Use Cramer's Rule to solve the system. You may use the calculator for computations only - do not use any matrix functions. Show all work
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Solution
Therefore the value of
[tex]\begin{gathered} x=-1 \\ y=\frac{5}{2}=2.5 \end{gathered}[/tex]
Related Questions
If ∆ABC = ∆EDF where the coordinates of A(0,2), B(2,4), and C(2,-1), what is the measure of DF?A-3B-3.1C-5D-5.9Please respond quickly
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The triangles ABC and EDF are congruent, meaning they have the same side lengths and angles measures.
The measure of DF, as both triangles are congruent, is equal to the measure of BC.
We can calculate the length of BC using the distance formula:
[tex]\begin{gathered} D=\sqrt[]{(x_c-x_b)^2+(y_c-y_b_{})^2} \\ D=\sqrt[]{(2-2)^2+(-1-4)^2} \\ D=\sqrt[]{0^2+(-5)^2} \\ D=\sqrt[]{(-5)^2} \\ D=|-5| \\ D=5 \end{gathered}[/tex]As BC is congruent with DF and BC=5, the length of DF is 5 units.
Solve for x. 9x + 7 - 3 - 4x = -26
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Starting with the equation:
[tex]9x+7-3-4x=-26[/tex]Rewrite using the commutative property of addition to bring together similar terms:
[tex]9x-4x+7-3=-26[/tex]Add like terms on the left hand side of the equation:
[tex]5x+4=-26[/tex]Substract 4 fom both sides of the equation:
[tex]\begin{gathered} 5x=-26-4 \\ =-30 \end{gathered}[/tex]Divide both sides by 5:
[tex]\begin{gathered} x=-\frac{30}{5} \\ =-6 \end{gathered}[/tex]Plug in the value of x=-6 into the original equation to check your answer:
[tex]\begin{gathered} 9x+7-3-4x=-26 \\ \Rightarrow9(-6)+7-3-4(-6)=-26 \\ \Rightarrow-54+7-3+24=-26 \\ \Rightarrow-26=-26 \end{gathered}[/tex]Therefore:
[tex]x=-6[/tex]15 m 9 m 9 m 9 m Find the area of this figure. I m2
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we divide the figure to calculate each area and add them at the end
Parallelogram Area
[tex]\begin{gathered} A_P=b\times h \\ A_P=15\times9 \\ A_P=135 \end{gathered}[/tex]
Triangle Area
[tex]\begin{gathered} A_T=\frac{b\times h}{2} \\ \\ A_T=\frac{6\times9}{2} \\ \\ A_T=27 \end{gathered}[/tex]Total Area
[tex]\begin{gathered} A=A_T+A_P \\ A=27+135 \\ A=162 \end{gathered}[/tex]the are of this figure is 162 square meters
The figure represents the side view of a rectangular frame for metal shelves. Two diagonal bracessupport the frame.8 ft2 ftWhich is closest to the measure of x?7°14°28°76
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AD=BC=8 ft
AB=CD=2 ft
Then,
[tex]\begin{gathered} AC=BD=\sqrt[]{2^2+8^2} \\ =\sqrt[]{68} \\ OA=OB=OC=OD=\frac{\sqrt[]{68}}{2}\text{ ft} \end{gathered}[/tex]In triangle BDC,
[tex]\begin{gathered} \tan \angle BDC=\frac{8}{2} \\ =4 \\ \angle BDC=75.963 \\ \angle DBC=14.04 \end{gathered}[/tex][tex]\begin{gathered} OE=\frac{8}{2} \\ =4\text{ ft} \\ \angle BDC=\angle OCD=75.96 \end{gathered}[/tex]In triangle ODC,
[tex]\begin{gathered} \angle ODC+\angle OCD+\angle OCD=180 \\ \\ \angle\text{DOC}=180-(2\cdot75.96) \\ \angle DOC=28 \\ \angle X=\angle DOC=28 \end{gathered}[/tex]So, the correct option is option C.
Statistic Questions
All of the following statements, except for one, contains an error.
Which statement does not contain an error?
A) The relationship between height and the ability to reach things is strong and positive. The correlation is 1.15.
B) The relationship between height and weight is strong and positive. The correlation is 0.95.
C) The relationship between height and gender is strong and positive. The correlation is 0.95.
D) The relationship between age and height is negative for the elderly. The correlation is –1.25 .
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The correct statement regarding the correlation coefficient is given as follows:
B) The relationship between height and weight is strong and positive. The correlation is 0.95.
What is a correlation coefficient?The correlation coefficient between two variables is an index that measures correlation between these variables, assuming values between -1 and 1.
As the values have to be between -1 and 1, statements A and D are false, as the coefficients have values greater than 1 or less than -1.
From the image given at the end of the answer, the variables are given as follows:
Height.Weight.The scatter plot is increasing, hence statement B is correct, as there is a positive correlation between the variables.
Missing InformationThe graph is given by the image at the end of the answer.
More can be learned about correlation coefficients at brainly.com/question/16355498
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1. The number of people attending a school meeting was 80. There were four times as many parents as supervisors atthe meeting. How many supervisors attended the meeting? How many parents?Let x = number of supervisors at the meeting.4x = number of parents at the meeting
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Step 1: Write out the information provided in the question.
Number of people attending the meeting is 80.
Let the number of supervisors be x
Since there were four times as many parents as supervisors, then the number of parents will be 4x
Step 2: convert the above information to mathematical equation, the number of people attending the meeting equals to the sum of the parents and the supervisors, thus,
[tex]x+4x=80[/tex]Step 3: Solve the above equation to get the value of x
[tex]\begin{gathered} x+4x=80 \\ 5x=80 \\ \frac{5x}{5}=\frac{80}{5}(\text{divide both side by 5)} \\ x=16 \end{gathered}[/tex]Step 4: Since the number of supervisors equals x which is 16, the number of parents attending the meeting will be 4x which is
[tex]4x\Rightarrow4\times16=64[/tex]Hence, 16 supervisors and 64 parents attended the meeting
Given the function f(x) =x2-3x-10, determine the function of its reflection over the x axis.....x squared minus 3x minus 10.
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1) Examining the function f(x)= x²-3x -10 to get this function reflected over the x axis,
We'll need to multiply the "a" parameter by -1, so that we can get:
f(x) = -x²-3x -10
to the nearest hundreds it says in red it got cropped out
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The Circumference of the circle = 2 π r
Given the radius = r = 13 cm
So,
C = 2 * π r = 2 * 3.14 * 13 = 81.64 cm
So, to the nearest hundredth = 81.64 cm
Try, check and revise, or write an equation to solve each problem. 1).The volume of a cube is 79.507 cubic inches. -How long is each edge of the cube? 2). What are the two whole numbers whose product is 294 and whose quotient is 6? 3). Tickets for a concert are sold for $ 8 for the stalls and $ 6 for the gallery. For one function, 400 seats were sold for a total of $ 2,888. How many seats of each type were sold? 4). Aaron bought 6 books and 2 notebooks for $ 46.86. Erin bought 2 books and 6 notebooks for $ 27.78. How much does a book cost?
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Answer:
4.3inches
Explanation:
1) Volume of a cube is expressed as;
[tex]V=L^3[/tex]L is the length of each side of the cube
Given
Volume of a cube = 79.507 cubic inches
Substitute into the formula and get L
[tex]\begin{gathered} 79.507=L^3 \\ L^3\text{ = }79.507 \\ L\text{ = }\sqrt[3]{79.507} \\ L\text{ }=4.3\text{inches} \end{gathered}[/tex]hence eahc edge of the cube is 4.3inches
In five years time job will be four times as old as his son Mark. Two years ago Jon was eleven times as old as mark how old are Jon and mark now
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Given that In five years time job will be four times as old as his son Mark and Two years ago Jon was eleven times as old as mark.
Let the age of job and mark now be x and y years old.
So, in five years the age of job will be x + 5 and the age of his son mark will be y + 5.
According to the question,
[tex]\begin{gathered} x+5=4(y+5) \\ x+5=4y+20 \\ x-4y=15 \end{gathered}[/tex]Two years ago, the age of job was x - 2 and the age of his son mark was y - 2.
So, according to the question.
[tex]\begin{gathered} x-2=11(y-2) \\ x-2=11y-22 \\ x-11y=-20 \end{gathered}[/tex]From the first equation, we have x = 4y + 15. Substitute this value in the second equation and solve:
[tex]\begin{gathered} 4y+15-11y=-20 \\ -7y=-35 \\ y=5 \end{gathered}[/tex]Substitute y = 5 in x = 4y + 15.
[tex]\begin{gathered} x=4(5)+15 \\ x=20+15 \\ x=35 \end{gathered}[/tex]Thus, the present age of job is 35 years and the present age of his son mark is 5 years.
Brenda received a gift card for an internet cafe. The cost,y, of renting a computer and using it for x hours at the cafe is shown in the graph below. Which equation represents the same relationship as the graph?
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In order to find the equation of the graph, we need to get two points on the graph.
Two points on the graph are points (2, 24) and (4, 33)
The next step is to find the slope of the graph, using the two points above
[tex]\begin{gathered} \text{ slope, m = }\frac{y_2-y_1}{x_2-x_1} \\ \text{ (x}_1,y_1)=(2,24)_{} \\ (x_2,y_{2_{}})=(4,\text{ 33)} \\ m=\frac{33-24}{4-2} \\ m=\frac{9}{2} \\ m=4.5 \end{gathered}[/tex]Then, using slope and one point formula, find the equation of the line
[tex]\begin{gathered} \text{ y-y}_1=m(x-x_1) \\ m=\text{ 4.5, (x}_1,y_1)=(2,24) \\ y-24=4.5(x-2) \\ y-24=4.5x-9 \\ y=4.5x-9+24 \\ y=4.5x+15 \end{gathered}[/tex]The correct answer is y= 4.5x + 15
4. The perimeter of a rectangular garden is 36 feet. The length of the garden is 6 less than twicethe width. Find the length and width of the garden.Variable:Equation:Variable:Equation:LengthWidth
Answers
From the question, we've been given the perimeter of the rectangular garden to be 36ft and we're told that the length is 6 less than twice the width of the garden
12. Given.4(9.2), B(-1,y), C(-5, 16),and D(-8. 11), find the value ofy so that ABCD
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ok, we need to draw both segment of lines... that are parallel.
We need to re draw, because we need more space for point C (-5,16)
The steps to solve this problem are:
1) We draw segment line CD... later,
2) we express the segment line AB,
3) We find the slopes of both segments
4) finally, we found the value of y.
Do you understand? or have questions of the process?
We have done the segment line CD, after that from the graphic we can make a prediction of the value of y, because we need to find a line perpendicular to cd.. like this one (green in the graphic)... line green will be perpendicular to line yellow...
Now, we find the general equation of the yellow line.. that's it:
[tex]\begin{gathered} \text{slope = m = }\frac{\text{(y}_2-y_1\text{)}}{(x_2-x_1)};\text{ C(x}_1,y_1)=C(-5,16);\text{ D(x}_2,y_2\text{)}=D(-8,11) \\ \text{ m = }\frac{\text{(y}_2-y_1\text{)}}{(x_2-x_1)}=\frac{\text{(11}-16\text{)}}{(-8-(-5))}=\frac{\text{(11}-16\text{)}}{(-8+5)}=\frac{-5}{-3}=\frac{5}{3} \\ m=\frac{5}{3} \end{gathered}[/tex]After that, we should remember that two lines are paralell when a multiplication of its slopes it's equal to -1, like this:
[tex]\begin{gathered} \text{slope 1 }\cdot\text{ slope 2 = -1} \\ m_1\cdot m_2=-1 \\ \frac{5}{3}.m_2=-1 \\ m_2=\frac{-3}{5} \end{gathered}[/tex]Finally, we find the generall equation of the line green with the point A(9,2) and the value of its slope m2, we apply:
[tex]\begin{gathered} (y-y_1)=m(x-x_1);\text{ A(x}_1,y_1)=A(9,2);\text{ m=}\frac{-3}{5};\text{ We replace and get} \\ y-2=\frac{-3}{5}(x-9) \\ y=\frac{-3}{5}x+\frac{3}{5}\cdot\frac{9}{1}+2 \\ y=\frac{-3}{5}x+\frac{27}{5}+2 \\ y=\frac{-3}{5}x+\frac{37}{5} \end{gathered}[/tex]Now, to find the value of y in the poin B, we replace the value of x = -1 in the equation of the green line, like this:
[tex]\begin{gathered} y=\frac{-3}{5}x+\frac{37}{5};\text{ x=-1} \\ y=\frac{-3}{5}(-1)+\frac{37}{5} \\ y=\frac{3}{5}+\frac{37}{5}=\frac{40}{5}=8 \end{gathered}[/tex]The answer has the value of 8. In graphic is similar.. green line... It's not equal because I do the graphic at inexact way.
What is this triangle called
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The answer is called a Scalene Traingle, and this is because the three angles aren't equal the sides can't be equal too.
a woman earns $3000 per month and budgets $420 per month for food. what percent of her monthly income is spent on food
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In order to calculate the required percentage, first calculate the quotient between the money spent for food and the total money of the incomes:
420/3000 = 0.14
next, multiply the previous result by 100:
0.14 x 100 = 14%
Hence, the percentage spent in food is 14%
He has only hundreds, tens, and ones blocks. Part A How can Asher model the number 1,414?
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ANSWER:
14 blocks of hundreds
1 blocks of tens
4 blocks of ones
STEP-BY-STEP EXPLANATION:
The first thing is to decompose the number 1414, like this:
[tex]1414=1000+400+10+4[/tex]Since we have only hundreds, tens, and ones blocks.
[tex]1414=1400+10+4[/tex]Therefore, would be:
14 blocks of hundreds
1 blocks of tens
4 blocks of ones
Answer:
use ten 100 blocks,four 10 blocks,and fourteen 1s blocks.
Step-by-step explanation:
hope that helps.
estimates by first rounding each number to the place value 1.8×3.62
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By estimation you have:
3.62 ≈ 4.0
1.8 ≈ 2.0
2.0 x 4.0 = 8.0
how to solve this one k(k-9)
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Simplify the expression by multipliaction of terms.
[tex]\begin{gathered} k(k-9)=k\cdot k-9\cdot k \\ =k^2-9k \end{gathered}[/tex]So answer is
[tex]k^2-9k[/tex]Marvin is hoping to buy a used car for S4025. His parents give him $275 towards the car. To earn the rest of the money he plans to mowlawns for $50 per yard. How many yards will he need to mow to earn enough money to buy the car?O 86 yardsO 50 yardsO 80 yardsO 75 yards
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Let's call the amount of yards he needs to mown as 'y'. The total value of the car is $4025, since he already have $275 from his father, the rest of the money will be the difference between those values. The rest of the money, he plans to gain by working at a rate of $50 per yard. Writing all of those informations as an equation, we get:
[tex]4025-275=50y[/tex]To find the amount of yards he needs to mow, we just have to solve this equation for 'y':
[tex]\begin{gathered} 4025-275=50y \\ 3750=50y \\ y=\frac{3750}{50}=75 \end{gathered}[/tex]He needs to mow 75 yards to buy the car.
graphing on the coordinate plane how does absolute value help you write a number sentence to help you find the distance
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Given:
The points 7 and -7.
Required:
We need to find the distance between 7 and -7 by using absolute values.
Explanation:
1)
We need to subtract the given numbers to find the distance.
Subtract 7 from -7 and take absolutely to find the distance.
[tex]Distance=|-7-7|[/tex]Just add the absolute value of each number together, put a negative sign in front,
[tex]Distance=|-(|-7|+|-7|)|[/tex][tex]Distance=|-(7+7)|[/tex][tex]Distance=|-14|[/tex][tex]Distance=14[/tex][tex]We\text{ know that abosulute values of negative number is postive.}[/tex]The absolute value of a number is never negative.
Answer:
The distance is non-negative. so absolute values help to avoid the negative values for distance since the absolute value of a number is never negative.
2)
Subtract 5 from -5 and take absolutely to find the distance.
[tex]Distance=|-5-5|[/tex]Just add the absolute value of each number together, put a negative sign in front,
[tex]Distance=|-(|-5|+|-5|)|[/tex][tex]Distance=|-(5+5)|[/tex][tex]Distance=|-10|[/tex][tex]Distance=10[/tex]Answer:
The distance is non-negative. so absolute values help to avoid the negative values for distance since the absolute value of a number is never negative
3)
Subtract 2 from -2 and take absolutely to find the distance.
[tex]Distance=|-2-2|[/tex][tex]Distance=|-4|[/tex][tex]Distance=4[/tex]Answer:
The distance is non-negative. so absolute values help to avoid the negative values for distance since the absolute value of a number is never negative
Final answer:
1)
The absolute value of the difference between 7 and -7 is 14.
The distance is non-negative. so absolute values help to avoid the negative values for distance since the absolute value of a number is never negative.
2)
The absolute value of the difference between 5 and -5 is 10.
The distance is non-negative. so absolute values help to avoid the negative values for distance since the absolute value of a number is never negative.
3)
The absolute value of the difference between 2 and -2 is 4.
The distance is non-negative. so absolute values help to avoid the negative values for distance since the absolute value of a number is never negative.
Can someone verify and corrrect me if I did it wrong please
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Solution:
Given the triangle
Let h represent the hypotenuse
[tex]\begin{gathered} h^2=8^2+15^2\text{ \lparen pythagoras theorem\rparen} \\ h^2=64+225 \\ h^2=289 \\ h=\sqrt{289} \\ h=17 \end{gathered}[/tex][tex](a)\text{ }sin\theta=\frac{opposite}{hypotenuse\text{ }}\text{ = }\frac{15}{17}[/tex][tex](b)\text{ cos}\theta=\frac{adjacent}{hypotenuse}=\frac{8}{17}[/tex][tex](c)\text{ Tan}\theta=\frac{opposite\text{ }}{adjacent}=\frac{15}{8}[/tex][tex](d)\text{ Csc}\theta=\frac{1}{sin\theta}=\frac{1}{\frac{15}{17}}\text{ = }\frac{17}{15}[/tex][tex](e)\text{ Sec}\theta=\frac{1}{cos\theta}=\frac{1}{\frac{8}{17}}=\frac{17}{8}[/tex][tex](f)\text{ Cot}\theta=\frac{1}{tan\theta}=\frac{1}{\frac{15}{8}}=\frac{8}{15}[/tex]Can someone calculate this using the correct number of significant figures? 7166.0-2.4*10^23
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Writing both terms in scientific notation, we have:
7166.0 = 7.1660*10³
So, this term has 4 significant figures (.1660)
2.4*10^23 is already written in scientific notation. So it has 1 significant figure (.4)
Now, when summing or subtracting two quantities, the number of significant figures of the result equals the smaller number of significant figures. So, in this case, the result has 1 significant figure.
Then, proceeding with the calculation, we have:
7166.0 - 2.4*10^23 = 7.1660*10³ - 2.4*10^23 = (7.1660 - 2.4*10^20) * 10³
= (7.1660 - 240,000,000,000,000,000,000.0) * 10³
= -239,999,999,999,999,999,992.8340
Finally, we need to round the first significant figure, so there will be only one significant figure in the result:
-239,999,999,999,999,999,992.8
Evaluate the function when x= -2,0, and 59) v(x)=12-2x-5
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we have the function
[tex]V(x)=12-2x-5[/tex]Combine like terms and rewrite the given function
[tex]V(x)=7-2x[/tex]Evaluate for x=-2
[tex]\begin{gathered} V(-2)=7-2(-2) \\ V(-2)=7+4 \\ V(-2)=11 \end{gathered}[/tex]Evaluate for x=0
[tex]\begin{gathered} V(0)=7-2(0) \\ V(0)=7 \end{gathered}[/tex]Evaluate for x=5
[tex]\begin{gathered} V(5)=7-2(5) \\ V(5)=7-10 \\ V(5)=-3 \end{gathered}[/tex]A student takes a 10 question multiple choice quiz- each question having 4 choices. Suppose a student randomly picks an answer for each question. Find the following.
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Assume that an A is a 90% (getting at least 9 questions out of 10 right).
The probability that exactly 9 questions are right is 10 (choose one question to get wrong) * (1/4)^9 (1/4 chance of getting each question right) * (3/4) (chance of getting the wrong question wrong) = 10∗3∗(1/4)10 .
The probability that all 10 questions are right is (1/4)10 (1/4 chance of getting each question right).
The total probability of getting an A is (10∗3+1)(1/4)10=31410, or about 0.002956%.
I hope I helped! If I misinterpreted your question, please let me know and I'll try my best to help.
I need help on solving this Did I get the right answer ? And do the table right ?
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At which angle is secant of theta equals negative radical 2 question mark
Answers
The equation is given to be:
[tex]\sec\theta=-\sqrt{2}[/tex]Recall that sec is the inverse of cos. Thus, we have:
[tex]\frac{1}{\cos\theta}=-\sqrt{2}[/tex]Rewriting the equation, we have:
[tex]\cos\theta=-\frac{1}{\sqrt{2}}[/tex]We can find the arccos of both sides:
[tex]\theta=\arccos(-\frac{1}{\sqrt{2}})[/tex]Since we know that:
[tex]\cos(-x)=\cos(x)[/tex]Then, we have:
[tex]\theta=\arccos(\frac{1}{\sqrt{2}})[/tex]Recall the identity:
[tex]\arccos(\frac{1}{\sqrt{2}})=\frac{3\pi}{4}+2\pi n,\:θ=\frac{5\pi}{4}+2\pi n[/tex]Therefore, the answer is the SECOND OPTION.
The ratio of girls to boys on Mr.Miller's team is 4 to 5. If thereare 60 boys on his team, thenhow many students are there onhis team?
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We have a ratio is 4 girls to 5 boys. There are 60 boys, then, we have:
[tex]\frac{4}{5}=\frac{x}{60}\Rightarrow x=\frac{60\cdot4}{5}\Rightarrow x=\frac{240}{5}\Rightarrow x=48[/tex]Then, we have 48 girls in the class.
Therefore, there are 60 boys + 48 girls = 108 students on Mr. Miller's team.
Write the ratio as a fraction in lowest terms.35 minutes to 5 hours
Answers
7 : 60
Explanation:Note that:
1 hour = 60 minutes
5 hours = 5 x 60 minutes
5 hours = 300 minutes
35 minutes : 5 hours = 35 minutes : 300 minutes
35 minutes : 5 hours = 35 : 300
Divide both the numerator and denominator by 5
35 minutes : 5 hours = (35 ÷ 5) : (300 ÷ 5)
35 minutes : 5 hours = 7 : 60
Angles C and D are acute angles of a right triangle. Given sin D=2/7, which statement is true?
Answers
Answer
Option D is correct.
Cos C = (2/7)
Explanation
In a right-angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
A sketch of this right triangle will be
This sketch allows Sin D = (2/7)
To know the right answer, we need to find the last side of the triangle
The Pythagoras Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
For this question,
a = 2
b = ?
hyp = 7
a² + b² = (hyp)²
2² + b² = 7²
4 + b² = 49
b² = 49 - 4
b² = 45
b = √45
So, we can evaluate each of these
Cos D = (√45)/7
Cos C = (2/7)
Hope this Helps!!!
Answer: cos C = 2/7
Step-by-step explanation: I took the test.
You rent an apartment that costs $1,400 per month during the first year, but the rent is set to go up 10.5% per year. What would be the rent of the apartment during the 6th year of living in the apartment?
Answers
We will determine the rent cost after 6 years as follows:
[tex]S=1400(1+0.105)^6\Rightarrow S=2548.600147[/tex][tex]\Rightarrow S\approx2548.6[/tex]So, the rent cost after 6 years would be approximately $2548.6.