In triangle ABC, m∠A = 110º, m∠B = 45º and m∠C = 25º. Which of the numbered choices correctly relates the lengths of the sides of the triangle?
1) AB < BC < CA 2) AC < BC< AB
3) AB < AC < BC 4) BC < AC < AB
Answers
The lengths of the sides of the triangle ABC is AB<AC<BC. Therefore, option 4 is the correct answer.
What is the triangle inequality theorem?If one side of a triangle is longer than another side, then the angle opposite the longer side will be larger than the angle opposite the shorter side.
Given that, in triangle ABC, m∠A = 110°, m∠B = 45° and m∠C = 25°.
Opposite to m∠A is side BC, opposite to m∠B is side AC and opposite to m∠C is side AB.
Here, largest angle is ∠A, so the longer side is BC and
Smaller angle is ∠C, so the shortest side is AB and
Now, AB<AC<BC
Therefore, option 4 is the correct answer.
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Related Questions
Clark Kent walks 3 miles west and then 4 miles north. How far is it for Superman to fly in a straight line back to his starting point? (It makes a right triangle.)
Answers
a^2+b^2=c^2
3^2+4^2=c^2
9+16=c^2
25=c^2
sqr 25=sqr c^2
5=c
If arc AXC = 235°, what is m∠ABC?
117.5°
60°
55°
125°
Answers
The measure of the exterior angle of the circle ∠ABC = 55°
What is the Area of the Sector?In circles, a sector is said to be a part of a circle made of the arc of the circle together with its two radii. This means that it is a portion of the circle formed by a portion of the circumference (arc) and radii of the circle at both endpoints of the arc.
The formula for Area of a sector is given as;
A = θ/360 x πr²
where;
θ is the central angle of the sector
r is radius
Given data ,
Let the measure of the arc be represented as A = 235°
So , the difference of the measures of arc = 235 - 125°
Now , the measure of the external angle ∠ABC = ( 235 - 125 ) / 2
So , the external angle ∠ABC = 55°
Hence , the measure of angle ∠ABC = 55°
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You invest an initial $4,500 in an account that has an annual interest rate of 4.5%, compounded daily. How much money will you have in the account after 10 years? Round to the nearest whole number
Answers
Use the graph below for this question:
graph of parabola going through 0, 3 and 2, negative 5.
What is the average rate of change from x = 0 to x = 2?
− 4
− 8
1
5
Can you please help me?
Answers
The average rate of change from x = 0 to x = 2 for the parabola described in the question is -4. Hence the correct option is 1.
The average rate of change of a function between two points is calculated by subtracting the y-values (function outputs) and dividing by the difference in x-values (inputs). In this case, to find the average rate of change of the parabola from x = 0 to x = 2, we use the points (0, 3) and (2, -5).
The average rate of change = (y2 - y1) / (x2 - x1)
Substitute in the given points: ( -5 - 3 ) / ( 2 - 0 )
Simplify the expression: -8 / 2 = -4
An electrician charges a $50 house call fee and $65 per hour for the work. Which algebraic expression represents this situation to represent the total cost for h hours of work?
Answers
Thus:
$50+$65h
The algebraic expression is Total Cost = 65h + 50.
Explanation:To represent the total cost for h hours of work, we need to consider the house call fee of $50 and the hourly rate of $65. The total cost will depend on the number of hours worked.
We can calculate the total cost using the expression: Total Cost = (Hourly Rate * Number of Hours) + House Call Fee.
Therefore, the algebraic expression that represents this situation is: Total Cost = 65h + 50.
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Maggie was thinking of a number. If she multiply the number by 3 ,subtracted by 8 ,added by 2 times the 5 original number . the result was 48. write an equation that the number satisfies. Then answer it.
Answers
number is ?
3.?-8+2.5.?=48
13.?=56
?=56/13
To solve the word problem, we set up and solved an algebraic equation. Maggie's original number is approximately 4.31 after converting the written problem into the equation 3x - 8 + 10x = 48 and solving for 'x'.
The goal is to translate the word problem into an algebraic equation and solve for the unknown number. If Maggie is thinking of a number, let's use 'x' to represent this unknown number. According to the problem, she multiplies the number by 3, subtracts 8, and then adds 2 times the original number 5 times. The result of these operations is 48. Here's how you set up the equation:
3x - 8 + 10x = 48
The next step is to combine like terms:
13x - 8 = 48
Now we add 8 to both sides of the equation:
13x = 56
The last step is to divide both sides by 13 to solve for x:
x = 56 / 13
x = 4.3077 or approximately 4.31 if rounded to two decimal places.
Therefore, Maggie's number is approximately 4.31.
the midpoint of a segment is (2,-5), and one of the endpoints is (3,6). where is the other endpoint?
Answers
(3, 6) is (2+1, -5+11) is an end point
therefor the other end point should be (2-1, -5-11) = (1, -16)
You could visualise this better if you draw it
Hope this helps, I don't really know a better way to explain it, sorry =P
Temperature rose 9°f in 3 hours if the starting wad -5°f what was the final temperature
Answers
Use the stem and leaf plot shown to answer the following question.
What is the upper quartile median value?
37
40
41
Answers
Q1 = 23
Q2 = 34
Q3 = 40 <== ur upper quartile median value
Answer:
The upper quartile median value is 40. Therefore second option is correct.
Step-by-step explanation:
Stem is first digit of a number and leaf is last digit of a number.
Stem 1 leaf 4 can be written as 14.
From the given table, the observations can be written as
[tex]16,18,23,25,26,34,37,37,40,41,46[/tex]
Total number of observations is 11, which is an odd number.
[tex]median=\frac{n+1}{2}\text{th term}[/tex]
[tex]median=\frac{11+1}{2}\text{th term}=6\text{th term}[/tex]
Therefore median is 34.
We have 5 terms before 34 and 5 terms after 34.
[tex]Q_1=\frac{n+1}{4}\text{th term}=3\text{th term}[/tex]
[tex]Q_1=23[/tex]
[tex]Q_3=\frac{3(n+1)}{4}\text{th term}=9\text{th term}[/tex]
[tex]Q_3=40[/tex]
Q₃ is also known as upper quartile median value. Therefore second option is correct.
Use the formula P = 2l + 2w to find the length of a rectangle whose perimeter is 57 inches and whose width is 13 inches.
Answers
57 = 2L + 2(13)
57 = 2L + 26
-26 -26
31 = 2L
2 2
15.5 = L
You are making a scale drawing out of your classroom using the scale 1 inch: 3 feet. The floor of your classroom is a rectangle with a length of 21 feet and a width of 18 feet. What should the length and width of the floor in your drawing be?
Answers
21 feet : 3 feet = 7 inches
18 feet : 3 feet = 6 inches
The dimensions of the floor in drawing are 7 inches × 6 inches
daniel team scored 40 points at the game danielscored 50% of the teams points how many poits did daniel scored
Answers
If M(-8, 12) is the midpoint of segment PQ, and P(8, 0), find the coordinates of Q.
Answers
Q(x2,y2)=(a,b)
M(x,y)=(-8,12)
x1+x2/2=-8;y1+y2/2=12
8+x2=-16;0+y2=24
x2=-24;y2=24
Q(x2,y2)=(-24,24)
Let f(x) = 7x − 13. find f−1(x). (1 point)13x − 77 over quantity of x plus 13quantity of x plus 13 over 71 over quantity 7 x minus 13
Answers
f (x)+13=7x
x=f (x)+13/7
f^-1 (x)=x+13/7
I will post a graph and using it you have to figure out 4 things.
(i.) (lim x->60-) f(x)
(ii.) (lim x->60+) f(x)
(iii.) What can you conclude about (lim x->60) f(x)? How is this shown by the graph?
(iv.) What aspect of costs of renting a car causes the graph to jump vertically by the same amount at its discontinuities?
Answers
(ii.) (lim x->60+) f(x) = 68
(iii.) It can be concluded that the function is not continuous at x = 60 which is shown on the graph by the gap in the two lines at x = 60.
(iv.) the fixed cost causes the graph to jump vertically at the points of its dicontinuities.
Compare 0.409 and 0.490 with >,<,=
Answers
hope this helps you
in a parallelogram consecutive angles are _
Answers
The distance a spring will stretch varies directly with how much weight is attached to the spring. if a spring stretches 9 inches with 100 pounds attached, how far will it stretch with 90 pounds attached? round to the nearest tenth of an inch.
Answers
Cross multiply to get 810 = 100x
Divide both sides by 100 to get x = 81 inches
Find the area of the regular polygon. Give the answer to the nearest tenth.
dodecagon with a perimeter of 108 cm ...?
Answers
Length of each side = 108/12 = 9 cm.
Length of the apothem = (9/2)/tan 15 = 9/2tan 15 = 16.79 cm
Area of each triangle = 9/2(16.79) = 75.57 cm^2
Therefore, area of the dodecagon = 12(75.57) = 906.9 cm^2
a 12 sided regular polygon is composed of 24 right triangles with one side
half the length of a side = 4.5 cm
the other side is 4.5 / tan (360/24) = 4.5 / tan(15)
A = 24 (1/2) 4.5^2 / tan(15) = 906.9 cm^2
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solve for x. round to nearest tenth if needed.
1. 7r-7=2r+18
a.r=-5
b.r=5
c.r=2.2
d.r=1.2
2. 2x+12=18-x
a.x=3
b.x=10
c.x=6
d.x=2
3. 8x-3=15x+18
a.x=-3
b.x=3
c.x=2.1
d.x=0.9
4. 6y-6=4y+16
a.y=2.2
b.y=-2.2
c.y=11
d.y=5
5. 3(x-4)=5(x+2)
a.x=11
b.x=-11
c.x=1
d.x=-1
Answers
-----------------
2x+x=18-12→3x=6→x=2
---------------
8x-15x=18+3→-7x=21→x=-3
----------------
6y-4y=16+6→2y=22→y=11
--------------
3x-12=5x+10→3x-5x=10+12→-2x=22→x=-11
On solving the linear equations given, we get the values as 5, 2, -3, 11 and -11 for the equations 7r - 7 = 2r + 18, 2x + 12 = 18 - x, 8x - 3 = 15x + 18, 6y - 6 = 4y + 16 and 3(x - 4) = 5(x + 2) respectively.
What is Linear Equation?Linear equations are equations which includes one or more variables and constants with the highest degree of the variable being 1.
1. 7r - 7 = 2r + 18
Taking the variables on one side and constants on the other side,
7r - 2r = 18 + 7
5r = 25
r = 5
2. 2x + 12 = 18 - x
2x + x = 18 - 12
3x = 6
x = 2
3. 8x - 3 = 15x + 18
8x - 15x = 18 + 3
-7x = 21
x = -3
4. 6y - 6 = 4y + 16
6y - 4y = 16 + 6
2y = 22
y = 11
5. 3(x - 4) = 5(x + 2)
Multiplying each term inside the bracket by the term outside,
3x - 12 = 5x + 10
3x - 5x = 10 + 12
-2x = 22
x = -11
Hence we got the values of the unknowns as 5, 2, -3, 11 and -11 for the equations 7r - 7 = 2r + 18, 2x + 12 = 18 - x, 8x - 3 = 15x + 18, 6y - 6 = 4y + 16 and 3(x - 4) = 5(x + 2) respectively.
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alfonso makes $8 per hour working at movie theater and $12 per hour working at a restaurant. Next week Alfonso is scheduled to work 6 hours at a the movie theater. which of the following inequalities represents the amount of hours (h) that alfonso needs to work at the restaurant next week to earn at least $144 between his two jobs
Answers
What is the greatest common factor of 20, 45x?
Answers
If you subtract the death rate from the birth rate of a population, you will calculate what?
A. the arithmetic growth rate.
B. the expansion rate.
C. the carrying capacity.
D. the intrinsic growth rate.
Answers
If you subtract the death rate from the birth rate of a population, you will calculate the carrying capacity.
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Subtracting the death rate from the birth rate of a population calculates its intrinsic growth rate, expressed as dN = (b - d)N, where 'r' is the intrinsic rate of increase.
When you subtract the death rate (D) from the birth rate (B) of a population, you calculate the intrinsic growth rate of the population. The birth rate is typically expressed on a per capita basis, shown as B = bN, where 'b' represents the per capita birth rate and 'N' is the number of individuals in the population. Similarly, the death rate is expressed as D = dN, where 'd' is the per capita death rate. To find the population growth rate at a specific point in time, differential calculus is used to obtain an instant-specific measurement:
dN = (b - d)N
This formula simplifies the relationship between the birth and death rates, where 'b - d' is substituted with 'r', representing the intrinsic rate of increase. Therefore, the correct answer to the student's question is D. the intrinsic growth rate.
Which of the following shows the extraneous solution to the logarithmic equation below?
log3(18x^3)-log3(2x)=log3(144)
x=-16
x=-8
x=-4
x=-2
Answers
than our equation becomes.
log3((18x^3)/(2x)) = log3(144) or
log3(9x^2) = log3(144)
for x= -4 we get that left side is equal to right side
log3(9*(-4)^2) = log3(144)
but if you put that value of x=-4 in start you will get log3(18(-4)^3) which is log of negative value which is imposible. That is why x=-4 is extraneous solution.
The value that shows the extraneous solution to the logarithmic equation below is x = -4
Extraneous solutions to a system of equationGiven the logarithmic function expressed as:
log3(18x^3)-log3(2x)=log3(144)
This can also be written as:
log3(18x^3/2x) = log3(144)
log3 (9x^2) -= log3 (144)
Cancel out the log function to have:
9x^2 = 144
Divide both sides by 9
x^2 = 144/9
x^2 = 16
x = ±4
Hence the value that shows the extraneous solution to the logarithmic equation below is x = -4
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Which ordered pair is a solution to this equation?
(x+3)y = 14
A. (3, 2)
B. (5, 2)
C. (11, 1)
D.(7, 2)
Answers
Hope this helps and if you need any more help just ask!! :)
What is the ratio 15 : 24 written in lowest terms?
a. 3 : 5
b. 5 : 8
c. 3 : 4
d. 7 : 8 user: ratio for 6 and 30?
Answers
divide both sides by 3
b. 5:8
for 6:30
divide both sides by 6
1:5
its b i done the test
is it possible for a line to pass through only one quadrant?
How about four quadrants? explain
Answers
yes it is possible for a line to only be in one quadrant and it is also possible for a line to be in multiple quadrants basically it can be any place on a plane
Arcsin(sin(3pi)) ...?
Answers
arc sin (sin 3pi) = theta
where theta is the angle ur looking for
so that becomes
sin (theta) = sin 3pi
sin (theta) = 0
theta = 0, pi
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What are the 2 types of unbiased samples?
Answers
Which of the following is not an example of using the distributive property to multiply 12 times 22?
a. 12(20 + 2)
b. 22(10 + 2)
c. 10(2 · 22)
Answers
It doesn't have the correct format and is mixed up.