Please help with this question

Answer:

-9/17 is the answer

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]

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:

3a3a3a

3·3·3a^3

Step-by-step explanation:

(3a)^3 = (3a) (3a) (3a)

          = 3*3*3 * a *a *a

          = 3*3*3 * a^3

Answer:

3a3a3a

3·3·3a^3

Step-by-step explanation:

The answer is:

The third option is the correct option.

[tex](y+4)^{2}=22=y^{2}+8y-6[/tex]

To find the correct answer, we need to expand the notable product of the given choices, and then, compare it to the given expression.

Also, we must remember how to expand the following notable product:

[tex](a+-b)^{2}=a^{2}+-2*ab+b^{2}[/tex]

We are looking for the following expression:

[tex]y^{2}+8y-6=0[/tex]

So, solving we have:

[tex](y+4)^{2}=10\\\\y^{2}+2*4y+4^{2} =10\\\\y^{2}+8y+16=10\\\\y^{2}+2*4y+16-10=0\\\\y^{2}+2*4y+6=0[/tex]

Hence, we know that the first option is not the correct option.

[tex](y-4)^{2}=10\\\\y^{2}-2*4y+4^{2}=28\\\\y^{2}-8y+16=28\\\\y^{2}-8y+16-28=0\\\\y^{2}-8y-12=0[/tex]

Hence, we know that the second option is not the correct option.

[tex](y+4)^{2}=22\\\\y^{2}+2*4y+4^{2} =22\\\\y^{2}+8y+16=22\\\\y^{2}+2*4y+16-22=0\\\\y^{2}+8y-6=0[/tex]

Hence, we know that the third  option is the correct option.

Have a nice day!

Answer:

0.03

Step-by-step explanation:

fraction = part/whole

= 27/900

= 3/100

=0.03

decimal value = 0.03

Answer:

72π in³

Step-by-step explanation:

Volume of a cylinder is:

V = πr²h

where r is radius (half of diameter) and h is height.

Here, r = d/2 = 3 in, and h = 8 in.

V = π (3 in)² (8 in)

V = 72π in³

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:

-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:

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:

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;

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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;

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Answer:

true

Step-by-step explanation:

numbers divisble by 10 have to be divisible by 5 because the prime factors are 5 and 2

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]

Answer:

1,12×10^6

Step-by-step explanation:

Answer:

Around 17.716 inches

Step-by-step explanation:

Answer:

17.7 inches to the nearest tenth

Step-by-step explanation:

Recall that

1 in=2.54 cm

This implies that;

[tex]1cm=\frac{1}{2.54} in.[/tex]

Or

[tex]1cm=\frac{50}{127} in.[/tex]

This implies that;

[tex]45 cm=45\times\frac{50}{127}in[/tex]

[tex]45 cm=45\times\frac{50}{127}in[/tex]

This simplifies to;

[tex]45 cm=17.7 in[/tex] to the nearest tenth.

Answer:

14.5 years.

Step-by-step explanation:

Given that you invest $150 at 7% interest compounded annually. Now we need to find about in how many years will you have $400. Then round the  answer ot the nearest tenth of a year.

So plug the given values into compound interest formula.

[tex]A=P\left(1+r\right)^t[/tex]

[tex]400=150\left(1+0.07\right)^t[/tex]

[tex]\frac{400}{150}=\left(1+0.07\right)^t[/tex]

[tex]\ln\left(\frac{400}{150}\right)=\ln\left(1+0.07\right)^t[/tex]

[tex]\ln\left(\frac{400}{150}\right)=\ln\left(1.07\right)^t[/tex]

[tex]\ln\left(\frac{400}{150}\right)=t\cdot\ln\left(1.07\right)[/tex]

[tex]\frac{\ln\left(\frac{400}{150}\right)}{\ln\left(1.07\right)}=t[/tex]

[tex]14.4967313882=t[/tex]

Which is approx 14.5 years.

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]

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]

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

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:

B.  8 in^2.

Step-by-step explanation:

Let the width be x inches, then the length = x + 2 inches.

So by The Pythagoras theorem:

(√20)^2 =  x^2 + (x + 2)^2

x^2 + x^2 + 4x + 4 = 20

2x^2 + 4x - 16 = 0

x^2 + 2x - 8 = 0

(x + 4)(x - 2) = 0

x = 2, -4    (we ignore the negative so x = 2)

So the area = 2 * (2 + 2)

= 8 in^2.

Answer:

B

Step-by-step explanation:

L = W + 2

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

(W + 2)2 + W2 = [tex]\sqrt{20} ^{2[/tex]  

2[tex]w^{2}[/tex] + 4W + 4 = 20

2[tex]w^{2}[/tex] + 4W − 16 = 0

W = 2 or W = −4

And,

L = W + 2

L = 2 + 2

L = 4

Therefore,

A = LW = (4)(2) = 8

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:

2

Step-by-step explanation:

The degree of a polynomial is determined by the largest exponent of the variable within the expression

y³ is of degree 3

xy² is of degree 1 + 2 = 3 ← sum the exponents of the 2 variables

Thus x²y³ is of degree 2 + 3 = 5

For the expression 5x?y³ + xy² + 8 to be a trinomial with a degree of 5, then the missing exponent of the x term must be 2.

Polynomial is an expression that involves only the operations of addition, subtraction, multiplication of variables.

Polynomials are classified based on degree as linear, quadratic, cubic and so on. A trinomial is a polynomial with three terms.

For the expression 5x?y³ + xy² + 8 to be a trinomial with a degree of 5, then the missing exponent of the x term must be 2.

Find out more on Polynomial at: https://brainly.com/question/2833285

the answer is x = -28

Answer:

-12

Step-by-step explanation:

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

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]

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