which angle is supplementary to∠2?
Answers
supplementary angles are two angles whose sum is exactly 180, for example:
In this diagram ∠A and ∠B are supplementary
Related Questions
1. The slant height of a cone is 5cm and the radius of its base is 3cm. Find correct to the nearest
whole number the volume of the cone (A) 48cm3 (B) 47cm3 (C) 38cm3 (D)13cm3
Answers
The volume of the cone is 13 cm³. option D
How to determine the volumeTo determine the volume of the cone, we have that;
The formula for calculating the volume of a cone is expressed as;
Volume = (1/3)πr ²√(L ² - r ²).
Such that;
r is the radiusL is the slant heightSubstitute the values, we have;
Volume = 1/3 × 3.14 ² × √(25 - 9)
Find the squares, we get;
Volume, V = 1/3 × 9. 86 × √16
Find the square root
Volume, V = 1/3 × 9.86 × 4
Volume, V = 13 cm³
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Evaluate 1/5÷21/5 Give your answer as a mixed number in its simplest form.
Answers
Answer:
the answer is: 1/21 !!
ANSWER
1/5 ÷ 21/5
= 1/5 × 5/21
= 1/21
= 0/1/21
Therefore my answer is 0 whole number 1/21
Which of the following rational functions is graphed below?
Answers
Answer:
B
Step-by-step explanation:
Cuz I graphed it, and it looked the same
Find the area of the parallelogram whose vertices are listed. (0,0), (3,7), (7,4), (10,11)
Answers
The area of the given parallelogram with vertices (0,0), (3,7), (7,4), and (10,11) is 37 sq. units.
How to calculate the area of the parallelogram with vertices?The area of the parallelogram is
A = |\(\vec a\) × \(\vec b\)| sq. units
Where '\(\vec a\)' and '\(\vec b\)' are the adjacents vectors of the parallelogram
\(\vec a\) × \(\vec b\) - is the cross product
|\(\vec a\) × \(\vec b\)| - is the absolute value of the magnitude of the cross product
Calculation:It is given that,
A parallelogram with vertices A(0,0), B(3,7), C(10,11), and D(7,4)
Then, the adjacent vectors are calculated by
\(\vec a\) = \(\vec {AD}\)
= \(\vec D-\vec A\)
= <7-0, 4-0>
= <7, 4>
\(\vec b\) = \(\vec {AB}\)
= \(\vec B-\vec A\)
= <3-0, 7-0>
= <3, 7>
So, the cross product of these two vectors is,
\(\vec a \times \vec b\) = \(\left[\begin{array}{ccc}i&j&k\\3&7&0\\7&4&0\end{array}\right]\)
= i(0) - j(0) + k(12 - 49)
= -37k
The magnitude of the cross product = \(\sqrt{(-37)^2}\) = 37
Then, the area of the given parallelogram is
A = |\(\vec a\) × \(\vec b\)| = |37| = 37 sq. units.
Hence, the area of the given parallelogram is 37 sq. units.
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Find the radius of a circle that has an area of 121 pi ft2.
Answers
Answer: 11
Step-by-step explanation:
area = 121 pi = pi r^2 Divide both sides by pi
121 = r^2
r= 11
What is the unit rate of $3.49 of cupcakes
Answers
When adding and subtracting numbers in Scientific Notation, the powers of the base 10 must be the same exponent so that you have "like terms". When multiplying and dividing numbers in Scientific Notation, you do not have to have the same power of the base 10. You can simply follow the exponent rules for multiplying and dividing with the like base 10. True or False I NEED HELP NOW
Answers
Answer:
The answer is true!
Step-by-step explanation
Using the pencil, plot the point (-1,-6).
Answers
Answer:
sorry but you need to do this one by yourself
Step-by-step explanation:
Answer:
move the dot on the grid 1 left and 6 down :)
Step-by-step explanation:
Write down in terms of n, an expression for the nth term
of the following sequences
a) 25 20 15 10 5
Answers
Answer:
Solution,
First term (a) = 25
Common difference (d) = Second term - first term = 20 - 25 = -5
Now,
nth term = a + (n - 1)d = 25 + (n - 1) (-5) = 25 - 5n +5 = 30 - 5n
The nth term of the series is 30 - 5n
Answer:
The nth term will be:
\(a_n=-5n+30\)
Step-by-step explanation:
Given the sequence
25, 20, 15, 10, 5
An Arithmetic sequence has a constant difference 'd' and is defined by
\(a_n=a_1+\left(n-1\right)d\)
Computing the common difference of all the adjacent terms
\(25,\:20,\:15,\:10,\:5\)
\(20-25=-5,\:\quad \:15-20=-5,\:\quad \:10-15=-5,\:\quad \:5-10=-5\)
As the difference between all the adjacent terms is the same and equal to
\(d=-5\)
Also, the first term is:
\(a_1=25\)
Hence, the nth term will be:
\(a_n=a_1+\left(n-1\right)d\)
\(a_n=-5\left(n-1\right)+25\) ∵ \(a_1=25\), \(d=-5\)
\(a_n=-5n+30\)
Therefore, the nth term will be:
\(a_n=-5n+30\)
The box plots display data collected when two teachers asked their classes how many pencils they lose in a school year.
A box plot uses a number line from 5 to 47 with tick marks every one unit. The box extends from 8 to 14 on the number line. A line in the box is at 11. The lines outside the box end at 7 and 45. The graph is titled Mr. Johnson's Class, and the line is labeled Number Of Pencils.
A box plot uses a number line from 0 to 51 with tick marks every one unit. The box extends from 12 to 21 on the number line. A line in the box is at 14.5. The lines outside the box end at 0 and 50. The graph is titled Mr. Simpson's Class, and the line is labeled Number Of Pencils.
Which class lost the most pencils overall based on the data displayed?
Mr. Simpson's class; it has a larger median value 14.5 pencils
Mr. Johnson's class; it has a larger median of 11 pencils
Mr. Simpson's class; it has a narrow spread in the data
Mr. Johnson's class; it has a wide spread in the data
Answers
Answer:
A) Mr. Simpson's class; it has a larger median value 14.5 pencils.
Step-by-step explanation:
A box plot is a visual display of the five-number summary:
Minimum value = The value at the end of the left whisker.Lower quartile (Q₁) = The left side of the box.Median (Q₂) = The vertical line inside the box.Upper quartile (Q₃) = The right side of the boxMaximum = The value at the end of the right whisker.From inspection of the box plots (attached), the measures of central tendency (median) and dispersion (range and IQR) are:
Mr Johnson's class:
Median = 11IQR = Q₃ - Q₁ = 14 - 8 = 6Range = max - min = 45 - 7 = 38Mr Simpson's class:
Median = 14.5IQR = Q₃ - Q₁ = 21 - 12 = 9Range = max - min = 50 - 0 = 50In a box plot, the median is a measure of central tendency and tells us the location of the middle value in the dataset. It divides the data into two equal halves, with 50% of the values falling below the median and 50% above it.
The median number of pencils lost in Mr Simpson's class is greater than the median number of pencils lost in Mr Johnson's class. Therefore, Mr. Simpson's class has a larger median value.
The spread of data in a dataset can be measured using both the range and the interquartile range (IQR).
As Mr Simpson's class has a greater IQR and range than Mr Johnson's class, the data in Mr Simpson's class is more spread out than in Mr Johnson's class.
In summary, as Mr Simpson's class has a larger median 14.5 and a wider spread of data, then Mr Simpson's class lost the most pencils overall.
Olivia says that to compare two positive fractions, the one with the largerdenominator is smaller because it divides the whole into smaller pieces. How do yourespond?
Answers
Let us assume that the fractions are 1/2 and 1/5. 1/5 has the larger denominator. By converting them to decimal,
1/2 = 0.5
1/5 = 0.2
We can see that 0.2 is smaller than 0.5. This also means that 1/5 is smaller than 1/2. This is so because for the larger denominator, the numerator is divided into smaller pieces compared to when it is divided by the smaller denominator. Thus, Olivia's reasoning is correct.
What are the coordinates of the point on the directed line segment from (-6,4) to
(9,-8) that partitions the segment into a ratio of 5 to 1?
Answers
The required point's coordinates are (0,3).
What is an equation?A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.
It demonstrates the equality of the relationship between the printed statements on the left and right.
Left side equals right side in all formulas.
To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.
A statement is not an equation if it lacks the equals sign. When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.
Hence, The required point's coordinates are (0,3).
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Choose the items that complete the sentence about the key features of f(x) = 8x.
Answers
Answer:
See below.
Step-by-step explanation:
Y-intercept - 1
Asymptote - 0
Range - y>0
-hope it helps
what is the y intercept of this graph
Answers
Answer:
The y-intercept is the point at which the graph crosses the y-axis. At this point, the x-coordinate is zero.
PLS HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
it will be choice 3
Step-by-step explanation:
as if you bend each shape of each of them the only choice that will give you a pyramide with a omitted side
Please help i think the answer is c but im not sure
Answers
Answer:
It's C
Step-by-step explanation:
Because the angle measurements are the same on rectangles and they have the same side lengths but the one on the right is a smaller rectangle which its only half the side of the bigger one.
Evaluate the inverse trigonometric function Sin^-1(-1). Give answers in both radians and degrees.
A) Sin^-1(-1) = -pi or -180°
B) Sin^-1(-1) = 3pi/2 or 270°
C) Sin^-1(-1) = pi or 180°
D) Sin^-1(-1) = -pi/2 or -90°
Answers
Answer:
B) Sin^-1(-1) = 3pi/2 or 270°
D) Sin^-1(-1) = -pi/2 or -90°
Step-by-step explanation:
Sine function:
The sine function is -1 at 270º(-90º), which is 3pi/2 = -pi/2.
Inverse sine:
The input of the inverse sine function is a value, and the output are the angles which have the sine equal to the input.
Sin^-1(-1)
Angles for which the sine are -1, that is 3pi/2 or 270° and -pi/2 or -90°. Thus, options B and D are correct.
In Illinois, 9% of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders; that is, they have been arrested previously for a DUI offence. Suppose 41 people arrested for DUI in Illinois are selected at random. You may assume that this is a binomial distribution.
Required:
a. What is the probability that exactly 3 people are repeat offenders?
b. What is the probability that at least one person is a repeat offender?
c. What is the mean number of repeat offenders?
d. What is the standard deviation of the number of repeat offenders?
Answers
Answer:
a) 21.58% probability that exactly 3 people are repeat offenders
b) 97.91% probability that at least one person is a repeat offender
c) 3.69
d) 1.83
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
And p is the probability of X happening.
The expected value of the binomial distribution is:
\(E(X) = np\)
The standard deviation of the binomial distribution is:
\(\sqrt{V(X)} = \sqrt{np(1-p)}\)
9% of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders
This means that \(p = 0.09\)
41 people arrested for DUI in Illinois are selected at random.
This means that \(n = 41\)
a. What is the probability that exactly 3 people are repeat offenders?
This is P(X = 3).
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 3) = C_{41,3}.(0.09)^{3}.(0.91)^{38} = 0.2158\)
21.58% probability that exactly 3 people are repeat offenders
b. What is the probability that at least one person is a repeat offender?
Either none are repeat offenders, or at least one is. The sum of the probabilities of these outcomes is 1. So
\(P(X = 0) + P(X \geq 1) = 1\)
We want \(P(X \geq 1)\).
Then
\(P(X \geq 1) = 1 - P(X = 0)\)
In which
\(P(X = 0) = C_{41,0}.(0.09)^{0}.(0.91)^{41} = 0.0209\)
\(P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0209 = 0.9791\)
97.91% probability that at least one person is a repeat offender
c. What is the mean number of repeat offenders?
\(E(X) = np = 41*0.09 = 3.69\)
d. What is the standard deviation of the number of repeat offenders?
\(\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{41*0.09*0.91} = 1.83\)
work out the length of the container. Giver your answer to the nearest whole centimetre.
Dennis is making a container for tomato plant. The container will be in the shape of a cuboid.
missing length ? 40cm by 55cm.
The capacity of the container will be 180 litres.
1 Litre =1000cm cuboid.
Answers
Answer:
Length of the container = 82 cm
Step-by-step explanation:
Given:
Breadth of the container is 40 cm and height of the container is 55 cm
Volume of the container is 180 litres
To find: length of the container
Solution:
A container is in the shape of the cuboid.
Volume of cuboid = length × breadth × height
Put breadth = 40 cm , height = 55 cm and volume = 180 litres = 180000 \(cm^3\)
(as 1 litre = 1000 \(cm^3\) )
Therefore,
\(180000=length\,\times \,40\times 55\\length = \frac{180000}{40\times 55}=81.82\approx 82\,\,cm\)
if s (x) = 2 - x^2 and t (x) = 3x, what is s (t(- 7) )?
Answers
Step-by-step explanation:
to start, you need to understand what t(-7) is
t(-7) = 3(-7)
t(-7) = -21
that being said
s(t(-7)) = 2 - (-21)^2
s(t(-7)) = 2 - 441
s(t(-7)) = -439
A new mixture of self - tanning & moisturizing lotions for everyday use is being developed . This mixture is made by mixing 700 ounces of everyday moisturizing lotion for $0.70 per ounce with self - tanning lotion worth $2 per ounce. If the new self - tanning & moisturizing lotion mixture is to cost $ 1.30 per ounce, how many ounces of the self-tanning lotion should be in the mixture?
The mixture should have ( ) ounces of the self - tanning lotion.
Answers
Compare the best estimate for 1.789/178 and 0.05. Which is less?
Answers
Answer:
The smaller number in 0.01
Step-by-step explanation:
To find this answer, just take the fraction and find the quotient of both numbers.
1.789/178 = 0.01005056179
Now take the quotient and compare it to 0.05.
Is 0.01 larger or 0.05 - the answer is 0.01.
Find the distance between the two points rounding to the nearest tenth
(-4, 2) and (3, 5)
Answers
Answer:
-8.66666666666666666666666666666666666
-9
Step-by-step explanation:
f(s) = 3s + 2
p(s) = s³ + 4s
Find (f • p)(-5)
Answers
Step-by-step explanation:
To evaluate (f • p)(-5), we first need to find the composite function f(p(-5)):
p(-5) = (-5)³ + 4(-5) = -125 - 20 = -145
f(p(-5)) = 3(-145) + 2 = -435 + 2 = -433
Therefore, (f • p)(-5) = f(p(-5)) = -433.
The numbers 840 and 8316, written as the products. of their prime factors, are 840= 2¹ × 3 × 5 × 7 and 8316= 22 x 3³ x 7 x 11. Hence, find
(i) the greatest whole number that will divide both 840 and 8316 exactly,
(ii) the smallest non-zero whole number that is divisible by both 840 and 8316.
Pls help asap
Answers
Answer:
1) 84
2) 83160
Step-by-step explanation:
Greatest common divisor and Least common multiple
840 = 2³ * 3 * 5 * 7
8316 = 2² * 3³ * 7 * 11
i) The greatest whole number that will divide both 840 and 8316 is the
Greatest common divisor. Find only the common factors.
Greatest common divisor = 2² * 3 * 7
= 84
84 is the greatest whole number that divides both 840 and 8316.
Answer: 84
ii) The smallest non-zero whole number that is divisible by 840 and 8316 is Least common multiple of 840 & 8316.
Least common multiple = 2³ * 3³ * 5 * 7 * 11
= 8 * 27 * 5 * 7 * 11
=83160
I will give the BRAINEST
The picture goes with the question.
If m<1 =(8x-8)
and m<3=
=(7x+8), what is the measure of <2
Answers
Answer:
m<1= m<2
8 x-8= 7x+8
x=16
m<1= 120
m<2 = 180-120=60
Step-by-step explanation:
not strictly sure about my answer but I think...from the picture, the measure of 1 and 3 look equal which implies that
m<1 = m<3
8x-8=7x+8 add 8
8x =7x+16 subtract 7x
x=16
which indicates that
m<1=8x-8
=8(16)-8
=120 units
and
m<3=7x+8
=7(16)+8
=64 units
therefore...since the measure are at a point, like angles...they add up to 360°
m<2=(360°-(120°+64°))/2
=88°
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Answers
Answer:
a) zero triangles.
b) one triangle.
Step-by-step explanation:
In triangle ABC:
A, B and C are the interior angles.a, b and c are the sides opposite the corresponding interior angles.Part (a)Given:
∠A = 51°a = 10 cmb = 28 cmLaw of Sines
\(\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}\)
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
To determine if any triangles are possible, substitute the given values into the Law of Sines to find angle B:
\(\implies \sf \dfrac{\sin 51^{\circ}}{10}=\dfrac{\sin B}{28}\)
\(\implies \sf \sin B=\dfrac{28\sin 51^{\circ}}{10}\)
\(\implies \sf \sin B=2.176008...\)
As -1 ≤ sin B ≤ 1, there is no solution for angle B.
Therefore, zero triangles are possible.
----------------------------------------------------------------------------------
Part (b)Given:
∠C = 30°a = 24 cmc = 12 cmLaw of Sines
\(\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}\)
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
To determine if any triangles are possible, substitute the given values into the Law of Sines to find angle A:
\(\implies \sf \dfrac{\sin A}{24}=\dfrac{\sin 30^{\circ}}{12}\)
\(\implies \sf \sin A=\dfrac{24\sin 30^{\circ}}{12}\)
\(\implies \sf \sin A=1\)
\(\implies \sf A=\sin^{-1}(1)\)
\(\implies \sf A=90^{\circ}\)
Therefore, one triangle is possible (see attachment).
Find what value of x makes the equation true
Answers
\(\sf\purple{The\:value\:of\:x\:is\:10.4.}\)✅
Step-by-step explanation:
\( \frac{(10x - 4)}{5} = 20 \\ ✒ \: 10x - 4 = 20 \times 5 \\ ✒ \: 10x = 100 + 4 \\ ✒10x = 104 \\ ✒ \: x = \frac{104}{10} \\ ✒ \: x = 10.4\)
\(\sf\red{Therefore,\:the\:value\:of\:x\:is\:10.4.}\)
To verify:-
\( \frac{(10x - 4)}{5} = 20 \\ ✒ \: \frac{10 \times 10.4 - 4}{5} = 20 \\ ✒ \: \frac{104 - 4}{5} = 20 \\ ✒ \: \frac{100}{5} = 20 \\ ✒ \: 20 = 20 \\ ✒ \: L.H.S.=R. H. S\)
Hence verified. ✔
\(\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘\)
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The coordinate 1 has a weight of 4, and the coordinate 4 has a weight of 2. Find the weighted average.
Answers
Answer: 3
Step-by-step explanation: This is the average between your 2 numbers, 4 and 2.
Answer: its 2
Step-by-step explanation: i guessed and i got it right after this other dud said 3....ITS 2
A camera is capable of snapping (3/4) of a picture per. how long will take the camera to snap 6 picture