How do you graph a system of linear inequalities?
Making a graph of linear inequalities is similar to making a graph of linear equations. But with inequalities, we find a region instead of a line.
What is linear inequality?
Linear inequalities are mathematical statements that are made up of two expressions which are compared using inequality symbols.
The following steps are to be followed to make a graph of linear inequality:-
1. Solve the inequality for y.
2. Considering the inequality as a linear equation graph the line. ( If the inequality sign does not contain an equal sign then draw a dashed line; if the inequality contains an equal sign then draw a solid line.
3. Shade the region that satisfies the inequality.
Hence, a system of linear inequality is graphed similarly to that of a linear equation, but a region is obtained.
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Write 2 different equations you could use to solve for side m?
2. The Equation for value x is, x= 13 sin 52.
3. The value of m, m = l cos <N
4. The length of Hypotenuse is 7.92 m.
What is Trigonometry?The branch of mathematics concerned with specific functions of angles and their application to calculations. In trigonometry, there are six functions of an angle that are often utilised. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their names and acronyms (csc).
Given:
2. P= x
H= 13 cm
Using Trigonometry
sin 52 = P/ H
sin 52 = x/ 13
x= 13 sin 52.
3. P = n, B= m and H= l
Using Trigonometry
cos <N= B/H
cos <N= m / l
m = l cos <N
and, using Pythagoras theorem
H² = P² + B²
l²= m² + n²
m= √( l² - n²)
4. P = 7m
angle= 62
Using Trigonometry
sin 62 = 7/ H
0.88295 = 7/ H
H = 7/ 0.88295
H = 7.92 m
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Simplify: m² ∙ m⁶ ∙ m =
Answer:
Option A) m^9.
Step-by-step explanation:
To simplify the given expression, we can use the rules of exponents which state that when we multiply powers with the same base, we can add their exponents.
So, m² ∙ m⁶ ∙ m can be simplified as:
m² × m⁶ × m = m^(2+6+1) = m^9
Therefore, the simplified form of m² ∙ m⁶ ∙ m is m^9.
So im trying to dind the data tabls numbers and the equation
the equation fro the line can be written in the slope-intercept form,
for that we would need to find the slope and the y intercept on the line,
the slope can be found by using two of the points from the line.
the points we are selecting are (20,32) and (30,45) which are points that are approximate to the line drawn.
use the points given and the definition of the slope to find it:
\(m=\frac{y_2-y_1}{x_2-x_1}\)It should look something like this
\(\begin{gathered} m=\frac{45-32}{30-20} \\ m=\frac{13}{10} \end{gathered}\)according to the graph the intercept is the point it crosses the y-intercept which in this case is 10.
the equation of the line will be
\(y=\frac{13}{10}x+10\)Using the equation of the line construct the data table by giving the values for x
0-10-20-30-40-50
it should look like this
in order to find the y side we use the equation, i will do an example with x as 10
\(\begin{gathered} y=\frac{13}{10}\cdot(10)+10 \\ y=13+10 \\ y=23 \end{gathered}\)apply the same to find the corresponding value to each x.
finish by making the exact graph for the equation and data table we just found
What is a formula for the nth term of the given sequence?
3,5,7...
Answer:
You can always find the 'nth term' by using this formula: nth term = dn + (a - d) Where d is the difference between the terms, a is the first term and n is the term number.
Mr. Allen has a class of 18 students. He can spend S18 on each student to buy math supplies for the year. He first buys all of his students calculators, which
costs a total of $124.20. After buying the calculators, how much does he have left to spend on each student?
Answer
$199.8
Explanation:
Find the total amount of money he had in the begining. It says that he can spend $18 on each student. He has 18 students so you would multiply that by the $18 he can spend which gives a total of $324 then you subtract the total cost of the calculators from it which then gives you $199.8
perform the indicated operation 10/14+11/14
Choose the expression that is equivalent to the expression n − n + n − n.
jaxson mom is 35,wich is 3 times as old as jaxson. what is the equation that reprsents this situation and is jaxson age.
Answer:
Step-by-step explanation:
Let J be Jaxson's age.
According to the problem, Jaxson's mom is 35, which is three times as old as Jaxson. So, we can write:
Jaxson's mom's age = 3 times Jaxson's age
35 = 3J
To find Jaxson's age, we can solve for J by dividing both sides of the equation by 3:
35/3 = J
Jaxson's age is approximately 11.67 years old (rounded to two decimal places).
Which of the following is NOT the same for both sets of data?
MEAN?
MEDIAN?
MODE?
RANGE?
Answer:
Mode
Step-by-step explanation:
As you can see, the mode on the first data set is 10, the mode on the other is 30.
Match the system of linear equations on the left with its solution type on the right
1. Y=2x-1
Y=2x+1
2. Y-4x=-2
Solution for the given System of linear equation is:
Infinite number of solution(2, -3)(-2, 4)Infinite number of solutionWhat are System of equation?Simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
There are four methods to solving systems of equations: graphing, substitution, elimination and matrices.
Given, the system of linear equations on the left with its solution type on the right
For Y=2x-1 and Y=2x+1
Adding both equation, we will get y = 4x
Thus, these equations have infinite number of solution
For 2x - y = 7 and 3x + y = 3
Adding these equations
5x = 10
x= 2
Substitute the value in equation 1
y = -3
Thus, solution is (2, - 3)
therefore, the Solution for the given System of linear equation is:
Infinite number of solution(2, -3)(-2, 4)Infinite number of solutionLearn more about System of equation here:
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Complete question:
3x+4>16 what is the soultion?
The solution to the inequality expression 3x + 4 > 16 is x > 4
How to determine the solution to the expression?From the question, we have the following parameters that can be used in our computation:
3x + 4 > 16
Subtract 4 from both sides of the expression
So, we have the following representation
3x > 12
Divide by 3
x > 4
Hence, the solution is x > 4
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This year you earned $75,500. Last year you earned $72,400. What was the rate of change on your earnings since last year
Answer:
4.28%
Step-by-step explanation:
We Know
Last year you earned $72,400
This year you earned $75,500
What was the rate of change in your earnings since last year?
We Take
(75,500 ÷ 72,400) x 100 ≈ 104.28%
Then We Take
104.28 - 100 = 4.28%
So, the earning increased by about 4.28%.
The triangle is rotated 90 degrees clockwise around the pount (0,0)
Answer:
(2,6)
Step-by-step explanation:
Option:B
The triangle is rotated 90 degree clockwise around the point (0,0). The point is (-6,2) is made to rotate. The image so formed is at the point (2,6).
i was hoping someone could help me find the answers
A) We will determine the annual rate of change between 1991 and 2006 as follows:
We replace the values in the expression and solve for r, thatt is:
\(15000=34000(1+r)^{15}\Rightarrow\frac{15}{34}=(1+r)^{15}\)\(\Rightarrow\sqrt[15]{\frac{15}{34}}=1+r\Rightarrow\Rightarrow r=\sqrt[15]{\frac{15}{34}}-1\)\(\Rightarrow r=-0.0530926\ldots\Rightarrow r\approx-0.0531\)So, the annual rate of change between 1991 and 2006 was of approximately -5%.
B) The correct answer in percentage form is -5.31%.
C) If we assume that te car value continues to drop by the same percentage, for the year 210 would have been:
\(S\approx34000(1-0.0531)^{19}\Rightarrow S\approx12057.49614\)So, the value would end up being approximately $12057.5.
a vitamin c capsule weighs 500 mg what is it weight in grams?
Answer:
0.5 grams
Step-by-step explanation:
1 mg = (1/1000) g = 0.001 g
500mg = (500/1000)g = 0.5g
hope this helps!! p.s. i really need brainliest :)
You are playing a video game. For each diamond you collect, you earn 110 points. You also earn 80 bonus points by completing the level in less than 2 minutes. You need to earn more than 2000 points to continue on to the next level. Write and solve an inequality that represents the number d of diamonds you must collect in less than 2 minutes to advance to the next level.
NEED HELP ASAP
Answer:
i need helppppppppppppppp
Step-by-step explanation:
The following sample of observations was randomly selected. (Round your answers to 2 decimal places.)
x: 4 5 3 6 10
y: 4 6 5 7 7
Required:
Determine the regression equation
Answer:
The regression equation is:
\(y=3.77+0.36 x\)
Step-by-step explanation:
The general form of a regression equation is:
\(y=\alpha +\beta x\)
Here,
α = intercept
β = slope
Compute the value of intercept and slope as follows:
\(\begin{aligned} \alpha &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 29 \cdot 186 - 28 \cdot 173}{ 5 \cdot 186 - 28^2} =3.767\approx 3.77 \\ \\\beta &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 5 \cdot 173 - 28 \cdot 29 }{ 5 \cdot 186 - \left( 28 \right)^2} =0.363\approx 0.36\end{aligned}\)
The regression equation is:
\(y=3.77+0.36 x\)
You are walking along a path y= 2x + 12 and your
best friend is walking along 4x + y = 6. At what point will
you cross paths?
Answer:
(-1,10)
Step-by-step explanation:
At the point when the paths cross, the respective x and y values of each equation will be equal.
Your path is y=2x+12, and your friends path is 4x+y=6. Sub 2x+12 in for y (from your path's equation) into your friends equation to find the value of x:
4x+2x+12=6
6x=-6
x=-1
y=2x+12
y=2(-1)+12=10
So you will cross paths at (-1,10)
A set of data items is normally distributed with a mean of 80 and a standard deviation of 9. Convert 71 to a z-score.
271 = 0
(Type an integer or a decimal.)
The z-score for 71 is -1.
Understanding Z-score calculationz-score is a measure of how many standard deviations an observation or data point is away from the mean of a distribution.
It is calculated by subtracting the mean from the observation and then dividing the result by the standard deviation: z = (x - μ) / σ
A positive z-score means that the data point is above the mean, while a negative z-score means that it is below the mean.
Applying the formula to solve our question
Here is a proven formula to use:
z = (x - μ) / σ
where:
x = the data item (x = 71)
μ = the mean of the distribution (μ = 80)
σ = the standard deviation of the distribution (σ = 9)
Substituting the values, we get:
z = (71 - 80) / 9
z = -1
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The point P=(1/2,y)lies on the unit circle shown below. What is the value of y in simplest form?
The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.
To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.
Plugging in the coordinates of the point P = (1/2, y), we get:
(1/2)^2 + y^2 = 1
1/4 + y^2 = 1
y^2 = 1 - 1/4
y^2 = 3/4.
To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).
Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.
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Find the distance between (3,3) and (-1,2)
Answer:
(4,-1)
Step-by-step explanation:
You go right 4 to get to 3, and -1 to get to 2.
Hope this helps!
When the members of a family discussed where their annual reunion should take place, they found that out of all the
family members, 10 would not go to a park, 8 would not go to a beach, 12 would not go to the family cottage, 4 would
go to neither a park nor a beach, 6 would go to neither a beach nor the family cottage, 7 would go to neither a park nor
the family cottage, 3 would not go to a park or a beach or to the family cottage, and 2 would go to all three places.
What is the total number of family members?
There are 4 total family members.
(Simplify your answer.)
Next
The total number of family members will be 30.
How to calculate the total numberLet's call the total number of family members "x".
From the information given:
x - 10 family members won't go to the park
x - 8 family members won't go to the beach
x - 12 family members won't go to the family cottage
4 family members will go to neither park nor beach
6 family members will go to neither beach nor family cottage
7 family members will go to neither park nor family cottage
So, the total number of people who won't go to either park, beach, or family cottage is 4 + 6 + 7 = 17
And the total number of people who will go to one or two of these three places is x - (10 + 8 + 12 + 17) = x - 47
The total number of family members will be:
x - 47 - 17 = 0
x - 30 = 0.
x = 0 + 30
x = 30
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What are the center and radius if the equation (x-2)^2 + (y-9)^2
Step-by-step explanation:
(x-2)^2 + (y-9)^2 = r^2
this is of the form fora circle with center h,k and radius r
(x-h)^2 + (y-k)^2 = r^2
for the equation given center = 2, 9 and radius = r
Find the quotient of 10^-4/10^2
The quotient of 10⁻⁴/10² is 10⁻⁶
How to Find the quotient of 10⁻⁴/10²?Quotient is the result obtained by dividing one quantity by another. It represents the value that is obtained after division.
For example, if you divide 20 by 2, the quotient is 10 because 20 divided by 2 equals 10.
Division law states that:
10ᵃ / 10ᵇ = 10ᵃ⁻ᵇ
In this case have:
10⁻⁴/10² = 10⁻⁴⁻² (Division law)
10⁻⁴/10² = 10⁻⁶
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can anyone plz with steps (not for useless man )
\(\boxed{\sf \displaystyle{\lim_{x\to a}}(x^n)=a^n}\)
\(\\ \sf\longmapsto \displaystyle{\lim_{x\to \infty}}(\sqrt{3x}-\sqrt{x-5})\)
\(\\ \sf\longmapsto \displaystyle{\lim_{x\to \infty}}\sqrt{3x}-\displaystyle{\lim_{x\to \infty}}\sqrt{x-5}\)
\(\\ \sf\longmapsto \infty^{\dfrac{1}{2}}-\sqrt{\infty-5}\)
\(\\ \sf\longmapsto \infty-\sqrt{\infty}\)
\(\\ \sf\longmapsto\infty-\infty\)
\(\\ \sf\longmapsto\infty\)
2 to the power of =32
I need it to day
Given:QT bisects SP, SP bisects QT
Prove: QRS=SRT
Answer:
I DOnt get please more info
Step-by-step explanation:
Which of the following is the graph of y=-(x-2)³-5?
-5-4-3-2-1
-5-4-3
S
-2+
-3
? 4
-4
-5
997
-6
-7
-8.
-9
& co
-10
1 2 3 45 x
1
2345
X
Answer:
Step-by-step explanation:
I cannot see the graphs.
Find the unit rate (constant of proportionality) of the distance traveled.
Number of hours
0.25 1.5 2.5 3
Distance traveled (km) 3 18 30 36
Answer:
12.
Step-by-step explanation:
if to re-write the given condition, then
\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)
it is clear, the required constant is 12 (12 per hour).