Janeka forgot to divide by 2 to get the radius and then square and multiply by pi.
since the diameter is 20 the radius would be 10. so i the equation you would replace the 20 with 10 bc she but the diameter in instead of the radius which r=radius
A sinusoidal source is usually described by the function cos(ωt+ϕ), where the units of the frequency ω are radians/second and the units of the phase angle ϕ are degrees. this means that the product ωt has the units radians, which cannot be added to the phase angle in degrees. to evaluate the value of the sinusoidal source at a given time, you must transform the product ωt to degrees or the phase angle to radians before performing the addition in the cosine argument. if the voltage source is given by v(t)=50cos(2000t−45∘) mv, find v(392.7 μs). express your answer with the appropriate units.
Answer:
49.999999999999974312306505198184 V
Step-by-step explanation:
Step 1: you see 45°, which gives you a easy conversion [tex]\frac \pi 4[/tex]).
Now, [tex]t = 392.7 \mu s = 392.7* 10^{-6} s[/tex], start replacing.
[tex]V= 50 cos ( 2* 10^3 * 392.7 *10^{-6} -\frac \pi 4) = 50 cos (0.7854 - \frac \pi 4) =\\ 49.999999999999974312306505198184 V[/tex]
For the system shown below, what are the coordinates of the solution that lies in quadrant 1?
Write your answer in the form (a,b) without using spaces.
[tex]3y^2-5x^2=7\\3y^2-x^2=23[/tex]
The answer in the first quadrant is
(2,3)
Jocelyn invests $1,600 in an account that earns 2.5% annual interest. Marcus invests $400 in an account that earns 5.4% annual interest. Find when the value of Marcus's investment equals the value of Jocelyn's investment and find the common value of the investments at that time. If necessary, enter the year to the nearest tenth and the value to the nearest cent.
Answer:
Total = Principal * (1 + rate) ^ years
We have to solve this for years:
Years = {log(total) -log(Principal)} ÷ log(1 + rate)
Jocelyn: Years = {log(total) -log(1,600)} ÷ log(1.025)
Marcus: Years = {log(total) -log(400)} ÷ log(1.054)
We know the years must be equal but we won't know the total so we'll call that "x".
[log(x) -log(1,600)] ÷ log(1.025) = [log(x) -log(400)] ÷ log(1.054)
EDITED TO ADD
Time is about 49 Years 8 Months and total is about 5,454.00
We know the years must be equal
Step-by-step explanation:
which is a rule that describes the translation of a point from 4, -8 to 7, -10
(x, y) > (x + 3, y - 2)
(x, y) > (x + 3, y + 2)
(x, y) > x - 3, y - 2
(x, y) > (x - 3, y + 2)
Answer:
[tex]\large\boxed{(x,\ y)\to (x+3,\ y-2)}[/tex]
Step-by-step explanation:
[tex](4,\ -8)\to(7,\ -10)\\\\4\to7\Rightarrow4+3=7\\\\-8\to-10\Rightarrow-8-2=-10\\\\\text{Conclusion}\\\\(x,\ y)\to (x+3,\ y-2)[/tex]
Answer:
first choice: (x, y) ------> (x + 3, y - 2)
Step-by-step explanation:
The x-coordinate started as 4. Then it became 7. To change from 4 to 7, you add 3. The rule for x is to add 3.
The y-coordinate started as -8. Then it became -10. To go from -8 to -10, you subtract 2. The rule for y is to subtract 2.
Look at the choices, and pick the one that adds 3 to x and subtract 2 from y.
The answer is the first choice: (x, y) ------> (x + 3, y - 2)
50 POINTS!! :) A dog that has been tethered has a 20 foot lead makes the path shown here. If the length of the path is 45 feet, the measure of angle 0 is ___ radians.
Answer:
The measure of angle theta is [tex]\theta=2.25\ radians[/tex]
Step-by-step explanation:
step 1
Find the circumference of the circle
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=20\ ft[/tex]
substitute
[tex]C=2\pi (20)[/tex]
[tex]C=40\pi\ ft[/tex]
step 2
Find the measure of angle theta
we know that
The circumference of a circle subtends a central angle of [tex]2\pi\ radians[/tex]
so
using proportion
Find out the measure of the central angle by a length of arc equal to 45 ft
[tex]\frac{40\pi}{2\pi}=\frac{45}{\theta}\\ \\\theta=2*45/40\\ \\ \theta=2.25\ radians[/tex]
Answer: 2.25 radians
Step-by-step explanation:
A ball is thrown with a slingshot at a velocity of 110 ft./sec. at an angle 20 degrees above the ground from a height of 4.5 ft. Approximately how long does it take for the ball to hit the ground? Acceleration due to gravity is 32 ft./s^2.
A. 2.35 seconds
B. 2.47 seconds
C. 6.46 seconds
D. 6.50 seconds
Answer:
T= 2.35 seconds
Step-by-step explanation:
⇒The question is on the time of flight.
⇒Time of flight is the time taken for a projected object to reach the ground.It depends on the projectile angle and the initial velocity of the projectile
Given;
Initial velocity of ball= 110ft./sec.
The projectile angle= 20°
Acceleration due to gravity, g=32 ft./s²
⇒Formulae for time of fright T= (2×u×sin Ф)/g
Where T=time of fright, u=initial velocity of projectile, Ф=projectile angle and g=acceleration due o gravity.
Substituting values
T= (2×u×sin Ф)/g
T=( 2×110×sin 20°) / 32
T= 2.35 seconds
Answer:
Option B - Time taken for the ball to hit the ground is 2.47 seconds.
Step-by-step explanation:
Given : A ball is thrown with a slingshot at a velocity of 110 ft./sec. at an angle 20 degrees above the ground from a height of 4.5 ft.
To find : How long does it take for the ball to hit the ground?
Solution :
According to question,
The equation that models the height of the ball in feet as a function of time is
[tex]h(t) = h_0 + v_0t -16t^2[/tex]
Where, [tex]h_0[/tex] is the initial height,
[tex]v_0[/tex] is the initial velocity and
t is the time in seconds.
We have given,
Initial height, [tex]h_0=4.5 ft.[/tex]
A ball is thrown with a slingshot at a velocity of 110 ft./sec. at an angle 20 degrees.
The initial speed, [tex]v_0=110\times \sin(206\circ)[/tex]
[tex]v_0=37.62ft/s[/tex]
We have to find the time for the ball to hit the ground i.e. h(t)=0
Substitute all the values in the formula,
[tex]0 =4.5+ 37.62t -16t^2[/tex]
Applying quadratic formula to solve the equation,
The solution of quadratic general equation [tex]ax^2+bc+c=0[/tex] is
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Where, a=-16 , b=37.62 , c=4.5
Substituting in the formula,
[tex]t=\frac{-37.62\±\sqrt{(37.62)^2 -4(-16)(4.5)}}{2(-16)}[/tex]
[tex]t=\frac{-37.62\±\sqrt{1703.2644}}{-32}[/tex]
[tex]t=\frac{-37.62\±41.270}{-32}[/tex]
[tex]t=\frac{-37.62+41.270}{-32},\frac{-37.62-41.270}{-32}[/tex]
[tex]t=-0.114,2.47[/tex]
neglecting the negative value
t=2.47 seconds
Therefore,Option B is correct.
Time taken for the ball to hit the ground is 2.47 seconds.
Rachel is making nachos for a party. The recipe calls for 2/3 cups of cheese for each plate of nachos. How many plates can she make with five cups of cheese
Answer:
[tex]7\frac{1}{2}\ plates[/tex]
Step-by-step explanation:
we know that
The recipe calls for 2/3 cups of cheese for each plate of nachos
so
using proportion
Find out how many plates can she make with five cups of cheese
let
x ----> the number of plates
[tex]\frac{1}{(2/3)}\frac{plate}{cups} =\frac{x}{5} \frac{plates}{cups}\\ \\x=5/(2/3)\\ \\x=7.5\ plates[/tex]
Convert to mixed number
[tex]7.5=\frac{14}{2}+\frac{1}{2}=7\frac{1}{2}\ plates[/tex]
She can make 7.5plates with 5 cups of cheese
Ratios and proportionsAccording to the question, we are told that the recipe calls for 2/3 cups of cheese for each plate of nachos. This is expressed as:
2/3 cups of cheese = 1 plate of nachos
In order to calculate the number of plates she can make with five cups of cheese
5 cups = x
Cross multiply
2/3x = 5
2x = 15
x = 7.5 plates
Hence she can make 7.5plates with 5 cups of cheese
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Find the equation of the line specified. The line passes through the points ( -2, 3) and ( -4, 7)
Answer:
[tex]y=-2x-1[/tex]
Step-by-step explanation:
Let the first coordinate point be (x_1,y_1) and the second coordinate point be (x_2,y_2)
So
x_1 = -2
y_1 = 3
x_2 = -4
y_2 = 7
Now we can use the formula for equation of line to figure it our.
Equation of line formula is [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Plugging in the known values and arranging in slope-intercept form, we have:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\y-3=\frac{7-3}{-4-(-2)}(x-(-2))\\y-3=\frac{4}{-2}(x+2)\\y-3=-2(x+2)\\y-3=-2x-4\\y=-2x-4+3\\y=-2x-1[/tex]
This is the equation of the line passing through the points ( -2, 3) and ( -4, 7)
Final answer:
To find the equation of the line, the slope is calculated as -2, using the point-slope form with one of the points yields y - 3 = -2(x + 2). Simplifying this, the equation of the line is y = -2x - 1.
Explanation:
To find the equation of a line passing through two points, first, determine the slope (m) of the line. The slope is calculated as the change in y (vertical) divided by the change in x (horizontal). For the points (-2, 3) and (-4, 7), the slope is:
m = (y2 - y1) / (x2 - x1) = (7 - 3) / (-4 + 2) = 4 / (-2) = -2.
Next, use the point-slope form:
y - y1 = m(x - x1),
where (x1, y1) is a point the line passes through. Using point (-2, 3) and the slope -2:
y - 3 = -2(x + 2).
Rewrite this equation in slope-intercept form (y = mx + b) by simplifying and solving for y:
y = -2x - 4 + 3,
y = -2x - 1.
Therefore, the equation of the line passing through the points ( -2, 3) and ( -4, 7) is y = -2x - 1.
Please help!! Having a hard time with this question...!
A quadrilateral is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work and/or explain how you got your answer.
m∠z=
I know this because…
m∠x=
I know this because…
m∠y=
I know this because…
(Please answer the question presented in the format in the question)
Answer:
Step-by-step explanation:
The angle you can get right away is z.
z + 93 = 180
z + 93 - 93 = 180 - 93
z = 87
===============
The next step is to solve for y. You need to draw a line from y to the center and another one from z to the center.
The triangle containing part of y and part of z has a central angle of 106 degrees.
Part of y + partz + 106 = 180
part of y + partz = 74
part of y = partz = 37 The triangle is isosceles because 2 of the legs are radii.
Do the same thing from 93 to the center and the other part of y to the center.
The central angle is 58
The two other angles are equal
part of y + part of 93 + 58 = 180
partofy + partof93 = 180 - 58
partofy + partof93 = 122
partofy = part93 = 61
So
y = 61 + 37 = 98
========================
x + y = 180 (opposite angles in a quadrillateral that fits in a circle = 180)
x + 98 = 180
x = 82
====================
x = 82
y = 98
z = 87
Vince read 1 /4 of his book on Monday. He read 2/ 4 more of his book on Tuesday. How much of his book did Vince read on the two days?
Answer:3/4
Step-by-step explanation: Since he read 1/4 on Monday and 2/4 on Tuesday that would add up to 3/4
The variables x and y vary inversely with a constant variation of 6. Find y when x=12.
Answer:
y = 1/2
Step-by-step explanation:
If two variables x and y vary inversely, then:
xy = k
where k is the constant variation.
In this case:
xy = 6
When x = 12:
12y = 6
y = 1/2
The value of y when x is 12 is 2 (option C)
What is inverse variation?Inverse variation is the relationship between two variables, such that if the value of one variable increases then the value of the other variable decreases. Example is the price of a commodity and the quantity acquired, the higher the price, the lower of commodity bought and vice- versa.
here, we have,
Inverse relationship between two quantities x and y is expressed as:
x= ky
where k is the constant
k = 6
when x = 12
12 = 6y
divide both sides by 6
y = 12/6
y = 2
therefore the value of y when x is 12 is 2
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In a certain college, 33% of the physics majors belong to ethnic minorities. find the probability that, from a random sample of 10 physics majors, exactly 4 do not belong to an ethnic minority.
If a random student has a 33% probability of belonging to a minority, then there is a 67% chance that they do not. In a sample of 10 students, the probability that exactly 4 do not belong to a minority is
[tex]\dbinom{10}40.67^4(1-0.67)^{10-4}\approx0.0547[/tex]
25) A group of 35 people are going to run a
race. The top three runners earn gold,
silver, and bronze medals.
A) Permutation: 39,270
B) Combination: 78,540
© Combination: 19.635
Permutation: 157,080
Answer:
A
Step-by-step explanation:
There are calculators online that you can use to answer this, some even show you the work step by step
What is the slope of the line shown below?
A. 2/3
B. -3/2
C. 3/2
D. -2/3
Answer:
A
Step-by-step explanation:
The line passes through the points (-3,-7) and (9,1).
The slope of the line can be calculted using formula
[tex]\dfrac{y_2-y_1}{x_2-x_1}.[/tex]
Thus, the slope of the given line is
[tex]\dfrac{1-(-7)}{9-(-3)}=\dfrac{8}{12}=\dfrac{2}{3}.[/tex]
Answer:
A
Step-by-step explanation:
slope is given by the formula:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
We need 2 points to find a line's slope.
The first point is (-3,-7) hence x_1 = -3 & y_1 = -7.The second point is (9,1) hence x_2 = 9 & y_2 = 1.Plugging these into the slope formula, we will get the slope:
[tex]\frac{1--7}{9--3}\\=\frac{1+7}{9+3}\\=\frac{8}{12}\\=\frac{2}{3}[/tex]
correct answer is A
Line segment AB has a slope of 4/3 and contains point A (6,-5). What is the y-coordinate of point Q(2, y) if QA is perpendicular to line segment AB.
Answers:
y = −2
y = −1
y = 2
y = −3
[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope~of~AB}{\cfrac{4}{3}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{3}{4}}\qquad \stackrel{negative~reciprocal}{-\cfrac{3}{4}}}\impliedby \textit{slope of QA} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf A(\stackrel{x_1}{6}~,~\stackrel{y_1}{-5})\qquad Q(\stackrel{x_2}{2}~,~\stackrel{y_2}{y}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{y-(-5)}{2-6}=\stackrel{\textit{QA's slope}}{-\cfrac{3}{4}}\implies \cfrac{y+5}{-4}=\cfrac{-3}{4} \\\\\\ 4y+20=12\implies 4y=-8\implies y=\cfrac{-8}{4}\implies \boxed{y=-2}[/tex]
The Wright family recently went out to dinner. They ordered two pizzas at $14.95 each, a salad at $4.35, and four drinks at $2.49 each. The sales tax is 7.675 %. Mr. Wright paid with a $50 bill. Mr. Wright always leaves a 15% tip on the total bill (excluding tax). How much more money will he need in order to leave a 15% tip?
A
$ 3.00
B
$ 4.23
C
$ 6.00
D
$ 7.20
Answer:
B
Step-by-step explanation:
First
Get totals for food items:
Pizza $14.95 ×2=$29.90
Salad=$4.35
Drinks $2.49 ×4=$9.76
Total Bill
$29.90
$ 4.35
+$ 9.76
$44.21 Food Bill
Second Step
Find Tip Amount Before Tax
Total Bill $44.21 × .15=$6.63 Tip
Third Step
Find Tax on Total Food Bill
$44.21 × .07675=$3.39
Fourth Step
Find amount left from paying bill with tax.
Total Bill including tax:
$44.21 (bill) +$3.39 tax=$47.60
Cash $ 50.00
Total Bill - $47.60
$ 2.40 Change left over
Fifth Step
Find amount needed to give $6.63 tip from above.
We have $2.40 we need $6.63
Subtract $6.33 -$2.40=$4.23 more money needed for tip
The correct option is B. $ 4.23. Mr. Wright needs an additional $4.23 to leave a 15% tip.
First, we need to calculate the total cost of the meal before tax and tip. The Wright family ordered two pizzas at $14.95 each, a salad at $4.35, and four drinks at $2.49 each. So, the cost of the pizzas is [tex]2 \times $14.95[/tex], the salad is $4.35, and the drinks are 4 \times $2.49.
Cost of pizzas: [tex]2 \times $14.95 = $29.90[/tex]
Cost of salad: $4.35
Cost of drinks: [tex]4 \times $2.49 = $9.96[/tex]
Total cost before tax: [tex]\$29.90 +\$\4.35 + \$\9.96 = \$\44.[/tex]21
Next, we calculate the sales tax, which is 7.675% of the total cost before tax.
Sales tax: [tex]\$\44.21 \times 7.675% = \$\44.21 \times 0.07675 = \$\3.39[/tex]
Now, we add the sales tax to the total cost before tax to get the total cost including tax.
Total cost with tax: [tex]\$\44.21 + \$\3.39 = \$\47.60[/tex]
Mr. Wright wants to leave a 15% tip on the total bill before tax. So, we calculate 15% of the total cost before tax.
Tip: [tex]\$\44.21 \times 15% = \$\44.21 \times \$\0.15 \times \$\ 6.63[/tex]
Mr. Wright paid with a $50 bill, so we subtract the total cost with tax from $50 to find out how much change he should receive.
Change from [tex]\$50: $50 - $47.60 = $2.40\[/tex]
To find out how much more money Mr. Wright needs to leave a 15% tip, we subtract the change he receives from the tip amount.
Additional money needed: [tex]\$6.63 - $2.40 = $4.23\[/tex]
Therefore, Mr. Wright needs an additional $4.23 to leave a 15% tip.
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
A number generator was used to simulate the percentage of students in a town who enjoy playing video games. The process simulates randomly selecting 100 students from the town and was repeated 20 times. The percentage of students who play video games is shown in the dot plot. Which statement is true about the student population of the town?
Answer:
Step-by-step explanation:
Notice that the greatest number of dots is over the '70,' indicating that 70% of the students in the town enjoy playing video games.
This problem has to do as much with your ability to interpret graphs as to apply statistics concepts correctly.
20 points. It’s in the picture. Right answer only please
I believe it’s B. hope it’s right!
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
The owner of a chain of dance studios releases a report to the media. The report shows that participation in dance classes has increased by 5% in each of the past three years.
Which statement describes the most likely reason the owner releases the report?
Answer:
B
Step-by-step explanation:
I would say that the owner wants people to believe that dance classes are a good form of exercise.
20 points!!! Hurry hurry hurry!! Distance between points
Answer:
This is just a guess so I'm sorry if its wrong but I'd guess that it's A
Answer:
It is A
Step-by-step explanation:
You can use the Pythagorean Theorem a^2+b^2=c^2
3^2+5^2=c^2
9+25=c^2
34=c^2
square root of 34=c
The second term of an arithmetic sequence is 7. The sum of the first 4 terms of the arithmetic sequence is 12. Find the first term, and the common difference, d, of the sequence.
*Please help*
Answer:
15 is the answer
Step-by-step explanation:
What is the difference of 21x / 3x^2 - 2 and 7 / 3x^2 - 2. Show steps
Answer:
Final answer is [tex]\frac{21x-7}{3x^2-2}[/tex]
Step-by-step explanation:
We have been given two terms [tex]\frac{21x}{3x^2-2}[/tex]
and [tex]\frac{7}{3x^2-2}[/tex]
Now we need to find their difference. So let's subtract them
[tex]\frac{21x}{3x^2-2}-\frac{7}{3x^2-2}[/tex]
Denominators are equal so we can easily subtract numerators
[tex]=\frac{21x-7}{3x^2-2}[/tex]
We may factor the numerator but we won't get any factor in denominator that can be cancelled with numerator.
Hence final answer is [tex]\frac{21x-7}{3x^2-2}[/tex]
Elroy and Rose are at Schematic to buy a school planner. There are 333 colors (purple, red, and blue) and 222 formats (lined and unlined) offered. They each created a display to represent the sample space of randomly picking a color and a format.
Answer:
Both
Step-by-step explanation:
The total number of options that will be are 6. The representation made by both Elroy and Rose is correct.
What is the total number of options available?The total number of options available is the product of a total number of options available in different sectors.
Given that number of colors is 3 while the number of formats is two. Therefore, the total number of options that are available will be 6 which is the product of the two.
As we can see that both have pointed out each of the six options, therefore, the representation made by both Elroy and Rose is correct.
Learn more about Number of options:
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CAN LIFT 10 POUNDS BY PUTTING 30 POUNDS OF WEIGHT ON A LEAVER HOW MUCH FORCE NEEDED TO LIFT A 25 POUND WEIGHT
Answer:
Is it a decimal?
Step-by-step explanation:
The diameter of an open parachute is 15 ft. if the distance from the parachute to the center of the diameter is 8 ft, what is the length of the suspension line (from the harness to the edge of the open chute)?
The length of the suspension line from the harness to the edge of the open chute is approximately 10.97 ft.
Explanation:To find the length of the suspension line, we can use the Pythagorean theorem. The distance from the parachute to the center of the diameter is the radius of the parachute, which is half the diameter. Therefore, the radius is 15 ft / 2 = 7.5 ft. The suspension line is the hypotenuse of a right triangle with one leg being the radius and the other leg being the distance from the parachute to the edge of the open chute. Using the Pythagorean theorem, we can calculate the length of the suspension line as follows:
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Help me find the mean of this data set.
74
67
74.25
64
72
67.75
73
66
68
72
68
68
69
70
72
76
70
68
68
72
74
71
66
71
67
70
71.5
71
72
70
71.5
74
69
70.5
72
75.5
71.5
72
69.5
71
74
74
72
74
75
Answer:
Finding the mean is very simple, add them all together and divide that sum by the number of data points you have; in this case there are 45
Step-by-step explanation:
[tex]\frac{74+67+74.25+64+72+...}{45}[/tex] = mean
I really need help on this I have no clue how to do this and my new teacher have a foreign accent so I can’t understand her
Answer:
sinθ = 12/15 -> 4/5
cosθ = 9/15 -> 3/5
tanθ = 12/9 -> 4/3
cscθ = 15/12 -> 5/4
secθ = 15/9 -> 5/3
cotθ = 9/12 -> 3/4
Step-by-step explanation:
The theta is where you would use to identify the numbers for the trig functions. The adjacent side is the one closest to the theta (but not the diagonal line, that is the hypotenuse), and the opposite line is the line next to the adjacent line.
For the first three trig functions, would use the method Soh Cah Toa.
Sin = opp/hypotenus, Cosine = adjacent/hypotenuse, and Tangent = opposite/adjacent. Then, there is cosecant(csc) = hyp/opp, secant = hyp/adj, and cotangent = adj/opp.
Kari wants to measure the height of a tree. She walks exactly 105 feet away from the base of the tree and looks up to the top of it. The angle from the ground to the top of the tree is 33 degrees. This particular tree grows at an angle of 86 degrees with respect to the ground rather than vertically. How tall is the tree to the nearest tenth of a foot?
Answer:
68.2 feet
Step-by-step explanation:
The angle of elevation, the one from the ground up, is given as 33 degrees. If Kari is 105 feet from the tree, that serves as the measure of the base of the right triangle. We are looking for the height of the tree, which is the side opposite the angle. What we have, then, is the angle (33 degrees), the side adjacent to the angle (105 ft), and we are looking for the side opposite the angle (x). What we need to use is the tangent ratio, which relates the side opposite the angle to the side adjacent to the angle, as follows:
[tex]tan33=\frac{x}{105}[/tex]
To solve for x we multiply both sides of the equation by 105 to get 105tan33°=x. Plug that into your calculator in degree mode to get 68.18779729. Round from there to get 68.2 feet.
Solve. 10x^2 = 6 + 9x10x 2 =6+9x10, x, start superscript, 2, end superscript, equals, 6, plus, 9, x Choose 1 answer: Choose 1 answer: (Choice A) A x =\dfrac{5 \pm \sqrt{65}}{-2}x= ?2 5± 65 ? ? x, equals, start fraction, 5, plus minus, square root of, 65, end square root, divided by, minus, 2, end fraction (Choice B) B x =\dfrac{9 \pm \sqrt{321}}{20}x= 20 9± 321 ? ? x, equals, start fraction, 9, plus minus, square root of, 321, end square root, divided by, 20, end fraction (Choice C) C x =\dfrac{4 \pm \sqrt{26}}{10}x= 10 4± 26 ? ? x, equals, start fraction, 4, plus minus, square root of, 26, end square root, divided by, 10, end fraction (Choice D) D x =\dfrac{-1 \pm \sqrt{109}}{18}x= 18 ?1± 109 ? ?
Answer:
Option B.
Step-by-step explanation:
If a quadratic equation is defined as
[tex]ax^2+bx+c=0[/tex] .... (1)
then the quadratic formula is
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
The given equation is
[tex]10x^2=6+9x[/tex]
It can rewritten as
[tex]10x^2-9x-6=0[/tex] .... (2)
On comparing (1) and (2) we get
[tex]a=10,b=-9,c=-6[/tex]
Using quadratic formula we get
[tex]x=\dfrac{-(-9)\pm \sqrt{(-9)^2-4(10)(-6)}}{2(10)}[/tex]
[tex]x=\dfrac{9\pm \sqrt{81+240}}{20}[/tex]
[tex]x=\dfrac{9\pm \sqrt{321}}{20}[/tex]
Therefore, the correct option is B.
Answer:
B
Step-by-step explanation:
I got it right
Which pair of angles are coterminal with 120°?
240°, 600°
-240°, -600°
180°, -360°
-60°, 300°
Answer:
-240°, -600°
Step-by-step explanation:
Coterminal angles are angles that land in the same spot around a circle.
So, that means they do full turns of the circle to reach each other.
To find coterminal angles of a given angle (here 120 degrees), you add or subtract 360 (the number of degrees in a full circle). That can go in both positive or negative directions.
So, from 120 degrees, let's find the coterminal angle that is 1 rotation above and one rotation below:
120 + 360 = 480
120 - 360 = -240
You see that 480 isn't among the possible answers, so one part of the answer is -240. If you subtract another 360 degrees, you end up with -600 degrees... so the answer is -240°, -600°