20. A doctor measured a patient's resting pulse rate at 80 beats per minute. Draw a
graph to show the relationship between time and the number of times the patient's
heart beats.
Use it to estimate how many times the patient's heart will beat in 18 minutes. Write an
equation in Y = mx + b form.,

Answer:

[tex]\large\boxed{x^6-y^6=(x-y)(x+y)(x^2+y^2-xy)(x^2+y^2+xy)}[/tex]

Step-by-step explanation:

[tex]x^6-y^6=x^{(2)(3)}-y^{(2)(3)}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=(x^2)^3-(y^2)^3\qquad\text{use}\ a^3-b^3=(a-b)(a^2+ab+b^2)\\\\=(x^2-y^2)\bigg((x^2)^2+x^2y^2+(y^2)^2\bigg)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(x-y)(x+y)\bigg((x^2)^2+2x^2y^2+(y^2)^2-x^2y^2\bigg)\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\=(x-y)(x+y)\bigg((x^2+y^2)^2-x^2y^2\bigg)\\\\=(x-y)(x+y)\bigg((x^2+y^2)^2-(xy)^2\bigg)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(x-y)(x+y)(x^2+y^2-xy)(x^2+y^2+xy)[/tex]

Answer:

(x²)³ - (y²)³ = (x² - y²)(x^4 + x²y² + y^4)

Step-by-step explanation:

x^6 - y^6 is the difference of two cubes:  (x²)³ - (y²)³.  Differences of cubes can be factored as follows:  a³ - b³ = (a - b)(a² + ab + b²).

Thus, (x²)³ - (y²)³ = (x² - y²)(x^4 + x²y² + y^4)

Answer:

see explanation

Step-by-step explanation:

Given

Ax - bx - y = z ( add y to both sides )

Ax - bx = z + y ← factor out x from both terms on the left side

x(A - b) = z + y ← divide both sides by (A - b)

x = [tex]\frac{z+y}{A-b}[/tex]

Answer:

4

Step-by-step explanation:

The given expression is

[tex]4-\frac{4}{n}+\frac{5}{n}+\frac{15}{3n^2}[/tex]

We want to find the value of this expression as n approaches infinity.

Recall that as n approaches infinity, [tex]\frac{c}{n}[/tex], where c is a constant approaches zero.

The value of the given expression then becomes;

[tex]4-0+0+0=4[/tex]

Answer:

162

Step-by-step explanation:

Answer:

2.16 * (10^-5).

Step-by-step explanation:

5 = -log H+

5 = log (1 / H+)

1/ H+ = 10^5

H+ = 10^-5

In a similar fashion  the other brand has H+ of 10^-4.5.

So the difference in hydrogen ion concentration =  10^(-4.5) - 10^(-5)

= 2.16 * (10^-5).

2.16 × 10⁻⁵ is the  difference in the concentration of hydrogen ions between the two brands of vinegar.

pH is a numerical indicator of how acidic or basic aqueous and other liquid solutions are. The phrase, which is frequently used in biology, agronomy, and chemistry, converts the hydrogen ion concentration, which typically ranges between 1 and 1014 gram-equivalents per litre, into numbers ranging from 0 to 14.

The hydrogen ion concentration in pure water, which has a pH of 7, is 107 gram-equivalents per litre, making it neutral (neither acidic or alkaline). A solution having a pH below 7 is referred to as acidic, and one with a pH over 7 is referred to as basic, or alkaline.

5 = -log H+

5 = log (1 / H+)

1/ H+ = 10^5

H+ = 10^-5

difference=  10^(-4.5) - 10^(-5)

               = 2.16 × 10⁻⁵

Therefore, 2.16 × 10⁻⁵ is the  difference in the concentration of hydrogen ions between the two brands of vinegar.

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Answer:

[tex]\large\boxed{x=\dfrac{1}{2}=0.5}[/tex]

Step-by-step explanation:

[tex]\dfrac{5}{6x}=\dfrac{10}{3}\qquad\text{cross multiply}\\\\(6x)(10)=(5)(6)\\\\60x=30\qquad\text{divide both sides by 60}\\\\x=\dfrac{30}{60}\\\\x=\dfrac{1}{2}[/tex]

Answer:22

Step-by-step explanation:

22-7=15.

15/3=5

So the answer is 5

The number will be 22.

The fraction is numerical representation of the numbers in the form of numerator and denominator.

We have,

Let, a number =  x

Now,

According to the question,

[tex]\frac{x-7}{3} = 5[/tex]

So,

Now, multiply by 3 on both sides,

i.e.

[tex]\frac{(x-7)}{3} *3 = 5*3[/tex]

We get,

x - 7 = 15

⇒

x = 22

So, value of x is 22.

Hence, we can say that the number will be 22.

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Answer: Option A

Step-by-step explanation:

A relation between two variables x and y is considered a function if and only if, for each input value x there is only one output value y.

If for an input value [tex]x_0[/tex] there are two output values [tex]y_1[/tex] and [tex]y_2[/tex] then the relation is not a function.

Therefore, to answer this question, identify the table in which each value of x has only one value of y.

You may notice that the option that meets this requirement is option A

Note that in option B, there are two output values 17 and 16 for x = -4.

So this relationship is not a function.

In option C there are 2 output values for x = -5

In option D there are 2 output values for x = -11

Answer:

the correct answer is x = 3x - 5

Answer:

D

Step-by-step explanation:

Distribute the 1/2:

1/2(8x+4)

4x + 2

Distribute the 1/3:

1/3(9-3x)

3 - x

Add:

4x + 2 + 3 - x

3x +5

I hope this helps!

Answer:

D

Step-by-step explanation:

Distribute the 1/2:

1/2(8x+4)

4x + 2

Distribute the 1/3:

1/3(9-3x)

3 - x

Add:

4x + 2 + 3 - x

3x +5

I hope this helps!

I copy and pasted the answer above mine

ANSWER

D. 4

EXPLANATION

The given polynomial is

[tex]3 {x}^{6} + 5 - {x}^{2} + 4 {x}^{5}- 9x[/tex]

The term in degree 5 in this polynomial is

[tex]4 {x}^{5} [/tex]

The coefficient of this term is the constant that is multiplying the variable raised to exponent 5.

This number is 4.

Therefore the coefficient of term in degree 5 is 4

The correct answer is D.

Final answer:

The expression that is 444 times as large as the expression 34 - 15 is (4 x 34) - 15.

Explanation:

To find the expression that is 444 times as large as the expression 34 - 15, we need to multiply the expression by 444. The correct expression is option C, which is (4 x 34) - 15. Let's break it down:

First, we perform the multiplication: 4 x 34 = 136.

Then, we subtract 15 from the result: 136 - 15 = 121.

Therefore, the expression (4 x 34) - 15 is 444 times as large as the expression 34 - 15.

Answer: The correct answer is inverted

Step-by-step explanation:

Answer:

Step-by-step explanation:

An angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.

Therefore we have the equation:

[tex]\dfrac{x+8}{10}=\dfrac{2x-5}{14}[/tex]              cross multiply

[tex]14(x+8)=10(2x-5)[/tex]             use the distributive property

[tex](14)(x)+(14)(8)=(10)(2x)+(10)(-5)[/tex]

[tex]14x+112=20x-50[/tex]           subtract 112 from both sides

[tex]14x=20x-162[/tex]           subtract 20x from both sides

[tex]-6x=-162[/tex]         divide both sides by (-6)

[tex]x=27[/tex]

ANSWER

D. 18 m^2

EXPLANATION

The area of a kite is half the product of the diagonals.

The diagonals of the kite are

3+3=6m

and

2+4=6m

The area of the kite

[tex] = \frac{1}{2} \times 6 \times 6[/tex]

[tex] = 3 \times 6[/tex]

[tex] = 18 {m}^{2} [/tex]

The correct answer is D.

The area of kite using the diagonal length 6m and 6 m is 18 m².

Thus, option (d) is correct.

Given:

length of diagonal 1 = 3+ 3 = 6 m

length of diagonal 2 = 2+ 4 = 6 m

Using the formula of Area of Kite

[tex]{\text} Area of kite[/tex] = [tex]\dfrac{1}{2} *[/tex] [tex]{\text} product \; of \;diagonal[/tex]

Now, substituting the values of diagonal into the formula as

[tex]{\text} Area of kite[/tex] = [tex]\dfrac{1}{2} *[/tex] [tex]{\text} (6 * 6)[/tex]

                   = [tex]\dfrac{1}{2} *[/tex] [tex]{\text} (36)[/tex]

                   = 18 m²

Thus, the area is 18 m².

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Answer:

6.25716517287

Step-by-step explanation:

Area of circle = π × r²

→ 123 = π × r²

⇒ Divide both sides by π

→ 39.1521160006 = r²

⇒ Square root both sides

→ 6.25716517287 = r

You can use the Pythagorean Theorem to find the hypotenuse. Then you should be able to find the altitude.

First you must have the quadratic equal to zero. In order to do this you must subtract 7 to both sides

x^2 + 20x + (100 - 7) = 7 - 7

x^2 + 20x + 93 = 0

Now you must find two numbers who's sum equals 20 and their multiplication equal 93

Are there any? NO!

This means that you have to use the formula:

[tex]\frac{-b±\sqrt{b^{2} - 4ac} }{2a}[/tex]

In this case:

a = 1

b = 20

c = 93

[tex]\frac{-(20) plus/minus\sqrt{20^{2} - 4(1)(93)} }{2*1}[/tex]

[tex]\frac{-20 plus/minus\sqrt{400 - 372} }{2}[/tex]

[tex]\frac{-20 plus/minus\sqrt{28} }{2}[/tex]

^^^We must simplify √28

√28 = 2√7

so...

[tex]\frac{-20 plus/minus 2\sqrt{7} }{2}[/tex]

simplify further:

[tex]-10 plus/minus\sqrt{7[/tex]

-10 + √7

or

-10 - √7

***plus/minus = ±

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

10

Step-by-step explanation:

The perimeter will also be halved:  (1/2)(20) = 10.

Example:  a rectangle of length 14 ft and width 8 ft has perimeter P = 2(14 ft) + 2(8 ft), or 28 ft + 16 ft = 44 ft.

If we halve the length and width, we get 7 ft and 4 ft, and the P is

2(7 ft) + 2(4 ft) = 14 ft + 8 ft = 22 ft, which is half of the original perimeter 44.

Arrange the numbers in order from smallest to largest:

28, 35, 40, 40, 45, 52, 54, 58, 60

Median is the middle value  = 45

Mode is the number that appears most = 40

Mean is the average. Add the numbers and divide:

412/9 = 45.77 = 45.78

Range is difference between  highest and lowest = 60 - 28 = 32

Answer:8>4n=6 or 8>4+n=6

Step-by-step explanation:

Let's solve the equation step by step. The problem statement can be translated into a mathematical equation:
"Eight more than the product of a number and 4 is equal to 6."
Let x be the number we are looking for. When the problem says "the product of a number and 4," we can express this as 4 * x or 4x. The phrase "eight more than" implies we are to add 8 to the product of the number and 4, making the expression 4x + 8. According to the statement, this expression is equal to 6. Thus, we write the equation as:
4x + 8 = 6
To find the value of x, we will follow these steps:
1. Subtract 8 from both sides of the equation to isolate the term with x on one side.
4x + 8 - 8 = 6 - 8
This simplifies to:
4x = -2
2. Divide both sides of the equation by 4 to solve for x.
4x / 4 = -2 / 4
This simplifies to:
x = -1/2
So the number we were looking for, represented as x, is -1/2.

For this case we have the following numbers:

[tex]\frac {11} {18} = 0.611111111111\\\frac {5} {9} = 0,555555555556[/tex]

Note that [tex]\frac {11} {18}[/tex]is greater than[tex]\frac {5} {9},[/tex] so the inequality sign must be placed with the opening towards [tex]\frac {11} {18}[/tex].

Answer:

[tex]\frac {11} {18}> \frac {5} {9}[/tex]

9.92

You must look at which number has the decimal closest to 9.99

Here are the numbers in order from least to greatest

9.81, 9.82, 9.83, 9.92

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer: 9.92

Step-by-step explanation: If you had $9.92, $9.82, $9.83 or $9.81. the most amount of money there is $9.92 because it is the closest to $10. which is more money than the least amount $9.81

Answer:

The ones that give a rational number answer are:

C+D

A*B

C*D

A*A

Step-by-step explanation:

A+B does not give a rational number answer; √3+2√3 = 3√3

C+D is a rational number; √25=5 and √16=4; 5+4=9.

A+D is not a rational number; √3+√16 = √3+4

A*B is a rational number; √3*2√3 = 2√9 = 2*3 = 6

B*D is not a rational number; 2√3*√16 = 2√3*4 = 8√3

C*D is a rational number; √25*√16 = 5*4 = 20

A*A is a rational number; √3*√3 = √9 = 3

Answer:

[tex]21.5\%[/tex]

Step-by-step explanation:

we know that

The probability that a point in the square below  is in the shaded region, is equal to divide the area of the shaded region by the area of the square

step 1

Find the area of the shaded region

The area is equal to the area of the square minus the area of the circle

[tex]A=b^{2} -\pi(r)^{2}[/tex]

we have

[tex]b=12\ cm[/tex] ---> length side of the square

[tex]r=12/2=6\ cm[/tex] ----> the radius is half the diameter

assume

[tex]\pi =3.14[/tex]

substitute

[tex]A=12^{2} -(3.14)(6)^{2}[/tex]

[tex]A=30.96\ cm^{2}[/tex]

step 2

Find the area of the square

[tex]A=b^{2}[/tex]

we have

[tex]b=12\ cm[/tex] ---> length side of the square

substitute

[tex]A=12^{2}=144\ cm^{2}[/tex]

step 3

Find the probability

[tex]P=30.96/144=0.215[/tex]

Convert to percent form

[tex]0.215*100=21.5\%[/tex]

Step-by-step explanation:

Question 4? is (maybe) C because a square and a rectangle's diagonals are perpendicular.

Question 5- True

Question 6- False, a square is always a rombi but a rombi isn't always a square.

Question 7- True

Question 8- True, because if they didn' then they wouldn't equal 360 degrees and the sum of a trapezoids interior angles has to add up to 360 degrees.

ANSWER

C. sin 126°

EXPLANATION

-576° is coterminal with ±216,±144.

Therefore

cos (-576°)=cos(±216°)=cos(±144°)

The principal angle for -576° is 36° .

Since the terminal side of -576° is in the second quadrant and the cosine ratio is negative in the second quadrant,

cos (-576°)=-cos (±36°)

Also from complementary angles

cos (-576°)=-cos (36°)=-sin (90-36)=-sin(54°)

A=24

B=76

C=25

D= 19

Step-by-step explanation:

.......

Final answer:

The probabilities are matched as follows: A-24%, B-76%, C-19%, and D-25%. These are calculated based on the total number of balls of each color and the fraction that are labeled to win a prize.

Explanation:

The question provides a scenario where there are 24 yellow balls and 76 red balls in a box, and one-fourth of each color are labeled "Win a prize." We are asked to match descriptions of probabilities with their corresponding percent values.

A: Probability that a randomly selected ball labeled "Win a prize" is yellow = (1/4 * 24) / ((1/4 * 24) + (1/4 * 76)) * 100 = 6 / (6 + 19) * 100 = 24%.

B: Probability that a randomly selected ball labeled "Win a prize" is red = (1/4 * 76) / ((1/4 * 24) + (1/4 * 76)) * 100 = 19 / (6 + 19) * 100 = 76%.

C: Probability that a randomly selected ball is labeled "Win a prize" and is red = (1/4 * 76) / 100 = 19%.

D: Probability that a randomly selected yellow ball is labeled "Win a prize" = (1/4 * 24) / 24 * 100 = 25%.

Answer:

Step-by-step explanation:

The formula of a volume of a cylinder:

[tex]V=\pi r^2H[/tex]

r - radius

H - height

We have r = 6cm and H = 8cm. Substitute:

[tex]V=\pi(6^2)(8)=\pi(36)(8)=288\pi\ cm^3[/tex]

[tex]\pi\approx3.14\to V\approx(288)(3.14)=904.32\ cm^3[/tex]

Answer:

904.32 cm³

Step-by-step explanation:

The volume (V) of a cylinder is calculated using the formula

V = πr²h ( r is the radius of the base and h the height )

here r = 6 and h = 8, so

V = 3.14 × 6² × 8

   = 3.14 × 36 × 8 ≈ 904.32 cm³

Answer:

The amount after three years is $12831.8

Step-by-step explanation:

* Lets revise the compound interest

- The formula for compound interest is  A = P (1 + r/n)^(nt)

 Where:

# A = the value of the investment with interest

# P = the initial investment amount  

# r = the annual interest rate (decimal)

# n = the number of times that interest is compounded per unit t

# t = the time the money is invested

* Now lets solve the problem

∵ The initial amount is $9000

∴ P = $9000

∵ The rate is 12%

∴ r = 12/100 = 0.12

∵ The interest is compound quarterly

∴ n = 4

∵ The money invested for 3 years

∴ t = 3

∵ A = P (1 + r/n)^(nt)

∴ A = 9000(1 + 0.12/4)^(4×3)

∴ A = 9000(1 + 0.03)^12

∴ A = 9000(1.03)^12 = $12831.8