can someone help me find the area of the triangle? and can you give me step by step so i can better understand it? thank you!!

Answer:

-x^2+21x+18/ x^3-x^3-16x-20

Step-by-step explanation:

-x^2+21x+18/ (x-5)(x^2+4x+4)

= -x^2+21x+18/ x^3+4x^2+4x-5x^2-20x-20

= -x^2+21x+18/ x^3-x^2-16x-20

Answer

x = 20

Explanation

Multiply the entire equation by 2 to get rid of the fraction.

x/2 * 2 = x

-4 * 2 = -8

6 * 2 = 12

Now, we have:

x - 8 = 12

To complete, add 8 to both sides

x = 20

For this case we must find the value of "x" of the following equation:

[tex]\frac {x} {2} -4 = 6[/tex]

So:

We add 4 sides of the equation:

[tex]\frac {x} {2} = 6 + 4\\\frac {x} {2} = 10[/tex]

We multiply by 2 on both sides of the equation:

[tex]x = 20[/tex]

Thus, the value of the variable x is 20

Answer:

[tex]x = 20[/tex]

Answer: OPTION C

Step-by-step explanation:

Complete the square:

Having the equation in the form [tex]ax^2+bx=c[/tex], you need to add [tex](\frac{b}{2})^2[/tex] to both sides of the equation:

You can identify that "b" in the equation [tex]x^2+6x=5[/tex] is:

[tex]b=6[/tex]

Then:

[tex](\frac{6}{2})^2=3^2[/tex]

Add this to both sides:

[tex]x^2+6x+3^2=5+3^2[/tex]

Rewriting, you get:

[tex](x+3)^2=14[/tex]

Solve for "x":

 [tex]x+3=\±\sqrt{14}\\\\x+3=\±\sqrt{14}\\\\x=\±\sqrt{14}-3[/tex]

Then, the solutions are:

[tex]x=-3+\sqrt{14}\ or\ x=-3-\sqrt{14}[/tex]

Answer:

-12

Step-by-step explanation:

c = 2x + 3. The third side of the triangle is 2x + 3.

The key to solve this problem is using the perimeter of a triangle equation which is P = a + b + c, where a, b, and c are the sides of the triangle.

We know that the perimeter P = 3x² + 7x, let's suppose a = 6x - 7, b = 3x² - x + 4, and c is the unknow.

Clearing c from the equation:

c = P - (a + b)

c = 3x² + 7x - (6x - 7 + 3x² - x + 4)

c = 3x² + 7x - 6x + 7 - 3x² +x - 4

Grouping the equal terms:

c = 3x² - 3x² + 7x + x - 6x + 7 - 4

c = 0 + 8x - 6x + 3

c = 2x + 3

Answer:

expression

A mathematical symbol, or combination of symbols, representing a value, or relation. Example:  

2

+

2

=

4

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation:

The given expression is x- [tex]\frac{15}{x}[/tex] = 2

and we have to solve this for the value of x,

( x- [tex]\frac{15}{x}[/tex]) = (2)

[tex]\frac{x^{2}-15 }{x} =2[/tex]

x² - 15 = 2x

x² - 2x - 15 = 0

x² - 5x + 3x - 15 = 0

x ( x-5 ) + 3(x - 5) = 0

( x+3 )( x-5 ) = 0

( x+3) = 0

x = -3

or ( x- 5 ) = 0

x = 5

Therefore, x = -3 and 5 will be the solution.

Option E is the answer.

ANSWER

[tex]P(4)'= \frac{1}{3} [/tex]

EXPLANATION

The sample space of rolling a 6-sided die is

{1,2,3,4,5,6}

The even numbers apart from 4, are

{2,6}

The probability of rolling an even number that is not 4 is

[tex]P(4)'= \frac{2}{6} = \frac{1}{3} [/tex]

at 10:30 there will be 64 bacteria

Answer:

At 10:20 a.m., there will be 16 cells in the bottle.

At 10:30 a.m. there will be 64 cells in the bottle .

Step-by-step explanation:

Answer:

The answer would be eight.

Step-by-step explanation:

The range is the difference between the largest and smallest number you need to make sure you have them in order or it won’t work.

Answer:

the answer is eight

Step-by-step explanation:

For this case we have by definition, that an irrational number is a number that can not be expressed as a fraction \ frac {a} {b}, where a and b are integers and b is different from zero.

A) [tex]\sqrt {100} = 10[/tex], it is rational

B)[tex]\frac {1} {8}[/tex], it is rational

C) [tex]-2.2675[/tex], it is rational

D) [tex]\sqrt [3] {16},[/tex] it is not rational.

Answer:

Option D

The only option that represents an irrational number is D) ∛16.

An irrational number is a number that cannot be expressed as a fraction (ratio) of two integers and has an infinite decimal representation without any repeating pattern.

Let's analyze each option:

A) √100:

The square root of 100 is 10, which is a rational number. It can be expressed as the fraction 10/1.

Therefore, option A) is a rational number.

B) 1/8:

The fraction 1/8 can be expressed as a ratio of two integers. It is equal to 0.125 in decimal form.

Since the decimal representation terminates after a finite number of decimal places, option B) is not an irrational number.

C) - 2.2675:

The number -2.2675 is a decimal number, but it is not an irrational number.

It can be expressed as a rational number by writing it as a fraction. Hence, option C) is not an irrational number.

D) ∛16:

The symbol ∛ represents the cube root. The cube root of 16 is approximately 2.5198.

This number is an irrational number because it cannot be expressed as a fraction of two integers, and its decimal representation continues indefinitely without a repeating pattern.

In summary, the only option that represents an irrational number is D) ∛16.

Learn more about irrational number click;

https://brainly.com/question/28973373

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Answer:

80

Step-by-step explanation:

Kumar needs only $80 to buy bicycle.

Subtraction is mathematic operation. Which is used to remove terms or objects in expression.

Given, bicycle costs $375.25.

And so for he has saved $295.25

To find the rest of money, we subtract the total cost to a saved money.

required money = $375.25 - $295.25 = $80

Therefore, he needs only $80 to buy a bicycle.

To learn more about the subtraction;

https://brainly.com/question/2346316

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Answer:

(-1,6)

Step-by-step explanation:

P= 1A + 2B

AP + PB

= 1(-3,6) + 2(0,6)

3

= (-3,6) + (0,12)

3

= (-3 + 18)

3

= (-1,6)

Answer:

Yes, the following equation is a quadratic function in vertex form

Step-by-step explanation:

we know that

The quadratic function of the vertical parabola into vertex form is equal to

[tex]y=a(x-h)^{2} +k[/tex]

where

(h,k) is the vertex of the parabola

If the coefficient a is > 0 ----> the parabola open upward (vertex is a minimum)

If the coefficient a is < 0 ----> the parabola open downward (vertex is a maximum)

in this problem we have

[tex]y=4(x-2)^{2} +6[/tex]

The squared term contain the x-coordinate of the vertex

[tex]h=2[/tex]

The constant term is the y-coordinate of the vertex

[tex]k=6[/tex]

The vertex is the point (2,6)

The coefficient is equal to

[tex]a=4[/tex] ----> open upward (vertex is a minimum)

Answer:

9?

Step-by-step explanation:

ANSWER

A. [-3,4]

EXPLANATION

We want to determine from the graph the interval on which

[tex]f(x) \geqslant 0[/tex]

This refers to the interval on which the the graph lies on or above the x-axis.

This interval is from x=-3 to x= 4

The correct choice is A. [-3,4]

Answer:

the answer is 77

Step-by-step explanation:

46.20 divided by 60 cents = 77

ANSWER

[tex](8, -1)[/tex]

EXPLANATION

If (8,-4) is on the graph of f(x), then

[tex]f(8) = - 4[/tex]

The corresponding point for the function

[tex]f(x) + 3[/tex]

is

[tex](8,f(8)+3)[/tex]

We substitute to obtain:

[tex](8, - 4+3)[/tex]

We now simplify to get;

[tex](8, -1)[/tex]

The corresponding point on f(x)+3 is therefore

[tex](8, -1)[/tex]

tan(theta)=tan(pi+theta)

So your answer would be 5pi/3

Answer:

The angle measure [tex]\frac{5\pi}{3}[/tex] has the same value as [tex]\frac{2\pi}{3}[/tex]

Step-by-step explanation:

[tex]tan(\theta)=tan(\pi+\theta)[/tex]

[tex]tan(\theta)=tan(\pi+\theta)[/tex]

so, here [tex]\theta=\frac{2\pi}{3}[/tex]

[tex]tan(\frac{2\pi}{3})=tan(\pi+\frac{2\pi}{3})[/tex]

[tex]tan(\frac{2\pi}{3})=tan(\frac{5\pi}{3})[/tex]

Hence, The angle measure [tex]\frac{5\pi}{3}[/tex] has the same value as [tex]\frac{2\pi}{3}[/tex]

28 (unit)^2

find the differences in the x (4) and y (7) coordinates

times them together as you normally find the area of rectangle (L×W)

Answer:

5 : 4

Step-by-step explanation:

To simplify the ratio , find the greatest common factor of 60 and 48, then divide both parts of the ratio by it

the greatest common factor of 60 and 48 is 12, hence

60 ÷ 12 : 48 : 12 = 5 : 4 ← in simplest form

30:24 = 10:8 = 5:4

Step-by-step explanation:

First divide them by 2

then divide the answer (30:24) with 3

then divide the answer with 2

And the answer comes as 5:4

Answer:

[tex]\log_2(\frac{\frac{x^3}{3}}{x+4})[/tex]

Step-by-step explanation:

The given logarithmic expression;

[tex]3\log_2x-(\log_23-\log_2(x+4))[/tex]

Expand the parenthesis:

[tex]3\log_2x-\log_23+\log_2(x+4)[/tex]

Use the product rule on the last two terms;

[tex]\log_aM+\log_aN=\log_aMN[/tex]

[tex]3\log_2x-\log_23(x+4)[/tex]

[tex]3\log_2x-\log_23(x+4)[/tex]

Apply the power rule:

[tex]\log_2x^3-\log_23(x+4))[/tex]

We now apply the quotient rule of logarithms:

[tex]\log_aM+\log_aN=\log_a(\frac{M}{N})[/tex]

[tex]\log_2x^3-\log_23(x+4)=\log_2(\frac{x^3}{3(x+4)})[/tex]

Or

[tex]\log_2x^3-\log_23(x+4)=\log_2(\frac{\frac{x^3}{3}}{x+4})[/tex]

tan <B is 16/30 which is 8/15

Answer:

Step-by-step explanation: It’s gotta be b or c.

Answer:

f(-3) = -5/2

f(-1) = 3/2

f(3) = 3/4

Step-by-step explanation:

To find the values, we just have to replace by the values given (-3, -1, 3).  Since there are different definitions of the function depending on the range of x, we just have to pick the right one before replacing x by its value.

x = -3

When x ≤ -1, the function is 7/2 + 2x

So, x = -3 is certainly  ≤ -1, so....

f(-3) = 7/2 + 2 (-3) = 7/2 - 6 = 7/2 - 12/2 = -5/2

x = -1

When x ≤ -1, the function is 7/2 + 2x

So, we do the same calculation:

f(-1) = 7/2 + 2 (-1) = 7/2 - 2 = 7/2 - 4/2 = 3/2

x = 3

When x ≥ 3, the function is defined as: (1/4)x or x/4.  So,

f(3) = 3/4

The output values of f(-3), f(-1), and f(3) in the piece-wise function are -5/2,  3/2, and 3/4 respectively.  

To determine the output value of f(-3), f(-1), and f(3) in the piece-wise function, we simply plug in the values of x in the piece that is within the domain.

To solve for f(-3), plug x = -3 into the piece with the domain of x ≤ -1:

f( x ) = 7/2 + 2x

Pug in x = -3:

f( -3 ) = 7/2 + 2(-3)

f( -3 ) = -5/2

To solve for f(-1), plug x = -1 into the piece with the domain of x ≤ -1:

f( x ) = 7/2 + 2x

Pug in x = -1:

f( -3 ) = 7/2 + 2(-1)

f( -3 ) = 7/2 - 2

f( -3 ) = 3/2

To solve for f(3), plug x = 3 into the piece with the domain of x ≥ 3:

f( x ) = (1/4)x

Pug in x = 3:

f( 3 ) = (1/4) × 3

f( 3 ) = 3/4

Therefore, the values for f(-3), f(-1), and f(3) are -5/2,  3/2, and 3/4 respectively.  

Answer:

M = $22.62

C = $75.38

Step-by-step explanation:

Selling Price = $98

Markup = 30%

Selling Price = 100 + 30 = 130%

130% = $98

1% = 98/130

Markup

= 98/130 x 30  

= $22.62

Cost Price

= 98/130 x 100

= $75.38

Answer:

H

Step-by-step explanation:

The parallel line BC divides the sides AD and AE in proportion, that is

[tex]\frac{AB}{BD}[/tex] = [tex]\frac{AC}{CE}[/tex], that is

[tex]\frac{2}{3}[/tex] = [tex]\frac{AC}{4}[/tex] ( cross- multiply )

3AC = 8 ( divide both sides by 3 )

AC = [tex]\frac{8}{3}[/tex] = 2 [tex]\frac{2}{3}[/tex], hence

AE = AC + CE

     = 2 [tex]\frac{2}{3}[/tex] + 4 = 6 [tex]\frac{2}{3}[/tex] → H

the answer is x = -28

Answer:

x = classic

x + 2342 = contemporary

3500 = x + (x +2342)

3500= 2x + 2342

and then you would just solve the equation, but it does not ask for a solution

Step-by-step explanation:

x = classic

x + 2342 = contemporary

3500 = x + (x +2342)

3500= 2x + 2342

Answer: Jared has a total of 3500 dvds of two types, contemporarys and classics.

we also know that Jared has 2342 more contemporary dvds than classics.

Now, how we write this as system of equations?

if x is the number of classics, and y the number of contemporarys, then:

1) x + y = 3500

and

2) y - x = 2342

this is the system of equations, but just for fun we can solve it!

in the second equation we can leave y alone in the right side ande get: y = 2342 + x, and then replace it in the first equation.

x + y = 3500

x + (2342 + x) = 3500

2*x = 3500 - 2342 =1158

x = 1158/2 = 579

So Jared has 579 classic titles.

then:

y + x =3500

y + 579 = 3500

y = 3500 - 579 = 2921

And Jared has 2921 contemporary titles.

Answer:

length of segment AB is 13

OR

AB = 13

Step-by-step explanation:

Use the Pythagorean Theorem with c being the length of segment AB.

a^2 + b^2 = c^2

5^2 + 12^2 = c^2

169 = c ^2 (square root both sides to get c by itself)

13 = c