what does a flowchart proof

Answer:

The given equation 3x^2-4x+21 has no factors.

Step-by-step explanation:

[tex]3x^2-4x+21[/tex] We need to factorize this equation.

For factorization we split the middle term such that their sum is equal to middle term and product is equal to product of first and last term of the given expression.

in Our case : 63x^2

We need to find two factors of 63x^2 whose sum is equal to -4x

Factors of 63= 1,3,7,9,21,63

1* 63

3*21

7*9

None of the above factors sum is equal to -4.

So, the given equation 3x^2-4x+21 has no factors.

Answer:

No factors.

Step-by-step explanation:

The polynomial is not factorable with rational numbers. If you are on some advanced math, you would be able to be able to factor this.

Answer:

Y = 963

Step-by-step explanation:

The digits of Y add to 18.  The first digit is 3 times the third digit.  The second  digit is 2 times the third digit.  Y is a three digit number.​

Let Y a three digit number be: abc

First digit = a , Second digit = b, Third digit = c

Also given,

The digits of Y add to 18. => a+b+c = 18     eq(i)

The first digit is 3 times the third digit. => a = 3c     eq(ii)

The second digit is 2 times the third digit. => b = 2c     eq(iii)

Putting value of a and b in eq(i)

3c + 2c + c = 18

6c = 18

c= 18/6

c = 3

Putting value of c in eq(ii) and eq(iii)

a= 3c => a=3(3) => a= 9

b= 2c => b=2(3) => b = 6

Thus, Y = abc

Y = 963

Answer:

(- 1, 3)

Step-by-step explanation:

To find the y- coordinate, substitute x = - 1 into the equation

y - 3 = 2(x + 1) ( add 3 to both sides )

y = 2(x + 1) + 3 ← substitute x = - 1

y = 2(- 1 + 1) + 3 = (2 × 0) + 3 = 0 + 3 = 3

Answer:

-0.01851851851

Step-by-step explanation:

Answer:

[tex]-\dfrac{3}{2}[/tex]

Step-by-step explanation:

[tex]\dfrac{\frac{2}{3} }{\frac{4}{-9} } [/tex]

[tex]= \dfrac{2}{3} \div \dfrac{4}{-9}[/tex]

[tex]= \dfrac{2}{3} \times \dfrac{-9}{4}[/tex]

[tex]= \dfrac{-18}{12}[/tex]

[tex]= -\dfrac{3}{2}[/tex]

Answer: 13

Step-by-step explanation: If there are 9 floors from where Tanisha's office is to the ground, but then also 4 more floors to her car, that would simply be 9+4. There are 13 floors between Tanisha's office and her car.

Answer:

Step-by-step explanation:

Since this is not an equation, we're not looking to "solve."  Rather, we're to subtract the 2nd polynomial from the 1st one.

 -24x² + 18x + 6

-(               6x + 3)

------------------------------

-24x² + 12x   +3 (answer ... this is called a "difference" and is the

                              result of subtraction)

The simplified expression is 3( -8x² + 4x + 1).

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

(-24x² +18x+6) - (6x+3)

Now, simplifying the polynomial

= -24x² +18x+6 - 6x - 3

= -24x² + 12x + 3

= 3( -8x² + 4x + 1)

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Answer:

X= -1

You're welcome! Love ya!! <3

Answer:

The correct answer is x = -1

Step-by-step explanation:

It is given an expression with variable x

3(x + 1) = -2(x - 1) - 4

To solve the given expression

3(x + 1) = -2(x - 1) - 4

3x + 3 = -2x + 2 - 4   ( open the bracket)

3x + 2x = 2 - 4 -3

5x = -5

x = -5/5 = -1

Therefore the value of x = -1

The correct answer is x = -1

Answer:

a = [tex]\frac{G}{4c-3b}[/tex]

Step-by-step explanation:

Given

G = 4ca - 3ba ← factor out a from each term on the right side

G = a(4c - 3b) ← divide both sides by (4c - 3b)

a = [tex]\frac{G}{4c-3b}[/tex]

Answer:

8x^2 - 25x +7

Step-by-step explanation:

Substitute the polynomials in

A^2 - (B+C)

(3x-4)^2 - (x+7+x^2+2), simplify the equation

Using foil method, (9x^2-24x+16) - (x+7+x^2+2)

(9x^2-24x+16)-(x^2+x+9), distribute the minus/negative sign to the second parenthesis

(9x^2-24x+16) - x^2-x-9, combine like terms

8x^2 - 25x +7

Answer:

[tex]\large\boxed{x=-3\pm\sqrt{21}}[/tex]

Step-by-step explanation:

[tex]x^2+6x=12\\\\x^2+2(x)(3)=12\qquad\text{add}\ 3^2\ \text{to both sides}\\\\x^2+2(x)(3)+3^2=12+3^2\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+3)^2=12+9\\\\(x+3)^2=21\iff x+3\pm\sqrt{21}\qquad\text{subtract 3 from both sides}\\\\x=-3\pm\sqrt{21}[/tex]

Answer:

x=1

Step-by-step explanation:

We can find the slope given two points by

m = (y2-y1)/(x2-x1)

2 = (6--2)/(x--3)

2 = (6+2)/(x+3)

2 = 8/(x+3)

Multiply each side by x+3

2(x+3) = 8/(x+3) * (x+3)

2(x+3) = 8

Divide each side by 2

2/2 (x+3) = 8/2

x+3 = 4

Subtract 3 from each side

x+3-3=4-3

x =1

Answer:

C- 42

Step-by-step explanation:

there are 8 ounces in a cup so 12 x 8 = 96 oz

96/2.25 = 42.6666666667

Rounded back to 42

By using all the chocolate cream, at most the number of eclairs that can be made is:

                 C) 42

It is given that:

You have 12 cups of chocolate cream to fill eclairs.

Each eclair requires 2.25 ounces of filling.

We know that:

The universal conversion that is used is:

  1 cups=8 ounces

and hence,

12 cups= 12×8=96 ounces.

Hence, the number of ounces of chocolate cream to fill eclairs= 96 ounces

Also,

amount of filling required by 1 eclair= 2.25 ounces.

Hence, Number of eclairs that can be made is:

[tex]Number\ of\ eclairs=\dfrac{96}{2.25}\\\\i.e.\\\\Number\ of\ eclairs=42.67[/tex]

This means that:

Atmost the number of eclairs than can be made= 42

The probability that a hat randomly chosen from Gina's inventory will be a helmet is 2 out of 12, which simplifies to 1 out of 6.

The subject of this question is probability, which is a branch of mathematics. Gina has 12 different hats, out of which 2 are helmets. The probability of an event happening is calculated as the number of ways the event can happen divided by the total number of outcomes.

So in this case, there are 2 helmets out of a total of 12 hats. So, the probability that a hat randomly chosen from Gina's inventory will be a helmet is 2 out of 12. You can also simplify this probability by dividing both the numerator and the denominator by the greatest common divisor, which is 2 in this case. Therefore, the simplified probability is 1 out of 6.

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The probability of choosing a randomly selected hat from Gina's inventory to be a helmet is 1/6.

To find the probability of selecting a helmet from Gina's inventory, we need to divide the number of helmets by the total number of hats in her inventory.

Gina has 12 hats, including 2 helmets, so the probability is

= 2 helmets / 12 hats

= 1/6.

Therefore, the probability of choosing a randomly selected hat from Gina's inventory to be a helmet is 1/6.

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Answer:

Part 1) The six trigonometric functions in the procedure

Part 2) The six trigonometric functions in the procedure

Part 3) The six trigonometric functions in the procedure

Part 4) The value of x is [tex]x=7\sqrt{2}\ units[/tex] and the value of y is [tex]y=7\ units[/tex]

Part 5) The value of x is [tex]x=5\ units[/tex] and the value of y is [tex]y=5\sqrt{3}\ units[/tex]

Part 6) The value of x is [tex]x=2\sqrt{3}\ units[/tex] and the value of y is [tex]y=\sqrt{3}\ units[/tex]

Part 7)  [tex]cos(27\°)=0.8910[/tex]

Part 8)  [tex]tan(5\°)=0.0875[/tex]

Part 9)  [tex]sin(48\°)=0.7431[/tex]

Part 10) [tex]cot(81\°)=0.1584[/tex]

Part 11) [tex]csc(23\°)=2.5593[/tex]

Part 12) [tex]sec(66\°)=2.4586[/tex]

Part 13) [tex]cot(13\°)=4.3315[/tex]

Part 14) [tex]sin(32\°)=0.5299[/tex]

Step-by-step explanation:

Note The complete answers in the attached file

Part 1) In the right triangle of the figure find the hypotenuse

Applying Pythagoras theorem

[tex]c^{2} =8^{2}+15^{2}\\c^{2}=289\\c=17\ units[/tex]

1) Find the [tex]sin(\theta)[/tex]

[tex]sin(\theta)=\frac{8}{17}[/tex] ----> opposite side angle [tex]\theta[/tex] divided by the hypotenuse

2) Find the [tex]cos(\theta)[/tex]

[tex]cos(\theta)=\frac{15}{17}[/tex] ----> adjacent side angle [tex]\theta[/tex] divided by the hypotenuse

3) Find the [tex]tan(\theta)[/tex]

[tex]tan(\theta)=\frac{8}{15}[/tex] ----> opposite side angle [tex]\theta[/tex] divided by the adjacent side angle [tex]\theta[/tex]

4) Find the [tex]cot(\theta)[/tex]

[tex]cot(\theta)=\frac{15}{8}[/tex] ----> adjacent side angle [tex]\theta[/tex] divided by the opposite side angle [tex]\theta[/tex]

5) Find the [tex]sec(\theta)[/tex]

[tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex]

[tex]sec(\theta)=\frac{17}{15}[/tex]  ----> hypotenuse divided by the adjacent side angle [tex]\theta[/tex]

6) Find the [tex]csc(\theta)[/tex]

[tex]csc(\theta)=\frac{1}{sin(\theta)}[/tex]

[tex]csc(\theta)=\frac{17}{8}[/tex]  ----> hypotenuse divided by the opposite side angle [tex]\theta[/tex]

Part 2) In the right triangle of the figure find the adjacent side angle [tex]\theta[/tex]

Applying Pythagoras theorem

[tex]5^{2} =2^{2}+a^{2}\\ a^{2}=5^{2}-2^{2}\\a^{2}=21\\a=\sqrt{21}\ units[/tex]  

1) Find the [tex]sin(\theta)[/tex]

[tex]sin(\theta)=\frac{2}{5}[/tex] ----> opposite side angle [tex]\theta[/tex] divided by the hypotenuse

2) Find the [tex]cos(\theta)[/tex]

[tex]cos(\theta)=\frac{\sqrt{21}}{5}[/tex] ----> adjacent side angle [tex]\theta[/tex] divided by the hypotenuse

3) Find the [tex]tan(\theta)[/tex]

[tex]tan(\theta)=\frac{2}{\sqrt{21}}[/tex] ----> opposite side angle [tex]\theta[/tex] divided by the adjacent side angle [tex]\theta[/tex]

4) Find the [tex]cot(\theta)[/tex]

[tex]cot(\theta)=\frac{\sqrt{21}}{2}[/tex] ----> adjacent side angle [tex]\theta[/tex] divided by the opposite side angle [tex]\theta[/tex]

5) Find the [tex]sec(\theta)[/tex]

[tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex]

[tex]sec(\theta)=\frac{5}{\sqrt{21}}[/tex]  ----> hypotenuse divided by the adjacent side angle [tex]\theta[/tex]

6) Find the [tex]csc(\theta)[/tex]

[tex]csc(\theta)=\frac{1}{sin(\theta)}[/tex]

[tex]csc(\theta)=\frac{5}{2}[/tex]  ----> hypotenuse divided by the opposite side angle [tex]\theta[/tex]

Part 3) In the right triangle of the figure find the opposite side angle [tex]\theta[/tex]

Applying Pythagoras theorem

[tex]3^{2} =1^{2}+b^{2}\\ b^{2}=3^{2}-1^{2}\\b^{2}=8\\b=\sqrt{8}\ units[/tex]  

1) Find the [tex]sin(\theta)[/tex]

[tex]sin(\theta)=\frac{\sqrt{8}}{3}[/tex] ----> opposite side angle [tex]\theta[/tex] divided by the hypotenuse

2) Find the [tex]cos(\theta)[/tex]

[tex]cos(\theta)=\frac{\sqrt{1}}{3}[/tex] ----> adjacent side angle [tex]\theta[/tex] divided by the hypotenuse

3) Find the [tex]tan(\theta)[/tex]

[tex]tan(\theta)=\frac{\sqrt{8}}{1}[/tex] ----> opposite side angle [tex]\theta[/tex] divided by the adjacent side angle [tex]\theta[/tex]

4) Find the [tex]cot(\theta)[/tex]

[tex]cot(\theta)=\frac{1}{\sqrt{8}}[/tex] ----> adjacent side angle [tex]\theta[/tex] divided by the opposite side angle [tex]\theta[/tex]

5) Find the [tex]sec(\theta)[/tex]

[tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex]

[tex]sec(\theta)=\frac{3}{1}[/tex]  ----> hypotenuse divided by the adjacent side angle [tex]\theta[/tex]

6) Find the [tex]csc(\theta)[/tex]

[tex]csc(\theta)=\frac{1}{sin(\theta)}[/tex]

[tex]csc(\theta)=\frac{3}{\sqrt{8}}[/tex]  ----> hypotenuse divided by the opposite side angle [tex]\theta[/tex]

Part 4) In the right triangle of the figure

a) Find the value of x

 we know that

[tex]sin(45\°)=\frac{7}{x}[/tex]

[tex]x=\frac{7}{sin(45\°)}[/tex]

Remember that

[tex]sin(45\°)=\frac{\sqrt{2}}{2}[/tex]

substitute

[tex]x=\frac{7}{\frac{\sqrt{2}}{2}}[/tex]

[tex]x=\frac{14}{\sqrt{2}}[/tex]

[tex]x=7\sqrt{2}\ units[/tex]

b) Find the value of y

The value of [tex]y=7\ units[/tex] ----> by triangle 45°-90°-45° measures

Note The complete answers in the attached file

Answer:

(5/2, +-(square root 17)/ 2)

Step-by-step explanation:

1. find a,b, and c of the quadratic

2. use the quadratic formula to solve

The two values of roots of the equation is 4.56 , 0.44 .

An equation is a statement where two algebraic expressions are equated by an equal sign.

The equation given is

x² - 5x +2 = 0

the roots of the equation is given by

[tex]\rm \dfrac{ -b \pm \sqrt { b^2 - 4ac}}{2a}[/tex]

[tex]\rm \dfrac{ 5 \pm \sqrt { 25 - 4 * 1 * 2}}{2 *1}[/tex]

x = [tex]\rm \dfrac{ 5 \pm \sqrt { 17}}{2}[/tex]

Therefore the two values of roots of the equation is 4.56 , 0.44 .

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square root both sides, divide by v both sides, divide by 2 both sides, divide pCd both sides

Answer:

B) 23

Step-by-step explanation:

Table:            Algebra | No algebra | Total

Physics        |      4           Step 1: 8      12

No physics  |Step 2: 15

Total            |      19                              30

We look for the number of people who are in algebra and no physics or physics and no algebra.

1. 12 - 4 = 8

2. 19 - 4 = 15

3. We find the total of those numbers: 15 + 8 = 23

Answer: 27

Step-by-step explanation:

Answer:

1.  52

2. 2.9

Step-by-step explanation:

To find the mean, we take all the numbers, add them up then divide by the number of numbers.

1.  mean height

mean = (50+54+52+56+48)/5

            =260/5

            =52

52 inches

2.  mean score

There are 5+3+12+2+6+6+4 students = 38 students

Multiply the number of students times the score and add together

total points =  (0*5+1*3+2*12+3*2+4*6+5*6+6*4)

        = 111

The mean is the total points  divided by the number of students

mean = 111/38

        =2.92

Answer:

[tex]\bar x = 52inch\\\bar x_w = 2.92[/tex]

Step-by-step explanation:

According to the data recorded in the table, the average of the students' heights is calculated with the expression for the arithmetic mean:

[tex]\bar x =\frac{1}{n} \sum x_i[/tex]

[tex]\bar x = \frac{1}{5}(48 + 50 + 52 + 54 + 56) = \frac{260}{5} = 52[/tex]inch.

In the same way, the weighted average must be used to find the average football score:

[tex]\bar x_w = \frac{\sum x_i * w_i}{\sum w_i}[/tex], where wi are the frequencies of each response.

[tex]\bar x_w = (0 * 5 + 1 * 3 + 2 * 12 + 3 * 2 + 4 * 6 + 5 * 6 + 6 * 4) / (5 + 3 + 12 + 2 + 6 + 6 + 4) = \frac{111}{38} = 2.92[/tex]

Answer: 7

Step-by-step explanation:

volume of a cylinder = πr²h

441π = π *r²* 9

divide both sides by 9π

49 = r²

r =√49 = 7

Answer:

49

Step-by-step explanation:

Answer:

Option B. [tex]-2x+30[/tex]

Step-by-step explanation:

we know that

The blue area is equal to the area of complete rectangle minus the area of the  white rectangle

so

[tex]A=(5+3x)(6)-(5)(4x)\\\\ A=(30+18x)-(20x)\\ \\A=-2x+30[/tex]

I think it's B hope you got it right

The correct answer is B. The scores on Friday have a greater median and a greater interquartile range than the scores on Saturday.

The box plots represent the bowling scores of a team on Friday and Saturday. Let’s analyze the information from the plots:

Friday Box Plot:

The median (Q2) is higher than the median for Saturday.

The interquartile range (IQR) is larger than the IQR for Saturday.

Saturday Box Plot:

The median (Q2) is lower than the median for Friday.

The interquartile range (IQR) is smaller than the IQR for Friday.

Based on this analysis, we can draw the following conclusion:

B. The scores on Friday have a greater median and a greater interquartile range than the scores on Saturday.

Therefore, the correct answer is B.

Answer:

x = ± [tex]\sqrt{3}[/tex]

Step-by-step explanation:

Given

3x² - 9 = 0 ( add 9 to both sides )

3x² = 9 ( divide both sides by 3 )

x² = 3 ( take the square root of both sides )

x = ± [tex]\sqrt{3}[/tex]

Answer:

834451800

Step-by-step explanation:

C(n,r)=?

C(n,r)=C(35,12)

=35!(12!(35−12)!)

=35!12!×23!

=8.344518E+8

= 834451800

Answer:

The approximate value of the area is [tex]153.86\ m^{2}[/tex]

Step-by-step explanation:

we know that

The area of the circle (landing pad) is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=7\ m[/tex]

substitute

[tex]A=\pi (7)^{2}[/tex]

[tex]A=49\pi\ m^{2}[/tex] ----> exact value of the area

Find the approximate value

assume [tex]\pi=3.14[/tex]

[tex]A=49(3.14)=153.86\ m^{2}[/tex] ------> approximate value of the area

Answer:

Area of Circular landing pad = 307.72 m^2

Step-by-step explanation:

Area of Circular landing pad = 2πr^2

where r = radius of circular landing pad = 7m

π = 22/7 = 3.14

by placing all these value in the formula

Area of Circular landing pad = 2*3.14*(7^2)

Area of Circular landing pad = 6.28*49

Area of Circular landing pad = 307.72 m^2

Answer 88.5 I think I don’t know if it’s right

Step-by-step explanation:

Multiply it by 3

If you were three years old on Saturn, which has a year length equivalent to 29.5 Earth years, you'd be 88.5 years old on Earth.

The subject of your question is focused on the comparison of time passage on different planets--in this case, how years on Saturn compare to years on Earth. In terms of the Solar system, a year on any planet is determined by how long it takes to orbit the Sun. Given that one Saturn year equals 29.5 Earth years, if you were three years old on Saturn, you'd be 88.5 years old on Earth (Because 29.5 * 3 = 88.5).

This is calculated simply by multiplying the number of Saturn years by the equivalent in Earth years. This concept can be applied to other planets as well, as each has its own specific length of year based on its orbit around the Sun.

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Answer:

3.576 cm

Step-by-step explanation:

radius of ball, r=?

Given:

Density, p = 0.600g/mL

mass, m= 115g

finding volume, v of ball by using formula p=m/v

v= m/p

= 115/0.600

=191.666 mL^3

=191.666 cm^3

Now using formula v= (4/3)πr^3 to find radius, r of the ball

r^3= 3v/4π

   = 3(191.666)/4π

   =45.75 cm

r   =3.5767 cm !

ANSWER

The discriminant is -3

EXPLANATION

The given quadratic equation is:

[tex] {x}^{2} + 3x - 6 = 0[/tex]

Comparing this equation to:

[tex]a {x}^{2} + bx + c = 0[/tex]

we have

a=1, b=3, and c=-6

The discriminant is calculated using the formula,

[tex]D = {b}^{2} - 4ac[/tex]

We substitute the values to get:

[tex]D = {3}^{2} - 4(1)(3)[/tex]

[tex]D = 9 - 12[/tex]

[tex]D = - 3[/tex]

Answer:

Discriminant = 33

Step-by-step explanation:

Solution of a quadratic equation ax² + bx + c = 0

Discriminant  = (b² - 4ac)

It is given that, x² + 3x - 6 = 0

To find the value of discriminant

x² + 3x - 6 = 0

Here a = 1, b = 3 and c = -6

Discriminant  = (b² - 4ac)

 =  (3² - 4 * 1 * (-6))

 = (9 +24) = 33

Therefore discriminant  of given equation is 33

Answer:

V = x³ + 10x² cm³

Step-by-step explanation:

The volume (V) of the triangular prism is calculated using the formula

V = area of triangular face × length

Area of triangular face = [tex]\frac{1}{2}[/tex] bh ( b is base and h is height )

here b = 2x and h = x, thus

A = [tex]\frac{1}{2}[/tex] × 2x × x = [tex]\frac{1}{2}[/tex] × 2x² = x²

length = x + 10, hence

V = x²(x + 10) = x³ + 10x²

the answer would be 24.0.

Answer:

[tex]132\ in^{2}[/tex] is closest to the total surface area of the box

Step-by-step explanation:

we know that

The surface area of the box is equal to

[tex]SA=2B+PH[/tex]

where

B is the area of the base

P is the perimeter of the base

H is the height of the box

we have

[tex]L=7\frac{3}{4}\ in=\frac{7*4+3}{4}=\frac{31}{4}\ in[/tex]

[tex]W=3\frac{1}{4}\ in=\frac{3*4+1}{4}=\frac{13}{4}\ in[/tex]

[tex]H=3\frac{7}{8}\ in=\frac{3*8+7}{8}=\frac{31}{8}\ in[/tex]

Find the area of the base B

[tex]B=LW[/tex]

[tex]B=(\frac{31}{4})(\frac{13}{4})=\frac{403}{16}\ in^{2}[/tex]

Find the perimeter of the base P

[tex]P=2(L+W)[/tex]

[tex]P=2(\frac{31}{4}+\frac{13}{4}))[/tex]

[tex]P=2(\frac{44}{4})=22\ in[/tex]

Find the surface area

[tex]SA=2(\frac{403}{16})+22(\frac{31}{8})[/tex]

[tex]SA=(\frac{403}{8})+(\frac{682}{8})[/tex]

[tex]SA=\frac{1,085}{8}=135.625\ in^{2}[/tex]