In the figure to the right point O is the midpoint of segment
AB
. Through point O is drawn a line
OX
.perpendicular to
AB
. Prove that any point on line
OX
is equidistant from A and B.
Answers
Answer:
See proof below
Step-by-step explanation:
Point O is the midpoint of segment AB. Through point O is drawn a line OX perpendicular to AB. Consider two triangles AOX and BOX. These triangles are right triangles, because OX is perpendicular to AB. In these triangles:
OX=OX (reflexive property of congruence);AO=OB (by the definition of the midpoint O).Thus, [tex]\triangle AOX\cong \triangle BOX[/tex] by LL theorem.
Congruent triangles have congruent corresponding sides, then AX=BX. This means that point X is equidistant from points A and B.
Related Questions
1. Write an expression for "n decreased by 3."
Answers
Answer:
n-3
Step-by-step explanation:
Answer: The required expression is [tex]n-3.[/tex]
Step-by-step explanation: We are given to write an expression for the following statement :
"n decreased by 3."
We know that
if we are decreasing a units from some quantity b, then we should subtract a from b.
This is written as follows :
[tex]E=b-a.[/tex]
Therefore, for the given expression, we should subtract 3 from n.
This can be written as :
[tex]E=n-3.[/tex]
Thus, the required expression is [tex]n-3.[/tex]
Making sure I’m doing this write... please give a walkthrough explanation! :)
144= -12(x+5)
(I’m solving for x)
Answers
Start by distributing:
-12(x+5) = (-12 * x) + (-12 * 5) = -12x - 60
144 = -12x - 60
Add 60 to both sides to start isolating your variable:
204 = -12x
Solve for x by dividing both sides by -12:
x = -17
Step-by-step explanation:
multiply -12 with x and 5, after you get the answer. subtract 60 on the left and right, after getting 84 divide it by -12 and the final answer will be -7
According to the manufacturer, about 26% of sour candy in a package of Sandy's Sours are grape. What is the probability that the first grape candy chosen from the bag will be, at LEAST, the third candy chosen overall?
Answers
To find the probability that the first grape candy chosen from the bag will be, at least, the third candy chosen overall, you multiply the probability that a candy is not grape (0.74) by itself (since we're considering two independent events, both candies not being grape). The answer is 0.5476.
Explanation:The subject of this question is probability which is a branch of mathematics. You're looking to find the probability that the first grape candy drawn from a bag of Sandy's Sours will be, at least, the third candy chosen overall.
Given that 26% of the candies are grape, the probability that the first candy drawn is not grape is 1 - 0.26 = 0.74 (or 74%). Since we're looking for the first grape candy to be the third candy drawn or later, we need the first two candies to be not grape.
The probability that the first candy drawn is not grape is 0.74. Because each candy draw is an independent event (the result of one draw does not affect the results of any other draws), the probability that neither the first nor the second candy drawn is grape is 0.74 * 0.74 = 0.5476 (or 54.76%).
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Lombardi pizza sells one 20in cheese pizza or two 12in pizzas for 12.99. Determine which size gives more pizza.
Answers
My guess is the two 12 inch pizza which in a total is 24 I’m not really good at math but I think this is the correct answer
Answer:
Two 12 inch pizzas
Step-by-step explanation:
Multiply12x2= 24 inches compared to 1 20inch pizza
Please Solve #25 Thx
Answers
check the picture below.
notice, we can find the area of the pink triangle (garden), since we know its base and height, we can also find the areas of the yellow triangle (lawn), since we also know its base and height.
[tex]\bf \stackrel{\textit{area of the garden}}{\cfrac{1}{2}(40)(70)}\implies 1400~\hfill \stackrel{\textit{area of the lawn}}{\cfrac{1}{2}(100)(70)}\implies 3500 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{\textit{area of the lawn}}{\textit{area of the garden}}\qquad \qquad \cfrac{3500}{1400}\implies \cfrac{5}{2}\implies 2\frac{1}{2}\textit{ times larger}[/tex]
There are 96 coins in a bottle. 1\2 of the coins are £1 coins. The rest of the coins are 50p coins. work out the total value of the 96 coins I need help with this
Answers
Answer:
£72
Step-by-step explanation:
Firstly, if half of 96 coins are £1 coins then:
96/2 * 1 = value of half the coins = £48
Now, we simply need to multiply 96/2 by 0.5 to find the value of these coins:
48 * 0.5 = 24
Now we can add the two:
48 + 24 = 72
So the value of the 96 coins are £72.
Hope this helps!
ll the members of a construction crew work at the same pace. Six of them working together are able to pour foundation in 22 hours. a How many hours would this job take if the number of workers decreased by factor of 2?
Answers
Answer:
44 hours
Step-by-step explanation:
Decreasing the people by a factor of 2 means we have 3 people
The job takes 6* 22 = 132 people hours
When we decrease the people, it will take more hours
132 people hours = 3 people * t hours
Divide each side by 3
132/3 = 3t/3
44 = t
It will take 44 hours
Travis is sewing a pillow for his Home Arts class. The pillow will be made from 2 identical rectangles. Each rectangle is 1 1/2 feet wide and 1 3/4 feet long. How many square feet of material is used in the sewing of the pillow?
Answers
Answer:
11/4
Step-by-step explanation:
Type the correct answer in each box. Spell all words correctly.
A sequence of transformations maps ∆ABC onto ∆A″B″C″. The type of transformation that maps ∆ABC onto ∆A′B′C′ is a
.
When ∆A′B′C′ is reflected across the line x = -2 to form ∆A″B″C″, vertex
of ∆A″B″C″ will have the same coordinates as B′.
Answers
Answer:
Reflection
Step-by-step explanation:
When we reflect a point on the x axis, the y coordinate changes its sign.
For example if a Point P has coordinates (x,y), it will be (x, -y) after reflection on the x axis.
A (-6,2) reflected on the x axis becomes A' (-6, -2)
B (-2,6) reflected on the x axis becomes B' (-2, -6)
C (-4,2) reflected on the x axis becomes C' (-4, -2)
So, the type of transformation that maps ∆ABC onto ∆A′B′C′ is a reflection on the x axis.
Answer:
Reflection
Step-by-step explanation:
When we reflect a point on the x axis, the y coordinate changes its sign.
For example if a Point P has coordinates (x,y), it will be (x, -y) after reflection on the x axis.
A (-6,2) reflected on the x axis becomes A' (-6, -2)
B (-2,6) reflected on the x axis becomes B' (-2, -6)
C (-4,2) reflected on the x axis becomes C' (-4, -2)
So, the type of transformation that maps ∆ABC onto ∆A′B′C′ is a reflection on the x axis.
Step-by-step explanation:
Yesterday, Julie’s bank account balance was $39.99. Today, she made a withdrawal from her account. The current balance is –$10.28.
How much did she withdraw from her account?
A). $50.27
B). $29.71
C). $0.00
D). $19.61
Answers
Answer:
A). $50.27
Step-by-step explanation:
Add $39.99 and -$10.28 to get $50.27
Final answer:
Julie withdrew $50.27 from her account, which can be calculated by adding her previous balance of $39.99 to the absolute value of her negative current balance, $10.28.
Explanation:
The question asks to determine how much was withdrawn from Julie's bank account, given that her balance went from $39.99 to -$10.28. To do this, we subtract the current balance from the previous balance. So the calculation is $39.99 - (-$10.28).
First, subtracting a negative is the same as adding its absolute value, so the equation can be rewritten as $39.99 + $10.28.
When these two values are added together, we get a total of $50.27. This means that Julie withdrew $50.27 from her account.
Therefore, the correct answer is A). $50.27.
Given the sequence -1,3,7,11 find a25
Answers
It'a an arithmetic sequence.
[tex]a_1=-1\\a_2=-1+4=3\\a_3=3+4=7\\a_4=7+4=11\\\vdots\\\\\text{The general formula of nth term of an arithmetic sequence:}\\\\a_n=a_1+(n-1)d\\\\\text{We have:}\\\\a_1=-1,\ d=4\\\\\text{Substitute:}\\\\a_n=-1+(n-1)(4)=-1+4n-4=4n-5\\\\\text{We want }\ a_{25}.\ \text{Substitute n = 25 to the formula:}\\\\a_{25}=4(25)-5=100-5=95\\\\Answer:\ \boxed{a_{25}=95}[/tex]
Which data set matches the box and whisker plot? A. 12.5, 15, 17, 23, 23, 24, 26, 29, 31, 32, 33 B. 11, 13, 16, 19, 23, 23, 24, 29, 31, 33, 34 C. 11, 12, 15, 18, 24, 24, 25, 27, 30, 32, 34 D. 10.5, 12, 15, 17, 23, 23, 24, 26, 29, 34
Answers
Answer:
c
Step-by-step explanation:
What is the measure of abc ?
Answers
Answer:
Option D 63°
Step-by-step explanation:
Two secants AE and CD intersect each other at point B inside the circle.
So by secants theorem,
[tex]\frac{m(AC)+m(DE)}{2}[/tex] = ∠ABC = ∠DBE
= [tex]\frac{1}{2}[/tex] ( 82 + 44 )
= [tex]\frac{1}{2}[/tex] ( 126)
= 63
Option D 63° is the answer.
Charlene sold 15 magazines subscriptions for the fundraiser. Mark sold 17 subscriptions and Paul sold 12. How many magazine subscriptions did they sell in all?
Let s represent subscriptions
Equation:______
They sold_____ subscriptions in all.
Answers
The sold 44 magazine subscriptions in total.
Charlene, Mark, and Paul sold a combined total of 44 magazine subscriptions for their fundraiser.
Explanation:In this problem, Charlene, Mark, and Paul collectively sold magazine subscriptions. We need to find the total number of subscriptions sold. We can do this using simple addition: Charlene sold 15 subscriptions, Mark sold 17 subscriptions, and Paul sold 12 subscriptions. Therefore, using s to represent total subscriptions, our equation would be: s = 15 (Charlene's sales) + 17 (Mark's sales) + 12 (Paul's sales). Summing the numbers, s = 44. Hence, they sold 44 subscriptions in total.
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let x = -5
evaluate the function for y
y=4.7x-6
Answers
Answer:
y = -29.5
Step-by-step explanation:
y = 4.7x - 6
x = -5
y = 4.7(-5) - 6
y = -23.5 - 6
y = -29.5
Given g(x)=3x+5, find g(-6)
Answers
g(-6) This means that x = -6, so you can plug in -6 for "x" in the equation
g(x) = 3x + 5
g(-6) = 3(-6) + 5
g(-6) = -18 + 5
g(-6) = -13
To find g(-6), substitute -6 into the given function and simplify the expression.
Explanation:To find g(-6), we substitute -6 into the given function, g(x) = 3x+5.
So, g(-6) = 3*(-6) + 5
g(-6) = -18 + 5
g(-6) = -13
Therefore, g(-6) = -13.
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Find the sum or difference.
16/17 + 3/17=?
A.19/17
B.9/34
C.1/2
Please help me
Answers
Enzel goes online to buy a graphing calculator. He finds a site that currently has a promotion of 15% off on all orders over $50. Enzel decides to buy his graphing calculator, with a price tag of $83, at this site because he knows that he will get the 15% discount when he checks out. Enzel pays 4.5% sales tax on the discounted price and pays a shipping fee of $6.35. What is the total of Enzel’s online purchase?
Answers
So firstly, we need to find the discounted price. Since this is going to be a decrease by percentage, we will be using this format:
(1 - p)m(p = percentage in decimal form and m = original price)In this case:
[tex]15\% = 0.15\\\\(1-0.15)*83\\0.85*83\\70.55[/tex]
Now that we have the discounted price, we must apply the 4.5% sales tax. Since this is going to be an increase by percentage, we will be using this format:
(1 + p)mIn this case:
[tex]4.5\%=0.045\\\\(1+0.045)*73.55\\1.045*70.55\\73.72[/tex]
Now we have the discounted price with the sales tax. Now all we have to do is add the shipping fee:
[tex]73.72+6.35=80.07[/tex]
AnswerThe total price of Enzel's purchase is $80.07.
Answer:
A) $80.07
Step-by-step explanation:
for all the lazy ones who don't want to actually learn :)
ED2020
A developer has 7 1/2 acres of land to build houses on. If each house is to be built on 1/4 acre plot, how many houses can he build?
Answers
Answer:
He could build 30 houses.
Step-by-step explanation:
7 1/2 divided by 1/2 equals 30!
Answer: 30 houses can be built
Step-by-step explanation:
A recursive rule for an arithmetic sequence is a1=-2; an=an-1 -9
What is an explicit rule for this sequence?
Answers
The explicit rule for the given arithmetic sequence is an = -2 + (n - 1) * (-9)
Explanation:An arithmetic sequence is a sequence of numbers in which each term is found by adding a common difference to the previous term. In this case, the recursive rule for the arithmetic sequence is given as a1 = -2 and an = an-1 - 9.
To find the explicit rule for this sequence, we need to find a formula that directly calculates the nth term of the sequence. We can do this by examining the pattern in the sequence:
First term: a1 = -2Second term: a2 = a1 - 9 = -2 - 9 = -11Third term: a3 = a2 - 9 = -11 - 9 = -20Fourth term: a4 = a3 - 9 = -20 - 9 = -29...From the pattern, we can see that each term is obtained by subtracting 9 from the previous term. So, the explicit rule for this arithmetic sequence is given by:
an = a1 + (n - 1) * d
where a1 is the first term, n is the term number, and d is the common difference. Plugging in the values, we have:
an = -2 + (n - 1) * (-9)
Simplifying this equation gives the explicit rule for the sequence.
Final answer:
The explicit rule for the arithmetic sequence is an = -2 + (n-1)(-9).
Explanation:
An explicit rule for an arithmetic sequence is given by the formula:
an = a1 + (n-1)d
Where:
an is the nth term of the sequence
a1 is the first term of the sequence
n is the position of the term in the sequence
d is the common difference between consecutive terms
In this case, the first term (a1) is -2 and the common difference (d) is -9. Therefore, the explicit rule for this sequence is:
an = -2 + (n-1)(-9)
there are 11 regular players and 5 substitute players on a soccer team how many players are on 15 soccer teams ??
Answers
Answer:
225 players (including the substitutes)
Step-by-step explanation:
11 regular player and 4 substitutes makes 15 team members per team.
15 players on each team times 15 teams gives you 225 players in total.
The total number of players on 15 soccer teams can be calculated by multiplying the total number of players (including regular and substitute) on one team (16 players) by the number of teams (15), which equals 240 players.
Explanation:The subject of this question is Mathematics, and it's referencing a concept of multiplication in a real-world context. To determine the total number of players on 15 soccer teams, you consider that each team is composed of 11 regular players and 5 substitutes. So, the total number of players on one team is 16 (11 regular players + 5 substitutes).
To find out the number of players on 15 teams, you multiply the number of players on one team by 15. That is, 16 players * 15 teams = 240 players. So, there are 240 players on 15 soccer teams.
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Here is the new question, plz solve this one for me
Answers
Answer:
1805.4
Step-by-step explanation:
Answer:
the answer is 1,710 it is adding 30 each time
Step-by-step explanation:
1 month=1,500
2 months=1,530
3 months=1,560
4 months=1,590
5 months=1,620
6 months=1,650
7 months=1,680
8 months=1,710
How many solutions are there to the equation below? 4(x-5)=3x+7
A. 1
B. 0
C. Infinitely Many
Answers
Answer:
A. 1
Step-by-step explanation:
4(x - 5) = 3x + 7
4x - 20 = 3x + 7
+ 20 = + 20
4x = 3x + 27
-3x -3x
1x = 27
x = 27
The answer is A.1
An equation is formed of two equal expressions. There exists only one solution to the problem which is equal to 27. Thus, the correct option is A.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution of the equation can be found as shown below,
4(x-5)=3x+7
4x - 20 = 3x + 7
4x - 3x = 20 + 7
x = 27
Hence, there exists only one solution to the problem which is equal to 27. Thus, the correct option is A.
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Y=-4x y=x^2-12 solve the system of equations
Answers
Answer:
(-6, 24) and (2, -8)
(-6, 24) and (2, -8) is the answer.
What's the easiest way to remedy a system of equations?
There are three strategies used to resolve structures of equations: graphing, substitution, and elimination. To solve a gadget via graphing, you honestly graph the given equations and locate the factor(s) in which they all intersect. The coordinate of this point will provide you with the values of the variables that you are fixing.
How do you remedy a gadget of equations without graphing?To remedy a machine of linear equations without graphing, you may use the substitution technique. This method works by way of solving one of the linear equations for one of the variables, then substituting this price for the same variable in the different linear equation and solving for the other variable.
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The sum of the speeds of two trains is 718.7 miles per hour. If the speed of the first train is 3.3 mph faster than that of the second train, find the speeds of each.
Answers
Answer:
2x + 3.3 = 718.7 mph
Step-by-step explanation:
Jasmine practices the piano for 10 minutes on Monday. Every day she increases her practice time by 5. If she continues this pattern, how many minutes will she practice on the 7th day?
Answers
Answer:
40 minutes
Step-by-step explanation:
Day 1) Monday --> 10 min.
Day 2) Tuesday --> 15 min.
Day 3) Wednesday --> 20 min.
Day 4 )Thursday --> 25 min.
Day 5) Friday --> 30 min.
Day 6) Saturday --> 35 min.
Day 7) Sunday --> 40 min.
Using the formula for the nth term in an arithmetic sequence, we find that Jasmine will practice for 40 minutes on the 7th day.
Explanation:The problem can be solved by using arithmetic progression. The first term of this sequence is the amount of time Jasmine spent practicing on Monday, which is 10 minutes. The common difference is the amount of time she adds to her practice every day, which is 5 minutes. To find out how long she will practice on the 7th day, we can use the formula for the nth term in an arithmetic sequence: a + (n-1)d.
Plugging in our values, we find:
10 + (7-1)*5 = 10 + 30 = 40.
So, Jasmine will practice for 40 minutes on the 7th day.
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A small airplane takes off from point A and continues to climb upward in a straight line, as shown in the diagram. What is the plane’s distance from point A when it reaches point C?
A. 6,900 feet
B. 7,000 feet
C. 11,636 feet
D. 12,600 feet
E. 13,400 feet
Answers
Answer:
The distance from A to C is 12600 ft
Step-by-step explanation:
We can use similar triangles to help us solve the problem.
5600 ft AC
------------- = --------------
5200 ft 5200 + 6500
5600 ft AC
------------- = --------------
5200 ft 11700
We can solve using cross products
11700* 5600 = AC *5200
65520000=5200 AC
Divide each side 5200
65520000/5200 = AC
12600 =AC
Answer:
12600
Step-by-step explanation:
what type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue a.find a mixture that will make the same shade of green but a smaller amount
Answers
Answer:
Step-by-step explanation:
We are given that a shade of green is prepared using 2 cups of yellow and 3.5 cups of blue.
We want to make the same shade of green, but lesser quantity. We can assume a smaller value for either of the yellow or the blue colors, and find the corresponding value of the other to figure out the answer.
Let us assume that 1 cup of yellow is mixed with x cups of blue to prepare the same shade of the green. Now we can set up the ratios as shown below:
[tex]\frac{1}{x}=\frac{2}{3.5}\\2x=3.5\\x=1.75[/tex]
Therefore, 1 cup of yellow and 1.75 cups of blue color will also make the same shade of green
PLZ HELP URGENT 30 POINTS!!!!!
Which of the following
functions maps 3 to -5
F(x)=4-x^2
F(x)=x-5
F(x)=-x+2
F(x)=x+8
Answers
Answer:
F(x)=4-x^2
Step-by-step explanation:
I am assuming that x=3 and y=-5
Put in x =3
F(3)=4-3^2 = 4-9 =-5 Yes
F(3)=3-5 = -2 No
F(3)=-3+2 = -1 No
F(3)=3+8=11 No
Which of the following would earn the same amount of interest as a $600 principal with 2.5% interest for 6 years?
Answers
To earn the same amount of simple interest as $600 with 2.5% interest over six years ($90), another investment combination that would yield the same interest amount is $1,000 at 3% interest for 3 years.
Explanation:The student is asking which investment would earn the same amount of simple interest as a principal of $600 with 2.5% interest over 6 years. The formula for calculating simple interest is Interest = Principal imes Rate imes Time. For the given principal of $600 with 2.5% interest over 6 years, the interest earned would be:
Interest = $600 imes 0.025 imes 6
Interest = $90
To find another investment with the same interest earned, one must find a principal, rate, and time that satisfy the equation:
Interest Earned = New Principal imes New Rate imes New Time = $90
An example would be a principal of $1,000 with 3% interest for 3 years:
Interest Earned = $1,000 imes 0.03 imes 3
Interest Earned = $90
This indicates that both investments would earn the same amount of interest over their respective periods.