Graph the system of linear inequalities and shade in the solution set. If there are no solutions, graph the corresponding lines and do not shade in any region X - y > 2 Y < - 1/3x + 1

tan(3x)

Explanation

Step 1

remember some property

then

I hope this helps you

Answer:

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Answer:

[tex](x,y)=\left(\; \boxed{-3,4} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]

[tex](x,y)=\left(\; \boxed{5,0} \; \right)\quad \textsf{(larger $x$-value)}[/tex]

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}\;x+2y=5\\x^2+y^2=25\end{cases}[/tex]

To solve by the method of substitution, rearrange the first equation to make x the subject:

[tex]\implies x=5-2y[/tex]

Substitute the found expression for x into the second equation and rearrange so that the equation equals zero:

[tex]\begin{aligned}x=5-2y \implies (5-2y)^2+y^2&=25\\25-20y+4y^2+y^2&=25\\5y^2-20y+25&=25\\5y^2-20y&=0\end{aligned}[/tex]

Factor the equation:

[tex]\begin{aligned}5y^2-20y&=0\\5y(y-4)&=0\end{aligned}[/tex]

Apply the zero-product property and solve for y:

[tex]5y=0 \implies y=0[/tex]

[tex]y-4=0 \implies y=4[/tex]

Substitute the found values of y into the first equation and solve for x:

[tex]\begin{aligned}y=0 \implies x+2(0)&=5\\x&=5\end{aligned}[/tex]

[tex]\begin{aligned}y=4 \implies x+2(4)&=5\\x+8&=5\\x&=-3\end{aligned}[/tex]

Therefore, the solutions are:

[tex](x,y)=\left(\; \boxed{-3,4} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]

[tex](x,y)=\left(\; \boxed{5,0} \; \right)\quad \textsf{(larger $x$-value)}[/tex]

Given,

The coordinates of the vertices of the pentagon is,

A(-7.42,2.42), B(0,7.88), C(7.42,2.42),D(4.605,-6.35), and E(-4.605-6.35)

Required

The approximate perimeter of the pentagon.

The perimeter of the pentagon is calculated as,

The length of side AB is,

The length of side BC is,

The length of side CD is,

The length of DE is,

The length of AE is,

The perimeter of the pentagon is,

Hence, the perimeter of the pantagon is 46.0568.

The slope of the given equation is ,

Slope of perellel line will also be same = 1/3 ,

The equation of perellel line is ,

given data:

to find whether they form an proposition.

using cross product,

the cross product are not equal.

Thus, they donot form a proposition.

Answer:

Explanations:

Given the equation;

In order to get the missing coordinate in the ordered pair (0, ?), we will substitute x = 0 into the equation and get the corresponding y-value as shown:

Divide both sides of the equation by 4;

Therefore, the missing coordinate will be 3 to have (0, 3)

The ordered pair given is 12.5, 5

This means that

When x = 12.5, y = 5

Looking at the given equations, if we substitute the values of x and y, the correct option would be C

The equation is expressed as

x = y + 7.5

By substituting, it becomes

12.5 = 5 + 7.5

12.5 = 12.5

The correct option is C

If both trianlges are congruent, we get that:

This way,

Solving for x :

This way, we get that x = 11

Answer: Option 4

To answer this questions we need to remember the standard score formula given by:

where x is the value we are looking for, mu si the mean and sigma is the standard deviation.

a.

We need the probability:

using the standard score this is equivalent to:

Using a normal distribution table we have:

Therefore the probability to select a person with more than 95 IQ points is 63.1%.

b.

Following the same reasoning as before we have:

Therefore the probability to select a person with less than 125 IQ points is 95.2%

c.

To find how many people of this sample have more less than 110 points we need to find that probability:

Multiplying this value with the sample size we have

Therefore 598 people will have an IQ less than 110.

d.

By the same reasoning as before we have:

Multiplying this value with the sample size we have

Therefore 3 people will have an IQ greater than 140.

Given:

The graph is:

Find-:

(a)

Find the probability that a real number between 4 and 6 is picked.

(b)

Find the probability that a real number between 4 and 7 is picked.

Explanation-:

The area of the region

The probability is:

The total outcomes is:

(a)

Probability to the 4 and 6

The 4 to 6v region is B

(B)

Probability for 4 to 7

The region B and C

We have the following:

solving by the square root property

6

The given absolute value expression is:

Substitute x = 2.1, y = 3, z = -4.2 into the given expression:

This can be simplifed as:

Since |4.2-4.2| = 0, the expression above becomes:

0 + 6

= 6

Therefore, the absolute value of the expression, after simplification, is 6

1. To find the nearest ten of 3315.

Since 15 is midway between 10 and 20.

So, the nearest ten of 3315 is 3320.

2. To find the nearest hundred miles of 4,184 miles:

184 is closest to 200.

Hence, the nearest hundred miles of 4,200 miles.

3.

A) To find the nearest hundred thousand of 846,025:

846,025 is closest to 800,000.

Hence, nearest hundred thousand of 846,025 is 800,000.

B) To find the nearest ten thousand of 846,025:

46,025 is closest to 50,000.

Hence, nearest ten thousand of 846,025 is 850,000.

C) Comparing the results of Part A and Part B,

The rounded number of Part B is greater.

Given:

Round the mass of the large car to the nearest thousand.

Because 1985 is between 1,000 and 2,000 and closer to 2,000 ,the number should round up to 2,000.

Option D is the correct answer.

Given data:

The given discount through coupon is d=15%.

The original price of camera is c=$45.00.

The discount on the given amount is,

Thus, the amount saved is $6.75.

Given:

x = 2 gallons of paint

y = 400 square feet of area

The graph representing the given point (x,y) = (2, 400) is number 4: linear 12 gallons.

Then, to estimate how many gallons of paint Marie requires to paint an area of 2,400 square feet.

We locate the point y = 2400 and find the corresponding x value. This is:

x = 12

Answer:

* the graph is the fourth one

* 12 gallons

as it is about growth, the integer is positive, therefore

answer is b) 4"

Looking at the diagram, the box method has already been applied. The simplified answer would be gotten by adding up each term in the boxes while taking into consideration, the signs of each term. It becomes

- 15x - 15 - 12x^2 - 12x^3

Rearranging the terms in descending order of the exponents, it becomes

- 12x^3 - 12x^2 - 15x - 15 15x - 15 - 12x

Answer:

y=3x+27

2y= x+16or,

or,y= x+16/2

Okay, here we have this:

Inicially we have 5000 students, let's calculate how many were left in 2019:

Students in 2019=5000*0.9

Students in 2019=4500

Now, let's finally calculate how many were left in 2020:

Students in 2020=4500*0.95

Students in 2020=4275

Finally in 2020 they were 4275 students

we need to know the formula of the area of a rectangle

we already know A and l we need to clear w

we need to do the division

1) the value of x is 7

1) From the diagram, the angles with the red ink are equal.

SInce the two angles at the base are equal, we call the triangle an isosceles triangle.

This triangle have two sides and two angle equal.

As a result, the sides opposite the angles given in the triangle are equal to each other.

The sides opposite the angles are x and 7. So, x is equal to 7.

Hence, the value of x is 7

The same principle or procedure can be applied to question number 2.

The solution to the given equation is;

Therefore, the value of 32x shall be;

The answer is 16

The points (x,y) whose values satisfy the equation -5y=13 belong to the graph of that equation.

First, isolate y by dividing both sides of the equation by -5 and simplifying:

Then, the points (x,y) belon to the graph of the equation -5y=13 whenever the value of y is -13/5, regardless of the value of x. Then, choose two different values of x to find two points that belong to the graph. For example, x=0 and x=2. Then, this two points belong to the graph:

Notice that -13/5=-2.6,

Plot the points (0,-2.6) and (2,-2.6) in a coordinate plane:

Since the given equation is linear, the graph of the equation is a straight line. We can draw a straight line between any two points given. Draw a line between (0,-2.6) and (2,-2.6) to find the graph of the equation -5y=13:

2/7 is in reduced terms already

no simplification can be made over this fraction.

hope it is clear

(a)

Since X can only assume whole values, it is a discrete random variable.

(b)

The sum of all probabilities in the table must be equal to 1, so we have:

(c)

The values of x smaller than 5 in the table are 3 and 4, so we have:

(d)

For x between 4 and 6, we have:

(e)

Looking at the table, for x = 3 we have:

We know that Max exercises 4 hours during each 7-day-week.

After 35 days (5 weeks), the number of hours would be

(4, 5)

The given function is:

y = f(x + 1) + 2

There are many ordered pairs that can be on the graph of y = f(x + 1) + 2, but with the information given will can look for one of them.

Let x = 4

y = f(x + 1) + 2

y = f(4 + 1) + 2

y = f(5) + 2

Since it is given that f(5) = 3, the equation above can be simplified to get the value of y.

y = f(5) + 2

y = 3 + 2

y = 5

Therefore, an ordered pair that must be on the graph of y = f(x+1) + 2 is (4, 5)

ANSWER

The second data set is more spread out

EXPLANATION

The standard deviation measures the spread of a data distribution. The more spread out a data distribution is, the greater its standard deviation.

In this problem, the second data set has twice the standard deviation of the first data set, so it's more spread out.