find the slope. A. y= -1/2x - 19/2.

To begin we need to find the value of a

We apply the Pythagorean theorem

Now we find theta

Here we use the tangent that is the oppositive side over the adjacent side

Let me write here an example of a common number/term in both numerator and denominator that we can cancel.

In the above example, we are able to cancel out the common number 4 because they are stand alone numbers. We can divide 4 by 4 and that is 1. Hence, the answer is just xy.

Another example:

In the above example, we are able to cancel out (x + 2) because this term is a common factor to both numerator and denominator.

In the example, we can also see that -1 is a common number however, we cannot cancel it out because the number -1 is not a standalone factor. It is paired with other number/variable. (x - 1) and (2x - 1) are both factors but are not the same, that is why, we are not able to cancel that.

Another example:

As we can see above, (x + 2) is a common term however, we cannot cancel it. We can only cancel common terms if they are common factors of both numerator and denominator. (Notice the plus sign in the middle. )

The term (x + 2) above is not a factor of the numerator and denominator, hence, we cannot cancel it.

We have to find the solutions to the equation:

The absolute value function is in fact a piecewise function, so it may have two solutions.

We consider for the first solution that the argument inside the absolute function is positive, that is x + 4 > 0. Then, we will have:

Now, we consider that the the argument is negative and is made positive by the absolute value function (it will shift the sign, which can be represented by a multiplication by -1). This means that x + 4 < 0, and the solution will be:

We can see it in a graph as:

Answer: the solutions are x = 4 and x = -12.

we are asked about the claim that the fraction -12 / 8 is equivalent to the decimal expression -0.125... (repeating)

Without evaluating the expression, we can say that the clain is INCORRECT, since just the quotient 12/8 should give a number LARGER than "1" (one) in magnitude (the number 12 is larger than the number 8 in the denominator. We can also say that such division cannot ever give a repeating decimal at infinity, since divisions of integer numbers by 8 or 4 never render a repeating decimal, but a finite number of decimals.

Answer:

14980

Step-by-step explanation:

    4 2 8
x
        3 5
-----------
  2  1  4 0        --->  428 x 5
1  2  8 4           --->  428 x 3 but since 3 is in the 10s place we shift by 1
---------------              to the left. You can think of that 1248 as 12480
1  4  9  8 0       --> add the two rows

Hope that helps. I tried my best to explain :)

Answer:

  4 2 8

×     3 5

+  2 1 4 0

+  1   2 8 4  

=  1   4 9 8 0

Step-by-step explanation:

Step 1

The given body fat percentage = 19.2%

The given body weight = 153 pounds

Required: To find how many pounds of his weight is made up of fat.

Step 2

Find out what 19.2% of his weight is

Hence, the pounds of his weight made up of fat to the nearest tenth = 29.4 pounds

The probability of getting exactly 1 blue marble from a bag which is  filled with 5 blue and 4 red marbles is 40/81.

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

A bag is filled with 5 blue and 4 red marbles.

The total number of marble in the bag are,

5+4=9

One marble is taken at random from the bag, the color is noted and then it is replaced. The probability of getting blue marble is,

P(B)=5/9

probability of getting red marble is,

P(R)=4/9

The Probability of getting red marble in first pick and  probability of getting blue marble in second pick

P1=5/9×4/9=20/81

The Probability of getting blue marble in first pick and probability of getting red marble in second pick is,

p2=4/9×5/9=20/81

The exactly 1 blue is taken out, when first marble is red and second is blue or the first one is blue and second one is red. Thus, the probability of getting exactly 1 blue is,

P=p1+p2

=20/81+20/81

40/81

Hence the probability of getting exactly 1 blue marble from a bag which is  filled with 5 blue and 4 red marbles is 40/81.

Learn more about the probability here;

brainly.com/question/24756209

#SPJ1

Given the algebraic expression below

The first term of the algebraic expression is

The first term "7s" is a variable term.

The variable of the first term is "s"

The coefficient of the variable term is 7

Let:

x = Number of months

y1 = Total cost for Club A

y2 = Total cost for Club B

a = Fee of Club A per month

b = Fee of Club B per month

c = Initial fee of Club A

d = Initial fee of Club B

so:

So, the total cost will be the same for:

The cost will be the same for the month number 5. And the total cost will be:

$145

ANSWER

g'(0.1) = 4

EXPLANATION

As stated, g(x) is a composition of two functions: f(x) and 2x. To find its derivative, we have to use the chain rule,

So, the derivative of g(x) = f(2x) is twice the derivative of f(x) and, therefore,

Hence, g'(0.1) = 4.

ok

that is the rule

just identify a and b in your problem

a = x

b = 6

Substitute in the theorem, and simplify

The side lengths given form a triangle

Let the lengths of the sides of the triangle be "a", "b" and "c"

For the length to form sides of a triangle, the sum of any two sides of the triangle must be greater than the third as shown:

Given the sides of the triangle as 34km, 27km, and 58km

Let a = 34km, b = 27km and c = 58km

Substituting these values in the expression above to check if it is true:

Since the inequality expression supports the theorem above, hence the side lengths given form a triangle

The percentage of discount is 37%

Here, we want to calculate the percentage of discount

The first thing we need to do here is to calculate the discount amount

Mathematically, we have this as;

Now, we find the percentage of 24.99 is this discount

We have this as;

The percentage of discount is approximately 37%

Answer:

x = 3/2 = 1.5

Explanation:

The initial equation is:

To solve the equation, we need to multiply both sides by 250 as:

This fraction can be simplified as:

Therefore, the value of x is 3/2 as a fraction or it is 1.5 as a decimal.

Since he has the same number of nickels as dimes.

x = nickels

x = dimes

500 - 2x = quarters

the total value of the coins is $72.50

5x + 10x + 25(500-2x) = 7250

Solve for x

15x + 25(500) + 25(-2x) = 7250

15x + 12,500 - 50x = 7250

Combine like terms

15x - 50x = 7250 - 12500

-35x = -5250

Divide both sides of the equation by -35

-35x/-35 = -5250/-35

x = 150

150 quarters

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

f(x)=x²

f(1/2x) = ?

graph of y=f(1/2x) = ?

Step 02:

b. f(1/2x)

x ===> 1/2x

Step 03:

c. Graph:

We give values to x, and we obtain the values of y.

f(x) = 1/4 x²

e.g.

if x = 4

y = 1/4 (4)² = 1/4 * 16 = 4

That is the solution for b. and c.

The correct options regarding each function are as follows:

1.

2.

3.

4.

5.

6.

The graph is classified as continuous or discrete as follows:

Hence only function 5 is discrete, the other are all continuous.

In the graph of a function, the domain and the range are given as follows:

Hence the domain and the range for the functions in this problem are given as follows:

1.

2.

3.

4.

5.

6.

A graph represents a function if it has no vertically aligned points, that is, each input is mapped to only one output.

Hence only item 1 is not a function, as the two inputs x = -3 and x = 2 are mapped to multiple outputs.

More can be learned about functions are https://brainly.com/question/24808124

#SPJ1

The whole numbers are defined as the positive integers including zero. The whole number does not contain any decimal or fractional part.

An integer is a number with no decimal or fractional part, from the set of negative and positive numbers, including zero.

A rational number is a number that is of the form p/q where p and q are integers and q is not equal to 0.

An irrational number is a type of real number which cannot be represented as a simple fraction.

Real numbers include rational numbers like positive and negative integers, fractions, and irrational numbers. In other words, any number that we can think of, except complex numbers, is a real number.

Therefore,

The formula for determining the volume of a cylinder is expressed as

V = pi * r^2h

Where

V represents volume of cylinder

pi is a constant whose value is 3.142

r represents radius of cylinder

h represents height of cylinder

From the information given,

h = 10

r = 3

V = 3.142 * 3^2 * 10

V = 282.78 in^3

The closest measurement is option A

Segment addition

The sum of the lenghts of the segments OB and Bk will give the total lenght OK

Step-by-step explanation:

we have a right-angled triangle.

so, we can use Pythagoras

c² = a² + b²

c is the Hypotenuse, a and b are the legs.

in our case

c² = 6² + 6² = 36 + 36 = 72

c = Hypotenuse = sqrt(72) = 8.485281374... cm

Answer:

Step-by-step explanation:

An isosceles right triangle has 6 cm legs . Find the length of the hypotenuse

hypotenuse² = 6² + 6²

hypotenuse² = 36 + 36

hypotenuse² = 72

hypotenuse = √72 (or 8.49)

Given the set of data

sort

Commute data (x)

24,25,27,30, 35,35,46,50,52

Commute distance (y)

20,20,29,20,34,39,29,34,50

The line of best fit is given by

with

R= 0.75

with function

Correct answer

option D

Answer: r ≈ 0.75

              t ≈ 0.8d + 11.5

Step-by-step explanation:

You have to use a graphing calculator to solve this problem.

This is the correct answer (I just took the test).

The Quadratic format is

The answer to the question is that the factors must multiply to form c

Answer

• a) 8

• b) 4/8

• c) 4/8

Explanation

Given

• Blue cards: 4, {B1, B2, B3, B4}

• Red cards: 4 {R1, R2, R3, R4}

• A = card drawn is blue

• B = card drawn is odd-numbered {B1, R1, B3, R3}

Procedure

• a) elements in the sample space

There are: S = {B1, B2, B3, B4, R1, R2, R3, R4}

Thus, the number of elements in the sample space is n(S) = 8.

• b) P(A)

Can be calculated as follows:

• c) P(B)

Can be calculated as follows:

In the  Polynomial  function  f(x)= [tex]2x^{3} -11x^{2} -12x+36 =0 then[/tex]

So all the zeros of f(x) algebraically

[tex]\mathrm{f}(\mathrm{x}) \ are\ \mathrm{x}=-2, \mathrm{x}=\frac{3}{2}, \mathrm{x}=6$[/tex].

Step: 1

Given[tex]$f(x)=2 x^3-11 x^2-12 x+36$and $f(6)=0 \Rightarrow(x-6)$ is factor of $f(x)$now $f(x)=2 x^3-11 x^2-12 x+36$$$[/tex]

[tex]\begin{aligned}&\Rightarrow \mathrm{f}(\mathrm{x})=\left(2 \mathrm{x}^2-12 \mathrm{x}^2\right)+\left(\mathrm{x}^2-\right. \\&\Rightarrow \mathrm{f}(\mathrm{x})=2 \mathrm{x}^2(\mathrm{x}-6)+(\mathrm{x}-6)^2 \\&\Rightarrow \mathrm{f}(\mathrm{x})=(\mathrm{x}-6)\left(2 \mathrm{x}^2+\mathrm{x}-6\right)\end{aligned}$$[/tex]

Step: 2

Now consider [tex]$2 x^2+x-6=2 x^2+4 x-3 x-6$$$\begin{aligned}&\Rightarrow 2 x(x+2)-3(x+2) \\&\Rightarrow 2 x^2+x-6=(2 x-3)(x+2)\end{aligned}$$[/tex]

[tex]$5 \circ f(x)=(x-6)\left(2 x^2+x-6\right)$$$\Rightarrow \mathrm{f}(\mathrm{x})=(x-6)(2 \mathrm{x}-3)(\mathrm{x}+2)$$[/tex]

Step: 3

so for finding zeros of

[tex]$f(x) \rightarrow f(x)=0$$$\Rightarrow(x-6)(2 x-3)(x+2)=0$$$$\Rightarrow(x-6)=0 ;(2 x-3)=0 ;(x+2)=0$$[/tex]

[tex]$$\Rightarrow x=6, x=\frac{3}{2} ; x=-2$$[/tex]

Explanation: Please refer to solution in this step.

Answer:

So required zeros of

[tex]\mathrm{f}(\mathrm{x}) \ are\ \mathrm{x}=-2, \mathrm{x}=\frac{3}{2}, \mathrm{x}=6$[/tex]

A polynomial consists of two words, poly and nominal. "Poly" means many and "nomial" means  term, and so when  combined, polynomials can be said to be "algebraic expressions with many terms." Let's go ahead and start by defining polynomial functions and their types.

The polynomial function in standard form is:

f(x) =  [tex]a_{n}x^{n} +a_{n-1} x^{n-1} +.....a_{2} x^{2} +a_{1} x+a0[/tex]

This algebraic expression is called a polynomial function of the variable x. The name of a polynomial is determined by the number of terms it contains.

The three most common polynomials we usually encounter are

To learn more about polynomial function, refer;

https://brainly.com/question/12976257

#SPJ13

You have the following equation:

5x - 3y = -45

In order to solve the previous equation for y, you proceed as follow:

5x - 3y = -45 subtract 5x both sides

- 3y = -45 - 5x multiply by -1 both sides

(-1)(-3y) = (-1)(-45 - 5x)

3y = 45 + 5x divide by 3 both sides

y = 45/3 + 5/3 x order the right side

y = 5/3 x + 15

Hence, the solution for y is y = 5/3 x + 15

the function is d= f(t)

when t1= 1 , d1= 5

when t2= 4, d2= 20

Thus if d is a function of t

and the rate of change is constant

then d = 5t is the function

The equation of a line parallel to y=-x and passes through (1,3) is x+y=4

The coordinates of a line pass through the equation of a line.

Two parallel lines make the same angle with respect to the x-axis ie. make the same slope.

We have been given that the line is parallel to y=-x or x+y=0

Thus, they will be having the same slope which is -1.

Since, in the equation Ax+By+C=0, the slope is equal to -A/B

So putting the values in the equation y=mx+c where m is the slope and c is the constant

y=-x+c

Now we know that the equation passes through (1,3)

So, putting values 1=-3+c which gives c=4

Therefore, the equation of the line is y=-x+4 or x+y=4.

To know more about slope, visit:

https://brainly.com/question/2491620

#SPJ13

Answer:

3d - 15.70 = 2.30

Step-by-step explanation:

We don't know the cost of one DVD, so let's use d to represent this unknown variable. Eddie sold 3 DVDs, so 3 multiplied by d equals his total earnings.

Eddie then used $15.70 of his earnings to buy a pair of headphones. We can represent this by subtracting 15.70 from the total earnings (3d).

After buying/subtracting the price of the headphones from his total earnings, Eddie had $2.30 left over, which can be represented by making 3d - 15.70 equal 2.30.

So, the final equation turns out to be:  3d - 25.70 = 2.30

:)