Find the measure of the indicated angle to the nearest degree.A. 63B. 25C. 31D. 27
Answers
The point of the problem is to remember the cosine relation. It says, in this case, that
[tex]\cos (?)=\frac{\text{adjacent side}}{Hypotenuse}\Rightarrow\begin{cases}\text{adjacent side}=6 \\ \text{Hypotenuse}=13\end{cases}\Rightarrow\cos (?)=\frac{6}{13}[/tex]Converting the last equation by the inverse function, we get
[tex]?=\cos ^{-1}(\frac{6}{13})\approx62.5[/tex]For the first decimal place (5) equals 5, and by the rounding rule to the nearest degree, we get 63. The answer is A.
Related Questions
translate the following into an equation:6 less decreased by twice a number results in 8
Answers
Let the number be x.
Twice the number means 2 * x = 2x
Twice the number decreased by 6 means
2x - 6
Given that the result is 8, we have
2x - 6 = 8
Which graph shows the same linear equation shown in the table below?
Answers
I'm drawing now
_______________________
Option C
Given that 1 inch = 2.54 centimeters how many centimeters are in 6 feet?
Answers
Answer:
182.88 centimeters are in 6 feet!
Step-by-step explanation:
I hope this helped! c:
Answer:
182.88 centimetersStep-by-step explanation:
If
1 in. = 2.54 cm.
and
12 in. = 1 ft.
lets convert cm into feet
1 * 12 = 12 (how many inches are in a foot )
2.54 * 12 = 30.48 (how many centimeters are in a foot)
so now that we know how many centimeters are in a foot, we can find out how many centimeters are in 6 feet
30.48 * 6 = 182.88
182.88 centimeters are in 6 feetDante is arranging 11 cans of food in a row on a shelf. He has 7 cans of beans, 3 cans of peas, and 1 can of carrots. In how many distinct orders can the cans be arranged if two cans of the same food are considered identical (not distinct)?
Answers
Given:
The number of cans of food =11
The number of cans of beans=7
the number of cans of peas=3
the number of cans of carrots=1
Condition : two cans of the same food are considered identical.
To arrange the n objects in order,
[tex]\begin{gathered} \text{Number of ways= }\frac{n!}{r_1!r_2!r_3!} \\ =\frac{11!}{7!3!1!} \\ =\frac{39916800}{30240} \\ =1320 \end{gathered}[/tex]Answer: the number of ways are 1320.
Write a rule for the nth term of the geometric sequence given a_2 = 64, r = 1/4
Answers
The n-th term of a geometric sequence is given by the formula:
[tex]\begin{gathered} U_n=a_1r^{n-1} \\ r=\text{ common ration} \\ a_1=\text{ first term} \end{gathered}[/tex]Given that:
[tex]\begin{gathered} a_2=64 \\ r=\frac{1}{4} \\ n=2 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} a_2=a_1(\frac{1}{4})^{2-1}=64 \\ a_1(\frac{1}{4})=64 \\ a_1=64\times4 \\ =256 \end{gathered}[/tex]Therefore, the rule for the nth term of the sequence is
[tex]\begin{gathered} U_n=a_1r^{n-1} \\ U_n=256_{}(\frac{1}{4})^{n-1} \end{gathered}[/tex]Find the annual fixed expense for car insurance if John makes
six payments in a year at $174.45 each?
Answers
The annual fixed expense for car insurance is $ 1,046.70.
It is given in the question that John makes six payments in a year at $174.45 each.
We have to find the annual fixed expense for car insurance.
We know that,
The annual fixed expense for the car insurance will be 6 times the individual payment given in the question.
Hence, by simple multiplication, we can write,
Annual fixed expense for the car insurance = 6*174.45 = $ 1,046.70
Car insurance
Car insurance is a type of financial protection that covers the cost of another driver’s medical bills and repairs if you cause an accident with your car, or in case your car is stolen or damaged some other way.
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1. Write the equation of the line with a slope of -3 that passes through the point (1,9).y=3x + 12y=3x + 6y=-32 +6y=-3x+12
Answers
Answer:
y = -3x + 12
Explanation:
The equation of a line with slope m that passes through the point (x1, y1) can be calculated as:
[tex]y-y_1=m(x-x_1)[/tex]So, replacing m by -3, and (x1, y1) by (1, 9), we get:
[tex]y-9=-3(x-1)[/tex]Finally, solving for y, we get:
[tex]\begin{gathered} y-9=-3x-3(-1) \\ y-9=-3x+3 \\ y-9+9=-3x+3+9 \\ y=-3x+12 \end{gathered}[/tex]Therefore, the answer is:
y = -3x + 12
Consider an investment whose return is normally distributed with a mean of 10% and a standard deviation of 5%. (2.4)
Justify which statistics methodology needs to be used in the above context and
a) Determine the probability of losing money.
b) Find the probability of losing money when the standard deviation is equal to 10%.
Answers
a) The probability of losing money when standard deviation is 5% is 2.27%
b) The probability of losing money when standard deviation is 10% is 15.87%
Given,
There is an investment whose return is normally distributed.
The mean of the distribution = 10%
The standard deviation of the distribution = 5%
a) We have to determine the probability of losing money:
Lets take,
x = -0.005%
Now,
P(z ≤ (-10.005 / 5) ) = P(z ≤ - 2.001) = 0.02275
Now,
0.02275 × 100 = 2.27
That is,
The probability of losing money is 2.27%
b) We have to find the probability of losing money when the standard deviation is 10%
Let x be 0.01%
Now,
P(z ≤ (-10.01/10)) = P(z ≤ -1.001) = 0.15866
Now,
0.15866 × 100 = 15.87
That is,
The probability of losing money is 15.87%
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Find the equation of the line described. Write your answer in standard form. Vertical and containing (10,14)
Answers
We have here a special case where the line is vertical. In this case, the line has an "infinite" slope (or it is not defined). Therefore, since the line is vertical and contains the point (10, 14), the line is given by the equation:
[tex]x=10[/tex]The standard form of the line is given by the general equation:
[tex]Ax+By=C[/tex]Then, we can rewrite the equation as follows:
[tex]x+0y=10[/tex]We can see that this line contains the point (10,14):
We can see that the vertical line, x + 0y = 10 passes through the point (10, 14).
In summary, the line is given by x + 0y = 10 (A = 1, B = 0, C = 10).
Model x2 + 3x + 5 in the Gizmo by dragging or clicking blue x?-tiles, green x-tiles, and yellow 1-tilesinto the top bin. How many of each type of tile did you use?
Answers
A.
x^2 and 2x^2 means:
3 x^2 tiles
3x - 4x = -x
ONE -x tiles
5 - 1 is "4"
B.
2x^2 - 4x - 1
This is just an expression
so there are 2 x^2 tiles, 4 -x tiles and one 1-tiles
Given the following linear function sketch the graph of the function and find the domain and range.
F(x)=2/7x-2
pls show how did u solve it
Answers
Linear function f(x) = 2/7x - 2
It has no domain or range restrictions, so both of them include all real numbers.
Doman x ∈ ( - ∞, + ∞),Range y ∈ ( - ∞, + ∞).The graph is attached
The coordinates of three vertices of a rectangle are (3,7), (-3,5), and (0,-4). What are the coordinates of the fourth vertex?A. (6,-2)B. (-2,6)C. (6,2)D. (-2,-6)
Answers
ANSWER
A. (6, -2)
EXPLANATION
Let's graph these three vertices,
The fourth vertex must be at the same distance from (0, -4) as vertex (3, 7) is from (-3, 5),
Note that the horizontal distance between these two points is 6 units and the vertical distance is 2 units. The fourth vertex is,
[tex](0+6,-4+2)=(6,-2)[/tex]Hence, the fourth vertex is (6, -2)
< BackSee SolutionShow ExampleRecord: 1/3 Score: 1 Penalty: 1 offComplete: 11% Grade: 0%Brianna AllenFinding the Slope from PointsJon 03, 7:15:08 PMWhat is the slope of the line that passes through the points (4, -9) and (8, -3)?Write your answer in simplest form.
Answers
To obtain the slope of the line that passes through the two given points, the following steps are recommended:
Step 1: Recall the formula for the slope of a line that passes through any two points (x1, y1) and (x2, y2), as follows:
[tex]\text{slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]Step 2: Apply the formula to find the slope of the line that passes through the points (4, -9) and (8, -3), as follows:
[tex]\begin{gathered} \text{Given that:} \\ (x_1,y_1_{})=(4,-9) \\ (x_2,y_2)=(8,-3) \\ \text{Thus:} \\ \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow\text{slope}=\frac{-3_{}-(-9)_{}}{8_{}-4_{}}=\frac{-3+9}{4}=\frac{6}{4}=\frac{3}{2} \\ \Rightarrow\text{slope}=\frac{3}{2} \end{gathered}[/tex]Therefore, the slope of the line that passes through the points (4, -9) and (8, -3) is 3/2
Which calculation and answer show how to convert 13 to a decimal?
Answers
when evalueatong the expression 13/15,
13 serves as the dividend and
15 is the divisor
Divisor is always placed outside the division sign and the dividend inside.
According to the option, you can see that 15 which is the divisor is placed outside and 13 is placed inside.
check the diagram below:
Option A is the correct answer in this case
J is the midpoint of CT if CJ=5x-3 and JT=2x+21 find CT
Answers
Since J is the midpoint of the CT segment, then:
[tex]\begin{gathered} CJ=JT \\ 5x-3=2x+21 \end{gathered}[/tex]Now, you can solve the equation for x:
[tex]\begin{gathered} 5x-3=2x+21 \\ \text{ Add 3 from both sides of the equation} \\ 5x-3+3=2x+21+3 \\ 5x=2x+24 \\ \text{ Subtract 2x from both sides of the equation} \\ 5x-2x=2x+24-2x \\ 3x=24 \\ \text{ Divide by 3 from both sides of the equation} \\ \frac{3x}{3}=\frac{24}{3} \\ x=8 \end{gathered}[/tex]Replace the value of x into the equation for segment CJ or segment JT to find out what its measure is. For example in the equation of the segment CJ:
[tex]\begin{gathered} CJ=5x-3 \\ x=8 \\ CJ=5(8)-3 \\ CJ=40-3 \\ CJ=37 \end{gathered}[/tex]Finally, you have
[tex]\begin{gathered} CJ=37 \\ CJ=JT \\ 37=JT \\ \text{ Then} \\ CT=CJ+JT \\ CT=37+37 \\ CT=74 \end{gathered}[/tex]Therefore, the measure of the segment CT is 74.
The angle of elevation to the top of a Building in New York is found to be 11 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building. Round to the tenths. Hint: 1 mile = 5280 feet
Your answer is __________ feet.
Answers
The height of the building is given as 1026.43 feet
What is angle of elevation?This is the term that is used to refer to the angle that is usually formed from the horizontal line to the angle of sight of a person.
We have to make use of the trig function that tells us that
tan(∅) = opposite length /adjacent length.
where ∅ = 11 degrees
adjacent length = 1
opposite length = x
When we put these values in the formula we would have
tan 11 = x / 1
0.1944 = x /1
we have to cross multiply to get x
x = 0.1944 x 1
= 0.1944
Then the height of the building would be 0.1944 x 5280 feet
= 1026.43 feet
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What is the value of the expression below when w = 3?3w² - 6w - 4
Answers
ANSWER:
5
STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]3w^2-6w-4\:[/tex]We substitute the value of w, when it is equal to 3, just like this:
[tex]\begin{gathered} 3\left(3\right)^2-6\left(3\right)-4\: \\ \\ 3\cdot \:9-6\left(3\right)-4 \\ \\ 27-18-4 \\ \\ 5 \end{gathered}[/tex]The value of the expression is equal to 5
A particular lawn requires 6 bags of fertilizer. A lawn next door requires 4 bags of fertilizer. How big is the lawn next door?A. 10 feet square feetB. 24 feet square feetC. 50 feet square feetD. Not enough information is given
Answers
Answer:
D. Not enough information is given
Explanation:
To know the size of the lawn next door, we would need a relation between the square feet and the number of bags of fertilizer.
Since all we know is the bags of fertilizer for the particular lawn and the lawn next door, we can say that we didn't have enough information to answer the question.
Therefore, the answer is:
D. Not enough information is given
A pool is filled to 3/4 of its capacity 1/9 of water in the pool, evaporates. If the pool can hold 24,000 gallons when it is full, how many gallons of water will have to be added in order to fill the pool?A. 6,000B. 8,000C.12,000D.16,000
Answers
First, the pool was filled to 3/4 of its capacity, which is equal to:
[tex]24000\cdot\frac{3}{4}gal=18000gal.[/tex]Then, 1/9 of the water evaporated remaining 8/9 of the 18000 gal:
[tex]18000\text{gal}\frac{8}{9}=16000gal.[/tex]Therefore, to fill the pool we need to add:
[tex]24000-16000[/tex]gallons of water.
Answer: B. 8000.
Jerry takes out a 30-year mortgage for $170,000.00 to buy a condo. His monthly mortgage payment is $939.00. How much interest will he pay over the life of the loan? Round your answer to the nearest whole dollar.
Answers
Okay, here we have this:
Considering the provided information we obtain the following:
Mortgage capital=$170,000
Total payment = Monthly payment * 12 months of the year * number of years
Total payment = $939*12*30
Total payment = $338,040
Total payment = Mortgage capital + Interest
Replacing we obtain:
Total payment = Mortgage capital + Interest
$338,040=$170,000+interest
Interest= $338,040-$170,000
Total Interest=$168,040
Finally we obtain that the total interest is $168040.
I need help with this practice Having trouble solving it The subject is trigonometry
Answers
To solve the problem, we will make use of the identity:
[tex]\cos (\alpha-\beta)=\cos (\alpha)\cos (\beta)+\sin (\alpha)\sin (\beta)_{}[/tex]ANGLE α
The angle lies in the second quadrant. The only positive ratio is the sine.
If we have that:
[tex]\tan \alpha=-\frac{12}{5}[/tex]Displaying this on a triangle for ease of working, we have:
Therefore, the length of the hypotenuse will be:
[tex]\begin{gathered} x=\sqrt[]{12^2+5^2}=\sqrt[]{144+25}=\sqrt[]{169} \\ x=13 \end{gathered}[/tex]Therefore, we have that:
[tex]\begin{gathered} \sin \alpha=\frac{12}{13} \\ \cos \alpha=-\frac{5}{13} \end{gathered}[/tex]ANGLE β
This angle lies in the fourth quadrant. Only the cosine ratio is positive in this quadrant.
We are given in the question:
[tex]\cos \beta=\frac{3}{5}[/tex]Displaying this on a triangle for ease of working, we have:
Therefore, using the Pythagorean Triplets, we have that:
[tex]y=4[/tex]Therefore, we have that:
[tex]\sin \beta=-\frac{4}{5}[/tex]SOLVING THE IDENTITY
Applying the identity quoted earlier, we have:
[tex]\begin{gathered} \cos (\alpha-\beta)=\cos (\alpha)\cos (\beta)+\sin (\alpha)\sin (\beta)_{} \\ \cos (\alpha-\beta)=(-\frac{5}{13})(\frac{3}{5})+(\frac{12}{13})(-\frac{4}{5}) \\ \cos (\alpha-\beta)=-\frac{63}{65} \end{gathered}[/tex]Find the surface area of the cylinderA). 188.4 ft^2B). 226.08 ft^2C). 244.92 ft^2D). 282.6 ft^2
Answers
To solve this problem, we will use the following formula for the surface area of a cylinder:
[tex]A=2\pi rh+2\pi r^2,[/tex]where r is the radius of the base, and h is the height of the cylinder.
Substituting h= 10 ft, and r = 3 ft in the above formula, we get:
[tex]A=2\pi(3ft)(10ft)+2\pi(3ft)^2.[/tex]Simplifying, we get:
[tex]A=244.92ft^2.[/tex]Answer: Option C.
The perimeter of a quarter circle is 3.57 kilometers. What is the quarter circle's radius? Use 3.14 for . kilometers Siubmit explain
Answers
Given:
It is given that the perimeter of a quarter circle is 3.57 km.
To find :
The radius of the quarter circle.
Explanation :
The perimeter of the quarter circle is
[tex]P=\frac{2\pi r}{4}\text{ }+2r[/tex]Substitute the value of perimeter in the above formula
[tex]3.57=\frac{\pi r}{2}+2r[/tex][tex]3.57=(\frac{3.14}{2}+1)r[/tex][tex]3.57=2.57r[/tex][tex]r=1.39[/tex]Answer
Hence the radius of a quarter circle is 1.39 km.
Fine all the missing side lengths and angle measured of each triangle.
Answers
Answer:
[tex]\begin{gathered} AT=8\sqrt[]{3} \\ AC=8 \\ mStep-by-step explanation:To find the missing lengths of the triangle, use trigonometric ratios for right triangles, which are represented by the following equations:
[tex]\begin{gathered} \sin (\text{angle)=}\frac{\text{ opposite}}{\text{ hypotenuse}}_{} \\ \cos (\text{angle)}=\frac{\text{adjacent}}{\text{hypotenuse}} \\ \tan (\text{angle)}=\frac{\text{ opposite}}{\text{ adjacent}} \end{gathered}[/tex]Then, find the opposite and adjacent side given the 60 degrees angle:
[tex]\begin{gathered} \sin (60)=\frac{AT}{16} \\ AT=16\cdot\sin (60) \\ AT=8\sqrt[]{3} \\ \\ \cos (60)=\frac{AC}{16} \\ AC=16\cdot\cos (60) \\ AC=8 \end{gathered}[/tex]Now, since the intern angles of a triangle must add up to 180 degrees, given two of the angles find the missing angle:
[tex]\begin{gathered} mThird-degree, with zeros of -3, -2, and 1, and passes through the point (4, 10).
Answers
The required third degree expression is 1/7 (x³ + 2x² - 5x - 6)
Given,
Find a third degree expression f(x) that has zeros -3, -2, 1 and the equation y = f(x) passes through (4, 10). ,
If the roots/zeroes of a nth order expression are given as r₁, r₂, r₃....rₙ, the expression is given by f(x) = c(x - r₁) (x - r₂) (x - r₃)....(x - rₙ)
Since we know the three roots of the third degree expression, the function is;
f(x) = c(x - (-3)) (x - (-2)) (x - 1)
= c(x + 3) (x + 2) (x - 1)
= c (x³ + 2x² - 5x - 6)
Also y = f(x), passes through(4, 10) , so
10 = c(4³ + 2 x 4² - 5 x 4 - 6)
10 = c(64 + 32 - 20 - 6)
10 = 70c
c = 10/70 = 1/7
∴Required expression is 1/7 (x³ + 2x² - 5x - 6)
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Karine invests $6,100 in an account with an annual interest rate of 4.5% compounded daily for 2 years.What is the return on investment for Karine's account?
Answers
The return on investment for Katerine's account = 9.4%
Explanation:Amount invested is the principal
Principal, P = $6,100
Annual Interest Rate, r = 4.5% = 0.045
The interest is compounded daily
Number of times the interest is compounded per year, n = 365
Number of years, t = 2 years
The amount after 2 years is calculated as:
[tex]\begin{gathered} A(t)=P(1+\frac{r}{n})^{nt} \\ A=6100(1+\frac{0.045}{365})^{365(2)} \\ A=6100(1.094) \\ A=6673.4 \end{gathered}[/tex]The amount after 2 years = $6673.4
The interest = Amount - Principal
The interest = $6673.4 - $6100
The interest = $573.4
The return on investment is calculated as:
[tex]\begin{gathered} \text{ROI = }\frac{Interest}{Pr\text{incipal}}\times100\text{ \%} \\ \text{ROI}=\frac{573.4}{6100}\times100\text{ \%} \\ \text{ROI = }9.4\text{ \%} \end{gathered}[/tex]The return on investment for Katerine's account = 9.4%
A line's slope is -5. The line passes through the point (5, 30). Find an equation for this line in both point-slope and slope-intercept form A) An equation for this line in point-slope form is:B) An equation for this line in slope-intercept form is.
Answers
Answer:
y - 30 = 5(x - 5) (point slope form)
slope intercept form is y = 5x+5
Explanation:
Given the following
Slope m = -5
Point = (5, 30)
x0 = 5 and y= = 30
The equation of the line in point slope form is expressed as y-y0 = m(x-x0)
Substitute
y - 30 = -5(x - 5) (point slope form)
Express in slope intercept form (y = mx+c)
y - 30 = -5x + 25
y = -5x + 25 + 30
y = -5x + 55
Hence the equation of the line in slope intercept form is y = -5x+55
express the quadratic function f(x)=3x^2 + 6x - 2 in the form a(x + h)^2 + k where a,h and k are constants
Answers
Answer:
Explanation:
Given:
[tex]f(x)=3x^2+6x-2[/tex]First, we do completing the square on the given function to express it into vertex form. So,
We write it in the form:
[tex]\begin{gathered} x^2+2ax+a^2 \\ \end{gathered}[/tex]And, factor out 3: So,
[tex]\begin{gathered} 3(x^2+2x-\frac{2}{3}) \\ \text{where:} \\ 2a=2\text{ or a=1} \\ \text{Hence} \\ 3(x^2-2x-\frac{2}{3}+1^2-1^2) \end{gathered}[/tex]Since:
[tex]\begin{gathered} x^2+2ax+a^2=(x+a)^2 \\ So, \\ x^2+2x+1^2=(x+1)^2 \end{gathered}[/tex]Then,
[tex]\begin{gathered} 3(x^2-2x-\frac{2}{3}+1^2-1^2) \\ =3((x+1)^2-\frac{2}{3}-1^2) \\ \text{Simplify} \\ f(x)=3(x+1)^2-2-3 \\ f(x)=3(x+1)^2-5 \end{gathered}[/tex]Therefore, the answer is:
[tex]f(x)=3(x+1)^2-5[/tex]the answer is red show me how to get to the answer
Answers
The given expression is:
[tex]\frac{5\sqrt{4}}{\sqrt{3}}[/tex]The first step is to find the square root of 4 in the numerator, that is:
[tex]\sqrt{4}\text{ = 2}[/tex]Substitute this into the given expression:
[tex]\frac{5(2)}{\sqrt{3}}[/tex][tex]\frac{10}{\sqrt{3}}[/tex]The next step is to rationalize, that is, multiply the numerator and the denominator by √3
[tex]\frac{10}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}}[/tex][tex]\frac{10\sqrt{3}}{\sqrt{9}}[/tex]Since √9 = 3[tex]\frac{10\sqrt{3}}{3}[/tex]what is the value of x in the solutions to the system of equations below3x-8y=112y+x=13
Answers
Given system of equations
3x - 8y = 11 ______________________1
2y + x = 13 ______________________ 2
Use the substution method
How to use the substitution method
1. pick one of the equation
2. make one of the variable subject of relation
3. substitute
From equation (1)
2y + x = 13
x = 13 - 2y
substitute x from equation 1 to 2.
3(13 - 2y) - 8y = 11
39 - 6y - 8y = 11
39 - 11 = 6y + 8y
28 = 14y
y = 28/14
y = 2
Next, substitute y in equation 2 to find x.
x = 13 - 2y
x = 13 - 2(2)
x = 13 - 4
x = 9
Final answer x = 9
