Answer:
[tex]x=\frac{\pi }{4}[/tex]
Step-by-step explanation:
csc(2x) = 2
is also the same as
sin(2x) = 1/2
so we have to solve for sin(x)=1/2
[tex]x=\frac{\pi }{2}[/tex]
but we want to sin(2x) = 1/2 so we make it.
[tex]\\2x=\frac{\pi }{2} \\x=\frac{\pi }{4}[/tex]
A box is 9 inches by 11 inches. The donuts have a radius of 1.25 inches. How many donuts can fit in the box?
Answer:
14 donuts
Step-by-step explanation:
Packing circles in a rectangular space is always an interesting problem. Sometimes, it works well to put them on a grid. Other times, more circles can be packed in if they are somewhat off-grid. The details depend on the specific dimensions.
The attached shows a way to fit 14 donuts in the box.
_____
Additional comment
Packing them on a square grid allows only 12 donuts to be put in the box.
For the graph given, select the statement that best represents the given system of equations.6x + 4y = 2 3x + 2y = 1
A. inconsistent
B. consistent and independent
C. not enough information
D. coincident
Answer:
D. coincidentStep-by-step explanation:
An coincident system of equations means that it has infinite solutions, because one line is on the other one. This happens when their equation are the same, or their "parent" line is the same.
So, given equations are:
6x + 4y = 2 and 3x + 2y = 1
Observe that if we divide the first by 2, we have
[tex]\frac{6x+4y}{2} =\frac{2}{2}[/tex]
[tex]\frac{6x}{2}+\frac{4y}{2} =1[/tex]
[tex]3x+2y=1[/tex]
As you can see, using the first equation, we found that it has the same "parent" equation than the second equation. In other words, they are basically the same. This means that they represent the same line, so, the system is coincident and they have infinite solutions.
The answer is coincident :)
write two equations that when graphed look like this *see image*. please help its due soon and i will give ya 75 points for answering, thanks, 5 stars, and brainlist.
The graph is showing the equation of circle x²+y²=4
What is a circle?A circle is a two-dimensional geometry on the plane having a centre point and the circular line is drawn equidistant from the centre point.
The given graph in the question represents the equation of the circle cutting the points on the x-axis and y-axis at 4 which is the radius of the circle.
The equation will be as follows:-
x²+y²=4
Hence the graph is showing the equation of circle x²+y²=4
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Two legs of a right triangle measure 3 inches and 4 inches. Which of the following choice for the
length of the third side will make the triangle a right triangle?
Answer:
5 inchStep-by-step explanation:
Two legs of a right triangle measure 3 inches and 4 inches. Which of the following choice for the length of the third side will make the triangle a right triangle?
not having the choices we solve with Pythagoraslet the unknow side xx = √(3²+4²)
x = √(9 + 16)
x = √25
x = 5Need help for this please
Answer:
Using 22/7 as pi, the area of a circle with a diameter of 14 metres is:
154 m²
Step-by-step explanation:
To solve, use the formula for the area of a circle.
Formula for area of a circleRemember the formula for area of a circle. Be careful not to mix up the formula for area with the formula for circumference!
[tex]A = \pi r^{2}[/tex]
From the question, we know:
π = 22/7d = 14 mTo use the formula, we need the radius ("r").
Radius ("r")The radius is a line that goes from the centre point of the circle to the circle outline. It is half the length of the diameter.
Diameter ("d")The diagram shows the diameter ("d"), which goes through the centre point of the circle. It is twice the length of the radius.
Solve for "r".
r = d/2
r = (14 m)/2
r = 7 m
Solve for area using formulaSubstitute r = 7 m and π = 22/7 into the formula for the area of a circle.
[tex]A = \pi r^{2}[/tex] Start with the formula and substitute.
[tex]\displaystyle{A = \frac{22}{7} (7\ m)^{2}}[/tex] Square "7" and the "m".
Remember that the answer for area is always squared units.
[tex]\displaystyle{A = \frac{22}{7} (49\ m^{2})}[/tex]
Multiplying a fraction and whole number is the same as multiplying the whole number in the numerator (top of the fraction).
[tex]\displaystyle{A = \frac{22*49}{7}m^{2}}[/tex] Simplify the numerator.
[tex]\displaystyle{A = \frac{1078}{7}m^{2}}[/tex] Divide.
[tex]A = 154\ m^{2}[/tex] Final answer
∴ The area of the circle is 154 m².
Suppose the heights of the members of a population follow a normal
distribution. If the mean height of the population is 72 inches and the
standard deviation is 3 inches, 99.7% of the population will have a height
within which range?
A. 63 inches to 81 inches
B. 66 inches to 78 inches
C. 60 inches to 84 inches
D. 69 inches to 75 inches
The option (A) 63 inches to 81 inches is correct after using the empirical Rule.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
We have:
The mean height of the population is 72 inches and the standard deviation is 3 inches, 99.7% of the population will have a height
99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean.
The lower range = 72 – 3(3) = 63 inches
The upper range = 72 + 3(3) = 81 inches
Thus, the option (A) 63 inches to 81 inches is correct after using the empirical Rule.
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What are the y-intercept and the slope of the line represented in the graph?
A. y-intercept = -4 and slope = -2
B. y-interecept = 4 and slope = -2
C. y-interecept = 2 and slope = 4
D. y-interecept = 4 and slope = -4
I need help with number 2 please
Answer:
B
Step-by-step explanation:
2.
what is the middle between 2 numbers (any numbers, really) ?
you add both numbers and divide the result by 2.
the same here :
(-3 + 24) / 2 = 21/2 = 10 1/2
proof :
what is the distance from -3 to 10 1/2 ? it is 10 1/2 from 0 to 10 1/2 plus 3 from -3 to 0 = 10 1/2 + 3 = 13 1/2.
what is the distance from 10 1/2 to 24 ? it is 13 from 11 to 24, and another half from 10 1/2 to 11. so, in total 13 1/2.
both distances are equal, so it is proven for 10 1/2 to be the midpoint.
i need help with 7th grade math please need help ASAP + brainleist
Answer:
Area = 6647.610055 cm^2
Circumference = 289.02652413 cm
Step-by-step explanation:
Area of Circle: Area = π*r^2
Circumference: C = 2*π*r or π*d
Area = π * 46^2 = 6647.610055
Circumference = 2*π*46 = 289.02652413
Find the value of y that satisfies the given conditions. Then graph the line on a separate sheet of paper. The line containing (−4, 9) and (4, 3) is parallel to the line containing (−8, 1) and (4, y).
Answer:
so first do nothing and just fail health class
The value of y that satisfies given conditions is y = - 8.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
We also know that slope(m) = (y₂ -y₁)/(x₂ - x₁).
So, lines parallel to each other have the same slope hence to find the value of y we'll equate their slopes.
∴ (3 - 9)/(4 + 4) = (y - 1)/(4 + 8).
-6/8 = (y - 1)/12.
-3/4 = (y - 1)/12.
-36/4 = y - 1.
- 9 = y - 1.
y = - 8.
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If 4x+2=11, what is the value of 2x-1 ?
Answer:
Step-by-step explanation:
4x + 2 = 11
4x = 9
x = 9/4
2(9/4) - 1
9/2 - 2/2= 7/2
URGENT!!! Which function, g or h, is the inverse function for function ƒ?
the function h because the graphs of ƒ and h are symmetrical about the line y = x
the function g because the graphs of ƒ and g are symmetrical about the line y = x
the function g because the graphs of ƒ and g are symmetrical about the x-axis
the function h because the graphs of ƒ and h are symmetrical about the y-axis
Answer:
The answer is The function h because the graphs of f and h are symmetrical about the line y = x.
Step-by-step explanation:
A function and its inverse function become symmetrical across the line y = x.
Please help! 5th-grade math!
It is a quadrilateral, parallelogram, and a rhombus
Answer:
quadrilateral, parallelogram, and rhombus.
Step-by-step explanation:
All quadrilaterals have 4 sides, all parallelograms have 2 sets of parallel sides, and a rhombus has diagonals that bisect each other perpendicularly.
The formula for the area of a triangle is, where b is the length of the base and h is the height.
Find the height of a triangle that has an area of 30 square units and a base measuring 12 units.
Answer: The formula for area of a triangle is area equals base times height divided by 2. the height is 5 units.
Step-by-step explanation:
2
7
What is the area of the triangle?
units?
Step-by-step explanation:
the area of a triangle is always
baseline × height / 2
where baseline and height are perpendicular (at a 90° angle) to each other.
so, in our case the area is
7 × 2 / 2 = 7 × 1 = 7 units²
4. (x + 4)2 + (y – 5)2 = 25
Center:
Radius:
Answer:
Center = (-4, 5)
Radius = 5
Step-by-step explanation:
Equation of a Circle :
(x - h)² + (y - k)² = r²(h, k) = coordinates of the centerr = radiusFinding the center :
h = -(4) = -4k = 5Center = (-4, 5)Finding the radius :
r² = 25r = √25radius = 5William William mowed 75% of the lawn in 33 minutes. Part A Which equation can be used to find how many minutes it will take for William to mow the whole lawn if he continues at the same rate? 75n=33 33n=75 0.33n=75 75n100=33 Part B How many minutes will it take for William to mow the whole lawn?
The equation that can be used to find out the total time it will take to William to mow the lawn is (75n) / 100=33.
What is an equation?This is a mathematical expression that represents a situation including a value that is not known.
In this case the best equation would be 75n / 100=33 as this is the only one that includes all the factors:
75% out of a 100% that is unknown (n)100 (represents the percentage)33 (total of minutes completing 75%)What is the result of this equation?75n / 100=33n/ 100 = 33/75n/100 =0.44n= 0.44 x 100n = 44 minutesLearn more about equations in: https://brainly.com/question/10413253
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The contingency table below shows the results of a random sample of 400 state
that was conducted to see whether their opinions on a bill are
representatives
related to their party affiliation.
Opinion
Party
Approve
Disapprove
Totals
No
Opinion
Republican
84
40
28
152
Democrat
100
48
36
184
Independent
20
32
12
64
Totals:
204
120
76
400
What is the expected frequency for the cell E3,1? Round your answer to the
nearest tenth.
32.6
45.3
28.9
38.3
Answer:
what is this question man .......
Help with the linear equations
Answer:
[tex]y \: intercept = - 1 \frac{1}{2} [/tex]
Step-by-step explanation:
The y intercept form for the equation of a line is
[tex]y = mx + c[/tex]
You should note that c represents the y-intercept of the line (where the line touches the y-axis)
[tex]y = mx + c \\ \\ we \:were\: given \:the \:equation \:y = x - \frac{3}{2} \\ \\ therefore \: the\: value \:of \:c \:is\: - \frac{3}{2} \:or -1 \frac {1}{2}[/tex]
A computer generates 90 integers from 1 to 8 at random. The results are recorded in this table. Outcome 1 2 3 4 5 6 7 8 Number of times outcome occurred 26 8 10 12 8 6 9 11 What is the experimental probability of the computer generating a 3 or a 5? 9% 20% 18% 40%
Answer:
20%
Step-by-step explanation: I took the test
Mike put 210 baseballs into 7 trash bins. He put the same number of baseballs in each bin. He took 2 trash bins of baseballs to the
baseball field. How many baseballs did Mike take?
A. 30
B. 896
C. 90
D. 60
Answer:
D. 60
Step-by-step explanation:
210 baseballs divided evenly between 7 trash bins = 30 balls per bin
2 trash bins multiplied by 30 balls per bin = 60 balls in two bins
Hope this helps!
Need this answered ASAP can’t find it anywhere online
Answer:
The value of the rational expression when x = -3 is undefined.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra II
Rational Functions
Asymptotes, HolesStep-by-step explanation:
Step 1: Define
Identify given.
[tex]\displaystyle \frac{x}{x^2 - 9} ,\ x = -3[/tex]
Step 2: Find Value
[Rational Expression] Substitute in x:∴ since we can't divide by 0, our rational expression when x = -3 will have to be undefined.
___
Topic: Algebra II
3(x+1)=5(x−2)+7
solve for x
solve the inequality:
0.2(x + 20) – 3 > –7 – 6.2x
Answer:
[tex]\huge\boxed{\sf x > -1.25}[/tex]
Step-by-step explanation:
Given inequality:0.2 (x + 20) - 3 > -7 - 6.2x
Distribute
0.2x + 4 - 3 > -7 - 6.2x
0.2x + 1 > -7 - 6.2x
Add 6.2x to both sides
0.2x + 6.2x + 1 > -7
6.4x + 1 > -7
Subtract 1 to both sides
6.4x > -7 - 1
6.4x > -8
Divide 6.4 to both sides
x > -8/6.4
x > -1.25
[tex]\rule[225]{225}{2}[/tex]
Answer:
x > -1.25
Step-by-step explanation:
Using the distributive property: a(b + c) → ab + ac
1. Distribute '0.2'
0.2(x) + 0.2(20) - 3 > -7 - 6.2x
0.2x + 4 - 3 > -7 - 6.2x
0.2x + 1 > -7 - 6.2x
2. Add '6.2x' to both sides
0.2x + 6.2x + 1 > -7 - 6.2x + 6.2x
6.4x + 1 > -7
3. Subtract '1' from both sides
6.4x + 1 - 1 > -7 - 1
6.4x > -8
4. Divide both sides by '6.4' to isolate the variable
6.4x ÷ 6.4 > -8 ÷ 6.4
x > -1.25
Final answer: x > -1.25
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please solve the given problem
Answer:
x = -47.1
x = -3.35454... (2-digit repeat)
Step-by-step explanation:
Each of the absolute value functions causes the overall behavior of the equation to change where that absolute value function's argument is zero. Those values of x are -7, -5/2, -2/5.
These breakpoints cause the domain of the equation to be divided into 4 parts. A graphing calculator shows us that solutions exist only in the two regions ...
x < -7-7 ≤ x < -5/2In those regions, the equation simplifies to ...
x < -72(-(x +2/5)) -2(-(x +7)) = 2/3x +(-(x +5/2))
x(-2 +2) -4/5 +14 = x(2/3 -1) -5/2 . . . . collect terms
15.7 = -1/3x . . . . . . add 5/2
x = -47.1 . . . . . . . multiply by -3
__
-7 ≤ x < -5/22(-(x +2/5)) -2(x +7) = 2/3x +(-(x +5/2))
x(-2 -2) -4/5 -14 = x(2/3 -1) -5/2 . . . . collect terms
(-3 2/3)x = 12.3 . . . . . . . . add 1/3x +14.8
x = -36.9/11 = -369/110
x = -3 39/110 ≈ -3.35454... (2-digit repeat)
Help please need quickly like rn
Answer:
288 m^3
Step-by-step explanation:
V=(1/3)Bh, where B is base, and h is height
The base will use the equation A=(1/2)bh
B = (1/2)12x9
B = 54
the height is given: 16m
substitute into Volume equation:
V=(1/3)54x16
V=288
A news report suggested that an adult should drink a minimum of 4 pints of water per day. based on this report determine the minimum amount of water an adult should drink, in fluid ounces, per week.
Answer:
448 fl oz/week
Step-by-step explanation:
1 week = 7 days
4 pints per day × 7 days/week = 28 pints per week
1 pint = 16 fl oz
28 pints/week × 16 fl oz/pint = 448 fl oz/week
On a place-value chart, you use exactly 12 counters to represent one decimal number and exactly 15 counters to represent another decimal number.
When you add the two numbers, you get a number you can represent with only 9 counters.
When you subtract the two numbers, you need more than 9 counters for the result.
• What could your numbers be For adding it be
• Explain how you came up with your numbers and why they work.
The possible number represented by the 9 counter is 27
How to determine the possible number?The counters are given as:
12 counters and 15 counters
When added, we get a number that can be represented by 9 counters.
This means that:
12 + 15 = 9x
Evaluate the sum
27 = 9x
Divide by 9
x = 3
When subtracted, you need more than 9 counters.
This means that:
x = 15 - 12 = 3
So, we conclude that the number is a multiple of 3 and 9
In other words, the decimal number is a multiple of 9 (i.e. 27)
Hence, the possible number is 27
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The diagram below shows the shape of the pool at Tori's house. Tori wants to out a fence all around the pool
The expression for the perimeter of the pool is 8x + 20 and the cost of fencing the pool is 27.76x + 69.4
How to complete the missing sides?There are two missing sides in the figure, and they can be calculated using the subtraction operation.
The equations to calculate the missing sides are:
Missing side 1 = 5x - 2 - (-6 + 4x)
Missing side 2 = 12 - x - (3x - 3)
Evaluate the equations
Side 1 = x + 4
Side 2 = 15 - 4x
Hence, the missing sides are x + 4 and 15 - 4x
The perimeter of the poolThis is the sum of the side lengths of the pool.
So, we have:
Perimeter = 5x - 2 + 12 - x - 6 + 4x + 3x - 3 + x + 4 + 15 - 4x
Collect like terms
Perimeter = 5x - x + 4x + x - 4x + 3x - 2 + 12 - 6 - 3 + 4 + 15
Evaluate
Perimeter = 8x + 20
Hence, the perimeter of the pool is 8x + 20
An equation to solve for xIn (b), we have:
P = 8x + 20
Where P represents the perimeter of the pool
The cost of fencing the poolThe cost of fencing the pool is the product of the perimeter and the unit cost per foot.
So, we have:
C = (8x + 20) * 3.47
Expand
C = 27.76x + 69.4
Hence, the cost of fencing the pool is 27.76x + 69.4
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A rug had a length of 9 feet and a width of 3 feet what is the perimeter of the rug
Answer:
24 ft
Step-by-step explanation:
to find the perimeter of rug is you have to add 9+9+3+3= 24