(Solve the problem & round to four decimal places as needed.)

Solution:

To graph, a linear inequality in two variables (say, x and y ), first get y alone on one side. Then consider the related equation obtained by changing the inequality sign to an equals sign. The graph of this equation is a line.

If the inequality is strict ( < or > ), graph a dashed line. If the inequality is not strict ( ≤ and ≥ ), graph a solid line.

For example,

Consider the linear inequality in two variables below

Step 1:

Put x=0 and find y

Step 2:

Put y=0 and find x

Hence,

We are going to use the coordinates below to graph the inequality using a solid line because

The inequality sign used is greater than or equal to

Hence,

The graph of the inequality will be

From the graph, the range of the graph, the y values range from zero down; so the range is given by;

Option

We have to use the simple interest formula

Where P = 250; r = 0.10 (10%); t = 6. Replacing these values, we have

Hence, after 6 years, you have $400.

If we subtract this amount from the investment, we get the profits.

Given the System of Inequalities:

1. Take the first inequality and solve for "y":

Notice that direction of the symbol changes, because you had to multiply both sides of the inequality by a negative number.

Now you can identify that the boundary line is:

Since it is written in Slope-Intercept Form, you can identify that its slope is:

And its y-intercept is:

Notice that the symbol of the inequality is:

That indicates that the line is dashed and the shaded region is above the line.

Knowing all this information, you can graph the first inequality on the Coordinate Plane.

2. Apply the same procedure to graph the second inequality. Solving for "y", you get:

Notice that the boundary line is:

Where:

Since the symbol is:

The line is dashed and the shaded region is above the line.

Knowing this, you can graph the second inequality.

3. Look at the graph of the System of Inequalities:

Notice that:

-The black line is the boundary line of the first inequality and the green line is the boundary line of the second inequality.

- The solution of the system is the intersection region. It is the region where the shaded region of the first inequality and the shaded region of the second inequality, intersect.

4. Plot the points given in the options on the graph of the Systems:

5. You can identify that this point is in the intersection region:

Therefore, it is a solution.

Hence, the answer is: Option B.

Explanation

When two expressions are not equivalent, you can use an inequality symbol

now, when comparing two expressions that are equivalent , WE CAN NOT USE an inequality simbol, instead of we need to use The equals sign or equal sign formerly known as the equality sign

for example

the = symbold indicates that both sides have the same value ( rigth and left)

I hope this helps you

Given that 11v - 8 = 3

add 8 to both sides

11v = 3 + 8

11v = 11

Divide both sides by 11

v = 1

to simplify 4v - 8

= 4 (1) - 8

= 4 - 8

= -4

Answer:

Step-by-step explanation:

Since the square fountain measures 4 meters on each side and the walkway will be one meter wide, let's make a diagram to see the situation:

Then, to calculate the area of the walkway (green shaded region)

Now, how many colored stones will be needed if one bag covers 1 square meter:

There are 20 square meters on the walkway, then will be needed 20 bags of colored stones.

A bag of colored stones costs $24.99, then multiply 20 by $24.99:

The most appropriate choice for linear equation will be given by -

w = -8 is the required answer

What is linear equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here

[tex]4(3w - 2) = 8(2w+3)\\12w - 8 = 16w+24\\16w - 12w = -8-24\\4w = -32\\w = -\frac{32}{4}\\w = -8[/tex]

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Tyrone randomly interviewed 55 8th graders at the Westwood Mall Saturday afternoon to determine their reason for going to the mall.

Based on the results he made the following claim.

"Two out of four middle school students visit the mall to go shopping".

Let us analyze each of the given options.

a. Tyrone only interviewed students in the food court.

There is no evidence that suggests the interview was conducted at the food court so this is not the correct answer.

b. Tyrone did not survey enough 8th graders to draw a valid conclusion

He interviewed 55 8th graders which are more than enough students so this is not misleading.

c. Tyrone did not use a random sample of 8th graders

It is given in the question that he used a random sample so this is not misleading.

d. Since Tyrone surveyed only 8th graders, his sample is not representative of all middle school students.

If you notice closely, Tyrone interviewed only 8th graders whereas the claim was about all middle school students.

So this is clearly misleading, 8th graders do not represent all middle school students.

Therefore, option d is correct.

SOLUTION

(a) The equation in function notation is

Hence the answer is

(b). f(23) becomes

f(35) becomes

f(41) becomes

Depending on the angle we are analyzing on the right triangle, each side of it takes a different name. In this case, we are going to name them depending on the angle A. Then,

a: opposite side (to A)

b: adjacent side

c: hypotenuse

We know that the formula for cot(A) is:

Replacing it with a and b:

Since a = 3:

We have an expression for cot(A) but we do not know its exact value yet. First we have to find the value of b to find it out.

We do this using the Pythagorean Theorem. Its formula is given by the equation:

Since

a = 3

and

c = √51

Then,

solving the equation for b:

Then,

b= √42

Therefore, the equation for cot(A) is:

The function given is

We are to find the inverse of the function

let f(x) =y

Then, we make x the subject of the formula from here

Then The inverse of the function becomes

Therefore the fourth option is correct

If both triangles are congruent by the HL theorem, then their hypotenuses are equal and at least one of the corresponding legs is equal too.

Hypothenuses:

From this expression, you can calculate the value of m

Legs:

Replace the expression with the calculated value of m

Now pass the n-related term to the left side of the equation and the numbers to the right side:

And divide both sides of the expression by 3

So, for m=3 and n=6 the triangles are congruent by HL

-(x+ 5) + 3x

Distributing the -1:

(-1)*x + (-1)*5 + 3x

-x - 5 + 3x

Combining similar terms:

(-x + 3x) - 5

2x - 5

An algebraic expression which represents the translation of "The sum of a number and -41 is equal to the quotient of the number and 11" is z - 1 = z/11.

In order to translate a word problem into an algebraic expression, we would have to assign a variable to the unknown number:

Let z represent the unknown number.

The sum of a number and -41 is given by:

z + (-1) = z - 1   ....equation 1.

The quotient of the number and 11 is given by:

z/11  .....equation 2.

Next, we would equate equation 1 and equation 2 as follows:

Translation; z - 1 = z/11

Read more on algebraic expression here: https://brainly.com/question/4344214

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Solution

- The question would like us to solve the quadratic equation:

- The solution to this equation is given below:

- Thus, the linear factors are

Given:

Function is:

Find-:

Check for solution

Explanation-:

The value of "y" is:

For (0,8)

Check value of "y" at x = 0 then,

So (0,8) it is not a solution.

Check (3,-7) the value of "x" is 3

So (3,-7) is the solution of function.

Check for (1 , 2) value of "x" is 1.

So, (1,2) is the solution.

Check for (4,-5) the value of "x" is 4.

So, (4,-5) is not a solution

Math | English | Art | Total

Boys 13 25 11 49

Girls 7 20 6 33

Total 20 45 17 82

1) Let's set a table, based on the given information:

• Since there are 20 students enrolled in Math let's place it into the Total, 20 -13 = 7

• 82 students altogether.

• 11 boys are in Art , 17 altogethe then 17 -11 = 6 girls

• 20+6+7 = 20+13 = 33 girls altogether.

• 82 -33 =49 13 +x +11 = 49 x = 49 -24=25

• And lastly English: 20 +25 = 45

2) That's our table:

Math | English | Art | Total

Boys 13 25 11 49

Girls 7 20 6 33

Total 20 45 17 82

Step-by-step explanation:

since M is the midpoint, it means that AM = MB.

so,

b² + 5b = 3b + 35

b² + 2b - 35 = 0

the general solution to such a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case (x is called b, don't get confused, as this is not the factor of x) this gives us

b = (-2 ± sqrt(2² - 4×1×-35))/(2×1) =

= (-2 ± sqrt(4 + 140))/2 = (-2 ± sqrt(144))/2 =

= (-2 ± 12)/2 = -1 ± 6

b1 = -1 + 6 = 5

b2 = -1 - 6 = -7

therefore, we have 2 solutions

b = 5

AM = 5² + 5×5 = 25 + 25 = 50

b = -7

AM = (-7)² + 5×-7 = 49 - 35 = 14

control, as AM = MB

MB = 3×5 + 35 = 15 + 35 = 50

or

MB = 3×-7 + 35 = -21 + 35 = 14

AM = MB in both cases, so, all is correct.

Always remember that the slope is the number of units on the Y-axis in relation to the X movement.

A horizontal line always has a slope of 0. (it is not increasing in the Y-axis)

Answer:

length: 21 cm

width: 16 cm

Step-by-step explanation:

. A rectangle has two lengths and two widths, or two sides that are vertical (up and down) and two sides that are horizontal (left and right)

. In order to find the perimeter we must add up all four side lengths.

. You can find the perimeter of a rectangle by adding the length and the width then multiplying by 2, because there are two of each side length.

P = 2(l+w)

In the question the perimeter is given, which is 74.

We can divide 74 by 2 so that we can find the sum of the length and width.

74/2 = 37

l + w = 37

In the question is states that the length is 5 inches longer than the width.

l = (5 + w)

There are two widths and two lengths in a rectangle, the measurement of the two lengths is 5 inches longer than the two widths.

5 + w + w = 37

5 + 2w = 37

Now that we have our equation we can solve for w, or the width.

1. Move the term containing the variable to the left

5 + 2w = 37

2w + 5 = 37

2. Subtract 5 from both sides of the equation, the opposite of adding 5

2w + 5 = 37

2w + 5 - 5 = 37 - 5

2w = 32

3. Divide by 2 in both sides of the equation, the opposite of multiplying 2

2w = 32

2w/2 = 32/2

4. Cancel out the 2s on the left, but leave the x

2w/2 = 32/2

w = 16

So, now that w, or the width = 16, we can find the length:

l = 5 + w

l = 5 + 16

l = 21

You can check your answer by plugging in our values into the original perimeter formula:

P = 2(l+w)

P = 2(21 + 16)

P = 2(37)

P = 74, so my answer is correct, because 74 is the perimeter given in the question.

The domain of a function is all values of x the function can have.

Since this function has radicals, and the value inside a radical needs to be positive or zero, and also the denominator of a fraction can't be zero, we have the following conditions:

Since the first condition contains the second, so the domain set is represented by the second condition:

The first figure has 3 tiles

The second figure has 8 tiles

The third figure has 15 tiles

The 4th figure has 24 tiles

The 5th figure has 35 tiles

The 6th figure has 48 tiles

Each time we increased row and column

So the rule is

a(n) = n(n + 2)

Let us use the rule to find figure 46

n = 46

The number of tiles in figure 46 is 2208

Answer:

Surface area = 1084 in²

Step-by-step explanation:

To find the surface area of a right cone, we can use the following formula:

[tex]\boxed{{Area = \pi r^2 + \pi rl}}[/tex],

where:

• r = radius

• l = slant height.

In the question, we are told that the diameter of the cone is 30 in. Therefore its radius is (30 ÷ 2 = ) 15 in. We are also told that its height is 8 in.

Using this information and the formula above, we can calculate the surface area of the cone:

Surface area = [tex]\pi \times (15)^2 + \pi \times 15 \times 8[/tex]

                     = [tex]345 \pi[/tex]

                     [tex]\approx[/tex] 1084 in²

The given expression is

LCM of 8 and 4 is 8, making the denominator 8.

Hence the answer is

Answer:

Explanation:

Here, we want to get the amount of money that would guarantee that a person has more money than 80%

That means the probability is greater than 80% or 0.8

Thus, we need to get the z-score that corresponds to this probability

Using a z-score table, we can get this as follows:

We will now get the value from the obtained z-score

Mathematically:

Substituting the values, we have it that:

To be a function, it is nesessary that the values of x correspond to a unique value of y (a value of x cannot correspond to 2 different values of y). The same value of y can correspond to two or more values of x

As in the given data each value of x has just one value of y. Then, it is a function.

The result for the division is:

Step 1: Write the coefficients of the numerator on the right-hand side, and the opposite of the constant term in the denominator on the left-hand side.

20..............2 || 3 || 5 || 9

..................2

Step 2: Multiply 20 by 2 and add the result to 3

20..............2.......................|| 3 || 5 || 9

..................2*20 = 40

....................2 || 3 + 40 = 43

Step 3: Multiply 43 by 20, and add the result to 5

20..............2 || 3 .........................|| 5 || 9

...................... 40.......20*43 = 860

....................2||43 .......5+860=865

Step 4: Multiply 865 by 20, and add the result to 9

20..............2 || 3 || 5 ..........................|| 9

...................... 40 ||860......20*865=17300

....................2||43||865...9 + 17300=17309

The coefficients are 2, 43, 865, 17309

The quotient is:

and the remainder is 17309

So, we can write:

3(y-4) - 5(y+8)

3y - 12 - 5y - 40

-2y - 52

Answer:

Option is the the. correct answer A