Answer:
[tex]\displaystyle x=\biggr\{\frac{\pi}{6},\frac{11\pi}{6}\biggr\}[/tex]
Step-by-step explanation:
[tex]\displaystyle 5\cos x-\sqrt{3}=3\cos x;\:0\leq x < 2\pi\\\\5-\frac{\sqrt{3}}{\cos x}=3\\ \\-\sqrt{3}\sec x=-2\\\\\sec x=\frac{2}{\sqrt{3}}\\\\\sec x=\frac{2\sqrt{3}}{3}\\ \\\cos x=\frac{3}{2\sqrt{3}}\\ \\\cos x=\frac{3\sqrt{3}}{6}\\ \\\cos x=\frac{\sqrt{3}}{2}\\\\x=\biggr\{\frac{\pi}{6},\frac{11\pi}{6}\biggr\}[/tex]
PLEASE HELP ILL MARK BRAINEST!!!!
What is the value of 64-9.41?
Answer:
54.59
Step-by-step explanation:
carry the 10 over and 1-.41 is .59
What is the variance of the data set? round to the nearest hundredths. 0.40 0.72 1.15 2.14
The variance of the data set is 0.43.
What is the variance?The variance is used to measure the spread or the dispersion of a dataset using all the data points in the dataset. The variance is the sum of the squared difference between the data point and the mean.
The first step is to determine the mean: (0.40 + 0.72 + 1.15 + 2.14) / 4
= 4.41 / 4= 1.10
The second step is to subtract the mean from each of the data point and square the difference:
(0.40 - 1.10) ² = 0.49(0.72 - 1.10)² = 0.14(1.15 - 1.10)² = 0.0025(2.14 - 1.10)² = 1.08Add the sum of the squared differences and divide by 4 : 1.7125/4 = 0.43
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Find the equation of the line parallel to 6x+5y=1 and passing through (-4,-2)
Hi Student!
The first step that we need to take before trying to solve the problem is that we need to take out important information from the problem. The first important piece of information that is given to us is that we are trying to find an equation of a line that is parallel to a different line. This means that our slope is going to be the same as the initial line given. The second piece of information that is given is a point through which our line passes through which will help us greatly when solving for our line.
The next step that we must take is to solve for y in the given equation so we can see what the slope is.
Subtract 6x from both sides
[tex]6x + 5y = 1[/tex][tex]6x - 6x + 5y = 1 - 6x[/tex][tex]5y = 1 - 6x[/tex]Divide both sides by 5
[tex]\frac{5y}{5} = \frac{1 - 6x}{5}[/tex][tex]y= \frac{1}{5} - \frac{6x}{5}[/tex][tex]y=- 1.2x+ 0.2[/tex]Now that we have completely solved for y, we can see that the slope is -1.2 using the y = mx + b formula which states that m is the slope.
Moving onto the next step, we must use the point-slope formula to determine what the new equation is that has the same slope and passes through (-4, -2).
Insert the Values
[tex](y-y_1)=m(x-x_1)[/tex][tex](y-(-2))=-1.2(x-(-4))[/tex]Simplify the Equation
[tex]y+2=-1.2(x+4)[/tex]Distribute the Equation
[tex]y+2=(-1.2*x)+(-1.2*4)[/tex][tex]y+2=-1.2x-4.8[/tex]Subtract 2 from both sides (to isolate y)
[tex]y+2 - 2=-1.2x-4.8- 2[/tex][tex]y=-1.2x-6.8[/tex]Therefore, our final answer for the equation of the line parallel to 6x + 5y = 1 and that passes through (-4, -2) is y = -1.2x - 6.8.
what is 16/18 and 4/18 in its simplest form ?
Answer:
in fractions
16/18 = 8/9
4/18 = 2/9
Answer:
8/9 and 2/9
Step-by-step explanation:
for 16/18
divide the numerator and denominator by 2 to option it's simplest form
16/18÷2/2 = 8/9
for 4/18
also divide the numerator and denominator by 2 to get the simplest form.
4/18 ÷2/2= 2/9
Find the circumference,
18 ft
Answer:
56.549 feet
Step-by-step explanation:
Diameter. ft in m
18′0″ 56.55. 678.6 17.24
18′1″ 56.81.
18′2″ 57.07. 684.9
18′3″ 57.33. 688.0
18′4″ 57.60. 691.2
18′5″ 57.86. 694.3 17.64
18′6″ 58.12. 697.4 17.71
18′7″ 58.38 700.6 17.79
18′8″ 58.64 703.7 17.87
18′9″ 58.90. 706.9 17.95
18′10″ 59.17. 710.0 18.03
18′11″ 59.43. 713.1 18.11
The graph below shows the relationship between the number of months different students practiced tennis and the number of matches they won:
The title of the graph is Tennis Matches. On x axis, the label is Number of Months of Practice. On y axis, the label is Number of Matches Won. The scale on the y axis is from 0 to 22 at increments of 2, and the scale on the x axis is from 0 to 12 at increments of 2. The points plotted on the graph are the ordered pairs 0, 2 and 1, 5 and 2, 8 and 3, 9 and 4, 10 and 5, 12 and 6, 13 and 7, 16 and 8,17 and 9, 18 and 10,20. A straight line is drawn joining the ordered pairs 0, 3.3 and 2, 6.8 and 4, 10 and 6, 13.5 and 8, 17 and 10, 20.5.
Part A: What is the approximate y-intercept of the line of best fit and what does it represent? (5 points)
Part B: Write the equation for the line of best fit in the slope-intercept form and use it to predict the number of matches that could be won after 13 months of practice. Show your work and include the points used to calculate the slope. (5 points)
Part A
y-intercept: 3
It represents that after 0 months practice, the number of matches won is 3.
Part B
slope intercept form: y = mx + b
Here to find slope,
take two points: (5, 12), (0, 3)
[tex]\sf slope: \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{rise}{run}[/tex]
[tex]\rightarrow \sf slope = \dfrac{3-12}{0-5} = 1.8[/tex]
Equation:
y - y1 = m(x- x1)
y - 12 = 1.8(x - 5)
y = 1.8x - 9 + 12
y = 1.8x + 3
To find Matches won after 13 months
insert x = 13
y = 1.8(13) + 3
y = 26.4 ≈ 26 matches
The team could have won 26 matches after 13 months practice.
Answer:
See below ~
Step-by-step explanation:
Part A :
The approximate y-intercept of the line is about (0, 3)This represents that with 0 months of practice, 3 matches are wonPart B :
Finding the slopeTake two points on the line : (0, 3) and (5, 12)m = y₂ - y₁ / x₂ - x₁m = 12 - 3 / 5 - 0m = 9/5m = 1.8 (slope)Forming the equation :
y = mx + b (where m is the slope and b is the y-intercept)y = 1.8x + 3Predicting how many matches can be won with 13 months of practice :
Here, x (number of months) = 13y = 1.8(13) + 3y = 23.4 + 3y = 26.4y = 26 matches (roughly)Graph on the same axes: y =x^2-4 and y=4-x^2. Write an equation for the part of the graph which is above of the x-axis.
The graph can be seen at the end, and the piecewise function for the part above the x-axis is:
f(x) = x^2 - 4 if x ∈ (-∞, -2] or x ∈ [2, ∞)
f(x) = 4 - x^2 if x ∈ (-2, 2).
How to write the equation?
First, we need to graph both functions, so we can see when each one is positive, the graphs of:
y = x^2 - 4
y = 4 - x^2
Can be seen at the end.
So, the first function is positive in the interval (-∞, -2] and [2, ∞), and the second function is positive in the interval (-2, 2)
So for the part of the function above the x-axis we have a piecewise function:
f(x) = x^2 - 4 if x ∈ (-∞, -2] or x ∈ [2, ∞)
f(x) = 4 - x^2 if x ∈ (-2, 2).
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Answer:
y= |x^2-4|
Step-by-step explanation:
Once you graph y=x^2-4 and y=4-x^2, you will get a graph like the first picture. The equation for the parts above the x-axis would be y=|x^2-4| and would graph like the second picture.
The fulcrum of a lever is the point on which it turns. based on the function, how many pounds of force are needed to lift the rock if the distance from the fulcrum is 6 feet? pounds of force
The amount of force that is required to lift the rock if the distance from the fulcrum is 6 feet is 10 lb of force.
Calculations and Parameters:Based on the given graph, we can see the curve passing through the point (1.5,40), (2,30), (2.5,24), (3,20), and (4,15).
These points satisfy by the equation
y= 60/x
and,
x is the distance in feet from the fulcrum y is needed force in pounds.If we input the value of x into the equation,
y= 60/6
= 10 lbs of force.
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Answer:
Keep it simple: answer 10
Step-by-step explanation:
6) please help solve sin²3theta=1
Answer:
Step-by-step explanation:
Find the surface area of the cone to the nearest square unit. Use π = 3.14.
Answer:
339.12 cm²
Explanation:
surface area of cone: πr² + πrl
where "r" is radius, "l" is slant height
Here given:
radius: 6 cmslant height: 12 cmSolve for surface area:
πr² + πrl(3.14)(6)² + (3.14)(6)(12)113.04 + 226.08339.12 cm²So
TSA
πr(r+l)π(6)(6+12)6π(18)108π339.12cm²PLEASE HELP ME!!!!!!!
Graph the function () = 12 (2) squared on the coordinate plane
The coordinates are
-2,4
-1,1
0,0
1,1
2,4
1. The height of a right triangular prism is 1 5/6 inches. Each side of the triangular base measures 10 inches, and the height of the base is 8 2/3 inches. The triangular prism is placed atop a cube whose side measures 10 inches so that one of the triangular prism’s bases lies completely on one side of the cube.
What is the surface area of the solid formed?
If the height of a right triangular prism is 1 5/6 inches. The surface area of the solid formed is: 598.33 in².
Surface areaFirst step
Right triangular prism=1 5/6 inches= 11/6 inches
Height of the base=8 2/3 inches = 26/3 inches
Second step
Surface area = 5(10× 10) + (0.5÷ 10 × 26/3) + 3(10× 11/6)
Surface area = 5(100) +43.33+ 3(18.33)
Surface area = 500) +43.33 + 55
Surface area = 598.33 in²
Therefore the surface area of the solid formed is about 598.33 in²
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can someone help me with this thank you
10+5h = 25
thank you thank you thank you
Answer:
h=3
Step-by-step explanation:
Here's the explanation
Move 10 to the other side
5h=25-10
5h=15
h=15/5
h=3
10+5h=25
10+5h-10=25-10
5h=15
[tex]\frac{5h}{5}=\frac{15}{5}[/tex]
h=3
the answer is 3
hi can you ya'll help me
Step-by-step explanation:
[tex]3 \sqrt{3 \:} + \sqrt{3} [/tex]
Simplify,then combine each:
[tex] = 4 \sqrt{3} [/tex]
or
[tex]3 \sqrt{3 \:} + \sqrt{3} [/tex]
=5.196+1.732
=6.928
[tex] \approx6.930[/tex]
A store buys 6 sweaters for $30 and sells them for $132. How much profit does the store make per sweater?
Emma has a mask collection. she keeps 190 of the masks on her wall, which is 38% of her entire collection. what is the total number of masks in emma's collection?
Answer:
262 Masks
Step-by-step explanation:
190×0.38=72.2 but there cannot be 0.2 masks so it becomes 72. 190+72=262.
The total number of masks in Emma's collection is 262 Masks.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that Emma has a mask collection. she keeps 190 of the masks on her wall, which is 38% of her entire collection.
The total number of masks will be calculated as,
190×0.38=72.2
But there cannot be 0.2 masks so it becomes 72.
Total mask = 190+72
Total mask =262.
Therefore, the total number of masks in Emma's collection is 262 Masks.
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Help me with this question please
Volume of a Cylinder = pi x r^2 x height
diameter = 10, so radius = 5
height = 6
Volume = pi x 5^2 x 6
Volume = pi x 25 x 6
Volume = 150pi
Answer: 150pi cubic feet
Hope this helps!
Regardless of how the graph is oriented in the standard
(x,y) coordinate plane, NO graph in one of the
following categories has a vertical line of symmetry.
Which one?
F. Line
G. Square
H. Pentagon
J. Parallelogram
K. Scalene triangle
Answer:
the answer is j because it's impossible to draw a line through the center of any parallelogram that divides the figure into two equal halves that are mirror images of each other
Out of the given options, the shape that does not have a vertical line of symmetry is J. Parallelogram.
The correct answer is J. Parallelogram.
A vertical line of symmetry means that if a line is drawn vertically through the shape, the two halves will be mirror images of each other.
In the case of a line (F), it is one-dimensional and does not have an area, so it does not have any symmetry.
A square (G) has four sides of equal length and four right angles. It has both vertical and horizontal lines of symmetry, dividing it into four congruent quadrants.
A pentagon (H) is a five-sided polygon. Depending on its shape and orientation, it may or may not have a vertical line of symmetry. For example, a regular pentagon does have a vertical line of symmetry, while an irregular pentagon may not.
A parallelogram (J) is a four-sided polygon with opposite sides that are parallel and equal in length. It does not have a vertical line of symmetry because its opposite sides are not mirror images of each other.
A scalene triangle (K) is a triangle with no equal sides or equal angles. It does not have a vertical line of symmetry because its sides and angles are not symmetric.
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I need help with this one pls
Answer:
5/8
Step-by-step explanation:
Please help me with my math please.?
Answer:
x = 6, y = 0, m = -1
y = mx + b
0 = -1(6) + b
0 = -6 + b
6 = b
y = -1x + (6)
Step-by-step explanation:
^^^
See answer, pretty simple.
So
equation
y=mx+b0=-1(6)+bb-6=0b=6So equation
y=-x+6pls pls pls help me i am giving you a ton of points and pls explain how you got the answer.
The expected value of the defective skateboard will be 4/25. Then the correct option is B.
What is probability distribution?Probability distribution of a random variable is the collection of value and its probability pair for values of that considered random variable.
It might be a function, a table, etc.
The table is shown below.
Then the expected value of the defected skateboard will be
p = 0 x 9/10 + 1 x 1/20 + 2 x 1/25 + 3 x 1/100
p = 1/20 + 2/25 + 3/100
p = 5/100 + 8/100 + 3/100
p = 16/100
p = 4/25
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please help i really need it
Answer:
6/63
Step-by-step explanation:
To find the probability in fraction form you must first add all the evidence together and then use that number as the denominator
Answer:
2/21
Step-by-step explanation:
There were a total of 7+6+12+19+19=63 spins, 6 of which blue.
So, you can make the fraction 6/63=2/21 to represent the probability of the spinner landing on blue the next spin
QUESTION 3 Simplify the following expression 3.1.1 Add:-4
x+6+11x - 5
Answer:
-24 + (-55) = -79
Step-by-step explanation:
-4x+6+11x - 5
Step-by-step explanation:
[tex] = x + 6 + 11x - 5[/tex]
Organize the expression....
[tex] = x + 11x + 6 - 5[/tex]
Simplify the expression...
[tex] = 12x + 1[/tex]
...
The local grocery store is being remodeled. The width of the floor is 84 feet and the length of the floor is 71 feet. What is the perimeter of the floor?
Answer:
the perimeter is the width added to the length
Determine the domain and the range of the relation, and tell whether the relation is a function.
{(10,10), (26,−6), (40,10), (10,1), (56,1)}
Answer:
Step-by-step explanation:
How do you tell if a relation is a function using domain and range?
Find the domain by listing all the x values from the relation. Find the range by listing all the y values from the ordered pairs. Repeated values within the domain or range don't have to be listed more than once. In order for a relation to be a function, each x must correspond with only one y value.
which means
There is not a function
because the domain value 10 is paired with both and 10 and 1
and the domain is 10,26,40,56
When Tekai purchased groceries, he paid
8.5% in sales tax, which amounted to $12.40.
What was full amount, including tax, that
Tekai paid for the groceries?
Answer:
I think the full amount was $a18.50
GIVING BRAINLIESTT!!
Answer:
15) A
Step-by-step explanation:
4x-2 + 7x + 17 = 180
11x + 15 = 180
11x = 165
x = 15
Because the two angles (4x-2 and 7x+17) are linear, we can say that they add up to 180 degrees.
4x-2+7x+17 = 180 Now, simplify like terms
11x + 15 = 180
11x = 165
x = 15
Thus, the value of x would be 15 (choice 1)
The scatterplot represents the total fee for hours renting a bike. The line of best fit for the data is y = 6.855x + 10.215.
A graph shows hours of rental labeled 2 to 6 on the horizontal axis and cost in dollars on the vertical axis. A line increases from 0 to 6.
Which table shows the correct residual values for the data set?
A 3-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled given with entries 14.95, 25.50, 32, 38.95, 42.50. The third column is labeled residual value with entries negative 2.12, 1.575, 1.22, 1.315, negative 1.99.
A 3-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled given with entries 14.95, 25.50, 32, 38.95, 42.50. The third column is labeled residual value with entries 2.12, negative 1.575, negative 1.22, negative 1.315, 1.99.
A 3-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled given with entries 14.95, 25.50, 32, 38.95, 42.50. The third column is labeled residual value with entries 2.12, negative 1.575, 1.22, negative 1.315, 1.99.
A 3-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled given with entries 14.95, 25.50, 32, 38.95, 42.50. The third column is labeled residual value with entries negative 2.12, 1.575, negative 1.22, 1.315, negative 1.99.
The table shows the correct residual values for the data set regarding the scatterplot is D. A 3-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5.
What is a scatterplot?It should be noted that a scatterplot simply means a type of data display which shows the relationship between the variables.
In this case, the table shows the correct residual values for the data set regarding the scatterplot is a 3-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5.
The second column is labeled given with entries 14.95, 25.50, 32, 38.95, 42.50. The third column is labeled residual value with entries negative 2.12, 1.575, negative 1.22, 1.315, negative 1.99.
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HELPPP. DO TODAY SO PLEASE HELP!!!!!!!!!!
Answer:
47/6cm or [tex]7\frac{5}{6}[/tex]cm
Step-by-step explanation:
FE= [tex]2\frac{2}{3}[/tex]
FA= 5/12
AB= 2/3
CD=2
ED=[tex]1\frac{1}{4}[/tex]
BC= 5/6
All=47/6 or [tex]7\frac{5}{6}[/tex]