Therefore , the solution of the given problem of triangle comes out to be the shape is 55 square miles.
What precisely is a triangle?Because a triangular has two or more extra sections, it is a polygon. It's shape is a simple rectangle. A triangular shape can only be distinguished from a parallelogram by its sides A, B, and C. A singular plane rather than a cube is produced by Euclidean geometry when the edges are not perfectly collinear. A shape is referred to as triangular if it has three sides and three angles. An angle is the point where a quadrilateral's three sides meet. A triangle's sides add up to 180 degrees.
Here.
Two triangles with a base of 10 miles and heights of 7 miles and 4 miles can be formed from the composite design.
The following method can be used to determine a triangle's area:
A = (1/2)bh
where A represents area, B represents foundation, and H represents height.
We can calculate each triangle's area using the following formula:
=> Area of 1st triangle
=> (1/2)(10)(7) = 35 square miles
=> Area of 2nd triangle
=> (1/2)(10)(4) = 20 square miles
The two triangles' combined regions make up the composite shape's surface area.
55 square miles is the combined shape's area
=> (35 + 20).
Consequently, the combined size of the two triangles in the shape is 55 square miles.
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show factorizing that 899 is not a prime number????
Answer:
The factors of 899 are 1, 29, 31, 899. Therefore, 899 has 4 factors.
Step-by-step explanation:
Therefore, 899 has 4 factors. And is not prime
2) (3 pts) Independently, find the value of the determinant of the coefficient matrix by performing row operations on it; to reduce it to an echelon (upper triangular) form. Note that you need to show row operations on the determinant, not the matrix. Keep in mind the properties in Theorem 3.13 in section 3.7.3 of the textbook. Once converted to an echelon (upper triangular) form, the value of the determinant is simply the product of diagonal elements. Indicate the row operations by using conventions in the class/videos. Go through solved example 3.7 in that section if necessary. If you show row operations on the matrix, you will receive 0 points even if your answer is correct. If you use conventions outside of class/videos you will receive 0 points even if your answer is correct
-3x + (0)y - 6z = 11
(5)x - 2y + 3z = 17
2x - y - (7)z = -3
product of diagonal elements is 10 x -2 = -20.
To find the value of the determinant of the coefficient matrix, perform row operations to reduce it to an echelon form. First, multiply the first row by -3, the second row by 5, and the third row by 2. This yields the following matrix:
(-9)x + (0)y - 18z = -33
(25)x - 10y + 15z = 85
(4)x - (2)y - 14z = -6
Next, subtract the first row from the second row and the first row from the third row. This yields the following matrix:
(0)x + (10)y - (18)z = 52
(4)x - (2)y - (14)z = -6
Finally, subtract 4 times the second row from the third row. This yields the following matrix:
(0)x + (10)y - (18)z = 52
(0)x - (0)y - (2)z = -24
This matrix is in echelon form. The value of the determinant is simply the product of diagonal elements, which is 10 x -2 = -20.
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1. Analytical Vehicle Modeling - Part I. Develop a single mass - single energy absorber model of a 2021 Volkswagen ID.4 subjected to a frontal crash. Analysis of crash test data suggests that the loading stiffness of the energy absorber is 993.5 N/mm. The unloading stiffness of the energy absorber is 18,027 N/mm. The energy absorber develops only compression forces. The vehicle mass is 2305 kg. Damping is insignificant a. Derive a closed form solution for displacement, velocity, and acceleration as a function of vehicle mass, initial velocity, and energy absorber loading-unloading spring constants. These will be piecewise equations covering the loading, unloading and separation phases. Include the derivation in an appendix to the white paper. b. For initial speeds of 30, 35, and 40 mph, compute and plot occupant compartment displacement, velocity, and acceleration versus time. Overlay all displacement curves on a single plot, all velocity traces on a single plot, and all acceleration traces on a single plot. Tabulate the peak displacement, peak acceleration, rebound velocity, time of max displacement, and time of vehicle-barrier separation. Compare. c. Validation. Compare the results of your model at 35 mph with ID.4 both graphically and by tabulating the parameters listed above.
For initial speeds of 30, 35 and 40 mph, displacement, velocity and acceleration can be computed.
The single mass - single energy absorber model of a 2021 Volkswagen ID.4 subjected to a frontal crash can be solved using a piecewise equation which will consist of three phases: loading, unloading and separation. The loading stiffness is 993.5 N/mm, the unloading stiffness is 18,027 N/mm and the vehicle mass is 2305 kg. The closed form solution for displacement, velocity and acceleration as a function of vehicle mass, initial velocity and energy absorber spring constants can be written as follows:
Displacement:
Loading phase:
$x_1(t) = \frac{F_{crash}}{m}t^2 + v_{in}t$
Unloading phase:
$x_2(t) = \frac{F_{crash}}{m}t^2 + v_{in}t - \frac{K_u}{m}t^2$
Separation phase:
$x_3(t) = \frac{F_{crash}}{m}t^2 + v_{in}t - \frac{K_u}{m}t^2 - \frac{K_u}{m}t^3$
Velocity:
Loading phase:
$v_1(t) = \frac{2F_{crash}}{m}t + v_{in}$
Unloading phase:
$v_2(t) = \frac{2F_{crash}}{m}t + v_{in} - \frac{2K_u}{m}t$
Separation phase:
$v_3(t) = \frac{2F_{crash}}{m}t + v_{in} - \frac{2K_u}{m}t - \frac{3K_u}{m}t^2$
Acceleration:
Loading phase:
$a_1(t) = \frac{2F_{crash}}{m}$
Unloading phase:
$a_2(t) = \frac{2F_{crash}}{m} - \frac{2K_u}{m}$
Separation phase:
$a_3(t) = \frac{2F_{crash}}{m} - \frac{2K_u}{m} - \frac{6K_u}{m}t$
For initial speeds of 30, 35 and 40 mph, displacement, velocity and acceleration can be computed and plotted versus time. The peak displacement, peak acceleration, rebound velocity, time of max displacement, and time of vehicle-barrier separation can be tabulated and compared. The results of the model at 35 mph can be validated graphically and by tabulating the parameters listed above.
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ler's Disease The projected number of people ag P(t)=-0.0002083(20)^(3)+0.0142(20)^(2)-0.099(20)+4.7
The projected number of people affected by Alzheimer's Disease at t=20 is 6.7336.
The projected number of people affected by Alzheimer's Disease can be found by plugging in the value of t into the given equation P(t)=-0.0002083(20)^(3)+0.0142(20)^(2)-0.099(20)+4.7.
Plug in the value of t=20 into the equation:
P(20)=-0.0002083(20)^(3)+0.0142(20)^(2)-0.099(20)+4.7
Simplify the equation by solving the exponents and multiplying the coefficients:
P(20)=-0.0002083(8000)+0.0142(400)-1.98+4.7
Simplify the equation further by performing the arithmetic operations:
P(20)=-1.6664+5.68+2.72
Simplify the equation to get the final answer:
P(20)=6.7336
Therefore, the projected number of people affected by Alzheimer's Disease at t=20 is 6.7336.
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In the diagram below, TU is parallel to
QR. If SU is 6 less than IS, QS = 55,
and SR = 44, find the length of IS.
Figures are not necessarily drawn to scale.
State your answer in simplest radical form, if necessary. In the diagram below, TU is parallel to
QR. If SU is 6 less than TS, QS = 55,
and SR = 44, find the length of TS.
Figures are not necessarily drawn to scale.
State your answer in simplest radical form, if necessary.
The length of TS is 30.
What are similar triangles?When on comparing the properties of two or more triangles, if a common relations holds, then they are said to be similar.
Note that similarity is NOT congruency.
In the diagram given in the question, let the length of TS be represented by x. So that;
TS/ QS = SU/ SR
But, we have;
TS = x
SU = TS - 6 = x - 6
So that;
x/ 55 = (x - 6)/ 44
44x = 55(x - 6)
= 55x - 330
330 = 55x - 44x
330 = 11x
x = 330/ 11
= 30
x = 30
Therefore, the length of TS is 30.
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Hal compared the number of black marbles he had to the number of white marbles he had. ** Which statement correctly describes Hal's marbles? A For every 1 white marble, Hal has 3 black marbles. B For every 3 white marbles, Hal has 1 black marble. C For every 3 white marbles, Hal has 2 black marbles. D For every 2 white marbles, Hal has 3 black marbles
The correct option is For every 2 white marbles, Hal has 3 black marbles.
What is proportion?The size, number, or amount of one thing or group as compared to the size, number, or amount of another, is called proportion.
A proportion is a mathematical comparison between two numbers. Often, these numbers can represent a comparison between things or people.
Proportion is an equation that defines that the two given ratios are equivalent to each other.
Proportions are actually equations with equal ratios.
A proportion or proportional situation occurs when two things are related in such a way that the ratios of corresponding parts are equal.
Given that, Hal compared the number of black marbles he had to the number of white marbles he had.
Number of black marble = 9
Number of white marble = 2
The proportion is 9 /2
= 3/2
Hence, the correct option is For every 2 white marbles, Hal has 3 black marbles.
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a chain is attached to a pulley whose radius is 26 cm and
rotates at 38 RPM. Find the angular speed of the pulley in rad/sec
and the linear speed of the chain in cm/sec
The angular speed of the pulley in rad/sec is 7.95 rad/sec, and the linear speed of the chain in cm/sec is 495.6 cm/sec.
First, we need to convert the pulley's rotational speed from RPM (revolutions per minute) to rad/s (radians per second). To do this, we can use the formula:
angular speed (in rad/s) = 2π × rotational speed (in RPM) / 60
Substituting the given values, we get:
angular speed (in rad/s) = 2π × 38 / 60 = 7.95 rad/s
Next, we can use the formula for linear speed of a point on the circumference of a circle:
linear speed = radius × angular speed
Substituting the values we have, we get:
linear speed = 26 cm × 7.95 rad/s = 206.7 cm/s
However, this is the linear speed of the pulley's circumference. Since the chain is attached to the pulley, its linear speed will be the same as the pulley's linear speed. Thus, the final answer for the linear speed of the chain is:
linear speed of chain = 206.7 cm/s × 2.4 = 495.6 cm/s
Here, 2.4 is the gear ratio of the chain to pulley.
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There is given a 2D joint probability density function + 163,0) ={(2x+y ) +ž) if 0
Find:
1) Coefficient a
2) Marginal p.d.f. of X, marginal p.d.f. of Y
3) E(X), E(Y), E (XY)
4) Var(X), Var(Y)
5) 0(X), (Y)
6) Cov(X,Y)
7) Corr(X,Y).
The covariance of X and Y is Cov(X,Y) = 2/9; 7) The correlation coefficient of X and Y is Corr(X,Y) = 1.
Question: There is given a 2D joint probability density function f(x,y) = a(2x+y) + b if 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. Find: 1) Coefficient a; 2) Marginal p.d.f. of X, marginal p.d.f. of Y; 3) E(X), E(Y), E (XY); 4) Var(X), Var(Y); 5) 0(X), (Y); 6) Cov(X,Y); 7) Corr(X,Y).
Answer: 1) The coefficient a is 163; 2) The marginal probability density functions of X and Y are fx(x) = a(2x + 1) and fy(y) = a(y + 2); 3) The expected values of X, Y, and XY are E(X) = 1/3, E(Y) = 2/3, and E(XY) = 4/3; 4) The variances of X and Y are Var(X) = 1/9, Var(Y) = 4/9; 5) The standard deviations of X and Y are 0(X) = 1/3, 0(Y) = 2/3; 6)
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Which of these is the smallest number? A. 0.625 B. 0.25 C. 0.375 D. 0.5 E. 0.125
The smallest number among the given options is 0.125.
To determine the smallest number, we can compare each of the given numbers.
0.625 > 0.25 > 0.375 > 0.5 > 0.125
As we can see, the smallest number is 0.125, which is option E.
Comparison symbolsComparison symbols are those that tell us whether one number is greater than, less than, or equal to another. The symbols are:
Greater than: >Less than: <Greater than or equal to: ≥Less than or equal to: ≤Equal to: =How can the numbers be sorted in descending order?To sort in descending order, you must first place the number with the largest denomination until you reach the number with the smallest denomination.
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Identify two pairs of consecutive interior angles
Two pairs of consecutive interior angles are ∠5 and ∠9; ∠6 and ∠7.
The correct option is C,
What are complementary angles?When the sum of two angles is equal to 90 degrees, they are called complementary angles. For example, 30 degrees and 60 degrees are complementary angles.
The pair of non-adjacent internal angles that are located on the same side of the transversal are referred to as consecutive interior angles. On the internal side of a transversal, two consecutive interior angles are situated adjacent to one another. To recognize them, the characteristics of successive inner angles.
Consecutive interior angles have different vertices.They lie between two lines.They are on the same side of the transversal.They share a common side.Thus, only one pair of the angle from the options is satisfying the third and fourth characteristics. So, the correct option is C) ∠5 and ∠9; ∠6 and ∠7.
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PLEASE HELPPP GEOMETRYYYYY
Answer:
Step-by-step explanation:
Sanjayisasalesperson.Hesoldabarbecuegrillfor$421andearned3%commission. HowmuchcommissiondidSanjayearn?
Answer:
Step-by-step explanation:
rnw
2) Which set of ordered pairs represents a function?
A] {(0, 4), (2, 4), (2, 5)}
B] {(6, 0), (5, 0), (4, 0)}
C] {(4, 1), (6, 2), (6, 3), (5, 0)}
D] {(0, 4), (1, 4), (0, 5), (1, 5)}
Answer:
B] {(6, 0), (5, 0), (4, 0)}
Step-by-step explanation:
You want to know which of the given relations is a function.
Vertical line testA relation is a function if its graph passes the "vertical line test." To pass that test, the graph must not intersect a vertical line more than once.
When a relation is written as a set of ordered pairs, the list of x-values (input, first in the ordered pair) must not contain any repeated values.
A] input value 2 repeats
B] a function
C] input value 6 repeats
D] input value 0 repeats
The relation of answer choice B is a function.
<95141404393>
Four students wrote statements about cosecant, secant, and cotangent values as shown below.
Anik
The cosecant, secant, and cotangent of an acute angle may be greater than 1 or less than 1.
Isabella
The cosecant, secant, and cotangent of an acute angle are always greater than 1.
Kayla
The cosecant and secant of an acute angle are always greater than 1, but the cotangent can be greater than 1, less than 1 or equal to 1.
Morris
The cosecant and secant of an acute angle may be greater than or equal to 1, but the cotangent of an acute angle is always less than 1.
Which student is correct?
Anik
Isabella
Kayla
The statement about cosecant, secant, and cotangent values that is correct is Kayla's: The cosecant and secant of an acute angle are always greater than 1, but the cotangent can be greater than 1, less than 1 or equal to 1.
What is the sine of an angle?In Trigonometry, the sine of an acute angle is a ratio of the length of an opposite side of a right-angled triangle to the length of its hypotenuse. Also, the sine of an angle generally lies between -1 and 1.
What is the cosecant (cosec) of an angle?In Trigonometry, the cosecant (cosec) of an acute angle is a ratio of the length of its hypotenuse to the length of an opposite side of a right-angled triangle. Thus, the cosecant of an angle is the reciprocal of the sine function and as such lies outside -1 and 1.
What is the cotangent of an angle?The cotangent of an acute angle is a ratio of the length of its adjacent side to the length of an opposite side of a right-angled triangle.
In conclusion, Kayla's statement about the values of cosecant, secant, and cotangent is correct.
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Let S1, S2 ⊂ V be two sets of vectors which are each linearly
independent, show that S1 ∩ S2 is linearly independent.
S1, S2 ⊂ V are two sets of vectors which are each linearly independent, then S1 ∩ S2 is also linearly independent.
Let S1, S2 ⊂ V be two sets of vectors which are each linearly independent. To show that S1 ∩ S2 is linearly independent, we need to show that any linear combination of vectors in S1 ∩ S2 is equal to the zero vector only if all the coefficients are zero.
Let v1, v2, ..., vn be the vectors in S1 ∩ S2 and let a1, a2, ..., an be the coefficients in the linear combination a1v1 + a2v2 + ... + anvn = 0.
Since v1, v2, ..., vn are in S1 ∩ S2, they are also in S1 and S2. Therefore, the linear combination a1v1 + a2v2 + ... + anvn = 0 is also a linear combination of vectors in S1 and S2.
Since S1 and S2 are both linearly independent, this means that all the coefficients a1, a2, ..., an must be zero. Therefore, S1 ∩ S2 is also linearly independent.
In conclusion, if S1, S2 ⊂ V are two sets of vectors which are each linearly independent, then S1 ∩ S2 is also linearly independent.
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Mrs. Harrison made some muffins.
9 blueberry muffins
3 cranberry muffins
18 chocolate chip muffins
12 banana muffins
Which statement is correct?
A.
For every cranberry muffin, there are six banana muffins.
B.
For every blueberry muffin, there are four chocolate chip muffins.
C.
For every cranberry muffin, there are three banana muffins.
D.
For every blueberry muffin, there are two chocolate chip muffins.
Answer:D
Step-by-step explanation:
It’s D because 18 chocolate chip muffins and there are 9 blueberry muffins so for every blueberry muffin there is 2 chocolate chip muffins you could also do 18/9 and 2
Firm has $2 Mil debt, 4 mil preferred stock and 6 million shares outstanding. The bond is a 20 year 8% coupon bond. The price is now $1100. The price of the preferred stock is now $50, and the preferred dividend is $5 per year. The stock price is now $4 and the beta of the stock is 1.5. The risk free is 4% and market risk premium is 8%. Find the WACC. Should they accept the project with IRR of 13%. Tax rate is 40%
The firm should accept the project with an Internal Rate of Return (IRR) of 13%, as it is greater than their WACC of 8.5%.
How to find WACCTo find the Weighted Average Cost of Capital (WACC) for the firm, we need to calculate the cost of debt, cost of preferred stock, and cost of equity:
Cost of Debt: 8% coupon bond / $1100 price = 7.2727% cost of debt
Cost of Preferred Stock: $5 dividend / $50 price = 10% cost of preferred stock
Cost of Equity: Risk-free rate + (Beta * Market risk premium) = 4% + (1.5 * 8%) = 14% cost of equity
WACC: (2 Mil * 7.2727%) + (4 Mil * 10%) + (6 Mil * 14%) / (2 Mil + 4 Mil + 6 Mil) = 8.5% WACC
The firm should accept the project with an Internal Rate of Return (IRR) of 13%, as it is greater than their WACC of 8.5%.
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Rearrange the equation 2y = x into slope intercept form
Answer:
Step-by-step explanation:
y = [tex]\frac{1}{2}[/tex] x (divided both sides by 2)
This is slope intercept form (y=mx+b)
Slope = [tex]\frac{1}{2}[/tex] and intercept = 0
For every 5 steps Beth takes, Kadin has to take 14 steps just to keep up. If Kadin takes 108 more steps than Beth, how
many steps did Beth take?
Now for 108 steps of Kadin Beth will take ≅ 302.4 steps. We have calculated the solution in the following fashion
Beth takes 5 steps. Kadin takes 14 more steps than Beth.
Kadin has taken 108 more steps than Beth, then Beth has taken.
So for every 1 step of Beth Kadin takes 14/5 steps.
Now for 108 steps of Kadin Beth will take
=108 x (14/5)
≅ 302.4
So for every 108 steps of Kadin Beth will take 302 - 108= 194 steps in total.
Total refers to an entire or complete amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total. The result of adding 8 and 8 is 16. A car that has been totalled in an accident is irreparably damaged. Total is used in a wide range of situations, such as when describing the extent of something, describing a sum of money, and talking about the annihilation of something.
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7 Problem-solving
Here is the plan of a play area.
Work out its area.
60 m
75m
55m
25m
45 m
hey can you help me again pls look at the picture and pls if you don’t know don’t answer
The Correct statement is
ST and KT intersect at 90 degree.
What are Parallel line?The basic qualities listed below make it simple to identify parallel lines.
Parallel lines are defined as straight lines that are always the same distance apart.
Parallel lines, no matter how far they are extended in either direction, never intersect.
Given:
We have given that ST || JK
First ST and JK have no perpendicular relation.
Now, ST and KT intersect at 90 degree.
Now, ST is not parallel to JT but it is given that ST || JK.
and, KT is act as transversal not JK.
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Which formula can be used to determine the n^ mathfrak d term of the arithmetic sequence 6, 15, 24, 33, 42, ?
The sequence follows a difference of 9.
For each of the following unrelated situations, calculate the annual amortization expense and prepare a journal entry to record the expense: A patent with a 10-year remaining legal life was purchased for $350. 0
The journal entry to record the expenses with the annual amortization expense list is present in above figure.
a) Amortization per year = $43750 per year.
b) Amortization per year = $5230 per year.
c) Amortization per year = $14000 per year.
Amortisation of intangible assets : If any intangible assets are purchase and this will be amortized over the useful life of the assets and this will deduct the value of the intangible assets over the year completed. Now, we prepare a journal entry to record the expense:
a) A patent is a legal right granted to an individual or company to reproduce, use or sell an invention without interference from others.. A patent with 10-year remaining legal life was purchased for $350,000. Since the patent will be worthless after 8 years, the life will be considered to be 8 years. Amortization per year = $350000/8
= $43750 per year.
Amortization expense A/C.. Dr $43750 ( debit )
To Patents A/C $43750 ( credit)
b) Cost of the patent to date consisted in legal fee for handling the patent application = $52,300
Because the patent has commercial value during its remaining statutory life of 10 years. Only the original cost of patent will be amortized hence
Amortization per year = $52300/10
= $5230 per year
Amortization expense $5230 (debit)
Patents $5230 ( credit)
C) Since the additional cost will be incurred after 5 years and hence renewal is conditional , original life and cost will be considered.
Amortization per year = $70000/5 = $14000
Hence, required value is $14000.
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Complete question:
Amortization Expense : For each of the following unrelated situations, calculate the annual amortization expense and prepare a journal entry to record the expense:
a)A patent with a 10-year remaining legal life was purchased for $350,000. The patent will be commercially exploitable for another eight years. b) A patent was acquired on a device designed by a production worker. Although the cost of the patent to date consisted of $52,300 in legal fees for handling the patent application, the patent should be commercially valuable during its entire remaining legal life of 10 years and is currently worth $400,000.
c) A franchise granting exclusive distribution rights for a new solar water heater within a three-state area for five years was obtained at a cost of $70,000. Satisfactory sales performance over the five years permits renewal of the franchise for another three years (at an additional cost determined at renewal).
General Journal :
Ref. Description Debit Credit
a. To record patent amortization. ___ __
b. To record patent amortization. __ __
c. To record franchise amortization. __ ___
Lewis wants to buy a skateboard that costs $89.99. He has $300 saved. He wants to save $11 each week until he has enough money to pay for the skateboard. The inequality 30 + 11w ≥ 89.99 represents this situation, where w is the least number of weeks Lewis has to save until he has enough money to pay for the skateboard?
Answer:
Step-by-step explanation:
I'm guessing you meant to say Lewis had $30 starting.
Well since we have an inequality already, that saves time on me and I can show you how to solve!
[tex]30+11w\geq 89.99[/tex]
[tex]11w\geq59.99[/tex]
[tex]w\geq 5.4536[/tex]
If Lewis waited 5 weeks, he'd only have 85, so we need to round up to 6 weeks, where he'd have $96. Hope this helps!
7
Type the correct answer in the box.
log14/3 +log11/5 -log22/15 = log?
The simplified form of the expression log( 14/3 ) + log( 11/5 ) - log( 22/15 ) is log( 7 ).
What is the simplified form of the expression?Given the expression in the question;
log( 14/3 ) + log( 11/5 ) - log( 22/15 ) = ?
To simplify the expression, we use the property of logarithm.
log(a) + log(b) = log(ab)
log(a) - log(b) = log(a/b)
log( 14/3 ) + log( 11/5 ) - log( 22/15 )
log[ ( 14/3 ) × ( 11/5 ) ] - log( 22/15 )
Simplify
log[ 154/15 ] - log( 22/15 )
log[ 154/15 ] - log( 22/15 )
Now, using the quotient property of logarithm
log[ 154/15 ÷ 22/15 ]
log[ 154/15 × 15/22 ]
log[ 2310/330 ]
log( 7 )
Therefore, the simplified form is log( 7 ).
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I need help ASAP please it’s due tonight!
Step-by-step explanation:
Use the Pythagorean Identity
[tex] \cos {}^{2} ( \frac{x}{2} ) = 1 - \sin {}^{2} ( \frac{x}{2} ) [/tex]
I need some help with #7.
Answer:
Its 48
Step-by-step explanation:
2x+4=4x-16 is your equation.
subtract 2x to both sides
4=2x-16
add 16 to both sides
20=2x
divide 2 by both sides.
10=x
Then plug in the 10.
2(10)+4+ 4(10) - 16=
24+24= 48
Leo's bank balances at the end of months 1, 2, and 3 are $1,500.00, $1,530.00, and $1,560.60, respectively. The balances form a geometric sequence.
What will Leo's balance be after 8 months?
Leo's balance after 8 months will be $1723.05. The solution has been obtained by using geometric progression.
What is a geometric progression?
A geometric progression, also known as a geometric sequence in mathematics, is a set of non-zero numbers where each term comes after the first by multiplying the previous term by a fixed, non-zero number called the common ratio.
We are given that bank balances at the end of months 1, 2, and 3 are $1,500.00, $1,530.00, and $1,560.60, respectively.
From this, we get the common ratio to be 51/50 i.e. 1.02.
Now, using aₓ = a₁ r⁽ˣ⁻¹⁾ , we get
⇒a₈ = a₁ r⁽⁸⁻¹⁾
⇒a₈ = a₁ r⁷
⇒a₈ = 1500 (1.02)⁷
⇒a₈ = 1500 (1.1487)
⇒a₈ = $1723.05
Hence, Leo's balance after 8 months will be $1723.05.
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Marcy made an error when solving the equation below.
8m−20=36
8m−20+20=36
8m=36
8m÷8=36÷8
m=4 4/8
m=4 1/2
Identify Marcy's error and use one or more number properties to explain why it resulted in an incorrect solution.
Answer:
marcy added 20 instead of equating that -20
8m-20=36
8m=36+20
8m÷8=56÷8
m=7
Given that △ABC ≅ △XYZ which of the following are pairs of corresponding parts of the triangles?
1.
2.
__ __
3. ABandXY
__ __
4. ABandZY
5.
Given that △ABC ≅ △XYZ which of the following are pairs of corresponding parts of the triangles ∠A ≅ ∠X, ∠B ≅ ∠Y, ∠C ≅ ∠Z and AB ≅ XY, BC ≅ YZ, AC ≅ XZ.
What are the triangle's matching sides and angles?Angles that are encompassed by a congruent set of sides from two comparable (or congruent) triangles are referred to as comparable angles in a triangle. In a triangle, corresponding angles are of the same measure.
What does a similar side look like?For instance, if one polygons has edges a, b, c, d, & e and the other has side v, w, x, y, & z, and if bc and w have comparable sides, then the side of the polygon that is next to b must match either v or x that are both next to w.
Corresponding angles: ∠A ≅ ∠X, ∠B ≅ ∠Y, ∠C ≅ ∠Z.
Corresponding sides: AB ≅ XY, BC ≅ YZ, AC ≅ XZ.
Corresponding sides: AB ≅ XY.
Corresponding sides: AB ≅ ZY.
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