The intersection of sets A and B
The intersection of two sets is the set of elements that are common to both sets. To find the intersection of sets A and B, we simply look for the elements that are in both sets. In this case, the intersection of A and B is {h, o, e}.
The union of two sets is the set of elements that are in either one of the sets or both. To find the union of sets A and B, we simply combine the elements from both sets, making sure to not include any duplicates. In this case, the union of A and B is {h, o, m, e, u, s}.
So, the intersection of sets A and B is {h, o, e} and the union of sets A and B is {h, o, m, e, u, s}.
Here is the solution in HTML:
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5x – 4 = 5x
What value could you write in after 5x that would make the equation true for: no values of x?
Answer:
No solution
Step-by-step explanation: no values of x
What is the approximate distance from Denver to Chicago? Use a proportional relationship to solve the problem. Show your work.
We can observe that Denver and Chicago are separated by 1,114 miles by changing the units.
What is changing the unit?Changing the unit is the process of converting a given quantity from one unit of measurement to another. This is done to ensure accuracy and consistency in measurement. This process is used in many different areas of life, from converting between metric and imperial measurements in cooking to converting between Fahrenheit and Celsius in temperature measurement.
We now employ the conversion in the left-hand corner. We can simplify this as: since each unit equals 557 miles,
2 units equal 1,114 miles (2 * 557 miles).
The distance between Denver and Chicago is 1,114 miles.
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Prove that AD CONGRUENT TO BC
ABDC is a rectangle, we can conclude that AD is congruent to BC.
What is Triangle ?
Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.
In the given diagram, we have a parallelogram ABCD. To prove that AD is congruent to BC, we need to show that ABDC is a rectangle.
Here's the proof:
Since ABCD is a parallelogram, we know that:
AB is parallel to CD
BC is parallel to AD
Also, we have:
∠A + ∠B = 180° (opposite angles of a parallelogram)
∠D + ∠C = 180° (opposite angles of a parallelogram)
From the diagram, we can see that:
∠A + ∠D = 180° (adjacent angles of a parallelogram)
∠B + ∠C = 180° (adjacent angles of a parallelogram)
Adding the last two equations, we get:
∠A + ∠D + ∠B + ∠C = 360°
But we know that the sum of the angles in a rectangle is 360°. Therefore, if we can prove that ABDC is a rectangle, we can conclude that AD is congruent to BC.
To show that ABDC is a rectangle, we need to prove that:
AB is perpendicular to BC
BC is perpendicular to CD
CD is perpendicular to AD
AD is perpendicular to AB
Since AB is parallel to CD and BC is parallel to AD, we can conclude that ∠ABC and ∠CDA are alternate interior angles and are therefore congruent. Similarly, ∠ABD and ∠DCB are alternate interior angles and are congruent.
Now, we can prove that ABDC is a rectangle by showing that all its angles are right angles. We can do this by proving that:
∠ABC + ∠ABD = 90° (interior angles of a triangle)
∠CDA + ∠DCB = 90° (interior angles of a triangle)
Since ∠ABC and ∠CDA are congruent, and ∠ABD and ∠DCB are congruent, we have:
∠ABC + ∠ABD = ∠CDA + ∠DCB
Substituting the values of these angles, we get:
2∠ABC = 2∠CDA
∠ABC = ∠CDA
Therefore, ∠ABC and ∠CDA are both 45 degrees. Similarly, we can show that ∠ABD and ∠DCB are both 45 degrees. Hence, all angles of ABDC are 90 degrees, and we have proven that ABDC is a rectangle.
Since , ABDC is a rectangle, we can conclude that AD is congruent to BC.
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pls help! Will mark brainliest!!
Match the following terms to the correct location on the transverse wave.
From the given information provided, A is crest, B is wavelength, C is trough, D is amplitude, E is equilibrium line in the transverse wave.
Amplitude: The maximum displacement of wave from its equilibrium position. In other words, it is the height of the wave measured from the midpoint (or equilibrium position) to the crest or trough.
Wavelength: The distance between two consecutive crests or troughs of a wave. It is usually denoted by Greek letter lambda (λ) and measured in meters.
Crest: The highest point or peak of a wave. It is the point on the wave with maximum positive displacement from the equilibrium position.
Trough: The lowest point of a wave. It is the point on the wave with maximum negative displacement from the equilibrium position.
Equilibrium: The position where there is no net force acting on an object. In the context of waves, the equilibrium position is the position where there is no displacement of the medium through which the wave is travelling.
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The following frequency table summarizes this year's injuries on the Canadian Rounders cricket team.
Number of injured players Number of matches
0
00
4
44
1
11
5
55
2
22
2
22
3
33
3
33
4
44
2
22
Based on this data, what is a reasonable estimate of the probability that the Canadian Rounders have
0
00 players injured for their next match?
Answer:
25%
Step-by-step explanation:
Number of favorable outcomes 4
Total number of outcomes=4+5+2+3+2=16
4/16=0.25
0.25x100=25
25%
A tent shaped like a triangular prism with the dimensions shown. If the volume of the tent is 12.6 cubic meters, what is the center height, h, of the tent
The base is 2.8m the height that connects the 2 bases is 4.5m
The center height of the tent is 1.57 meters.
What is Triangle?Triangle is a polygon with three sides and three angles. It is one of the basic shapes in geometry. Triangles come in a variety of forms, including equilateral, isosceles and scalene. The sum of the three interior angles of a triangle is always 180°, making it one of the few geometric shapes whose angles add up to a fixed number. Triangles are the strongest shape, making them ideal for construction and engineering projects.
Using the formula for the volume of a triangular prism, V = B x H x L, we can determine the center height, h, of the tent:
V = B x H x L
12.6 = 2.8 x H x 4.5
H = 12.6 ÷ (2.8 x 4.5)
H = 1.57 meters
Therefore, the center height of the tent is 1.57 meters.
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JUSTDRAW WHERE TO PUT THE POINT I CANT WITH COORDINATES
Fill in the table for y = 2x² - 6.
X y
-0
2
4
Answer:
6969696969696969695969696966969696969696969699६9६9६9६959596869494982285959585868586868696959695968684828282828३8474747474848475757718१883757474839485747747474747474747474747484858384848485858587575757585848484848585857494857585958584858585858685969686(696066969686868696960
Suppose the annual interest rate is 7.5% and the interest is compounded annually. How much will an investment of $1,000 be worth after 3 years?
The investment οf $1,000 will be wοrth $1,225.04 after 3 years.
What is Cοmpοund interest?Cοmpοund interest is interest οn the principal amοunt οr lοan which is calculated accοrding tο the number οf cοmpοunds in οne year.
In this, the interest earned in each periοd is based οn the tοtal amοunt, which includes bοth the principal and the accumulated interest.
The fοrmula used fοr cοmpοund interest is
[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]Here we have
The principal amοunt is $ 1000
The annual interest rate here is 7.5%
The interest is cοmpounded annually.
The time periοd is 3 years
Using the fοrmula,
[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]
A = 1,000 (1 + 0.075/1)⁽¹⁽³⁾⁾
= 1,000 (1.075)³
= $1,225.04
Therefοre,
The investment of $1,000 will be wοrth $1,225.04 after 3 years.
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Triangle XYZ is drawn with vertices X(−2, 4), Y(−9, 3), Z(−10, 7). Determine the line of reflection that produces Z′(10, 7).
y-axis
x-axis
y = 3
x = −4
The line of reflection that produces Z′(10, 7) is y - axis.
What is a triangle?A triangle is a two - dimensional figure with three sides and three angles.
The sum of the angles of the triangle is equal to 180 degrees.
∠A + ∠B + ∠C = 180°
Given is a Triangle XYZ is drawn with vertices X(−2, 4), Y(−9, 3), Z(−10, 7). Determine the line of reflection that produces Z′(10, 7).
The rule for a reflection over the y -axis is (x, y) → (−x, y). We can write the reflection as -
Z(- 10, 7) → Z'(10, 7)
Therefore, the line of reflection that produces Z′(10, 7) is y - axis.
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The line of reflection that produces Z′(10, 7) is y - axis.
What is a triangle?
A triangle is a two - dimensional figure with three sides and three angles.
The sum of the angles of the triangle is equal to 180 degrees.
∠A + ∠B + ∠C = 180°
Given is a Triangle XYZ is drawn with vertices X(−2, 4), Y(−9, 3), Z(−10, 7). Determine the line of reflection that produces Z′(10, 7).
The rule for a reflection over the y -axis is (x, y) → (−x, y). We can write the reflection as -
Z(- 10, 7) → Z'(10, 7)
Therefore, the line of reflection that produces Z′(10, 7) is y - axis.
Identify the number of solutions of the polynomial equation. Then find all the solutions. 4x^(5)-8x^(4) +6x^(3)=0
The number of solutions of the polynomial equation, 4x^(5)-8x^(4) +6x^(3)=0 is 5 and the solutions are x=0, x=3/2, and x=1.
The polynomial equation at hand is of degree 5, which means that the highest power of the variable present in any term is 5.
Therefore, we can infer that the equation can be written in the form of ax^5 + bx^4 + cx^3 + dx^2 + ex + f = 0, where a, b, c, d, e, and f are constants and x is the variable. To solve this equation, we can try factoring it:
4x^(5)-8x^(4) +6x^(3)=0
2x^(3)(2x^(2)-4x+3)=0
2x^(3)(2x-3)(x-1)=0
The solutions are x=0, x=3/2, and x=1.
Therefore, the number of solutions of the polynomial equation is 5 and the solutions are x=0, x=3/2, and x=1.
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Use the properties of exponents to rewrite $y=5e^{-0. 7t}$ in the form $y=a(1+r)^t$ or $y=a(1-r)^t$. Round the value of $r$ to the nearest thousandth. Then find the percent rate of change to the nearest tenth of percent
We can rewrite y=[tex]5e^{-0.7t}[/tex] using the properties of exponents as follows:
y=[tex]5e^{-0.7t} =5(e^{-0.7)t} =5(\frac{1}{e^{0.7} })t[/tex]
We can recognize [tex]\frac{1}{e^{0.7} }[/tex] as a base for exponential function that can be written in the form 1 ±r We know that is an increasing function, so [tex]e^{0.7}[/tex]≥1
therefore [tex]\frac{1}{e^{0.7\\} }[/tex]≥1 which means we must use the form y=a[tex](1-r^){t}[/tex]
To find the percent rate of change, we can use the formula:
percent rate of change=|r|×100
So, the percent rate of change is:
=|0.503|×100
Rounding to the nearest tenth of a percent, we get a percent rate of change of approximately 50.3%.
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Determine which point from the specified set satisfies the system of equations.
y =-1/3x + 3
y = -3/4x + 8
Select Choice
(12,-1)
(9,0)
(8,14)
Answer:
y= -1/3x+3
Step-by-step explanation:
we only need to look at the gradient as the gradient of both equations is not the same.
gradient= -1-0/12-9
= -1/3
hence, the answer is y= -1/3x+3
Three squares with areas of 112 cm2,28 cm2, and 63 cm2 are displayed on a computer monitor. What is the sum (in radical form) of the perimeters of these squares? The sum of the perimeters is cm.
The sum of the perimeters of the three squares displayed on the computer monitor is 36√7 cm.
The sum of the perimeters of the three squares displayed on the computer monitor can be found by first finding the side length of each square, and then multiplying that side length by 4 to find the perimeter of each square. Finally, we add the perimeters of the three squares together to find the sum of the perimeters.
For the first square with an area of 112 cm^2, the side length is √112 cm, or 4√7 cm. The perimeter of this square is 4(4√7 cm) = 16√7 cm.
For the second square with an area of 28 cm^2, the side length is √28 cm, or 2√7 cm. The perimeter of this square is 4(2√7 cm) = 8√7 cm.
For the third square with an area of 63 cm^2, the side length is √63 cm, or 3√7 cm. The perimeter of this square is 4(3√7 cm) = 12√7 cm.
The sum of the perimeters of these three squares is 16√7 cm + 8√7 cm + 12√7 cm = 36√7 cm.
Therefore, the sum of the perimeters of the three squares displayed on the computer monitor is 36√7 cm.
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What is the profit for buying pencils for $2 each and selling them for $2,40 and manage to sell $40 and what is the profit and loss
The profit for buying pencils for $2 each and selling them for $2.40 is $6.40 and there is no loss.
The profit is the difference between the selling price and the cost price of the pencils. In this case, the profit per pencil is $2.40 - $2 = $0.40.
Since the total sales amount is $40, the number of pencils sold is $40/$2.40 = 16.67, which we can round down to 16 pencils. Therefore, the total profit is 16 * $0.40 = $6.40.
There is no loss in this scenario, as the selling price is higher than the cost price. Loss occurs when the selling price is lower than the cost price.
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vide as indicated. Simplify the answer. (x^(2)+11x+28)/(x^(2)+4x-21)-:(x^(2)+2x-8)/(6x-18)
To solve this problem, we need to first find the common denominator of the two fractions and then subtract the numerators. The common denominator is (x^(2)+4x-21)*(6x-18).
So, we can rewrite the problem as:
[(x^(2)+11x+28)*(6x-18) - (x^(2)+2x-8)*(x^(2)+4x-21)]/[(x^(2)+4x-21)*(6x-18)]
Next, we need to simplify the numerators by distributing and combining like terms:
[(6x^(3)-18x^(2)+66x^(2)-198x+168x-504) - (x^(4)+4x^(3)-21x^(2)+2x^(3)+8x^(2)-16x-8x^(2)-32x+168)]/[(x^(2)+4x-21)*(6x-18)]
[(6x^(3)-18x^(2)+66x^(2)-198x+168x-504) - (x^(4)+6x^(3)-21x^(2)+8x^(2)-48x+168)]/[(x^(2)+4x-21)*(6x-18)]
[(6x^(3)-18x^(2)+66x^(2)-198x+168x-504) - x^(4)-6x^(3)+21x^(2)-8x^(2)+48x-168]/[(x^(2)+4x-21)*(6x-18)]
Next, we can combine like terms in the numerator:
[-x^(4)+12x^(2)-30x-336]/[(x^(2)+4x-21)*(6x-18)]
Finally, we can simplify the denominator by factoring:
[-x^(4)+12x^(2)-30x-336]/[(x+7)(x-3)*(6x-18)]
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Your retirement account earns 7%, compounded quarterly. How much must the account contain when you retire if you want to withdraw $4000 at the end of each quarter for 30 years? ANSWER: _______dollars Round your final answer to the nearest cent. Note: This is almost identical to example 3 (only the payment amount is different), so check out the example 3 video if you need help.
__________
Therefore, the retirement account must contain $2,758,686.58 when you retire in order to withdraw $4000 at the end of each quarter for 30 years.
To find the amount that the retirement account must contain when you retire, we can use the formula for the future value of an annuity due:
FV = PMT * [(1 + r/n)^(n*t) - 1] / (r/n) * (1 + r/n)
Where FV is the future value, PMT is the payment amount, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.
In this case, PMT = $4000, r = 0.07, n = 4 (since the account is compounded quarterly), and t = 30.
Plugging these values into the formula, we get:
FV = 4000 * [(1 + 0.07/4)^(4*30) - 1] / (0.07/4) * (1 + 0.07/4)
FV = 4000 * [(1.0175)^120 - 1] / (0.0175) * (1.0175)
FV = 4000 * 11.9478 / 0.0175 * 1.0175
FV = $2,758,686.58
Therefore, the retirement account must contain $2,758,686.58 when you retire in order to withdraw $4000 at the end of each quarter for 30 years.
Round your final answer to the nearest cent, the retirement account must contain $2,758,686.58.
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The equation px²+16x+4=0 is certified by x=-2/3. Find the value of p and x
P therefοre has a value οf 45/2 and x = -0.4.
What is equatiοn?A mathematical assertiοn that twο expressiοns are equivalent is knοwn as an equatiοn. It frequently includes οne οr mοre variables, which are unknοwable things with a wide range οf pοssible values. Finding the value οr values οf the variable that make the equatiοn true is the aim οf equatiοn sοlving. Mοst equatiοns take the fοrm: expressiοn is alsο expressiοn. Fοr instance, the fοrmula x + 2 = 5 states that the prοduct οf x and 2 is 5.
given
If the answer tο the equatiοn px² + 16x + 4 = 0 is x=-2/3, we can be cοnfident that we will οbtain an equivalence if we replace x = -2/3 in the fοrmula.
Adding x=-2/3 tο the sοlutiοn results in:
p(-2/3)² + 16(-2/3) + 4 = 0
Simplifying the phrase:
(4/9)p - (32/3) + 4 = 0
(4/9)p = (32/3) - 4
(4/9)p = (20/3)
By adding (9/4) tο bοth ends, we get:
p = (20/3) * (9/4)
p = 15
P therefοre has a value οf 45/2.
For x,
15x² + 16x + 4 = 0
3x(5x + 2) + 2(5x + 2)
(3x + 2)(5x + 2)
x = -2/3 and x = -0.4
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A book sold 38,100 copies in its first month of release. Suppose this represents 7.1% of the number of copies sold to date. How many copies have been sold to date?
The book sold 38,100 copies in its first month of release. then approximately 537,324 copies have been sold to date.
What is the percentage?
A percentage is a ratio, fraction, or portion of a whole which is represented as 100.
Let "x" be the total number of copies sold to date.
According to the problem, 38,100 is 7.1% of x, which can be written as:
38,100 = 0.071x
To find x, we can solve for it by dividing both sides of the equation by 0.071:
x = 38,100 / 0.071
x = 537,323.94 (rounded to the nearest whole number)
Therefore, approximately 537,324 copies have been sold to date.
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Part A. Write a system of linear equations for which there is no solution. Part B. When a system of equations is solved algebraically, how do you know that the system has no solution? Part C. Use your system of equations to explain your reasoning
The system of linear equations will be 2x+3y=8, 4x+6y=15.
Which mathematical equation is the most challenging?
A mathematics issue have baffled the finest scientists in the world for decades. The Diophantine equation x3+y3+z3=k, where k is the sum of all of the numbers from 1 to 100, is sometimes referred to as the "sum of three cubes."
What is an equation's most basic form?
The lowest corresponding fraction of the integer is its simplest form. How to determine the simplest form: Look for shared components in the denominator and numerator. Verify if a fractional integer includes a prime number.
For example:
2x+3y=8
4x+6y=15
Part C:
Using the example above,
2x+3y=8
4x+6y=15
If we multiply the first equation by , we get:
4x+6y=16
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Find m for the investment of $1000.00 for 2 years at 1.8% compounded semi-annually. A) 1
B) 0.9% C) 2 D) 4
(B) 0.9%. We can use the formula for compound interest to find the value of the investment after 2 years:
A = P(1 + r/n)^(nt)
where A is the amount of money after the time period, P is the principal (initial investment), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
Plugging in the given values, we get:
A = 1000(1 + 0.018/2)^(2*2)
= 1000(1 + 0.009)^4
= 1000(1.009)^4
≈ 1083.02
So the investment is worth approximately $1083.02 after 2 years.
To find the interest rate per year, we can use the formula:
r = n[(A/P)^(1/nt) - 1]
Plugging in the values we know, we get:
r = 2[(1083.02/1000)^(1/(2*2)) - 1]
= 2[(1.08302)^(1/4) - 1]
≈ 0.9%
Therefore, the answer is (B) 0.9%.
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write an equivalent expression to 8k - (5 + 2k) without parentheses
Answer:
8k - (5 + 2k) can be simplified by distributing the negative sign to the terms inside the parentheses:
8k - 5 - 2k
Then, we can combine like terms by adding the constants -5 and 8k:
6k - 5
Therefore, an equivalent expression to 8k - (5 + 2k) without parentheses is 6k - 5.
If mario jumps 3 times and luigi jumps 62 times. What is mario’s jumps times luigi’s jumps?
Answer:
21 times
Step-by-step explanation:
3x21=62
explain what is meant when a correlation between two variables is
said to be statistically significant ?
Statistically significant means that the relationship between two variables is likely to be real and not due to chance. If the p-value is lower than the predetermined threshold, usually 0.05, then the correlation is said to be statistically significant.
When a correlation between two variables is said to be statistically significant, it means that the relationship between the two variables is not due to chance or random error. In other words, the relationship is likely to be a real one and not just a coincidence.
Statistical significance is often determined by calculating a p-value, which is the probability of observing a relationship as strong as the one observed if there was no actual relationship between the variables. If the p-value is less than a predetermined threshold, usually 0.05, the relationship is considered to be statistically significant. This means that there is less than a 5% chance that the relationship observed is due to random error.
Therefore, It is usually determined by calculating a p-value, which measures the probability that the relationship between two variables is due to random chance.
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The graph represents a functional relationship.
81x
6
4
2
-2
&
-
-6-
do d
-8
-10
-12-
-14
2 4 6 8 10 12 14 16 18
X
Which value is an input of the function?
O-14
0-2
04
Answer:
Last answer choice: 4
Step-by-step explanation:
The set of inputs to the graphed function is he set of all x values for which the function has a defined value
Looking at the answer choices we see that the graph does not go the negative x region nor does it have a value for 0
So x = 4 is an input, and the resultant output y from the graph = 0
Answer
Last answer choice: 4
Peter drove a total of 1000km and used 100 litres of petrol
Calculate the rate at which the petrol was used in kilometers per little
The rate at which the petrol was used in kilometers per liter is 10 km/L that means that for every litre of petrol used for driving, Peter's car could travel 10 kilometers.
Peter drove a thousand km and used 100 liters of petrol. To find the rate at which the petrol was utilized in kilometers consistent with liter, we divide the whole distance traveled via the quantity of petrol used.
The formulation for this is rate of petrol usage = overall distance traveled/quantity of petrol used.
Rate of petrol usage = total distance traveled/quantity of petrol used
Substituting the values we get,
= 1000 km / 100 L
= 10 km/L
This means that for every liter of petrol used, Peter was capable of travel 10 kilometers.
Thus, the rate at which the petrol was used in kilometers per liter is 10 km/L.
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Help as much anything is appreciated!
Due to length restrictions, we kindly invite to read the explanation to see the lenghts of each 30-60-90 right triangles.
How to resolve a 30-60-90 right triangle
In this problem we find six cases of 30-60-90 right triangles, that is, right triangles whose inner angles have the following measures: 30°, 60°, 90°. The length of sides can be found by the following relationships:
The leg adjacent to 60° is 1 / 2 times the hypotenuse.The leg adjacent to 30° is √3 / 2 times the hypotenuse.The leg adjacent 30° is √3 times the leg adjacent to 60°.Now we proceed to determine the missing length:
Case 1:
PV = 4 / (1 / 2)
PV = 8
VT = √3 · 4
VT = 4√3
Case 2:
PT = 2 / √3
PT = 2√3 / 3
PV = 2 / (√3 / 2)
PV = 4√3 / 3
Case 3:
PT = (1 / 2) · 3
PT = 3 / 2
VT = 3√3 / 2
Case 4:
PT = 7 / √3
PT = 7√3 / 3
PV = 7 / (√3 / 2)
PV = 14√3 / 3
Case 5:
VT = √3 · (1 / 2)
VT = √3 / 2
PV = (1 / 2) / (1 / 2)
PV = 1
Case 6:
PV = 100
PT = 50
VT = 50√3
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Determine the total number of eggs in 7 dozen eggs
The total number of eggs in 7 dozens of eggs is 84 eggs
What is a Word Problem?Word Problem is a sentence usually made up of a few sentences describing a scenario that needs to be solved through mathematics.
How to determine this
When a dozen mean a group of twelves things
When 1 dozen of an egg = 12 eggs
To get the total number of eggs in 7 dozens of eggs
Let x represent the total number of eggs
When 1 dozen = 12 eggs
7 dozens = x
x = 7 dozens * 12 eggs/1 dozen
x = 84 eggs/1
x = 84 eggs
Therefore, 84 eggs make 7 dozens of eggs
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Isabella is deep-sea diving with two friends. Stacy is exploring a coral reef 6.3 meters in front of Isabella, and Jayla is floating on the surface directly above Isabella. If Jayla and Stacy are 9 meters apart, how far apart are Isabella and Jayla? If necessary, round to the nearest tenth.
Isabella and Jayla are thus separated by about 11.0 metres.
What is the idea of the Pythagorean Theorem?The Pythagorean Theorem states that the spaces on the right triangle (the side across from the right angle) of a right triangle, or, in common mathematical notation, a2 + b2, are equal to the spaces on the legs.
The Pythagoras formula can be used to resolve this issue. Let's call the distance between Isabella and Jayla "x". Then we have:
x² = (6.3)² + (9)²
Simplifying:
x² = 39.69 + 81
x² = 120.69
Taking the square root of both sides:
x ≈ 10.98
Rounding to the nearest tenth, we get:
x ≈ 11.0
Therefore, Isabella and Jayla are approximately 11.0 meters apart.
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Rearrange the parallelogram as a rectangle. Then find the area.
The area of the rectangle is 9 square units
How to determine the area of the rectangleFirst, we need to know the properties of a rectangle. They are;
A rectangle is a quadrilateralThe opposite sides are parallel and equal to each otherEach interior angle is equal to 90 degreesThe sum of all the interior angles is equal to 360 degreesThe diagonals bisect each otherBoth the diagonals have the same lengthFrom the diagram shown, we have that;
Length of the transformed shape(parallelogram to rectangle) = 3 units
Width = 3 units
The formula for the area of a rectangle is expressed as;
Area = lw
Substitute the values
Area = 3(3)
Area = 9 square units
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