Answers
The flowchart that is used to prove GR ║ F_K is presented as follows;
∠RND and ∠FDP are supplementary ⇒ ∠RND + ∠FDP = 180°
Given [tex]{}[/tex] Definition of supplementary
∠KDN ≅ ∠FDP [tex]{}[/tex] ⇒ ∠KDN = ∠FDP
Vertical angles are congruent[tex]{}[/tex] Definition of congruent angles
∠RND and ∠KDN are same side interior angles [tex]{}[/tex] ⇒∠RND + ∠KDN = 180°
Definition of same side interior angles[tex]{}[/tex] Substitution property
[tex]{}[/tex] GR ║ F_K
Same side interior angles formed between parallel lines that have a common transversal are supplementaryWhat are the relationships between the angles formed between parallel lines that have a common transversal?The relationships between the angles formed by a transversal and two parallel lines are;
Corresponding angles are congruentSame side interior angles are supplementaryLinear pair angles are supplementaryVertical angles are congruentAlternate interior angles are congruentAlternate exterior angles are congruentDefinition of congruency;
Two lines, shape or figure are said to be congruent if they have the same size and shape.
Supplementary angles;
Supplementary angles are angles that have a sum of 180°
Substitution property of equality
The substitution property sates that if an expression a = b, then the expression b can replace a in any equation and the equation will remain valid.
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Related Questions
Last week, the total weight of the members of a weight loss support group was 2,500 pounds. This week, it was 2,525 pounds. What percent heavier is the group now? %
Answers
The percent increase from 2,500 pounds this week to 2,525 pounds is 1% increase
How to find the percent increase of the weights?From the question, we have the following parameters that can be used in our computation:
Initial weight = 2500 pounds
New weight = 2525 pounds
The percentage increment is then calculated as
Percentage = (Final value - Initial value)/Initial value * 100%
Substitute the known values in the above equation
Percentage = (2525 - 2500)/2500 * 100%
Evaluate the difference
So, we have
Percentage = 25/2500 * 100%
Evaluate the quotient
So, we have
Percentage = 0.01 * 100%
Evaluate the product
So, we have
Percentage = 1%
Hence, the percent increase is 1% increase
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Chris works at an electronics store. He earns $10 per hour plus 12.5% commission on his computer sales. Today, Chris worked 5.5 hours and sold $1100 in computers. How much did Chris earn in total today?
Answers
By solving a simple equation we can see that Chris earned $192.50.
How much did Chirs earn Today?
We know that Chris wins $10 per hour plus the 12.5% of the total amount he solds in computers.
So, if he works 5.5 hours and sold $1,100 in computers, the amount that he earns is given by the equation:
E = $10*5.5 + $1,100*( 12.5%/100%)
E = $10*5.5 + $1,100*(0.125) = $192.50
Then we conclude that Chris earned $192.50 today.
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Is 4.5 greater, less than, or equal to 4 and 1/2
Answers
Answer:
equal to
Step-by-step explanation:
4 + 1/2= 4+ 0.5= 4.5
4.5=4.5
Last year, Leila opened an investment account with $8800. At the end of the year, the amount in the account had decreased by 6%.
Answers
Answer:
The new value is $8,272
Step-by-step explanation:
8800 x (1 - 0.06) = 8272
11. Corey bought 25 gallons of gas to fill up his pickup truck. He paid for the part of the total with a $25 gift card and was left owing $26. How much did he pay per gallon for the gas?
Answers
Answer:
I believe that the answer is $2.04, per gallon.
Step-by-step explanation:
I added the $25 he paid with the gift card, and the $26, which was $51 that Corey paid in total. Corey had gotten 25 gallons and they want to figure out how much he paid for each gallon. So we take the total he spent divided by the number of gallons he had gotten. So 51/25=2.04
Hope this helps!!!!
Whats ?? Also right an addition expression to get the same answer Answer ASAP
Answers
Answer:
p=-10
Step-by-step explanation:
-10-20=-30
Subtracting a negative from a negative will result in a higher negative, the same can be said for -10-20. Removing 10 from -20 will result in a lower answer. This is 20.
Does anyone know the answer to this problem?
Answers
It is a scalene triangle .
What is a scalene triangle?A triangle called a Scalene Triangle in geometry is one with equally spaced-apart sides. It indicates that all three angles and all three sides of a scalene triangle are of different sizes. According to sides, there are three different kinds of triangles.The sides and angles of the triangles are used to define them. A triangle is represented as a three-sided polygon in geometry and is a closed, two-dimensional plane object having three sides and three angles. There are three edges and three vertices.acc to our quesion-
all the sides of triangle are unequal
if all sides are unequal ,it is called scalene triangle.
hence,It is a scalene triangle .
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What should be added to 5/6 to get 41/24
Answers
Answer: 26/24
Step-by-step explanation:
First we have to convert 5/6 with a denominator of 24 so 6 times what makes 24, that is 4 & whatever you do with the denominator, you have to do it with the numerator. So 5 times 4 is 20, the new fraction is 20/24. Now, we need to find what we need to add with 20/24 to get 41/24, so we subtract 20/24 from 41/24 & that is 21/24. We can check if it's correct by adding both 21/24 and 20/24 & that makes 41/24.
5/6 + x = 41/24
x = 41/24 - 5/6
x = 41 - ( 5 multiplied by 4) / 24
x = 41 - 20 / 24
x = 22 / 24
x = 21/3 / 24/3
Final answer x = 7/8
If y varies directly as x, find the constant of variation and the direct variation equation for the situation.
y = 0.1 when x = 0.2
Answers
[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" varies with "x"}}{y=kx}\hspace{5em} \textit{we know that} \begin{cases} y=0.1\\ x=0.2 \end{cases} \\\\\\ 0.1=k(0.2)\implies \cfrac{0.1}{0.2}=k\implies 0.5=k\hspace{5em}\boxed{y=0.5x}[/tex]
Sebastian bought x gallons of gas at a price of $2.91 per gallon at his local gas station. When he paid for the gas, Sebastian also paid $11.40 for granola bars and a box of tissues.
If Sebastian filled 10 gallons of gas, how much did he spend in all at the gas station?
A. $3.92
B. $24.71
C. $40.50
D. $116.91
Answers
If Sebastian filled 10 gallons of gas, the total amount he spent at the gas station was C. $40.50.
How is the total amount determined?Using the mathematical operations of multiplication and addition, we can compute the total amount that Sebastian spent at the gas station.
We first determine the total cost of gas that Sebastian bought by multiplying the unit cost by the quantity.
Secondly, we add the above total cost to the total cost of other items he bought at the station to arrive at the total amount spent.
The cost of gas per gallon = $2.91
The number of gallons of gas bought = 10
The total cost of gas = $29.10 ($2.91 x 10)
The total cost of granola bars and tissues = $11.40
The total amount spent = $40.50 ($29.10 + $11.40)
Thus, mathematically, Sebastian spent C. $40.50 at the gas station.
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how many groups 1/4 are in 3/4
Answers
There are 3 1/4's in 3/4, hope this helps.
Answer: 3
Step-by-step explanation: since they are the same denominator it is basically asking how many 1s go in 3
Convert 0.8 grams to grains
Answers
Answer:
12.3459 grains
Step-by-step explanation:
Answer:
12.346 grains
Step-by-step explanation:
for an approximate result, multiply the mass value by 15.432
( which is basically 0.8 times 15.432)
Find the difference between the sums to ten terms of the AP and GP whose first two terms are-2 and 4.
Answers
The difference between the sum of first 10 terms of AP and GP where the first term and second term is 2 and 4 respectively is -932
What is Arithmetic Progression and Geometric Progression?
An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The general form of a GP is a, ar, ar2, ar3 and so on
Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
Given data ,
First term = -2
Second term = 4
A)
For Arithmetic Progression
First term a = -2
Second term = 4
Common difference d = Second term - First term
= 4 - ( -2 )
= 6
And Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
n = 10 terms
Sₙ = ( 10/2 ) [ (2x- 2) + ( 9 ) x 6]
Sₙ = 5 [ -4 + 54 ]
Sₙ = 5 x 50
Sₙ = 250
Therefore , Sum of first 10 terms of an AP is 250
B)
For Geometric Progression
First term a = -2
Second term = 4
Common ratio = Second term / First term
= 4 / -2
= -2
And Sum of first n terms of an GP : Sₙ = a( 1 - rⁿ ) / ( 1 - r )
n = 10
Sₙ = 2( 1 - ( -2 )¹⁰ ) / 1 - ( -2 )
Sₙ = 2 ( 1 - 1024 ) / 3
Sₙ = ( 2 x (-1023) ) / 3
Sₙ = 2 x ( - 341 )
Sₙ = - 682
Therefore , Sum of first 10 terms of an GP is -682
The difference between the sum of first 10 terms of AP and GP is GP - AP
= -682 - 250
= -932
Hence , The difference between the sum of first 10 terms of AP and GP where the first term and second term is 2 and 4 respectively is -932
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Which ordered pair is a solution of the equation? 2 x + 4 y = 6 x − y 2x+4y=6x−y
Answers
The solution to the equation given as 2x + 4y = 6x − y has the ordered pair of (3, 4)
How to determine the ordered pair of the solution?From the question, we have the following equation that can be used in our computation:
2x+4y=6x−y
Solving further, we need to collect the like terms
So, the equation becomes
2x - 6x = -4y - y
Next, we evaluate the like terms in the above equation
So, we have the following representation
-4x = -3y
Divide both sides by -3
The equation becomes
x = 3/4y
At this point, we assume any value for y and then solve for x
Assume that the value of y is 4
So, we have the following representation
x = 3/4 * 4
Evaluate the products
x = 3
So, we have
x = 3 and y = 4
Express as ordered pairs
(x, y) = (3, 4)
Hence, the ordered pair of the solution is (3, 4)
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How would you investigate the complaints from renters who are
unhappy about their monthly rents?
What statistical measurement would be used?
Answers
To investigate the complaints from renters who are unhappy about their monthly rents, the mean rents can be collected
The statistical measurement that would be used is the ANOVA.
What is a mean?A dataset's mean (also known as the arithmetic mean, as opposed to the geometric mean) is the sum of all values divided by the total number of values. It is the most widely used measure of central tendency and is frequently referred to as the "average."
ANOVA is an abbreviation for Analysis of Variance. It is a statistical test invented by Ronald Fisher in 1918 that has been in use ever since. Simply said, ANOVA determines whether or not there are statistical differences between the means of three or more independent groups. The most basic type is one-way ANOVA. To know of the meansare the same, the ANOVA can be used.
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Factor 64+ 60. Write your answer in the form a(b + c) where a is the GCF of 64 and 60
Answers
64 + 60 = 2x2x2x2x2x2 + 2x2x3x5 = 2x2(2x2x2x2 + 3x5) = 4(16 + 15)
You accidentally inhale some mildly poisonous fumes. From a blood sample poison concentration exponentially
Answers
The exponential function giving the concentration after t hours is given as follows:
[tex]C(t) = 0.00372(0.9359)^t[/tex]
What is an exponential function?The standard modelling of an exponential function is presented as follows:
[tex]y = a(b)^x[/tex]
The meaning of the variables of the equation are given as follows:
a is the initial value of the exponential function, that is, the numeric value of y when x = 0.b is the rate of change of the exponential function, giving by how much y is multiplied when x increases by one.The initial value of the exponential function is given as follows:
a = 0.00372.
After eight hours, the concentration is given as follows:
C(8) = 0.00219.
Hence the rate of change is obtained as follows:
[tex]C(t) = 0.00372b^t[/tex]
[tex]0.00219 = 0.00372b^8[/tex]
[tex]b^8 = \frac{0.00219}{0.00372}[/tex]
[tex]b = \sqrt[8]{\frac{0.00219}{0.00372}}[/tex]
[tex]b = \left(\frac{0.00219}{0.00372}\right)^{\frac{1}{8}}[/tex]
b = 0.9359.
Hence the equation is:
[tex]C(t) = 0.00372(0.9359)^t[/tex]
Missing InformationThe problem is given by the image at the end of the answer, and it asks for the exponential function modelling the situation.
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How do I solve this question
Answers
Answer:
the answer is down there
Pedro walks 3/8 of a mile in a 1/4 of an hour. How many miles does he walk in an hour
Answers
Answer:
S=3/8 miles
T=1/4 hour
V=S/T = 3/8 ÷ 1/4 = (3×4)÷8 = 3/2 miles in an hour
The green basilisk enclosure will include a rectangular pond in one corner. The width of the
pond will be 3 inches less than the width, w, of the enclosure.
W-3
The area of the water's surface is given by this expression: w² - w - 6.
Question
Question 1
Factor the area expression, w² - w - 6.
Replace the values of A and B to write the expression in factored form.
(w - A) (w + B)
Answers
After factorization we get the two terms ( w - 3 ) ( w + 2 )
And the values of A and B as 3 and 2 respectively .
That is A = 3 and B = 2.
The given expression is w² - w - 6.
This question can be calculated easily by middle term split
First step is to multiply the first and the last term
which will give us - 6
thus now we have to look for two number which when either added or subtracted will give us - 1
Thus we can write it as :
w² - 3 w + 2 w - 6
Now take the terms which are common
and we will get
w ( w - 3 ) + 2 ( w - 3 )
( w - 3 ) ( w + 2 )
Thus if we compare it with (w - A) (w + B)
we will get the values of A and B as
3 and 2 respectively .
That is A = 3 and B = 2
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Eugene has a collection of 140 pet rocks. Of these rocks, 35% are sedimentary, 40% are igneous, and the rest are metamorphic. How many are metamorphic?
Answers
Answer:
25% or 35 rocks.
Step-by-step explanation:
To find this answer, simply add up 40% and 35% to get 75%. Now, 100% is the most we can have. So, 100 - 75 = 25%.
To find even more in depth of exactly how much 25% of 140 is, we can simply move the decimal point from 25 over twice to get 0.25. The term "of" means multiply:
0.25 x 140 = 35 rocks.
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Choose from the drop-down menus to match the trigonometric expression with its value
Answers
The values that match the various trigonometric identity are;
1) sin²/₅π cos π/₁₀ + cos²/₅π sin π/₁₀ = 1
2) cos 13 cos 47 + sin 13 sin 47 = 0.5
3) sin²/₅π cos ⁸/₅π + cos²/₅π sin ⁸/₅π = 0
How to solve Trigonometric Identities?Trigonometric identities are defined as the equations that involves the trigonometric functions that are true for every value of the variables involved.
1) We know that the trigonometric identity sin(A + B) is expressed as;
sin(A + B) = sinAcosB + cosAsinB
We are given;
sin²/₅π cos π/₁₀ + cos²/₅π sin π/₁₀
Applying the trigonometric identity above, gives us;
sin(²/₅π + π/₁₀)
= sin(5π/10)
= sin(π/2)
= 1
2) We know that the trigonometric identity sin(A + B) is expressed as;
cos(A + B) = cosAcosB − sinAsinB.
We are given;
cos 13 cos 47 + sin 13 sin 47
Applying the trigonometric identity above, gives us;
cos(13 + 47)
= cos 60
= 0.5
3) We know that the trigonometric identity sin(A + B) is expressed as;
sin(A + B) = sinAcosB + cosAsinB
We are given;
sin²/₅π cos ⁸/₅π + cos²/₅π sin ⁸/₅π
Applying the trigonometric identity above, gives us;
sin(²/₅π + ⁸/₅π)
= sin(¹⁰/₅π)
= sin(2π)
= 0
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3. Simplify the expression below.
√-100-2√√-16
A. -12i
B. -2i
C. 12i
D. 2i
Answers
Use the drawing tools to graph the solution to this system of inequalities on the coordinate plane.
y> 2x+4
x+y≤6
Answers
The graph of inequalities equation on coordinate plane is given below ↓↓↓
Difference between equality and inequality equations
Both mathematical phrases, equality and inequality , are created by connecting two expressions.The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols show that the two expressions in an inequality are not always equal: >, <, ≤ or ≥. Or in simple words the equation which has '=' sign is an equality equation while the inequality equation has the signs are >, <, ≤ or ≥.
The inequalities equation is ,
y> 2x+4
x+y≤6
so, the graph is ↓↓↓
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Man is ordering new tile for her kitchen floor the area of the floor is 115.4 ft.² and she wants to order between 15% and 20% extra of the material
Answers
The order for the extra materials that are ordered by the man will be between 17.31 ft² and 23.08 ft².
How to calculate the value?From the information, the man is ordering new tile for her kitchen floor the area of the floor is 115.4 ft.² and wants to order between 15% and 20% extra of the material.
It should be noted that 15% of the material will be:
= 15% × 115.4
= 17.31 ft²
It should be noted that 20% of the material will be:
= 20% × 115.4
= 23.08 ft²
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Solve: √x-4= -2
a) x=2
b) x=8
c) There is no solution.
d) x=0
Answers
Answer: There is no solution
Step-by-step explanation:
The formatting of the question isn't clear, but I'll still explore both possibilities. If the square root is only applied to x, we can solve for the variable by adding 4 to both sides and then squaring both sides, which would give us 4. Since that is not an answer choice, it means the square root applies to x-4. With this problem, we square both sides right away. That gives us x=0, but plug 0 back into the original equation. Doing so gives us the square root of -4, which is not possible with real numbers, only with imaginary numbers.
In order for a gear to work in a piece of machinery, the radius of the gear, r, must be greater than 4 cm, but not exceed 4.1 cm. Which compound inequality represents the situation?
r > 4 and r ≤ 4.1
r > 4 or r ≤ 4.1
r < 4 and r ≥ 4.1
r < 4 or r ≥ 4.1
Answers
Answer:cap
Step-by-step explanation:C A P
Write log₂ A as a natural logarithm.
Answers
Answer:
ln A / ln 2
Step-by-step explanation:
Using the change of base rule: ln A / ln 2
Which ratio is equivalent to 9 : 180?
Answers
Answer:
18:360 is the correct answer
Alex house is 15 blocks from school. Carlene lives 7 blocks from Alex's house. Which equation represents the location of Carlene's house in relation to the school?
|x+7|=15
|x-7|=15
|x+15|=7
|x-15|=7
Answers
Answer:
Answer is b
Step-by-step explanation:
Because
|x-7|=15--->x=15+7, x=22