There is no value of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by 7.
For d=7, we can see that:
3² - 1 = 8 is divisible by 7, but 5² - 1 = 24 is not divisible by 7.
For larger values of d such as 11, 13, 77, and 1001, we can use a similar approach to see if there are any values of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by d. However, finding an exact value of n for larger values of d may be difficult without using more advanced mathematical methods.
In general, the number of values of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by a given integer d will depend on the properties of the numbers 3, 5, and d. For example, if d is a prime number that is not a divisor of either 3 or 5, it is likely that there are only a few values of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by d.
However, if d is a composite number or a divisor of either 3 or 5, there may be more values of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by d. Whether there are finitely or infinitely many such n will depend on the specific values of 3, 5, and d.
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Carlie's stock rose by points in trading today. Let represent yesterday's stock price at closing and represent today's stock price at closing.
i) What is a formula that correctly relates and ?
ii) If yesterday's closing price was , what was today's closing price?
i. The formula that correctly relates Y and T is T=Y+1 and today's closing price is 33.
Given information is that:
Carlie's stock rose by 1 point in trading today.
Let Y represent yesterday's stock price at closing
Let T represent today's stock price at closing
=> formula that correctly relates Y and T is:
T=Y+1
ii) If yesterday's closing price was 32 what was today's closing price?
today's closing price = yesterday's closing price + 1
<=> T=Y+1
<=> T=32+1=33.
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True or False, the standard deviation is the positive square root of the variance.
Since, the formula for variance is Variance = (σ)², where σ denotes standard deviation, the statement "the standard deviation is the positive square root of the variance" is false.
What is standard deviation?
The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.
The dispersion of the set of data values is measured by the standard deviation. The sigma symbol (σ) serves as its symbol.
This indicates that the data values tend to be more dispersed over a greater range for a higher standard deviation. While a lower number of standard deviation results from data being closer to its mean.
Variance, which is the expectation of the squared standard deviation, is a measure of how widely distributed the data are with respect to their mean.
As a result, the relationship between standard deviation and variance can be expressed numerically as, Variance = (σ)².
Therefore, standard deviation is not square root of variance.
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Find the range for the measure of the third side of a triangle given that the measures of two sides are 13 and 27.
Based on the Triangle Inequality Theorem, the range is: 14 < third side < 40.
What is the Triangle Inequality Theorem?The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side. In other words, the length of any one side of a triangle must be less than the sum of the lengths of the other two sides.
This theorem is used to determine the possible range of lengths for the sides of a triangle and to test whether a set of given lengths can form a triangle.
So, the range for the measure of the third side of a triangle given that the measures of two sides are 13 and 27 is:
14 < third side < 40.
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Naomi wants to save $100 000, so she makes quarterly payments of$1500 into an account that earns 4.4%/a compounded quarterly. How long will it take her to reach her goal?
It will take Naomi approximately 4 quarters and 8 months, or 4.67 quarters to reach her goal.
How to calculate?To find the number of quarters required to reach $100,000 with a quarterly payment of $1500 and an interest rate of 4.4% compounded quarterly, we will use the formula below:
N = log((A / P) + 1) / log(1 + r)
Where:
N = number of quarters
A = target amount ($100,000)
P = payment per quarter ($1500)
r = interest rate per quarter (4.4%/4 = 1.1%)
Substituting the values, we have that
N = log((100,000 / 1500) + 1) / log(1 + 0.011)
N = log(66.67) / log(1.011)
N = 4.67 quarters
In conclusion, It will take Naomi approximately 4 quarters and 8 months, or 4.67 quarters to reach her goal.
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Find the distance between A (-8, -3) and B (-5, -2). Write your answer as
a radical and as a decimal rounded to the nearest tenth.
Answer first 8-5=3 3-2=1 5,1 is you answer kind sir mam or them
Step-by-step explanation:
Una persona consume de promedio 250 m' de Coca Cola al día. Cuinto dinero en dólares gasta
anualmente en dicha bebida? (Suponer que llitro vale $0,75)
Calcula cuántos litros consumes al año
el consumo medio es de 250 cm³ en 1 día
Eso significa 1000 cm³ en 4 días. 1000 cm³ = 1 litro
Entonces 1 año = 365 días.
dividelo entre 4 dias
entonces cuantos litros se consumen al año
365 días * 1 Litro / 4 días = 91,25 Litros por año
si 1 litro cuesta 0.75$.
91,75 litros * $0,75 = $68.437.
redondeado a $68.44
About Sobre El Litro
El litro es una unidad de medida de volumen. Sin embargo, el litro no es una unidad estándar internacional, sino que se ha identificado como una de las "unidades no estándar aceptadas para su uso con Standard". La unidad estándar internacional de volumen es el metro cúbico (m³).
1L = 1dm³ = 1000 cm³ = 1000 cc
1 ml = 1 cm³ = 1 cc l
Un litro corresponde a:
0,001 metros cúbicos
1000 centímetros cúbicos
1 decímetro cúbico
Cubo de botones de 10 centímetros de lado.
Un metro cúbico (m³) contiene 1.000 litros. Entonces los litros también se pueden dividir en unidades más pequeñas.
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How To Convert Mcg To Mg Manually?
To Convert Mcg To Mg, divide your mcg figure by 1000
How To Convert Mcg To Mg?
1 milligram (mg) = 1000 micrograms (mg)
1 microgram (mcg) = 1/1000
=0.001 milligrams (mg)
Input:
Choose "mcg to mg conversion" or "mg to mcg conversion" from the top drop-down list, respectively.After that, note the number that needs to be transformed.At last. By pressing calculate, you can quickly convert between mcg and mg.To learn more about mcg to mg conversion refer to:
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Divide the number of mcg by 1000 to convert it to mg .A microgram is equal to 0.000001 g in micrograms because the prefix "micro-" in this context stands for 10-6.
How is mcg to mg converted? Divide the number of mcg by 1000 to convert it to mg.A microgram is equal to 0.000001 g in micrograms because the prefix "micro-" in this context stands for 10-6.Consequently, we set 1,000 mcg as the same as 1 mg.The mass in milligrams is multiplied by 1,000 to convert to micrograms, and the number of milligrams is divided by 0.001 to convert to micrograms for the conversion of mcg to mg units.Thousandth of a gram and 1,000 micrograms make up a milligram.Typically, the letter "mg" stands in for a milligram.The unit of measurement for a microgram is one millionth of a gram and one thousandth of a milligram.mcg or ug is the most common abbreviation.
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a test charge of 1µc is placed halfway between a charge of 3.2µc and another of 8.2 µc separated by 10 cm. what is the magnitude of the force (in newtons) on the test charge?
The magnitude of the force on the test charge will be the magnitude of the net force acting on the test charge due to its interaction with the other 2 charges.
The magnitude of the force on a test charge is the measurement of the strength of the interaction between the test charge and other charges.
In this scenario, a test charge of 1 µc is placed halfway between two charges of 3.2 µc and 8.2 µc separated by 10 cm. To find the magnitude of the force on the test charge, we can use Coulomb's law.
The magnitude of the force is given by the formula
=> F = k * q1 * q2 / r²,
where k is the Coulomb constant, q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
The magnitude of the force between the test charge and the 3.2 µc charge is given by the formula
=> F = k * 1 * 3.2 / (0.05²).
The magnitude of the force between the test charge and the 8.2 µc charge is given by the formula
=> F = k * 1 * 8.2 / (0.05²).
The magnitude of the force on the test charge is the sum of these two forces, which can be calculated using the formula
=> F = k * q1 * q2 / r².
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The area of a rhombu i 216 quare cm and the length of one diagonal i 24cm. What i the leght of the econd diagonal
The perimeter of the rhombus be 60 cm.
What is the perpendicular bisector of a diagonals?It is a rhombus or square if the diagonals of a quadrilateral are perpendicular bisectors of one another.
Lines that cut through the middle of each side of a triangle's perpendicular bisector are perpendicular to the provided side.
check to see if the diagonals of a rhombus cut the angles; if they do, the object is a rhombus. The diagonals can also be checked to verify if they are perpendicular bisectors of one another, or if they cross at a right angle.
One way to describe a perpendicular bisector is as a line that divides another line segment into two equal portions by crossing it perpendicularly.
[tex]$$\begin{aligned}& \text { Area of rhombus }=\frac{1}{2} \times D_1 \times D_2 \\& 216=\frac{1}{2} \times 24 \times D_2\end{aligned}$$[/tex]
(1) [tex]$\mathrm{D}_2=\frac{216}{12}=18$[/tex]
(2) Diagonals perpendicular bisector of each other
[tex]$$\begin{aligned}& \mathrm{OA}=\mathrm{DC}=12 \& \mathrm{DB}=\mathrm{OD}=9 \\& \mathrm{AB}^2=12^2+9^2=144+81=225 \\& \mathrm{AB}=15 \mathrm{~cm}\end{aligned}$$[/tex]
(3) perimeter [tex]$=4 \times 15=60 \mathrm{~cm}$[/tex].
The complete question is:
The area of a rhombus is 216 sq. cm. If its one diagonal is 24 cm; find :
(i) length of its other diagonal,
(ii) length of its side,
(iii) perimeter of the rhombus.
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If you flip a coin and roll a 6 66-sided die, what is the probability that you will flip a heads and roll less than a 6 66?.
When we calculate the probability of multiple events occurring, we use the concept of conditional probability.
Conditional probability is the probability of one event occurring given that another event has already occurred. In this case, the first event is flipping a heads, and the second event is rolling less than a 6 on a 66-sided die.
To find the probability of both events occurring, we multiply the individual probabilities:
P(heads and roll less than 6) = P(heads) * P(roll less than 6 | heads)
Here, P(heads) is the probability of flipping a heads, which is 1/2 for a fair coin. P(roll less than 6 | heads) is the probability of rolling less than a 6 given that we have already flipped a heads, which is 5/66 for a fair 66-sided die.
So:
P(heads and roll less than 6) = 1/2 * 5/66
P(heads and roll less than 6) = 5/132
So, the probability of flipping a heads and rolling less than a 6 on a fair 66-sided die is 5/132.
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We multiply the individual probabilities in order to determine the likelihood that both occurrences will occur:
P(heads and roll under 6) equals P(heads) Times P(roll under 6 | heads).
So:
P(heads and roll less than 6) is equal to 1/2 * 5/66.
P(heads, roll less than 6), equals 5/132
Therefore, the likelihood of getting a number less than a 6 on a fair 66-sided die is 5/132.
two linear equations in two variables have no solution. the equations are
When two linear equations in two variables have no solution, it means that the equations are not compatible. This means that the equations cannot be solved simultaneously, as there is no set of values that can satisfy both equations. This can be seen by graphing the equations on a coordinate plane. If the two lines are parallel, then they will never intersect, and thus, there is no solution. If the two lines are the same line, then they will intersect at every point, and thus, any point on the line is a solution.
In the case of two linear equations in two variables, if the equations are not parallel and not the same line, then the equations will intersect at one point. This point is the solution to the two equations. If the equations are not parallel and not the same line, but do not intersect, then there is no solution. This means that the equations are incompatible and cannot be solved simultaneously.
In summary, two linear equations in two variables have no solution when the equations are incompatible. This means that the equations are either parallel or the same line, but do not intersect. In this case, there is no set of values that can satisfy both equations, and thus, there is no solution.
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Two linear equations in two variables have no solution if and only if the lines represented by the equations are parallel and do not intersect.
In other words, the lines do not have a common point, which means that there is no pair of values for the variables that satisfy both equations simultaneously.
Here's an example:
y = 2x + 1
y = 2x + 3
In this case, the lines represented by the equations are parallel and do not intersect, so there is no solution for the system of equations.
You can see this graphically by plotting the lines on a coordinate plane: the lines are close to each other, but they never intersect, so there is no common point that satisfies both equations.
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Help me answer this question
In the regular hexagon, there will be only one line axis of symmetry.
What is the axis of symmetry?Axial symmetrical is similarity around an axis; an item is internally symmetric if it retains its appearance when turned around an axis.
The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.
The regular hexagon is shown.
In the regular hexagon, the upper triangle and the lower triangle are shaded. Then there will be only one line axis of symmetry.
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A runner is training for a half marathon. On Wednesday, she ran 6 miles in 50 minutes. On Thursday, she ran 4 miles in 32 minutes. Assume she ran at a constant rate each day. On which day did she run faster? By how much faster did she run?
The day she runs faster is Wednesday.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
On Wednesday:
She ran 6 miles in 50 minutes.
Unit rate:
= 6/50
= 0.12 miles per minute _____(1)
On Thursday:
She ran 4 miles in 32 minutes.
Unit rate:
= 4/32
= 0.125 miles per minute _______(2)
From (1) and (2),
0.12 > 0.125
Thus,
On Wednesday she runs faster.
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Points P (−2, 1), R (−2, −5), and Q (−6, −5)...Points P (−2, 1), R (−2, −5), and Q (−6, −5) create triangle PQR, which is then translated 1 unit down and 3 units to the right.What is the new x-coordinate of R?
Due to the triangle being translated 1 unit down and 3 units to the right, the new x-coordinate of R is now -2+3 = 1.R's x-coordinate was 2, thus 2 Plus 3 equals 1.
Triangle PQR is formed by points P (2, 1), R (2, 5) and Q (6, 5) and is then translated 1 unit downward and 3 units to the right. This indicates that all three points move three units to the right and one unit down. We may utilise R's initial x-coordinate, which was -2, to determine its new x-coordinate. Then, as R is being translated three units to the right, we add three to it. Consequently, R's new x-coordinate is now -2 + 3 = 1. Triangle PQR has been translated one unit down and three units to the right, giving rise to a new x-coordinate of R of 1. We must first determine the coordinates of each of the three triangle's points in order to determine the new x-coordinate of R. Point P is situated at (2, 1), point R at (2, 5) and point Q at (6, 5) respectively.
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Find a vector orthogonal to both 2, 2, 0 and to 0, 2, 5 of the form 1
The vector orthogonal for both vectors is [tex](20, -10, -4) / \sqrt{444}[/tex] = ([tex]20 / \sqrt{444}[/tex], [tex]-10 / \sqrt{444}[/tex], [tex]-4 / \sqrt{444}[/tex])
What is an orthogonal vector?
An orthogonal vector is a vector that is perpendicular to another vector in a given space. In other words, two vectors are orthogonal if their dot product is equal to zero.
To find a vector orthogonal to both 2, 2, 0 and 0, 2, 5 of the form 1, we can take the cross product of the two vectors, which results in a vector that is orthogonal to both. The cross product of 2, 2, 0 and 0, 2, 5 is given by:
(2, 2, 0) x (0, 2, 5) = (20, -10, -4)
So, a vector orthogonal to both 2, 2, 0 and 0, 2, 5 is given by (20, -10, -4). We can normalize this vector by dividing it by its magnitude, which is equal to sqrt(20^2 + (-10)^2 + (-4)^2) = sqrt(444). The normalized vector will be of the form 1:
[tex](20, -10, -4) / \sqrt{444}[/tex] = ([tex]20 / \sqrt{444}[/tex], [tex]-10 / \sqrt{444}[/tex], [tex]-4 / \sqrt{444}[/tex])
Hence, the vector orthogonal for both vectors is [tex](20, -10, -4) / \sqrt{444}[/tex] = ([tex]20 / \sqrt{444}[/tex], [tex]-10 / \sqrt{444}[/tex], [tex]-4 / \sqrt{444}[/tex]).
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find the area of equilateral triangle would length of one side is 4√3
The area of the equilateral triangle is A = 12*√3 square units.
How to find the area of the triangle?We know that for a equilateral triangle of side length S is given by the formula below:
A = (√3/4)*S²
Here we know that the sidelength is 4√3, then we can replace that on the expression above to get:
A = (√3/4)*(4√3)²
A = (√3/4)*16*3
A = √3*(4*3)
A = 12*√3
That is the area of the equilateral triangle.
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Solve. -3r = 9
Quetion 1 option:
r = 3
r = 12
r = -3
r = -27
Answer:
r=-3
Step-by-step explanation:
divide both sides by -3
-3r/-3=9/-33
r=-3
if there are 32 fluid ounces in a quart and 1.057 quarts in a liter, how many milliliters are there in exactly one fluid ounce?
One fluid ounce is equivalent to 29.5735 milliliters. both are unit of measurement of volume.
converting between metric units (such as grams or meters) and imperial units (such as ounces or feet) is a common type of unit conversion. The process of unit conversion involves using a conversion factor, which is a ratio that relates the units being converted.
To convert fluid ounces to milliliters, multiply the number of fluid ounces by 29.5735. To convert from fluid ounces to liters, divide the number of fluid ounces by 32, since there are 32 fluid ounces in a quart.
Then, multiply the number of quarts by 1.057, since there are 1.057 quarts in a liter. Finally, convert the number of liters to milliliters by multiplying the number of liters by 1000. The resulting value is the number of milliliters in one fluid ounce.
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A steady current I flows down a long cylindrical wire of radius a.
(a) Find the magnetic field, both inside and outside the wire, if all the current is uniformly distributed over the outside surface of the wire only. (b) Find the magnetic field, both inside and outside the wire, if the current is distributed in such a way that the current density J is proportional tos^2, where s is the distance from the axis.
(c) Show that your answers to (a) and (b) are consistent with the magnetostatic boundary conditions (Griffiths Eqn (5.76)) at the outside surface s = a.
(d) For the situation of part (a), determine the vector potential A everywhere.
For the situation in part (b), the boundary condition is given by B·n = μ_0J/2πa, where n is the unit normal vector to the surface of the wire and J is the current density. This is consistent with the magnetic
(a) The magnetic field outside the wire is given by B = μ_0I/2πs, where I is the current and s is the distance from the axis of the wire. The magnetic field inside the wire is zero.
(b) The magnetic field outside the wire is given by B = μ_0J/2πs, where J is the current density and s is the distance from the axis of the wire. The magnetic field inside the wire is given by B = μ_0J/2πa, where a is the radius of the wire.
(c) For the situation in part (a), the boundary condition is given by B·n = μ_0I/2πa, where n is the unit normal vector to the surface of the wire and I is the current. This is consistent with the magnetic field outside the wire, which is given by B = μ_0I/2πs.
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What is the probability of randomly drawing and immediately Eating 3 red m&ms in a row from a bag that contains 7 red m&ms out of 25 m&ms total
The probability of randomly drawing and immediately eating three red M&Ms in a row from a bag that contains 7 red M&Ms out of 25 M&Ms total is 1/280.
This can be calculated by using the formula for probability, which is n/(N), where n is the number of desired outcomes and N is the total number of outcomes. In this case, n is equal to 7 (the number of red M&Ms) and N is equal to 25 (the total number of M&Ms). Therefore, the probability is 7/25, which simplifies to 1/280.In this case, the probability of drawing three red M&Ms in a row is 3 out of 25, or 3/25.
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A regular pentagon, a regular octagon, and SBY meet at a point. What is the mSBY ?
The mSBY is the measure of the interior angle formed when three lines meet at a point. In this case, the three lines are a regular pentagon, a regular octagon, and SBY.
To calculate the mSBY, we must first calculate the measure of each of the other two angles. A regular pentagon has five sides, and each angle measures 108°. A regular octagon has eight sides, and each angle measures 135°. To calculate the mSBY, we must use the formula mSBY = 180° - (mP + mO). Using this formula, we can calculate that the mSBY is 37°: 180° - (108° + 135°) = 37°.
To visualize this, imagine three lines coming together at a point, forming an interior angle. The measure of the interior angle is the mSBY. The measure of the regular pentagon angle is 108°, and the measure of the regular octagon angle is 135°. When these two angles are added together, they equal 243°. Since the sum of the interior angles of a triangle is 180°, the measure of the interior angle must be 180° - 243°, which is 37°.
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how many ounces is 2 cups
16 ounces in 2 cups.
how many ounces is 2 cups?
1 cup = 8 ounces
so, 2 cup = 2 x 8
=16 ounces
A number of distinct units of mass, weight, or volume are derived from the uncia, an ancient Roman unit of measurement, including the ounce, which is almost unmodified.
The avoirdupois ounce, or precisely 28.349523125 g, is 1/16 of an avoirdupois pound and is used in both the United States and the United Kingdom.
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One ounce, abbreviated as "oz," is 480 grains, or 31.103 grams, and it is a measure of weight that is one-twelfth of a Troy or Apothecaries' pound.2 Cups = 16 Ounces
2 cups equals how many ounces? A weight measurement equal to one-sixteenth of a pound (avoirdupois); one ounce weighs 437.5 grains or 28.349 grams..A weight measurement equal to one-sixteenth of a pound (avoirdupois); one ounce weighs 437.5 grains or 28.349 grams.One ounce, abbreviated as "oz," is 480 grains, or 31.103 grams, and it is a measure of weight that is one-twelfth of a Troy or Apothecaries' pound.One-sixteenth of a pound is equivalent to one ounce, which is a unit of weight measurement.The smallest common unit of weight measurement in the United States is the ounce, therefore small things like pencils and deodorant sticks are frequently weighed in ounces.In the troy and apothecaries' systems, an ounce weighs 480 grains, or 1/12 pound, while the avoirdupois system values it at 1/16 pound (437 1/2 grains). 2 Cups = 16 OuncesTo learn more about Ounces refer
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PLEASE HELP 30 pts for this
A) Base = 10 units, Height = 7 units, and Area = 35 square units.
B) Base = 11 units, Height = 6 units, and Area = 33 square units.
C) Base = 10 units, Height = 4 units, and Area = 20 square units.
D) Base = 4 units, Height = 11 units, and Area = 22 square units.
What is the area of the triangle?
The area of a triangle is a measure of the space contained within its three sides. It can be calculated by multiplying the base of the triangle by its height and dividing the result by two. In mathematics, the formula for the area of a triangle is:
A = (1/2)bh
where b is the base and h is the height of the triangle.
For figure A)
The base of the triangle would be = 10 units
The height of the triangle is = 7 units.
Area of the triangle = 1/2 * 10 * 7
= 35 square units.
For figure B)
The base of the triangle would be = 11 units
The height of the triangle is = 6 units.
Area of the triangle = 1/2 * 11 * 6
= 33 square units.
For figure C)
The base of the triangle would be = 10 units
The height of the triangle is = 4 units.
Area of the triangle = 1/2 * 10 * 4
= 20 square units.
For figure D)
The base of the triangle would be = 4 units
The height of the triangle is = 11 units.
Area of the triangle = 1/2 * 4 * 11
= 22 square units.
Hence,
A) Base = 10 units, Height = 7 units, and Area = 35 square units.
B) Base = 11 units, Height = 6 units, and Area = 33 square units.
C) Base = 10 units, Height = 4 units, and Area = 20 square units.
D) Base = 4 units, Height = 11 units, and Area = 22 square units.
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Factor this equation
a^2+4b^2
Answer:
a2 + 4b2
Step-by-step explanation:
Triangle def is similar to triangle abc solve for y DEF 37. 5 20 27. 5 ABC y 12 16. 5
There are two triangles ABC and DEF with sides are (37.5, 20, 27.5) and (y, 12, 16.5) and the value of y is 22.59.
Triangle is consists of 3 sides and there are many types of triangles like equilateral triangle, obtuse triangle and right-angled triangle and the triangle has many properties .
Triangle has three edges and three vertices.
A triangle with vertices A,B,C can be denoted as Triangle ABC
The sides of triangle ABC is (37.5, 20, 27.5)
The sides of triangle DEF is (y, 12, 16.5)
By similarity property we get,
37.5/y = 20/12 = 27.5/16.5
37.5/y = 1.66 = 1.66
so by equating values we get , y = 37.5/1.66
so the value of variable y is 22.59.
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question content area the complement of a. P(B | A)b. P(A | BC)c. P(AC | B)d. P(A I B)
a. independent event P(AuB)=P(A)+P(B) b. mutually exclusive event P(AuB) = P(A) + P(B) - P(AnB) c. independent event P(A and B) = P(A).P(B)
d. complement P(A') = 1 - P(A)
a. For two events A and B the union of the two sets is simply all the elements present in both set. This can be expressed as
P(AuB)=P(A)+P(B)
b. Two events are said to be mutually exclusive if they cannot occur at the same time. i.e no same element must be present in both events at a time. This can be expressed as
P(AuB) = P(A) + P(B) - P(AnB)
c. event A and event B are said to be independent if the incidence of event A does not affect the probability of the event B.
This can be expressed as
P(A and B) = P(A).P(B)
d. complement of an event are simply all the occurrence not in he set but in the universal set.
the complement of set A can be expressed as
P(A') = 1 - P(A)
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let a1 , a2 , and b . for what value(s) of h is b in the plane spanned by a1 and a2?
-17 is value(s) of h is b in the plane .
A straightforward explanation of a vector ?
A quantity or phenomena with both magnitude and direction being independent of one another is called a vector. Additionally, the phrase designates how such a quantity is represented mathematically or geometrically.
Velocity, momentum, force, electromagnetic fields, and weight are some natural examples of vectors.
For the plane spanned by a1 and a2, y is a linear combination of a1 and a2 if it is in the plane.
y = a a1 + b a2 where a and b are constants.
[4,1,h] = a[1,4,-2] + b[-2,-3,7]
[4,1,h] = [a - 2b,4a -3b,-2a+ 7b] by the rules of vector addition and multiplication. Vectors are equal if their components are equal
4 = a - 2b
1 = 4a - 3b
h = -2a + 7b
We can solve for a and b from the first two equations to find h:
a = -2
b = -3
h = -17
We see that -2[1,4,-2] - 3[-2,-3,7] = [4,1,-17].
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The complete question is -
For what value(s) of h is b in the plane spanned by a1 and a2?
a1 = [1, 4, -2] a2 = [-2, -3, 7] b = [4, 1, h]
An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown. Which best describes the range of possible values for the third side of the triangle?x < 12. 5, x > 18. 912. 5 < x < 18. 9x < 6, x > 266 < x < 26.
The range of possible values for the third side of the triangle is d)6 < x < 26.
The third side of an acute triangle must be shorter than the sum of the other two sides and longer than the difference between the other two sides. By using the Pythagorean Theorem, we can find the range of possible values for the third side.
The Pythagorean Theorem states that the sum of the squares of the two sides of a right triangle equals the square of the hypotenuse. So, for this triangle, we have 10^2 + 16^2 = x^2.
Solve for x: x^2 = 256, so x = √256 = 16.
The third side must be shorter than the sum of the other two sides. So, the maximum value for x is 16 + 10 = 26.
The third side must be longer than the difference of the other two sides. So, the minimum value for x is 16 - 10 = 6.
Therefore, the range of possible values for the third side of the triangle is 6 < x < 26.
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An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown.
Which best describes the range of possible values for the third side of the triangle?
x < 12.5, x > 18.9
12.5 < x < 18.9
x < 6, x > 26
6 < x < 26
if u and v are orthogonal what is the magnitude of u×v
The magnitude of u × v is 0, if u and v are orthogonal
Orthogonal;
By virtue of being perpendicular to one another, orthogonal objects are connected in Euclidean geometry. Lines or line segments are said to be connected orthogonally if they are perpendicular at the point of intersection. Similar to this, if two vectors create a 90-degree angle, they are said to be orthogonal.
What use does orthogonal serve?
The orthogonal matrix's determinant has a value of 1. Its nature is symmetrical. The transpose and inverse of an orthogonal matrix are equivalent. The orthogonal matrix's eigenvalues are also equal to 1, and its eigenvectors are both orthogonal and real.
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fritz can build a bookcase in 8 hours and holly can build it in 10 hours. after working together for 3 hours, fritz leaves. how long will it take holly to finish the bookcase by herself?