The smaller side of the triangle from missing sides is 63cm.
What is a triangle?
In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.
Based on the sides of a triangle, a triangle is classified into 3 types, namely:
Scalene Triangle – All the sides are of different measures.
Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.
Equilateral Triangle – All the 3 sides of a triangle are of the same measure.
Based on the angles of a triangle, a triangle is classified into 3 types, namely:
Acute Angle Triangle – All the angles of a triangle is less than 90°.
Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.
Right Angle Triangle – One of the angles of a triangle is equal to 90°.
Now,
According to Pythagorean theorem,
H^2=P^2+B^2
Where H=hypotenuse, B=base, P=Perpendicular
Given base=16
let perpendicular=x then hypotenuse=x+2 as The lengths of the other two sides are consecutive odd integers
Therefore, (x+2)^2=x^2+16^2
x^2+4+4x=256+x^2
x=63 and x+2=65
Hence,
The smaller side of the triangle from missing sides is 63cm.
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A solid object is made with the combination of a cylinder and a cone having same radii. The height of the cylinder and the slant height of the cone are 28 cm and 17 cm respectively. If the total cost of painting the total surface of the solid object at the rate of rs. 140per 100sq.cm is rs 2851.20,find the height of the cone.
Answer:
Let's call the radius of the cylinder and cone "r".
The surface area of the cylinder is: 2πr(r + h) = 2πr^2 + 2πrh
The surface area of the cone is: πr(l + r) = πrl + πr^2
The total surface area of the solid object is the sum of the surface area of the cylinder and the cone: 2πr^2 + 2πrh + πrl + πr^2 = (2π + π)r^2 + 2πrh + πrl
We are given that the total cost of painting the solid object is Rs. 2851.20 and the rate of painting is Rs. 140 per 100 sq cm.
So the total surface area of the solid object is: 2851200/140 = 20580 sq cm
Now we can substitute the values we know into the equation for the total surface area: 20580 = (2π + π)r^2 + 2πrh + πrl
We also know that the height of the cylinder is 28 cm and the slant height of the cone is 17 cm.
We can use the Pythagorean theorem to find the height of the cone: h^2 + r^2 = (l/2)^2
Solving this equation for h, we get: h = √(l^2/4 - r^2)
Now we can substitute the given values and solve for the height of the cone:
h = √(17^2/4 - r^2) = √(289/4 - r^2)
We don't have any information about the radius of the cylinder and cone, so we cannot solve for h in terms of r, but we can find the height of the cone by assuming the value of radius.
Let's assume the radius of the cylinder and cone is 5cm.
h = √(289/4 - 5^2) = √(289/4 - 25) = √(289/4 - 25) = √(64) = 8cm
So, the height of the cone is 8cm.
Please note that this is a theoretical height as it is based on the assumption of radius being 5cm, the actual height of the cone may be different if the radius is different.
which expression has the same value as 1 2/3 + (-8 1/2)
Answer:
(-41)/6 or -6 5/6 as a mixed fraction
Step-by-step explanation:
Simplify the following:
1 + 2/3 - (8 + 1/2)
Put 8 + 1/2 over the common denominator 2. 8 + 1/2 = (2×8)/2 + 1/2:
1 + 2/3 - ((2×8)/2 + 1/2)
2×8 = 16:
1 + 2/3 - (16/2 + 1/2)
16/2 + 1/2 = (16 + 1)/2:
1 + 2/3 - ((16 + 1)/2)
16 + 1 = 17:
1 + 2/3 - 17/2
Put 1 + 2/3 - 17/2 over the common denominator 6. 1 + 2/3 - 17/2 = 6/6 + (2×2)/6 + (3 (-17))/6:
6/6 + (2×2)/6 + (3 (-17))/6
2×2 = 4:
6/6 + 4/6 + (3 (-17))/6
3 (-17) = -51:
6/6 + 4/6 + (-51)/6
6/6 + 4/6 - 51/6 = (6 + 4 - 51)/6:
(6 + 4 - 51)/6
6 + 4 = 10:
(10 - 51)/6
10 - 51 = -(51 - 10):
(-(51 - 10))/6
| 5 | 1
- | 1 | 0
| 4 | 1:
Answer: (-41)/6
Let f(t) = 3t + 2. For each of the following, state whether the –1 if included is an inverse or a reciprocal and then solve exactly for p. (a) f(p) = 5 (c) (f(p))⁻¹ = : 5 (b) f⁻¹(p) = 5 (d) f (p⁻¹) = 5
In (a) and (d), the -1 is a reciprocal, as -1 is being multiplied by f(p) or f(p⁻¹) respectively, and the solutions for p are p = 2 and p = -7/3 respectively. In (b) and (c), the -1 is an inverse, as it is part of the inverse of f(p), and the solutions for p are p = 7 and p = 5/3 respectively.
(a) f(p) = 5 is not an inverse or a reciprocal. To solve for p, we can use the equation f(p) = 5 and solve for p. We do this by subtracting 2 from both sides of the equation to get 3p = 3, and then dividing both sides by 3 to get p = 1.
(b) f⁻¹(p) = 5 is an inverse and we can solve for p using the equation f⁻¹(p) = 5. To do this, we subtract 2 from both sides to get 3p = 3, and then divide both sides by 3 to get p = 1.
(c) (f(p))⁻¹ = 5 is a reciprocal and we can solve for p using the equation (f(p))⁻¹ = 5. To do this, we first divide both sides of the equation by 5 to get 1/f(p) = 1. Then, we multiply both sides by f(p) to get f(p) = 5. Finally, we subtract 2 from both sides to get 3p = 3, and then divide both sides by 3 to get p = 1.
(d) f (p⁻¹) = 5 is not an inverse or a reciprocal. To solve for p, we can use the equation f (p⁻¹) = 5 and solve for p. We do this by multiplying both sides of the equation by p⁻¹ to get f(p) = 5p⁻¹. Then, we subtract 2 from both sides to get 3p = 5p⁻¹ - 2, and then multiply both sides by 3 to get 9p = 5p⁻¹ - 6. Finally, we add 6 to both sides to get 9p + 6 = 5p⁻¹, and then divide both sides by 4 to get p = 1.
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PLEASE HELP!!!!!!
A radical equation is being solved below, but has missing work.
Fill in the missing steps, check for extraneous solutions.
(Picture attached)
By algebra properties, the radical equation [tex]3 \cdot \sqrt[4]{(x - 2)^{3}} - 4 = 20[/tex] has the following extraneous solution: x = - 14.
How to find extraneous solutions in a radical equation
A solution for a radical equation is extraneous when result leads to an absurdity (i.e. 3 = 4). In this problem, we proceed to show how to solve a radical equation by means of algebra properties. First, write the entire radical equation:
[tex]3 \cdot \sqrt[4]{(x - 2)^{3}} - 4 = 20[/tex]
Second, use compatibility with addition:
[tex]3\cdot \sqrt [4]{(x-2)^{3}} = 24[/tex]
Third, use compatibility with multiplication:
[tex]\sqrt [4] {(x - 2)^{3}} = 8[/tex]
Fourth, use a relationship between powers and roots:
[tex](x - 2)^{\frac {3}{4}} = 8[/tex]
Fifth, elevate both sides to 4 / 3 to cancel exponent on left side:
[tex]x - 2 = 8^{\frac {4}{3}}[/tex]
Sixth, solve the power constant:
x - 2 ≈ ± 16
Seventh, apply absolute value properties:
x - 2 = 16 or x - 2 = - 16
Eighth, use compatibility with addition once again:
x = 18 or x = - 14
Ninth, check for extraneous solutions:
x = 18
[tex]3\cdot \sqrt [4]{(18-2)^{3}} = 24[/tex]
24 = 24
x = - 14
[tex]3\cdot \sqrt [4]{(- 14-2)^{3}} = 24[/tex]
NaN
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which of the following would be a line of reflection that would map abcd onto itself? square abcd with c at 1 comma 3, d at 1 comma 1, a at 3 comma 1, and b at 3 comma 3. y = 1 2x + y = 2 x + y = 4 x + y = 1
The line of reflection would be x+y =4, Hence the correct option is C.
The equation of a line's standard form is given as follows:
[tex]y = mx+c[/tex]
Where m is the slope and c is the y-intercept of the line.
The slope can be determined by
[tex]m =\dfrac{(y_2 - y_1)}{(x_2 - x_1)}[/tex]
Now, Along its diagonals should be reflected in order to reflect it back to itself.
The diagonals will pass through the points [tex]A(3, 1)[/tex] and [tex]C( 1,3)[/tex]
Hence, The slope of the line is,
[tex]m =\dfrac{(y_2 - y_1)}{(x_2 - x_1)}[/tex]
[tex]m =\dfrac{(3 - 1)}{(1 - 3}[/tex]
[tex]m =\dfrac{(2)}{(- 2)}[/tex]
[tex]m = - 1[/tex]
Hence, The equation of the line AC,
[tex](y - y_1) = m(x-x_1)[/tex]
It passes through the point (1,3)
[tex](y - 3) = -1( x-1 )[/tex]
[tex]y - 3 = -x +1[/tex]
[tex]y +x =4[/tex]
Therefore, Option C is true.
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five cars have a race. the honda beat the dodge but couldn't overtake the smart car. the mini failed to overtake the audi but beat the smart car. which car came first?
The average Honda beat the Dodge but couldn't pass the Smart Car, and the Mini couldn't pass the Audi, so the Audi won the race.
The Honda was able to defeat the Dodge but was unable to pass the Smart Car, so it was the Audi that arrived first in the race.
The Mini was then forced to settle for defeating the Smart Car after failing to pass the Audi. The Audi was the only vehicle that was able to stave off the competition and maintain its lead all the way to the finish line, making it the eventual race winner. Following the Audi in that order, the Honda, Dodge, Smart Car, and Mini were all overrun by the vehicle in front of them before the Mini was able to surpass the Smart Car and finish in fourth place.
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8. The Nebraska license plate has 6 characters. The first three are letters A thru Z. The second
three are numbers 0 thru 9. How many different license plates could there be without repetition?
(page 3 problems 11, 12a, and 12b)
Six digit license plate:
_
lotter
number number number
Answer:
Below
Step-by-step explanation:
First position 26 possibilities
second 25
third 24
fourth 10
fifth 9
sixth 8
multiply all of these numbers together = 11 232 000 possible plates
which abelian groups are isomorphic to subgroups of s6
The subgroups of S6 include the following abelian groups: Z₁, Z₂, Z₃, Z₆, Z₂ x Z₂, and Z₃ x Z₂
A subgroup of a group is isomorphic to another group if there is a bijective homomorphism between the two groups, meaning there is a one-to-one correspondence between their elements that preserves the group operation. In this case, the subgroup of S6 (the symmetric group on 6 elements) is isomorphic to one of the abelian groups.
It is known that the number of subgroups of a finite group is bounded above by the number of its elements, so there are only finitely many possible subgroups of S6 to consider. The most common abelian groups are the cyclic groups Zₙ, and any group that is isomorphic to a direct sum of cyclic groups is also abelian.
It is known that the subgroups of S6 include the following abelian groups: Z₁, Z₂, Z₃, Z₆, Z₂ x Z₂, and Z₃ x Z₂. These are the only abelian groups that can be isomorphic to subgroups of S6. Note that there may be non-abelian subgroups of S6 as well.
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Which substantive audit sampling technique uses a statistical sampling approach?
Stratified sampling.
Attribute sampling.
Monetary Unit
Sampling or MUS.
The substantive audit sampling technique uses a statistical sampling approach is Sampling or MUS.
Sampling is a powerful tool in auditing as it allows the auditor to make conclusions about the population without having to test all the transactions, balances or data.
Substantive audit sampling refers to the use of samples in an audit process to make conclusions about a population of transactions, balances or other data.
There are three main substantive audit sampling techniques: Stratified Sampling, Attribute Sampling and Monetary Unit Sampling.
Monetary Unit Sampling or MUS is a statistical sampling approach that focuses on the monetary value of transactions.
The auditor will select a sample of transactions and calculate the expected deviation rate.
This technique is used when the auditor is focused on testing material balances and ensuring that they are correct.
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let x be binomial with n=10. the probability x equals 3.5 is _____.
This does not make sense as x is a discrete variable, so it cannot take on a value of 3.5.
A binomial variable is a discrete variable, meaning it can only take on certain values. In this case, x can take on values from 0 to 10 (inclusive). Since 3.5 is not one of these values, it does not make sense to calculate the probability that x equals 3.5.
This does not make sense as x is a discrete variable, so it cannot take on a value of 3.5.
A binomial variable is a discrete variable, meaning it can only take on certain values that are determined by the given parameters. For example, if the binomial variable x is defined as the number of heads in 10 flips of a coin, then x can only take on values from 0 to 10 (inclusive). Since 3.5 is not one of these values, it does not make sense to calculate the probability that x equals 3.5.
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2. en un taller fueron reparados durante un mes 120 vehículos entre automóviles y motos. el número de ruedas de los vehículosreparados fue de 336 exactamente. ¿cuántas motos se repararon?
36 motorcycles were repaired during the month.
To solve this problem, we can use the formula for the total number of wheels of a vehicle, which is equal to the number of vehicles multiplied by the number of wheels per vehicle. In this case, the number of wheels per vehicle is 4 since both autos and motorcycles have 4 wheels each. This formula can be expressed as: Wheels = Vehicles × Wheels per Vehicle.
We can substitute the given values of the total number of wheels (336) and the number of wheels per vehicle (4) into the formula, and solve for the number of vehicles (V): Wheels = Vehicles × Wheels per Vehicle → 336 = Vehicles × 4 → Vehicles = 336 ÷ 4 → Vehicles = 84.
Since we know that both autos and motorcycles were repaired, and the total number of vehicles was 84, we can use the information that 120 vehicles were repaired to solve for the number of motorcycles (M) that were repaired.
If the total number of vehicles was 84, and 120 vehicles were repaired, then the number of motorcycles that were repaired must be equal to the difference between the total number of vehicles and the total number of autos, which is 120 - 84 = 36.
Therefore, 36 motorcycles were repaired during the month.
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A factory sampled hundreds of 9oz bags of chips off of one of their production lines to make sure the bags had the appropriate
amount of chips. They found the amount of chips to be normally distributed with = 9.12 ounces and o= .05 ounces.
PART A
Given this information, fill out the normal distribution chart below for the weight of 9oz bags of chips from this factory.
The probability that a bag of chip is lower than 9.07 oz of weight is 0.1587.
What is Normal Distribution ?A continuous probability distribution for a real-valued random variable is called a normal distribution or a Gaussian distribution.
An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center of the range.
The normal distribution defines how a variable's values are distributed, just like any probability distribution does. Because it properly depicts the distribution of values for many natural occurrences, it is the most significant probability distribution in statistics.
the mean of the data = 9.12 oz
The SD = 0.05 oz
The probability of the bag to be less than 9.07 oz
x = 9.07
z = x - mean / SD = 9.07 - 9.12/0.05 = - 1
for z = -ve
Ф(z) = 1 - Ф(-z) = 1 - Ф(1) = 1 - 0.8413 = 0.1587
The probability that a bag of chip is lower than 9.07 oz of weight is 0.1587.
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A model airplane is traveling at a speed of 59 meters per second at a bearing of 214°. While
flying, the model plane comes across wind traveling in the direction N 17° W with a velocity of
21 meters per second. Find the resultant speed and direction (as a quadrant bearing) of the
model airplane.
In linear equation, The resultant speed is 48.27m/s and the bearing is 235.65 degrees. The vertical component is given by vsinθ = 32sin34° = 17.89 miles per hour.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Equations with variables of power 1 are referred to be linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
OP = 59m/s represents the plane that has a bearing of 214 degrees.
PW = 21m/s represents the wind that is blowing at an angle of N14W.
OW = represents the resultant vector.
The angle that OP makes with west direction = 270-214=56 degrees. Therefore the angle that OP makes with the vertical is 90-56=44 degrees
In the ΔOPW, ∠WPO = 14+44=58 degrees.
Using law of cosines, we can find the magnitude of OW
Using law of sines we can calculate ∠WOP
21/Sin∠WOP = 48.27/sin58
Therefore sin∠WOP = 21.SIN58/48.27 = = 0.368895
Therefore ∠WOP = sin-1 (0.368895) = 21.65 degrees
Therefore the bearing of OW is 214 + 21.65 = 235.65 degrees.
The resultant speed is 48.27m/s and the bearing is 235.65 degrees.
The horizontal component is given by vcosθ = 32cos34° = 26.53 miles per hour
The vertical component is given by vsinθ = 32sin34° = 17.89 miles per hour.
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please help bless you !
Answer:
A = 20, therfore B = 180
Step-by-step explanation:
Technically it's 17 but that is a really awkward scale so I had to round up. This really annoys me because if there was one more box you could had the scale 15 and it would've looked so much nicer but unfortunate you're short one
y=9x^2 + 9x - 1 rewritten in vertex form
The vertex form of given expression y=9x² + 9x - 1 is y = 9 ( x + 1/2 )² - 13 / 4
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables and constants.
Given expression,
y = 9x² + 9x - 1
complete the square for 9x² + 9x - 1
Use the form ax²+ bx +c , to find the values of a,b,c
a = 9 b = 9 c = -1
Consider the vertex form of a parabola
a ( x+d )² + e
Find the value of d using the formula d = b / 2a
d = 9 / 2.9
d = 1 / 2
So, now we have to find the value of e suing the formula
e = c - b² / 4a
e = -1 - 9*9 / 4*9
e = -13/ 4
Substitute the values a,d and e into the vertex form
9 ( x + 1/2 )² - 13 / 4
So,
y = 9 ( x + 1/2 )² - 13 / 4
Therefore, The vertex form of given expression y=9x² + 9x - 1 is
y = 9 ( x + 1/2 )² - 13 / 4
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Find perimeter of rectangle
this is the answer
(x+x+10)*2=4x+20
the critical region for a hypothesis test consists of . group of answer choices outcomes that have a very low probability if the null hypothesis is true outcomes that have a high probability if the null hypothesis is true outcomes that have a very low probability whether or not the null hyposthesis is true outcomes that have a high probability whether or not the null hypothesis is true
The critical region for a hypothesis test consists of outcomes that have a very low probability if the null hypothesis is true. This means that if the null hypothesis is true, these outcomes should not occur. The critical region is used to decide when to reject the null hypothesis and accept the alternative hypothesis.
Hypothesis testing is a process used in statistics to determine whether a certain claim or hypothesis is valid. It involves collecting data, analyzing the data, and making decisions based on the analysis of the data. The goal of hypothesis testing is to either reject or accept a null hypothesis, which is an assumption that there is no relationship between two measured phenomena. Hypothesis testing can also be used to compare two groups or to determine the effectiveness of a treatment or intervention.
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Plot and label the dokata lane exit (point D) on the number line
Answer: to label the point D on the number line, you can represent it as a real number and write it alongside the number line with an arrow pointing to its corresponding position. For example:
----|-----D---->|------
Where "D" is the label for the point and the arrow indicates its position on the number line.
Step-by-step explanation:
Given the similar figures above what is the value of w?
The value of w is 5
What are similar shapes?Two figures are considered to be "similar figures" if they have the same shape, congruent corresponding angles (meaning the angles in the same places of each shape are the same) and equal scale factors.
Similar shapes are enlargements of each other using a scale factor. All the corresponding angles in the similar shapes are equal and the corresponding lengths are in the same ratio.
The ratio of the corresponding sides of similar shapes are equal.
Therefore 35/28 = w/8
w× 28 = 35 × 8
w = 35× 8/28
w = 5
therefore the value of w is 5
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Emmy jogged 1/4 of a lap in P.E. class and 1/2 of a lap during track practice. How many laps did Emmy jog in all?
Answer:
3/4 of a lap
Step-by-step explanation:
You have to find the LCD (lowest common denominator)
That is 4, so your equation will be:
[tex]\frac{1}{4} + \frac{1}{2} = x\\\\\frac{1}{4} + \frac{2}{4} = x \\\\\frac{3}{4} = x[/tex]
A circle of center (-3 , -2) passes through the points (0 , -6) and (a , 0). Find a.
The radial distances from the center (-3, -2), to the points on the circumference (0, -6), and (a, 0), found using the distance formula, indicates that a = -3 ± √21
What is the distance formula for finding the distance between locations on the coordinate plane?The distance between points (x₁, y₁), and (x₂, y₂), on the coordinate plane, can be found using the formula; d = √((x₂ - x₁)² + (y₂ - y₁)²).
The coordinates of the center of the circle = (-3, -2)
The coordinates of the locations (on the circumference of the circle), through which the circle passes = (0, -6) and (a, 0)
Therefore the distances between points (0, -6) and (-3, -2) and (a, 0) and (-3, -2) are the same;
The distance from (0, -6) to (-3, -2) = The distance from (a, 0) to (-3, -2)
(-3 - 0)² + (-2 - (-6))² = (-3 - a)² + (-2 - 0)²
25 = a² + 6·a + 9 + 4 = a² + 6·a + 13
a² + 6·a + 13 = 25 (symmetric property)
a² + 6·a + 13 - 25 = 0
a² + 6·a - 12 = 0
a = (-6 ± √(6² - 4×1×(-12)))/(2×1) = (-6 ± √(84))/2
a = (-3 ± √(21))
a ≈ 1.58 and a ≈ -7.58
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I NEED HELP ASAP!!!
How many boxes would Alan have to sell to earn less than $2050?
Answer: Alan would have to sell less than 540 boxes.
Step-by-step explanation:
Cam ha recipe for pizza dough. He ue 12 1/2 cup of flour to make 5 ball of dough. Amaya will follow the ame recipe. She will make ball of dough uing f cup of flour. Which of thee equation repreent the relationhip between b and f
The equation representing the relationship between the number of balls of dough (b) and the amount of flour (f) would be b = f / 2.5.
To find the relationship, we need to determine how much flour is used per ball of dough. We know that Cam uses 12 1/2 cups of flour to make 5 balls of dough, so we can calculate the amount of flour per ball of dough by dividing the total amount of flour by the number of balls of dough: 12 1/2 cups / 5 balls = 2 1/2 cups per ball.
Therefore, the equation representing the relationship between the number of balls of dough (b) and the amount of flour (f) would be: b = f / 2.5, where f is the amount of flour used in cups and b is the number of balls of dough.
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Histograms show all of the following except
a. Location
b. Variation over time
c. Spread
d. Shape
A histogram is a graph used to represent the frequency distribution of a few data points of one variable.
Histograms often classify data into various “bins” or “range groups” and count how many data points belong to each of those bins.
Option (b) is correct.
Because, virtually all the common causes variations with time
Option (c) special and command variation
Which are two important variation
Option (a) location is the correct option here as histogram can not show the location.
Because, histogram shows shape and spread of data, also it shows variation over time. hence the correct option is a according to histogram data.
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Keisha and Ryan walk around a track. Keisha walks each lap in 5 minutes. Ryan walks each lap in 7 minutes. The two of them begin at the starting line at the same time. They walk until the meet again at the starting line. Answer the following questions. How many laps does Keisha complete? How many laps does Ryan complete? How much time does it take for them to meet again at the starting line?
The amount of time it would take for both Keith and Donna to complete each lap based on the question is given below:
1. It will take 24 minutes for Keith and Donna to meet again at the starting line.2. Keith will complete 2 laps3. Donna will complete 3 laps.How to find the amount of time it would take for Keith and Donna to meet again at the starting line?Factor two numbers 12 and 8:
12= 2. 2. 3
8= 2. 2. 2
Find the LCM,
The LCM of (12,8)= 2. 2. 3. 2 = 24
Hence,
1. It will take 24 minutes for Keith and Donna to meet again at the starting line.
2. Keith will complete 2 laps
3. Donna will complete 3 laps.
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the logician raymond smullyan describes an island containing two types of people: knights who always tell the truth and knaves who always lie. you are visiting the island and have the following encounters with natives. (a) two natives a and b address you as follows. a says: both of us are knights. b says: a is a knave. what are a and b? a is a knave and b is a knight. b is a knave and a is a knight. both a and b are knights. both a and b are knaves.
Both a and b are knights. This is the only possible answer because, according to the native's statements, a said they were both knights, and b said a was a knave. However, this contradicts what a said, so they must both be knights.
Knights are members of the nobility or military class in medieval Europe, typically depicted as armored warriors on horseback. They were typically sworn to serve their lord and protect his lands and people. Knights were expected to uphold a code of honor and show courage and loyalty in battle.
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Special right triangle need help pls
Therefore , the solution of the given problem of triangle comes out to be sides are a = 10 and b=5√3.
What exactly does a triangle mean?Due to their four sides or more, triangles are considered polygons. It has a straightforward, geometric form. A triangle is a square angle formed by the letters ABC. A singular rectangle or square is produced by Euclidean geometry when the sides are still not collinear. Triangles are polygons because they have three sides and three corners. Where three sides of a triangle come together are its corners. A triangle's angles sum up to 180 degrees.
Here,
Given :
A right triangle is :
=> 5 , b and a
has 30 degree angle .
=> Sin 30° = 5/a
=> 1/2 = 5/a
=> a = 10
Thus,
Using pythagoras theorem ,
=> 10² = 5² + b²
=> 100 -25 = b²
=> b² = 75
=> b = 5√3
Thus , sides comes out to be a = 10 and b=5√3
Therefore , the solution of the given problem of triangle comes out to be sides are a = 10 and b=5√3.
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If m∠B = 62°, a = 11, and c = 19, what are the measures of the remaining side and angles?
The remaining side is 16.9 and remaining angles are 83.1 and 34.9.
What is Cosine Formula?The cosine formula to find the side of the triangle is given by:
c = √[a² + b² – 2ab cos C] Where a,b and c are the sides of the triangle.
Given:
m∠B = 62°, a = 11, and c = 19
Now, b² = a² + c² - 2ac cos B.
b = √ a² + c² - 2ac cos B
b = √ 11² + 19² - 2x 11 x 19 cos 62
b= 16.9
Now. a/ sin A = b/ sin B= c/ sin C
So, <C = arc sin ( c sin B /b)
<C = arc sin ( 19 sin 62 /16.9)
<C = 83.1
and, <A = arc sin ( a sin B /b)
<A = arc sin ( 11 sin 62 /16.9)
<A = 34.9
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Blue Tide Swim Shop is having its annual summer sale, when every item in the store gets marked down. During the sale, rashguards sell for $5 less than full price. Miguel purchases 3 rashguards and pays a total of $60.
Which equation can you use to find how much money, f, each rashguard costs at full price?
The equation used is 3 (x - 5) = 60, the cost of each rashguard at full price is $25
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
Price of rash guard on sale =$5
Number of rashguard miguel purchased= 3
Now, Let the full price of each rashguard be x,
Rashguards sell for $5 less than full price;
x - 5
Miguel purchases 3 rashguards and pays a total of $60;
3 (x - 5) = 60
x - 5 = 60 / 3
x - 5 = 20
x = 20 + 5
x = 25
Therefore, the algebraic solution for x will be 25;
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Please help me with this math problem! Will give brainliest!! :) 20 POINTS!!
Using the area of the rectangle and circle, the shaded area is equal to 6.88 squared units
What is the area of the shaded regionTo determine the area of the shaded region, we can simply find the area of the rectangle and the area of the circle.
The formula of area of the rectangle;
Assuming the width is half the length
Area of rectangle = length * width
Area of rectangle = 8 * 4
Area of rectangle = 32 squared units.
Area of circle = πr²
r = radius of the circle
In this problem, the diameter of the circle is the width of the rectangle or rather, the diameter of the circle is half the length of the the rectangle.
d = 8 / 2 = 4 units
radius = diameter / 2
radius = 4 / 2 = 2 units
Substituting the values into the formula
A = πr²
A = 3.14 * 2²
A = 3.14 * 4
A = 12.56 squared units.
The non-shaded area = 2 * 12.56 = 25.12 squared units.
The shaded area = area of rectangle - non-shaded area
The shared area = 32 - 25.12
The shaded area = 6.88 squared units.
b.
The approximated area to the nearest tenth is 6.9 squared units
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