Answers
Look at the picture.
[tex]x=0\ \vee\ x=\pi\ \vee\ x=\dfrac{3\pi}{2}[/tex]
Related Questions
A boy spent 2/3 money on book store,1/3 money on craft store and has left $8. How much money he has at first?
Answers
2/3s of 26 is 24 minus 36 is 12
so at first He would have to have $36
shirts are onsale at 3 for $15.50. how many shirts can you buy with $139.50.
Answers
Multiply 9 by 3 and you get your answer: 27 Shirts
First you take the $139.50 and divide it by $15.50
139.50 / 15.50 = 9
Then you take the 9 and multiply it by 3, be cause there are 3 shirts per $15.50
9 x 3 = 27
You can buy a total of 27 shirts with $139.50
A quality control expert randomly samples 60 pairs of sunglasses and finds 5 defective pairs. predict how many defective pairs will be in a shipment of 420 sunglasses.
Answers
7*5=35 sunglasses
For this case the first thing you should do is find the percentage of sunglasses that are defective.
For this, we make the following rule of three:
60 pairs -------------------> 100%
5 pairs ---------------------> x
From here, we clear the value of x.
We have then:
[tex] x = (\frac{5}{60}) * (100)
x = 8.3%
[/tex]
We now look for the amount of sunglasses that may come with defects.
We have then:
[tex] N = (0.083) * (420)
N = 34.86
[/tex]
Rounding to the nearest whole number:
[tex] N = 35
[/tex]
Answer:
About 35 defective pairs will be in a shipment of 420 sunglasses
A jacket is discounted 40% the jacket is now 38.70 dollars what was the original price
Answers
To find the original price, you'll first need to convert 40% into a decimal. You can do this by moving the decimal point twice to the left. So now you have 0.40. Now you'll need to divide 38.70 by 0.40. Once you've done that, you'll get the original price
The original price of the jacket was $96.75
I hope this helps!
Drag and drop the symbols to enter the equation of the circle in standard form with center and radius given. Center (-8, -3), radius = 2 times the square root
please answer before 1:00
Answers
(x-a)²+(y-b)²=r²
where:
(a,b) is the center and r is the radius.
Given that (a,b) is (-8,-3) and r=2 units
then the equation of the circle will be:
(x-(-8))²+(y-(-3))²=2²
simplifying the above we get:
(x+8)²+(y+3)²=4
What is the correct order of operations for simplifying the expression (x+3)^2-(x^2+9)/2x^2
Answers
The correct order of operations for simplifying the expression (x+3)^2 - [tex](x^2+9)/2x^2[/tex] is as follows:
1. Square the binomial (x+3) to get x^2 + 6x + 9.
2. Divide each term in (x^2+9) by [tex]2x^2[/tex] to get [tex]1/2 + 9/2x^2[/tex].
3. Substitute the simplified expressions back into the original expression: [tex]x^2 + 6x + 9 - (1/2 + 9/2x^2).[/tex]
The correct order of operations for simplifying the expression (x+3)^2 - (x^2+9)/2x^2 is as follows:
1. Start by simplifying the expression within the parentheses: (x+3)^2. This means squaring the binomial (x+3). To do this, you multiply the binomial by itself: (x+3) * (x+3). This results in [tex]x^2 + 6x + 9.[/tex]
2. Next, simplify the expression within the second set of parentheses: (x^2+9).
3. Now, divide [tex](x^2+9)[/tex] by 2x^2. To do this, divide each term in (x^2+9) by 2x^2. This gives us [tex](x^2/2x^2)[/tex] [tex]+ (9/2x^2)[/tex]. Simplifying further, we get 1/2 + [tex]9/2x^2[/tex].
4. Finally, substitute the simplified expressions back into the original expression: [tex]x^2 + 6x + 9 - (1/2 + 9/2x^2).[/tex]
An insect flies 20 feet in 1 second. how fast does the insect fly in miles per hour?
Answers
All of the units cancel other than miles divided by hours which is what we need.
Now we do (20 * 60 * 60 * 1) / 5280 which is 13.636363 (repeating) or 13.6364 miles per hour.
John is weighing his jars of coins. His jar of pennies weighs 84.96 ounces, and his jar of nickels weighs 3.11 kilograms. There are 0.0283495 kilograms per ounce. Which jar weighs more, and how many more pounds does it weigh?
Answers
The correct answer is 1.55 lbs.
Justin is a musician. For eight months a year, he teaches school and is paid $34,780 annually. During the summer months, he teaches private students and plays in clubs, earning another $5,700. What is his average monthly salary, based on his yearly earnings?
Answers
First, we'll need to add the two values together. This gives us $40,480. Then, since we know that there are 12 months in a year, we need to divide the total amount by 12. This gives us, on average, $3373.33 each month.
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
Solve for v in the formula v = u + 10t when u = 16 and t = 4. a. v = -22 c. v = 56 b. v = 3 d. v = 40
Answers
You put 16 in for u and 4 in for t
v = (16) + 10(4)
Multiply
v = 16 + 40
Add
v = 56
The answer is v = 56
Hope this helps!
Determine whether quantities vary directly or inversely and find the constant of variation. A teacher grades 25 students essays in 4 hours. Assuming he grades at the same speed, how long will it take him to grade 35 essays?
Answers
The number of essays graded varies directly with the number of hours worked, with a constant rate of 6.25 essays per hour. Therefore, it will take approximately 5.6 hours for a teacher to grade 35 essays at this rate.
The scenario presented describes a situation where the number of essays graded is directly proportional to the number of hours worked. This means that as the number of essays increases, the hours required to grade them also increase, assuming the grading speed (rate) is constant. To find the constant of variation (or rate of grading), we divide the number of essays by the number of hours.
If a teacher grades 25 essays in 4 hours, the rate would be 25 essays÷4 hours = 6.25 essays per hour. To find out how long it will take to grade 35 essays at this rate, we divide the number of essays by the rate:
35 essays ÷ (6.25 essays per hour) = 5.6 hours.
So, it will take the teacher approximately 5.6 hours to grade 35 essays given the constant grading speed.
the dimensions of a rectangle can be expressed as x-3 and x+8. If the area of the rectangle is 42 square feet. Find the dimensions of the rectangle.
Answers
the area of a rectangle=length*width
let
length=x-3
width=x+8
area=42 ft²
so
42=(x-3)*(x+8)----------> x²+8x-3x-24=42--------> x²+5x-66=0
using a graph tool-------> to resolve the second order equation
see the attached figure
the solution is
x=6
hence
length=x-3------> 6-3-----> 3 ft
width=x+8 ------> 6+8----> 14 ft
the answer is
the dimensions of the rectangle are 3 ft x 14 ft
Line segment AB has endpoints A(10, 4) and B(2, 8). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:4. A) (6, 6) B) (2, 56 5 ) C) ( 24 5 , 42 5 ) D) ( 42 5 , 24 5 )
Answers
How do I factorise
6-42x
Answers
FACTORING: 6 - 42x
STEPS:
6 - 42x
-42x + 6
= -6(7x - 1)
FINAL ANSWER: -6(7x - 1)
Answer:
[tex]6(-7x+1)[/tex]
Step-by-step explanation:
Given: The equation [tex]6-42x[/tex].
To find: Factorize the given equation.
Solution:
The given expression is:
[tex]6-42x[/tex]
which can be rewritten as:
[tex]-42x+6[/tex]
Upon solving the above expression and Taking 6 common from both the terms of the expression ,we get
[tex]6(-7x+1)[/tex]
which is the required factorized form of the given expression.
In March, a family starts saving for a vacation they are planning for the end of August. The family expects the vacation to cost $1327. They start with $120. At the beginning of each month they plan to deposit 20% more than the previous month. Will they have enough money for their trip? If not, how much more do they need? Select the correct answer below and, if necessary, fill in the answer box within your choice.
Answers
March: 120
April: 120+(120×20)/100=120+24=144
May: 144+(144×20)/100=144+18,8=162,8
June: 162,8+(162.8×20)/100=162,8+32.56=195.36
July: 195.36+(195.36×20)/100=195.36+23.87=219.23
August: 219.23+(219.23×20)/100=219.23+43.85=263.08
120+144+162.8+195.36+219.23+263.08=1105.19
So the answer is no.
One thousand tickets were sold for a baseball game there were one hundred more adult tickets sold than student tickets, and there were fou times as many tickets sold to students as to children. how many of each type of ticket were sold.
Answers
400 Student tickets
100 Children tickets
Let x = adults
Let y = Students
Let z = children
Then set up this system of equations
x +y + z = 100
y - 4z = 0
x - y = 100
Solve using elimination and combination.
Group A represents males on the football team at Grizzly High School. Group B represents the men’s cross country team at Grizzly High School. Both teams are played during the same season. What can you conclude about the groups A and B?
A.
There are not any students who play in either football or run cross country.
B.
There are not any students who run only cross country .
C.
There are not any students who play only football..
D.
There are not any students who are in both sports, football and cross country.
Answers
You actually can't tell if their is a team with no one and the other team has players. B and C are wrong for the same reason A was wrong..
Your answer from this bunch is D but it's not clear that it is right. One team could practice on Tuesdays and Thursdays and the other on Mondays and Wednesdays. I don't know what you'd do on game day. But schools have worked that problem out, I'm sure. There would not be a conflict.
D <<<<<<< answer
Answer:
D.
There are not any students who are in both sports, football and cross country.
Step-by-step explanation:
The radius of this ball is 24 inches. Which equation gives the ball's surface area, in square inches?
Answers
PLEASE HELP!!! The question is in the picture!
Answers
vertical component=110 N*sin 25°-----> -46.5 N (down)
horizontal component=110 N *cos 25°----> -99.7 N (left)
the vector diagram in the attached figure
what is 3x times x???
Answers
3x × x = 3x²
Hope I helped! :3
3 x squared:) hope this helps
What transformation matrix would result in a 300 degrees counterclockwise rotation about the origin?
i cant type all of the options, but they all look like fractions inside brackets, some with square root signs.
Answers
[tex]\begin{pmatrix}cos\:\theta &-sin\:\theta \\ sin\:\theta &cos\:\theta \end{pmatrix}[/tex]
The given angle is θ=300°.
The values we need are
[tex]cos\left(300^{\circ} \right)=\frac{1}{2}[/tex]
[tex]sin\left(300^{\circ} \right)=-\frac{\sqrt{3}}{2}[/tex]
Substituting these into the given transformation matrix, we have
[tex]\begin{pmatrix}\frac{1}{2}&\frac{\sqrt{3}}{2}\\ -\frac{\sqrt{3}}{2}&\frac{1}{2}\end{pmatrix}[/tex]
the answer is B
hope this helps :)
What is the measure of ∠F, to the nearest degree?
44°
57°
71°
78°
Answers
Answer:
Option A. 44°
Step-by-step explanation:
In a given triangle FGH sides have been given as FG = 7 yards, FH = 6 yards, and GH = 5 yards.
We have to calculate the approximate value of ∠F.
We apply the cosine rule in the given triangle.
5² = 7² + 6² - 2×7×6×cosF
25 = 49 + 36 - 84× cosF
25 = 85 - 84 cosF
84cosF = 85 - 25 = 60
[tex]cosF=\frac{60}{84}=0.71428[/tex]
[tex]F=cos^{-1}( 0.71428) = 44.4[/tex]
F = 44°
Therefore option A. 44° is the correct answer.
You travel 5 miles downstream in a kayak at a speed of r miles per hour. You turn around and travel 6 miles upstream at a speed of 0.6r miles per hour. Finally, you turn around and return to your original starting point at a speed of r+1 miles per hour.
Answers
This high school physics problem deals with relative velocity and vector addition by describing a journey in a kayak under varying speeds amidst a river current. To solve such a problem, the total time taken is found by adding the individual times for each part of the journey, each calculated by dividing the distance by the speed of the kayak.
Explanation:The subject matter of this question involves understanding of the concept of relative velocity, a topic usually taught in high school physics. The student is navigating a kayak in the river with varying speeds relative to different sections of the journey, demonstrating the behavior of an object in a current or wind. In essence, the motion of the kayak is a combination of its own propelled movement and the movement of the river current.
To solve the mathematical aspect of such a problem, you would typically find the total time taken for each segment of the journey by dividing the distance of that segment by the speed at which the kayak is moving. Adding these times together will give the total time taken for the whole journey. Finally, you should understand this as an example of vector addition, where the total velocity of the kayak is the vector sum of its velocity relative to the water and the water's velocity relative to the riverbank.
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A rectangular plot of land that contains 1500 square meters will be fenced and divided into two equal portions by an additional fence parallel to two sides. find the dimensions of the land that require the least amount of fencing.
Answers
The perimeter will be:
2x+3w=1500
thus
3w=(1500-2x)
w=(1500-2x)/3
w=500-2/3x
The area will be:
A=x*w
A=x(500-2/3x)
A=500x-(2/3)x²
The above is a quadratic equation; thus finding the axis of symmetry we will evaluate for the value of x that will give us maximum area.
Axis of symmetry:
x=-b/(2a)
from our equation:
a=(-2/3) and b=500
thus
x=-500/[2(-2/3)]
x=375
the length will be 375 m
The width will be 250 m
Write an equation of the line with the given slope and containing the given point. write the equation in the slope-intercept form yequals=mxplus+b. slope negative 3−3; through (22,negative 10−10)
Answers
m=-3
y=-3x+b
(22,-10), To find b substitute x=22, and y=-10 into y=-3x+b.
-10=-3*22+b
-10+66=b
b=56
y= - 3x+56
The sum of two consecutive numbers is 131 .What are the two numbers ?
Answers
n + (n + 1) = 131n + n + 1 = 1312n + 1 = 131 |-12n = 130 |:2n = 65n+1 = 66
Answer: 65 and 66.
The sum of two consecutive numbers is 131. What are the two numbers?
Answer is provided in the image attached.
A 9.5-foot pole casts a shadow that is 29 feet long. What is the approximate measure of angle L? The triangle is JKL and K=90 degrees.
Answers
Answer:
A. 0.32 rad
Step-by-step explanation:
Final answer:
To find the angle L in a triangle where a 9.5-foot pole casts a 29-foot shadow, calculate the angle using the tangent function, yielding an approximate angle of 72.8 degrees.
Explanation:
A 9.5-foot pole casts a shadow that is 29 feet long. What is the approximate measure of angle L?
First, determine the scale factor between the pole and its shadow: 29 feet (length of shadow) ÷ 9.5 feet (length of pole) = 3.05.
Next, calculate the angle L using the tangent function: tan(L) = opposite/adjacent = 29/9.5 ≈ 3.05. Taking the inverse tangent gives L ≈ 72.8 degrees.
A coffee machine can be adjusted to deliver any fixed number of ounces of coffee. if the machine has a standard deviation in delivery equal to 0.4 ounce, what should be the mean setting so that an 8-ounce cup will overflow only 0.5% of the time?
Answers
The question can be addressed using the principles of Normal Distribution. Given the z-chart, 8 ounces is the observed value for the 99.5th percentile, which equates to approximately 2.58 standard deviations. Therefore, the mean setting of the coffee machine should be set around 8 ounces for the cup to overflow only 0.5% of the time.
Explanation:The situation described in the question is a typical case of application of Normal Distribution. As a reminder, in a Normal Distribution, 99.7% of the values lie within 3 standard deviations of the mean. The question states that the cup should overflow only 0.5% of the time. Therefore, we need to consider the 99.5% of the left side under the normal curve (as we're considering the upper limit), which corresponds to around 2.58 standard deviations under the normal curve.
Given that the standard deviation (σ) is 0.4 ounces, using the formula X = μ + Zσ (where Z is the Z-score corresponding to the desired percentile, μ is the mean we want to find, and X is the threshold value where the cup overflows at 8 ounces), we can substitute the known values and solve for μ.
Therefore, 8 = μ + 2.58 * 0.4 Solving for μ gives us around μ = 7.966, or about 8 ounces. Hence, the mean setting of the coffee machine should be set around 8 ounces to ensure that the cup will overflow only 0.5% of the time.
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Identify intervals on which the function is increasing, decreasing, or constant.
g(x) = 1 - (x - 7)^2
Select one:
a. Increasing: x < 7; decreasing: x > 7
b. Increasing: x < -7; decreasing: x > -7
c. Increasing: x > 1; decreasing: x < 1
d. Increasing: x < 1; decreasing: x > 1
Answers
what is the length of the diagonal AC in the rectangle below?
Answers
Then use Pythagorean Theorem to find BD (the hypotenuse of right triangle DCB). So Pythag here would be:
[tex]BC^2+DC^2=BD^2[/tex]
See attached picture for full work.