(2) = 2
Step-by-step explanation:
substitute x = 2 into p(x)
p(2) = - 3(2 - 4)² + 14
= - 3(- 2)² + 14
= - 3(4) + 14
= - 12 + 14
= 2
READING Jen's assignment is to read at least 85 pages of a novel. Jen has read 31 pages. How many pages p does Jen have left to read?
Inequality is [tex]p + 31 \ge 85[/tex]
Solution is [tex]p \ge 54[/tex]
===============================================
Explanation:
p = number of pages left to read
31 = number of pages already read
p+31 = total number of pages (unread + read)
This total must be 85 or larger, so that's how we end up with [tex]p+31 \ge 85[/tex]
To solve this inequality, we subtract 31 from both sides to end up with [tex]p \ge 54[/tex] which means Jen still needs to read at least 54 pages.
is -2/3 a natural number
Answer:
no it is not because natural numbers are whole numbers :)
hope this was helpful!
.5.1 The height AB (hint: Theorem of Pythagoras)
Answer: give me the context please
Step-by-step explanation:
Use the graph shown to complete the following sentence.
If (4, y ) is an ordered pair of the function, then y =
.
Answer: If (4, y ) is an ordered pair of the function, then y = 1
Step-by-step explanation:
The known x coordinate for the position (4,y) is 4.
We'll just refer to it as y since we don't know the y coordinate just yet.
On the x axis, trace a vertical line through 4 (see related remark below).
Thus in red (see attached image).
The red line crosses the graph at the point (4,1)
so this tells us that,
y = 1
Although it's helpful to see how it turns out, you are not need to draw a vertical red line.
You will be able to visually perceive the solution without these extra lines after you become accustomed to these kinds of situations.
Therefore,
If (4, y ) is an ordered pair of the function, then y = 1
y = 1
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solve for y 2x + 4y = -1
Answer:
y = -1/4 -x/2
Step-by-step explanation:
The solution is attached.
9/10 divided by 4/5 pls help
Robert buys cheese and lemons at the store.
He pays a total of $24.36.
He pays a total of $5.31 for the cheese.
He buys 5 bags of lemons that each cost the same amount.
●
●
Write and solve an equation which can be used to determine x, how much each bag of
lemons costs.
The equation is 24.36 = 5.31 + 5 * x and the cost of each bag of lemon is $3.81
How to write and solve an equation which can be used to determine x?The given parameters are:
He pays a total of $24.36.He pays a total of $5.31 for the cheese.He buys 5 bags of lemons that each cost the same amount.The above means that
Total = Cheese + Bags of lemon * 5
This gives
24.36 = 5.31 + 5 * x
Collect the like terms
So, we have
24.36 - 5.31 = 5 * x
Evaluate the like terms
So, we have
19.05 = 5 * x
Divide through by 5
So, we have
x = 3.81
Hence, the equation is 24.36 = 5.31 + 5 * x and the cost of each bag of lemon is $3.81
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Help me asap this is a quick one !
What is the value of the expression?
Answer:
13/6
Step-by-step explanation:
1 Simplify \sqrt{8}
8
to 2\sqrt{2}2
2
.
\frac{2}{6\times 2\sqrt{2}}\sqrt{2}-(-\frac{18}{\sqrt{81}})
6×2
2
2
2
−(−
81
18
)
2 Simplify 6\times 2\sqrt{2}6×2
2
to 12\sqrt{2}12
2
.
\frac{2}{12\sqrt{2}}\sqrt{2}-(-\frac{18}{\sqrt{81}})
12
2
2
2
−(−
81
18
)
3 Since 9\times 9=819×9=81, the square root of 8181 is 99.
\frac{2}{12\sqrt{2}}\sqrt{2}-(-\frac{18}{9})
12
2
2
2
−(−
9
18
)
4 Simplify \frac{18}{9}
9
18
to 22.
\frac{2}{12\sqrt{2}}\sqrt{2}-(-2)
12
2
2
2
−(−2)
5 Rationalize the denominator: \frac{2}{12\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{2\sqrt{2}}{12\times 2}
12
2
2
⋅
2
2
=
12×2
2
2
.
\frac{2\sqrt{2}}{12\times 2}\sqrt{2}-(-2)
12×2
2
2
2
−(−2)
6 Simplify 12\times 212×2 to 2424.
\frac{2\sqrt{2}}{24}\sqrt{2}-(-2)
24
2
2
2
−(−2)
7 Simplify \frac{2\sqrt{2}}{24}
24
2
2
to \frac{\sqrt{2}}{12}
12
2
.
\frac{\sqrt{2}}{12}\sqrt{2}-(-2)
12
2
2
−(−2)
8 Use this rule: \frac{a}{b} \times c=\frac{ac}{b}
b
a
×c=
b
ac
.
\frac{\sqrt{2}\sqrt{2}}{12}-(-2)
12
2
2
−(−2)
9 Simplify \sqrt{2}\sqrt{2}
2
2
to \sqrt{4}
4
.
\frac{\sqrt{4}}{12}-(-2)
12
4
−(−2)
10 Since 2\times 2=42×2=4, the square root of 44 is 22.
\frac{2}{12}-(-2)
12
2
−(−2)
11 Simplify \frac{2}{12}
12
2
to \frac{1}{6}
6
1
.
\frac{1}{6}-(-2)
6
1
−(−2)
12 Remove parentheses.
\frac{1}{6}+2
6
1
+2
13 Simplify.
\frac{13}{6}
6
13
Done
How are line symmetry and rotational symmetry related?
A symmetrical figure is one that is identical on both sides of a line. Rotational symmetry occurs when an object is rotated and retains the same appearance as the original figure.
Symmetry:
In common parlance, symmetry refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term "symmetry" has a more precise definition and is typically used to refer to an object that is invariant under certain transformations such as translation, reflection, rotation, or scaling.Rotational symmetry:
In geometry, rotational symmetry, also recognized as radial symmetry, is the property that a shape has when it looks the same after a partial turn rotation. The degree of rotational symmetry of an object is the number of distinct orientations in which it appears exactly the same for each rotation.Relation:
The relation between line symmetry and rotational symmetry is that s symmetrical figure is one that has the same appearance on both sides of a line. Rotational symmetry occurs when an object is rotated and retains its original appearance.Therefore, a symmetrical figure is one that is identical on both sides of a line. Rotational symmetry occurs when an object is rotated and retains the same appearance as the original figure.
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Would like the answer and an explanation.
Answer:
Step-by-step explanation:
triangles are similar so:
[tex]\frac{10}{10+14} = \frac{x}{36}[/tex]
24x=360
x=15
Can someone please help me I don’t understand and it’s a really important homework
Answer:
The large box weighs 18.75 and the small box weights 15.75
Step-by-step explanation:
We are looking to find 2 variables so we will need two equations.
Let l = the large box weight
Let s = the small box weight
7l + 9s + 273 5l +3s = 141
I want to add these two equations together and have one of the variables be eliminated. The way both equations are written now, neither variable will drop out. I see that 9 is a multiple of 3. If I multiply the second equation all the way through by - 3, the s variable will be eliminated.
-3(5l +3s) -3(141) Multiple everything by -3
-15l -9s = -423 Now I will add this to the original equation 7l + 9s = 273
7l + 9s = 273
-8l = -150 Divide both sides by -8
l = 18.75 This is the weight of the large box.
Plug in 18.75 to either of the ordinal equations to find the weight of the small box.
5l + 3s = 141
5(18.75) + 3s = 141 Distribute the 5
93.75 + 3s = 141 Subtract 93.75 from both sides
3s = 47.25 Divide both sides by 3
s = 15.75
Check:
Plug in 15.75 for s and 18.75 for l into both of the original equation to see if they equal.
7l + 9s = 273
7(18.75) + 9(15.75) =273
131.25 + 141.75 = 273 Checks
5l + 3s = 141
5(18.75) + 3(15.75) = 141
93.75 + 47.25 = 141
141 = 141 Checks
find the values of C for which C(x+2)—(x+2)(x–2)=0 has just one solution. please help me ASAP
==================================================
Work Shown:
C(x+2) - (x+2)(x-2) = 0
(x+2)(C-(x-2)) = 0
(x+2)(C-x+2) = 0
x+2 = 0 or C-x+2 = 0
x = -2 or x = C+2
If we want one solution only, then we must make C+2 = -2 which solves to C = -4
If C = -4, then x = C+2 = -4+2 = -2 which matches with the first solution mentioned. If C is anything else but -4, then we'd have two different solutions (eg: C = 10 leads to x = C+2 = 12 as the other solution)
HELP
Joseph buys a subway pass for $55. Every time he rides the subway, money is deducted from the value of the pass. He rode the subway 5 times and $40 was deducted from the value of the pass. How much was deducted from Joseph's account for each ticket? Write a mathematical expression to represent this situation; then find the answer.
1) The mathematical expression that represents this scenario is T = 40/5.
2) The value of T in the equation is $8.
What is a mathematical expression?A mathematical expression is a mathematical statement that has two different numbers (known or unknown) and at least one operation.
For instance, an equation is a mathematical equation showing that two variables are equal.
Data and Calculations:The payment for a subway pass = $55
The number of subway rides = 5
The total amount deducted from the value of the pass = $40
This implies that each subway ride costs = $8 ($40/5)
If T is the cost of a ticket and the total cost incurred for 5 subway rides is $40, therefore T = 40/5.
Thus, the mathematical expression that represents this scenario is T = 40/5.
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Prove the vector property. Let →a = and →b = < x₂ ,y₂ > .
commutative: →a + →b = →b + →a
The commutative property [tex]\overrightarrow{a}+\overrightarrow{b}=\overrightarrow{b}+\overrightarrow{a}[/tex] has been proved.
Commutative property:
The commutative property states that the changes the order or position of two numbers while adding or multiplying them does not change the end result.
The general form of commutative property is
A + B = B + A
For example, while adding the number 4, and 5
4 + 5 = 5 + 4 = 9.
Which means both yields the same result.
Given,
Let
[tex]\overrightarrow{a}= < x_1,y_1 >[/tex]
and
[tex]\overrightarrow{b}= < x_2,y_2 >[/tex]
Now we need to prove the commutative property[tex]\overrightarrow{a}+\overrightarrow{b}=\overrightarrow{b}+\overrightarrow{a}[/tex].
We know that,
"The vectors are defined as an object containing both magnitude and direction. Vector describes the movement of an object from one point to another."
Based on the commutative property,
We have to to apply the value of [tex]\overrightarrow{a}[/tex]and[tex]\overrightarrow{b}[/tex] to the equation,
Then we get,
[tex]\implies\overrightarrow{a}+\overrightarrow{b}=\overrightarrow{b}+\overrightarrow{a}[/tex]
=> <x₁, y₁> + <x₂, y₂> = <x₂, y₂> + <x₁, y₁>
While looking at the expression we know that,
Both are equal.
Then the commutative property has been proved.
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serve this for me
[tex]x + 3 > 19 = 3x[/tex]
For the given set of inequality, the value of x is 8.
What is an inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
Given, the equation is -
x+ 3 > 19 = 3x
⇒ x + 3 > 19 - 3x
Subtracting 3 from bot sides
⇒ x > 16 - 3x
subtracting x from both sides
⇒ 16 - 2x > 0
⇒ x = 8
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whats the slope for (29, 11) and (-3, -7)
The slope of the given points are (29, 11) and (-3, -7):
= 0.5625.
What is slope?A line's slope indicates whether sharp it is.. The slope is defined mathematically as "climb overrun" (change in y divided by change in x).
What is the definition of slope in a straight line?In general, a line's slope indicates its steepness as well as direction. The slope of a straight line connecting two points (x1,y1) and (x2,y2) can be simply calculated by subtracting the coordinates of both the points. The slope is commonly denoted by the letter'm.'
According to the given data:X₁ = 29
Y₁ = 11
X₂ = -3
Y₂ = -7
The slope is the degree of tilt a line has and it may be positive, negative, zero, or undefined.
slope = (y₂ - y₁) / (x₂ - x₁)
Substituting the value in the given formula:
slope = [tex]\frac{(-7 - 11)}{(-3 - 29)}[/tex]
= -18 / -32
= -9 / -16
= 0.5625
The slope of the given points are (29, 11) and (-3, -7) = 0.5625.
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A ramp goes from a doorway of a building to the ground. The end of the ramp connected to the doorway is 2 feet above the ground. The horizontal distance from the bottom of the ramp to the building is 15 feet. What is the angle of elevation of the ramp to the nearest degree?
The angle of elevation of the ramp to the nearest degree is 8°
How to determine the angle of elevationFrom the information given, we have the following deductions;
The end of the ramp connected to the doorway is 2 feet above the ground, this is the opposite side The horizontal distance from the bottom of the ramp to the building is 15 feet, this is the adjacent sideThe tangent identity is expressed as;
tan θ = opposite/ adjacent
substitute the values
tan θ = 2/ 15
find the ratio
tan θ = 0. 1333
Find the tangent inverse of the value
θ = [tex]tan^-^1(0. 1333)[/tex]
θ = 7. 79 °
θ = 8° in the nearest degree
Thus, the angle of elevation of the ramp to the nearest degree is 8°
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