By the symmetric property of congruence is ∠FSJ ≅∠UPR.
It is required to find the solution.
What is symmetry ?Symmetry is defined as a proportionate and balanced similarity that is found in two halves of an object, that is, one-half is the mirror image of the other half. A 2D shape is symmetrical if a line can be drawn through it and either side is a reflection of the other.
Given:
The symmetric property is if y = x then x = y. The order of what is on the left or right side of the equation does not matter. It's like saying 2+3 = 5 is the same as 5 = 2+3.
According to given question we have,
This idea can be extended to congruences because congruent angles have the same measure.
Congruent angles are two or more angles that are identical to each other. Thus, the measure of these angles is equal to each other.
So, ∠UPR ≅∠FSJ, then ∠FSJ ≅∠UPR.
Therefore, by the symmetric property of congruence is ∠FSJ ≅∠UPR.
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Find two consecutive odd integers whose sum is -36.
someone pls pls help
In March, a family starts saving for a vacation they are planning for the end of August. The family expects the vacation to cost $ 1375 . They start with $125 . Each month they plan to deposit 20% more than the previous month. Will they have enough money for their trip? If not, how much more do they need?
Will they have enough money for their trip?Yes.They will have $1407.35
If not, how much more do they need?
Given:
a1 = $125
r = 1.25
n = 6(march-august)
[tex]S_n=\frac{a(1-r^{n})}{1-r} \\\\S_6=\frac{125(1-(1.25)^{6})}{1-1.25}\\\\S_6=1407.35[/tex]
The family will have $1407.35 after making the final deposit in August.
So, they will have enough money for their trip.
They have an additional amount of $32.35 ($1407.35-$ 1375)
What is a geometric sequence?
A geometric progression is sometimes referred to as a geometric sequence in mathematics .It 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.A progression is a sequence, whereas a series is a sum, which is how they differ from one another.The complete question is:
In March, a family starts saving for a vacation they are planning for the end of August. The family expects the vacation to cost $ 1375 . They start with $125 . Each month they plan to deposit 25% more than the previous month. Will they have enough money for their trip? If not, how much more do they need?
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Solve the solution for X/8+2=3x/4-3
Answer:
x=8
Step-by-step explanation:
multiply both sides of the equation by 8
combine like terms
divide both sides of the equation by -5
p³ = 1/8 please help me if anybody can .
Answer:
[tex]p= \dfrac{1}{2}[/tex]
Step-by-step explanation:
Given equation:
[tex]p^3=\dfrac{1}{8}[/tex]
Cube root both sides:
[tex]\implies \sqrt[3]{p^3}= \sqrt[3]{\dfrac{1}{8}}[/tex]
[tex]\implies p= \sqrt[3]{\dfrac{1}{8}}[/tex]
[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]
[tex]\implies p= \left(\dfrac{1}{8}\right)^{\frac{1}{3}}[/tex]
[tex]\textsf{Apply exponent rule} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}:[/tex]
[tex]\implies p= \dfrac{1^{\frac{1}{3}}}{8^{\frac{1}{3}}}[/tex]
[tex]\textsf{Apply exponent rule} \quad 1^a=1:[/tex]
[tex]\implies p= \dfrac{1}{8^{\frac{1}{3}}}[/tex]
Rewrite 8 as 2³:
[tex]\implies p= \dfrac{1}{(2^3)^{\frac{1}{3}}}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies p= \dfrac{1}{2^{(3 \cdot \frac{1}{3})}}[/tex]
Simplify:
[tex]\implies p= \dfrac{1}{2^{\frac{3}{3}}}[/tex]
[tex]\implies p= \dfrac{1}{2^{1}}[/tex]
[tex]\implies p= \dfrac{1}{2}[/tex]
Find an equation of the line with the given slope and containing the given point. Write the equation using function notation.
slope: 5/6 through (-18,6)
f(x)=
Answer:
5x - 6y + 126 = 0
Step-by-step explanation:
y-y1=m(x-x1)
y - 6 = 5/6 (x - (-18))
6y - 36 = 5x + 90
5x - 6y + 126 = 0
Please help me asap. xb
Answer:
a ) mean = 1.8
b ) new mean = 11.8
c ) new mean = 23.6
hope this helps
what geometric figure is for a table top
Most table tops are square, rectangular, or circular.
Indicate which property is illustrated in step 3 =(8+6)+11
Answer:
Inverse Property of Addition
Step-by-step explanation:
The table shows the number of species in the United States listed as endangered and threatened.
a. Find the probability that a randomly selected endangered species is a bird.
b. Find the probability that a randomly selected mammal is endangered.
Based on the table of the number of species in the United States, the probability that a randomly selected endangered species is a bird is 17.1%
The probability that a randomly selected mammal is endangered is 81.4%.
What is the probability?The probability that when an endangered species is selected randomly, it is a bird can be found as:
= Number of endangered birds / Number of endangered species
= 80 / (70 + 80 + 318)
= 17.1%
The probability that should a randomly selected mammal be picked, the mammal is endangered is:
= Number of endangered mammals / Number of mammals
= 70 / (70 + 16)
= 81.4%
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how do you write out 7 multiplied by the difference between v and 5 gives 14.
15 points
7
Solve each equation. Check the solution. 4/2a = 5/a +6
Solution of polynomial 4/2a = 5/a +6 is , [tex]a=-\frac{1}{2}[/tex]
What are polynomial functions ?In mathematics, polynomial function can be defined as the equation which consist of coefficient, variables and exponents. A polynomial equation has positive numbers as their exponent which is also known as its degree. All the equations such as monomials, quadratic equation, cubic equation, linear equation of one degree, two degree and more which has non negative number as their powers all are part of polynomial equation and can be taken as types of the polynomial equations.
Some examples of polynomial equation are :
2x+53x = 93x² + 5x+19(x-3)³According to question,
[tex]\frac{4}{2a} = \frac{5}{a} +6\\\\= > \frac{2}{a} = \frac{5}{a} +6\\\\= > 5 + 6a =2\\ \\= > 6a = -3\\\\= > a = -\frac{3}{6} =-\frac{1}{2}[/tex]
Thus a = -1/2
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find the sum of first 15 multiples of 8
Suppose medical records indicate that the length of a newborn babies(in inches) is normally distributed with a mean of 20 and a standard deviation of 2.6 point find the probability that a given infant is between 17.4 and 22.6 inches long?
Answer:
P(17.4 < X < 22.6) = P((X-20)/2.6 < (22.6-20)/2.6) = P(Z < 1.38)
From a standard normal table, we find that P(Z < 1.38) = 0.9128
Step-by-step explanation:
Give me Brainliest if that helped! :)
a. What is the 46 th term of the arithmetic sequence that begins 3,5,7, ........... ?
The 46th term of a Arithmetic Progression (AP) is (a₄₆ = 95.)
What is the AP arithmetic progression sequence?The difference between the two numerical orders is a constant value in Arithmetic Progression (AP). Another name for it is Arithmetic Sequence.
We'd end up coming across a few key words in AP, which were denoted as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)The AP can also be defined in terms of common differences, as shown below.
The method for calculating an AP's n-th term is as follows: an = a + (n − 1) × dThe following is the arithmetic progression sum: Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, in the question, the given sequence is; 3,5,7, ...........
Assume the first term is'a₁' = 3
Assume 'a₂' = 5 is the second term.
Assume the third term is 'a₃' = 7
Find the common difference;
d = a₂ - a₁
Substitute the values in the above equation;
d = 5 - 3 = 2
Now, to calculate the value of the 46th term use the formula of nth term.
an = a + (n − 1) × d , n = total number of terms = 46.
Substitute all the values;
a₄₆ = 5 + (46 - 1) × 2
a₄₆ = 5 + 45 × 2
a₄₆ = 5 + 90
a₄₆ = 95
Therefore, the value of the 46th term is estimated as 95.
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In Δ S Z U, U J=9, V I=3 , and Z T=18 . Find the length.
SV
In Δ SZU, UJ = 9, VI = 3 , and ZT = 18 then the value of SV = 9.
What is meant by centroid theorem?The triangle's centroid is the point where the three medians intersect. According to the centroid theorem, the centroid is 23 times the distance from each vertex to the midpoint of the opposite side.
The centroid has the unique property that the distance from a vertex to the centroid is twice that of the distance from the centroid to the midpoint of the side opposite that vertex for each median. In addition, the three medians of a triangle divide the triangle into six equal-area regions.
Given: In Δ SZU, UJ = 9, VI = 3 , and ZT = 18 .
Since ZV ≅ VU, Y is the midpoint of UZ and SV is a median of Δ ZSU. Similarly, points Y and T are also midpoints of SZ and SU, respectively, so YU and ZT are also medians. Therefore, point J is the centroid of
Δ ZSU and, according to the Centroid Theorem, SJ is 2/3 of SV.
SJ = 2/3 (SV)
= 2/3 (SJ + VJ)
simplifying the above equation, we get
(3SJ/2) - SJ = VJ
SJ/2 = 3
SJ = 4.5
Therefore, to find SV, we can now add SJ and VJ
SV = SJ + VJ
= 6 + 3
= 9
Therefore, the value of SV = 9.
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In ®B, C E=13.5 . Find BD . Round to the nearest hundredth.
The length of BD is 4.29
BF is the radius of circle and CE is the chord. BF perpendicularly bisects the chord into two equal halves. Thus, we can say that -
CD = 1/2CE
Keep the values in equation to find the value of CD
CD = 1/2×13.5
CD = 6.75
Now, taking BCD as right angled triangle, we can say -
BC is hypotenuse, CD is base and BD is perpendicular. Using Pythagoras theorem to find the length of BD.
BC² = CD² + BD²
8² = 6.75² + BD²
BD² = 64 - 45.5625
BD² = 18.4375
BD = √ 18.4375
BD = 4.29
Hence, the length of BD is 4.29
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The complete question is attached in the image below.
11 divided by 1925 can you show the work
Answer: 175
Step-by-step explanation:
3x = 7 + 14
i need help with this help please
answer:
7
explanation:
7+14=21
21/3=7
Answer:
Step-by-step explanation:
3x = 7 + 14
3x = 21 (7 + 14 = 21)
x = 7 (divide 3 from both sides) (3x / 3 = x and 21 / 3 = 7)
The income from the spanish club's bake sale was $300. expenses for the sale totaled $30. use integer addition to find the total profit or loss from the bake sale.
Using integer addition, the total profit from the Spanish Club's bake sale is $270.
Integer refers to whole numbers(non-fractional numbers) that can either be positive or negative, and zero.
Adding positive integers will result to a positive integer while adding negative integers will result to a negative integer. But, adding a negative integer to a positive integer is the same as subtracting its positive.
If the income from the Spanish Club's bake sale was $300 and the expenses for the sale is $30, the total profit will be:
income = +$300
expenses = -$30
Using integer addition,
profit = income + expenses
profit = +$300 + (-$30)
profit = $300 - $30
profit = $270
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A student walked 100 meters north, then 100 meters west. How many more meters did the student walk compared to their total displacement from their starting point?.
Using Pythagorean theorem, the student walked 53.58 meters more compared to the total displacement from the starting point.
If a student walks 100 meters north, then 100 meters west, then the path he travels resembles the sides of a right triangle (see attached photo).
Using Pythagorean theorem, we can solve for the total displacement from the starting point to the end point.
c^2 = a^2 + b^2
where c is the total displacement from the starting point to the end point
a is the distance he walks up north
b is the distance he walks to the west
c^2 = 100^2 + 100^2
c^2 = 10,000 + 10,000
c^2 = 20,000
c = 141.42 meters
Comparing the total distance the student walked and the total displacement from the starting point to the end point by subtraction.
100 meters + 100 meters - 141.42 meters = 53.58 meters
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A triangular land has length of edges 55 m, 60 m and 65 m respectively. Find the length o the fence around it.
The length of the fence around the triangular land is equal to 180 meters.
What is the length of the fence around the triangular land with given edge lengths?
The perimeter of a figure is the sum of the side lengths of the figure. Triangles have three sides and we need to determine the perimeter of the triangular land. If we know that l₁ = 55 meters, l₂ = 60 meters and l₃ = 65 meters, then the perimeter of the figure is:
p = l₁ + l₂ + l₃
p = 55 m + 60 m + 65 m
p = 180 m
The length of the fence around the triangular land is equal to 180 meters.
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The graph represents this system of equations: A system of equations. 2 x plus y equals 3. 2 x minus 5 y equals 15.
A coordinate grid with 2 lines. One line passes through (0, 3) and (1.5, 0). The other line passes through (0, negative 3) and (2.5, negative 2).
What is the solution to the system of equations represented by the graph?
(0, –3)
(1, 1)
(1.5, 0 )
(2.5, –2)
The solution to the system of equations is (2.5, -2)
How to determine the solution to the system of equations?The system of equations is given as:
2x + y = 3
2x - 5y = 15
Subtract the equations to eliminate the variable x
This is represented as
2x - 2x + y - -5y = 3 - 15
Evaluate the like terms in the above equation
So, we have
y + 5y = 3 - 15
Evaluate the like terms in the above equation
So, we have
6y = -12
Divide both sides of the above equation by 6
So, we have
y = -2
Substitute y = -2 in 2x + y = 3
2x - 2 = 3
This gives
2x = 5
Divide by 2
x = 2.5
Hence, the solution to the system of equations is (2.5, -2)
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Answer:
2.5, -2
Step-by-step explanation:
Mr.Shaw has 140 books in his library at home he wants to place an equal number of books on each shelf using the rules of divisibility what are some posiible numbers of shelves Mr. Shaw could use?
Mr. Shaw can use 70 shelves with 2 books each.
or
Mr. Shaw can use 35 shelves with 4 books each.
or
Mr. Shaw can use 28 shelves with 5 books each.
or
Mr. Shaw can use 20 shelves with 7 books each.
or
Mr. Shaw can use 14 shelves with 10 books each.
Mr. Shaw has 140 books in his library.
Divisibility rule of 2:
A number is always entirely divisible by 2 if it is even or has an even last digits, such as 2,4,6,8, or 0.
The last digit of 140 is 0 which is an even number. So, 140 is divisible by 2.
Therefore,
Number of shelves = 140/2 = 70
Divisibility rule of 4:
An integer is divisible by 4 if its last two digits are also divisible by 4. A number is divisible by 4 if its last two digits are zeros since 4 divides 100.
The last two digits of 140 are 4 and 0.
Now, 40/ 2 = 20. Hence, 140 is divisible by 4.
Therefore,
Number of shelves = 140/4 = 35
Divisibility rule of 5:
If the last digit of a given integer is either 5 or 0, then the number is divisible by 5 according to the divisibility rule of five.
Since the last digit of the number 140 is 0. Hence 140 is divisible by 5.
Therefore,
Shelves = 140 / 5 = 28
Now,
Divisibility rule of 7:
According to the divisibility rule of 7, if a number is divisible by seven, then "the difference between twice the unit digit of the provided number and the remaining part of the given number should be a multiple of seven or it should be equal to zero."
140 = 14 - 2 × 0 = 14
Since 14 is divisible by 7. Hence 140 is divisible by 7.
Therefore,
Number of shelves = 140 / 7 = 20
Similarly,
Divisibility rule of 10:
The divisibility rule for 10 states that any number whose last digit is 0, is divisible by 10.
As the last digit of 140 is 0, hence 140 is divisible by 10.
Therefore,
Number of shelves = 140/10 = 14
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5x - 3 = 12
what is this for inverse operations?
One section of a football stadium has 10 seats in the front row, row A. Each of the rows behind row A has 6 more seats than the row immediately in front of it. What is the total number of seats in rows A-E of the stadium?
Answer:
Step-by-step explanation:
has 25 sections of seating
Determine whether \triangle X Y Z is an acute, right, or obtuse triangle for the given vertices. Explain.
X(3,1),Y(3,7),Z(11,1)
The ΔXYZ is an Right Angled triangle.
Pythagoras Theorem states that the sum square of two sides of triangle is equal to the square of longest side.
Distance Formula is used to calculate distance between two points A(a,b) and B(c,d)
denoted by [tex]d=\sqrt{(c-a)^{2} +(d-b)^{2} }[/tex]
In the given question , first calculate the length of each side of the triangle.
given X(3,1),Y(3,7),Z(11,1)
using distance formula
XY=[tex]\sqrt{(3-3)^{2} +(7-1)^{2} } =\sqrt{36} =6[/tex]
YZ=[tex]\sqrt{(11-3)^{2} +(1-7)^{2} } =\sqrt{8^{2}+(-6)^{2} } =\sqrt{64+36}= \sqrt{100} =10[/tex]
XZ=[tex]\sqrt{(11-3)^{2}+(1-1)^{2} } =\sqrt{8^{2} } =\sqrt{64} =8[/tex]
The longest side is 10 and other two sides are 8,6.
by using Pythagoras Theorem
[tex]hypotnuse^{2} =base^{2} +perpendicular^{2}[/tex]
[tex]YZ^{2} =XY^{2} +XZ^{2} \\ \\ 10^{2} =8^{2} +6^{2} \\ \\ 100=64+36\\ \\ 100=100[/tex]
Since Pythagoras Theorem is satisfied It is a right angled triangle.
Therefore , The ΔXYZ is an Right Angled triangle.
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HELP give the coordinates of one point in the solution set.
The coordinates of one point in the solution set are (2, 0)
How to give the coordinates of one point in the solution set?The system of inequality is given as
-7x + 3y < 3
5x + 7y ≥ -7
The graph that completes the question is added as an attachment
From the question, we also have the graph that represents the inequalities in the above system of inequality
As a general rule, the shaded region in a system of inequality represents the solution set
From the attached graph, the point (2, 0) is in the shaded region
Hence, the coordinates of one point in the solution set are (2, 0)
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I need help ASAP
Last question needed
Using it's concept, the domain of function m is given as follows:
-∞ < x < ∞.
What is the domain of a function?The domain of a function is the set that contains all the values of the input. In a graph, it is the set that contains all values of x of function.
In this problem, the function is defined for all real values of x, as it keeps increasing to left and right, hence the domain of function m is given as follows:
-∞ < x < ∞.
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please help me with this one
Answer: 48x⁸y⁶
Step-by-step explanation:
[tex]6x^2y^3(2x^2y)^3=\\6x^2y^32^3(x^2)&^3y^3=\\(6)(8)(x^2)(x^{(2)(3)}})(y^{3+3})=\\48(x^2)(x^6)y^6=\\48x^{2+6}y^6=\\48x^8y^6[/tex]
Answer:
[tex]48 {x}^{8} y^{6} [/tex]
Step-by-step explanation:
[tex]1. \: 6 {x}^{2} y {}^{3} \times 2 {}^{3}( {x}^{2}) {}^{3} y {}^{3} \\ 2. \: 6x {}^{2} y {}^{3} \times 8( {x}^{2} ) {}^{3} y {}^{3} \\ 3. \: 6x {}^{2} y {}^{3} \times 8x {}^{6} y {}^{3} \\ 4. \: (6 \times 8)x {}^{2}x {}^{6} y {}^{3} y {}^{3} \\ 5. \: 48 {x}^{2} x {}^{6} y {}^{3} y {}^{3} \\ 6. \: 48x {}^{2 + 6} y {}^{3 + 3} \\ 7. \: 48x {}^{8} y {}^{3 + 3} \\ 8. \: 48x {}^{8} y {}^{6} [/tex]
Write each logarithmic expression as a single logarithm. log₅ x - 1/5 log₅ y
By using logarithim quotient rule the given lograthimic expression log₅ x - 1/5 log₅ y can be written as log₅ (x/y^(1/5)).
According to the given question.
We have lograthimic expression.
log₅ x - 1/5 log₅ y
As we know that, a logarithmic expression is an expression that involves the logarithm of an expression containing a variable.
Also according to the logratimic quotient rule we know that
[tex]log_{b} (\frac{m}{n} ) = logm - logn[/tex]
Thereofore,by using logarithim quotient rule the given lograthimic expression log₅ x - 1/5 log₅ y can be written as
log₅ x - 1/5 log₅ y
= log₅ x - log₅ (y^(1/5))
= log₅ (x/y^(1/5))
Hence, by using logarithim quotient rule the given lograthimic expression log₅ x - 1/5 log₅ y can be written as log₅ (x/y^(1/5)).
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