Find the equation of the line though the point (-3, -2) and perpendicular to the line y = 2/3x-2.Write your answer in the form y=mx+b.

You can notice that the given function is symmetric respect to the y-axis.

It means that the value of the function for both x and -x is the same:

This is the characteristic of a even function.

Hence, the answer is B

Solution:

Given the vector h;

The vector in component form is;

Let us revise an important note

Positive numbers are increasing from 0 to positive infinity

Negative numbers are increasing from negative infinity to 0

If we divide 1 by 2, then the answer is 1/2 which is less than 2

That means the quotient is less than the divisor

If we divide 1 by -2, then the answer is -1/2 which is greater than -2

That means the quotient is greater than the divisor

Then the answer is

The result is greater than the number

The answer is A

Step-by-step explanation:

we have the 2 numbers x and (x+2).

x × (x + 2) = 143

x² + 2x = 143

x² + 2x - 143 = 0

the general solution to such a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case this is

x = (-2 ± sqrt(2² - 4×1×-143))/(2×1) =

= (-2 ± sqrt(4 + 572))/2 = (-2 ± sqrt(576))/2 =

= (-2 ± 24)/2 = (-1 ± 12)

x1 = -1 + 12 = 11

x2 = -1 - 12 = -13

so, we have 2 solutions : 11 and 13, -13 and -11

11× 13 = 143

-11×-13 = 143

Step-by-step explanation:

a probability is always

desired cases / totally possible cases

the first case I assume means that we need the probability to pick 2 odd-numbered balls in a row, if we do not put the first drawn ball back into the box.

starting condition :

15 basks in total.

1, 3, 5, 7, 9, 11, 13, 15 = 8 odd numbered balls

2, 4, 6, 8, 10, 12, 14 = 7 even numbered balls

the probability for the first ball to be odd numbered :

8/15

now we have

14 remaining balls in total.

7 remaining odd numbered balls.

the probability of the second ball being odd numbered is

7/14 = 1/2

so, the probability of both as one combined event is

8/15 × 1/2 = 4/15 = 0.266666666...

now back to the starting condition.

the probability to pick an even numbered ball is

7/15

we put the ball back in and pull a second time.

the probability to an even numbered ball is

7/15

so, the probability of both as one combined event is

7/15 × 7/15 = 49/225 = 0.217777777...

We need to solve the following expression:

The order of operations is a rule that tells the correct sequence of steps for evaluationf a math expression. We can remember the order using PEMDAS: Parenthesis, Exponents, Multiplication and Division (from left to right).

Then, in our expression, we must solve parenthesis first. It yields

The next step is to raise exponents,

and now, the multiplication step

then, we get 70-64 and the solution is 6.

The symmetry of a quadratic equation is given by the line that passes through its vertex, so in order to find the axis of symmetry we need to find the coordinate of the vertex, which is done below.

Where "a" is the number multiplying the square factor and "b" is the number multiplying the factor that isn't squared. To find these two constants we need to expand the equation given.

We have that a = 1 and b = 4, therefore:

The axis of symmetry for this quadratic equation is x=-2.

The Pythagoras theorem gives the relation for the right-angle triangle between the perpendicular, base, and hypotenuse thus the perpendicular x will be 14.70.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.

Triangle is a very common figure to deal with in our daily life.

In a triangle, the sum of all three angles is 180°

As per the given right-angle triangle,

Pythagoras' theorem states that in a right-angle triangle →

Hyp² = Perp² + Base²

In the given triangle Hyp = 21 , Base = 15 and Perp = x

So,

21² = x² + 15²

x² = 21² - 15²

x = √216 = 14.6993 ≈ 14.70

Hence "The value of x for the given right-angle triangle is 14.70 units".

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EXPLANATION

Since the Euclidean Geometry is the Geometry of the Flat Space, we can affirm that it's in two dimensions, where rotation and similarity make sense.

Although it may be expanded to three-dimensional space and beyond, it is still referred to as flat space. The concept is that all dimensions are equal and that they are equal everywhere in space.

The area of a square created on the diagonal of a rectangle, rectangular parallelepiped, or higher dimensional hyperrectangle is equal to the sum of the areas of the squares built on the mutually perpendicular sides of the rectangle, according to the Pythagorean Theorem.

This is known as Euclidean Geometry. Non-Euclidean Geometry, such as spherical, elliptic, hyperbolic, or relativistic geometry, is distinguished by the fact that the same Pythagorean theorem does not apply (though variations do).

So the true dilemma is when to utilize synthetic geometry instead of analytic geometry. Whenever possible, we could say. The challenge with synthetic geometry is that proofs and constructions frequently need some ingenuity on the prover's side.

Answer: 10

1/4 (25%) of 40 is 10, meaning Mai made 10 successful free throws.

Answer:

3/4

Step-by-step explanation:

To find the slope (gradient) of the line = change in y / change in x

[tex]slope=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }\\(x_{1} ,y_{1} ) = (-2,6)\\(x_{2} ,y_{2} ) = (-6,3)[/tex]

insert those coordinates in the equation:

[tex]slope=\frac{3-6}{-6-(-2)} =\frac{-3}{-4} =\frac{3}{4}[/tex]

The surface area of the triangular base pyramid is 19.75 mm².

The surface area of a triangular pyramid is the sum of the area of the whole sides of the triangular pyramid.

Therefore,

Surface area of a triangular pyramid = base area + 1 / 2 (perimeter × slant height)

The base of the triangular pyramid is an equilateral triangle. An equilateral triangle has congruent sides.

Therefore,

base area = 1 / 2 × 5 × 4.3

base area = 10.75 mm²

Hence,

perimeter of the base = 5 + 5 + 5 = 15 mm

Surface area of a triangular pyramid = 10.75 + 1 / 2 (15 × 3)

Surface area of a triangular pyramid = 10.75 + 1 / 2(18)

Surface area of a triangular pyramid = 10.75 + 9

Surface area of a triangular pyramid = 19.75 mm²

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Conditional Probability

First, we must complete the totals in the table as follows:

The formula for the conditional probability is:

Where A is an event we know has already occurred, B is an event we want to calculate its probability of occurrence, and P∩A is the probability of both occurring.

We know a female student has been selected, so that is our known event and:

The probability that a female student is also a senior is:

Substituting:

The required probability is 3/16

Given:

The point is (-2,3).

The parallel line is y=4x+2.

This is of the form

where slope m=4.

We know that the slope of the parallel lines is equal.

Thus we get the slope m =4 for the required line.

Consider the line equaiton

Substitute x= -2,y=3, and m =4 in the equation to find the value of b.

Adding 8 on both sides of the equation, we get

We get b=11.

Substitute m=4 and b=11 in the equation, we get

Hence the line equation that passes through the point (-2,3) and parallel to y=4x+2 is

The formula to find the volume of a triangular prism is the following:

where:

h - height

b - base length

w - width

for this problem:

h = 8 cm

b = 5 cm

w = 7 cm

then

solving this, we obtain that the volume of the triangular prism is 140 cm^3 or cubic centimeters

Answer: The account has been open for 3 years

Step-by-step explanation:

3% of $600 is 18

18*3 = 54

Answer:

3 years

have $600

interest $54

annual rate 3%

600 - 3% = 582 that is the money she has in bank without interest

600-582 = 18

54÷ 18= 3 years

you have the following equation:

3x - 2 = 2(x+1)

You have to specify the property used in each step to get the solution of the previous equation. You obtain the following:

1. 3x - 2 = 2(x + 1) given

2. 3x - 2 = 2x + 2 distribution prop

3. 3x - 2x - 2 = 2x - 2x + 2 subtraction 2x both sides - subtraction prop

x - 2 = 2

4. x - 2 + 2 = 2 + 2 summation 2 both sides - addition prop

x = 4

Okay, here we have this:

Considering that P(AUB)=P(A)+P(B)-P(AintersectionB), we obtain that:

P(B)=P(AUB)-P(A)+P(AnB)

P(B)=(13/24)-(1/4)+(1/12)

P(B)=3/8

Finally we obtain that P(B) is equal to 3/8.

Solution

- Linear:

The general form of a linear function is

- Quadratic:

The general form of a quadratic function is:

- Exponential:

The general form of an exponential function is:

- Now that we know the general forms of these functions, we can proceed to solve the question.

- The amount a person is paid per hour in wages is the amount that the person collects for every hour that he works

- Let us imagine that a person receives $a for every hour worked.

- This means that:

After 1 hour, the person makes $a

After 2 hours, the person makes $a + $a = $2a

After 3 hours, the person makes $a + $a +$a = $3a

- We can therefore generalize as follows:

Thus, after x hours, the person makes:

- Thus, the function representing the amount a person makes per hour of work is given by:

- Comparing this result with the 3 function definitions above, we can see that this corresponds to a Linear function

Final Answer

The answer is Linear

Given:

Total number of cub scouts is 20 and the number of scout is 10 more than 2 times the number of adult leaders.

Required:

We need to find the number of adult leaders.

Explanation:

Lets consider cub scouts as c and adult leaders as a so the

and the formula for adult is

simplify as:

Final answer:

Number of adult leaders is 5

Equation

P = 2300 + 90(N)

Total payment after selling 23 copies of History is Fun.

P= 2300 + 90(23)

P= 2300 + 2070 (Multiplying)

P= 4370 (Adding)

The answer is $4370

1. Given the expression:

You can use the FOIL method to multiply the binomials. Remember that the FOIL method is:

Then, you get:

Adding the like terms, you get:

2. Given:

You have to complete the square:

- Identify the coefficient of the x-term". In this case, this is -6.

- Divide -6 by 2 and square the result:

- Now add 9 to the polynomial and also subtract 9 from the polynomial:

- Finally, simplifying and completing the square, you get:

3. Given the expression:

You can simplify it as follows:

- Apply:

In this case:

Then:

- Adding the like terms, you get:

4. Given:

You need to complete the square by following the procedure used in expression 2.

In this case, the coefficient of the x-term is:

Then:

By Completing the square, you get:

Therefore, the answer is:

Given

An independent third party found the cost of a basic car repair service for a local magazine.

The mean cost is $217.00 with a standard deviation of $11.40.

To find: The repair costs which would be considered an “unusual” cost.

Explanation:

It is given that, the mean is 217.00, and the standard deviation is 11.40.

Consider, the distribution as a Normal distribution.

Then, the first range is defined as,

And, the second range is defined as,

Hence, the answer is option a) 192.53 since it does not belongs to the above ranges.

Remember that

For a 95% confidence interval --------> the value of z=1.960

Find out the value of

therefore

Solution

The integers are the set of real numbers consisting of the natural numbers, their additive inverses and zero. {...,−5,−4,−3,−2,−1,0,1,2,3,4,5,...} The set of integers is sometimes written J or Z for short. The sum, product, and difference of any two integers is also an integer.

The whole numbers are set of real numbers that includes zero and all positive counting numbers. Whereas, excludes fractions, negative integers, fractions, and decimals. All the whole numbers are also integers, because integers include all the positive and negative numbers

The integers are real numbers

Therefore the numbers are list of integers

The age of man is 63 years and the age of women is 21 years.

Given that, a character is criticized for marrying a woman when he is three times her age.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Let age of man be x and the age of women be y.

Now, x=3y ---------(1)

In 21 years time man will be twice her age.

x+21=2(y+21)

⇒ x+21=2y+42

⇒ x-2y=21 ---------(2)

Substitute equation (1) in (2), we get

3y-2y=21

⇒ y = 21

So, x=3y=63

Therefore, the age of man is 63 years and the age of women is 21 years.

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For this problem we are going to be working with the function:

where x is the time in minutes and f(x) represents the number of bacteria at any given time x.

Part 1.

To sketch the graph we need to determine some points of it; to get them we give values to x and plug them in the expression for the funtion.

If x=0 we have that:

Then we have the point (0,2200).

If x=10 we have that:

Then we have the point (10,2956.616).

If x=20 we have that:

Then we have the point (20,3973.445).

If x=30 we have that:

Then we have the point (30,5339.977).

If x=40 we have that:

Then we have the point (40,7176.483).

If x=50 we have that:

Then we have the point (50,9644.593).

Then we have the points (0,2200), (10,2956.616), (20,3973.445), (30,5339.977), (40,7176.483) and (50,9644.593). Plotting this points on the plane and joining them with a smooth line we have that the grah of the function is:

Part 2.

To determine how many bacteria were at the beginnning of the experiment we plug x=0 in the function describing the population, we did this in the previous question; therefore we conclude that there were 2200 bacteria at the beginning of the experiment.

Part 3.

We notice that the function fgiven has the form:

where a=2200 and r=0.03; for this type of function the growth rate in decimal form is given by r. Therefore we conclude that the percentage growth in this function is 3%.

Part 4.

To determine how many bacteria were in the experiment after one half hout we plug x=30 in the function give; we did this in part 1 of the proble.Therefore we conclude that after one half hour there were approximately 5340 bacteria cells. (for this part we roun to the neares whole number)

Part 5.

To determine how long it takes to have 7500 cells we plug f(x)=7500 in the expression given and solve the resulting equation for x:

To remove the base we need to remember that:

Then we have:

Now we use the change of base property for logarithms:

Then we have:

Therefore it takes 41 minutes to have 7500 cells.

The correct volume of the rectangular prism as calculated by Betty is 108 cubic yards

A rectangular prism is cuboid and an hexahedron that has 6 faces.

The formula for finding the volume of the rectangular prism is V = l•w•h

Where;

l = Length

w = Width

h = Height

The measurement of the prism, for which Karen is calculating the volume gives;

w = h

The amount larger Karen found that she made the width, which gives;

Width of the cube Karen used = (1 + 1/3) × w

Therefore;

h = (1 + 1/3) × w

The volume becomes;

V' = l × (1 + 1/3) × w × (1 - 1/3) × w = l•w²•(1²-1/3²)

V' = l•w²•(8/9)

The amount by which the volume increased, dV = 12 yd³

Which gives;

l•w²•(8/9) = l•w•h - 12 = l•w² - 12

l•w²•(8/9) - l•w² + 12 = 0

l•w²•(8/9) - l•w² + 12 = 0

l•w²/9 = 12

V = l•w² = 12 × 9 = 108

The correct volume of the prism is 108 cubic yards

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The slope of a line perpendicular to the line whose equation is 3x-5y=45 is -5/3.

So first of all, we have to find the slope of the given line. Convert it into Slope-Intercept Form.

The Slope - Intercept Form is : y = mx + c

Converting the given equation, we get :

3x - 5y = 45

5y = 3x + 45

y = (3/5)x + 15

Perpendicular Lines

The lines having opposite reciprocal slopes are perpendicular. That means you flip the sign (+/-) and flip the numerator and denominator. The slope of the line perpendicular to this one is -5/3.

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We know that

• Each protective coat is 2/27 inches thick.

• We need to fill 2/3 inches of this protective coat.

To solve this problem, we need to know the total number of the application needed to fill 2/3 inches. We can form the following expression

We solve for x