From equation 1 and 2, you can see that XY = YZ and Z = ZW, hence according to the transitive property, we can conclude that XY ≅ ZW.
Midpoint of coordinateA midpoint is a point that divides a line of a segment into two equal parts. It also means that the point bisects the given line.
If the point Y is the midpoint of XZ, then;
XY + YZ = XZ and;
XY = YZ .........1
Similarly, if Z is the midpoint of YW, then;
YZ + ZW = YW and;
YZ = ZW ..........2
From equation 1 and 2, you can see that XY = YZ and Z = ZW, hence according to the transitive property, we can conclude that XY ≅ ZW.
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Harry drove for 3 hours on the freeway, then decreased his speed by 20 miles per hour and drove for 6 more hours on a country road. If his total trip was 483 miles, then what was his speed on the freeway?
Harry's speed on the freeway is 67 miles per hour
Time Harry drove on freeway = 3 hours
Time Harry drove on country road = 6 hours
Total distance covered by him = 483 miles
Let his speed be x miles per hour
Formula to be used:
Speed*Time = Distance
Therefore, the distance covered by him on the freeway = 3x -----(1)
Distance covered by him on country road = 6(x - 20)------(2)
Formulating the equations using (1) and (2)
3x + 6(x-20) = 483
3x + 6x - 120 = 483
9x = 603
x = 67 miles per hour
So, his speed on the freeway is 67 miles per hour and on the country road it is 47 miles per hour
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Halle el resultado de:
pls ayuda necesito hacer esta tarea :c
Usando la propiedad exponencial, hay que el resultado es: 125/64.
¿Cómo aplicar la propiedad exponencial?Con el expoente negativo, hay que:
[tex]\left(\frac{a}{b}\right)^{-x} = \left(\frac{b}{a}\right)^{x}[/tex]
Así, la expresion equivalente es dada por:
[tex]\left(\frac{16}{25}\right)^{-\frac{3}{2}} = \left(\frac{25}{16}\right)^{\frac{3}{2}}[/tex]
Hay que 25 = 5² y 16 = 4², así:
[tex]\left(\frac{25}{16}\right)^{\frac{3}{2}} = \left(\frac{5^2}{4^2}\right)^{\frac{3}{2}} = \left(\frac{5}{4}\right)^3 = \frac{125}{64}[/tex]
Así, hay que el resultado es: 125/64.
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two ships leave a harbor at the same time. the first ship heads north at 20 miles per hour, and the second ship heads west at 15 miles per hour. write an expression that gives the distance d between the ships after t hours.
The expression that gives the distance, d, between the ships after t hours is d = 25t
Calculating DistanceFrom the question, we are to write an expression that gives the distance, d, between the ships after t hours
First, we will determine the distance the ships have traveled after t hours
Using the formula,
Distance = Speed × Time
Thus,
The first ship would have traveled
20 × t miles
= 20t miles
The second ship would have traveled
15 × t miles
= 15t miles
Using the Pythagorean theorem,
The distance, d, between the ships after t hours is
d² = (20t)² + (15t)²
d² = 400t² + 225t²
d² = 625t²
d = √(625t²)
d = 25t miles
Hence, the expression that gives the distance, d, between the ships after t hours is d = 25t
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The data measured on ordinal scale exhibits all the properties of data measured on? nominal scale. nominal and interval scales. interval scale. ratio scale.
The data measured on ordinal scale exhibits all the properties of data measured on nominal scale.
What is nominal scale?A nominal scale can be described as the scale of measurement which is been assign events or objects with respect to a discrete categories.
However in relation with nominal scale, Ordinal scale serves as the 2nd level of measurement which help to give the reports of ranking as well as ordering of the data however the degree of variation is not usually considered, hence data measured on ordinal scale exhibits all the properties of data measured on nominal scale.
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the number of hours it takes for ice to melt varies inversely with the air temperature. suppose a block of ice melts in 2 hours when the temperature is 65 degrees celsius.
The value of the constant of variation is 130
What is constant of variation?Constant of variation can be defined as the ratio between two variables in an inverse variation on a direct variation.
In direct variation equations = k and y = kx, In inverse variation equations xy = k and y = , k is the constant of variation.From the information given, we have that;
The number of hours is x
The temperature is y
x α 1/ y
x = k/y
k = xy
Substitute the values
k = 2 × 65
k= 130
Thus, the value of the constant of variation is 130
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The complete question:
the number of hours it takes for a block of ice to melt varies inversely as the temperature. If it takes 2 hours for a square inch of ice to melt at 65 degrees find the constant of variation
A bike wheel.
The weight of a full steel bead tire is approximately 800 grams, while a lighter wheel weighs only 700 grams. What is the weight of each tire in pounds? There are 453.592 grams in one pound. Round answers to 2 decimal places.
Answer: BABABAB
Step-by-step explanation:
BHBAHBABAHBABHABHBAHBABHABHBAbhaBHBA
ROUND off the answers using the rules for approximate numbers.
Problems: 97.83 - 4.378 + 5.92
and 1,342.8+ 85.32 + 173.54 + 16
The value of the numbers given will be:
1. 108
2. 1618
How to calculate the values?1. The expression given will be calculated as:
= 97.83 - 4.378 + 5.92
= 98 + 4 + 6
= 108
2. 1,342.8+ 85.32 + 173.54 + 16
= 1343 + 85 + 174 + 16
= 1618
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in triangle abc, angle b is 120∘ . it contains bisectors aa1, bb1 and cc1. prove that the angle a1b1c1 is 90∘
The triangle formed by the feet of angle bisectors of a triangle with a single angle measure of 120° is the Right Triangle.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.So,
In triangle ABC, ∠A = 120°.
Let AD, BE, and CF be the respective angle bisectors of A, B, and C.AC in ABD is the exterior angles bisector (as DAC=CAX=60°).BE is the internal angle bisector that meets at E. E is the ex-center of ABCD.As a result, DE is the exterior angle bisector of ABCD.
Then, ADE=EDC, and ADC=2ADE.Similarly, for the ABC, F is ex-center because AB is the exterior angle bisector and CF is the interior angle bisector.
As a result, DF is the exterior angle bisector.
∠ADF = ∠FDB, ∠BDA = 2∠ADFBC is a straight line.
∠BDA+∠ADC=180°2∠ADF+2∠ADE=180°∠ADF+∠ADE=90°So, DEF is the right triangle.
As a result, the triangle formed by the feet of angle bisectors of a triangle with a single angle measure of 120° is the Right Triangle.
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The correct form of the question is given below:
Prove in any ΔABC, if one angle is 120°, the Δ formed by the feet of the angle bisectors is right-angled.
you bought a pair of jeans for $42.95 and a sweater for $36.99 . what was the cash price including a 5% sales tax?
Answer:
Step-by-step explanation:
jeans $42.95
sweater + $36.99
total = $69.94
tax + 5% ($3.497 round to nearest hundredth ($3.50))
total with tax = 73.44
hope this helped!!!! let me know if you need anymore help with this :) have a good day!
Is 0. 19
a rational or irrational? Explain
Answer:
It's rational, because it can be converted into a reasonable fraction.
➯ Hope this helps!
A football team has attempted 6 running plays. The change in field position resulting from each play is shown in the table. What is the average change in field position per running play?
–6 yards per play
–1 yard per play
0 yards per play
1 yard per play
Answer:
-1 yard per play
play 6 - play 3=0
play 2 - play 4=0
play 1 - play 5 = -6
hope it helped
with show work needed. a and b.
a)
Solution,
Given,
Cost for 1 pen = $ 1.50
= 1.50×100 cents
= 150 cents
Cost for 1 ruler = 80 cents
No. of Pens needed to be bought = x
No. of rulers needed to be bought = x+10
Now,
Cost for x pens = x×150 cents
= 150x cents
Cost for (x+10) rulers = (x+10)×80 cents
= 80x cents+800 cents
Then,
Total cost = 150x cents+(80x cents+800 cents)
= 150x cents+80x cents+800 cents
= 230x cents+800 cents
= $(230x ÷ 100)+$(800 ÷ 100)
= $2.3x + $8
Therefore,Louise spent $2.3x and $8 as total amount
b)
Sorry,I dont know inequality
I'm very confused about this, please explain this to me.
The angles of the given triangle are 136°,24°, and 20°.
Given that a triangle has angles as 4y°,(y-10)°, and 20° and asked to find out the angles of the given triangle
The sum of the angles of the triangle =180°
⇒4y°+(y-10)° + 20°=180° { adding the given angles and equating it to 180° as the sum of the angles in the triangle is 180°}
⇒5y+10=180°.{added all the given angles and equated it to 180°}
⇒5y=170°
⇒y=34°
⇒4y=136°, (y-10)°=24° and 20°
Therefore the angles of the given triangle are 136°,24°, and 20°.
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Read following problem. Identify what you need to know. Then use the information in the problem to solve. Show your work.
R S is the midsegment of trapezoid M N O P . What is the length of RS ?
A 14 units B 19 units C 23 units D 26 units
Answer:
ssdf
Step-by-step explanation:
dbd beddbees sveveusbs wie eje edidjebebe djebejdjebe ejd s
lf m/1 = 2x + 3, and m/2 = 3x + 7, which is the value of x?
The value of x is -(11/7).
This problem is related to solving an algebraic equation.
In algebra there are many types of equations such as linear equation in one variable and two variable.
Here we have been given two variables and two equations which means we can solve the equation. To solve an equation in algebra it is important that the number of unknowns is equal to the number of equations given.
Given, m/1=2x+3 i.e., m=2x+3
also m/2=3x+7 i.e., m=6x+14
Now equating both the values of m;
2x+3=6x+14
⇒6x-2x=3-14
⇒4x=-11
∴ x= -(11/4)
Hence, the value of x is -11/4.
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Statistics expert daniel yankelovich believes that ________ give americans a certain amount of self-esteem and a fairly clear idea of who they are.
Statistics expert daniel yankelovich believes that middle-class values give Americans a certain amount of self-esteem and a fairly clear idea of who they are.
Who is a statistician?This is the title that is used to refer to the people that have being trained in such a way that they are able to apply statistical approaches and methods to the real life problems that exists in the environment.
They are known to be able to get the solutions to problems by the use of models of statistics and analyzing them as well.
Hence we can say that Statistics expert daniel yankelovich believes that middle-class values give Americans a certain amount of self-esteem and a fairly clear idea of who they are
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Multiple Choice Question.
Show Work Needed.
First of all, every number in each row is odd, so we can eliminate 392 and 394.
The number of elements in each row forms an arithmetic sequence:
• 1st row : 1 element
• 2nd row : 3 elements - and 3 - 1 = 2
• 3rd row : 5 elements - and 5 - 3 = 2
• 4th row : 7 elements - and 7 - 5 = 2
and so on, so that the [tex]n[/tex]-th row has [tex]1 + 2(n-1) = 2n - 1[/tex] elements.
This means that in [tex]n-1[/tex] complete rows, there is a total of
[tex]\displaystyle \sum_{i=1}^{n-1} (2i-1) = n^2 - 2n + 1[/tex]
elements, so that the first element in the subsequent [tex]n[/tex]-th row is the [tex](n^2-2n+2)[/tex]-th number in the sequence {1, 3, 5, 7, …}, i.e the [tex](n^2-2n+2)[/tex]-th odd positive integer. To compute the sum, I use the following well-known formulas.
[tex]\displaystyle \sum_{i=1}^n 1 = n[/tex]
[tex]\displaystyle \sum_{i=1}^n i = \frac{n(n+1)}2[/tex]
Now, the [tex]n[/tex]-th term of the sequence {1, 3, 5, 7, …} is simply [tex]2n-1[/tex], the [tex]n[/tex]-th odd positive integer. So the first element in the [tex]n[/tex]-th row is
[tex]2(n^2-2n+2) - 1 = 2n^2 - 4n + 3[/tex]
and hence the 1st element of the 15th row is
[tex]2\cdot15^2 - 4\cdot15 + 3 = \boxed{393}[/tex]
Awnser for me quickly pleaseee
Answer:
137 ≤ 15x +
Step-by-step explanation:
A new Community Sports Complex is being built in Del Rio. The perimeter of the rectangular playing field is 528 yards. The length of the field is 6 yards less than quadruple the width. What are the dimensions of
the playing field?
The width is yards.
The length is yards.
Save
The dimensions of the playing field the width is 54 yards and the length is 210 yards.
Given that the perimeter of the rectangular playing field is 528 yards and the length of the field is 6 yards less than quadruple the width.
Let the width of the rectangular playing field is x yards and it is given that the length of the field is 6 yards less than quadruple the width means the length is 4x-6.
As we know that the perimeter of the rectangle is two times the sum of length and breadth so.
P=2(l+w)
As it is given that the perimeter is 528 yards.
So, we will substitute all the values in the formula, we get
528=2(4x-6+x)
528=2(5x-6)
528=10x-12
528+12=10x-12+12
540=10x
540/10=10x/10
54=x
Now, substitute this values in l=4x-6 to find the length, we get
l=4(54)-6
l=216-6
l=210
Hence, the dimension of the playing field when the perimeter of the rectangular playing field is 528 yards is width is 54 yards and length is 210 yards.
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solve the equation x/3-6=5
Answer: x= 33
Step-by-step explanation: hope this helps!!!
Lashonna passed back 140 papers, if these papers were in stacks of 28 how many stacks of papers did lashonna pass back
By unitary method we can say that number of stacks of papers Lashona will pass back from 140 if each stack conatins 28 papers is 5.
According to the given question.
Total number of papers Lashonna passed back = 140
And one stack is made up of 28 papers.
As we know that, the unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Therefore,
By unitary method number of stacks of papers would be made from 140 if each stack conatins 28 papers
= 140/28
= 5
Hence, by unitary method we can say that number of stacks of papers Lashona will pass back from 140 if each stack conatins 28 papers is 5.
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Find the 59th term of the arithmetic sequence 29, 37, 45, ...
Answer:
AP = 29,37,45,...
d= t2-t1
=37-29
=8
n=59
t59=?
tn=a+(n-1)d
t59=29+(59-1)8
t59=28+58×8
t59=28 + 464
t59=492
Step-by-step explanation:
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five times square of a number is equal to 45
Answer:
x can be -3, or +3
Step-by-step explanation:
The equation would be
5[tex]x^{2}[/tex] = 45
Divide both sides by 5
[tex]x^{2}[/tex] = 9
Take the square root of both sides
x = ± 3
If 3 books are picked at random from a shelf containing 5 novels, 3 books of poems, and a dictionary, what is the probability that:________
The probability that:
a dictionary is selected = [tex]\frac{1}{9}[/tex]two novels and a book of novels is selected = [tex]\frac{5}{14}[/tex]What is probability?Probability refers to the possibility of the occurrence of an event.
P(E) = probability of occurrence of an event E = [tex]\frac{Number Of Favourable Outcomes}{Total Number Of Outcomes}[/tex]
Now,
(a) Total number of books = 5 + 3 + 1 = 9
Probability of getting a dictionary = [tex]\frac{1}{9}[/tex]
(b) Number of ways to select 3 books out of 9 books = [tex]\binom{9}{3}[/tex] = [tex]\frac{9!}{3!(6!)} = \frac{9\times\ 8 \times 7}{6}[/tex] = 84
Number of ways to select 1 out of 3 books of poems = [tex]\binom{3}{1} = \frac{3!}{2!}[/tex] = 3
Number of ways to select 2 out of 5 novels = [tex]\binom{5}{2} = \frac{5!}{2! 3!} = \frac{5\times 4}{2} = 10[/tex]
Thus, the probability of getting 2 novels and 1 book of poem = [tex]\frac{3\times10}{84} = \frac{10}{28} = \frac{5}{14}[/tex]
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(COMPLETE QUESTION:
If three books are picked at random from a shelf containing 5 novels, 3 books of poems, and a dictionary, what is the probability that (a) a dictionary is selected? (b) 2 novels and 1 book of poems are selected?)
The sum of two numbers is 88. If one number is 4 more than half the other number, determine the two numbers by setting up a linear equation.
a. 44
b. 56
c. 61.3
d. 126
e. 138
f. 176
The two numbers by setting up a linear equation are 56 and 32
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the two numbers by setting up a linear equation?Let the two numbers be x and y
Where
y = 4 + 1/2x
So, we have
x + y = 88
Substitute y = 4 + 1/2x in x + y = 88
x + 4 + 1/2x = 88
Evaluate
1.5x = 84
Divide by 1.5
x = 56
Substitute x = 56 in y = 4 + 1/2x
y = 4 + 1/2 * 56
Evaluate
y = 32
Hence, the two numbers by setting up a linear equation are 56 and 32
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I need help , please quickly!
Choose the associated property
The Associative property is not displayed by any of the given equations.
The associative property of several binary operations in mathematics states that the outcome will not change if the parenthesis in an expression are rearranged.
The order in which the operations are carried out within an expression that has two or more instances of the same associative operator in a row doesn't matter as long as the order of the operands is left untouched.
Examples of associative property :
[tex]{\displaystyle {\begin{aligned}(7+8)+1&=7+(8+1)=9\,\\5\times (3\times 7)&=(5\times 3)\times 7=24.\end{aligned}}}[/tex]
The parentheses were rearranged on each line, but the expression values were left alone. It can be argued that "addition and multiplication of real numbers are associative operations" because this is true for addition and multiplication of all real numbers.
Here 8=8+0 displays additive identity property.
10×1=10 displays multiplicative identity
5+0=5 displays displays additive identity property.
[tex]5\times \frac{1}{5}=1[/tex] displays multiplicative inverse property.
[tex]3+\frac{3}{4} =3+\frac{3}{4}[/tex] displays reflexive property.
Hence no equation displays associative property.
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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Royston is driving to a popular amusement park with his family. Royston’s car had 1515 gallons of gas at the start of the trip. During the trip, he stopped at a gas station and refueled the car with 535 gallons. If the car consumed 1745 gallons of gas during the trip, there are still gallons of gas remaining in the tank. 100 points
Answer: 3 gallons of gas left
Step-by-step explanation: since the car started out with 15 1/5 and then fills up 5 3/5 now there is 20 4/5 in the car then since the car consumed 17 4/5 just subtract the 17 4/5 from 20 4/5 and then you get 3 gallons left since 17 - 20 = 3 and 4/5 - 4/5 = 0/0 or 0 the answer is just 3 gallons left
Answer: it is 3 gallons
Step-by-step explanation:
what is the perimeter of a triangle with the points (-9,4) (7,4) and (7, -8)
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-9}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{7}~,~\stackrel{y_2}{4}) ~\hfill AB=\sqrt{(~~ 7- (-9)~~)^2 + (~~ 4- 4~~)^2} \\\\\\ ~\hfill AB=\sqrt{( 16)^2 + ( 0)^2}\implies \boxed{AB=16} \\\\\\ B(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad C(\stackrel{x_2}{7}~,~\stackrel{y_2}{-8}) ~\hfill BC=\sqrt{(~~ 7- 7~~)^2 + (~~ -8- 4~~)^2}[/tex]
[tex]~\hfill BC=\sqrt{( 0)^2 + ( -12)^2}\implies \boxed{BC=12} \\\\\\ C(\stackrel{x_1}{7}~,~\stackrel{y_1}{-8})\qquad A(\stackrel{x_2}{-9}~,~\stackrel{y_2}{4}) ~\hfill CA=\sqrt{(~~ -9- 7~~)^2 + (~~ 4- (-8)~~)^2} \\\\\\ ~\hfill CA=\sqrt{( -16)^2 + (12)^2}\implies CA=\sqrt{400}\implies \boxed{CA=20} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{Perimeter}{16~~ + ~~12~~ + ~~20\implies \text{\LARGE 48}}[/tex]
Matter is in a liquid state when its temperature is between its melting point and its boiling point. Suppose that some substance has a melting point of -48.39°C and a
boiling point of 313.31°C. What is the range of temperatures in degrees Fahrenheit for which this substance is not in a liquid state? (Hint: C=5/9(F-32)) Express the range
as an inequality
Let x represent the temperature in degrees Fahrenheit. What is the range of temperatures for which this substance is not in a liquid state?
(Type an inequality or a compound inequality. Simplify your answer. Use integers or decimals for any numbers in the expression Round to three decimal places as needed)
[tex]Answer:\ -55.102^0F\leq t^0\leq 595.958^0F[/tex]
Step-by-step explanation:
[tex]\displaystyle\\C^0=\frac{5}{9} (F^0-32^0)\\[/tex]
Let's multiply both parts of the equation by 9/5:
[tex]\displaystyle\\\frac{9}{5} C^0=F^0-32^0\\\\\frac{9}{5} C^0+32^0=F^0-32^0+32^0\\\\\frac{9}{5} C^0+32^0=F^0\\\\Thus,\\\\F^0=1.8C^0+32^0[/tex]
[tex]t=-48.39^0C\\Hence,\\t^0(F)=1.8(-48.39^0)+32^0\\t^0(F)=-87.102^0+32^0\\t^0(F)=-55.102^0[/tex]
[tex]t=313,31^0C\\Hence,\\t^0(F)=1.8(313,31^0)+32^0\\t^0(F)=563.958^0+32^0\\t^0(F)=595.958^0[/tex]
[tex]Thus,\\-55.102^0F\leq t^0\leq 595.958^0F[/tex]
what is the product of 2x-5 and 3x+4? A. 5x - 1 B.6x² - 7x- 20 C.6x² - 20 D. 6x² + 7x - 20
Answer:
B. 6x²-7x-20
Step-by-step explanation:
(2x-5)(3x+4)
2x(3x+4)-5(3x+4)
Use distributive property.
6x²+8x-15x-20
Combine like terms.
6x²-7x-20
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