The values of x and y of the parallelogram PQRS are x = 2 and y = 11
What is the side length of the parallelogram?We're given the dimensions of parallelogram PQRS as;
PT = y
TR = 5x + 1
QT = 2y
TS = 6x + 10
T is the intersection of the two diagonals PR and QS and so the diagonals bisect each other.
The diagonal PR is cut into PT and TR, both of which are congruent or equal. Thus, PT = TR.
Similarly, the other diagonal QS is split in half as well. The two equal pieces are QT and TS. So QT = TS.
PT = TR
y = 5x + 1
and
QT = TS
2y = 6x + 10
Plugging the values gives;
2y = 6x + 10
2(y) = 6x + 10
2(5x + 1) = 6x + 10
2*5x + 2*1 = 6x + 10
10x + 2 = 6x + 10
10x + 2 - 6x = 6x + 10 - 6x
4x + 2 = 10
4x + 2 - 2 = 10 - 2
4x = 8
4x/4 = 8/4
x = 2
If x = 2, then y is...
y = 5x+1
y = 5*x+1
y = 5*2+1
y = 10+1
y = 11
Thus, the values of x and y of the parallelogram PQRS are x = 2 and y = 11
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Write each expression in simplest form. (x¹/₃/y⁻³/₃)⁹
The simplest form of the expression [tex](\frac{x^{\frac{1}{3} }}{y^{\frac{-3}{3} }} )^{9}[/tex] is yx³.
The simplest form of a fraction is one with a reasonably prime denominator and numerator. It indicates that, except for 1, there is no common factor between the fraction's numerator (upper portion or top) and denominator (lower part or bottom).
A fraction is a number that has been expressed as a quotient by dividing the numerator by the denominator. Both are integers in a simple fraction. In a complex fraction, a fraction can be found in either the numerator or the denominator.
An expression is made up of a number, a variable, or a combination of a number, a variable, and operation symbols. Two expressions joined by an equal sign form an equation.
Consider the expression,
[tex](\frac{x^{\frac{1}{3} }}{y^{\frac{-3}{3} }} )^{9}[/tex]
[tex](\frac{x^{\frac{1}{3} }}{y^{\frac{-3}{3} }} )^{9}=\frac{x^{\frac{1}{3} }}{y^{-1}}[/tex]
We know, x⁻¹ = 1/x
[tex](\frac{x^{\frac{1}{3} }}{y^{\frac{-3}{3} }} )^{9}=(yx^{\frac{1}{3} })^{9}[/tex]
[tex](\frac{x^{\frac{1}{3} }}{y^{\frac{-3}{3} }} )^{9}=(y^{9})(x^{\frac{1}{3}\times 9})[/tex]
[tex](\frac{x^{\frac{1}{3} }}{y^{\frac{-3}{3} }} )^{9}=(yx^{3})[/tex]
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Which ordered pair could you remove from the relation {(–1, 0), (1, 3), (2, 2), (2, 3), (3, 1)} so that it becomes a function?
(1, 3) or (2, 3)
(1, 3) or (3, 1)
(2, 2) or (2, 3)
(2, 3) or (3, 1)
Answer:
(2, 2) or (2, 3)
Step-by-step explanation:
two of the same number in x place means it is not a function. elimination on of these will make it a function.
combine like terms to create an equivalent expression
[tex]-\frac{4}{7} +(-\frac{2}{7} p)+\frac{1}{7}[/tex]
-4/7p+(-2/7p)+1/7
An expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it. (-6p+1)/7 is an equivalent fraction of -4/7p+(-2/7p)+1/7.
What is Expression?An expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it.
The given expression is
-4/7p+(-2/7p)+1/7
In the given expression there is a variable p and a constant.
We have to add the terms which having p.
(-4/7+(-2/7))p+1/7
=(-4/7-2/7)p+1/7
=-6/7p+1/7
=(-6p+1)/7
Therefore (-6p+1)/7 is an equivalent fraction of -4/7p+(-2/7p)+1/7.
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What is the total surface area of the square pyramid?
48 square meters
64 square meters
76 square meters
88 square meters
Greetings from Brasil...
Observing the attached figure we conclude that we have a square of side 4 and 4 triangles of base 4 and height 6. With this information we can conclude that:
Looking at the attached figure, we conclude that we have a square of side 4 and 4 triangles of base 4 and height 6. Let At be the area of the triangle and As be the area of the square. With this information we can conclude that:
Atotal = 4At + As
Atotal = 4(4.6/2) + 4²
Atotal = 64a.u.5(x – 10) = 30 – 15x
Answer:
x=4
Step-by-step explanation:
=5x-50=30-15x.
=20x=80.
x=4
Solve the inequality
x²(x + 2)(x-7) ≥0
Answer:
this is not an answer please help me how to ask another question in brainly
5-(x-2)2 for x=-1
NEED HELP! What is the given value for this expression?
Answer:
3
Step-by-step explanation:
5-(x-2)2 for x= -1
it going to be
5-(-1-2)2
5- 1 x 2
5 - 2
=3
Answer:
- 4
Step-by-step explanation:
substitute x = - 1 into the expression
5 - (x - 2)²
= 5 - (- 1 - 2)²
= 5 - (- 3)²
= 5 - 9
= - 4
The question is in the picture attached below. Pls answer, will give 10 points. I know its less and its bcz I have only 13 points. When I get more, I will try to give it.
The missing terms in the given factorized expression are:
3x²y + 12xy² + 9xy = 3xy ( x + 4y + 3 )
What is an expression?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.
We have,
_ x²y + _ y² + 9 _ = 3x _ ( _ + 4y + _ )
We need to fill the boxes and make sure that both sides are equal.
We will remove the bracket on the right side.
i.e 3x _ _ + 12xy_ + 3x_ _
Now,
_ x²y + _ y² + 9 _ = 3x _ _ + 12xy_ + 3x_ _
We will make,
_ x²y and 3x _ _ equal.
_ y² and 12xy_ equal.
9 _ and + 3x_ _ equal.
So,
(3)x²y = 3x (x)(y)
(12x)y² = 12xy(y)
9 (xy) = 3x(y)(3)
Thus the missing terms in the given factorized expression are:
3x²y + 12xy² + 9xy = 3xy ( x + 4y + 3 )
3x²y + 12xy² + 9xy = 3x²y + 12xy² + 9xy
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2.)A cylinder which has a height of 90cm and diameter 14cm is closed at both ends find in its total surface area is the volume of the cylinder [take π = 22/7 ].
3.) A container is 24m long, 9m wide and 8m high - How many books can it hold if each bottle book is 20cm bong, 16cm wide and 6cm thick? Solution. d
Answer:
A =3960 as the surface area. B=309 books.
Step-by-step explanation:
SA=
[tex]2\pirh + \pir \times r[/tex]
so 2*22/7*7*90+22/7*7*7.
=
[tex]3960cm {}^{2} [/tex]
B.get the volume of the box - volume of the book
Please help I got this question wrong and I am not sure why
The partial derivatives for this problem are given as follows:
[tex]\frac{\partial z}{\partial x} = -\frac{x}{\sqrt{\frac{1 - x^2 - 4y^2}{7}}}[/tex][tex]\frac{\partial z}{\partial y} = -\frac{4y}{\sqrt{\frac{1 - x^2 - 4y^2}{7}}}[/tex]How to find the partial derivatives of a function?To find the partial derivatives of a function, we apply the same rules that we apply for complete derivatives, just considering the variables for which we are not deriving the function as constants.
For this problem, the function is given as follows:
x² + 4y² + 7z² = 1.
The function for z is given by:
7z² = 1 - x² - 4y²
[tex]z = \sqrt{\frac{1 - x^2 - 4y^2}{7}}[/tex]
As a function of x, the derivative will be given by:
[tex]\frac{\partial z}{\partial x} = -\frac{x}{\sqrt{\frac{1 - x^2 - 4y^2}{7}}}[/tex]
Because the derivative of the inside term as a function of x is of -2x, then we apply the derivative of the root and simplify -2 with 2.
For the derivative as a function of y, we follow the same procedure, with the lone difference being the the inside derivative is of -8y, then:
[tex]\frac{\partial z}{\partial y} = -\frac{4y}{\sqrt{\frac{1 - x^2 - 4y^2}{7}}}[/tex]
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draw a ring around the number equivalent to five hundreths
500 5.00 0.50 0.05
Work Shown:
five hundredths = 5/100 = 0.05
The human heart beats an average of 70 times per minute. How many times will it beat per year?
Answer:
36792000
Step-by-step explanation:
you look up how many minutes in a year then multiply by 70
The scale of a map is 1cm : 79 km. What is the actual distance between two towns that are 4cm apart on the map?
Answer:
316 km
Step-by-step explanation:
multiply 79 x 4
Hannah painted a 50 square foot wall in her home. The graph shows the remaining Square feet to paint as a linear function of X, The number of minutes spent painting. what is the domain and range of the function?
Answer:
Domain: 0 ≤ x ≤ 25
Range: 0 ≤ y ≤ 50 where y = f(x)
Step-by-step explanation:
Domain is the set of all x values. Here x is the number of minutes spent painting and we can see its minimum value is y=0, maximum value is y=25 os domain of function is 0 ≤ x ≤ 25
Range of a function is the set of values of the function ie the outputs produced the function.
Let y = f(x) Then the y values range from minimum of y = 0 to maximum of y = 50. So range is 0 ≤ y ≤ 50 which is 0 ≤ y ≤ 50
2 μm
2 nm
2 mm
Which is bigger ? And which is smaller?
The bigger measurement is 2 mm and the smaller measurement is
2 μm.
Given, the measurements are :
2 μm
we know that to convert from micro meter to meter, we use:
1 μm = 0.01 meter.
2 μm = 2 × 0.01 m
2 μm = 0.02 m
2 μm = 2/100
2 μm = 2 × 10⁻² m
for 2 nm
we know that to convert from nano meter to meter, we use:
1 nm = 10⁻⁹ meters.
2 nm = 2 × 10⁻⁹ meters.
for 2 mm
we know that to convert from milli meter to meter, we use:
1 mm = 0.001 meters.
2 mm = 2 × 0.001 m
2 mm = 0.002 m
2 mm = 2/1000 m
2 mm = 2 × 10⁻³ m
therefore , 2 × 10⁻² m > 2 × 10⁻³ m > 2 × 10⁻⁹ m
we can notice that millimeter is the greatest and nanometer is the smallest.
Hence we get the greater and smaller measurements.
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11 + 3р — 7 = бр + 5 — 3р
Answer:
No solution, or empty set.
Step-by-step explanation:
If you solve this for p you will get 4 = 5, which is false. Therefore there is no solution to this equation.
Help, pls this is urgent
9/3 - 1/6
[tex] \frac{9}{3} - \frac{1}{6} = \frac{9 \times 2}{3 \times 2} - \frac{1}{6} = \frac{18}{6} - \frac{1}{6} \\ \\ \frac{18 - 1}{6} = \frac{17}{6} = 2 \frac{5}{6} [/tex]
Answer: 2 5/6
Step-by-step explanation:
9/3-1/6 is 2 5/6 what you do is cross multiply 9/3 and 1/6 to get 18/6 and 1/6 then you subtract across
Investing $10,000 in a savings account at 5% annual interest compounded semiannually will result in approximately how much money after 10 years?
Jacob is playing miniature golf. He states that he cannot hit the ball from the start, bounce it off the back wall once, and reach the hole in one shot. Is Jacob correct? Label the diagram to support your answer.
Jacob is playing miniature golf, then the ball is can not reach the hole in one shot, so Jacob is correct.
Jacob is playing miniature golf.
He states that he cannot hit the ball from the start.
Bounce it off the back wall once
And reach the hole in one shot.
So, we can write,
The ball is need to bounce off the back wall once.
The ball is can not reach the hole in one shot.
Jacob is correct.
It is not possible to hit the ball from the start,
Bounce it off the back wall once,
And reach the hole in one shot.
Therefore, Jacob is playing miniature golf, Then the Jacob is correct.
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Select all that apply: 21 days is equal to... Question 6 options: 504 hours 30,240 minutes 1081404 seconds 3 weeks 1 month
by using the operation of multiplication, we get that 21 days is equal to 3 weeks, 504 hours, 30240 minutes and 1,814,400 seconds.
We are given the total number of days as 21.
Now, we know that:
In 1 week, we have 7 days.
So, in 3 weeks = 7 × 3 = 21 days.
Also, 1 day has = 24 hours.
So, by using multiplication, we get that:
21 days = 24 × 21 hours
= 504 hours
Also,
1 hour = 60 minutes
504 hours will be calculated again by using multiplication.
504 hours = 504 × 60 = 30240 minutes
30240 hours = 1,814,400 seconds.
Therefore, by using the operation of multiplication, we get that 21 days is equal to 3 weeks, 504 hours, 30240 minutes and 1,814,400 seconds.
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Your question was incomplete. Please refer the content below:
21 days is equal to:
a) 3 weeks
b) 504 hours
c) 30240 minutes
d) 1,814,400 seconds
e) 1081404 seconds
Select all the correct options that apply.
Convert 7,620 cm³ into m³
Answer:
0.00762
Step-by-step explanation:
A rectangle's length is 8cm more than three times its width. It the perimeter is 128 cm, find the length.
Answer:
50
Step-by-step explanation:
Answer
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AriCakes1100
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2 answers
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The length is 50. You solve it by making an equation out of the information given. the rectangle's length(l) is 3 times its width(w) and its perimeter(p) is 128. So in order to solve this you need an equation to find the perimeter, isolating w to find l. It'll look something like this:
(3w+8)+(3w+8)+w+w=128
?You combine all like terms turning it into:
2(4w+8)=128
8w+16=128
8w=112
w=14
you use the value of w to solve for l as follows:
l=w*3+8
l=14*3+8
l=42+8
l=50
Find the value of x. PLEASE HELP
Subject: Proportions in Similar Triangles
Answer:
X=7
Step-by-step explanation:
use concept of similarity proportion between big and small triangle enclosed into it
9. Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is
most appropriate.
Temperatures of the ocean at various depths.
O Nominal
O Ratio
O Ordinal
O Interval
Answer: D (Interval)
Motherdeposited $30 000.00 at a bank for 5 years at a rate of 5% per annum. How much interest will she collect at the end of the 5 years?
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$30000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &5 \end{cases} \\\\\\ I = (30000)(0.05)(5) \implies I = 7500[/tex]
ced hanger diagram:
A circle has a mass of 6 grams and a square has a mass of 3 grams. Which is the mass
of a triangle?
Solve each equation. Show your work.
The mass of the triangle from the hanger diagram is found as 5 grams.
What is termed as the equilibrium of masses?When all of the forces acting on the object are balanced, the object is said to be in equilibrium. If the rightward forces are balanced by that of the leftward forces as well as the upward forces are balanced by that of the downward forces, the forces are said to be balanced. This does not necessarily imply that all of the forces seem to be equal to one another.For the given question;
Let the mass of each triangle be 'T'.
The mass of each circle be 'C'.
The mass of circle is 6 grams; C = 6 grams.
Let the mass of each square be 'S'.
The mass of each square is given as 3 grams; S = 3 grams.
As, the hanger is in equilibrium.
Mass of the left side = mass of the right side;
Put the values;
2T + 6S + 3C = 2C + 3S + 5T
Simplify the equation;
6S + 3C - 2C - 3S = 5T - 2T
3S + C = 3T
Or
3T = 3S + C
Put the values
3T = 3×3 + 6
3T = 15
T = 5
Thus, the mass of each triangle is 5 grams.
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What does a residual value of 1.3 mean when referring to the line of best fit of a data set?
A data point is 1.3 units above the line of best fit.
A data point is 1.3 units below the line of best fit.
The line of best fit has a slope of –1.3
The line of best fit has a slope of 1.3.
The line of best fit of a data set will be a data point is 1.3 units above the line of best fit. Option A is correct.
What is the line of best-fit ?The line of the greatest fit is a mathematical concept that links points scattered throughout a graph.
It's a sort of linear regression that makes use of scatter data to determine the best approach to characterize the relationship between the dots.
The line of best fit of a data set will be a data point is 1.3 units above the line of best fit.
Hence, option A is correct.
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Answer:
A
Step-by-step explanation:
(x + 1) ^4 (x + 3) − 2(x + 1)³(x + 3)²
Answer:EVALUATE
(x=3)(x=1) 4−2(x+3) 2(x+1) 3
Step-by-step explanation:
A six sided die has been tossed 4 times. how many sequences of these 4 outcomes contain at least one number greater than 4?
Answer: 1040 sequences
Step-by-step explanation:
a die has 6 faces, 6x6x6x6 = 1296 possible sequences in whole
you have to get rid of the sequences that don't work, 4x4x4x4 = 256 (these will fail because you need at least one number that is bigger than 4)
1296 (whole)-256 (failed) = 1040 sequences that could work
two is subtracted from a number, and then the differnece is divided by 3. te result is 30 what is the number