1. Using the drawing, if the measure of angle 2 is 42° and the measure of angle 3 is 52°, what is the measure of angle 6?
A. There isn't enough information to determine.
B. 104°
C. 86°
D. 94°
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2.If the areas of two similar hexagons are to each other as 5 : 2, and one side of the first hexagon is 25, what is the corresponding side in the other hexagon?
A. 3.16
B. 250.00
C. 10.00
D. 15.81
Answers
first is 86
we know because of the sum of the interior angles of a triangle being 180, and that 5 + 6 =180
Answer: The correct options are (1) (D) 94° and (2) (D) 15.81.
Step-by-step explanation: The calculations are as follows:
(1) In the attached figure, given that m∠2 = 42° and m∠3 = 52°.
We are to find the measure of ∠6.
In a triangle, the sum of the measures of two remote interior angles is equal to the measure of the exterior angle.
In the given triangle, ∠2 and ∠3 are remote interior angles and ∠6 is the exterior angle.
So, we have
[tex]m\angle 6=m\angle 2+m\angle 3=42^\circ+52^\circ=94^\circ.[/tex]
Thus, (D) 94° is the correct option.
(2) Given that the areas of two similar hexagons are related to each other as 5 : 2 and one side of the first hexagon is 25.
We are to find the corresponding side in the other hexagon.
Let, 'a' and 'b' be the lengths of the corresponding sides of the two similar hexagons.
The, the ratios of the area of the hexagons will be a² : b².
So, we have
[tex]\dfrac{a^2}{b^2}=\dfrac{5}{2}\\\\\\\Rightarrow \dfrac{25^2}{b^2}=\dfrac{5}{2}\\\\\\\Rightarrow b^2=2\times\dfrac{625}{5}\\\\\\\Rightarrow b^2=250\\\\\Rightarrow b=5\sqrt{10}=15.81.[/tex]
Thus, the correct option is (D) 15.81.
Related Questions
(4.9 x 10^-2) (9.80 x 10^2) = _____
Answers
4.9×10^-2 and 9.80×10^2 ( find the scientific notation)
.0049 for the first one
980. for the second one
Then you multiply:
.0049×980.=4.802
Your answer is 4.802
Quinn runs 3 miles 3 times every week. How many miles does Quinn run in 6 weeks
Answers
what is the sum of three consecutive odd integers is 75?
Answers
they are n, n+2, n+4
the sum is 75
n+n+2+n+4=75
3n+6=75
minus 6 both sides
3n=69
divide both sides by 3
n=23
n+2=25
n+4=27
the integers are 23,25,27
Avery and her friends attend a museum. It costs $5 to enter the main exhibit hall, with an added charge of $3 to view each special exhibit. Avery writes an equation that models the total price of visiting the museum as a function of the number of special exhibits they view. What is the slope and y-intercept of Avery’s model?
Answers
And y intercept =5+3x
Hence, slope = 3 and, y-intercept = 5.
What is function?
Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
Here, given that,
Avery and her friends attend a museum. It costs $5 to enter the main exhibit hall, with an added charge of $3 to view each special exhibit.
Avery writes an equation that models the total price of visiting the museum as a function of the number of special exhibits they view.
Now, let the function be,
f(x)= 3x+5 = the total price of visiting the museum
[where, x= special exhibit & 5=the main exhibit hall]
Let, y = f(x)
So, w get, y=3x+5
Hence, slope = 3
and, y-intercept = 5.
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ax-x=c
solve the equation for x
Answers
Like last problem, group the x out.
x(a-1) = c
Now divide.
x = c/a-1
Hope this helps!
which number has a 2 in position where it represents 10 times as much as the 2 in 4,523 a. 241 d. 612 c. 928 b. 2,175
Answers
The 2 in 4,523 is 20.
20 times 10= 200.
So the answer has to have a 2 in the hundreds place.
The number 2,175 is the correct answer because its 2 is in the 'hundreds' place which is 10 times as much as the 2 in the 'tens' place of the number 4,523.
Explanation:In the provided options for numbers, we are to find a number which has a 2 that represents 10 times as much as the 2 in 4,523. In number 4,523, the number 2 represents '20', that is, it is in the 'tens' place. Therefore, we are looking for a number where 2 is in the 'hundreds' place as the 'hundreds' place is 10 times the 'tens' place. From the options given, only number 2,175 fits this criterion as in this number, 2 is in the 'hundreds' place which is 10 times as much as the 'tens' place.
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What is the answer to -1 = 5+x divided by 6
Answers
-1=5+x
-1-5=5-5+x
x = -6
then, we will divide this answer by 6 as mentioned in the problem as follows:
-6/6 = -1
To do this, first we can solve the equation.
-1 = 5 + x
-5 -5
-6 = x, then divide -6 by 6 to get your answer.
Answer: x = -1
Which is the best estimate for the sum of 31,096 and
58,721?
Answers
A crane cable can support a maximum load of 17,000 kg. If a bucket has a mass of 4,000 kg and gravel has a mass of 1,500 kg for every cubic meter, how many cubic meters of gravel (g) can be safely lifted by the crane? Enter any fractions as reduced improper fractions.
Answers
4000 + 1500x = 17,000
1500x + 4000 = 17,000
Now solve for x
1500x + 4000 = 17000
1500x + 4000 - 4000= 17000 - 4000
1500x = 13000
1500x / 1500 = 13000 / 1500
x = [tex]\frac{26}{3}[/tex]
Shown in the figure is part of a design for a water slide. Find the total length of the slide to the nearest foot, if α = 25°, β = 31°, a = 35 ft, and b = 170 ft.
Answers
according to the figure L1 = a / sinβ = 25/ 0.57= 43.85 ft L3= a/sinα = 25 / 0.42=59.5 ft, for L2=b -L1-L3=96.62
so the total length is L=L1 + L2 + L3= 200ft
of the 150 people surveyed seven out of 10 said they owned at least one pet how many of the people surveyed owned pets
Answers
4,444,444 the digit in the hundreds thousands place is 10 times the value of the digit in the ten thousands place?
Answers
"true or false:
the digit in the hundreds thousands place is 10times the value of the digit in the ten thousands place"
then that would be true.
I'm not really sure what you're asking... sorry :|
Men in the age groups of 18-34 years need to be to run a marathon in 3 hours and 10 minutes to qualify for the boston marathon how many seconds is this?
Answers
You would take 3 hours to minutes which is 180 then add the following 10 minutes and convert it to seconds.
Use the rule y = -x + 7 to fill in the blank.
If (-1, y) is on the graph, then y =
Answers
Answer:
k no Im just joking it is y=6
Step-by-step explanation:
Using the rule y = -x + 7, when x is -1, the value for y in (-1, y) is 8.
Explanation:The rule given is y = -x + 7. If we insert x = -1 into the formula, we get y = -(-1) + 7, which simplifies to y = 1 + 7 and then further reduces to y = 8.
So, when (-1, y) is on the graph of the function, y equals to 8.
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An airplane can travel at a speed of 550 mph. Write and solve an equation to find the time it will take to fly from London to Montreal, a distance of approximately 3300 miles
Answers
The time it will take for an airplane to fly from London to Montreal at a speed of 550 mph covering a distance of 3300 miles is approximately 6 hours.
Explanation:To find the time it will take for an airplane to fly from London to Montreal, we can use the equation for speed, which is:
Speed = Distance \u00f7 Time
Knowing that the plane can travel at a speed of 550 mph and the distance from London to Montreal is 3300 miles, we can rearrange the equation to solve for time:
Time = Distance \u00f7 Speed
Time = 3300 miles \u00f7 550 mph
After calculating, we find that:
Time = 6 hours
Therefore, it will take the airplane approximately 6 hours to fly from London to Montreal at a constant speed of 550 mph, ignoring any other factors such as wind or air traffic delays.
To find the time it will take, we can use the formula Time = Distance/Speed. In this case, it will take approximately 6 hours to fly from London to Montreal.
Explanation:To find the time it will take to fly from London to Montreal, we can use the formula Time = Distance/Speed. In this case, the distance is approximately 3300 miles and the speed is 550 mph.
Plugging in the values into the formula, we get Time = 3300 miles / 550 mph = 6 hours. So, it will take approximately 6 hours to fly from London to Montreal.
Therefore, the time it will take to fly from London to Montreal is 6 hours.
(3 – 6y2)(y2 + 2) what is this
Answers
3(y^2 + 2) - 6y^2(y^2 + 2) =
3y^2 + 6 - 6y^4 - 12y^2 =
-6y^4 - 9y^2 + 6 <===
<ABD has a measure of 36 degrees. a)find the compliment of the angle b)find the supplement of that angle
Answers
b) The supplement of an angle is whatever number can be added to the original to add up to 180 degrees. The supplement of <ABD would be 180-36=144
Change the order and the grouping of the addends so that you can use mental math to find the sum. Then find the sum. 43+39+43+11=
Answers
Final answer:
By applying the commutative property of addition and rearranging the numbers for easier mental calculation, the sum of 43 + 39 + 43 + 11 can be found to be 136.
Explanation:
The question asks to change the order and the grouping of the addends for easier mental calculation, and then to find the sum of 43 + 39 + 43 + 11. By understanding the commutative property of addition, which states that numbers can be added in any order without changing the sum, we can rearrange these numbers for easier addition.
To use mental math effectively, grouping numbers that make round numbers or those that are easier to add can simplify the process. Here, we can group 43 and 43, which are identical, and 39 and 11, which sum up to a round number.
Therefore, by rearranging:
43 + 43 = 86
39 + 11 = 50
Adding these sums together:
86 + 50 = 136
By changing the order and grouping of the addends, we find that the sum is 136.
the school fun fair made 1,768 on games and 978 on food sales. how much money did the fun fair make on games and food.
Answers
-4+6(-4x+3) combining like terms & distributive property
Answers
Disribute 6 into both numbers in the parenthesis. So that means...
6 x 4x = 24x
6x3 = 18
Your new expression is:
-4 +24x +18
Combine ALL like terms:
-4 + 18 = 14
New Expression:
14 + 24x
And since you don't have any equal sign, that's as much as you can do to simplify the expression.
What is the value of the expression 3^−4 ?
Answers
When there is a negative exponent, do the problem the same, but make it it’s reciprocal:
3^-4
1/3^4
1/81
Hope this helped!
The required simplified value for the expression [tex]3^{-4}[/tex] is 1 / 81.
Given that,
To determine the simplified value of the expression [tex]3^{-4}[/tex] .
The process in mathematics to operate and interpret the function or expression to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
[tex]3^{-4} = 1/3^4[/tex]
3 * 3 * 3 * 3 = 9 * 9 = 81
[tex]3^{-4} = 1 / 81[/tex]
Thus the required simplified value for the expression [tex]3^{-4}[/tex] is 1 / 81.
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Segment PQ bisects segment ST at point R.
SR=2x+2 and ST=40
Find the length of segment SR.
a
SR=9
b
SR=40
c
SR=36
d
SR=20
Answers
2x+2, 2×9+2, 18+2, 20=sr
or simply 40÷2=20
Answer:
2(2x+2)=40, 4x+4=40, 4x=36, x=9..plug in 9..
2x+2, 2×9+2, 18+2, 20=sr
Step-by-step explanation:
I REALLY NEED HELP PLEEEASS Evelyn has $524.96 in her checking account. She must maintain a $500 balance to avoid a fee. She wrote a check for $32.50 today. Write and solve an inequality to solve for the least amount of money she needs to deposit to avoid a fee.
524.96 − 32.50 + x ≥ 500; x ≥ $7.54
524.96 − 32.50 + x ≤ 500; x ≤ $7.54
524.96 + 32.50 − x ≥ 500; x ≥ $57.46
524.96 + 32.50 − x ≤ 500; x ≤ $57.46
Thank you
Answers
The answer is A, because I said so and Im Albert Einstein´s nonrelative
Study the number 31,342. How many times less is the three in the hundreds place as compared to the three in the 10,000 place?
Answers
X to 2nd power equals 9/256
Answers
in which square is 25% not shaded
Answers
The teacher separated her class of twenty-eight student into two group. one group has 4 more than twice as many students as the other group. how many students are in each group?
Answers
x=group 1
y=group 2
x+y=28
2x+4=y
Isolate the variable in equation 1.
y=-x+28
Substitute it into equation 2.
-x+28=2x+4
Solve.
-3x=-24
x=8
Substitute it into one of the equations for y.
-x+28=y
-8+28=y
y=20
There are 8 students in one group and 20 students in the other.
Hope this helps!
x=28-y
x=4+2y
28-y=4+2y
28-4=2y+y
24=3y
24/3=y
y=8
x+y=28
x+(8)=28
x=28-8
x=20
(20)=4+2(8)
20=4+16
20=20
one group=20, other group=8
So far, 37 miles of a new highway have been completed. This is one mile less than two thirds of the entire length. How long will the new highway be when complete?
Answers
37 + 1 = 2/3x
38 = 2/3x
38 / (2/3) = x
38 * 3/2 = x
114/2 = x
57 = x <=== when complete, the highway will be 57 miles
The total length of the new highway, when complete, will be 57 miles.
Explanation:The question states that 37 miles of a new highway have been completed and this distance is one mile less than two thirds of the entire length of the highway. To solve this problem, we need to write an equation using the given information and solve for the variable representing the total length of the highway.
Let's denote the total length of the highway as 'x'. According to the problem, two thirds of this length minus one mile equals 37 miles. Forming an equation, we can write (2/3)x - 1 = 37.
To solve for 'x', first add 1 to both sides of the equation to get rid of the '-1' on the left, that gives us (2/3)x = 38. After, to completely isolate 'x', multiply both sides of the equation by the reciprocal of 2/3, which is 3/2. Doing this results in 'x' = 38 * (3/2) = 57 miles.
Therefore, the new highway will be 57 miles long when complete.
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1. Is it possible for a composite number to have more than one prime factorization? Is it possible for a number to have no prime factors? Why?
2.Give and example of how prime factorization could be used in the real world
Answers
Prime number are numbers that only has a factors of 1 and itself.
It is very possible for a composite number to have more than one prime factorization. But, it is not possible for a number to not have a prime factor.
When you factorize a number, you break it down into its most basic factors and these basic factors are all prime numbers.
Prime factorization is basically breaking down numbers to its most basic factors. It can be used in everyday living especially when we deal with numerical transactions like money and values.
4 divided by 10.2 =
Please help me
Answers
round to the nearest hundredth
0.39