Which graph represents an exponential growth function?

Answer:

We can start by using algebra to represent the given information in the problem in terms of variables. Let x be the cost of each candy bar. Then we can write the following equation:

3 + 7x = 31

This equation states that the total cost of the soft drink and the candy bars is $31, and the cost of the candy bars is 7 times the cost of each candy bar.

Now we can solve for x, the cost of each candy bar:

3 + 7x = 31

7x = 31 - 3

7x = 28

x = 28/7

x = 4

Each candy bar cost $4.

We can also check this by substituting this value back into the original equation to see if it is true:

3 + 7(4) = 31

3 + 28 = 31

31 = 31

This confirms that the cost of each candy bar is $4.

Step-by-step explanation:

Answer:

x = 7

Step-by-step explanation:

given f(x) = 3x - 1 and f(x) = 20, then equate the right sides to find x

3x - 1 = 20 ( add 1 to both sides )

3x = 21 ( divide both sides by 3 )

x = 7

Answer: x = 7

Step-by-step explanation:

f (x) = 20 eq_i

f (x) = 3x - 1 eq_ii

eq_i = eq_ii

20 = 3x - 1

3x = 20 + 1

x = 21 ÷ 3

x = 7 answer

hope that helps...

The amount that Pham will have to pay back is $8,602.80

The formula to calculate the compound interest is:

A = P(1 + r/n)^nt

Where A is the amount of the loan including interest, P is the principal or the initial amount borrowed, r is the interest rate, t is the number of years the loan is taken out for and n is the number of times the interest is compounded per year.

In this case, we know that:

P = $6,000

r = 6% (expressed as 0.06)

t = 72/12 = 6 (since the loan is for 72 months, or 6 years)

n = 1 (the interest is compounded annually)

So the formula becomes:

A = 6000(1 + 0.06)⁶

A = 6000(1.06)⁶

A = 6000 * 1.4338

A = $8,602.80

Therefore, Pham will have paid back $8,602.80, including interest, if he pays off the loan in 72 months.

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Logarithm is a mathematical operation that is the inverse of exponentiation. It is denoted by log b (x), which means the logarithm of x to base b.

For example, log2 8 = 3, since 23 = 8. Logarithm is useful in solving equations that involve exponential terms.

The properties of logarithm are:

1. log b 1 = 0: This property states that the logarithm of 1 is zero for any base b.

2. log b b = 1: This property states that the logarithm of any base b is 1.

3. log b (xy) = log b (x) + log b (y): This property states that the logarithm of the product of two numbers is equal to the sum of the logarithms of the two numbers. For example, log2 (8x32) = log2 8 + log2 32 = 3 + 5 = 8.

4. log b (x/y) = log b (x) - log b (y): This property states that the logarithm of the quotient of two numbers is equal to the difference of the logarithms of the two numbers. For example, log2 (8/32) = log2 8 - log2 32 = 3 - 5 = -2.

5. log b c = clog b (c): This property states that the logarithm of a number c to the base b is equal to c times the logarithm of b. For example, log2 32 = 32log2 2 = 5.

These properties of logarithm are very useful in solving mathematical problems involving exponential terms.

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Answer:

66, 68, 70, 72

Answer:

66 68 70 72

Step-by-step explanation:

it is what it is

Answer: Katie is 9 years old now. ✅

Step-by-step explanation:

By using the second equation, we can find that k = e+4,

then we can substitute k = e+4 into the first equation

k-9 = 2(e-9)

e+4-9 = 2(e-9)

e-5 = 2e-18

5 = e

so k = e + 4 = 5 + 4 = 9

Therefore, Katie is 9 years old now.

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The depreciation Straight Line Method charges a fixed depreciation amount on an annual basis for the duration of an asset. The original cost is the basis for computing the annual depreciation, which is constant year over year. This approach is additionally referred to as the "Original Cost method" or the "Fixed Instalment method."

What is straight line method answer?

  The value of an asset is steadily decreased via the Straight Line Method (SLM) of Depreciation until it reaches its scrap value. Depreciation is subtracted from the asset's value on an annual basis in a specified amount.

Why is the straight-line approach used?

The straight line approach is popular with accountants because it is simple to apply, produces fewer errors during the asset's lifetime, and costs the same amount for each accounting period.

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Answer:

x<-13 or x>-3

Step-by-step explanation:

solve 9 abs(x + 8)>45 = x<-13 or x>-3

Answer:

15

Step-by-step explanation:

Since the sum of all angles in a triangle is 180, we can make an equation

111 + 44 + 2x - 5 = 180

2x - 5 = 25

2x = 30

x = 15

The average depth of the Atlantic Ocean is given by the equation

A = 12,880 feet

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Let the average depth of the Atlantic ocean be A

From the graph the sum of the Atlantic Ocean’s average depth (in feet) and its greatest depth is 43,126 feet

The greatest depth of the Atlantic ocean is D = 30,246 feet

So , the equation will be

A + D = 43,126 feet   be equation (1)

Substituting the values in the equation , we get

A + 30,246 = 43,126

On simplifying the equation , we get

Subtracting 30,246 on both sides of the equation , we get

A = 43,126 - 30,246

A = 12,880 feet

Therefore , the value of A is 12,880 feet

Hence , the average depth is 12,880 feet

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The smaller sail boat's height, x, is 10.5 inches.

Congruence describes two triangles that have the same number of sides and angles on each side.

The two sails in the hypothetical situation have the same sides, and their proportions are:

7/8 = x/12

x = 12.7 / 8

x = 10.5

Thus, the smaller sail boat's height, x, is 10.5 inches.

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The complete question is-

Hays build model sailboats as a hobby. The dimensions of the sailboats are given. What is the height, x, of the smaller sailboat's sail? Enter your answer, as a decimal, in the box. x = in. Two sailboats with sails that are right triangles.  The top angle on the sails are marked congruent to each other. The smaler sail has a a height of x and a base of 7 inches. The lareger sail has a height of 12 inches and a base of 8 inches.

Answer:

  (d)  24,057

Step-by-step explanation:

Starting with 11 bacteria in a culture that triples in size every hour, you want to know the number grown in the 7th hour.

In hour 0, we have 11, and the growth factor per hour is 3. That means the population can be modeled by ...

  p = 11·3^t

where t is in hours.

In the 7th hour, the population will grow to 11·3^7 = 24,057.

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The additive inverse of 11 /- 25 is -11 /+ 25. This means that the two numbers have opposite signs and the same absolute value.

The additive inverse of a number is the number that, when added to the original number, results in a sum of zero. In other words, the two numbers have opposite signs and the same absolute value. For example, the additive inverse of 11 /- 25 is -11 /+ 25. This is because when adding 11 /- 25 and -11 /+ 25 together, the negative and positive signs cancel each other out and the absolute values add up to zero. The same concept applies to all numbers, not just integers. For example, the additive inverse of 4.7 is -4.7. When 4.7 and -4.7 are added together, the sum is 0. As such, the additive inverse of any number can be calculated by changing the sign of the number and leaving the absolute value the same.

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Using the change of base formula log base b of y equals log y over log b x = 4.69743.

To solve 3x + 1 = 15 for x, we can use the change of base formula, which states that log base b of y equals log y over log b. In this case, we can use log base 3 on both sides of the equation to solve for x.

First, we take the log base 3 of both sides of the equation:

log base 3 (15) = log base 3 (3x + 1)

Next, we can use the property of logarithms, which states that log base b (xy) = log base b (x) + log base b (y):

log base 3 (15) = log base 3 (3) + log base 3 (x + 1/3)

We can solve for x by subtracting log base 3 (3) from both sides of the equation:

log base 3 (15) - log base 3 (3) = log base 3 (x + 1/3)

We can then use the change of base formula to solve for x:

log 15/3 = log x + 1/3 over log 3

We can then solve for x by taking the antilog of both sides of the equation:

15/3 = x + 1/3

We can then solve for x by subtracting 1/3 from both sides of the equation:

15/3 - 1/3 = x

Finally, we can solve for x by dividing both sides of the equation by 3:

x = (15/3 - 1/3) / 3

Therefore, x = 4.69743.

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The rate of change of y with respect to x will be equal to 8 when there is a linear relationship between x and y.

The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one item by the equal amount of change in another. The relationship defining how one quantity changes in relation to the change in another quantity is given by the rate of change formula.

The rate of change is given by the formula:

Here, the value of points are (-2.5,-30) and (-1,-18)

Now, substituting these values in the formula, we get

Rate of change=

= 8

Hence, the rate of change of the y with respect to x will be equal to 8 when there is a linear relationship between x and y.

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Answer:

ab-ac

Step-by-step explanation:

a(b-c)=ab-ac

Therefore , the solution of the given problem of surface area comes out to be 46.80909  inch square.

The amount of space it occupies on the surface is a decent indication of its overall size. The complete surroundings is taken into account when calculating the area of a tri shape. Something's total size is determined by its surface area. The volume of water inside a cuboid is equal to the total of the volumes on each and every six of its rectangular sides. To calculate the box's measurements, use the formula below: In 2lh, 2lw, and 2hw, the region is identical (SA). The surface area of the multipurpose shape represents the region.

Here,

Given :

Length = 5 inches

Width = 3 inches

and

height = 2.5 inche

To find the total surface area for triangular prism

=>A=ah+bh+ch+1/2 √﹣a⁴ +2(ab)² +2(ac)²﹣b⁴+2(bc)² c⁴

=> 5·2.5+3·2.5+5·2.5+1/2√﹣5⁴+2·(5·3)²+2·(5·5)²﹣34+2·(3·5)²54

=> 46.80909 inch square

Therefore , the solution of the given problem of surface area comes out to be 46.80909  inch square.

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The area of the partial circle with a radius of 8 cm = 150.72 [tex]cm^{2}[/tex], then the we can use  [tex]\pi =3.14[/tex] value.

The circle is missing 1/4, so the area of it is just 3/4 of the whole area of the circle.

Area of a circle is the region occupied by the circle in a two-dimensional plane.

It can be determined easily using a formula, A = [tex]\pi r^{2}[/tex] , (Pi r-squared) where r is the radius of the circle.

The unit of area is the square unit, such as [tex]m^{2}[/tex], [tex]cm^{2}[/tex], etc.

Area of Circle = [tex]\pi r^{2}[/tex] or [tex]\frac{\pi d^{2} }{4}[/tex], square units. where π = 22/7 or 3.14.

Area of a circle,

A = [tex]\pi r^{2}[/tex]      (Equation-1)

Where,

r = radius

Given that,

r = 8cm

We can substitute equation-1,

A = [tex]\pi 8^{2}[/tex] cm * cm

A = [tex]64\pi[/tex] [tex]cm^{2}[/tex]

So,

We can write,

Whole one quarter,

[tex]\frac{4}{4} -\frac{1}{4}[/tex] [tex]=\frac{3}{4}[/tex]

We can get,

= [tex]\frac{3}{4} *64\pi[/tex]

= 48[tex]\pi[/tex]

We can substitute [tex]\pi =3.14[/tex] value,

Then,

= 48 * 3.14

= 150.72 [tex]cm^{2}[/tex]

Therefore,

The area of the partial circle with a radius of 8 cm = 150.72 [tex]cm^{2}[/tex], then the we can use  [tex]\pi =3.14[/tex] value.

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To graph 3-dimensional coordinates, you will need a 3-dimensional graph or plot. As with 2-dimensional coordinates, each point is labeled with three coordinates (x, y, z). You can then plot the point on a 3-dimensional graph by connecting the x, y and z coordinates with 3 lines.

1. Determine the coordinates of the point you want to plot.

2. Draw 3 axes on a graph paper or use a 3D graph on your computer.

3. Label each axis with the corresponding coordinate (x, y, z).

4. Plot the point by connecting the corresponding coordinates with 3 lines.

5. Add labels to the point to indicate which point it is and what the coordinates are.

To graph 3-dimensional coordinates, you will need a 3-dimensional graph or plot. As with 2-dimensional coordinates, each point is labeled with three coordinates (x, y, z). You can then plot the point on a 3-dimensional graph by connecting the x, y and z coordinates with 3 lines.

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Answer:

x = 3

Step-by-step explanation:

6x = 18

Divided both sides by 6

x = 3

Let's check

6(3) = 18

18 = 18

So, x = 3 is the correct answer.

Answer:

x = 3

Step-by-step explanation:

1) 6x = 18

2) Divide by 6.

6x = 18

6 6

x = 3

Answer:

Your Domain Will be (6,-12,-6,20)

Your Range will Be 36

Sorry i dont have work shown i just remember doing this problem and just gave answers glad to help and stay safe

Answer:

Domain: {6, -12, -6, 20}

Range: {0, -16 , 10 , -7}

Step-by-step explanation:

Domain and Range:

Domain: In the set of ordered pairs, domain is all the x-values.

Range: In the set of ordered pairs, range is all the y-values

Domain: {6, -12, -6, 20}

Range: {0, -16 , 10 , -7}

Answer:

1) The trick to making these fractions equivalent is to make sure they have the same denominator. to do this you need to know your multiplication facts. These are the multiples when you multiply two numbers together.

2) Since 24 is the largest denominator, you need the smallest denominator into 24ths, which you do by multiplying 8 x 3, giving you 24.

3) Whatever you do to the denominator, you do to the numerator, so multiply 5 x 3, which is 15.

4) New fraction for 5/8 becomes 15/24.

5) So 5/8 is equivalent. to 15/24.

Step-by-step explanation:

5/8 = x/24

5 x 3 = 15

8 x 3 24

Proof: Reduce 15/24 by dividing 3 into both numbers (15÷3) and (24÷3) = 5/8.

On solving the provided question, we can say that the money they would raise if they sell 1000 tickets will be given the equation that is  y = 24R/10

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

the money they would raise if they sell 1000 tickets

will be given the equation that is

M = 24/10R

y = 24R/10

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To enlarge a triangle by a scale factor greater than 1, identify the center of enlargement, multiply the coordinates of each point by the scale factor, connect the new points, and check the side lengths will be greater.

To enlarge a triangle with a center of enlargement, you can use the following steps:

It's important to note that in order to keep the triangle congruent during the dilation, the center of enlargement must be the centroid of the triangle and the scale factor should be the same for all the points of the triangle.

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Answer:

Slope intercept form is y = -x+7

Standard form is x+y = 7

Both forms represent the same line, just written in different ways of course.

The graph is shown below.

=====================================================

Explanation:

Let's check the answer you got.

The equation -1x+y=1 is the same as -x+y = 1

Plug the coordinates of the first point into this equation

-x+y = 1

-3+4 = 1

1 = 1

The first point is on the line -x+y = 1

Repeat similar steps for the other point

-x+y = 1

-(-1)+8 = 1

1+8 = 1

9 = 1

The two sides don't match up. We need the same number on both sides to get a true equation. The false equation tells us that (-1,8) is not on the line -x+y = 1.

In short, this rules out -x+y = 1 being the answer.

The next section will show one way to find the answer.

--------------------------------

First we'll need the slope of the line through (3,4) and (-1,8)

[tex](x_1,y_1) = (3,4) \text{ and } (x_2,y_2) = (-1,8)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{8 - 4}{-1 - 3}\\\\m = \frac{4}{-4}\\\\m = -1\\\\[/tex]

Then I'll use the y = mx+b template to find b. For the (x,y), use either point given to you. I'll use (3,4).

So,

y = mx+b

4 = -1*3+b

4 = -3+b

4+3 = b

7 = b

b = 7

We found that m = -1 and b = 7.

We go from y = mx+b to y = -1x+7 aka y = -x+7 which is the answer in slope intercept form.

To convert to standard form Ax+By = C, add x to both sides. The goal is to get the variable terms to one side, and the constant isolated on its own side.

y = -x+7

y+x = -x+7+x

x+y = 7 is the answer in standard form

--------------------------------

Check:

Plug (x,y) = (3,4) into the equation to see if we get a true result.

x+y = 7

3+4 = 7

7 = 7

That works out. Now do the other pair of coordinates (-1,8).

x+y = 7

-1+8 = 7

7 = 7

That works as well. The answers are fully confirmed to be correct.

If you wanted, you can use the equation y = -x+7 as the way to check the answer. It's up to you which you prefer better if it's slope-intercept or standard form.

Yet another way to check the answer is to use a graphing tool like GeoGebra. It's something I use all the time. See the screenshot diagram below.

Answer: 25,000

Step-by-step explanation: 125,000 x 0.2 = 25,000

So, on solving the question we can say here, in equation we have, (10x - 20) = 7x + 4; 3x = 24; x = 8

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

here, in equation we have,

(10x - 20) = 7x + 4

3x = 24

x = 8

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The absolute value of the complex number z = 2∠45° is therefore equal to 2.

Value can be defined as the worth of something, which may be monetary, social, or personal. It is an intangible concept that is based on individual beliefs and opinions. Value can be determined by considering the utility, quality, scarcity, desirability, and other factors associated with an item. Values can be measured in terms of tangible goods, such as money, or in terms of intangible goods, such as love or honor.

The absolute value of a complex number in polar form is the magnitude of the complex number. It is also referred to as the modulus of the complex number. To find the absolute value of a complex number in polar form, we need to use the following equation:

Absolute Value = r = |z| = √(a² + b²)

Where 'r' is the absolute value of the complex number, 'z' is the complex number, and 'a' and 'b' are the real and imaginary parts of the complex number respectively.

For example, if we have a complex number in polar form, such as z = 2∠45°, then the absolute value of the complex number is calculated by taking the square root of the sum of the squares of the real and imaginary parts:

Absolute Value = r = |2∠45°| = √(2² + 0²) = 2

The absolute value of the complex number z = 2∠45° is therefore equal to 2.

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The required representation of given number line is x ∈ (-10,  ∞).

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities, is at the core of social justice theories. However, because it frequently means different things to different people, it is prone to confusion in public discourse.

We have number line,

By using baby curve method.

The representation of the line is ,

Let the line is x axis

Then

x ≥-10

x ∈ (-10,  ∞)

Thus, the required inequality is  (-10,  ∞).

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