The ordered pairs that are in the solution set of the system of linear inequalities are (2 ,2), (3 , 1) and (4 , 2).
What is system of equations?A finite collection of equations for which we searched for the common solutions is referred to in mathematics as a system of equations, sometimes known as a set of simultaneous equations or an equation system.
Given the system of linear inequalities:
y > -3x + 2
y< 2x + 3
Substitute the value of x and y for each given ordered pair.
For (2, 2) x=2 and y =2:
y > -3x + 2
2 > -3(2) +2
2> -4 True.
y< 2x + 3
2 < 2(2) +3
2< 7 True
For (3, 1) x=3 and y=1:
1 > -3(3) + 2
1 > -7 True
y< 2x + 3
1 < 2(3) + 3
1< 9 True
For (4 , 2) x=4 and y =2
y > -3x + 2
2 > -3(4) +2
2 > -10 True.
y< 2x + 3
2 < 2(4) + 3
2 < 11 True.
Hence the ordered pairs (2 ,2), (3 , 1) and (4 , 2) are in the solution set of the system of linear inequalities.
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work out the size of angle x
Answer:
[tex]13^{\circ}[/tex]
Step-by-step explanation:
Consider the smaller of the two triangles with angle [tex]x[/tex].
Using vertically opposite angles, one of the angles of this triangle is [tex]85^{\circ}[/tex].
Using corresponding angles combined with angles on a straight line, one of the angles is [tex]82^{\circ}[/tex].
Angles in a triangle add to [tex]180^{\circ}[/tex], so [tex]x=13[/tex].
What does it mean to translate coordinates?
A translation is a transformation that occurs when a figure is moved from one location to another location without changing its size, shape or orientation. In the coordinate plane we can draw the translation if we know the direction and how far the figure should be moved.
Now, According to the question:
What does translation of coordinates mean?
A translation is a transformation that occurs when a figure is moved from one location to another location without changing its size, shape or orientation. In the coordinate plane we can draw the translation if we know the direction and how far the figure should be moved.
Transformations of Graphs
Vertically translating a graph is equivalent to shifting the base graph up or down in the direction of the y-axis. A graph is translated k units vertically by moving each point on the graph k units vertically.
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Find 1)
4 integral 0 f(x) dx
if f(x) = 2 for x < 2
= x for x ? 2
Answer:
X = 1 and below
Step-by-step explanation:
since X is less than 2.
the value of X will be 1 and below.
What is the solution to the equation 9 W 4 )- 7w 5 3w 2?
The solution to w in the equation 9(w - 4) - 7w = 5(3w - 2) is w = -2.
Now, According to the question:
The given Equation:
9(w-4)-7w=5(3w-2)
To solve for w we first need to simplify our equation, removing any brackets and adding together similar terms. This gives us:
9(w-4)-7w=5(3w-2)
9w - 36 -7w = 15w - 10
2w - 36 = 15w - 10
Next, we subtract 2w from both sides to have all the variables on one side of our equation, then we add 10 to both sides to move the numerical values to one side.
2w - 36 = 15w - 10
2w -2w - 36 = 15w - 2w - 10
-36 = 13w - 10
-36 + 10 = 13w - 10 + 10
-26 = 13w
Finally, we divide both sides by 13 to find the value of w.
w = -2
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The complete question is this :
What is the solution to the equation of 9(w - 4) - 7w = 5(3w - 2).
To be able to walk to the center $C$ of a circular fountain, a repair crew places a 16-foot plank from $A$ to $B$ and then a 10-foot plank from $D$ to $C$, where $D$ is the midpoint of $\overline{AB}$ . What is the area of the circular base of the fountain
The area of the circular base of the fountain is 179 square feet.
What is the area of the circular base ?A circle's area is equal to its radius, r, squared, then multiplied by the mathematical constant pi: A = pi x r2.
A cylinder has two bases that are two congruent circles at the top and bottom. The radius r of a cylinder is only the radius of the circular bases, and the height h of a cylinder is the perpendicular distance between these bases.
Combined area of the walkway and fountain: (3.14)112=379.94 ft2.
Fountain area: (3.14)8*2=200.96 feet
Walkway area: 379.94-200.96=178.98 square feet, which is also rounded to 179 square feet.
The area of the circular base of the fountain is 179 square feet.
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Please HURRY!!!
Which of the following must be true
where h is the height of the car in metres, t is the time that has elapsed in minutes and a, b and c are constants.
Find values for a, b and c that will effectively model your motion on the big wheel.
The graph of the variation of the height of a person on the Ferris wheel with time, created with MS Excel is attached
The values of the constants in the sinusoidal function, h = a + b·(c·t) are;
a = 30
b = -20
c = π/1.5
What is a sinusoidal function?A sinusoidal function is a periodic, oscillatory function, that is based on the sine (or cosine) trigonometric ratios.
The diameter of the Ferris wheel = 40 m
The location of the axle above the ground = 30 m
The time it takes to make a complete a rotation = 3 minutes
The formula for modelling the elevation or height, h, of a person above the ground is presented as follows;
h = a + b·cos(c·t)
The details in the question is that at time, t = 0, the person enters the wheel at the lowest point.
Therefore;
At t = 0, h = 30 - 40/2 = 10
h = 10 = a + b·cos(c × 0) = a + b·cos(0) = a + b
a + b = 10
Whereby the height of the axis of the wheel above the ground is a constant, for visibility in the analysis, let the constant a represent the constant height of the axis from the ground, we get;
a = 30
a + b = 10, therefore;
b = 10 - a
b = 10 - 30 = -20
b = -20
At t = 1.5 minutes, the location on the wheel the person enters is at the maximum height on the wheel = 30 + 20 = 50
50 = a + b·cos(1.5·c)
50 = 30 - 20 × cos(1.5·c)
20 × cos(1.5·c) = 30 - 50 = -20
cos(1.5·c) = -1
cos(π) = -1
Therefore; 1.5·c = π
c = π/1.5
The equation is therefore;
h = 30 - 20·cos((π/1.5)·t)
a = 30, b = -20, c = π/1.5
Please find attached a graph showing the variation of height with time of the motion on a Ferris created with MS Excel
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Please hurry its timed
The best option regarding the solutions of the trigonometric equation 2sin(θ) + 1 = 0 in this problem is given as follows:
d. θ = 330º + 360ºn, θ = 210 + 360ºn.
How to solve the trigonometric equation?The trigonometric equation for this problem is defined as follows:
2sin(θ) + 1 = 0
Then, isolating the sine, we have that:
2sin(θ) = -1
sin(θ) = -1/2.
The values of theta for which the sine is of negative 1/2 are given as follows:
θ = 210º, θ = 330º.
(as the sine is negative for the third and fourth quadrant, hence we have to find the equivalent angle to 30º in each of these quadrants).
One entire lap over the unit circle is equivalent to 360º, hence adding 360º n times to any of these solutions is also a solution to the trigonometric equation, meaning that option d is correct.
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Find volume of cylinder
I really need an answer for this FAST so if anybody can answer id really appreciate it :)
The volume of the cylinder on the image is:
v = 36,424 in³
So the correct option is the second one.
What is the volume of the cylinder?We know that for a cylinder of diameter D and height H, the volume is given by the formula:
V = pi*(D/2)²*H
Where pi = 3.14
Here we know that:
D = 40 inches.
H = 29 inches.
Replacing that in the formula for the volume we will get:
V = 3.14*(40 in/2)²*29 in = 36,424 in³
So the correct option is the second one.
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Choose three true statements about the angles of the figure
1: Z1 and the 55* angle are adjacent
2: mZ1=55* because Z1 and the 55* angle are vertical angles
3: mZ2=125* because Z2 and the 55* angle are supplementary
4: mZ2 cannot be determined from the information
5: mZ1=180*-55*
6: mZ2=180*-55*-45*
Three true statements about the angles of the given figure are,
1. angle 1 and the 55 degree angle are adjacent.
5. angle 1 = 180 degree - 55 degree
6. angle 2 = 180 degree - 55 degree - 45 degree.
How are complementary angles defined?Complementary angles are two angles whose measures add up to 90 degrees. For example, an angle of 45 degrees and an angle of 45 degrees are complementary. When two angles are complementary, they form a right angle. The symbol for complementary angles is ∠A + ∠B = 90°.
What is the difference between acute angles and obtuse angles?Acute angles are angles whose measure is less than 90 degrees. They are sharp angles that are less than a right angle. On the other hand, obtuse angles are angles whose measure is greater than 90 degrees. They are angles that are greater than a right angle and less than 180 degrees. In other words, obtuse angles are angles that are wider than a right angle but less than a straight angle.
Analysing all the statements given in the question,the corrrect options are
Option 1, since angle 1 and 55 degree share the same vertex.
Option 5, since the sum of angle 1 and 55 degree is 180 degrees being supplementary angles.
Option 6, since the sum of all the interior angles of a triangle is 180 degrees.
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400 families were surveyed. It was found that 90% had a TV set and 60% had a computer. Every family had at least one of these items. One of these families is randomly selected, and it is found that it has a computer. Find the probability that it also has a TV set.
A random selection of one of the families is made, and a computer is discovered there. P(computer AND TV) = 5/6.
How to find the Calculation?We surveyed 400 households. 60% of people had computers, while 90% of them had TVs.
These were something that every family owned at least one of.
A random selection of one of the families is made, and a computer is discovered there.
Check to see if there is a TV there as well.
union: # with computer, # with TV, - # with both, # with both
400 = 360 + 240 - # with both # with both = 200 / 400 = 0.9 * 400 + 0.6 * 400
P(computer AND TV) = 200/400 = 1/2 ——-
P(TV | computer) + P(TV and computer) / P(computer) = 0.5/0.6 = 5/6
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On a number line, suppose point E has a coordinate of -3 and EG=4. What are the possible coordinates of point G?
Answer:
[tex]-1\frac{1}{3}[/tex]
Step-by-step explanation:
We can approach this equation algebraically. Since we know E = -3, we can substitute it into our Second equation, giving us:
-3G = 4
Divide both sides by 3 gives us :
G = [tex]-\frac{4}{3}[/tex] = [tex]-1\frac{1}{3}[/tex]
So, the possible coordinate of G is [tex]-1\frac{1}{3}[/tex].
Hope this helped!
Unit rates are ALL AROUND US. If you have a phone, take a picture of a unit rate that you find at the grocery store, gas station, or as you are simply out and about. For your post, describe the picture and where you found your unit rate and what the unit rate was.
For your replies, think back and see if you recall seeing unit rates in those places. Describe how a unit rate could be used at the location where it was found.
A unit rate I found at the grocery store was 10 bananas/ $5 this describe the price for 10 bananas but can also be used to identify the price for 1 banana.
What is a unit rate?In mathematics, a unit rate can be defined as a mathematical expression that includes two units to show the rate of a specific activity. For example, the expression 50 kilometers/2 hours shows a car covers a distance of 50 kilometers in two hours, which can be simplied as 25 kilometers per hour.
What is an example of a unit rate that you can find at a grocery store?A unit rate I could observe last weekend while buying fruits and vegetables was 10 bananas/ $5. This unit rate is mainly used to inform buyers about the price of 10 bananas. However, this can also be simplified as $0.5 per banana and this would inform the buyers about the price per unit.
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What is the sign of 4.3•(-3.2)•0?
Answer:
no sign (not positive or negative)
Step-by-step explanation:
The value of the expression
4.3 ⋅ (-3.2) ⋅ 0
is 0, as the value of any number multiplied by zero is 0.
The number zero is neither positive or negative; hence there is no sign.
Approximately how many plant made pharmaceuticals are currently under different stages of discovery?
a. 100
b. 200
c. 300
d. 400
please select the best answer from the choices provided a b c d
Approximately 300 plants are made pharmaceuticals currently under different stages of discovery.
Why do you use the term pharmaceutical?
pharmaceutical, material used for repairing, changing, or treating organic processes as well as for illness diagnosis, treatment, or prevention. Pharma (Bachelor of Pharmacy): Course, Qualifications, Admission, Syllabus, Pay, and Scope.
What function do drugs serve?
Drugs are created, produced, and distributed by the pharmaceutical business. Its goal is not to define sickness. Drug manufacturers typically focus on ailments that have already been identified by the medical community.
The positive side effects of medications, such as those that lower blood pressure, treat infections, or reduce pain, are considered their advantages. The possibility that anything unfavorable or unexpected will occur to you as a result of using a medication is what we mean by "risks."
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A picosecond in one trillionth of a second. How many picoseconds are there in 12 minutes?
Answer:
720,000,000,000,000 or 720 trillion picoseconds.
Step-by-step explanation:
1 picosecond = 1 trillionth of a second. Therefore 1 second has 1 trillion picoseconds:
0.000 000 000 001 seconds = 1 picosecond
0.000 000 000 001 * 1,000,000,000,000 seconds = 1 * 1,000,000,000,000 picosecond
1 second = 1,000,000,000,000 picoseconds
Now, one minute is the same as 60 seconds so we multiply the equation by 60:
1 minute = 60 seconds = 60,000,000,000,000 picoseconds
Finally, we need 12 minutes to be converted to picoseconds.
12 minutes = 720 seconds = 720,000,000,000,000 picoseconds.
So therefore, 12 minutes is equal to 720,000,000,000,000 picoseconds or 720 trillion picoseconds.
Hope this helps!!!
. Mr. Johannsen has a farm with 3 cows, 8 chickens, and some ducks. If the total number of farm animal legs is 40, how many ducks does Mr. Johannsen have on his farm
The number of ducks on the farm is 12 legs / 2 legs/duck = 6 ducks.
To determine this:
Each cow has 4 legs, so the cows have 3 cows * 4 legs/cow = 12 legs.
Each chicken has 2 legs, so the chickens have 8 chickens * 2 legs/chicken = 16 legs.
We know the total number of farm animal legs is 40 legs.
So the number of duck legs can be calculated by subtracting the number of cow legs and chicken legs from the total number of farm animal legs: 40 legs - 12 legs - 16 legs = 12 legs.
Since each duck has 2 legs, the number of ducks on the farm is 12 legs / 2 legs/duck = 6 ducks.
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How many possible real solutions are there?
The number of real solution varies according to the degree of the equation and the nature of the equation, The answer is dependent on degree and nature.
What do you mean by a solution?In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.
What are ideal and real solutions?In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.
example:
A linear equation (degree 1) has one real solution.
A quadratic equation (degree 2) can have either two real solutions, one real solution or no real solutions, as it depends on the discriminant of the equation, as I explained in my previous answer.
A cubic equation (degree 3) can have one to three real solutions, depending on the coefficients of the equation.
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Question Progress
Here are some temperatures.
Ottawa
New York
Oslo
Moscow
-9.5 °C
-11.6 °C
-4.3 °C
-7.9 °C
a) Which place has the highest temperature?
b) What is the difference in temperature between Ottawa and Oslo?
The temperature in Moscow falls by 3.1°C.
c) What is the new temperature in Moscow?
The place with the highest temperature is Oslo.
The difference between the temperature in Ottawa and Oslo is 5.2 degrees Celsius .
The new temperature in Moscow is 11 degrees Celsius .
How to find the temperature ?When temperatures are in the negatives, the higher temperature would be the smaller number. Oslo therefore has the highest temperature at - 4.3 °C.
The difference between the temperature in Ottawa and Oslo can be found by subtracting the temperatures:
= - 4 . 3 - ( - 9 . 5 )
= - 4.3 + 9 .5
= 5. 2 degrees Celsius
The new temperature in Moscow is:
= - 7.9 - 3.1
= 11 degrees Celsius
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Can I join Wikipedia?
Yes , you can join Wikipedia as a creator who can help maintain the platform and update the content from time to time. There are also different types of job roles which you can find for Wikipedia .
You can also simply just create an account and start contributing as a member of Wikipedia.
For this the first step would be to select an appropriate username, which will be unique , as this will be used to identify and differentiate you from others. Then you can start contributing to Wikipedia and other Wikimedia projects.
Communicate with other editors via your own talk page. You can also opt in to exchanging emails with other users and thus increase your community.
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Natalia paid a total of 38.95 for 3 pizzas and a salad. The price of each pizza was p dollars. And the price of the salad was 11.98 what is the cost of 1 pizza
Answer:
The cost for 1 pizza is $8.99
Step-by-step explanation:
We know
Natalia paid a total of 38.95 for 3 pizzas and a salad
A salad = $11.98
We first find the total cost of 3 pizzas by
38.95 - 11.98 = $26.97
$26.97 is the cost for 3 pizzas; to find the cost of 1 pizza, we take
26.97 divided by 3 = $8.99
So, the cost for 1 pizza is $8.99
Answer:
The cost of 1 pizza is $8.99.
Step-by-step explanation:
Let
[tex]t[/tex] = total price
[tex]p[/tex] = pizzas
[tex]s[/tex] = salads
Natalia bought 3 pizzas and 1 salad
[tex]38.95=3p+1s[/tex]
We are given the price of the salad.
[tex]38.95=3p+11.98[/tex]
Now we can find the cost of 1 pizza.
Lets solve for [tex]p[/tex].
Subtract 11.98 from both sides of the equation.
[tex]26.97=3p[/tex]
Divide both sides of the equation by 3.
[tex]p=\frac{26.97}{3}\\p=8.99[/tex]
Consider the inequality X-3/6< x/4 -4. Which value of x is a solution to the inequality?
A.x=-10
B.x=-5
C.x=5
D.x=10
x=5 is the value of the x that is the solution of the given inequality.
Define inequality.Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
What are types of inequality.>,< and not equal to are types of inequality.
x=5 is the value of the x that is the solution of the given inequality.
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What is the angle of turn clockwise from South East to North?
N
A 45°
B 135°
C 225°
D 315°
The angle of a turn clockwise from South East to North is Option B 135°.
When determining the angle of turn, it is important to consider the direction of rotation (in this case, clockwise) and the starting and ending points (in this case, South East to North).
If we imagine the compass as a clock, with North at the 12 o'clock position, South at the 6 o'clock position, East at the 3 o'clock position, and West at the 9 o'clock position. Then South East would be at the 4:30 position and the North would be at the 12 o'clock position. To rotate from 4:30 (South East) to 12 o'clock (North) in a clockwise direction, we would have to rotate 135 degrees. Thus, the angle of a turn clockwise from South East to North is 135 degrees.
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4x + 4y = -8
-2x - 2y = 4
Answer: To solve this system of equations, you can use the substitution method.
First, you can solve one of the equations for one of the variables in terms of the other. For example, you can solve the first equation for y:
y = (-4x - 8)/4
Then, you can substitute this expression for y into the second equation to find the value of x:
-2x - 2((-4x - 8)/4) = 4
-2x + 4x + 8 = 4
2x = -4
x = -2
You can then substitute this value of x back into the first equation to find the value of y:
y = (-4(-2) - 8)/4 = (8 - 8)/4 = 0
Thus, the solution to the system of equations is x = -2 and y = 0.
Step-by-step explanation:
A 2 3/4inch candle burns down in 11 hours. At what rate does the candle A burn, in inches per hour?
Answer:
0.25 in/h
Step-by-step explanation:
1. change 2 3/4 t0 2.75
2. 2.75/11= 0.25
2 1/3 grams of spice A was mixed with 4 1/7 grams of spice B. The ratio of spice A to spice B is 1:
The ratio of spice A to spice B is : 49/87
Here, 2 1/3 grams of spice A was mixed with 4 1/7 grams of spice B.
First we convert the improper fraction into a proper fraction.
For improper fraction2 1/3,
2 1/3
= (2 × 3)/3 + 1/3
= 6/3 + 1/3
= (6 + 1)/3
= 7/3 which is a proper fraction.
and for 4 1/7
= (4 × 7)/7 + 1/7
= 28/7 + 1/7
= (28 + 1)/7
= 29/7
The ratio of spice A to spice B would be,
(2 1/3) / (4 1/7 )
= (7/3) / (29/7)
= (7/3) × (7/29)
= (7 × 7)/(3 × 29)
= 49/87
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What’s is
2^x=1/32•x=
Answer:
I believe it would be x=-5
Step-by-step explanation:
..
-2n = -1 1/4
................................
Answer:
n = 5/8
Step-by-step explanation:
-2n = -1 1/4
-1 1/4 = -5/4
So, our equation is
-2n = -5/4
Divided both sides by -2
n = 5/8
So, the answer is
n = 5/8
Solve for x.
x2=14
Responses
x=±18
x equals plus or minus 1 eighth
x=±12
x equals plus or minus 1 half
x=±116
x equals plus or minus 1 sixteenth
x=±2
The solution for x in the equation given as x² = 1/4 is (b) x = ±1/2
How to determine the solution for xFrom the question, we have the following parameters that can be used in our computation:
An equation
The equation as poorly stated in the question is represented as
x2=14
When written properly
We have the following representation
x² = 1/4
Solving further, we need to take the square root of both sides of the equation
So, we have the following representation
√x² = ±√1/4
Evaluate the exponents on the left-hand side
So, we have the following representation
x = ±√1/4
Evaluate the exponents on the right-hand side
So, we have the following representation
x = ±1/2
Hence, the solution is (b) x = ±1/2
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What is the Pythagorean theorem rounding of 16 and 18
The Pythagorean theorem rounding of 16 and 18 would be = 24 (approximately)
What is Pythagorean theorem?Pythagorean theorem is defined as the theorem that expresses the relationship that exists between the three side of a right angle triangle.
The relationship states that the square of the longest side is equal to the sum of the square of the other two sides.
That is, c² = a² + b²
Where, a = 16
b = 18
c² = 16²+18²
c² = 256 + 324
c² = 580
C =√580
C = 24.1
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