You leave your house and run 6 miles due west followed by 3.5 miles due north. At that time, what is your bearing from your house?
Answers
N 60° W
Explanation
Step 1
draw the situation
we have a right triangle, so we can use a trigonometric function to find the missing angle,
then
Let
[tex]\begin{gathered} \text{opposite side= 3.5 m} \\ \text{adjacent side=6 mi} \end{gathered}[/tex]so, we need a function that relates those values
[tex]\tan \alpha=\frac{opposite\text{ side}}{\text{adjacent side}}[/tex]replace
[tex]\begin{gathered} \tan x=\frac{3.5}{6} \\ \text{ Inverse tan in both sides} \\ \tan ^{-1}(\tan x)=\tan ^{-1}(\frac{3.5}{6}) \\ x=30.25 \\ \text{rounded } \\ x=30\text{ \degree} \end{gathered}[/tex]so, the direction is
N 60° W
Related Questions
Finds the measures of angle b and d given that m ll n. Explain.
Answers
Answer:
b = 60.7
d = 43.1
Explanation:
The angles of measure 60.7 and b are alternate interior angles because they are on opposite sides of the transversal and in the inside of the parallel lines m and n. These angles have the same measure, so
b = 60.7
Angle d and the angle of measure 136.9 form a straight line, so they sum to 180 degrees. Therefore, the measure of angle d is
d = 180 - 136.9 = 43.1
Therefore, the answers are
b = 60.7
d = 43.1
the product of a number of -9
Answers
If we have a number x, if we take the product of this number by -9:
[tex]-9\cdot x[/tex]Can I please get help with question 1 practice questions
Answers
Given:
Line pass through ( 3, 4)
Parallel to the,
[tex]y=-\frac{2}{3}x+1[/tex]Find-:
The equation of a line.
Explanation-:
The slope of the parallel line is also the same.
[tex]m_1=m_2[/tex]Where
m is the slope of a parallel line
The general equation of a line is:
[tex]y=mx+c[/tex]So the equation become is:
[tex]\begin{gathered} y=mx+c \\ \\ y=-\frac{2}{3}x+c \end{gathered}[/tex]The line pass ( 3,4)
That mean,
[tex](x,y)=(3,4)[/tex][tex]\begin{gathered} y=-\frac{2}{3}x+c \\ \\ (x,y)=(3,4) \\ \\ 4=-\frac{2}{3}(3)+c \\ \\ 4=-2+c \\ \\ c=4+2 \\ \\ c=6 \end{gathered}[/tex]So the equation of a line is:
[tex]\begin{gathered} y=-\frac{2}{3}x+6 \\ \\ y=\frac{-2x}{3}+\frac{18}{3} \\ \\ y=\frac{-2x+18}{3} \\ \\ 3y=-2x+18 \\ \\ 2x+3y=18 \end{gathered}[/tex]
Ramblin Roy is a dirt bike boy. One day he drives his dirt bike over to a big race. There were 178 vehicles at the race, a mix of cars and dirt bikes. Altogether there were 602 wheels on the vechicles. How many cars were there ( x) ? How many dirt bikes were there ( y ) ? A. ( 55, 123 ) B. ( 123, 55 ) C. ( 178 , 602 ) D. None of the above
Answers
There are x cars and y bikes.
The equation for the total number of vechiles is,
[tex]\begin{gathered} x+y=178 \\ y=178-x \end{gathered}[/tex]In a car, there are 4 vechiles and in a bike there are two wheels. So the equation for the wheels,
[tex]\begin{gathered} 4x+2y=602 \\ 2x+y=301 \end{gathered}[/tex]Substitute (178 - x) for y in the equation 2x + y = 301 to obtain the value of x.
[tex]\begin{gathered} 2x+178-x=301 \\ x=301-178 \\ =123 \end{gathered}[/tex]Substitute 123 for x in the equation y = 178 - x to obtain the value of y.
[tex]\begin{gathered} y=178-123 \\ =55 \end{gathered}[/tex]So number of cars are 123 and number of bikes are 55. So correct option is
B. ( 123, 55 )
Is the expression below quadratic?3x + 5y - 2A. TrueB.False
Answers
A quadratic expression is given by the following form:
[tex]Ax^2+Bx+C[/tex]Therefore:
[tex]3x+5y-2[/tex]Is not a quadratic expression
A 40 kilogram bag of seeds are spread out throughout the entire yard, how much in kilograms of seeds will not be watered? Percentage of my previous question is 96.1%In the last question 96.1% of grass was covered in water Their were 123 squares that got water except 5 of them so I divided 123 by 128 to find the percentage of grass covered by waterIf their were 5 squares that didn’t get water out of 128 then can’t we work from that? To find the 40 kilograms that wouldn’t get water from those 5 squares
Answers
5 squares of 128 didn't get water.
If 40kg are spread out throughout the entire yard, how much in kilograms of seeds will not be watered?
Use a rule of three to solve the question:
[tex]\begin{gathered} x=\frac{40\cdot5}{128} \\ \\ x=\frac{200}{128} \\ \\ x=1.56 \end{gathered}[/tex]Then, 1.56 kilograms of seeds will not be watered
Helaine graphed the equation 12x-4y=3 . what was the slope of Helaines line
Answers
The slope of Helaine's line is 3
Explanations:Note that:
The slope - Intercept form of the equation of a line is:
y = mx + c
Where m = the slope
c = the intercept
The given equation is:
12x - 4y = 3
Rewrite the above equation in the form y = mx + c
4y = 12x - 3
Divide through by 4
[tex]\begin{gathered} \frac{4y}{4}=\frac{12x}{4}-\frac{3}{4} \\ \\ y\text{ = 3x - }\frac{3}{4} \end{gathered}[/tex]The slope, m = 3
The intercept, c = -3/4
Therefore, the slope of Helaines line is 3
Hello! Please check the image attached to see the question!
Answers
To solve this question, we must break down the question into different scenarios.
The speed expression for the first rider is:
[tex]\begin{gathered} s=\frac{d}{t} \\ \text{let us make the distance the first rider covers as y.} \\ d=y\text{ miles} \\ t=3\text{ hours.} \\ s_1=\frac{y}{3} \end{gathered}[/tex]The speed expression for the second cyclist:
[tex]\begin{gathered} s=\frac{d}{t} \\ the\text{ first rider covered a distance of y miles, the remaining distance } \\ \text{left for the second cyclist to cover is:} \\ (108-y)\text{miles at the same time of 3 hours.} \\ s_2=\frac{108-y}{3} \end{gathered}[/tex]Since one cyclist cycles 3 times as fast as the other:
It is expressed thus:
[tex]\begin{gathered} s_1=3\times s_2 \\ s_1=3s_2 \end{gathered}[/tex]Now substitute the values for the speed expression into the expression above, we will have:
[tex]\frac{y}{3}=3\times(\frac{108-y}{3})[/tex]By solving the above expression, we will get the value of y (part of the distance travelled) and we can get the speed of the faster cyclist.
[tex]\begin{gathered} \frac{y}{3}=\frac{324-3y}{3} \\ y=324-3y \\ y+3y=324 \\ \end{gathered}[/tex][tex]\begin{gathered} 4y=324 \\ y=\frac{324}{4} \\ y=81\text{ miles.} \\ \\ So\text{ the speed of the faster cyclist will be:} \\ _{}=\frac{y}{3} \\ =\frac{81\text{ miles}}{3\text{ hours}} \\ =27mi\text{/h} \end{gathered}[/tex]The speed of the faster cyclist is 27 mi/h.
Determine the volume of the rectangular prism.3 cm3 cm5 1/4cm
Answers
Answer:
47.25 cubic centimetres
Explanation:
The volume of the prism is the product of its dimensions.
[tex]3\operatorname{cm}\times5\frac{1}{4}cm\times3\operatorname{cm}[/tex]Now,
[tex]5\frac{1}{4}=5+\frac{1}{4}[/tex]multiplying 5 by 4/4 gives
[tex]\frac{4\cdot5}{4}+\frac{1}{4}[/tex][tex]=\frac{21}{4}[/tex]Therefore,
[tex]3\operatorname{cm}\times5\frac{1}{4}cm\times3\operatorname{cm}=3\operatorname{cm}\times\frac{21}{4}cm\times3\operatorname{cm}[/tex][tex]=3\cdot\frac{21}{4}\cdot3\operatorname{cm}^3[/tex][tex]=\frac{3\cdot21\cdot3}{4}cm^3[/tex][tex]=\frac{189}{4}cm^3[/tex][tex]=47.25\operatorname{cm}^3[/tex]Find the distance between the pair of parallel lines with the given equations.y = -5xy = -5x + 26A) 5 unitsOB) 10V2 or about 14.14 unitsOC)/26 or about 5.10 unitsO D) 6 units
Answers
For two lines of the form:
[tex]\begin{gathered} y_1=a_1x+c_1 \\ \text{And} \\ y_2=a_2x+c_2 \end{gathered}[/tex]The distance between the two lines is:
Name the type of angle relationship. If no relationship exists, write "none. a. <1 and < 8 b. < 2 and < 3 C. < 5 and <7 d. < 2 and < 7 e. <1 and < 3 f. < 5 and <8
Answers
Answers:
a. ∠1 and ∠8: Alternate exterior Angles.
b. ∠2 and ∠3: None
c. ∠5 and ∠7: Corresponding angles.
d. ∠2 and ∠7: Alternate interior angles.
e. ∠1 and ∠3: Corresponding angles
f. ∠5 and ∠8: None
Explanation:
a. ∠1 and ∠8: Alternate exterior Angles. They are externals, on opposite sides, and they are formed by the transversal of two lines.
b. ∠2 and ∠3: None
c. ∠5 and ∠7: Corresponding angles. One is internal and the other is external and they are on the same side of the transversal.
d. ∠2 and ∠7: Alternate interior angles. They are interior, on opposite sides, and they are formed by the transversal of two lines.
e. ∠1 and ∠3: Corresponding angles. One is internal and the other is external and they are on the same side of the transversal.
f. ∠5 and ∠8: None
Lincoln went into a movie theater and bought 2 bags of popcorn and 4 candies, costing a total of $34. Zoey went into the same movie theater and bought 6 bags of popcorn and 5 candies, costing a total of $74. Determine the price of each bag of popcorn and the price of each candy.
Answers
12 each bags
Step-by-step explanation:
2x +4y =34
6x +5y =74
x =34- 4y ÷2
y = $3
x= $ 11
bag each price is $11
The price of one bag of popcorn is $9 and the price of one candy is $4.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
Let the price of 1 bag of popcorn = x
And price of 1 candy = y
Given that,
Lincoln buys 2 bags of popcorn and 4 candies for $34
implies that,
2x + 4y = 34 (1)
Also, Zoey buys 6 bags of popcorn and 5 candies for $74
implies that,
6x + 5y = 74 (2)
By solving equation (1) and (2),
x = 9 and y = 4
The price of one bag of popcorn is $9 and the price of one candy is $4.
To know more about Equation on:
https://brainly.com/question/187506
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If the m angle3 is 112 then find the value of the missing angle measure
Answers
Question:
Solution:
According to the diagram, we get the following equations:
Equation 1:
[tex]m\angle1\text{ + m}\angle2=180^{\circ}[/tex]Equation 2:
[tex]m\angle4\text{ + m}\angle3=180^{\circ}[/tex]the angle 3 is 112 degrees, so replacing this value into the previous equation, we get:
[tex]m\angle4+112^{\circ}=180^{\circ}[/tex]solving for angle 4, we get:
[tex]m\angle4\text{ }=180^{\circ}-112^{\circ}=68^{\circ}[/tex]now, note that
Equation 3:
[tex]m\angle4\text{ + m}\angle1=180^{\circ}[/tex]but the angle 4 is 68 degrees, so replacing this into the above equation, we get:
[tex]68^{\circ}\text{ + m}\angle1=180^{\circ}[/tex]solving for angle 1, we get :
[tex]\text{ m}\angle1=180^{\circ}-68^{\circ}=112^{\circ}[/tex]Finally, from equation 1, we get:
[tex]112^{\circ}\text{ + m}\angle2=180^{\circ}[/tex]then,
[tex]\text{ m}\angle2=180^{\circ}-112^{\circ}=68^{\circ}[/tex]we can conclude that the correct answer is:
[tex]\text{ m}\angle1=112^{\circ}[/tex][tex]\text{ m}\angle2=68^{\circ}[/tex][tex]\text{ m}\angle3=112^{\circ}[/tex][tex]m\angle4\text{ =}68^{\circ}[/tex]
Drag the red and blue dots along the x-axis and y-axis to graph 7x+3y=127x+3y=12
Answers
Answer:
Explanation:
A linear equation can be graphed in a simple manner. We just have to find two points that lie on the line of the equation and then connect them to produce a line.
Now what two points lie on 7x + 3y = 12?
Well, let us pick a point where x = 0. What is the y-coordinate? Putting x = 0 into our equation gives
[tex]\begin{gathered} 7(0)+3y=12 \\ 3y=12 \end{gathered}[/tex]diving both sides by 3 gives
[tex]\begin{gathered} y=12/3 \\ y=4 \end{gathered}[/tex]Hence a point with x = 0, y= 4 lies on the line. In other words, (0, 4) lies on the line.
We now need to find a second point that lies on the line. How about
12. Which of the following is a function?(A)(B)(C)(D) {(-5,9), (-2,-5),(1,-5),(5,-2)} (E){(-5,9),(-2,-5),(1,-5).(-5,-2)}
Answers
Explanation:
A relation is a function if and only if there is one value of x for different values of y.
This means that if we see repeated x-values then it's not a function. We can see this clearly in the graphs by drawing a vertical line for the values of x. Of the line crosses the graph more than once, then it's not a function.
In every graph the line crosses the graph more than once, so none of these options are functions.
Then, for a set of points we have to check the x-coordinate of each pair. If one repeats in the set, then it's not a function.
In the relation E x = -5 is repeated, so it's not a function. On the other hand, for relation D none of the x-coordinates are repeated. Therefore relation D IS a function
Answer:
Option D is a function
What is 57.629 in expanded form?
Answers
To write a number in expanded form, we have to separate it to see the math value of individual digits.
In this case, for the number 57.629, the expanded form is:
[tex]57.629=50+7+0.6+0.02+0.009[/tex]about 3.9×10 people live in California about 1.3×10 people live in Maine about how many more people live in California than in Maine
Answers
so the answer is
[tex]3.77\times10^7[/tex]There are 12 inches in 1 foot How many inches are in 2 feet? Enter your answer in the box There are inches in 2 feet.
Answers
24 "
1) Since there are 12 inches in 1 foot we can set a proportion, and find the missing measure:
inches feet
12 1
x 2
x = 12 * 2
x= 24
2) So there are 24 inches in 2 feet.
i need help woth this asap i cant get it wrong
Answers
The given equation is a quadratic equation. Recall, the standard form of a quadratic equation is expressed as
ax^2 + bx + c = 0
The given equation is
x^2 - 8x = - 128
By adding 128 to both sides of the equation, we have
x^2 - 8x + 128 = - 128 + 128
x^2 - 8x + 128 = 0
By comparing this equation with the standard form equation,
a = 1, b = - 8, c = 128
The formula for solving quadratic equations is expressed as
[tex]\begin{gathered} x\text{ = }\frac{-\text{ b }\pm\sqrt[]{b^2-4ac}}{2a} \\ By\text{ substituting the given values, it becomes} \\ x\text{ = }\frac{-\text{ - 8 }\pm\sqrt[]{-8^2-4(1\times128)}}{2\times1} \\ x\text{ = }\frac{8\pm\sqrt[]{64-512}}{2}\text{ = }\frac{8\pm\sqrt[]{-\text{ 448}}}{2}\text{ = }\frac{8\pm\sqrt[]{-64\text{ }\times\text{ 7}}}{2} \\ x\text{ }=\frac{8\pm(\sqrt[]{-64)}\times\sqrt[]{7}}{2} \\ \text{Note, }\sqrt[]{-\text{ 1}}\text{ = i} \\ \sqrt[]{-64}\text{ = 8i} \\ x\text{ = }\frac{8\pm8i\sqrt[]{7}}{2} \\ \text{Factoring out 2 in the numerator, we have} \\ x\text{ = }\frac{2(4\text{ }\pm4i\sqrt[]{7})}{2} \\ x\text{ = 4 }\pm4i\sqrt[]{7} \end{gathered}[/tex]Option A is correct
A random sample of 150 people are asked if they own dogs and 57 of them say yes what would you estimate the percentage of dog owners to be in this population
Answers
Answer:
38%
Step-by-step explanation:
Dog owners=57
Total population=157
Percentage of owners=(dog owners/total population) ×100=(57/157)×100=0.38×100=38%
Kayla is learning to sew a quilt. The first step is to use a pattern to cut squares from pieces of fabric. Onthe pattern, one side of the square starts at point (5,-4) and ends at point (5,2). If each unit on thepattern is one inch, how many inches long is the side of the square?
Answers
Answer:
6 inches
Explanation:
On the square pattern, one side of the square starts at point (5,-4) and ends at point (5,2).
To determine the length of a side of the square, find the distance between the endpoints.
From the endpoints: (5, -4) and (5,2)
The x-coordinates are the same, therefore, the distance between the endpoints is:
[tex]|2-(-4)|=|2+4|=6\text{ units}[/tex]If each unit on the pattern is one inch, the length of a side of the square is 6 inches.
What is the least common multiple of 12, 48 and 72
Answers
SOLUTIONS
What is the least common multiple of 12, 48 and 72
[tex]\begin{gathered} L.C.M=2\times2\times2\times2\times3\times3 \\ L.C.M=144 \end{gathered}[/tex]Therefore the least common multiple of 12, 48 and 72 = 144
(3m + n )(3m − n )solve by using foil
Answers
Given: The expression below
[tex](3m+n)(3m-n)[/tex]To: Solve using foil
Solution
foil means
F---- FIRST
O- OUTER
I ---- INNER
L ----- LAST
Let us apply the foil method
Therefore,
[tex]\begin{gathered} (3m+n)(3m-n) \\ =3m\times3m+3m\times-n+n\times3m+n\times-n \\ =9m^2-3mn+3mn-n^2 \\ -3mn+3mn=0 \\ Therefore \\ (3m+n)(3m-n)=9m^2-n^2 \end{gathered}[/tex]Hence, the solution is
9m² - n²
paper: 100 sheets for $.99, 500 sheets for $4.29. Which is a better buy?
Answers
Answer:
the second option/ 500 sheets for 4.29
Step-by-step explanation:
Answer:
sheets for 4.29 is better buy
Use the fact that the sum of the angles in a triangle is 180° for this question.Two angles of a triangle have the same measure and the third one is 9º greater than the measure ofeach of the other two. Find the measure of the angles in the triangle.The 2 SMALLER angles each have a measure ofThe LARGER angle has a measure of0Question Help: Message instructorSubmit QuestionJump to Answer
Answers
Let
x ------> measure of the two angles that have the same measure
y -----> teh larger angle
we have that
2x+y=180 --------> equation A
y=x+9 -------> equation B
substitute equation B in equation A
2x+(x+9)=180
solve for x
3x=180-9
3x=171
x=57 degrees
Find the value of y
y=x+9
y=57+9
y=66 degrees
therefore
The 2 SMALLER angles each have a measure of 57 degrees
The LARGER angle has a measure of 66 degrees
If m Angle EOF=26 and m Angle FOG=38, then what is the measure of Angle EOG? The diagram is not to scale.
Answers
Answer:
[tex]m\angle\text{EOG}=64^0[/tex]Explanation:
From the given statement.
[tex]\begin{gathered} m\angle\text{EOF}=26^0 \\ m\angle FOG=38^0 \end{gathered}[/tex]Now:
[tex]\begin{gathered} m\angle\text{EOG}=m\angle\text{EOF}+m\angle F\text{OG} \\ =26^0+38^0 \\ =64^0 \\ \text{Therefore:} \\ m\angle\text{EOG}=64^0 \end{gathered}[/tex]Question 11 of 44In ADEF, sin D = 36. What is cos E?
Answers
We will have the following:
[tex]\cos (E)=\frac{\sqrt[]{39^2-15^2}}{39}\Rightarrow\cos (E)=\frac{36}{39}[/tex]We remember that:
[tex]\cos (\alpha)=\frac{\text{adjacent side}}{hypotenuse}[/tex]Tom buys some shirts for $15 each. He has a coupon for $9 dollars off the total price. If he pays $36, how many shirts, s , did he buy
Answers
We have to find how many shirts (s) he has bought.
We know that each shirt costs $15, so the total cost of the shirts should be 15*s.
If we substract the discount, we have the total final cost C as:
[tex]C=15\cdot s-9[/tex]If we know that this total cost was $36, we can find the number of shirts as:
[tex]\begin{gathered} C=36 \\ 15s-9=36 \\ 15s=36+9 \\ 15s=45 \\ s=\frac{45}{15} \\ s=3 \end{gathered}[/tex]Answer: He bought 3 shirts (s = 3).
Identify the values of a, b, and c. b =
Answers
We have the following:
[tex]undefined[/tex]a random sample of 82 statistics student were asked about their latest test score pass or fail and rather they study for the test or not the following contingency table gives a two-way classification of their response
Answers
Given:
Sample size, n = 82
We have the repsonses on the table.
Suppose a student is randomly selected, let's determine the following probabilities.
Number that studied and pass = 22
Number of students that paased = 22 + 26 = 48
a) P(Did Study and Pass) =
[tex]P=\frac{\text{Number that studied and pass}}{\text{Total number of students}}=\frac{22}{82}=0.268[/tex]b) P(Did not Study and Fail):
Total number that failed = 10 + 24 = 34
Number that did not study and fail = 24
[tex]P=\frac{Number\text{ that did not study and fail}}{Total\text{ number of students}}=\frac{24}{82}=0.293[/tex]c) P(Pass or Did not Study):
[tex]P=\frac{26+22+24}{82}=\frac{72}{82}=0.878[/tex]d) P(Fail or did study):
[tex]P=\frac{10+24+22}{82}=0.683[/tex]e) P(Fail and Pass) = 0
This is zero since there is no inetrsection for students who fail and students who pass
ANSWER:
• P(Did Study and Pass) = 0.268
,• P(Did not Study and Fail) = 0.293
,• P(Pass or Did not Study) = 0.878
,• P(Fail or did Study) = 0.683
,• P(Fail and Pass) = 0