In parallelogram ABCD… Justify your answer with the applicable property.

Answer:

100

Explanation:

Given the expression

First, we evaluate the bracket and exponents.

This then gives us:

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

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.

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.

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Answer: Area is 153.94

Step-by-step explanation:

Area = π r 2

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.

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

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.

Segment addition

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

Let the age of the youngest child (Ben) be x years.

Since the ages are consecutive integers, the ages of the other 2 are (x + 1) and (x + 2).

It was given that the age of the youngest child is four more than eight times the age of the oldest child. This means that:

We can rearrange the equation above and solve for x as a quadratic equation:

Using the factorization method, we have:

Since the age cannot be negative, the age of the youngest child is 10.

Therefore, the ages are:

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%

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).

KL / JK = 2:7

JL = 162

JK = ?

JL = KL + JK = 162 KL = 2 JK = 7

KL / JK = 2.7

KL = 162 - JK

Substitution

(162 - JK) / JK = 2.7

Solve for JK

162 - JK = 2.7 JK

162 = 2.7 JK + JK

162 = 3.7 JK

JK = 162 / 3.7

JK = 43.8

Since this is a right triangle, we can use trig functions

cos theta = adj side/ hypotenuse

cos Q = QP / QR

cos 38 = QP / 25

25 cos 38 = QP

19.70026884= QP

Rounding to the nearest tenth

19.7 = QP

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.

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

Step 01:

Data

∆ABC~∆DEF

triangle 1:

AC = 10

area = 65 in²

triangle 2:

DF = 20

area = ?

Step 02:

We must apply the rules of similar triangles to find the solution. .

triangle 2 area * 10 = 65 in² * 20

triangle 2 area = (65 in² * 20 ) / 10

= 130 in²

The answer is:

The area of the big triangle is 130 in² .

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

EXPLANATION

First, let us make a sketch of the clock:

We have that for a minute hand:

For hour hand:

The hour and minute hand have their origin at 12.

At 11:20, the minute hand had moved 20 mins. This means that:

The hour hand had moved at 11 (and 20 mins more), which means:

Hence, in 680 mins:

Therefore, the angle formed between 11 and 12 at 11:20 is:

Hence, the angle formed at 11:20 is:

Now, let us convert to radians:

That is the obtuse angle formed in radians.

Answer: B. The statement is false because the derivative gives the rate of change of a function. It expresses slope, not value.

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,

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:

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.

31 years

We would apply the compound interest forula:

A = future amount = $1000

P = principal = $250

r = rate = 4.5% = 0.045

n = compounded quarterly = 4 times

n = 4

t = time = ?

Inserting the values into the formula:

It takes 31 years to reach $1000.

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

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The Quadratic format is

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

144

working the division:

The process:

7 ÷ 5 = 1 R 2

add the 2 to the next number: this gives 22

22 ÷ 5 = 4 R 2

add 2 to the next number: this gives 20

20 ÷ 5 = 4 R 0

The result of 720 ÷ 5 = 144

Solution:

Given:

From the table of values derived above;

The mean for males is;

The standard deviation is;

Hence,

Therefore, the population standard deviation for males is 21.24

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

If in three plays southside football team drove [tex]10\frac{1}{2}[/tex] yards, then the number of yard they drove average in each day is [tex]3\frac{1}{2}[/tex] yards

Number matches played by southside football team = 3

Total distance they drove = [tex]10\frac{1}{2}[/tex] yards

Convert the mixed fraction to the simple fraction

[tex]10\frac{1}{2}[/tex] yards = 21/2

Number of yards they drove average in each day = Total distance they drove ÷ Number matches played by southside football team

Substitute the values in the equation

= 21/2 ÷ 3

= 21/2 × (1/3)

= 7/2 yards

Convert the simple fraction to the mixed fraction

7/2 yards = [tex]3\frac{1}{2}[/tex] yards

Hence, if in three plays southside football team drove [tex]10\frac{1}{2}[/tex] yards, then the number of yard they drove average in each day is [tex]3\frac{1}{2}[/tex] yards

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