Answer:
\( \frac{2(x - 4)}{(x - 2)(x + 2)} \)
Step-by-step explanation:
\( \frac{2}{(x - 2)} - \frac{8}{ ({x}^{2} - 4 )} \\ \frac{2}{(x - 2)} - \frac{8}{(x - 2)(x + 2)} \\ \frac{2(x + 2) - 8}{(x - 2)(x + 2)} \\ \frac{2x + 4 - 8}{(x - 2)(x + 2)} \\ \frac{2x - 8}{(x - 2)(x + 2)} \\ \frac{2(x - 4)}{(x - 2)(x + 2)} \)
research topic 'the differential effect of inductive
instructions and deductive instructions'
The differential effect of inductive instructions and deductive instructions refers to the impact that these two types of instructional approaches have on learning and problem-solving abilities.
How to explain the informationInductive instructions involve presenting specific examples or cases and then drawing general conclusions or principles from them. This approach encourages learners to identify patterns, make generalizations, and develop hypotheses based on the observed data. Inductive reasoning moves from specific instances to a broader understanding of concepts or principles.
On the other hand, deductive instructions involve presenting general principles or rules first and then applying them to specific examples or cases. This approach emphasizes logical reasoning, where learners are guided to apply established rules to solve problems or make conclusions based on given premises. Deductive reasoning moves from a general understanding of concepts or principles to specific instances.
The differential effect of these two instructional approaches can vary depending on various factors, such as the learner's prior knowledge, cognitive abilities, and the nature of the task or subject matter.
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In the triangle below, with right angle ZL, suppose that mM=(5x+15)° and m N= (4x+3)⁰.
Find the degree measure of each angle in the triangle.
N
(4x + 3)°
15x+15)
Please help I’m super stressed and crying I need this
On solving the provided question, we can say that by using the triangle, ∠LNM=35° and ∠NML=55°
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
∠LNM=(4x+3)°
∠NML=(5x+15)°
∠NLM=90°
Since, its right angle triangle, sum of all angle is 180°
∠LNM+∠NML+∠NLM=180°
(4x+3)+(5x+15)+90=180°
9x+18=90°
9x=72
x=8
Hence,
∠LNM=(4x+3)°=4*8+3=35°
∠NML=(5x+15)°=5*8+15=55°
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Let AA and BB be two mutually exclusive events, such that P(A)=0.2272P(A)=0.2272 and P(B)=0.4506P(B)=0.4506. Find the following probability:
The probability that the events do not occur is 0.6778`.
The probability that the events do not occur is given by `P(Ac)=1-P(A)` and `P(Bc)=1-P(B)`.
The given probabilities are `P(A)=0.2272` and `P(B)=0.4506`.
Using the formula `P(A∪B)=P(A)+P(B)-P(A∩B)`, we have `P(A∩B) = P(A) + P(B) - P(A∪B)`
Using the fact that the two events are mutually exclusive, we get `P(A∩B) = 0`.
Thus, `P(A∪B) = P(A) + P(B) = 0.2272 + 0.4506 = 0.6778`.
The probability that either A or B but not both occurs is given by `P(AΔB) = P(A∪B) - P(A∩B) = 0.6778 - 0 = 0.6778`.
Hence, the required probability is `P(AΔB) = 0.6778`.
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Find the length of the segment indicated below
The length of line segment AB in the triangle using the midsegment theorem is 64.
What is the length of line segment AB?
The Midsegment Theorem states that "the segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side."
From the diagram:
Midsegment = 3x + 5
Third side = 7x + 1
First, we solve for x, using the midsegment theorem:
( 3x + 5 ) = 1/2 × ( 7x + 1 )
Multiply both sides by 2:
2( 3x + 5 ) = ( 7x + 1 )
6x + 10 = 7x + 1
Collect and add like terms:
7x - 6x = 10 - 1
x = 10 - 1
x = 9
Now, we solve for line AB:
Line AB = 7x + 1
Plug in x = 9
Line AB = 7(9) + 1
Line AB = 63 + 1
Line AB = 64
Therefore, the line segment AB is 64.
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Find the solution(s) to (x- 3) = 49. Check all that apply.
OA X=-10
B. Xx=-4
C. x-7
OD. X=-7
OE. X= 10
Answer:
B.x= -4 and E. x= 10 are the answers
the distances male long jumpers for state college jump are approximately normal with a mean of 263 inches and a standard deviation of 14 inches. suppose a male long jumper's jump ranked in the 75th percentile (75% of jumpers jumped less distance). how long was his jump?
The male long jumper's jump, which ranked in the 75th percentile, was approximately 272.436 inches long.
To find the length of the male long jumper's jump at the 75th percentile, we can use the concept of z-scores and the standard normal distribution.
The 75th percentile corresponds to a z-score of 0.674. Using this z-score, we can calculate the distance of the jump by multiplying it by the standard deviation and adding it to the mean:
Distance = (z-score * standard deviation) + mean
Distance = (0.674 * 14) + 263
Distance ≈ 9.436 + 263
Distance ≈ 272.436
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Please help
The price of a sweater decreased from 29.99 to 24.49. Find the percent decrease.
Answer:
The answer is 5.45%.
Step-by-step explanation:
29.99 - 24.49 = 5.5 which is the amount the price decreased.
Then, we divide the amount of decrease from the initial amount:
29.99 / 5.5 = 5.45
The answer is 5.45%
Please help me out the below problem.
Answer:
A=15x²
Step-by-step explanation:
hope that it will help you
The proper expression of A such that the fraction are equivalent is 15xy
Mathematical expression\(\frac{3x}{4y} =\frac{A}{20y^{2} }\)cross multiply
3x(20y²) = A4y
divide both sides by 4y
A = 3x(20y²) / 4y
A = 60xy² / 4y
Therefore,
A = 15xy
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"Punkin Chunkin," or Pumpkin Chunking, is the sport of launching pumpkins with
cannons and other mechanical devices as far as possible. Teams that compete in these
events have names such as American Chunker Inc., Fibonacci Unlimited II, Shooda Noed
Beter, and Snot Rocket. The world record was set in 2013, when a pumpkin was launched
to a height of 2250 feet and a distance of 4500 feet (measurements have been rounded
for simplicity). Assume the motion of the pumpkin was symmetrical. Write a quadratic
expression to relate the vertical displacement y, with the horizontal displacement x. How
high was the pumpkin when it was 100 ft away?
Answer:the answer is a
Step-by-step explanation:because I said so
PLZ HELP IF CAN<3 TEST IS DUE AT 3:50!! In America
4. From the top of a tower 14m high, the angle of depression of a student is 32° Make a scale drawing and find the distance of the student from the foot of the tower to the nearest 1/2
The distance of the student from the foot of the tower is 25.63m the nearest 1/2 is 25.5m.
Given that From the top of a tower 14m high
The angle of depression of a student is 32°
we can use trigonometry to find the distance from the foot of the tower to the student:
tan(32°) = opposite/adjacent = 14/distance
Rearranging this equation gives:
distance = 14/tan(32°)
= 25.63m
Therefore, the distance of the student from the foot of the tower is approximately 25.63m nearest 1/2, this is 25.5m.
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4. Use the contraction mapping theorem to show that for each kЄ (0, 1) the equation
X
f(x) = 1 + [f(2)dt (0 ≤ x ≤ k)
110
2 Metric Spaces
has exactly one solution ƒ = C([0, k]). Hence show that this result is also true
when k = 1.
Co
The function f : C([0, 1]) → C([0, 1]) defined byf(x) = 1 + [f(2)dt (0 ≤ x ≤ 1)110is still a contraction mapping with the same Lipschitz constant L. Therefore, by the contraction mapping theorem, f has a unique fixed point in C([0, 1]).
In the proof of the contraction mapping theorem, it is always required that the function we are going to apply it to satisfies some requirements. These requirements include the completeness of the space, which is usually a metric space, and the continuity of the function.
Theorem, Let (M, d) be a complete metric space and f : M → M be a contraction mapping with Lipschitz constant L < 1.
Then, f has a unique fixed point in M and, for any x0 ∈ M, the sequence {xn} defined by xn+1 = f(xn), n ∈ N converges to the fixed point of f. In the case of this problem, we have that our metric space is C([0, k]) with the supremum norm ||.||∞. Furthermore, we need to show that the function f : C([0, k]) → C([0, k]) defined byf(x) = 1 + [f(2)dt (0 ≤ x ≤ k)110is a contraction mapping. For this, we need to find a Lipschitz constant L such that L < 1.Let x, y ∈ C([0, k]), then |f(x) − f(y)| = |[f(2)dt (0 ≤ x ≤ k) − f(2)dt (0 ≤ y ≤ k)]| ≤ f(2)dt (0 ≤ x ≤ k) − f(2)dt (0 ≤ y ≤ k)| = ||f(2)dt (0 ≤ x ≤ k) − f(2)dt (0 ≤ y ≤ k)||∞.Now, we will use that the absolute value is smaller or equal to the supremum, which is a standard result in analysis:|h(t)| ≤ sup{|h(s)| : s ∈ [0, k]} = ||h||∞.
We can use this with h(t) = f(2)t and t ∈ [0, x].
Then, |f(2)dt (0 ≤ x ≤ k) − f(2)dt (0 ≤ y ≤ k)| ≤ ||f(2)dt (0 ≤ x ≤ k) − f(2)dt (0 ≤ y ≤ k)||∞ ≤ ||f(2)||∞ |x − y|.This means that the Lipschitz constant we can use is L = ||f(2)||∞ < 1. Therefore, by the contraction mapping theorem, we conclude that the function f has a unique fixed point in C([0, k]).Now, we need to show that this result is also true when k = 1. But, this is very simple. If k = 1, then our space is C([0, 1]), which is still complete with the supremum norm. Furthermore, the function f : C([0, 1]) → C([0, 1]) defined byf(x) = 1 + [f(2)dt (0 ≤ x ≤ 1)110is still a contraction mapping with the same Lipschitz constant L. Therefore, by the contraction mapping theorem, f has a unique fixed point in C([0, 1]).To know more about theorem visit
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A TV has an original price of $549. Enter the new price after the given percent of
change. 30% decrease
Answer:
384.3
Step-by-step explanation:
you work as an assistant coach on the university swim team and earn $13 per hour. one day, you decide to skip the hour-long practice and go to the county fair instead, which has an admission fee of $10
23$ is the total cost .
What is cost and example?
The definition of cost is to be valued at something or to lose. A loaf of bread costing $3 is an example of a cost. Giving up your freedom in order to grant freedom to another person is an illustration of cost.Fixed and variable costs are the two main categories of expenses incurred by enterprises. Variable costs change with output, whereas fixed costs do not. Overhead costs are another name for fixed expenses. They must be paid whether a company produces 100 or 1,000 widgets.the total cost = 13$ + 10$= 23$ because he losses a hour in work .
13$ and additionally spending 10$ in carnival .
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which expression is equivalent to y^4 -100?
Answer:
Using the difference of squares this can be rewritten as (y² + 10)(y² - 10).
Answer:
(y² + 10)(y² - 10)
Step-by-step explanation:
y^2=y^4
For a t-distribution with sample size 10, P (t > 1.96) 2 0.0408 and P (t < -1.96) 2 0.0408 . Which of the following is a property of the t-distribution illustrated by the probabilities? A. With sample size 10, the tails of the curve of the t-distribution have more area than the tails of the curve of the z-distribution. B. With sample size 10, the tails of the curve of the t-distribution have less area than the tails of the curve of the z-distribution. C. With sample size 10, the middle of the curve of the t-distribution has more area than the middle of the curve of the z-distribution. With sample size 10, the mean of the t-distribution is greater than the mean of the z-distribution. E. With sample size 10, the mean of the t-distribution is less than the mean of the z-distribution.
The correct option is A) With sample size 10, the tails of the curve of the t-distribution have more area than the tails of the curve of the z-distribution.
Explanation:Given:P(t > 1.96) = 0.0408P(t < -1.96) = 0.0408The t-distribution is different from the z-distribution because it has a thicker tail.The tail is thicker since the t-distribution is determined by the sample size, whereas the z-distribution is determined by the population size (the t-distribution is estimated with the standard error of the mean in this case).
A t-distribution with small degrees of freedom has a much thicker tail than a z-distribution with the same degrees of freedom. Because sample size is related to the degrees of freedom, it makes sense that t-distributions with smaller sample sizes will have thicker tails.
The population variance is replaced with the sample variance in the estimation of the t-distribution. As a result, the t-distribution has heavier tails than the z-distribution.
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What is the measure of angle x?
Answer:
46
Step-by-step explanation:
The type of angle below is called an alternate angle where the opposite angle is the equal size.
As the angle given is 46 the alternating angle would be 46!
Have a lovely day :)
Answer:
46 because 46 is alternative angle
Combine like terms to create an equivalent expression. 1.3 b 7.8 − 3.2 b
The equivalent expression is -1.9b + 7.8.
What is an equivalent phrase?There is a concept known as an analogous expression, which is an expression that has the same value as another expression but has a different appearance.
Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.
Combine similar phrases now:
The definition of like words is the terms that have the same variable raised to the same power. Only the numerical coefficients can change in algebra.
When we combine the term b's coefficient, we get
1.3b + 7.8–3.2b
= (1.3−3.2)⋅b + 7.8
By condensing the equation, we obtain
= (- 1.9) +b + 7.8
= −1.9b + 7.8
There is a condensed equivalent formula of -1.9b + 7.8.
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What percent students have height between 62 inches and 64 inch
Answer:The following list of data represents highway fuel consumption in miles per gallon. (mpg) for Hint: you will need to calculate the midpoint for each class. Age (yrs) C. What percentage of women are between 62.5 inches and 67.5 inches? 65. 68 ... If the top 15% of the students get A's, what is the cut-off score for an A? 75.
Step-by-step explanation:
sorry if this is wrong
Percent students having height between 62 & 64 inches, is 25%
As per the linear presentation, data is spread evenly between 58 to 66 inches.
The total 100% students are divided evenly in 8 segments, from 58 - 59 inches to 65 - 66 inches. So each segment has 100 / 8 = 12.5%
Hence, percentage students having 62 to 64 inches has 2 unit segments. They are 12.5 x 2 = 25% students.
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What is included in capital invested?
The capital includes :
Any financial contribution made to a business to assist in achieving and advancing its commercial goal is referred to as a capital investment. The phrase may also refer to a long-term purchase made by a company, such as one for land, equipment, businesses, etc.
When a corporation issues securities to equity investors and debt to bondholders, the total amount of debt and capital lease obligations are added to the amount of stock given to investors to determine the overall amount of money raised. This amount is referred to as invested capital. The balance sheet of the business does not include an item for invested capital because debt, capital leases, and stockholders' equity are all stated separately.
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La edad de Javier es el triple que la de su hijo y dentro de 10 años será el doble. ¿Qué edad tiene el hijo de Javier?
Answer:
can you put it in English
Yellow rectangles= X Yellow squares = positive Red squares = negative
1) 5x – 3 = 7
2) 3x + 4 = -2
3) 3x + 6 = -9
4) 2x - 4 = 14
5) 3x – 4 = 8
6) 4x + 7 = 11
Answer:
that is a great question, could u explain more? im serious
Step-by-step explanation:
Answer:
The large squares represent X squared, and had two sides, blue and red, to determine whether it is positive or negative (blue = positive, red = negative). There is also the long rectangles that represent X, with the positive side being green and the negative red. The side length of X is the same side length of X squared, which makes sense because X multiplied by X equals X squared. The smallest square pieces represent the number 1. The colours are yellow for positive and red for negative. These are the basic pieces used in algebra tiles. Hope this helps
Step-by-step explanation:
solve the cauchy problem (y+u)ux+yuy=(x-y), with u=1+x on y=1
The solution to the Cauchy problem is:
u(x,y) = x - y + e^(-(y-1))
To solve the given Cauchy problem, we can use the method of characteristics.
First, we write the system of ordinary differential equations for the characteristic curves:
dy/dt = y+u
du/dt = (x-y)/(y+u)
dx/dt = 1
Next, we need to solve these equations along with the initial condition y(0) = 1, u(0) = 1+x, and x(0) = x0.
Solving the first equation gives us y(t) = Ce^t - u(t), where C is a constant determined by the initial condition y(0) = 1. Substituting this into the second equation and simplifying, we get:
du/dt = (x - Ce^t)/(Ce^t + u)
This is a separable differential equation, which we can solve by separation of variables and integrating:
∫(Ce^t + u)du = ∫(x - Ce^t)dt
Simplifying and integrating gives us:
u(t) = x + Ce^-t - y(t)
Using the initial condition u(0) = 1+x, we find C = y(0) = 1. Substituting this into the equation above gives:
u(t) = x + e^-t - y(t)
Finally, we can solve for x(t) by integrating the third equation:
x(t) = t + x0
Now we have expressions for x, y, and u in terms of t and x0. To find the solution to the original PDE, we need to express u in terms of x and y. Substituting our expressions for x, y, and u into the PDE, we get:
(y + x0 + e^-t - y)(1) + y(Ce^t - x0 - e^-t + y) = (x - y)
Simplifying and canceling terms, we get:
Ce^t = x - x0
Substituting this into our expression for u above, we get:
u(x,y) = x - x0 + e^(-(y-1))
Therefore, the solution to the Cauchy problem is:
u(x,y) = x - y + e^(-(y-1))
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details scalcet9 10.5.004. 0/100 submissions used my notes ask your teacher find the vertex, focus, and directrix of the parabola. 5x2 16y
The vertex, focus, and directrix of the parabola 5x^2 + 16y = 0 are (0, 0), (-4/5, 0), and x = 4/5, respectively.
To find the vertex, focus, and directrix of the parabola with the equation 5x^2 + 16y, we can use the standard form of the equation for a parabola:
y = (1/4p)(x - h)^2 + k
where (h, k) is the vertex and p is the distance between the vertex and the focus or the vertex and the directrix.
Comparing the given equation to the standard form, we have:
5x^2 + 16y = 0
=> 16y = -5x^2
=> y = -(5/16)x^2
From this, we can determine that the vertex is at the origin (0, 0).
To find p, we can use the formula p = 1/(4a), where a is the coefficient of x^2. In this case, a = -5/16, so p = 1/(4*(-5/16)) = -4/5.
Therefore, the vertex is (0, 0), the focus is (-4/5, 0), and the directrix is x = 4/5.
In conclusion, the vertex, focus, and directrix of the parabola 5x^2 + 16y = 0 are (0, 0), (-4/5, 0), and x = 4/5, respectively.
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Jason worked 3 hours more than Keith. Jason worked 12 hours. Which equation represents this situation, if k is the numbers of hours Keith worked?
The equation that represents this situation, if k is the number of hours Keith worked is C. k + 3 = 12
A statement that affirms the equivalence of two expressions that are joined by the equals sign "=" is known mathematically as an equation. If Jason worked 12 hours, 3 more than Keith did, and k is the amount of hours Keith worked, then k + 3 = 12 is the proper equation to reflect the circumstance.
According to this calculation of the equation, the total number of hours Keith worked (k) plus the additional three hours equals 12, which agrees with the fact that Jason put in three more hours of labour than Keith did and worked for a total of 12 hours.
Complete Question:
Jason worked 3 more hours than Keith. Jason worked 12 hours. Which equation represents this situation, if k is the number of hours Keith worked?
A. 12 + k = 3
B. 12k = 3
C. k + 3 = 12
D. 3k = 12
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Write an expression for the nth term of the sequence. (Your formula should work for n = 1, 2,...) 1/3 middot 4, 2/4 middot 5, 3/5 middot 6, 4/6 middot 7,... Find the first five terms of the given recursively defined sequence. a_n = 3a_n - 1 + 5 and a_1 = 3
Expression for the nth term of the sequence: (n + 1) / (n + 3).The expression for the nth term of the sequence is (n + 1) / (n + 3). Using this formula, we found the first five terms of the sequence, which are 1/2, 3/5, 4/6, 5/7, and 3/4.
To find the expression for the nth term of the sequence, we observe that each term can be expressed as (n + 1) divided by (n + 3), where n represents the position of the term in the sequence.
Let's verify this formula with the given terms:
For n = 1: (1 + 1) / (1 + 3) = 2 / 4 = 1/2 (first term of the sequence)
For n = 2: (2 + 1) / (2 + 3) = 3 / 5 (second term of the sequence)
For n = 3: (3 + 1) / (3 + 3) = 4 / 6 (third term of the sequence)
For n = 4: (4 + 1) / (4 + 3) = 5 / 7 (fourth term of the sequence)
For n = 5: (5 + 1) / (5 + 3) = 6 / 8 = 3 / 4 (fifth term of the sequence)
Therefore, the first five terms of the given sequence are: 1/2, 3/5, 4/6, 5/7, 3/4.
The expression for the nth term of the sequence is (n + 1) / (n + 3). Using this formula, we found the first five terms of the sequence, which are 1/2, 3/5, 4/6, 5/7, and 3/4.
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6,7,7,8,9,10,10,10,10,13,13,14,14,15,15 box and whisker plot
The box and whisker plot can be created by :
Minimum value - 6
Maximum Value - 15
Median - 10
Quartiles - Q1 - 7.5, Q2 - 10, Q3 - 13.5
To create a box and whisker plot for the given data set {6,7,7,8,9,10,10,10,10,13,13,14,14,15,15}, we need to first find the minimum value, maximum value, median, and quartiles.
Minimum value: 6
Maximum value: 15
Median: To find the median, we need to first arrange the data set in ascending order:
6,7,7,8,9,10,10,10,10,13,13,14,14,15,15
The median is the middle value in the data set, which is 10.
Quartiles: To find the quartiles, we need to divide the data set into four equal parts.
First quartile (Q1): The first quartile is the median of the lower half of the data set. In our case, the lower half of the data set is:
6,7,7,8,9,10
The median of this set is (7+8)/2 = 7.5.
Second quartile (Q2): The second quartile is the median of the entire data set, which we already found to be 10.
Third quartile (Q3): The third quartile is the median of the upper half of the data set. In our case, the upper half of the data set is:
10,10,10,10,13,13,14,14,15,15
The median of this set is (13+14)/2 = 13.5.
Now, we can use the above information to create the box and whisker plot.
The horizontal line inside the box represents the median (10). The bottom of the box represents the first quartile (7.5), and the top of the box represents the third quartile (13.5). The whiskers extend from the box to the minimum value (6) and maximum value (15).
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Beth owes $17,000 on her car loan. The interest rate on her loan is 4.25%. She will be paying this loan off for 4 years.
How much will Beth pay altogether?
a. $2890
b. $19,890
c. $28,900
d. $ 45,900
Answer:
She has to pay $20078.7 amount.
Step-by-step explanation:
Beth owes 17,000 on her car loan. The interest rate on her loan is 4.25% She will be paying this loan off for 4 years
Triangle congruence geometry
Answer:
Not necessarily
Step-by-step explanation:
The triangles have two sides congruent to each other (BA and RA/BE). They also have angles BRA and BEA congruent, but these do not fit into any of the congruency theorems (SSS, SAS, ASA, or AAS).
Luke purchased a pair of Skullcandy earbuds for 24.95 dollars the sale tax is 7.25% 10 how much tax did he pay on the earbuds?a) $1.08b) $1.80c) $1.88d) $1.81
$1.81 (option D)
Explanation:The cost of Skullcandy earbuds = $24.95
sale tax = 7.25% = 0.0725
Tax = The cost of Skullcandy earbuds × sales tax
Tax = 24.95 × 0.0725
Tax = 1.8089
Tax he paid for the earbuds = $1.81 (option D)