3.13R Question:

Evaluate the exponential function f(x)=(1/12)^x

Answer:

[tex]x=\pm\sqrt{3i} ,\pm3i[/tex]

Step-by-step explanation:

1) Move all terms to one side.

[tex]{x}^{4}+12{x}^{2}+27=0[/tex]

2) Factor [tex]{x}^{4}+12{x}^{2}+27x[/tex].

1) Ask: Which two numbers add up to 12nd multiply to 27?

3 and 9

2) Rewrite the expression using the above.

[tex]({x}^{2}+3)({x}^{2}+9)[/tex]

Outcome: [tex]({x}^{2}+3)({x}^{2}+9)=0[/tex]

2) Solve for x.

1)Ask: When will[tex]({x}^{2}+3)({x}^{2}+9)[/tex] equal zero?

When [tex]{x}^{2}+3=0[/tex]or[tex]{x}^{2}+9=0[/tex]

2) Solve each of the 2 equations above.

[tex]x=\pm\sqrt{3i} ,\pm3i[/tex]

Thanks.

Step-by-step explanation:

(2/5x − 1) − (1/4x + 2)

2/5x − 1 − 1/4x - 2

8/20x - 1  - 5/20x - 2

3/20x - 1 - 2

3/20x - 3

Answer:

x=6

Step-by-step explanation:

11x-3=4x+39

-4x     -4x

7x-3=39

   +3  +3

7x=42

______

7      7

x=6

11(6)-3=66-3=63

4(6)+39=63

yw hope it helps

The algebraic expression of raise t to the 10th power then add the result to 3 is t¹⁰ + 3

An algebraic expression is an expression that is made up of variables and constants along with algebraic operations such as addition, subtraction, multiplication, exponent, etc.

Given: raise t to the 10th power then add the result to 3

Note: t is the variable here

Let's write algebraic expression now:

raise t to the 10th power => t¹⁰

then add the result to 3 => t¹⁰ + 3

Therefore, the algebraic expression is t¹⁰ + 3

Learn more about algebraic expression on:

https://brainly.com/question/4344214

#SPJ1

Step-by-step explanation:

[tex] \frac{dy}{dx} ( \sqrt{x} ) = \frac{1}{2 \sqrt{x} } [/tex]

The slope of the line at x=1 is

[tex] \frac{1}{2(1)} = \frac{1}{2} [/tex]

so our equation is

[tex]y - 1 = \frac{1}{2} (x - 1)[/tex]

[tex]y - 1 = \frac{1}{2} x - \frac{1}{2} [/tex]

[tex]y = \frac{1}{2} x + \frac{1}{2} [/tex]

Answer:

The end behavior of the function is that it approaches positive infinity as x decreases to negative infinity, and it also approaches positive infinity as x approaches positive infinity.

Step-by-step explanation:

The end behavior of a function is what happens to the value of the function as x approaches negative infinity and as x approaches positive infinity.

Graphing the function is very helpful to visualize the end behavior.

Here, the graph has the shape of a V with the vertex on the x-axis going up in value on both sides forever.

The function here is f(x) = 3|x|.

Let's try a few values for x to get an idea.

We will deal with x approaching positive infinity first.

f(0) = 3|0| = 0

Let's get larger and larger values for x, approaching positive infinity.

f(10) = 3|10| = 30

f(10,000) = 3|10,000| = 30,000

f(1,000,000) = 3|1,000,000| = 3,000,000

As you can see, as x increases, the value of f(x) also increases. As x approaches positive infinity, f(x) also approaches positive infinity.

Now let's look at values of x approaching negative infinity.

f(0) = 3|0| = 0

Let's get smaller and smaller values for x, approaching negative infinity.

f(-10) = 3|-10| = 30

f(-10,000) = 3|-10,000| = 30,000

f(-1,000,000) = 3|-1,000,000| = 3,000,000

As you can see, as x decreases, the value of f(x) increases. As x approaches negative infinity, f(x) approaches positive infinity.

The end behavior of the function is that it approaches positive infinity as x decreases to negative infinity, and it also approaches positive infinity as x approaches positive infinity.

The probability that a student chosen at random is in the choir or band or both is 0.911

Probability is the likelihood that an event will happen. This can range from an event being impossible to some likelihood to being absolutely certain. In mathematics terms, probability is on a scale from 0 to 1. Zero means the event is impossible, like rolling a seven on a die that only has digits from 1 to 6. One is an event that will happen, it is certain.

Total number of students in the school = 450

number of students in choir = 110

number of students in band = 240

number of students in both = 60

Probability a student chosen at random is in the choir or band or both is

110/450 + 60/450 + 240/450

= 410/450 which is 0.911

In conclusion, the probability of a student being in music, or band or both is 0.911

Learn more about probability: htps://brainly.com/question/25870256

#SPJ1

Answer:

  d = 23 1/3

Step-by-step explanation:

You want to solve the proportion (0.3d -1)/(3 1/3) = (0.84)/(7/15).

  [tex]\dfrac{0.3d-1}{3\dfrac{1}{3}}=\dfrac{0.84}{\dfrac{7}{15}}\qquad\text{given}\\\\\\\dfrac{3(0.3d-1)}{10}=\dfrac{15(0.84)}{7}\qquad\text{invert and multiply}\\\\0.09d -0.3=1.8\qquad\text{simplify}\\\\0.09d = 2.1\qquad\text{add 0.1}\\\\d=\dfrac{2.10}{0.09}=\dfrac{70}{3}\qquad\text{divide by 0.09}\\\\\boxed{d=23\dfrac{1}{3}}[/tex]

__

Check

  (0.3·(70/3) -1)/(3 1/3) = 0.84/(7/15)

  (7 -1)/(10/3) = 1.8

  6(3/10) = 1.8 . . . . . . true

Answer: 23 1/3

Step-by-step explanation:

The perimeter of the given triangle with given lengths is; 78

The perimeter of a triangle is defined as the sum total of the 3 side lengths of the triangle.

Now, we are given the triangle as QRS.

We are given that;

A is the midpoint of QR

B is the midpoint of RS

C is the midpoint of SQ

Thus;

QA = RA = 10

BR = SB = 15

SQ = 28

Thus;

Perimeter of Triangle = 2(10) + 2(15) + 28 = 78

Read more about Perimeter of triangle at; https://brainly.com/question/24382052

#SPJ1

During 30 days of summer, Val will spend $ 73.5 on electricity from the use of his air conditioner.

Any of the following algebraic expressions should be used: addition, subtraction, multiplication, and division. Bring the variable to the left side, then move all of the other values to the right side to determine the value of x. For the outcome, simplify the values.

Since Val's air conditioner uses 3,500 watts when running, and that Val Utilizes it for 7 hours during summer days, spending 10 cents per kilowatt hour, estimating how much money Val will spend during a 30-day summer must be done the following calculation:

3,500 watts = 3.5 kilowatts

3.5 kilowatts per hour = 35 cents

35 cents × 7 hours = 245 cents per day

245 cents per day × 30 days = 7,350 cents per month

7,350/100 = X

73.5 = X

Therefore, during 30 days of summer, Val will spend $ 73.5 on electricity from the use of his air conditioner.

To learn more about the value of x refer to:

https://brainly.com/question/27944341

#SPJ1

Answer: C

Step-by-step explanation:

[tex]A=\pi (17)^2 \approx 908[/tex]

Answer:

Answer C is correct

Step-by-step explanation:

The formula to find the area of a circle is:

A = πr²

Here,

r => radius = 17cm

Let us find the area of the circle.

A = πr²

A = 3.14 × 17 × 17

A = 907.46 cm²

Approx. = 908 cm²

Answer:

The quadratic function has the following sets of values below: (0,8) (2,10) (3,1). The quadratic functions represented as follows: f(x) = ax² + bx + c. using (0,8) 8 = a(0)² + b(0) + c. 8 = c. Therefore, using (2, 10)(3 , 1). f(x) = ax² + bx + c.

Answer:

A bar notation

Step-by-step explanation:

the line is called a bar notation

Answer:

If you have a line over a number (let's say there is a line over 0.2):

0.2, then it means that it is a repeating number.

So, a line over 0.2 would mean it is actually 0.2222222222 etc. They just don't want to right it out because it is way to long, and it is infinite.

Step-by-step explanation:

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 14 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

The number of tiles with the dimensions 3 cm x 3 cm are needed to cover the grid is 4.

Given that, a grid is 6 cm x 6 cm.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

Here,

Area of a grid is 6×6 =36 cm²

a) Area of a tile with 1 cm x 1 cm is

1×1 =1 cm²

Number of tiles = 36/1 =36

b) Area of a tile with 2 cm x 2 cm is

2×2 =4 cm²

Number of tiles = 36/4 =9

a) Area of a tile with 3 cm x 3 cm is

3×3 =9 cm²

Number of tiles = 36/9 =4

Therefore, the number of tiles with the dimensions 3 cm x 3 cm are

needed to cover the grid is 4.

Learn more about the area here:

https://brainly.com/question/27683633.

#SPJ1

Answer:

22m+16

Step-by-step explanation:

4(6m+4)-2m

4(6m)+4(4)-2m

24m+16-2m

24m-2m+16

22m+16

Hopes this helps please mark brainliest

43 distance diver descend from the rock to the coral

Two or more expressions with an Equal sign is called as Equation.

Given,

A deep sea driver descended from a rock with an elevation of -45.5 feet to a coral reef with an elevation of -88.5 feet

We need to find the distance between -45.5 ft and -88.5 ft.

So the distance between those numbers is given by:

|-45.5-(-88.5)|

|-45.5+88.5|

|88.5-45.5|

|43.0|

|43|  

43

Hence, 43 distance diver descend from the rock to the coral

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

Answer: D

Step-by-step explanation:

Using the formula for the volume of a rectangular prism,

[tex]x(8-2x)(11-2x)\\\\=x(88-38x+4x^2)\\\\=4x^3 -38x^2 +88x[/tex]

Answer:

√32

Step-by-step explanation:

c = [tex]\sqrt{4^2 + 4^2} = \sqrt{16 + 16} = \sqrt{32}[/tex]

Answer:

24 : 15 : 20

Step-by-step explanation:

express ratios in fractional form and express b and c in terms of a

[tex]\frac{a}{b}[/tex] = [tex]\frac{8}{5}[/tex] ( cross- multiply )

8b = 5a ( divide both sides by 8 )

b = [tex]\frac{5}{8}[/tex] a

also

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

3c = 4b ( divide both sides by 3 )

c = [tex]\frac{4}{3}[/tex] b = [tex]\frac{4}{3}[/tex] × [tex]\frac{5}{8}[/tex] a = [tex]\frac{5}{6}[/tex] a

Then

a : b : c

= a : [tex]\frac{5}{8}[/tex] a : [tex]\frac{5}{6}[/tex] a ( multiply each part by 24, the LCM of 8 and 6 )

= 24a : 15a : 20a ( divide each part by a )

= 24 : 15 : 20 ← in simplest form

Answer:

350:3=116.66666....

Step-by-step explanation:

so 1/3 is 116.6 (117)

Ratio of women in company is 117.

Good luck!

Thank me later.

Tadano

The time taken for the money to grow to $8670 at compound interest is approximately 9.24 years.

Given the amount of money that is the principal = $6000

Rate = 4% compounded quarterly.

Time = t

Amount = $8670

Now we know that the amount is calculated by the formula:

A = P(1+r/4)ⁿ

8670 = 6000(1+0.01)ⁿ

Hence

log 1.445 = n log 1.01

or, n = 36.99

Number of years = 36.99 / 4 = 9.24 years.

The interest that is added to a loan or deposit is referred to as compound interest. Compound interest is computed for a sum utilizing both the principal and interest already paid. The main distinction between compound interest and simple interest is this.

If we look at our bank statements, interest is usually credited to our account once a year. While the principle remains constant, the interest changes annually.

To learn more about interest visit:

https://brainly.com/question/13155407

#SPJ9

The values of the addition given will be:

6 + 9 = 15

0 + 9 = 9

2 + 3 = 5

11 + 90876 = 90887

Addition simply means sum. It is one of the basic operations that are used in Mathematics. In this case, the addition of two whole numbers will bring about the total amount of the value combined.

Therefore the addition will be the sum of the numbers. This will be:

6 + 9 will be:

= 6 + 9

= 15

0+9 will be:

= 0 + 9

= 15

2+3 will be:

= 2 + 3

= 5

11+90876 will be:

= 11 + 90876

= 90887

Learn more about addition on:

brainly.com/question/24536701

#SPJ1

Answer:

answer for first one is 8

for 2nd one is [tex]2(x+5)/3x^2-7[/tex]

for 3 rd one is [tex](x-5)/x[/tex]

for 4th one is [tex]3x^{2} n^{2} (7n-9)/7x-9[/tex]

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

It can not be a or b because the figure is upside-down.

It cannot be d because the figure would literally fly off the grid shown.

It must be C because the figure rotates 90° counterclockwise and moves 4 units to the right.

Answer:

[tex]h=2[/tex]

Step-by-step explanation:

[tex]A=bh \\ \\ 14=7h \\ \\ h=2[/tex]

Answer:

h = 2

Step-by-step explanation:

A = 14; b = 7

A = bh

14 = 7h

7h = 14

Divide both sides by 7.

h = 14/7

h = 2

Answer:

1,2,3,4,6,8,12,24 sub set

The rate for the balance to triple in 46 years is  2.42% .

$500 is compounded annually for 46 years. No other deposits are made.

The rate needed for the balance to triple in that time can be calculated as follows:

The interest rate as a percent can be calculated as follows:

For the principal to be tripled, the amount will be 500(3) = 1500 dollars

[tex]r = n((\frac{A}{P} )^{\frac{1}{nt} } -1)[/tex]

where

P = 500

A = 1500

n = 1

t = 46 years

r[tex]r = 1((\frac{1500}{500})^{\frac{1}{1(46)} } - 1 )[/tex]

[tex]r = 1((\frac{1500}{500})^{\frac{1}{46} } - 1 )[/tex]

r = 0.0241704

Then convert r to R as a percentage

R = r * 100

R = 0.0241704 * 100

R = 2.42% per year

learn more on compound interest here:https://brainly.com/question/12840579

#SPJ1

120 cm² is the surface area of the right triangular prism

The surface area of a right triangular prism can be determined using the formula below:

A = (S₁ + S₂ + h)L + bh    (Check the attached image for the labeling)

Given: S₁ = 3 cm,  S₂ = 5 cm, h = 4 cm, L =  6cm and b = 3 cm

Substitute these values into the formula:

A = (S₁ + S₂ + h)L + bh

A = (3 + 5 + 4)6 + 3(4)

A = (18)6 + 12

A = 120 cm²

Therefore, the surface area of the right triangular prism is 120 cm²

Learn more right triangular prism on:

https://brainly.com/question/26979119

#SPJ1

The correct representation of the solution to the inequality given; –3(2x – 5) < 5(2 – x) are;

It follows from the task content that the correct representation of the inequality given in the task content be determined.

The given inequality can be evaluated for the solution set as follows;

–3 (2x – 5) < 5 (2 – x)

-6x + 15 < 10 - 5x

-6x + 5x < 10 - 15

-x < -5

By dividing both sides by -1; we have;

x > 5.

On this note, the required representation is; An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

Read more on inequalities;

https://brainly.com/question/11613554

#SPJ1