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The exponential function in the graph shows the population of Greeville in the years since 2010. What real-world information is given by the point (6, 2707)?
options:
The population in 2006
The population in 2010
The population in 2016
The year in which the population is twice the population in 2010

Final answer:

To solve the problem, we use a system of equations: x + y = 64 and y = x + 18. The smaller number is found to be x = 23, and the larger number is y = 41.

Explanation:

To find the two numbers where their sum is 64 and the larger number is 18 more than the smaller number, we can set up a system of equations. Let x represent the smaller number and y represent the larger number. We have the following equations:

x + y = 64

y = x + 18

We can substitute the second equation into the first one to solve for x:

x + (x + 18) = 64

2x + 18 = 64

2x = 64 - 18

2x = 46

x = 23

Therefore, the smaller number is 23, and the larger number is:

y = x + 18

y = 23 + 18

y = 41

Hence, the two numbers are 23 and 41.

Answer:

4%.

Step-by-step explanation:

We have been given that Ethan invested £500 in the bank for 2 years. He earned £40 simple interest in total. We are asked to find the annual interest rate.

We will use simple interest formula to solve our given problem.

[tex]I=Prt[/tex], where,

I = Amount of interest,

P = Principal amount,

r = Annual interest rate in decimal form,

t = Time in years.

Upon substituting our given values in above formula, we will get:

[tex]40=500*r*2[/tex]

[tex]40=1000*r[/tex]

Now, we will divide both sides of our given equation by 100.

[tex]\frac{40}{1000}=\frac{1000*r}{1000}[/tex]

[tex]\frac{4}{100}=r[/tex]

[tex]\frac{1}{25}=r[/tex]

[tex]0.04=r[/tex]

Since our given interest rate is in decimal form, so we need to convert it in percentage.

[tex]0.04\times 100\%=4\%[/tex]

Therefore, the simple interest rate per annum is 4%.

Answer:

A. x-axis

Step-by-step explanation:

It is a mirror image. The doesn't change.

The figure J'K'M' is just reflected over the x-axis.

So it is reflection about the x-axis.

Therefore, answer is A. x-axis

Hope this will helpful.

Thank you.

Functions can be represented verbally, algebraically, graphically, and numerically. A relationship is a function when for every input, there is exactly one output which is described by the vertical line test. Graphs for different types of functions vary in shape.

Functions can be represented in four various ways: verbally, algebraically, graphically, and numerically. For instance, verbal representation uses words to describe the function. Algebraically, we express the function via an equation. Graphically, we visually represent the function through graphs. Numerically, we represent the function using a table.

A relationship is a function if for every input, there is exactly one output. In a graph, this corresponds to an instance where a vertical line drawn anywhere on the graph would intersect it at only one point. This is also known as the vertical line test.

Examples of different types of functions graphically could include (a) a linear graph, showing a straight line, (b) a quadratic graph, parabolic in shape, (c) an inverse graph, where y decreases as x increases, and (d) an exponential graph, where the rate of growth is proportional to the function's current value.

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To solve for h, rearrange the equation to h = r - xy, and to solve for r, rearrange it to r = xy + h. This process involves basic algebraic manipulation to isolate each variable on one side of the equation.

The original equation given is x = r - h/y. To solve for h, we need to get h by itself on one side of the equation. First, we can rearrange the equation to isolate h:

To solve for r, we take the original equation and solve for r explicitly:

Now we have both variables solved in terms of x, y, and each other.

The ordered pair of [tex]X'[/tex] is  [tex](3,3)[/tex]

Explanation

According to the below diagram, the co ordinates of [tex]\triangle XYZ[/tex] are:  [tex]X(3, -1), Y(4,-4)[/tex] and [tex]Z(1,-2)[/tex]

The triangle [tex]XYZ[/tex] is reflected across the line  [tex]y=1[/tex]  to create triangle [tex]X'Y'Z'[/tex]

Distance of the point [tex]X[/tex] from the line  [tex]y=1[/tex]  is  2 units.

So, the point  [tex]X'[/tex]  will be also 2 units above the line  [tex]y=1[/tex]. As the triangle is reflected across a horizontal line, so the [tex]x[/tex] co-ordinate of the point will remain same.

[tex]y[/tex] co-ordinate of the point [tex]X'[/tex] will be:  [tex]y=1+2 =3[/tex]

So, the ordered pair of [tex]X'[/tex] is  [tex](3,3)[/tex]

The investment today is 17 times greater than it was ten years ago.

To find out how many times greater the value of the investment is today compared to ten years ago, you can divide the current value by the value ten years ago.

So, let's do the calculation:

Current value = 2.125 × 10^4 dollars

Value ten years ago = 1.25 × 10^3 dollars

[tex]\( \text{Times Greater} = \frac{\text{Current Value}}{\text{Value Ten Years Ago}} \)[/tex]

Substitute the values:

[tex]\( \text{Times Greater} = \frac{2.125 \times 10^4}{1.25 \times 10^3} \)[/tex]

To divide these numbers, subtract the exponents:

[tex]\( 10^4 \div 10^3 = 10^{4-3} = 10^1 = 10 \)[/tex]

So,

[tex]\( \text{Times Greater} = \frac{2.125}{1.25} \times 10 = 1.7 \times 10 = 17 \)[/tex]

Therefore, the value of the investment today is 17 times greater than the value of the investment ten years ago.

If a transversal is perpendicular to one of the two parallel lines, it is parallel to the other line.

Given:

Parallel lines: AB and CD

Transversal: EF

EF is perpendicular to AB

To prove: EF is parallel to CD

Since EF is perpendicular to AB, ∠AFE = 90°.

Since AB and CD are parallel, corresponding angles are equal: ∠AFE = ∠CFE.

Now, ∠CFE = 90° (since ∠AFE = 90°).

This means EF is perpendicular to CD.

By the converse of the perpendicular transversal theorem, EF is parallel to CD.

Adding 0.5 to each value in the data set increases the mean to 3.67 while the range remains at 1.4. Hence, the correct answer is option b.

When a constant is added to each data value in a data set, the mean of the data set increases by that constant, while the range remains unchanged. In this case, adding 0.5 to each data value will increase the mean by 0.5 but the range will stay the same.

Given the original mean: 3.17 and original range: 1.4:

New mean = 3.17 + 0.5 = 3.67

New range = 1.4

Therefore, the correct answer is option b: mean: 3.67; range: 1.4.

All I know is that Number One is TRUE.

Hope this is helpful :)

Answer:

The answer is D because if you made a number line you would contrast them and there you get 612.

Step-by-step explanation:

Your Welcome;)

"sides ln and np have the same slope." and "sides lm and mn are proportional to sides no and op." are correct for Triangle lmn is similar to triangle nop. both are right triangles.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

"Congruent" means the same

Two triangles are said to be congruent if they both have same length and same angles.

"Similar" means the area and sides will be proportional, it means when we divide or multiply with a number we get the measure of the other.

If triangle lmn is similar to triangle nop. both are right triangles.

Then we need to check which options will be correct and holds.

a. sides ln and np have the same slope it is correct because the triangle will have same slopes

b. It must not be true "sides ln and np are congruent" because as they are congruent the sides should be same.

c.  triangle lmn and nop are congruent, is not true because there measures are different.

d. As the triangles are similar " sides lm and mn are proportional to sides no and op." must be true, because of proportionality.

Hence "sides ln and np have the same slope." and "sides lm and mn are proportional to sides no and op." are correct for Triangle lmn is similar to triangle nop. both are right triangles.

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The total capacity of the container is 30 gallons in volume.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying it with the value of a single unit.

Given is that the container that holds the water for the football team is 7/10 full. After pouring out 6 gallons of water, it is 1/2 full.

Assume that the container total capacity is [x] gallons. Then, according to the question -

7x/10 - 6 = x/2

7x/10 - x/2 = 6

x(0.7 - 0.5) = 6

0.2x = 6

x = 6/0.2

x = 6/(1/5)

x = 30 gallons

Therefore, the total capacity of the container is 30 gallons in volume.

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Answer: The answer is the last figure, figure (D). Attached the image.

Step-by-step explanation:  We are given four pairs of polygons and we are to select the pair in which the two polygons are not similar.

In the first pair of polygons, the ratio of the corresponding sides will be same as follows:

[tex]\dfrac{2}{\frac{2}{3}}=\dfrac{4}{\frac{4}{3}}=3.[/tex]

So, the polygons are similar.

In the second pair of polygons, the ratio of the corresponding sides will be same as follows:

[tex]\dfrac{2.82}{1.41}=\dfrac{2.24}{1.12}=\dfrac{3}{1.5}=2.[/tex]

So, the polygons are similar.

In the third pair of polygons, the ratio of the corresponding sides will be same as follows:

[tex]\dfrac{1.41}{1.41}=\dfrac{1.12}{1.12}=\dfrac{1.5}{1.5}=1.[/tex]

So, the polygons are similar.

In the fourth pair of polygons, we have

[tex]\dfrac{12}{\frac{4}{3}}=12\times\dfrac{3}{4}=9,[/tex]

and

[tex]\dfrac{4}{\frac{2}{3}}=4\times\dfrac{3}{2}=6\neq 9.[/tex]

So, the polygons are not similar in this case.

Thus, the last figure, attached herewith, is the correct option.

All of the figures are pair of similar polygons

Similar shapes have the same shape but may differ in size.

Their corresponding angles are equal, and their corresponding sides are in proportion.

This property allows for resizing through a constant scale factor while maintaining identical angles.

We can test of the polygons are similar by checking the ratio of their corresponding sides are equal.

Fig 1 = 2/2/3 = 3

4/4/3 = 3

therefore the pair of polygons in fig1 are similar.

fig 2 = 3/1.5 = 2

2.82/1.41 = 2

therefore fig2 is a pair of similar polygons.

Therefore, all of the figures are pair of similar polygons

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Assuming it looks like this, here's your answer. For future reference of course.

Answer:

Two tangents.

Step-by-step explanation:

A circle is given and we have to draw the tangents on the circle from an external point P. By the definition we can draw only two tangents on a circle from an external point P and no tangent can be drawn form a point within the circle.

Therefore answer is two.