Asymptote (horizontal) of f(x)=2(3)^-x

We got the factors which is prime numbers = 2 × 2 × 2 × 3

The technique of expressing all numbers as the product of primes is known as prime factorization. So, let's take something like the number 20 as an example. That can be divided into two components. "Well, that's 4 times 5," we can respond. Observe that 5 is a prime number.

For e.g, let's take number of 24 and factor it,

24/2 = 12

12/2 = 6

6/2 = 3

3/3 = 1

We got the factors which is prime numbers = 2 × 2 × 2 × 3

which is equal to given number i.e, 24.

See another example in image.

To read more about Prime Factorization.

https://brainly.com/question/25896797

#SPJ9

The length of the fence (including the gates) that was built around the park is (4w + 50) feet.

Here, we are given that a rectangular park is w ft wide and the park is 25 ft longer than its wide.

Thus, the length of the park = (w + 25) ft

Now, the park has to be fenced along all of its sides. Thus, we need to find the perimeter of the rectangular park.

The perimeter of a rectangle is given as-

2( length + breadth)

Thus, here, the perimeter will be-

2( w + 25 + w )

= 2( 2w + 25 )

= 4w + 50

Thus, the length of the fence (including the gates) that was built around the park is (4w + 50) feet.

Learn more about rectangles here-

https://brainly.com/question/25292087

#SPJ1

Answer: 0.25$ or a quarter

Step-by-step explanation:

Katlin bought 14 pencils, which cost her $3.50. So all you have to do is divide the amount ($) by the number of pencils.

3.50/14 = 0.25$

3.50 divided by 14

Each pencil cost a quarter

The equation of straight line of the points is given as y = -x - 2

To solve this problem, we simply need to find the equation of straight line which can be done by finding the slope of the line and then intercept of the line.

In the given points;

The formula of slope of a line is given as

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Substituting the values into the equation;

[tex]m = \frac{3 - (-6)}{-5 - 4} \\m = \frac{9}{-9} \\m = -1[/tex]

The slope of the line is equal to 1.

Let's find the intercept of the line

[tex]y = mx + c[/tex]

Taking point A;

[tex]y = mx + c\\-6 = -1(4) + c\\-6 = -4 + c\\c = -2[/tex]

The equation of the line is y = -x - 2

Translation: Find the equation of a straight line from two point A(4, -6) and B(-5, 3).

Learn more on equation of a line here;

https://brainly.com/question/18831322

#SPJ1

y=-2/5x-5 is the equation of a line into slope- intercept form

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The given equation is 6x + 15y = -75

six x plus fifteen y equal to minus seventy five

6x + 15y = -75

Subtract 6x from both sides

6x+15y-6x=-75-6x

15y=-75-6x

Divide both sides by 15

y=-75/15 -6/15 x

y=-5-2/5x

y=-2/5x-5

Hence y=-2/5x-5 is the equation of a line into slope- intercept form

To learn more on slope intercept form click:

https://brainly.com/question/9682526

#SPJ1

Answer:

Workers to be be added to finish the work in 24 hours = 348

Step-by-step explanation:

This is a problem involving inverse proportion

Here the number of days required to complete the job is inversely proportional to the number of workers- the more the workers, the less time it takes

We can state this as:
[tex]D \propto \dfrac{1}{N}[/tex]

where D = time in days required to complete the job and N is the number of workers that can do this in D days

The equation relating D and N can be stated as

[tex]D = k \dfrac{1}{N}[/tex]

This gives us k = D x N  (multiply by N both sides)

where k is a constant known as the constant of proportionality

Given data that D = 30 when N = 12, this constant of proportionality = D x N = 30 x 12 = 360

From the equation of proportionality we also get
N = k/D

So to complete the job in 24 hours = 1 day, substitute 1 for D and 360 for k to get
N = 360/1 = 360 workers

So you will need 360-12 = 348 workers if you expect to  finish the job in 24 hours = 1 day

The sale price of the backpack is $25.50.

The original price of the sweatshirt is $40.

From the information, the sale price of every item in a store is 85% of its usual price and the usual price of a backpack is $30.

The sale price will be:

= Percentage × Original price

= 85% × $30

= $25.50

The sale price of a sweatshirt is $34, its original price will be:

= 85% × x = $34

0.85x = $34

x = $34 / 0.85

x = $40

Learn more about price on:

brainly.com/question/1153322

#SPJ1

The distance between the Earth and the Sun is 1.5 extend eight kilometers, and the distance between Mars and the Sun is 2.2 8 X 10 eight kilometers. The scientific notation for the distance between Earth and Mars is 3.78 x 10^8 km.

The length of the line connecting two points is the distance between them. If the two points are on the same horizontal or vertical line, the distance can be calculated by subtracting the non-identical coordinates.

Distance is defined as an object's total movement without regard for direction. Distance can be defined as how much ground an object has covered regardless of its starting or ending point.

Given,

The distance between Earth and Sun = 1.5 x 10^8 km

The distance between Sun and Mars = 2.28 x 10^8 km

Therefore the distance between Earth and Mars =

(1.5 x 10^8 + 2.28 x 10^8) km

= (1.5 + 2.28) x 10^8 km

= 3.78 x 10^8 km (Ans)

To learn more about decimal addition, refer to:

https://brainly.com/question/19127052

#SPJ10

By solving a linear equation, we will see that the two consecutive integers are -8 and -7

We know that the sum of an integer and 6 times the next consecutive integer is -50.

So if x is the integer, x + 1 will be the next consecutive integer, then we can write the equation:

x + 6*(x + 1) = -50

So we need to solve a linear equation, it will give:

x + 6x + 6 = -50

7x + 6 = -50

7x = -50 - 6

7x = -56

x = -56/7 = -8

Then the next integer is:

x + 1 = -8 + 1 = -7

Learn more about linear equations:

https://brainly.com/question/1884491

#SPJ1

Answer:

Your answer is [tex]10x + 5[/tex]

Step-by-step explanation:

A coefficient is the number before the variable, in this case, 10.

A constant is the number with no variable attached to it, in this case, 5.

Given:

The length of the parallel sides,

a=17.4 m

b=44.1 m

The height, h=23.5 m

The measurements of the other two sides are,

c=27.5m and d=26.6m.

To find the area of the trapezium:

Using the formula,

Hence, the area of the figure is 722.6 sq. m (rounded to the nearest tenth).

To find the perimeter of the trapezium:

Hence, the perimeter of the figure is 115.6 m.

Answer:

b)

Step-by-step explanation:

2x+y=7

2x=7-y

x=(7-y)/2

Answer: B

Step-by-step explanation:

n

Step-by-step explanation:

ab + 3c = 2x

Subtract 3c from both sides

ab = 2x - 3c

Isolate b by dividing by a

b = (2x -3c)/a

The equivalent expression to 3x - [tex]\frac{1}{2}[/tex]y + 2 [tex]\frac{2}{3}[/tex]y - [tex]\frac{5}{6}[/tex]x is C. 2 [tex]\frac{1}{6}[/tex]x + 2 [tex]\frac{1}{6}[/tex]y

An expression is simply used to show the relationship between the variables that are given in the data.

The fractions given will be illustrated as:

3x - [tex]\frac{1}{2}[/tex]y + 2 [tex]\frac{2}{3}[/tex]y - [tex]\frac{5}{6}[/tex]x

Collect like terms

= 3x - x + 2 [tex]\frac{2}{3}[/tex]y - [tex]\frac{1}{2}[/tex]y

= 2 [tex]\frac{1}{6}[/tex]x + 2 [tex]\frac{4}{6}[/tex]y - [tex]\frac{3}{6}[/tex]y

= 2 [tex]\frac{1}{6}[/tex]x + 2 [tex]\frac{1}{6}[/tex]y

In conclusion, the correct option is C.

Learn more about expressions on:

brainly.com/question/723406

#SPJ1

3. The slope of the line through the  points (0, 10) & (24, 6) is  [tex]\frac{1}{4}[/tex]

4. The slope of the line through the points (0, 6) & (20, 14) is  [tex]\frac{2}{5}[/tex]

The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope of a line, or a section of a line connecting two points, is a measure of its steepness.

Or. A line's slope is the ratio of how much y increases as x increases by some amount. The slope-intercept form of an equation is when the equation of a line is written in the form y = mx + b. The slope of the line is given by m. And b is the value of b in the y-intercept point (0, b).

How are the slopes calculated?

3. We know that , slope = m

[tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex](x_{1}, y_{1})=(0, 10)\\\\(x_{2}, y_{2})=(24, 16)[/tex]

[tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m= \frac{16- 10}{24 -0}\\\\m= \frac{6}{24}\\\\m=\frac{1}{4}[/tex]

4. We know that , slope = m

[tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex](x_{1}, y_{1})=(0, 6)\\\\(x_{2}, y_{2})=(20, 14)[/tex]

[tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m= \frac{14- 6}{20 -0}\\\\m= \frac{8}{20}\\\\m=\frac{2}{5}[/tex]

To learn more about slopes, refer:

https://brainly.com/question/3493733

#SPJ9

Answer:

p = 5 ; q = -11

Step-by-step explanation:

      [tex]\sf (a - b)^2 = a^2 + b^2 - 2ab\\\\(\sqrt{5}-3)^2 = (\sqrt{5})^2+3^2-2*\sqrt{5}*3[/tex]

                       [tex]\sf = 5 + 9 -6\sqrt{5}\\\\= 14 - 6\sqrt{5}[/tex]

[tex]\sf \dfrac{(\sqrt{5}-3)^2}{\sqrt{5}+1}=\dfrac{14-6\sqrt{5}}{\sqrt{5}+1}[/tex]

 Multiply the denominator and the numerator by (√5 - 1).

                 [tex]\sf= \dfrac{(14-6\sqrt{5})(\sqrt{5}-1)}{(\sqrt{5}+1)(\sqrt{5}-1)}\\\\\\= \dfrac{14*\sqrt{5}-14*1-6\sqrt{5}*\sqrt{5}+6\sqrt{5}*1}{(\sqrt{5})^2-1^2}\\\\\\=\dfrac{14\sqrt{5}-14-6*5+6\sqrt{5}}{5-1}\\\\\\=\dfrac{14\sqrt{5}+6\sqrt{5}-14-30}{4}[/tex]

                 [tex]\sf = \dfrac{(14+6)\sqrt{5}-44}{4}\\\\\\= \dfrac{20\sqrt{5}-44}{4}\\\\=\dfrac{20\sqrt{5}}{4}-\dfrac{44}{4}\\\\\\=5\sqrt{5}-11[/tex]

p = 5

q = -11

The provided expression is equivalent to the expression mentioned in option (C) is correct.

It is defined as the combination of constants and variables with mathematical operators.

The number expression is:

[tex]= \dfrac{\sqrt[4]{6} }{\sqrt[3]{2} }[/tex]

After applying the integer exponent property:

[tex]= \dfrac{\sqrt[4]{6} }{\sqrt[3]{2} } \times\dfrac{\sqrt[3]{2^2} }{\sqrt[3]{2^2} }[/tex]   (rationalization)

[tex]= \dfrac{\sqrt[4]{6} \times\sqrt[3]{2}}{2 }[/tex]

= [tex]\rm \dfrac{\sqrt[12]{55296} }{2}[/tex]

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

Thus, the provided expression is equivalent to the expression mentioned in option (C) is correct.

Learn more about the expression here:

brainly.com/question/14083225

#SPJ1

Answer:

10+15x=?

Step-by-step explanation:

x=every week

Answer: y=15x+10

Step-by-step explanation: the y is the amount of money he has, the x is the number of weeks, and the 15 shows he gets 15 dollars a week and the 10 shows he starts with 10$

Answer:

(-1,2),(-1,-3),(3,-3)

Step-by-step explanation:

You times the coordinate by 1/3

The equation that represents the relationship between the weight and number of oranges is [tex]w[/tex]·[tex]g=24.5[/tex]

What is an equation?

An equation is a formula which represents the equality between two expression.

We are given each orange weight the same.

Let the weight of one orange be [tex]w[/tex].

Also we are given that there are [tex]g[/tex] oranges in the crate

Also the weight of the crate is 24.5 pounds

Now the equation representing the relationship between weight and number can be given by

[tex]w[/tex]·[tex]g=24.5[/tex]

Hence the equation representing the relationship between weight and number can be given by [tex]w[/tex]·[tex]g=24.5[/tex]

To learn more about the equation please refer

https://brainly.com/question/22688504

#SPJ9

( 5,0 ) and ( 0,4 ) are the x and y-intercept of the function 4x + 5y = 20 respectively.

The intercept of a line on a graph is simply the point at which it intersects either the x-axis or y-axis.

Given the data in the question;

Now, we find the intercepts of the equation of line, plug in y = 0 and solve for x

4x + 5y = 20

4x + 5(0) = 20

4x = 20

x = 20/4

x = 5

Hence, the x-intercept is ( 5,0 )

For the y-intercept, plug in x = 0 and solve for y

4(0) + 5y = 20

5y = 20

y = 20/5

y = 4

Hence, the y-intercept is ( 0,4 ).

Therefore the x and y-intercept are ( 5,0 ) and ( 0,4 ).

Learn more about intercepts here: https://brainly.com/question/16861385

#SPJ1

Answer:

-17 would be three tick marks to the right of  -20

-11 would be 9 tick marks to the right of -20 or 6 right of the tick mark for -17

-2 would be 18 tick marks to the right of -20 or 15 tick marks to the right of -17 or 9 tick marks to the right of -11

Step-by-step explanation:

-20, -19, -18,-17      This is what -17 is three tick marks to the right of -20  

-20 -19 -18 -17 -16  -15 -14 -13 -12 -11      

-20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2

Answer:

6 students have their own cell phone and 3 of them can use social media.

Step-by-step explanation:

One fifth of 30 is 6. One half of six is 3.

The total yield for an acre, T, in pounds as a function of the number of walnut tree per acre, x is given by T = -1.5x² + 95x.

In order to solve this word problem, we would assign variables to the number of walnut tree per acre and total yield for an acre, and then translate the word problem into algebraic equation as follows:

Mathematically, the total yield for an acre can be calculated by using this mathematical expression:

Total yield for an acre (T) = yield of each tree × number of trees per acre

Substituting the given parameters into the mathematical expression, we have the following;

Total yield for an acre (T) = [50 - 1.5(x - 30)] × x

Opening the bracket, we have:

Total yield for an acre (T) = [50 - 1.5x + 45] × x

Total yield for an acre (T) = 50x - 1.5x² + 45x

Next, we would rearrange the function by collecting like terms and simplifying as follows:

Total yield for an acre (T) = -1.5x² + (50x + 45x)

Total yield for an acre (T) = -1.5x² + 95x

Read more on total yield here: https://brainly.com/question/18523197

#SPJ1

Answer:

17

Step-by-step explanation:

So, you start with division. 15/3=5, so you have 5+4x3

Then, you have to multiply. 4x3=12, so you have 5+12

Finally, you do 5+12, which is 17.

So, the simplified expression is 17.

Answer:

Step-by-step explanation:

Simplify the expression

15 ÷ 3 + 4 x 3​                (Remember PEMDAS)

5 + 12 =

17

Answer:

ans is 12/15

Step-by-step explanation:

cos= b\h b is 12 and h is 15

branliest ?

The coordinates along the directed line segment is (-4, 5/3)

This involves dividing a line into proportional ratios

The points are given as:

A  = (-7, 2)

B = (2, 1)

The ratio on the segment can be represented as;

m : n = 1 : 2

So, we have the coordinates of the point that lies along the directed line segment to be

Point = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)

So, we have:

Point  = 1/(1 + 2) * (1 * 2 + 2 * -7, 1 * 1 + 2 * 2)

Evaluate

Point  = 1/3 * (-12, 5)

Evaluate the products

Point  = (-4, 5/3)

Hence, the coordinates of the point is (-4, 5/3)

Read more about line partitions at:

brainly.com/question/17374569

#SPJ1

Answer:

3. ∠A = 110°

4. ∠H = 70°

5. ∠D = 70°

6. ∠F = 70°

Step-by-step explanation:

In a parallelogram, adjacent angles are supplementary (sum to 180°).

⇒ ∠A + ∠B = 180°

⇒ ∠A + 70° = 180°

⇒ ∠A = 110°

In a parallelogram, opposite angles are congruent.

⇒ ∠C = ∠A = 110°

⇒ ∠D = ∠B = 70°

If two parallelograms are similar, their corresponding interior angles are congruent.

⇒ ∠A = ∠E = 110°

⇒ ∠B = ∠F = 70°

⇒ ∠C = ∠G = 110°

⇒ ∠D = ∠H = 70°

The numbers of + and - signs tikes in the expressions given in the question are:

a) two - , and zero +

b) two - , and one +

c) one + , and one -

What is expression?

A finite collection of symbols that are correctly created in line with context-dependent requirements is referred to as an expression or a mathematical expression. Mathematical symbols can be used to represent variables, operations, functions, brackets, punctuation, and grouping. They may also be used to denote the operation order or other aspects of the logical grammar.

a) Given expression, (-2) + (-6)

When + and - signs comes together we can consider it as - sign only.

Therefore, there are two -, and zero +.

The the result of this expression is -8.

b) Given expression, (-2) + 4 + (-2)

When + and - signs comes together we can consider it as - sign only.

Therefore, there are two -, and one +.

the the result of this expression is -4.

c) Given expression, 5 + (-8)

When + and - signs comes together we can consider it as - sign only.

Therefore, there are one +, and one -.

the the result of this expression is -3.

To know more about expression, go to link

https://brainly.com/question/112703

#SPJ13