We can conclude that triangle ΔPQR ≇ ΔXYZ.
What exactly do we mean by the congruency of a triangle?If all three corresponding angles are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent.These triangles can be moved, rotated, flipped, and turned to look exactly the same.They will coincide if they are repositioned.Two triangles are congruent if they satisfy the five congruence conditions.They are the side-side-side (SSS), the side-angle-side (SAS), the angle-side-angle (ASA), the angle-angle-side (AAS), and the right angle-hypotenuse-side (RHS).So,
Given: P(-3,-3), Q(-5,1), R(-2,6), X(2,-6), Y(3,3), Z(5,-1)
To find if ΔPQR ≅ ΔXYZ
Q = Z = (5,-1)R = X = (2,-6)P(-3,-3) ≠ Y(3,3)So, ΔPQR ≇ ΔXYZ.
Therefore, ΔPQR ≇ ΔXYZ.
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If the rope is 45.0 m in length and 7.0 mm in diameter, what is young's modulus for this material?
According to the given data young's modulus for this material = 5.73 *(10^8 ) pa
What exactly is Young's modulus?Young's modulus (E) of material seems to be the ratio of compressive loading () to tensile strain (). Where stress is defined as the amount of normal force per unit area ( = F/A) and strain is defined as extension per unit length ( = dl/l).
According to the given data:Youngs modulus Y of a material is given Y = FL/ADL
where
A = area
DL = change of length
L = original length
F = force
so here we apply
Y = 65*9.8* 45/(3.14* 3.5*3.5* 10^-6 * 1.3)
Y = 5.73 *(10^8 ) pa
According to the given data young's modulus for this material = 5.73 *(10^8 ) pa
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I understand that the question you are looking for is:
A nylon rope used by mountaineers elongates 1.30 m under the weight of a 65.0-kg climber. If the rope is 45.0 m in length and 7.0 mm in diameter, what is Young's modulus for this material?
What is the sum of each finite series?
a. Σ⁴° n=1 (3n - 8)
The sum of the given finite series is 2140
Sum notation is used to express long summation into a single formula.
Properties of sum operator:
If a is a constant, then Σₙa.b(n) = a Σₙ.b(n) Σ (a +b) = Σa + Σb[tex]\sum\limits^{40}_{n=1} {(3n-8)}=\sum\limits^{40}_{n=1} {3n}-\sum\limits^{40}_{n=1} {8}[/tex]
[tex]=3\sum\limits^{40}_{n=1} {n}-\sum\limits^{40}_{n=1} {8}[/tex]
[tex]=3\sum\limits^{40}_{n=1} {n}-8\times40[/tex]
[tex]=3(1+2+...+40)-8\times40[/tex]
[tex]=3.\frac{40}{2}. (1+40)-320[/tex]
= 2140
Hence, the sum of the given finite series is 2140
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Help me fast i'll mark you brainliest please.
The number of hours that the kayak rented for the total costs to be the same will be 2 hours.
How to illustrate the information?At 1 hour, the cost will be:
y = 7x + 9
= 7(1) + 9 = 16
At 2 hours, cost will be:
y = 7x + 9
y = 7(2) + 9
= 23
It should be noted that in the table, at 2 hours the cost is $23 also. Therefore, the number of hours that the kayak rented for the total costs to be the same will be 2 hours.
Also, shop B charges less per hour.
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pls answer these two questions ASAP
Answer:
Step-by-step explanation:
[tex]\displaystyle\\\frac{10px^2}{3c^2d} \div\frac{5px}{6c^2d^2} =\\\\\frac{10px^2}{3c^2d}*\frac{6c^2d^2}{5px} =\\\\\frac{60c^2d^2px^2}{15c^2dpx^2} =\\\\4d\\\\\\\frac{3}{x+7} \div\frac{8x^2-8x}{x^2+6x-7} =\\\\\frac{3}{x+7} \div\frac{8x(x-1)}{x^2-x+7x-7} =\\\\\frac{3}{x+7} \div\frac{8x(x-1)}{x(x-1)+7(x-1)} =\\\\\frac{3}{x+7} \div\frac{8x(x-1)}{(x-1)(x+7)} =\\\\\frac{3}{x+7} \div\frac{8x}{x+7} =\\\\\frac{3}{x+7} *\frac{x+7}{8x} \\\\\frac{3(x+7)}{8x(x+7)}=\\\\\frac{3}{8x}[/tex]
Simplify it.
Show steps please
√16x^2
Answer:
4[tex]x^{2}[/tex]
Step-by-step explanation:
1st seperate the equation
[tex]\sqrt{16}[/tex] and [tex]x^{2}[/tex]
square root of 16 is 4, and x squared stays the same, so the equation becomes
4[tex]x^{2}[/tex]
A foreign exchange student from Denmark would like to buy gifts for her family. She finds a special deal, 7 t-shirts for $07.93, that she would like to purchase for her family. However, her family only consists of 5 people. If she wants to purchase 5 -
shirts for her family members at that special rate, what would be the cost of these t-shirts in her currency of Krona? (Currency conversion rate is 1 U.S. Dollar 8.6064 Krona)
O 121.663 Krona
O 13.99 Krona
O 608.313 Krona
O69.95 Krona
The total cost of the shirts that the foreign student buy will be 48.71 Krona.
How to illustrate the information?From the information, the person finds a special deal, 7 t-shirts for $07.93, that she would like to purchase for her family.
Therefore, the total cost will be:
= $7.93 / 7 × 5
= $5.66
Therefore, the amount when converted to Krona will be:
= $5.66 × 8.6064
= $48.7
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Answer:
The answer is C "608.313 Krona"
Step-by-step explanation:
Got it right on my quiz.
A 12-pack of juice boxes costs $5.40. How much would an 18-pack of juice boxes cost if it is proportionate in price?
Answer: 8 dollars and 10 cents
Step-by-step explanation:
5.40 divided by 12 = .45
This means that each juice costs 45 cents
.45x18=8.10
Answer:
$8.10
Step-by-step explanation:
$5.40/12=$0.45 $0.45*18=$8.10
In a game of cards, 43 cards are used, including one joker. Four players are each, dealt 10 cards and the rest are put in a pile. If Greg doesn't have the joker, what is the probability that either his partner or the pile have the joker?
Probability that either his partner or the pile have the joker from the deck of 43 cards including one joker ,four players each have 10 cards and 3 cards in a pile is 13/33.
As given,
Total number of cards=43
Number of cards with each players =10
Number of cards in a pile =3
Greg doesn't have joker
Total cards left = 43-10
= 33
Probability either his or the pile have the joker = (10 +3)/33
= 13/33
Therefore, probability that either his partner or the pile have the joker is 13/33.
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An investor puts $1760.25 into
an insurance policy that pays
6.5% simple annual interest.
If no additional investment is made
into the policy, how much interest
should the investor expect at the end
of 15 years?
(Round to the nearest cent.)
The investor should expect $1716.24375 at the end of 15 years .
Formula for calculation of Simple Interest :
Simple Interest = ( Rate * Principal * no . of years ) / 100 , when no additional investment is made .
Here , principal = $1760.25 , rate = 6.5 , no . of years = 15 .
Substituting values in formula above ,
SI = ( 6.5 * 1760.25 * 15 ) / 100
= 1716.24375
Hence , the investor should expect $1716.24375 at the end
of 15 years .
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Find the geometric mean between each pair of numbers.
7 and 12
A group of products are averaged to determine central tendency using the geometric mean. The geometric mean of 7 and 12 is 2√21.
What is meant by geometric mean?The geometric mean in mathematics is a mean or average that, by using the product of the values of the numbers, shows the center tendency or usual value of a set of numbers.
The geometric mean, sometimes known as the compounded annual growth rate, is a tool used in finance to determine average growth rates.
The Geometric Mean (GM) is the average value or mean that reveals the central tendency of a group of numbers by adding up the values of those numbers.
Formula to calculate Geometric Mean is
x = √(a × b)
Where, a = 7 and b = 12
x = √(7 × 12)
x = √(7 × 4 × 3)
x = 2√21
The value of x = 2√21.
Therefore, the geometric mean between the pair of numbers 7 and 12 is 2√21.
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Please tell me the angles of x and y on letter B
Answer:
x = 100, y = 80
Step-by-step explanation:
100° and x° are alternate interior angles and are congruent , so
x = 100
x° and y° are a linear pair and sum to 180° , that is
100 + y = 180 ( subtract 100 from both sides )
y = 80
Classify each variable according to the set of numbers that best describes its values.
the number of times n a ball bounces; the height h from which the ball is dropped
The categorization of each variable according to the group of numbers that best captures its values is shown below:
Any integer from 0 to n.
Any number from 0 to h.
What is a variable?Any mathematical object can be represented by a variable in mathematics as a symbol and placeholder. A variable can, for example, represent a number, a vector, a matrix, a function, the argument of a function, a set, or a set's component.Numerous issues are resolved in a single computation by using variables in algebraic calculations as if they were explicit integers.For instance, by exchanging the variables that represent them in the quadratic formula with the numerical values of the coefficients in any given quadratic equation, the quadratic formula may solve any quadratic equation.In mathematical logic, a variable is either a sign for an undefined word of the theory (a "meta-variable") or a fundamental item of the theory that is changed without considering any potential intuitive meaning.To know more about variable, refer to the following link:
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The average temperature decrease of -6.5 degrees/km celsius is known as ________. group of answer choices dry adiabatic rate normal lapse rate stability environmental lapse rate maximum mixing depth
The average temperature decrease of -6.5 degrees/km Celsius is known as Normal lapse rate.
Normal lapse rate is defined as the decrease in the temperature while moving upwards in the atmosphere. Normally, the rate of decrease is 1 degree Celsius for every 165 meter rise in altitude or we can say that it is 6.5 degree Celsius for every 1 km rise in altitude.
This lapse rate is known as normal lapse rate or environmental lapse rate.
This is why when we move higher in the atmosphere, we experience low temperatures. On average this decrease is equal to the amount of temperature as discussed in the normal lapse rate.
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R-C=P solve the equation answer what the variable c equals
Answer:
C=r-p
Step-by-step explanation:
r-c=p
We need to solve the equation for Variable C
To get c alone we need to remove r from the left hand side
Subtract R from both sides
r-c=p
r-r-c=-r+P
-c=-r+P
Now divide both sides by -1 to get c alone
c=r-p
C is alone, it is solved for C
What expression
can be used to add 1/2 + 5/6
Answer:
(4/3)
Step-by-step explanation:
1 5
--------- + --------
2 6
1 (3) 5
--------- + --------
2(3) 6
3 5 8
------- + ------- = -------
6 6 6
8 ÷ 2 4
------- = -------
6 ÷ 2 3
I hope this helps!
The left and right page numbers of an open book are two consecutive integers whose sum is 253. Find these page numbers.
The consecutive page no. are 126 and 127.
WHAT ARE CONSECUTIVE INTEGERS ?An example of a run of consecutive integers is 1, 2, 3, 4. Another illustration is 7, 8, and 9. An integer sequence is a set of numbers where each term is one more than the term before it.
Continually following one another, from smallest to greatest, are consecutive numerals. For instance, the sequence of the numerals 1, 2, 3, 4, 5, and so forth.
The next two numbers are (n + 1) and (n + 2) if n is an integer. Take 1 for n as an example. Its subsequent numbers can be read as (2 and 3), or as (1 + 1) and (1 + 2).
CALCULATIONlet the consecutive page numbers be x and x+1
according to question ,
x + x + 1 = 253
2x = 252
x = 126
so the consecutive page numbers are 126 and 127.
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PLEASE ANSWER FAST ILL GIVE BRAINLIEST IF CORRECT
(02.04 MC)
Write an equation of a line that is perpendicular to y = 3x + 3 and passes through (−6, 3).
To make a line perpendicular, flip the denominator and numerator of the slope and make it positive if it was negative or negative if it was positive.
In this case, our slope is 3, so to make a perpendicular line, it would become: [tex]-\frac{1}{3}[/tex]
Now to make it pass through -6, 3 we need to plug in those numbers, and we'll be removing the 3 added at the end.
x = -6
y = 3
y = x
3 = [tex]-\frac{1}{3}[/tex](-6)
3 = 2
In order to make this true, we need to add 1 to the right side.
3 = 2 + 1
3 = 3
So, the equation would be [tex]y=-\frac{1}{3}x+1[/tex]
Simplify the quantity 7 minus one fourth times the square root of 16 end quantity squared plus the quantity 2 minus 5 end quantity squared. 27 45 324 900
The value of the expression (7 - 1/4 × ✓16)² + (2 - 5)² is 45.
How to calculate the expression?Based on the information given, the expression will be:
(7 - 1/4 × ✓16)² + (2 - 5)²
= (7 - 1)² + (-3)²
= 6² + 3²
= 36 + 9
= 45
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The picture shows the Alamillo Bridge in Seville, Spain. In the picture, $m\angle1=58^{\circ}$ and $m\angle2=24^{\circ}$ .
Answer:
Step-by-step explanation:
Find the midpoint of the line segment joining points A and B
A(8,- 7); B(2,3)
(5 , -2)
Step-by-step explanation:
mid point = ( (X1 + X2)/2 , (Y1 + Y2)/2 )
= ( (8 + 2)/2 , (-7 + 3)/2 )
= (5 , -2)
Answer ASAP (show work)
Answer:
y=17.50n+80.00 202.50
Step-by-step explanation:
y=17.50n+80.00
N is hours
Make N=7
17.50*7=122.50
80+122.50=202.50
is (36^7 + 6^13) divisible by 7?
Answer:
(36^7+6^13) is divisible by 7.
Step-by-step explanation:
(36^7+6^13)
First, solve the parentheses and exponents within it.
36^7=36*36*36*36*36*36*36=78364164096
6^13=6*6*6*6*6*6*6*6*6*6*6*6*6=13060694016
Add 78364164096 and 13060694016.
It equals 91424858112.
Divide 91424858112 by 7.
It results in 13060694016.
Hence, yes.
Hope this helps.
may someone help meee?
The expression given by (1/2)⁻¹ is equivalent to 2
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
(1/2)⁻¹
Taking the negative one exponent gives:
= 2 / 1
Simplifying the equation gives:
= 2
The expression given by (1/2)⁻¹ is equivalent to 2
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||3x+4|+5 |<1 , | | = absolute value
Answer:
Solution on screen
Step-by-step explanation:
I hope it's clear
Find the GCF of 45, 27, 72
please helpp ! tysm :3
Answer:
7.8
-1/5
-16.2
5 5/8
Step-by-step explanation:
Round 4.77527806851 to the nearest millionth
Answer:
4.775278.
Step-by-step explanation:
4.77527806851, when rounded to nearest millionth results in 4.775278.
Answer: 4.775278
Step-by-step explanation:
The place values go tenth, hundredth, thousandth, ten thousandth, hundred thousandth, and millionth. The place value after that is zero, so it stays as eight.
Write an equation in slope-intercept form for each line.
(4,-1) and (-2,-1)
With each line, a slope-intercept relationship (4,-1) and (-2,-1).
Y = 0 ,X = 5.
What is slope-intercept form?The slope-intercept form is just a means of stating a line's equation so that both the slope (steepness) as well as y-intercept (where another line crosses this same vertical y-axis) are obvious. This expression is frequently referred to as y = mx + b.
According to the given information:To begin, are using the slope formula to figure out the average slope between two points here.
Let:
x1 = 4
y1 = -1
x2 = -2
y2 = -1
m = (y2-y1)/(x2-x1)
= (-1 - (-1))/ (4-(-1))
= 0/5
= 0
So the slope is 0.
We must now calculate the y-intercept. This will be accomplished by converting a single of the points and also the slope together into a point-slope linear equation. y2-y1 = m(x2-x1).
Let’s plug in the point (5,0).
So we get y-(-0) = (0/5)(x-(-5)) ⇒ y+0
= (0/5)x + 0 ⇒ y
So,
Y = 0
X = 5
with each line, a slope-intercept relationship (4,-1) and (-2,-1).
Y = 0 ,X = 5
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The temperature at 1:00 pm was -7°C. By 5:00 pm the temperature increased by 11°C. What was the temperature at 5:00 pm?
how do I write the domain and range as an inequality here.
Check the picture below.
notice, the function namely f(x) or "y", has a hole at (-3 , 2), that means that the values for the range are anything less than 2, but never 2, so 1.1 is ok, 1.99 is also good, 1.999999999999999 is also ok, but never 2, thus y < 2.
Let's also notice, the arrowhead means the graph keeps on going to the left as well as to the bottom.
