Answers
Answer
x = 35°
y = 145°
z = 25°
Explanation
We are told to solve for x, y and z.
Considering the first triangle with angles 55°, x° and the right angle (90°).
The sum of angles in a triangle is 180°.
So,
x° + 55° + 90° = 180° (Sum of angles in a triangle is 180°)
x° + 145° = 180°
x = 180° - 145° = 35°
Then, we can solve for y. Angles x and y are on the same straight line, and the sum of angles on a straight line is 180°
x° + y° = 180°
35° + y° = 180°
y° = 180° - 35°
y° = 145°
We can then solve for z°. The big triangle has angles (55° + 10°), z° and the right angle (90°).
The sum of angles in a triangle is 180°.
So,
55° + 10° + z° + 90° = 180°
z° + 155° = 180°
z = 180° - 155°
z° = 25°
Hope this Helps!!!
Related Questions
Which number line represents the solution to the inequality
–4x – 12 < 12 ?
PLEASE ANSWER FAST
Answers
Answer:
x ≥ -6
Option C
Step-by-step explanation:
Hello!
We can solve the inequality by isolating x. Remember, flip the sign when you divide or multiply both sides by a negative number in an inequality.
Solve for x-4x - 12 ≤ 12-4x - 12 + 12 ≤ 12 + 12-4x ≤ 24-4x / -4 ≥ 24 / -4 => Flip the sign!x ≥ -6The answer is option c, all values greater than -6.
Can you please help me with 44Please use all 3 forms such as :up/down, as_,_ and limits
Answers
Given:
[tex]h(x)=(x-1)^3(x+3)^2[/tex]The x-intercepts of the given polynomial are
[tex]x-\text{intercepts }=1\text{ (multiplicity 3) and -3 (multiplicity 2)}[/tex]Substitute x=0 in h(x) to find y-intercepts.
[tex]\text{ y-intercepts =}(-1)^3(3)^2=-9[/tex][tex]\lim _{x\to-\infty}h(x)=\lim _{x\to-\infty}(x-1)^3(x+3)^2=-\infty[/tex][tex]as\text{ x}\rightarrow-\infty,\text{ h(x)}\rightarrow-\infty[/tex][tex]\lim _{x\to\infty}h(x)=\lim _{x\to\infty}(x-1)^3(x+3)^2=\infty[/tex][tex]as\text{ x}\rightarrow\infty,\text{ h(x)}\rightarrow\infty[/tex]The graph of the given polynomial h(x) is
The degree of the polynomial is 6=even and the leading coefficient=1=positive.
Both ends of the graph point up.
End behaviour is
up/up.
exponent hw.simplify
Answers
Answer:
4
Explanation:
Given the below;
[tex]4m^0[/tex]To simplify the above, we have to note that any number or variable raised to the power of 0 is 1.
So, we'll have;
[tex]4m^0=4\times1=4[/tex]To get the variable r alone on one side of the equation below, Amy multiplied both sides of the equation by 4. is she correct? Explain why or why not. Solve the equation. 4r = 124
Answers
Given the equation
4r=124
You have to clear the value of r, this is, that r ends up alone in one side of the equation and the rest of the terms of the equation stay in the other side.
As you can see r is being multiplied by 4, to nullify this multiplication you have to "reverse the operation" that is, divide it by four.
And for the equality to continue, every operation made in one side of the equation has to be done in the other side, this means that if you divide 4r by 4, you have to divide 12
Theo sales person makes $350 each week plus an additional $28 per sale. Theo wants his paycheck to be at least $550 each week. Solve the inequality and choose the best answer to the scenario.
Answers
Let x be the number of sales
350 + 28x > (larger than or equal to) 550
Subtract 350 from each side
28x > 200
x > 7.142 (Round up)
Therefore, x is 8.
clarissa's division test was a 60% the first six weeks and a 72% the second six weeks. find the percent change.
Answers
The required change in the percentage is 20%.
Given that,
clarissa's division test was 60% in the first six weeks and 72% in the second six weeks. To determine the percent change.
The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
According to the question,
The change in the percentage = (72 - 60) / 60 × 100
The change in the percentage = 20%
Thus, the required change in the percentage is 20%.
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used to figure for exercises two through nine period determine whether each pair of lines are parallel or perpendicular. right yes or no
Answers
2. q and v are parallel. YES
3. r and s are parallel. NO
4. r and t are parallel. NO
5. s and u are parallel. YES
6. q and s are perpendicular. NO
7. q and v are perpendicular. NO
8. r and s are perpendicular. YES
9. t and v are perpendicular. YES
The value of a collectible coin can be represented by the equation+9 74 where x represents the number ofyears that Consuello has owned the coin and y represents the total value, in dollars, of the coin. What was the valueof the coin when Consuello originally purchased it?
Answers
Given:
The value of a collectible coin can be represented by the equation
[tex]y=2x+9.74[/tex]Required:
We need to find the original purchased value
Explanation:
To find the orginal value we just put
[tex]x=0[/tex][tex]\begin{gathered} y=2*0+9.74 \\ y=9.74 \end{gathered}[/tex]Final answer:
The original value is $9.74
9) Find the slope of the line that passes through these two points. (0.3) and (4, -2)
Answers
To find the slope of the line that passes through points (0, 3) and (4, -2), we can use the formula for the slope of a line:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]We have then:
(0, 3) ---> x1 = 0, y1 = 3
(4, -2) --->x2 = 4, y2 = -2
Therefore:
[tex]m=\frac{-2-3}{4-0}\Rightarrow m=\frac{-5}{4}\Rightarrow m=-\frac{5}{4}[/tex]Then, the slope of the line that passes through points (0, 3) and (4, -2) is m = -5/4.
You have the option of loaning money to one friend who promises to pay simple interest or to another friend who promises to pay the same APR but compound the interest. Which would you choose, and why?
Answers
I would loan my money to the one who pays the compound interest.
This is because more money would be generated from the compound interest as it is based on the principal (Amount loaned) and also the interest generated from the loan. Unlike simple interest that is only based on the principal.
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 35 N acts on a certain object, the acceleration of the object is 5 m/s^2. If the force is changed to 49 N what will be the acceleration of the object?
Answers
Answer:The acceleration that an objects gains is given by the mass of the object.
If the acceleration of the object becomes 5 m/s² the force is 15 N.
Reason:
The given parameters are;
The acting force ∝ The acceleration of the object.
The acceleration given by an amount of force, F, of 18 N = 6 m/s²
Required:
The force acting on the object acceleration, a, is 5 m/s².
Solution:
According to Newton's Second Law of motion, we have;
F = m·a
Where;
m = The mass of the object
Therefore, we have;
From the conditions, F = 18 N, when a = 6 m/s², we have, the mass of the
given object is given as follows;
The force acting when the the acceleration, a = 5 m/s², is therefore;
F = 3 kg × 5 m/s² = 15 N
If the acceleration of the object becomes 5 m/s² the force is 15 N.
Step-by-step explanation:
I need help solving this I’m having trouble with it is from my trigonometry prep bookIf you can **** use Desmos to graph the function that is provided in the picture
Answers
So we have to graph the function:
[tex]f(x)=\cot (x+\frac{\pi}{6})[/tex]First is important to note that the cotangent can be defined by the quotient between the cosine and the sine:
[tex]\cot (x+\frac{\pi}{6})=\frac{\cos(x+\frac{\pi}{6})}{\sin(x+\frac{\pi}{6})}[/tex]By looking at this new expression we can infer a few things about the graph. First of all, we have a sine in the denominator which means that the denominator can be equal to 0. Let's assume that the denominator is 0 at x=a. Then the graph has a vertical asymptote at x=a. What's more, the sine is a periodic funtion that is equal to zero for an infinite amount of x values so the graph of the cotangent has infinite vertical asymptotes. The good part is that we just need to graph one full period and in the case of the cotangent one full period is completed between two consecutive vertical asymptote. So basically we have to find two consecutive vertical asymptote and graph the function between them.
So let's begin by finding two x values that makes the denominator equal to 0. The sine is equal to 0 when its argument is equal to 0 and the next value at which the sine is equal to zero is pi so:
[tex]\sin 0=0=\sin \pi[/tex]Then we can construct two equations:
[tex]\begin{gathered} \sin (x+\frac{\pi}{6})=0=\sin 0 \\ \sin (x+\frac{\pi}{6})=0=\sin \pi \end{gathered}[/tex]The equations are:
[tex]\begin{gathered} x+\frac{\pi}{6}=0 \\ x+\frac{\pi}{6}=\pi \end{gathered}[/tex]We can substract π/6 from both sides of both equations:
[tex]\begin{gathered} x+\frac{\pi}{6}-\frac{\pi}{6}=0-\frac{\pi}{6} \\ x=-\frac{\pi}{6} \\ x+\frac{\pi}{6}-\frac{\pi}{6}=\pi-\frac{\pi}{6} \\ x=\frac{5\pi}{6} \end{gathered}[/tex]So we have a vertical asymptote at x=-π/6 and another one at x=5π/6. This means that we just need to graph f(x) between these two vertical lines. It is also important to note that f(x) reaches positive or negative values when the value of x approaches to -π/6 or 5π/6.
Now that we have the asymptotes let's find the x-intercept i.e. the point where f(x) meets with the x-axis. This happens when f(x)=0 which happens when the numerator is equal to 0. Then we get:
[tex]\cos (x+\frac{\pi}{6})=0[/tex]The cosine is equal to zero at π/2 so we have:
[tex]\begin{gathered} \cos (x+\frac{\pi}{6})=0=\cos \frac{\pi}{2} \\ x+\frac{\pi}{6}=\frac{\pi}{2} \end{gathered}[/tex]We can substract π/6 from both sides:
[tex]\begin{gathered} x+\frac{\pi}{6}-\frac{\pi}{6}=\frac{\pi}{2}-\frac{\pi}{6} \\ x=\frac{\pi}{3} \end{gathered}[/tex]So the x-intercept is located at x=π/3. So for now we have the x-intercept and two vertical asymptotes so at the moment we have the following:
The black dot is the x-intercept at (π/3,0) and the dashed lines are the asymptotes. Our function passes through the black dot and is limited by the asymptotes.
We still need to find if it reaches positive or negative infinite values when approaching to the asymptotes. As we saw the function is equal to zero at x=π/3. This means that between the first asymptote and x=π/3 the function is either entirely positive or entirely negative. The same happens with the interval between x=π/3 and the second asymptote. So we have two intervals where the function mantains its sign: (-π/6,π/3) and (π/3,5π/6). Let's evaluate f(x) in one value of each interval and see if it's positive or negative there. For example, x=0 is inside the first interval and x=2 is inside the second interval:
[tex]\begin{gathered} f(0)=1.73205>0 \\ f(2)=-1.4067<0 \end{gathered}[/tex]So f(x) is positive at (-π/6,π/3) which means that as x approaches to -π/6 from the right it reaches positive infinite values. We also have that f(x) is negative at (π/3,5π/6) so as x approaches 5π/6 from the left the function reaches negative infinite values.
Using this information and the fact that the graph must pass throug the x-intercept we can graph the function. It should look like this:
And that's the graph of f(x).
a farmer has 150 yards of fencing to place around a rectangular garden. the fence will have an opening that is 1/3 of the gardens length(see picture). write a function a(x) that describes the area of the garden.Find the dimensions of the garden if it has the maximum area, and find the maximum area.
Answers
By forming equations, we know that the garden is 37.5 yards long, and 37.5 yards wide, and it has an opening that is 12.5 yards wide.
What are equations?A mathematical equation is a formula that uses the equals sign to express the equality of two expressions. A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 = 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.So, the dimensions and area of the garden:
Let x and y stand for length and width, respectively.There are 150 yards of fencing available, so:
2(x + y) = 150x + y = 75y = 75 - x ...(1)The garden's area (A) is given as follows:
A = xyA = x(75 - x)A = 75x - x²At A' = 0, the area is largest.
A' = 75 - 2x75 - 2x = 0x = 37.5 yardsy = 75 - x y = 75 - 37.5 = 37.5Garden opening: 1/3 × 37.5 = 12.5 yards
Therefore, by forming equations, we know that the garden is 37.5 yards long, and 37.5 yards wide, and it has an opening that is 12.5 yards wide.
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The correct question is given below:
A farmer has 150 yards of fencing to place around a rectangular garden. The fence will have an opening that is 1/3 of the garden's length. Write a function A(x) that describes the area of the garden, where x is the length of the garden. Find the dimensions if that has a maximum area, and find the maximum area
Answer:
The length is 45 yards.
The width is 37.5 yards.
The area is 1,687.5 yards
Step-by-step explanation:
I go to RSM too lolol
The other answer posted here was incorrect. Since the length and width DID have a relatively equal factor without the -12.5 yard opening taken into account, you'd usually get 37.5 yards.
BUT, if we use the width and subtract it from the total (which we'd get 75 yards left), we can see that in the total length, a sixth (it is 1/6th since we are taking both sides) is taken from that. 75 is easily dividable by 5, so we can take 15, and multiply it by 3. We'd then get 45 yards in total for each side (minus the 12.5 yard opening).
All you need to do now is multiply the length and width to get 1,687.5 yards.
Now get a 100 on that RSM assignment and get the bragging rights for your class. You can thank me later. Your homework is more important.
Your friend says, "If a quadrilateral has a pair of opposite sides that are congruent 6 points and a pair of opposite sides that are parallel, then it is a parallelogram." What is your friend's error? Explain.
Answers
to be a parallelogram we need to have the 2 pairs of sides to be parallel so the correct option is C
Question 6 of 25Simplify the radical expression below.이히O A.A.v28O B.9O c.NIC3
Answers
We need to simplify the next given expression:
[tex]\sqrt{\frac{2}{9}}[/tex]We can rewrite it as:
[tex]\sqrt{\frac{2}{9}}=\frac{\sqrt{2}}{\sqrt{9}}[/tex]Solve each square root:
√2 =√2
√9 = 3
Then, the result is:
[tex]=\frac{\sqrt{2}}{3}[/tex]Hence, the correct answer is option A.
Home Liquidators marks up its merchandise 35% on cost. What is the company’s equivalent markup on selling price?
Answers
The company’s equivalent markup on selling price is 26%.
What is markup?The markup is the gap between the selling price and the cost of a good or service. It is frequently represented as a percentage of the total cost. To cover the costs of doing business and generate a profit, a markup is added to the overall cost borne by the manufacturer of a good or service.
The following can be deduced based on the information:
Markup on cost = 35%
Cost = 100%
Selling price = 135%
Markup on selling price will be:
= (0.35/1.35 x 100)
= 26%
Therefore, the value is 26%.
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a shelf is in the shape of a triangle. find the angle of the triangle if the measure of the angles are in the ratio of x:x:4x.x=4x=
Answers
ANSWER
30°, 30° and 120°
EXPLANATION
We want to find the measures of the angles of the triangle if the ratio of the angles is x : x : 4x
In other words, the ratio is 1 : 1 : 4
The total angle in a triangle is 180°.
Therefore, we have to find the value of x. To do this, we first find the total ratio:
[tex]\begin{gathered} 1+1+4 \\ =6 \end{gathered}[/tex]Now, find x by apply ratios. x is equal to 1/6 of the total angle of the triangle:
[tex]\begin{gathered} x=\frac{1}{6}\cdot180 \\ x=30\degree \end{gathered}[/tex]Now, find 4x:
[tex]\begin{gathered} 4\cdot x=4\cdot30 \\ =120\degree \end{gathered}[/tex]Therefore, the ratio of angles is:
[tex]30\degree\colon30\degree\colon120\degree[/tex]In other words, the angles are 30°, 30° and 120°.
Find the slope of the two points: (-3,-2) & (5, -8)
ter Numerical value ONLY. NO Decimals
*
Answers
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-8}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{(-3)}}} \implies \cfrac{-8 +2}{5 +3} \implies \cfrac{ -6 }{ 8 } \implies - \cfrac{ 3 }{ 4 }[/tex]
I need help on 3 it says find the value of x round each answer to the nearest tenth
Answers
In problem 3, we have a right triangle with:
• cathetus ,a = 7,,
,• cathetus ,b = x,,
,• and hypotenuse ,h = 9,.
Pigatoras Theorem states that:
[tex]h^2=a^2+b^2.[/tex]Where a and b are cathetus and h the hypotenuse.
Replacing the data of the problem in the equation above, we have:
[tex]9^2=7^2+x^2.[/tex]Solving for x the last equation, we get:
[tex]\begin{gathered} 81=49+x^2, \\ x^2=81-49, \\ x^2=32, \\ x=\sqrt[]{32}\cong5.7. \end{gathered}[/tex]Answer
The value of x to the nearest tenth is 5.7.
I already wrote the answer I just need you to work it out for me please and thank you
Answers
Answer:
[tex]A=470\frac{1}{4}ft^2[/tex]Detailed Explanation: The area of the figure provided is the sum of two areas, a rectangle, and a triangle:
The total area is calculated next, and the necessary steps are shown as follows
[tex]\begin{gathered} A=A_1+A_2 \\ A_1=\frac{1}{2}(b\cdot h)=\frac{1}{2}\cdot\lbrack(25ft-22.5ft)\times19.8ft\rbrack \\ A_1=\frac{1}{2}\cdot\lbrack2.5ft\times19.8ft\rbrack=\frac{49.5ft^2}{2}=24.75ft^2 \\ A_1=24.75ft^2 \\ A_2=w\cdot h=22.5ft\cdot19.8ft=445.5ft^2 \\ A_2=445.5ft^2 \\ \therefore\Rightarrow \\ A=A_1+A_2=24.75ft^2+445.5ft^2 \\ A=470.25ft^2 \\ A=470\frac{1}{4}ft^2 \end{gathered}[/tex]!!PLEASE ANSWER FAST PLEASE!! Given f(x)=(1/4)(5-x)² what is the value of f(11)
Answers
Answer:
f(11) = 9
Explanation:
The equation for f(x) is:
[tex]f(x)=\frac{1}{4}(5-x)^2[/tex]To know the value of f(11), we need to replace x by 11 and solve, so:
[tex]\begin{gathered} f(11)=\frac{1}{4}(5-11)^2 \\ f(11)=\frac{1}{4}(-6)^2 \\ f(11)=\frac{1}{4}(36) \\ f(11)=9 \end{gathered}[/tex]Therefore, the value of f(11) is 9.
Joyce paid $154.00 for an item at the store that was 30 percent off the original price. What was the original price?
Answers
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Question 23A company's logo was designed using circles of 3 different sizes. The diameters of two of the circles are shown6 cm12 cmWhich measurement is closest to the area of the largest circle in square centimeters?D2021 Illuminate Education Inc.
Answers
SOLUTION
A company's logo was designed using circles of 3 different sizes. The diameters of two of the circles are shown:
6 cm
12 cm
Which measurement is closest to the area of the largest circle in square centimeters?
The measurement is closest to the area of the largest circle in square centimeters is
12 cm since it has a radius of 6 cm with 36 pi square centimetres; unlike the diameter
of 6 cm which has 3 cm radius and 9 pi square centimetres.
The correct answer is 12 cm.
In the figure, what set of angles are corresponding angles?angle 6 and angle 7angle 5 and angle 7angle 1 and angle 7angle 4 and angle 7
Answers
Step 1
In geometry, corresponding angles are formed where a line known as an intersecting transversal, crosses through a pair of straight lines. Corresponding angles are the pairs of angles that are found in the same relative position on different intersections.
Step 2
Find the set of corresponding angles
[tex]\text{Angle 4 and angle 7}[/tex]Hence, the set of corresponding angles is; angle 4 and angle 7
What is the total population of the four cities shown in the table? Express your answer in scientific notation and in standard form.
Answers
Scientific notation is a way of writing large or small numbers that have many digits in a simplified form. The index of the base 10 exponents indicates the number of digits there are after the decimal dot.
The table shows the population of 4 cities of Texas, Houston, San Antonio, El Paso, and Corpus Christi.
To determine the total population of all cities you have to add them together, the first step is to express each given population in standard form:
Houston:
[tex]2.3\cdot10^6[/tex]This notation indicates that there are 6 digits after the decimal dot, the first one is 3 and the other five digits are zero. The positive index indicates that this number is greater than 1, so to write the number in the standard form you have to erase the decimal dot:
[tex]2.3\cdot10^6=2300000[/tex]San Antonio:
[tex]1.5\cdot10^6[/tex]The notation indicates that there are 6 digits after the decimal point, the first one is 5 and the other five digits are zero. The positive exponent indicates that this number is greater than 1, so you have to erase the decimal dot:
[tex]1.5\cdot10^6=1500000[/tex]El Paso:
This population is already given in the standard form
[tex]680000[/tex]Corpus Christi:
[tex]3.2\cdot10^5[/tex]This notation indicates that there are 5 digits after the decimal dot, the first one is 5 and the next four are zero. The exponent is positive, so as mentioned before, this number is greater than one, and to write it in the standard form you have to erase the decimal dot:
[tex]3.2\cdot10^5=320000[/tex]Now that all values are expressed in the standard form you can add them:
[tex]2300000+1500000+680000+320000=4800000[/tex]In the standard form, the total population of the four cities is 4,800,000 people
To express this value using scientific notation you have to write the decimal dot after the first digit and then count the number of digits after the decimal dot.
When you use scientific notation you have to write only the digits that are different than zero.
There are 6 digits after the decimal dot, so the exponent of the base 10 number will be 6, and the result expressed in scientific notation is:
[tex]4.8\cdot10^6\text{people}[/tex]difference between managerial and financial accounting?
Answers
The main difference between managerial accounting and financial accounting is who the statement is being prepared for.
What differentiates managerial and financial accounting?There are several things that differentiate managerial accounting from financial accounting but the main one is the target of the financial statements.
Financial accounting is used for financial statements for those outside the company such as investors, customers, and the government. As such, it has to abide by certain standards.
Managerial accounting on the other hand, is for managers and decision makers in the company. It is less restrictive as the main goal is to provide information for managers and not those outside.
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Translate the sentence into an inequality, the product of c and 9 is greater than 16.
Answers
In order to write an inequality we can read the original statement in small parts.
In this case, the statement is:
"the product of c and 9 is greater than 16"
We have that "the product" is a multiplication
Then, "the product of c and 9" is the multiplication between c and 9:
9 · c
And, "the product of c and 9 is greater than 16" means that 9 · c is greater than 16:
9 · c > 16
Answer: 9 · c > 16When a stone is dropped in a pond ripples are formed and travel in concentric circles away from where the stone was dropped. The relationship between the time and area if the circles was analyzed and is shown in the computer output.
What is the equation of the least/squares regression line?
Answers
When a stone is dropped in a body of water, ripples are created and move outward in concentric rings. The least-squares regression line has the equation Area = 0.010 + 3.141 (Time2).
The least squares regression equation is the equation y=1x+0 that specifies the least squares regression line.
the least squares regression line's y=1x+0 equation.
What is relationship between time and distance?Time (t = d/v) or, alternatively, time = speed/distance (v = d/t).
Concentric circles are those that share a common center but have differing radii. It is described as two or more circles with the same center, in other words. An annulus is the space between two concentric circles with dissimilar radii.
Concentric circles are two or more circles with the same center but various radii. Congruent circles are any two or more circles that have the same radius but different centers.
Concentric circles are those that share a common center but have differing radii. It is described as two or more circles with the same center, in other words.
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Three cities, A, B, and C, are located so that city A is due east of city B. If city C is located 35° west of north from city B and is 100 miles from city A and 70 milesfrom city B, how far is city A from city B?City Ais 20 miles due east of city B.City A is 35 miles due east of city B.City A is 42 miles due east of city B.City A is 122 miles due east of city B.
Answers
Given:
City A is due east of city B.
City C is located 35° west of north from city B.
Distance between city C and city A is 100 miles.
Distance between city C and city B is 70 miles.
The objective is to find the distance between city A and city B.
The above situation can be represented as,
Thus the total angle of ∠B = 90°+35° = 125°.
Now the measure of angle A can be calculated by law of sines.
[tex]\begin{gathered} \frac{AC}{\sin B}=\frac{BC}{\sin A} \\ \frac{100}{\sin125\degree}=\frac{70}{\sin A} \\ \sin A=70\cdot\frac{\sin 125\degree}{100} \\ \sin A=0.573 \\ A=\sin ^{-1}(0.573) \\ A\approx35\degree \end{gathered}[/tex]By the angle sum property of triangle the value of angle C can be calculated as,
[tex]\begin{gathered} \angle A+\angle B+\angle C=180\degree \\ 35\degree+125\degree+\angle C=180\degree \\ \angle C=180\degree-35\degree-125\degree \\ \angle C=20\degree \end{gathered}[/tex]Now, the distance between A and B can be calculated by,
[tex]\begin{gathered} \frac{AB}{\sin C}=\frac{BC}{\sin A} \\ \frac{AB}{\sin20\degree}=\frac{70}{\sin 35\degree} \\ AB=\sin 20\degree\cdot\frac{70}{\sin 35\degree} \\ AB\approx42\text{ miles} \end{gathered}[/tex]Thus, the distance of city A is 42 miles due east of city B.
Hence, option (C) is the correct answer.
A parabola contains the following points.(-5,8),(2,-3),(3,1) which of the following systems of equations could be solved in order to find the equation that corresponds to this parabola?
Answers
Generic parabola equation:
y = a*x^2 + b*x + c
We have three points of the parabola:
(-5,8), (2,-3), (3,1)
For the point (-5, 8): x = -5, y = 8
8 = 25*a - 5*b + c
Point (2,-3): x = 2, y = -3
-3 = 4*a + 2*b + c
Point (3, 1): x = 3, y = 1
1 = 9*a + 3*b + c
Our system of equations:
8 = 25*a - 5*b + c
-3 = 4*a + 2*b + c
1 = 9*a + 3*b + c
The last option is the correct answer