Which angle is an exterior angle of the triangle? Triangle L M N. Angle L is 1, angle M is 2, angle N is 3. Side M N extends to form angle 4. 1 2 3 4
Answers
See the diagram below. The angles 1,2, and 3 are interior angles as they are inside the triangle. The exterior angle is outside the triangle, formed by extending one side out.
Angle 4 is an exterior angle of the triangle. So Option D is correct
What is an angle ?An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.
Interior angles:- The inner angle made by the intersection of two polygonal sides.
Exterior angles:- The outer angle made by the intersection of two polygonal sides.
Given that,
The triangle LMN,
Angle L is 1,
Angle M is 2,
Angle N is 3
It can be seen in the diagram.
The angles 1,2, and 3 are interior angles as they are inside the triangle. The exterior angle is outside the triangle, formed by extending one side out.
Hence, the exterior angle is 4
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Related Questions
what is the median of numbers 20,35,28,15,22,36,26
Answers
The median of the given data set is 26.
What is the median?In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.
Given the data set, we need to find the median.
So, let's arrange the numbers from smallest to largest in order to find the median.
\(\sf 15,20,22,26,28,35,36.\)
\(\text{Median}=\sf 26\)
Therefore, the median of the data set is 26.
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An amusement park is installing a new roller coaster. the park intends to charge $5 per adult and $3 per child for each ride. It hopes to earn back more than the $750,000 cost of construction in four years. with the best of weather, the park can provide 100000 adult rides and 75,000 child rides in one season.
Answers
Answer:
Cost = 750,000
Income per year = 5 x 100,000 + 75,000 x 3 = 725,000
Income for 4 years = 4 x 725,000 = 2,900,000
Profit = 2,900,000 - 750,000 = 2,150,000
Step-by-step explanation:
Pls help extra points
Answers
Answer:
B
the middle one
Step-by-step explanation:
Complete the following sentence
If x is to 6 as 10 is to 15, then x is equal to .
Answers
Answer:
x=4
Step-by-step explanation:
x/6 = 10/15
x/6 = 2/3
3x=12
Answer:
x=4
Step-by-step explanation:
To find this, you must first figure out the relationship between 10 and 15. Since 10 is 2/3 of 15, "x" must be 2/3 of 6.
To find "x", divide 6 by 3 to get 2, then 2 by 2 to get 2/3 of 6 (4). Thus meaning X = 4.
I hope this helps!
ξ = {numbers between 3 and 19}
P {3,4,5,67,8,10,11,12,16}
Q {3,5,6,7,9,10,12,13,17,18}
Find n(Q')
Answers
The number of elements in the Q complement set, n(Q') is 7
Sets : Calculating the number of elements in a setFrom the question, we are to determine the number of elements that are in the given set.
To find n(Q'),
First, we will determine the elements in Q'
NOTE: Q' means Q complement, that is, the elements that are present in the universal set but not in Q
The universal set is
ξ = {numbers between 3 and 19}
That is,
ξ = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19}
From the given information,
Q = {3, 5, 6, 7, 9, 10, 12, 13, 17, 18}
Therefore,
Q' = {4, 8, 11, 14, 15, 16, 19}
The value of n(Q') is the number of elements in the q' set
That is,
n(Q') = 7
Hence, n(Q') = 7
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10(4-7) What is the value of =(4-1) ?
-10
- 6
6
10
Answers
This is the formula of an arithmetic sequence.
a
n
=
a
1
+
d
(
n
−
1
)
a
n
=
a
1
+
d
(
n
-
1
)
Substitute in the values of
a
1
=
1
a
1
=
1
and
d
=
3
d
=
3
.
a
n
=
1
+
(
3
)
(
n
−
1
)
a
n
=
1
+
(
3
)
(
n
-
1
)
Simplify each term.
a
n
=
1
+
3
n
−
3
a
n
=
1
+
3
n
-
3
Subtract
3
3
from
1
1
.
a
n
=
3
n
−
2
Lucas recorded his lunch expenditure each day for one week in the table below.SEE IMAGEFind the mean, standard deviation, and variance of Lucas’s lunch expenditures. Round to the nearest thousandth.
Answers
Mean)
In general, the formula is
\(\operatorname{mean}=\frac{\text{ sum of elements in the dataset}}{\text{ number of elements in the dataset}}\)Thus, in our case,
\(\begin{gathered} \Rightarrow X=\operatorname{mean}=\frac{4.85+5.10+5.50+4.75+4.5+5+6}{7} \\ \Rightarrow X=\operatorname{mean}=5.1 \end{gathered}\)Thus, the mean is 5.1
Variance)
In general, the formula is
\(\text{Variance}=S^2=\sum ^{}_{}\frac{(x_i-X)^2}{N-1}\)Where x_i is each of the elements in the data set, X is the mean, and N is the number of elements in the data set.
Therefore, in our case,
\(\begin{gathered} N=7,X=5.1 \\ \Rightarrow S^2=\frac{1}{7-1}((4.85-5.1)^2+(5.1-5.1)^2+(5.5-5.1)^2+(4.75-5.1)^2+(4.5-5.1)^2+(5-5.1)^2+(6-5.1)^2) \\ \Rightarrow S^2=0.2541666\ldots \\ \Rightarrow S^2\approx0.254 \end{gathered}\)The variance is 0.254
Standard deviation)
If S^2 is the variance; then,
\(\text{ standard deviation}=\sigma=\sqrt[]{S^2}\)Hence, in our case,
\(\begin{gathered} \Rightarrow\sigma=\sqrt[]{0.2541666\ldots}\approx0.504149\ldots \\ \Rightarrow\sigma\approx0.504 \end{gathered}\)The standard deviation is 0.504
In the expression if 2X=5=8X then 12X= ? you subtract 2X from each sideto get 5=6X then multiply both sides by 2
Why do you multiply both sides by 2
Answers
The value of 12x in the expression is 10
You multiply 5 = 6x by 2 to get 12x
Calculating the value of 12x in the expression
From the question, we have the following parameters that can be used in our computation:
2x + 5 = 8x
You subtract 2X from each side to get
5 = 6x
Then multiply both sides by 2
This gives
10 = 12x
So, we have
12x = 10
Why do you multiply both sides by 2
You multiply by 2 because the question requests for the value of 12x
Since, we have solved for 6x, the next step is to multiply 6x by 2 to get 12x
i.e. 6x * 2 = 12x
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Which of the following is NOT true about unit rates?
Answers
You are at a restaurant and your bill comes to $34.78. You need to add the sales tax which
is 6%. You have one $20 bill, two $10 bills, one $5 bill, five $1 bills, and some pennies.
F
.
.
How much is your total bill including tax?
How much should you give the server so you do not get back any pennies?
What denominations will you use for this?
Use the equation editor to show your work.
Answers
In order to find the answer to this problem, we want to do the following:
First, we need to find the sales tax value:
$34.78 + 6% sales tax
$34.78 * 1.06
$36.87 (rounded to the nearest hundredth)
The total bill is equal to $36.87
Now to find which bills to give to the server:
$20 + $10 + $5 + $1 = $36
Then, you can give the server 87 pennies.
Answer:
Step-by-step explanation:
34.78 + 34.78(0.06) = 36.87 Total bill
Pay 37.07 and you get 15 cents back (1 dime, 1 nickel)
Pay with:
1-$20
1-$10
1-$5
2-$1
2-pennies
Total: 20+10+5+2+0.02 = $37.02
$37.02 - $36.87 = $0.15 (this is your change, no pennies)
What place value is 5678.321 what value is the 2 in
Answers
Answer:
Hundredths
Step-by-step explanation:
Kendall has dance lessons every Tuesday afternoon. About how many lessons does she have each month?
Answers
Explanation: Since most months have 4 weeks she would most likely be going about 4 times a month
\(f(x) = - 5x - 4\)
which function is the inverse of
Answers
Answer:
5 x - 4
Step-by-step explanation:
Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=x5+45 f - 1 ( x ) = x 5 + 4 5 is the inverse of f(x)=5x−4 f ( x ) = 5 x - 4 .
The terminal side of angle θ intersects the unit circle in the first quadrant at x=2/5. What are the exact values of sinθ and cosθ?
Answers
Answer:
sin(θ) = (√21)/5cos(θ) = 2/5Step-by-step explanation:
You want the exact values of sine and cosine of the angle whose terminal point is at x=2/5 on the unit circle in the first quadrant.
Pythagorean identityThe coordinates of a point on the unit circle are (cos(θ), sin(θ)). You already know that the x-coordinate is 2/5, so ...
cos(θ) = 2/5
The Pythagorean identity in trigonometric terms is ...
sin²(θ) +cos²(θ) = 1
Then the sine of the angle is ...
sin(θ) = √(1 -cos²(θ))
sin(θ) = √(1 -(2/5)²) = √((25 -4)/25)
sin(θ) = (√21)/5
The exact values of sine and cosine are ...
sin(θ) = (√21)/5cos(θ) = 2/5
Write an expression for the distance between arbitrary point (x,y) and the following points :
Answers
An expression for the distance between arbitrary point (x,y) and the following points is \(\sqrt{(x-7)^2+(y-2)^2}\).
What is the distance between two points ( p,q) and (x,y)?The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
\(D = √[(x-p)² + (y-q)²] D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.\)
We are given that;
A fixed pont (x,y)
Now, distance from point 1 (2,3)
\(D = √[(x-2)² + (y-3)²] D = \sqrt{(x-2)^2 + (y-3)^2} \: \rm\)
Distance from point 2 (-4,5)
\(D = √[(x+4)² + (y-5)²] D = \sqrt{(x+4)^2 + (y-5)^2} \: \rm\)
Distance from point 3 (7,2)
\(D = √[(x-7)² + (y-2)²] D = \sqrt{(x-7)^2 + (y-2)^2} \: \rm\)
Therefore, the distance expression between two points will be \(\sqrt{(x-7)^2+(y-2)^2}\)
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hich linear function has the steepest slope?
y = negative 8 x + 5
y minus 9 = negative 2 (x + 1)
y = 7 x minus 3
y + 2 = 6 (x + 10)
Answers
The function with the steepest slope is \(y = 7x - 3\).
The correct answer is C.
The linear function with the steepest slope is the one with the highest absolute value for the coefficient of x.
Let's compare the coefficients of x in each of the given functions:
\(y = -8x + 5\)
Slope: -8
\(y - 9 = -2(x + 1)\)
Simplifying, we get \(y - 9 = -2x - 2\)
Rearranging, we have \(y = -2x + 7\)
Slope: -2
\(y = 7x - 3\)
Slope: 7
\(y + 2 = 6(x + 10)\)
Simplifying, we get \(y + 2 = 6x + 60\)
Rearranging, we have \(y = 6x + 58\)
Slope: 6
Therefore, the steepest slope is the \(y = 7x - 3\).
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The point P=(1/2,y)lies on the unit circle shown below. What is the value of y in simplest form?
Answers
The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.
To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.
Plugging in the coordinates of the point P = (1/2, y), we get:
(1/2)^2 + y^2 = 1
1/4 + y^2 = 1
y^2 = 1 - 1/4
y^2 = 3/4.
To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).
Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.
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What is 1% of 3,098?
Answers
Answer:
30.98
Step-by-step explanation:
Answer:
30.98
Step-by-step explanation:
Zero(s) of multiplicity one:
Zero(s) of multiplicity two:
Zero(s) of multiplicity three:
Please look at photo for the full question. Thank you.
Answers
The zeros and the multiplicities are
Zero(s) of multiplicity one: x = 6Zero(s) of multiplicity two: x = 11Zero(s) of multiplicity three: x = -6 and x = -5How to determine the zeros and the multiplicitiesfrom the question, we have the following parameters that can be used in our computation:
f(x) = (x + 6)³(x - 11)²(x - 6)(x + 5)³
The power of each factor are the multiplicities
So, we have
Zero(s) of multiplicity one:
x - 6 = 0
Zero(s) of multiplicity two:
x - 11 = 0
Zero(s) of multiplicity three:
x + 6 = 0 and x + 5 = 0
When evaluated, we have
Zero(s) of multiplicity one:
x = 6
Zero(s) of multiplicity two:
x = 11
Zero(s) of multiplicity three:
x = -6 and x = -5
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help me find the slope please
Answers
Answer:
3/4
Step-by-step explanation:
Ok, so I see that the x-intercept is (4,0), while the y-intercept is(-3,0)
Slope is rise/run
Between these two points, the line rose 3 and horizontally went 4 units to the right. Therefore, the slope is 3/4.
Feel free to tell me if I did anything wrong! :)
Also, if you're still confused, I could explain it another way.
Can somebody solve number 5
Answers
What is the rate of change for the interval between 0 and
2 for the quadratic equation as f(x) = 2x² + x - 3
represented in the table?
O
23/1/2
04
05
O 10
Answers
\(\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x)= 2x^2 + x -3 \qquad \begin{cases} x_1=0\\ x_2=2 \end{cases}\implies \cfrac{f(2)-f(0)}{2 - 0} \\\\\\ \cfrac{[2(2)^2 + (2) -3]~~ - ~~[2(0)^2 +(0) -3]}{2}\implies \cfrac{7-(-3)}{2}\implies \cfrac{7+3}{2}\implies \text{\LARGE 5}\)
The rate of change for the interval between 0 and 2 for the quadratic equation will be 5. Then the correct option is C.
What is the average rate change?It is the average amount by which the function varied per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph depicting the function.
Average rate = [f(x₂) - f(x₁)] / [x₂ - x₁]
The function is given below.
f(x) = 2x² + x - 3
The rate of change of the function for the interval between 0 to 2 is calculated as,
Average rate = [f(2) - f(0)] / [2 - 0]
Average rate = [(2(2)² + 2 - 3) - (2(0)² + 0 - 3)] / 2
Average rate = 10 / 2
Average rate = 5
The rate of change for the interval between 0 and 2 for the quadratic equation will be 5. Then the correct option is C.
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How do we know where to label base and where to label height on a trapezium. does it matter where they are on the trapezium or does it have to be in rectangular please help on question
Answers
The labeling of bases and height in a trapezium is not fixed and can vary based on the context or problem. It doesn't matter where they are on the trapezium, as long as they are clearly defined and consistent within the given situation.
In a trapezium (or trapezoid), the labeling of the bases and height is not fixed or standardized. It can vary depending on the context or the specific problem being considered. However, there are a few general guidelines to keep in mind when labeling a trapezium.
Bases: The trapezium has two parallel sides, often referred to as the "top base" and the "bottom base." The bases are usually labeled based on their relative lengths or position in the trapezium. The longer parallel side is commonly referred to as the "top base," while the shorter parallel side is referred to as the "bottom base." However, this is not a strict rule and can vary depending on the problem or preference.
Height: The height of a trapezium is the perpendicular distance between the bases. It is generally labeled as a vertical line segment connecting the bases. The placement of the height is not fixed, and it can be drawn from any point on the top base to any point on the bottom base, as long as it forms a perpendicular line. The height is usually labeled with the symbol "h" or sometimes "x" or "y" depending on the context.
It's important to note that the labeling of the bases and height is primarily for communication and clarity. As long as the labeling is consistent and clearly defined within the given problem or context, it does not have to conform to any specific arrangement or be in a rectangular shape. The key is to ensure that the labels are clearly understood and can be used to calculate the desired quantities or solve the problem at hand.
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30c2 - 24c - 6
factor the trionomial
Answers
Answer:
\( 6(5c + 1)(c - 1) \)
Step-by-step explanation:
\( 30c^2 - 24c - 6 = \)
\( = 6(5c^2 - 4c - 1) \)
\( = 6(5c + 1)(c - 1) \)
Answer: \( 6(5c + 1)(c - 1) \)
Freddie made the number line below to model the laps he walks around a track at his
school. He walks a total of 1} miles. Each lap is į mile. How many laps does Freddie walk
around the track?
Answers
Answer:
On a standard running 400-meter track a mile is 4 laps… plus 9 more meters if you want to get all technical about it. A mile is specifically 1,609.3 meters.
Step-by-step explanation:
Abu is trying to decide which pet–sitting service he wants to use . Your Pets charges a $15 fee, plus $1 .75 per hour . Sit Pets charges an $11 fee, plus $2 .25 per hour . At how many hours will both services ...
Answers
Answer:I did not see the entire question but is assuming the question is asking how many hours for both services to cost the same.
Your Pets Cost =15+1.75x
Sit Pets Cost =11+2.25x
set both equations equal to each other
15+1.75x=11+2.25x
15-11 = (2.25-1.75)x
4=0.5x
x=8
Step-by-step explanation:
the figure is used as part of a visual description of an algebraic statement. Which of the following can be that algebraic statement?
A.a^2 +b^2=c^2
B.1/2 (a+b) =c
C.a•b=c
D.a^2•b^2=c^2
Answers
Answer: A.
Step-by-step explanation:
The correct algebraic statement is \(a^{2} +b^{2} =c^{2}\).
Pythagoras Theorem:It states that "the sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c)" i.e.
\(a^{2} +b^{2} =c^{2}\)
According to the given question
By Pythagoras theorem we can say that the algebraic statement A i.e.\(a^{2} +b^{2} =c^{2}\) is the correct one for the description of given figure.
Hence, option A i.e. \(a^{2} +b^{2} =c^{2}\) is the correct option.
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Factorize
2(x+y) ²+9 (x+y)+7
Answers
Answer:
(2x+2y+7)(x+y+7)
Step-by-step explanation:
I suspect this is what you are expected to do.
Define z=x+y
2z^2+9z+7
2z^2+2z+7z+7
2z(z+1)+7(z+1)
(2z+7)(z+1)
(2x+2y+7)(x+y+7)
6. Do planes GFE and HBC intersect? Explain.
Answers
Answer:
yes at line HE.
Step-by-step explanation:
Plane GFE is the plane that contains face EFGH of the prism.
Plane HBC is the plane that contains face BCEH of the prism.
The two planes do intersect, and their intersection is line HE.
c) Evaluate: 3√11x√2
Answers
Answer:
\(3\sqrt{22}\)
Step-by-step explanation:
The product of roots with the same index is equal to the root of the product \(3\sqrt{11*2}\)
Multiply
if the x is inside the square root