The area of the given irregular figure is 143 square inches.
What is area of irregular figure?
We divide an irregular shape into its component common shapes before calculating its area. After that, we add the areas of each shape. For instance, if a square and a triangle make up an irregular polygon, the area of the polygon is equal to the sum of their areas.
We have to divide the given irregular figure into known shapes.
That is rectangle and square.
Rectangles with sides '7 in and 10 in' and '12 in and 4 in' and the square of side 5 in.
So, the area of irregular figure is,
Area = Area of rectangle + Area of rectangle + Area of square
= (7 x 10) + (12 x 4) + 5^2
= 70 + 48 + 25
Area = 143
Hence, the area of the given irregular figure is 143 square inches.
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the fundamental theorem of arithmetic: for each positive integer n> 1 there is a unique set of primes. whose product is n. which assumption would be a component of a proof by mathematical induction or strong mathematical induction of this theorem?
Fundamental theorem of arithmetic states that each positive integer n is greater than 1 represented by unique set of prime numbers.
Explanation:
Fundamental theorem of arithmetic states that all the positive integer n is greater than 1 represented by multiples of prime numbers or the number itself is a prime number.
For example :
Let us consider 56 be a integer greater than 1
56 = 2 × 2 × 2 × 7
2 and 7 both are prime numbers
another example :
29 = 29 × 1
29 itself is a prime number.
Factorization of the given numbers itself prove the fundamental theorem of arithmetic.
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Given angle 1 is congruent to angle 3
prove angle 6 is congruent angle 4
Proof of angle 6 is congruent to angle 4 is given.
What is congruent?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
Angles of equal measure are said to have congruent angles.
Given,
∠1 ≅ ∠3
And we know from the vertical angles, property;
The angles opposite each other when two lines cross.
They are always equal.
And here we have two pairs of vertical angles,
So, ∠1 = ∠4
and ∠3 = ∠6
And ∠1 ≅ ∠3 is given.
So, ∠1 ≅ ∠4
and ∠3 ≅ ∠6
Comparing, we get
∠4 ≅ ∠6
Therefore, ∠4 ≅ ∠6 is proved.
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Cynthia is participating in the Spartan Super, a 10-mile obstacle course. She completes 4 miles of the obstacle course every hour. Cynthia’s distance from this finish line, y, after x hours is represented by the function 4x + y = 10.
a. Find the coordinates of the y-intercept.
Find the coordinate of the x-intercept
The coordinates of the y-intercept is (0, 10)
The coordinate of the x-intercept is (5 / 2, 0)
How to find the -intercept and x-intercept of a linear function?Cynthia is participating in the Spartan Super, a 10-mile obstacle course. She completes 4 miles of the obstacle course every hour.
Cynthia’s distance from this finish line, y, after x hours is represented by the function 4x + y = 10.
Therefore, the y-intercept is the point where a graph crosses the y-axis. In other words, it is the value of y when x = 0.
The x-intercept is where a line crosses the x-axis. The x-intercept is the value of x when y = 0.
Linear function in slope intercept form is as follows:
y = mx + b
where
m = slopeb = y-interceptHence,
4x + y = 10
y = -4x + 10
Hence, y-intercept is 10.
y = -4x + 10
Let's find x-intercept
0 = -4x + 10
-10 = -4x
x = 10 / 4
x = 5 / 2
x-intercept is 5 / 2.
Hence the coordinate of the y-intercept is (0, 10) and the x-intercept is (5 / 2, 0)
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!HELP! The tennis tournament that Amanda is playing has 10 games and the tennis tournament that Jennifer is playing has 8 games. What is the minimum amount of tournaments they each need to play in order to have played the same number of games? How many games would this be? Write to explain your thinking.
The minimum amount of tournaments Amanda and Jennifer each need to play in order to have played the 40 number of games are 4 and 5 respectively.
What is the LCM?Least Common Multiple is the meaning of the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It may also be computed using two or more real numbers.
Given that Amanda is playing has 10 games and the tennis tournament that Jennifer is playing has 8 games.
Now we will find the minimum same number of games in tournaments,
for that we will find the LCM of the numbers.
LCM of Amanda games in tournament and Jennifer games in tournament.
LCM of 10 and 8 is 40.
Therefore, the minimum amount of tournaments Amanda and Jennifer each need to play in order to have played the 40 number of games are 4 and 5 respectively.
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What is the answer to this equation 12 1/4 - 5 2/3
Answer:
6 7/12
Step-by-step explanation:
"12 1/4 - 5 2/3" is an expression. It is not said to equal anything. The "=" sign makes it an equation. But we can evalute an expression by simplyfying it. Let's do the subtraction. We first need to convert one of the fractions so that it has the same denominator as the other.
12 1/4 - 5 2/3 can be written as (12 - 5)+(1/4 - 2/3)
(12 - 5)+(1/4 - 2/3)
(7)+(1/4 - 2/3) Let's convert both fractions to have denominators of 12 [since 4*3 = 12]
7 + 1/4 - 2/3
7 + (1/4)*(3/3) - (2/3)*(4/4) [Multiply the tqo fractions by (3/3) and (4/4), repectively. This is OK since both are the equivalent of multiply by 1. But it converts the denominators so that we can now add or subtract.
7 + (3/12) - (8/12)
7 - (5/12)
or 6 7/12
if you select a random sample of full-time college students, there is an hance that the sample mean is less than how many hours per week?
The sample mean is less than 26.92 hours per week .
What is standard deviation?
Your dataset's average level of variability is represented by the standard deviation. In general, it reveals how far away from the mean each value is.
A low standard deviation denotes that values are grouped closely to the mean, while a high standard deviation denotes that values are typically spread widely from the mean.
Let X~ Normal (26, 4/√16) distribution ie Normal (26, 1) distribution
We want,
P(X<a) = 0.82
Using standard normal approximation,
P(z< (a-26)/1) = 0.82
Using standard normal distribution tables, we get
(a-26)/1 = 0.915
(Since P(z<0.915) = 0.82)
So, a= 26+0.915= 26.915
So the required value is 26.92 (rounded to two decimals)
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Solve using substitution.
Answer:
The answer is 2
Step-by-step explanation:
5x + 7y = -11
y = -3
Now, put the value of y in the given equation we get,
5x + 7y = -11
5x + 7(-3) = -11
5x - 21 = -11
5x - 21 + 21 = 21 - 11
5x = 10
5x/5 = 10/5
x = 2
Thus, The value of x is 2
find the equation of the line that contains the point p(4, 5) and is perpendicular to the graph of y = 5/4 x − 1.
Answer:
y = - [tex]\frac{4}{5}[/tex] x + [tex]\frac{41}{5}[/tex]
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{5}{4}[/tex] x - 1 ← is in slope- intercept form
with slope m = [tex]\frac{5}{4}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{5}{4} }[/tex] = - [tex]\frac{4}{5}[/tex] , then
y = - [tex]\frac{4}{5}[/tex] x + c ← is the partial equation of the perpendicular line
to find c substitute (4, 5 ) into the partial equation
5 = - [tex]\frac{16}{5}[/tex] + c ⇒ c = 5 + [tex]\frac{16}{5}[/tex] = [tex]\frac{25}{5}[/tex] + [tex]\frac{16}{5}[/tex] = [tex]\frac{41}{5}[/tex]
y = - [tex]\frac{4}{5}[/tex] x + [tex]\frac{41}{5}[/tex] ← equation of perpendicular line
Nevach and Michael are helping their friend Nabhitha move. If Nevaeh can
move 6 boxes for every 24 boxes that Michael moves, then how many boxes
can Michael move for every box that Nevaeh moves?
Michael boxes
24
Answer:
For every 1 box Naveah moves, Michael moves 4 boxes
Perpetual preferred stock from Franklin Inc. sells for $97.50 per share, and it pays an$8.50 annual dividend. If the company were to sell a new preferred issue, it would incur a flotation cost of 4.00% of the price paid by investors. What is the company's cost of preferred stock for use in calculating the WACC?
A) 8.72%
B) 9.08%
C) 9.44%
D) 9.82%
E) 10.22%
The company's cost of preferred stock is 9.08%, which means the correct answer is B) 9.08%. The cost of a service may be determined by the amount of time and expertise required to provide it. In general, cost is an important factor in determining the feasibility and profitability of a project or business venture.
Cost refers to the amount of money that is required to purchase or produce something. For example, the cost of a product may be determined by the amount of materials and labor that went into producing it, as well as any other expenses associated with bringing it to market.
To calculate the company's cost of preferred stock, we need to use the following formula:
Cost of preferred stock = annual dividend / price per share - flotation cost
In this case, the annual dividend is $8.50, the price per share is $97.50, and the flotation cost is 4.00% of the price paid by investors. Plugging these values into the formula, we get:
Cost of preferred stock = $8.50 / $97.50 - 4.00% = $8.50 / $97.50 * (1 - 0.04) = $8.50 / $93.80 = 0.0908
Therefore, the company's cost of preferred stock is 9.08%, which means the correct answer is B) 9.08%.
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a study was conducted at a university to analyze whether the preference for hamburgers or fried chicken is related to the gender of the student. the table below shows the results of the study: hamburgers fried chicken female: 15 23 male: 24 16 suppose we use this sample data and a .05 significance level to test the claim that the meal preference and the gender of the student are not related. what can we conclude?
To test the claim that meal preference and gender are not related, you can use a chi-squared test for independence.
The null hypothesis for this test is that there is no relationship between the variables, while the alternative hypothesis is that there is a relationship. To conduct the test, you will need to calculate the chi-squared statistic and compare it to the critical value from a chi-squared distribution with one degree of freedom. The degrees of freedom for this test are calculated as (number of rows - 1) * (number of columns - 1), which in this case is (2-1)*(2-1) = 1.
To calculate the chi-squared statistic, you will need to compare the observed frequencies in the table to the expected frequencies if the null hypothesis were true. The expected frequency for each cell is calculated as the row total * column total / sample size.
For example, the expected frequency for females who prefer hamburgers is (39 * 15)/59 = 12.71. The chi-squared statistic is then calculated as the sum of the squared differences between the observed and expected frequencies, divided by the expected frequencies. In this case, the chi-squared statistic would be:
((15-12.71)^2/12.71) + ((23-26.29)^2/26.29) + ((24-26.29)^2/26.29) + ((16-12.71)^2/12.71) = 7.39
To determine whether this result is statistically significant, you would compare the chi-squared statistic to the critical value from a chi-squared distribution with one degree of freedom. At a significance level of 0.05, the critical value is 3.84. Since the chi-squared statistic (7.39) is greater than the critical value (3.84), you can reject the null hypothesis and conclude that there is a relationship between meal preference and gender in this sample.
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The word problem below has too little information. Read carefully, then
choose the fact or facts needed to solve the problem.
In the reptile tent, there are albino alligators, saltwater crocodiles, and
freshwater crocodiles. How many more crocodiles than alligators are there in
the reptile tent?
A. All 6 crocodiles were in one large pool.
B. The two alligators were completely white.
C. Albino alligators are very rare.
D. Freshwater crocodiles have thin snouts.
C. Albino alligators are very rare.
What is crocodiles ?
Crocodiles are large reptiles found in tropical regions of Africa, Asia, the Americas and Australia. They are members of the order Crocodilia, which also includes caimans, gharials and alligators.
crocodiles are more than alligators in the reptile tent because Albino alligators are very rare. according to the passage there are more types of crocodiles ans less alligators.
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Add -0.25+ 3 1/6+ 2 1/12. Write in simplest form
Answer: 5
Step-by-step explanation: because
cantor showed that for any set a, we have |a| < |p(a)|. what does this statement mean? select the correct interpretation.
George Canter showed that, for any set a, we have |a|<|p(a)|. This is a well-known theorem of canter, known as the 'Canter's Theorem'.
Proving this theorem:
Proof: At the first instance, we need to show that, A bar ≤P(A) bar, we will define the injection by f:A→P(A) by: f(a)={a}. Let g be the contradiction.
We need to prove that there is no bijection g:A→P(A).
Now, Let: S={a∈A:a∉g(a)}⊆A.}
In the present condition, there are two possibilities, first, x∈S and second, x∉S.
Therefore,
1. If x∈S, then x∉g(x)=S, i.e., x∉S, a contradiction.
2. If x∉S, then x∈g(x)=S, i.e., x∈S, a contradiction.
Thus, such a bijection, is not possible.
This theorem, coined by Canter, basically implies that there is no largest cardinal number present. There are 'n' number of cardinal numbers present, i.e., there are infinite number of cardinal numbers.
Now, suppose that, A is a set of all sets, this was proved by the continuum hypothesis. But, the continuum hypothesis can't be proved. It can't be disproved also.
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The quotient of y and 3 added to 9 equals 10
Answer:
Step-by-step explanation:
Are you after a solution for y?
quotient of y and 3 is a fancy word for division
y/3+9=10
To solve for y subtract 9 from both sides
y/3+9-9=10-9
y/3=1
To solve for y
multiply both sides by 3
3(y/3)=1*3
y=3
Frames-for-All sells framed pictures to hotels and other corporations across the country. Last year, the company sold a total of 720,460 pictures. This year, they sold 972,621 picyures. What is the percent of increase in yearly sales?
The percent of increase in yearly sales is 35%.
What is a percentage increase?A percentage increase means the eventual increase in the quantity in percent form. The percentage increase formula is use to compare growth in a quantity from the initial value to its final value over a period of time.
The formula for getting a percentage increase is "[(Final Value - Initial Value)/Initial Value] × 100"
Initial value = 720,460 pictures
Final value = 972,621 pictures.
The percentage increase:
= [(972,621 - 720,460] / 720,460} * 100
= 0.35 * 100
= 35%
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using the points 0,2 and -3,4 write an equation in slope intercept form
Answer: y=—2/3x+2
Step-by-step explanation:
Find the solution to the system of equations.
y=3x-4
y=-2x+6
Answer:
Step-by-step explanation:
There a few ways to solve this system. Since each equation is set equal to y on the left side, that means that we can set the right side of each equation to be equal to each other. So,
3x - 4 = -2x + 6
This can now be solved for x:
5x - 4 = 6 (added 2x to each side)
5x = 10 (added 4 to each side)
x = 2 (divided each side by 5)
Now that we know what x must be, we can plug 5 in for x in either of the equations and solve for y:
y = 3(5) - 4
y = 6 -4
y=2
This means y should be 2. To make sure this answer is correct, we can plug our y and x numbers into the OTHER equation to see if it makes sense:
(2) = -2(2) + 6
2 = -4 + 6
2=2
That looks right, so x = 2 and y = 2
Right answer needed thank you!
The inequality - 2 · x + y > - 4 represents the figure on Cartesian plane.
How to derive the inequality shown in the image
In this problem we have a picture with a representation of a linear inequality of the form:
y > m · x + b
Where:
m - Slope of the line.b - Intercept of the line.By analytic geometry, a line can be generated from the knowledge of the location of two points on Cartesian plane. First, determine the equation of the line:
m · 0 + b = - 4
2 · m + b = 0
b = - 4
2 · m = - b
m = - b / 2
m = 2
Second, write the inequality:
y > 2 · x - 4
- 2 · x + y > - 4
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what is the term that describes measures that would be taken to decrease the size of a professional sports league or organization?
The term that describes measures that would be taken to decrease the size of a professional sports is contraction.
Contraction is the act of decreasing or drawing collectively to make smaller; the alternative of expansion. In this case, the proprietors need to lessen the wide variety of groups with the aid of using removing franchises which are dropping the maximum money. Players who're on Minor League or break up contracts aren't completely assured their salaries. A participant on a break up or Minor League settlement will earn the prorated part of his Major League earnings for time spent at the Major League roster.
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Check which of the following are the solutions of the equation 5x – 4y = 20.(i) (4, 0)(ii) (0, 5)(iii) (-2,5/2)(iv) (0, –5)(v) (2,-5/2)
(A) (4,0), (D) (0, -5), and (E)(2, -5/2) are the solutions of the given equation 5x – 4y = 20.
What are equations?The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.
The typical form for linear equations with two variables is Ax+By=C.
For instance, the linear equation 2x+3y=5 is in standard form.
So, we have the equation:
5x – 4y = 20
(A) (4,0)
=5x−4y
=5(4)−4(0)
=20
=RHS
(4,0): YES
(B) (0,5)
=5x−4y
=5(0)−4(5)
=−20
≠RHS
(0,5): NO
(C) (−2, 5/2)
=5x−4y
=5(−2)−4(5/2)
=−10−10
=−20
(−2, 5/2): NO
(D) (0, -5)
=5x−4y
=5(0)−4(−5)
=20
=RHS
(0, -5): YES
(E) (2, -5/2)
=5x−4y
=5(2)-4(-5/2)
=10+10
=20
=RHS
(2, -5/2): YES
Therefore, (A) (4,0), (D) (0, -5), and (E)(2, -5/2) are the solutions of the given equation 5x – 4y = 20.
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find2% of the product of 19 and the average of 63,500, 65,000 and 66,500
By using percentage, it can be calculated that
2% of the product of 19 and the average of 63,500, 65,000 and 66,500 = 24700
What is percentage?
Suppose, there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.
For example, 7% means [tex]\frac{7}{100}[/tex]. Here, 7 is expressed as a percentage of 100.
This is a problem on percentage
The numbers are 63,500, 65,000 and 66,500
Average = [tex]\frac{63500 + 65000 + 66500}{3}[/tex] = 65000
Product of 19 and 65000 = 65000 [tex]\times[/tex] 19 = 1235000
2% of 1235000 = [tex]\frac{2}{100} \times 1235000[/tex] = 24700
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If light can travel 31 times around the world in 4 seconds, find the number of times it can circle the world in 10 seconds.
Answer:
The answer is 77.5
Step-by-step explanation:
If light travels 31 times around the Earth in 4 seconds then in 8 seconds it would be 62 times and 15.5 is half of 31 and then we add 15.5 to 62 and we get 77.5. Hope this helps!
Answer:
In 4 seconds light can travel = 31 times
Then in 10 second it can travel=
31/4 ×10 =77.5times
b) The perimeter of the shape is 25.71 cm
Calculate the value of the radius x.
Take – to be 3.142
Answer:
Questions and answers
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Question
The perimeter of a shape is 25.71 cm calculate the value of the radius X takes pie to be 3.142
Answer · 15 votes
Answer:5 cmStep-by-step explanation:Given a semicircle with perimeter 25.71 cm, we are required to find the radius of the circle.Circumference of a Semicircle=Length of the Circular part+Length of the diameter[tex]=\pi r+2r[/tex][tex]If \: \pi=3.142, C=25.71\Then:\25.71=3.142r+2r (3.142+2)=25.71\5.142r=25.71 =25.71 \div5.142 =5cm[/tex]
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Question
The perimeter of the semicircle is 25.71 cm. Calculate the value
the manufacturer of cans of salmon that are supposed to have a net weight of 6 ounces tells you that the net weight is actually a normal random variable with a mean of 6.16 ounces and a standard deviation of 0.13 ounce. suppose that you draw a random sample of 38 cans. find the probability that the mean weight of the sample is less than 6.15 ounces.
The probability that the mean weight of the sample is less than 6.15 ounces as per the given data is 0.1806.
Mean, μ = 6.16 ounces
Standard Deviation, σ = 0.13 ounce
Sample size, n = 38
We are informed that the weight of the cans is distributed in a bell-shaped manner, which is a normal distribution.
Formula:
Z-score = ( x - ц) /standard deviation
Standard error due to sampling
=SD/√n
=0.13/ √(38)
=0.021
P(weight of the sample is less than 6.15 ounces)
P(X < 6.15) =P( Z< (6.15 - 6.16)/0.021 )
= P(Z> -0.476)
=0.1806 ( as per the Z- score table)
The probability that the sample's mean weight is less than 6.15 ounces is 0.1806.
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Translate the phrase into an algebraic expression.
The sum 9 of C and.
WHAT IS THE ANSWER.
A quarter of a year is 1/4 of a year. There are 12 months in a year. How many months are in a quarter of a year? Draw a diagram to illustrate the problem.
There are Three months in a quarter of a year.
To determine what is being asked, divide the total number by the denominator and get the portion using the numerator:
1 year = 4 quarters
1 quarter= [tex]\frac{1}{4}[/tex] year
1 year = 12 months
Thus,
1 quarter = (Total number of months in year) ÷ (Total number of quarters in a year)
1 quarter = [tex]\frac{12}{4}=3[/tex]
So, There are Three months in a quarter of a year.
One year typically refers to a period of 365 days or 12 months. It usually includes the entire calendar year from January 1st to December 31st. It can also refer to a fiscal year (a period of 12 consecutive months used for accounting purposes) or a school year (which may start in late summer).
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There are Three months in a quarter of a year.
To determine what is being asked, divide the total number by the denominator and get the portion using the numerator:
1 year = 4 quarters
1 quarter= [tex]\frac{1}{4}[/tex] year
1 year = 12 months
Thus,
1 quarter = (Total number of months in year) ÷ (Total number of quarters in a year)
1 quarter = [tex]\frac{12}{4} =3[/tex]
So, There are Three months in a quarter of a year.
One year typically refers to a period of 365 days or 12 months. It usually includes the entire calendar year from January 1st to December 31st. It can also refer to a fiscal year (a period of 12 consecutive months used for accounting purposes) or a school year (which may start in late summer).
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Answer this question:
Your friend thinks that the triangles shown below are congruent by SAS. Is your friend correct? Explain.
Choose the correct answer below.
A.
Yes, the figure indicates that three corresponding sides are congruent.
B.
No, the congruent angles are not the included angles.
C.
Yes, the figure indicates that two corresponding sides and their included angle are all congruent.
D.
No, the congruent sides are not the included sides.
E.
Yes, the figure indicates that two corresponding angles and their included side are all congruent.
F.
No, the figure only indicates that two corresponding sides are congruent, not three as required by the SAS Postulate.
Answer:
B. No, the congruent angles are not the included angles.
Step-by-step explanation:
The SAS (Side-Angle-Side) Postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
In the given figure, we can see that two sides of the two triangles are congruent: side AB is congruent to side DE, and side AC is congruent to side DF. However, the included angles, which are the angles formed by these sides, are not congruent. Angle BAC is not congruent to angle EDF.
Since the included angles are not congruent, we cannot use the SAS Postulate to conclude that the two triangles are congruent. Therefore, the correct answer is B: No, the congruent angles are not the included angles.
Answer:
B. No, the congruent angles are not the included angles.
Step-by-step explanation:
You want to know if the triangles shown are congruent by SAS.
SASThe SAS congruence postulate tells you that two triangles are congruent if the angles between corresponding congruent sides are congruent. (The A=angle is between the S=side in SAS.)
In the diagrams, the marked angles are not between the marked sides. The SAS postulate cannot be used with these triangles.
In short, ...
No, the congruent angles are not the included angles
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In FGH, h=840 inches. F=93° and G=49°. Find the length of g, to the nearest 10th of an inch.
The length of g 1029.8 in the given ΔFGH.
What is Trigonometric Functions?
Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
The Law of Sines (or Sine Rule) is very useful for solving triangles:
[tex]\frac{a}{sinA} = \frac{b}{sinB} + \frac{c}{sinC}[/tex]
840 / sin(38) = g /sin(49)
g = (840 / sin(38) ) *sin(49)
g= (840/0.615) *0.754 = 1029.8
Hence, the length of g 1029.8 in the given ΔFGH.
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a rowing team rowed miles while going with the current in the same amount of time as it took to row miles going against the current. the rate of the current was miles per hour. find the rate of the rowing team in still water.
The rowing team's speed in still water is 6 miles per hours for 6 hours 15 minutes.
Given that,
In the same time it took to row 25 miles against the current, a rowing team was able to row 50 miles while travelling with it. 2 miles per hour was the current's speed.
We have to calculate the rowing team's speed in still water.
We know that,
Let rowing rate in still water = r
And current rate = c = 2 mph
Rowing with the current means the overall speed is r + c = r + 2
Rowing against the current means the overall speed is r - c = r - 2
Distance = Rate × Time
50 = (r+2) × t ----->equation(1)
25 = (r-2) × t ----->equation(2)
By solving
Divide equation(1) by equation(2)
50/25 = (r+2) × t / (r-2) × t
2=r+2/r-2
2(r-2)=r+2
2r-4=r+2
2r-r=2+4
r=6mph
Substitute in equation(1)
50 = (r+2) × t
50=(6+2)×t
50=8t
t=50/8
t=6.25 hrs
t= 6 hours 15 minutes
Therefore, the rowing team's speed in still water is 6 miles per hours for 6 hours 15 minutes.
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