Answers
We will use the law of sines and law of cosines shown below
[tex]\begin{gathered} c=\sqrt{a^2+b^2-2ab\cos C}\rightarrow\text{ law of cosines} \\ and \\ \frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}\rightarrow\text{ law of sines} \end{gathered}[/tex]Therefore, in our case, finding side c.,
[tex]\begin{gathered} a=28,b=13,C=49\degree \\ \Rightarrow c=\sqrt{784+169-2*28*13cos(49\degree)} \\ \Rightarrow c\approx21.8 \end{gathered}[/tex]Thus, side c is approximately 21.8km.
Finding the missing angles using the law of sines,
[tex]\begin{gathered} A=\cos^{-1}(\frac{c^2+b^2-a^2}{2bc}) \\ \Rightarrow A=\cos^{-1}(\frac{21.8^2+13^2-28^2}{2*13*21.8}) \\ \Rightarrow A\approx104.3 \\ \end{gathered}[/tex]Similarly, in the case of angle B,
[tex]sinB=\frac{13}{21.8}sin(49\degree)\approx26.7\degree[/tex]Therefore, the answers are
c=21.8km,
Related Questions
I would like to work through how to determine whether this is even, odd or netiher.
Answers
We are given a function and are asked to determine if it's even, odd or neither. Our approach is to employ the negative test and modify the function to ascertain its status. This will be depicted below.
[tex]h(x)=-6x^3+x^2+8x+8[/tex]This is our original function, next, we find h(-x)
[tex]\begin{gathered} h(x)=-6x^3+x^2+8x+8 \\ h(-x)=-6(-_{}x)^3+(-x)^2+8(-x)+8 \\ h(-x)=6x^3+x^2-8x+8 \\ h(-x)=6x^3+x^2-8x+8 \\ h(-x)=-(-6x^3-x^2+8x-8) \end{gathered}[/tex]Looking at the function h(x) and h(-x), we have to put the polynomial in the correct degree. The input of the negative sign before the h(-x) function is to check if the function will maintain the same format with the original function, h(x). The disparity is what tells us if it is even, odd or neither of the two.
Now we know h(-x), we now use a certain set of conditions to test if function is even, odd or neither.
[tex]\begin{gathered} \text{if h(x)=h(-x), then function is even} \\ \text{if h(-x)=-h(x), then function is odd} \\ \text{if it is neither of the above, function is neither even nor odd.} \end{gathered}[/tex]In this case, based on the above criteria, the function is neither even nor odd.
Find the slope of every line that is parallel to the graph of equations
Answers
Note that parallel lines always have the same slope.
From the problem, the equation is :
[tex]y=-\frac{1}{4}x-2[/tex]and the slope is -1/4
Parallel lines must also have the same slope of -1/4
The answer is -1/4
if 5 ibs apples cost $2.99, how much would 3 ibs cost?
Answers
We know that 5 lbs of apples cost $2.99
To know how much do 3 lbs of apple cost, you can use cross multiplication
If 5 lbs cost $2.99
Then 3 lbs cost $x
The proportion between the price and the number of apples is the same, you have to calculate it as:
[tex]\begin{gathered} \frac{2.99}{5}=\frac{x}{3} \\ (\frac{2.99}{5})\cdot3=x \\ x=1.794 \end{gathered}[/tex]3 lbs of apples cost $1.79
can u help me with work?
Answers
the x-intercepts are all the x coodinates in which the function will be equal to 0
to find the x intercepts equal the equation to 0
[tex]f(x)=3\cdot(x-6)\cdot(x+4)[/tex]equal all factors involving the x to 0 because if there is any factor equal to 0 then the product between of al products will be 0 as well
[tex]\begin{gathered} 0=3\cdot(x+4)\cdot(x-6) \\ x+4=0 \\ x-6=0 \end{gathered}[/tex]solve both of the equations
[tex]\begin{gathered} x=-4 \\ x=6 \end{gathered}[/tex]the x-intercepts will be
(-4,0) & (6,0)
Select ALL the correct answers.Identify the two tables which represent quadratic relationships.A. x 0 1 2 3y -4 -8 -10 -10B. x 0 1 2 3y 3 4 5 6C. x 0 1 2 3y -2 -4 -8 -16D. x 0 1 2 3y 4 -4 -4 4E. x 0 1 2 3y 1 2 4 8F. x 0 1 2 3y -2 0 2 4
Answers
Step 1
The meaning of QUADRATIC EQUATION is any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.
Step 2
We are required to Identify the two tables which represent quadratic relationships.
In a quadratic equation, we have a polynomial in x with degree 2. Hence the result in y or P(x) do get repeated as a polynomial contains x² in it.
Looking at the tables we will observe that;
[tex]\begin{gathered} option\text{ B follows a sequence and is linear} \\ \end{gathered}[/tex][tex]Option\text{ E is not quadratic but exponential}[/tex][tex]Option\text{ F is not right}[/tex]The answers will be;
[tex]Option\text{ D and option A}[/tex]6. Let the measurement of ZBAC be 86° & ZBAD be 52°. What is the measurement of ZDAC? 1380 24° 52° 340
Answers
Monica has to solve the following problem: Warren travels 4,200 meters every hour. How far does he travel in four hours?
Which picture gives Monica all the information she needs to solve the problem?
Answers
Answer: A
Step-by-step explanation:
B is wrong A is right.
Two of the angles in a triangle measure 56° and 6° what is the measure of the third angle
Answers
The sum of angle in a triangle is 180°
If two of the angles in a triangle is 56° and 6°
Let x be the third angle
56 + 6 + x = 180° (sum of angle in a triangle)
62° + x = 180°
subtract 62° from both-side of the equation
x = 180° - 62°
x = 118°
Hence, the third side is 118°
What is the answer to 720x+(-20x)
Answers
720x + (-20x)
Remember
(+)(+) = (+)
(+)(-) = (-)
So + (-20x) will equal - 20x, so
720x + (-20x) = 720x - 20x
Subtract 20 from 720
720 - 20 = 700, so
720x + (-20x) = 720x - 20x = 700x
What is the factorization of the trinomial below?x^3 - 2x² - 35x
Answers
Notice that the factor x is a common factor for all three terms. Then, factor out x:
[tex]x^3-2x^2-35x=x(x^2-2x-35)[/tex]Notice that the factor x²-2x-35 is a quadratic expression.
Find two numbers whose sum is -2 and whose product is -35 to factor out the quadratic expression. Since 5-7 = -2 and (5)(-7)=-35, those two numbers are -7 and 5. Then, the quadratic expression can be factored out as:
[tex]x^2-2x-35=(x-7)(x+5)[/tex]Then:
[tex]x(x^2-2x-35)=x(x-7)(x+5)[/tex]Then, the factorization of the given trinomial is:
[tex]x^3-2x^2-35x=x(x-7)(x+5)[/tex]Therefore, the correct choice is option C) x(x-7)(x+5)
Part DWhat if the second six-sided die is replaced by an eight-sided die. How can you change the table to show the sample space for rolling a six-sideddie and then an eight-sided die? Explain.
Answers
For a sample space for rolling a six-sided die and then an eight-sided die is constructed as
We just change the probable events of the second die up to 8 and then combine it with the possible combinations with a normal six die, which is shown in the table above.
i need help with math
Answers
the new equation would be:
[tex]y=2500x+35000[/tex]if the new rate is changed to 3000. The new equation is:
[tex]y=3000x+32500[/tex]You have a combination lock with 3 secret digits. Find the 3 correct digits using the following clues and enter your answer below.
Answers
The first clue only tells us that there is one digit that is in the right place, so it could be any one of the following.
The second one tells us that one of the digits is right but in the wrong place, we still cannot confirm if 5 is the number we are talking about.
The fourth clue says that all the numbers are incorrect, so the digits are 2, 5, 0 or 1, now we must find out the correct order.
From clues 3 and 5 we can assume that 0 is one of the digits and that it comes first.
We will discard the number 5 because in clue 3 they talk about 2 correct digits, we already know that 0 is one and we choose 2 instead of the number five because of clues 1 and 2, which talk about only one digit in the correct place but in both of them the 5 remains in the same place.
The 3 digists are: 1, 0 and 2
The correct order is 012
Which interval notation represents a function white a range of all real numbers greater than -2 and less than 4?A.) -2
Answers
range = ? -2 < y < 4 According to the directions this is the inequality
Letter A is the right answer
how many five letter codes can be made if no letter can be used twice
Answers
The aritmetic sequence has the characteristic that each term is the term before plus a constant number. Then we can create the following system of equations:
[tex]\begin{gathered} x-34=p \\ 345-p=x \end{gathered}[/tex]where p is the constant value which is added in each term, and x the number between 34 and 345. If we replace the value of "x" from the second equation into the first one:
[tex]\begin{gathered} 345-p-34=p \\ 311=2p \\ 155.5=p \end{gathered}[/tex]Finally, the term betwen 34 and 345 is 34+p, 189.5
Hence the answer is 189.5
need help asappppppp
Answers
At first, we will find the volume of the cone and the volume of the sphere, then subtract them to find the answer
The rule of the volume of the cone is
[tex]V_c=\frac{1}{3}\times\pi\times r^2\times h[/tex]Since the height of the cone is 1 cm and its radius is 3 cm, then
h = 1 and r = 3
Substitute them in the rule above
[tex]\begin{gathered} V_c=\frac{1}{3}\times\pi\times(3)^2\times(1) \\ V_c=\frac{1}{3}\times\pi\times9\times1 \\ V_c=3\pi \end{gathered}[/tex]The formula of the volume of the sphere is
[tex]V_{sp}=\frac{4}{3}\times\pi\times r^3[/tex]Since the diameter of the sphere is 3 cm, then
[tex]\begin{gathered} r=\frac{1}{2}\times3 \\ r=\frac{3}{2} \\ r=1.5\operatorname{cm} \end{gathered}[/tex]Substitute it in the formula above
[tex]\begin{gathered} V_{sp}=\frac{4}{3}\times\pi\times(1.5)^3 \\ V_{sp}=4.5\pi \end{gathered}[/tex]Noe subtract them to find the answer
[tex]\begin{gathered} V=4.5\pi-3\pi \\ V=1.5\pi \end{gathered}[/tex]The amount of the extra soap is
[tex]1.5\pi cm^3[/tex]Identify the area of the polygon with vertices c (5, 3), a (8, -2), s (3, -4), and h (0, -2).Please help.
Answers
Answer:
To find the area of the polygon with vertices C(5, 3), A(8, -2), S(3, -4), and H(0, -2).
We have that formula for finding the area of the parallelogram with n vertices is,
[tex]=\frac{1}{2}\lbrack(x1y2+x2y3+x3y4+.\ldots+xny1)-(x2y1+x3y2+x4y3+\cdots+x1yn)\rbrack[/tex]we get that,
Area of the polygon with 4 vertices that is (x1,y1),(x2,y2),(x3,y3) and (x4,y4) is
[tex]=\frac{1}{2}\lbrack(x1y2+x2y3+x3y4+x4y1)-(x2y1+x3y2+x4y3+x1y4)\rbrack[/tex]Substituting the values we get,
[tex]=\frac{1}{2}\lbrack(5\times(-2)+8\times(-4)+3\times(-2)+0)-(8\times3+3\times(-2)+0+5\times(-2)\rbrack[/tex][tex]=\frac{1}{2}\lbrack(-10-32-6)-(24-6-10)\rbrack[/tex][tex]=\frac{1}{2}\lbrack-48-8\rbrack[/tex][tex]=\lvert\frac{1}{2}\times(-56)\rvert[/tex][tex]=\lvert-28\rvert=28[/tex][tex]=28\text{ sq.units}[/tex]An
Martha has 9 feet of red ribbon and 6 feet of green ribbon. How many yards of ribbon does she have altogether?Martha has _____ yards of ribbon.The solution is ______
Answers
Since we want the total amount, we first can add the red and green ribbon:
[tex]9+6=15[/tex]Martha has 15 feet of ribbon.
To converto to yards, we can just divide the amount in feet by 3. So, in yards:
[tex]\frac{15}{3}=5[/tex]So
Martha has 5 yards of ribbon.
order the numbers from least to greatest -2 3/4 negative 1/3 0.2 negative two negative 1 and 1/2 -0.8
Answers
So the numbers we have are:
-2, 3/4, -1/3, 0.2, -1, 1/2 & -0.8
So the numbers from least to greatest go as follows:
-2, -1, -0.8, -1/3, 0.2, 1/2, 3/4
factor the equation 3x^2y^2-15xy^2
Answers
3xy²(x - 5)
Explanation:The equation: 3x²y²-15xy²
x is common to both expression, we factorise it:
x(3xy² - 15y²)
y² is common to both expression, we factorise it:
xy²(3x - 15)
3 is common to both expression, we factorise it:
3xy²(x - 5)
Use the following figure and information to complete the proof. Given: m∥n Line l is a transversal of lines m and n. Prove: ∠3≅∠5
Answers
Answer:
1. Given.
2. Definition of vertical angles.
3. Vertical angles theorem.
4. Definition of corresponding angles.
5. Corresponding angles postulate.
6. Transitive property of congruence.
Explanation:
1. This statement is the given part of the problem
2. vertical angles are the pair of opposite angles that are formed when two line segments intersect. Angles 1 and 3 verify this definition, thus they're vertical angles.
3. The vertical angles theorem states that a pair of two vertical angles have the same measure.
4. Corresponding angles are the angles that are formed in matching corners with the transversal when two parallel lines are intersected by another line. Thus, angles 1 and 5 are corresponding angles.
5. The corresponding angles postulate states that, when two parallel lines are cut by a transversal, the resulting corresponding angles are congruent. Thus, angles 1 and 5 are congruent.
6. The transitive property of congruence states that if a is congruent to b and b is congruent to c, then a is congruent to c.
This means:
[tex]\angle3\cong\angle1\cong\angle5\Rightarrow\angle3\cong\angle5[/tex]
Evaluate the expression.
sin2 360° + cos2 360°
Answers
Answer:
1
Step-by-step explanation:
2. Kylie wants to earn $100 a month. She rakes leaves for $7 an hour and cleans windows for $6 an hour. Kylie cannot work more than 30 hours a week. Write the system of inequalities that represents this situation. Be sure to define your variables.
Answers
Let L be the amount of hours that Kylie works on raking leaves and W the amount of hours that she works on cleaning windows (on a week).
Since she cannot work more than 30 hours a week, and the total time spent working is L+W, then:
[tex]L+W<30[/tex]Since one month has 4 weeks, she should win $25 a week to earn $100 in a month. Since she gets paid $7 per hour for raking leaves, after L hours she would have won a total amount of 7L, and since she gets paid $6 for cleaning windows, she would have won 6W after W hours. The total amount of money earned would be 7L+6W, which should be greater than 25:
[tex]25\le7L+6W[/tex]Therefore, the system of inequalities that represents the situation, is:
[tex]\begin{gathered} L+W\le30 \\ 25\le7L+6W \end{gathered}[/tex]complete the statement type your answer as a number 3 gallons =pints
Answers
Answer:
[tex]3\text{ gallons = 24 pints}[/tex]Explanation:
We want to convert 3 gallons to pints.
Recall that;
[tex]1\text{ gallon = 8 pints}[/tex]So, for 3 gallons, we have;
[tex]3\text{ gallons = 3}\times8\text{ pints= 24 pints}[/tex]Therefore;
[tex]3\text{ gallons = 24 pints}[/tex]What is the product of 3x2 and 2xºy+5xy4?
Answers
SOLUTION
[tex]\begin{gathered} 3x^2(2x^3y+5xy^4) \\ 3x^2(2x^3y)+3x^2(5xy^4) \\ 6x^5y+15x^3y^4 \end{gathered}[/tex]So the first option is the correct answer
Write the exponential function / (x)=-4.2^(1-x) in the form f(x) = ab^x
Answers
Given the equation of the function f(x):
[tex]f(x)=-4\cdot2^{(1-x)}[/tex]We will use the following rules of the exponents:
[tex]\begin{gathered} a^{m+n}=a^m\cdot a^n \\ a^{-m}=\frac{1}{a^m} \\ a^{mn}=(a^m)^n \end{gathered}[/tex]So, we can rewrite f(x) as follows:
[tex]\begin{gathered} f(x)=-4\cdot2^{(1-x)} \\ f(x)=-4\cdot2^1\cdot2^{-x} \\ f(x)=-4\cdot2\cdot(2^{-1})^x \\ \\ f(x)=-8\cdot(\frac{1}{2})^x \end{gathered}[/tex]So, the answer will be option B
change percent to decimal 1,175%
Answers
The percentage can be changed to decimal as,
[tex]\begin{gathered} 1175\text{ Percent=}\frac{1175}{100} \\ =11.75 \end{gathered}[/tex]Thus, the required decimal is 11.75.
A swimming pool is in the form of a semicircular
Answers
The walk surrounding the pool has an area of 336.66 [tex]ft^{2}[/tex] .
A = ( Area of semicircle including side walk ) - ( Area of semicircle without side walk )
radius of smaller semicircle = 10 ft and radius of larger semicircle = 10 + 3 = 13 ft
A = [ ( 3.14 * [tex]13^{2}[/tex] ) / 2 ] - [ ( 3.14 * [tex]10^{2}[/tex] ) / 2 ]
= ( 530.66 - 314 ) / 2
= 108.33 [tex]ft^{2}[/tex]
Since we take walk on both sides , we will multiply it with 2
A = 2 * 108.33
A = 216.66[tex]ft^{2}[/tex]
One side of bigger rectangle = 20 + 3 + 3 = 26 ft
A = area of rectangle - area of square
A = ( 26 * 20 ) - [tex]20^{2}[/tex]
A = 120 [tex]ft^{2}[/tex]
Therefore ,
A = 216.66 + 120
A = 336.66 [tex]ft^{2}[/tex]
Hence , the walk surrounding the pool has an area of 336.66 [tex]ft^{2}[/tex] .
To learn more on area follow link :
https://brainly.com/question/28669602
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Jack is buying groceries. He decides to buy 50 total frozen entrees. He buys nothing but Burritos andHungry-Man Meals. The average price of a Hungry-Man Meal is $3.25 while the average price of a Burritois $2.00. If he spends $150 on all the frozen food, how many Hungry-Man Meals and Burritos did he buy?
Answers
Let x the total of Hungry-Man Meals bought.
let y the total of burritos bought.
He decides to buy 50 total frozen entrees.
x + y = 50
If we solve the equation for x
x = 50 - y
We also know that he spends $150 on all the frozen food.
Therefore:
x Hungry-Man Meals for $3.25
y burritos for $2.00
x(3.25) + y(2.00) = 150
3.25x + 2.00y = 150
Now substituting 50-y from the first equation into the second equation and solve for y:
3.25x + 2.00y = 150
3.25(50-y) + 2.00y = 150
3.25*50 - 3.25*y + 2.00y = 150
162.5 - 3.25y + 2.00y = 150
162.5 - 1.25y = 150
Subtract both sides by 150
162.5 - 150 - 1.25y = 150-150
12.5 -1.25y = 0
Add both sides 1.25y
12.5 -1.25y+1.25y= 0+1.25y
12.5 +0 = 1.25y
Divide both sides by 1.25
12.5/1.25 = 1.25y/1.25
10 = y
Substitute 10 for y in the result of the x equation:
x = 50 - y
x = 50- 10
x = 40
So 40 Hungry-Man meals and 10 burritos Jack bought.
they asking me to find the answer by using compatible numbers 9÷ 5,138 9 and ? are compatible. the estimate is?
Answers
SOLUTION
Now, 9 and 51 are not compatible because 51 cannot divide 9 without a remaider.
The compatible number with 9 that is close to 51 is 54.
Hence,
9 and 54 are compatible.
This will give us
[tex]\frac{5400}{9}=600[/tex]Hence,
The estimate is 600