After solving, the solution set of the give inequality is (-1, 3)
In the given question, we have to find the solution set of the given system of inequalities.
The given inequalities are
x+y≥2...................(1)
4x+y≥-1.................(2)
To solve the given inequality we use the elimination method.
Multiply equation 1 by 4 on both side, we get;
4x+4y≥8...................(3)
Subtract equation 3 and 2, we get;
3y≥9
Divide by 3 on both side we get;
y≥3
Put the value of y in equation 1
x+3≥2
Subtract 3 on both side, we get;
x≥-1
Hence, the solution set of the give inequality is (-1, 3).
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The write question is;
Which point is the solution set of the given system of inequalities?
x+y≥2
4x+y≥-1
Ariel has a plastic ice cream cone in her food playset. The ice cream cone is a half-sphere sitting on top of a cone. What is the approximate volume of the toy ice cream cone?.
Volume of ice cream Cone = 753.6[tex]cm^{3}[/tex]
What is Volume ?A three-dimensional space's occupied volume is measured. It is typically quantified using a variety of imperial or US-standard units as well as SI-derived units. The definition of length and volume are connected.
According to the given information
Volume of toy ice cream Cone = Volume of Cone + Volume of Hemisphere
We are given that
Radius of cone = Radius of hemisphere = 6 cm
Height of cone = 8 cm
So
Volume of Sphere = [tex]\frac{1}{2}[/tex] × [tex]\frac{4\pi r^{3} }{3}[/tex]
= 1/2 × 4/3 × 3.14 × [tex]6^{3}[/tex]
Volume of sphere = 452.16 [tex]cm^{3}[/tex]
Volume of Cone = [tex]\frac{\pi r^{2}h }{3}[/tex]
= 1/3 × 36 ×3.14 ×8
= 301.44 [tex]cm^{3}[/tex]
So
The Volume of ice cream cone = 452.16 [tex]cm^{3}[/tex] + 301.44 [tex]cm^{3}[/tex]
= 753.6[tex]cm^{3}[/tex]
Volume of ice cream Cone = 753.6[tex]cm^{3}[/tex]
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If a voltage of 0.5 V (volts) is driving a current of 0.03 A (amps) through a resistor, what is the resistance to the resistor, measured in ohms? Round to the nearest hundredths.
Answer:
To find the resistance of a resistor, you can use the formula R = V / I, where R is the resistance in ohms, V is the voltage in volts, and I is the current in amperes. Using the values provided, we can calculate the resistance as follows:
R = 0.5 V / 0.03 A = 16.67 ohms
Rounded to the nearest hundredths, the resistance is 16.67 ohms.
Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x2 + y2 = 5.
The surface area of the plane is π√14 sq. units.
It is given in the question that the equation of the plane = x+2y+3z=1 and that of the cylinder
= x² + y² = 5 [1]
Let J be the projection on the plane x+2y+3z=1
We know that the surface area of an equation is
∫∫j √{1+(∂z/∂x)² + (∂z/∂y)²} dA
We know that the plane is inside the cylinder.
By using the coordinates of the cylinder we can get
x = r cosθ and y = rsinθ
Squaring both sides gives us
x² = r²cos²θ
y² = r²sin²θ
Therefore we get,
x² + y² = r²cos²θ + r²sin²θ
= r²(cos²θ + sin²θ)
We know that cos²θ + sin²θ = 1. Hence,
= r² [2]
From equations [1] and equation [2] we get
r² = 5
or, r = √5
Hence,
J = {(r,θ)/ 0 ≤ r ≤ √5, 0 ≤ θ ≤ 2π}
Therefore,
x +2y + 3z =1
or, z = 1/3(1 - x - 2y)
Partially differentiating z with respect to x and with respect to y gives us
∂z/∂x = -1/3
and,
∂z/∂y = -2/3
Therefore,
We already know that Surface Area = ∫∫j √{1+(∂z/∂x)² + (∂z/∂y)²} dA
= ∫∫j √{1+ (-⅓) ² + (-⅔) ²} dA
= ∫∫j √(9+1+4)/√9 dA
= √14 /3∫∫j dA
=√14/2 [2π - 0]
= π√14 sq units
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A middle school took all of its 6th-grade students on a field trip to see a ballet at a theater that has 1500 seats. The students filled 1320 of the seats in the theater. What percentage of the seats in the theater were filled by the 6th graders on the trip?
The percentage of the seats in the theater that were filled by the 6th graders on the trip is 88%.
What percentage of the seats in the theater were filled by the 6th graders on the trip?Given that the middle school took all of its 6th-grade students on a field trip to see a ballet at a theater that has 1500 seats and the students filled 1320 of the seats in the theater.
The percentage of the seats in the theater were filled by the 6th graders on the trip will be:
= Number of 6th graders / Total students × 100
= 1320 / 1500 × 100
= 88%
The percentage is 88%.
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15. Zoey i playing volleyball with her friend. She hit the 0. 2 kg ball traight up for 4m Auming all energy i conerved, what wa the ball' velocity when it left Zoey' hand? Show all work
The ball' velocity when it left Zoey' hand is 8.85 m/s
What is the principle of conservation of energy?
The word "conservation" in physics describes anything that doesn't change. This indicates that a conserved quantity is represented by a variable in an equation that is constant over time. Its value is the same whether an event occurs before or after it.
In physics, there are a lot of conserved quantities. For making forecasts in what would otherwise be exceedingly complex situations, they are frequently remarkably useful. There are three fundamental quantities in mechanics that are conserved. They are power, forward motion, and angular momentum.
According to question
Mass of the ball = 0.2 kg
Maximum height of the ball = 4 m
Gravity = 9.8 m/s²
Therefore:
Using conservation of energy, we know that P.E. top = K.E. bottom. This tells us that the potential energy at the top is all converted to kinetic energy at the bottom. We can substitute the equations for potential energy and kinetic energy
Initial kinetic energy + Initial potential energy = Final kinetic energy + Final potential energy
1/2mv² + 0 = mgh + 0
½(0.2)v² = (0.2)(9.8)4
v² = 78.4
v = 8.854377…
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28 divided 66.29 please
Answer:
28 divided by 66.29 is approximately 0.4223. To find the exact result, you would need to perform long division. The process for doing this is as follows:
Begin by dividing the leftmost digit of the dividend (28 in this case) by the divisor (66.29). In this case, the result is 0 with a remainder of 28.
Bring down the next digit of the dividend (0 in this case), so that the dividend is now 280.
Divide 280 by 66.29. The result is 4 with a remainder of 36.29.
Bring down the next digit of the dividend (0 in this case), so that the dividend is now 36.29.
Divide 36.29 by 66.29. The result is 0.54 with a remainder of 0.29.
Bring down the next digit of the dividend (0 in this case), so that the dividend is now 0.29.
Divide 0.29 by 66.29. The result is 0.004 with a remainder of 0.
The remainder is 0, so the division is complete. The result is 0.004223.
Alternatively, you can use a calculator to perform the division. Just enter "28 / 66.29" and the calculator will give you the result.
Step-by-step explanation:
[tex]\sqrt{-240\\[/tex]
The required simplified solution of the given expression is 4√15i.
A simplified solution of the given expression √-240 is to be determined.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
The square root of the negative value induces the property of the complex number. (a complex number is a number that contains both the real and imaginary parts of the number)
Simplifying,
√-240= √4×4×-15
= 4 √-15
= 4√15i {∵ √-1 = i}
Thus, 4√15i is the required simplified solution to the provided expression.
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The question seems to be incomplete,
The complete question could be as,
Simplify the complex number √-240 ?
Show me how to do Literal Equations
Solve for X
360=2x+y
Answer:
[tex]x = 180 - \frac{y}{2}[/tex]
Step-by-step explanation:
Our goal here is to isolate [tex]x[/tex] on one side of the equals sign
[tex]360 = 2x + y[/tex]
Here we have 2 terms on the right side of the equals sign, [tex]2x[/tex] and [tex]y[/tex]
in order isolate the [tex]x[/tex] term we must subtract [tex]y[/tex]
However, if we subtract [tex]y[/tex] from one side of the equation we must also do the same to the other side to a maintain balanced equation.
[tex]360 = 2x + y[/tex]
[tex]-y[/tex] [tex]-y[/tex]
[tex]360 - y = 2x[/tex]
Now to remove "2" from [tex]2x[/tex] we must do the opposite of multiplication, which is division.
[tex]\frac{360}{2} - \frac{y}{2} = \frac{2x}{2}[/tex]
simplify.
[tex]180 - \frac{y}{2} = x[/tex]
a manufacturer is interested to develop a 95% confidence interval for the true mean cycle time of producing their headphones. assuming a margin of error of 1 minute, and standard deviation of 6 minutes from a previous sample, what is the appropriate sample size?
The appropriate sample size for the 95% confidence interval is given as follows:
139.
How to obtain the appropriate sample size?To obtain the appropriate sample size for the confidence interval, we need to look at it's equation for the margin of error, which is defined as follows:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which the parameters are listed as follows:
z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The margin of error and the population standard deviation have the values given as follows:
[tex]M = 1, \sigma = 6[/tex]
Then the sample size is obtained as follows:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]1 = 1.96\frac{6}{\sqrt{n}}[/tex]
[tex]\sqrt{n} = 1.96 \times 6[/tex]
[tex](\sqrt{n})^2 = (1.96 \times 6)^2[/tex]
n = 139 (rounded up, as for a sample size of 138 the margin of error would be slightly above 1).
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what is slope of y=4x-5 and what do you do to find it?
Answer:
4
Step-by-step explanation:
Slope form is:
y=mx+b
4 represents m
m is the slope, or change in y over change in x
Answer:
Using the slope-intercept form, the slope is −4 .
Step-by-step explanation:
The slope-intercept form is y=mx+by=mx+b, where mm is the slope and bb is the y-intercept.y=mx+by=mx+b
Using the slope-intercept form, the slope is −4-4.m=−4
How do I work out this question please help
factorise 3x + 12
Answer: 3(x+4)
Step-by-step explanation:
Let's start with what we know. To factor problems, we just find a common divisor. Here, the common divisor is 3 so:
3(x+4)
State the vector in component form for an object flying at 235 mph at a bearing of N55°W.
The vector in component form for an object flying at 235 mph at a bearing of N55°W is given as follows:
(-134.79, 192.5).
How to define the vector?The vector is composed by two components, the x-component and the y-component, as follows:
<x,y>.
The components are defined as follows:
x = vcos(θ).y = vsin(θ).In which the variables are defined as follows:
v is the velocity.θ is the angle.In the context of this problem, the values of these parameters are given as follows:
v = 235, θ = 55º.
The positions are given as follows:
West -> x negative.North -> y positive.Hence the components of the vector are given as follows:
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(2,3), slope =3 Using the equation y=Mx + b
The required equation of the line is given as y =3x - 3.
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
here,
As given in the question that, the line is passing through the point (2,3), and the slope line is 3, the equation of the line is to be determined.
The standard equation of the line is given as
y=Mx + b
Substitute values of point and slope in the above equation,
3 = 2×3 + b
b = -3
Put this b and M in the standard given equation,
y= 3x - 3
Thus, the required equation of the line is given as y =3x - 3.
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why is it important to evaluate non-critical paths that possess large variances or path times that are close to critical in duration?
All the given options are correct.
what is random?
The lack of pattern or predictability in events, whether it be apparent or real, is referred to as randomness. Sometimes there is no order or discernible pattern or combination in a random series of events, symbols, or processes.
a)Random uncertainty present in the network may exhibit cumulative interactions reflecting the inherent randomness of independent activities within the network.
b)An activity having only a relative small amount of slack could potentially exceed the critical time calculated from the expected critical path.
c)As statistical variances rise in relation to expected duration, the range of uncertainty in near-critical paths will exhibit wider dispersion.
Hence all the given options are correct.
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Complete Question
Why is it important to evaluate non-critical paths that possess large variances or path times that are close to critical in duration?
A) Random uncertainty present in the network may exhibit cumulative interactions reflecting the inherent randomness of independent activities within the network.
B) An activity having only a relative small amount of slack could potentially exceed the critical time calculated from the expected critical path.
C) As statistical variances rise in relation to expected duration, the range of uncertainty in near critical paths will exhibit wider dispersion.
D) All of the above.
What is the slope of the line that passes through 4 1 and 2 5?
The slope of the line that passes through (4,1) and (2,5) is -2.The slope of a line can be expressed in many ways, including as a fraction, decimal, or even in terms of the angle of inclination.
The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line.The slope of a line is calculated by finding the difference in the y-values (rise) divided by the difference in the x-values (run).
In this case, the rise is 5 - 1 = 4 and the run is 2 - 4 = -2.
Therefore, the slope of the line is 4/-2 = -2.
In the case of a horizontal line, the slope is 0, and in the case of a vertical line, the slope is undefined. The slope is a useful tool in mathematics as it can be used to determine the equation of a line, the rate of change on a graph, or the amount of change for every unit of time. It can also be used to determine the area between two points on a graph. Slope is an essential concept in mathematics and can be used to solve many types of problems.
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The measurement of angle A is 89°. Classify angle A as an acute, right, or obtuse angle.
Answer:
Acute angle
Step-by-step explanation:
Any angle less than 90° is acute.
Answer:
Acute.
Step-by-step explanation:
90 degree angle = Right Angle
Greater than 90 degrees = Obtuse Angle
Less than 90 degrees = Acute Angle
How old is my brother 3x9-18
Answer: 9
Step-by-step explanation:
3x9=27
27-18=9
Answer:
Step-by-step explanation:
dw
You are working on an air conditioning system. A roll of cylindrical copper tubing has an outside diameter of 78 7 8 inch and an inside diameter of 34 3 4 inch. How much refrigerant can 12 feet of the tubing hold?.
557,568 inch³ of refrigerant can be held by the tubing.
Here we have to find how much a refrigerant can hold.
Data given:
outer diameter (d) = 78inch
outer radius(r) = 39 inch
inner diameter (d') = 34 inch
inner radius (r') = 17inch
Height (h) = 12 feet
= 12 × 12
= 144 inch
the formula to find the volume of the cylinder:
volume= пr²h
So here we get
Refrigerant hold = Volume of the outer cylinder - the volume of the inner cylinder
= πr²h - πr'²h
= πh(r² - r'²)
= π ×144 ( 39² - 17²)
= π × 144 ×56 × 22
= 22/7 × 144 × 56 × 22
= 557,568 inch³
Therefore the refrigerant can hold 557,568 inch³.
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What is meant by 150 kilometers per hour?
The 150 kilometres per hour is the rate or speed of object.
The kilometres is indicative of distance and hour is indicative of time. So the fraction of kilometre and hour indicates the speed or rate of object. The rate or speed find wide applicability in calculations and can be indicative of multiple things.
For instance, the distance covered in an hour can signify the rate of descendence of bucket in the well, landing or flying of airplane, and other things. The same thing can also indicate speed in terms of distance travelled by any object like car, bus, airplane, protons, neutrons, atoms, gas molecules in an hour.
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what is 30 times 36 i really dont understand it
Answer:
1080
Step-by-step explanation:
Is a dilation with a scale factor greater than 1 is a reduction?
When the scale factor is greater than one, then the dilation is not a reduction.
What is a dilation?
Dilation is a process of changing a thing. It is a process of transformation that to make the objects smaller or larger, with the use of specific scale factor.
The new figure that is the result of dilation is known as the image. Initial figure is referred to as the pre-image.
What is a center of dilation?
Center of dilation is the resizing that happens from a point. The objects/figures are expanded or contracted from the center of dilation.
Scale factor is a figure by which the size of any geometrical figure can be resized, with respect to its original size. The scale factor is multiplied to get image.
Figure size increased, when the scale factor is greater than 1.
Thus, the dilation will be a expansion, when the scale factor is a greater than one.
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what is the best approximation for the area of this circle? use 3.14 to approximate pi.
The best approximation for the area of the circle is 201.0in³
What is an area?The size of a region on a planar or curved surface is expressed mathematically as area. The term "surface area" refers to the area of an open surface or the perimeter of a three-dimensional object, whereas "plane area" refers to the area of a shape or planar lamina. Area can be thought of as the amount of a certain thickness of material required to construct a model of the shape. For the areas of basic forms like circles, triangles, and rectangles, there are a number of well-known formulas. Any polygon can be divided into triangles to get its area using these formulas. Calculus is commonly needed to calculate the area of forms having curved boundaries. Calculus' historical growth was in large part driven by the issue of figuring out the area of plane figures.
It is possible to calculate a shape's area.
As we already know that,
The area of a circle=πr²
Here, r=8in
π=3.14
Then,
A=(3.14)(8²)
A=201.0in²
Therefore, Area=201.0in²
Hence, the best approximation for the area of the circle is 201.0in³
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The complete question is:
"What is the best approximation for the area of this circle? Use 3.14 to approximate pi. 25.1 in² 50.2 in² 201.0 in² 803.8 in² Circle with radius labeled 8 in."
Solve this equation: 33 + 7s = -3 ( 2s + 9 )
Answer:
Exact form:
[tex]s = - \frac{60}{13} [/tex]
Decimal form:
[tex]s = - 4.615384[/tex]
Mixed Number Form:
[tex]s = - 4 \frac{8}{13} [/tex]
Jake has a 10 inch stick which he cuts into 3 pieces. The first piece is twice as long as the second. If the three pieces can form a triangle, which of the following could NOT be the length if the third piece?Jake has a 10 inch stick which he cuts into 3 pieces. The first piece is twice as long as the second. If the three pieces can form a triangle, which of the following could NOT be the length if the third piece?
The measures that the third piece cannot assume are given as follows:
z < x - y if x is the greater measure.z > x + y if z is the greater measure.When a set of measurements can represent a triangle?A set of measurements can represent a triangle if the sum of the two smaller measurements is greater than the greater measures.
The sum of the measurements in this problem is given as follows:
x + y + z = 10.
The first piece is twice as long as the second,hence:
x = 2y.
Thus:
3y + z = 10.
The condition needed for a triangle to be formed is given as follows:
y + z > x if x is the greater measure.x + y > z if z is the greater measure.Missing InformationThe options are missing, hence the answer was given in general terms, with the concept used presented.
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According to the pattern shown below, what is the number in the blank?
1, 1 ,2,3,7,23 ,164,…
The number pattern is 1, 1 ,2,3,7,23 ,164,3,776
What is the definition of a number pattern?
Number pattern is a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers.
1 + 1 = 2 + 0 = 2
3 x 2 = 6 + 1 = 7
7 x 3 = 21 + 2 = 23
23 x 7 = 161 + 3 = 164
164 x 23 = 3772 + 4 = 3776
Therefore, The number pattern is 1, 1 ,2,3,7,23 ,164,3,776
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find a in degrees a=13 b=9 c=7
Answer: in image
Step-by-step explanation: j
Select the correct
function
that represents
this data.
A. f(x) = -6x +1
B. f(x) = 6x +1
C. f(x) = -6x - 1
Answer:
Step-by-step explanation:
o find the vertex of f(x)=x2−8x+7 , there are several things you can do. You could complete the square to get the equation into vertex ...
Latanya has $1.90 worth of nickels and dimes. She has a total of 24 nickels and dimes altogether. Determine the number of nickels and the number of dimes that Latanya has.
Answer:
10 nickels and 14 dimes
Step-by-step explanation:
Lance has saved $45. He earns $30 dollars every week walking dogs, which he
also saves.
Which function can be used to find t, the amount of money Lance will have
saved at the end of n weeks of walking dogs?
Answer: 30n+45=t
Step-by-step explanation:
Which absolute value functions will be narrower than the parent function, f(x) = |x|? check all that apply.
The absolute value function which will be narrower than the parent function is:
f(x) = 2.9|x|
Given parent function is f(x)=|x|
Now we have to find which function from given choices will be narrower than the parent function.
Notice that adding or subtracting some number from the parenth function only shifts the graph up, down, left of right side.
But that will not make function narrorwer or broader.
So f(x) = |x – 2| and f(x) = |x| + 3, can't be the answer.
Multiplying by some positive real number which is more than 1, makes function narrower.
Only f(x) = 2.9|x| from remaining choices fits that case.
Hence f(x) = 2.9|x| is the final answer.
f(x) = 1.2|x + 8| will also make the function narrower but will shift the parent function too.
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