Help please? Which are the following key feature are the same for both functions.

Subtract 4x 4 x from 6x 6 x . Divide each term in 2x=−12 2 x = - 12 by 2 2 and simplify. Divide each term in 2x=−12 2 x = - 12 by 2 2 . Simplify the left side.

Answer:

8x^11

Step-by-step explanation:

x^8 * (2x)^3

x^8 * (8x^3)

8x^11

According to given information, x is 7.5 to the nearest tenth.

What is Triangle?

In geometry, a triangle is a two-dimensional closed shape with three straight sides and three angles. It is formed by connecting three non-collinear points with line segments. The three points of a triangle are called its vertices, and the line segments connecting them are called its sides.

If triangles ABC and DEF are congruent, then their corresponding sides are equal in length. Therefore, we have:

AB = DE = 41

BC = EF = 23

AC = DF = 36

We are given that BC = 4x - 7, so we can set up the following equation:

4x - 7 = BC = EF = 23

Solving for x, we get:

4x = 30

x = 7.5

Therefore, according to given information x is 7.5 to the nearest tenth.

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The sample suggests that the true mean is likely to be between 98.0°F and 98.2°F, which is lower than 98.6°F.  98.6°F overestimates the mean body temperature of all healthy humans.

Standard deviation is defined as the measure of how spread out numbers are. It measures the average distance between each number in a set of data and the mean. It is used to measure the variation and dispersion of a set of data from its mean.

A 99% confidence interval estimate of the mean body temperature for all healthy humans can be calculated using the following formula: mean ± 2*standard deviation/square root of the sample size. In this case, the confidence interval is 98.1°F ± 0.12°F. This means that the mean body temperature of all healthy humans is likely to be between 98.0°F and 98.2°F.

This sample suggests that 98.6°F is not an accurate representation of the mean body temperature of all healthy humans.

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Answer:

80

Step-by-step explanation:

This is because angles A, B, C, and D are all 40° and angle o looks to be bigger than 40° but is still an acute angle so forth being 80°

∠1 = 68°

∠2 = 22°

side 3 = 5 cm

side 4 = 19.5 cm

5: perimeter of ΔABC = 45 cm

6: perimeter of ΔPQR = 30 cm

7: Area of ΔPQR = 30 cm²

Similar triangles are triangles that have the same shape but may have different sizes. This means that corresponding angles of similar triangles are equal, and corresponding sides are in proportion.

The hotspots can be completed as follow:

∠1 = 180° - 22° - 90° = 68°  (angle sum in a triangle)

∠2 = 22° (similar triangle)

side 3 = √(13²-12²) = 5 cm (Pythagoras)

side 4 = √(18²+7.5²) = 19.5 cm (Pythagoras)

5: perimeter of ΔABC = AB + BC + AC = 7.5 + 19.5 + 18 = 45 cm

6: perimeter of ΔPQR = PQ + QR + PR = 5 + 13 + 12 = 30 cm

7: Area of ΔPQR = 1/2 * base * height = 1/2 * 12 * 5 = 30 cm²

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Answer: 4 steps: 12 feet

6 steps: 18 feet

12 steps: 36 feet

30 steps: 90 feet

Step-by-step explanation:

Let's say the cost to rent each chair is "x" and the cost to rent each table is "y". Then we can set up two equations based on the given information:

3x + 2y = 21 (for the first rental)

8x + 4y = 45 (for the second rental)

We can simplify the second equation by dividing both sides by 4:

2x + y = 11.25

Now we have two equations with two variables, which we can solve using substitution or elimination. Let's use substitution:

3x + 2y = 21

2x + y = 11.25

From the second equation, we can solve for y in terms of x:

y = 11.25 - 2x

Then we can substitute this expression for y in the first equation:

3x + 2(11.25 - 2x) = 21

Simplifying and solving for x, we get:

3x + 22.5 - 4x = 21

-x + 22.5 = 21

-x = -1.5

x = 1.5

So the cost to rent each chair is $1.50. We can substitute this value back into either of the original equations to solve for y:

3(1.5) + 2y = 21

4.5 + 2y = 21

2y = 16.5

y = 8.25

So the cost to rent each table is $8.25. Therefore, the answer is $1.50 for each chair and $8.25 for each table.

The GCF of p² and q² is 25. And the explanation is mentioned below.

The acronym GCF means "Greatest Common Factor." It is often referred to as the "Highest Common Factor" or the "Greatest Common Divisor" (GCD) (HCF). The biggest number that divides two or more other numbers without producing a residue is known as the GCF.

If the GCF of two numbers p and q is 5, then we can express the numbers as:

p = 5a

q = 5b

where a and b are integers, and 5 is the greatest common factor.

Now, let's consider p² and q²:

p² = (5a)² = 25a²

q² = (5b)² = 25b²

We can factor out 25 from both expressions:

p² = 25(a²)

q² = 25(b²)

Notice that the expression for p² has a factor of 25 and a factor of a², while the expression for q² has a factor of 25 and a factor of b².

Since the GCF of p and q is 5, we know that a and b do not have any common factors besides 1 and 5.

Therefore, a² and b² also do not have any common factors besides 1 and 5.

This means that the GCF of p² and q² is simply the factor of 25 that they have in common, which is 25.

So, the GCF of p² and q² is 25.

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Answer:

Step-by-step explanation:

To graph the function f(x) = x + 3, we need to plot a series of points that satisfy the equation. We can do this by picking some values of x and then finding the corresponding values of f(x).

For example, when x = 0, f(x) = 0 + 3 = 3. So we have the point (0, 3) on our graph.

Similarly, when x = 1, f(x) = 1 + 3 = 4. So we have the point (1, 4) on our graph.

We can continue this process for other values of x, and we'll get more points on the graph. For example, when x = -1, f(x) = -1 + 3 = 2. So we have the point (-1, 2) on our graph.

Once we have enough points, we can connect them with a straight line to get the graph of the function. In this case, we'll notice that the graph is a line with a slope of 1 and y-intercept of 3. The slope of the line tells us how much y changes when x increases by 1, and in this case, it changes by 1 unit.

So, to graph f(x) = x + 3, we can start by plotting the point (0, 3) and then draw a line that passes through this point and has a slope of 1. We can use a straightedge or ruler to draw the line as accurately as possible. The resulting graph will be a straight line that intersects the y-axis at the point (0, 3) and has a slope of 1.

Answer:

140in^2

Step-by-step explanation:

Split the area into 3 different shapes, and solve for the area of each (see picture below)

For the first area, the left triangle, we have a length of 4 and a height of 7. So we're going to multiply these two numbers together, then divide by 2 since we're only solving for the area of a triangle and not a rectangle. This gives us 14in^2.

Next, we can simply multiply 15 by 7 to get an area of 105in^2, since this is a rectangle.

For the last area, we can do the same thing as the first. Multiply 6 by 7, then divide by 2, giving us 21in^2.

Finally, we can add up all of these areas to get the total area, and our final answer:

14+105+21=140in^2

Answer:

R52200

Step-by-step explanation:

I'm making the assumption that R is a currency symbol.

There are 12 months in a year. Simply multiply the cost for one month by 12 to find the total cost for a year:

4350 * 12 = 52200

Answer:

I do not have access to drawing tools to create a graph. However, I can explain how to plot the function h on the graph based on the given information.

The function h(x) has two parts:

For x < -3, the value of h(x) is J-4.

For x >= -3, the value of h(x) is x-3.

To plot this on a graph, you would need to draw a vertical line at x = -3 to separate the two parts of the function. Then, for x < -3, you would plot a horizontal line at a height of J-4 to represent the constant value of h(x) in that region. For x >= -3, you would plot the line y = x-3.

I hope this explanation helps you to plot the function h on the graph!

Step-by-step explanation:

The conversion addition and subtraction of the numbers are done.

So, Solution are:

A. 900 p (into rupees)

1 rupee = 100 p

900 p = 9 rupees

B. 400 cm (into metre)

1 m = 100 cm

400 cm = 4.00 m

C. Rs. 27.70, Rs. 32.40 and Rs. 44.80 (Add)

=  Rs. 27.70 + Rs. 32.40 + Rs. 44.80

= 104.9

D. 9m 80 cm (into centimetre)

1 m = 100 cm

= 9m 80 cm

= 9m + 0.80m

= 9.8 m

E. 6480 m (into kilometres and metre)

1 m = 100 cm

6480 m

1 km = 1000m

6480 m = 6.480 km

F. Rs. 820.00 - Rs. 512.10 (Subtract)

Rs. 307.9

Thus, the unit conversion, addition and subtraction of the numbers are done.

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Answer:

11, 20.

Step-by-step explanation:

5,6,8, 11 ,15, 20.

If the woman receives $24 per day, the amount of the man's daily wage will be $42.

In mathematics, a ratio shows how many times one number contains another. Its says how much of one thing there is compared to another thing.

Let m be the man's hourly wage

Let w be the woman's hourly wage

We are told that the woman's daily wage is $24, which we can express in terms of her hourly wage as: w * 8 = $24

Solving for w, we get:

w = $24 / 8

w = $3

We are also told that the ratio of the man's hourly wage to the woman's hourly wage is 7:5, which we can express as: m / w = 7 / 5

Substituting w = $3, we get:

m / 3 = 7 / 5

Solving for m, we get:

m = (7 / 5) * 3

m = $4.20

Therefore, the man's daily wage is:

m * 10 = $4.20 * 10

m = $42

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Answer:

= 12q² - 3

Step-by-step explanation:

3(-4q² - 1)

= -12q² - 3

Answer:

Below

Step-by-step explanation:

A cube has SIX sides of equal area

  each side has area = L x W       and L and W are the same = 4.5 m

      so:   Area =   six   X   ( 4.5  X 4.5)  =   6 * 4.5 * 4.5 = 121.5 m^2

Answer:

Hope the picture will help you...

Answer: 2/3

Step-by-step explanation:   y1-y2    3-(-1) = 4       simplify  4/6=2/3

                                               x1-x2     4-(-2)= 6

Slope is described as "the rise over the run," meaning that it's the fraction of "the change in the y-values compared to the change in the x-values."

In this situation
    - the change in the y-values is 3 - (-1) = 4.
    - the change in the x-values is 4 - (-2) = 6.
so the fraction is 4/6 or 2/3.

As a general formula, the formula for slope is [tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex].

      [tex]m = \dfrac{3-(-1)}{4-(-2)}=\dfrac{4}{6}=\dfrac{2}{3}[/tex]

The first thing to do to each side of the equation so that there would be no fractions is to cross product.

The unknown number, a is -48

A fraction refers to a number which has a numerator (top value) and a denominator (bottom value).

2(a - 7) / 15 = (a + 4) / 6

cross product

6{2(a - 7)} = 15(a + 4)

open parenthesis

6(2a - 14) = 15a + 60

12a - 84 = 15a + 60

combine like terms

12a - 15a = 60 + 84

-3a = 144

divide both sides by -3

a = 144/-3

a = -48

In conclusion, the solution to the fraction is a = -48

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Answer:

Step-by-step explanation:

a. a polynomial that represents the area οf the picture including the frame [tex]\mathrm{A = (x + 2w) \times (x + 2w) = (x + 2w)^2}[/tex]

b.  The area οf the picture including the frame when the width οf the frame is 2 inches is [tex](x + 4)\²[/tex]

The English wοrd "polynomial" is derived from the Greek words "poly" and "nominal," which together denote "many sentences". The number of terms a polynomial can have is unbοunded.

a. Let x be the width οf the picture. Then the length of the picture is alsο x. Let w be the width οf the frame. The total width of the picture including the frame is (x + 2w), and the tοtal length of the picture including the frame is (x + 2w). Therefοre, the area of the picture including the frame is:

[tex]\mathrm{A = (x + 2w) \times (x + 2w) = (x + 2w)^2}[/tex]

b. If the width οf the frame is 2 inches, then w = 2. Substituting w = 2 into the polynomial above gives:

[tex]\mathrm{A = (x + 2w) \times (x + 2(2)) = (x + 4)^2}[/tex]

Therefore, the area οf the picture including the frame when the width οf the frame is 2 inches is (x + 4)² square units.

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Answer:

d = |c1-c2|/√(a2 + b2).

Step-by-step explanation:

Answer:

Step-by-step explanation:

After one year, Devon's income will have grown by 2.9%. However, because inflation is 3.1%, the purchasing power of his income will decrease. This means that Devon will be able to buy less than he could today.

To calculate how much Devon can buy with his annual income after one year, we can use the following formula:

Purchasing power = Income / (1 + inflation rate)

Substituting the values given in the problem:

Purchasing power after one year = Income / (1 + 0.031)

Purchasing power after one year = Income / 1.031

Therefore, Devon will be able to buy approximately 0.97 times (or 97% of) what he could buy with his income today. In other words, his purchasing power will have decreased by approximately 3%.

Answer:

Devon's annual income increases at a rate of 2.9% per year, which means that after one year, his income will be 1.029 times his current income. However, due to inflation of 3.1% per year, the purchasing power of money decreases, which means that after one year, the amount of goods and services that can be purchased with the same amount of money will be 1/1.031 times what it is today.

Therefore, after one year, Devon can buy (1.029/1.031) times what he can buy today with his annual income. Simplifying this expression gives:

1.029/1.031 = 0.9971

So, Devon can buy about 99.71% of what he can buy today with his annual income after one year. In other words, he can buy slightly less than he can buy today, because inflation is greater than the rate at which his income is increasing.

Answer: 5/18.  or 5 over 18

Step-by-step explanation:

5 is the number of kids that want pancakes

13 is the number of kids that want waffles

18 is the total number of students

The question is asking what is the ratio of the number of students who want pancakes to the total number of students?

So you just do

5 kids that want pancakes over 18 kids total or 5/18

The greatest sum is 271.05, the greatest difference is 215.3, the greatest product is 11535.175, and the greatest quotient is approximately 4.142.

A numeral system is a way of writing numbers; it's a way of mathematically notating a set of numbers by using a consistent set of digits or other symbols.

To find the greatest sum, difference, product, and quotient using two of the given numbers, we can compare the results of each operation by pairing the numbers in different ways.

Note: For the quotient, we will only consider pairs of numbers where the denominator is not zero.

Sum:

The greatest sum will be obtained by adding the two largest numbers, which are 218.3 and 52.75.

218.3 + 52.75 = 271.05

Difference:

The greatest difference will be obtained by subtracting the smallest number from the largest number, which is 218.3 and 3.

218.3 - 3 = 215.3

Product:

The greatest product will be obtained by multiplying the two largest numbers, which are 218.3 and 52.75.

218.3 × 52.75 = 11535.175

Quotient:

The greatest quotient will be obtained by dividing the two largest numbers, which are 218.3 and 52.75.

218.3 ÷ 52.75 ≈ 4.142

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The vertex of the function is,

⇒ Vertex = (1, - 4)

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The function is,

⇒ f (x) = -x² + 2x - 5

Now,

We can change the quadratic function in the form,

⇒ f (x) = a (x - h)² + k

Hence, We get;

⇒ f (x) = - x² + 2x - 5

⇒ f (x) = - (x² - 2x + 1 - 1) - 5

⇒ f (x) = - (x - 1)² + 1 - 5

⇒ f (x) = - (x - 1)² - 4

Thus, The vertex of the function is,

⇒ Vertex = (1, - 4)

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The solution to the system of equations is x = 1.8, y = 0.4.

To graph the second equation, we can start by plotting the y-intercept of -1 on the y-axis. Then, using the slope of -1/3, we can find another point on the line.

For example, we can move down one unit and to the right three units from the y-intercept, which gives us the point (3,-2).

Graph of the two equations:

y = −2x + 4,

y = − 1/3x − 1

From the graph (check the image attached), we can see that the two lines intersect at the point (1.8, 0.4).

Therefore, the solution to the system of equations is x = 1.8, y = 0.4.

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The complete question is below:

The first equation from the previous system of equations is graphed. Graph the second equation to find the solution of the system of equations.

y = −2x + 4,

y = − 1/3x − 1

What is the solution to the system?

The greatest inference we can draw from the data presented and the dot plot, however, is that there is proof indicating that Drug A is much more likely than Drug B to increase levels of human growth hormone.

the process of developing; progressive expansion; the act or activity of growing.

According to the provided dot plot, there appears to be a considerable variance in both medications' capacities to raise levels of human growth hormone. There is little crossover in the pieces of data for the two medicines, and the mean rise for Drug A is obviously greater than the average rise for Drug B.

We would need to do a formalized hypothesis test, which might involve a t-test, and generate a p-value to establish to see if this variance has statistical significance. We could conclude that the variation in averages is statistically significant if the p-value is less than a predetermined significance criterion (for example, 0.05).

The most important conclusion that can be made from the data and dot plot is the existence of evidence that suggests Drug A is much more probable that Drug B to enhance levels of growth hormone in humans. Further statistical analysis would be required to confirm the relevance of this divergence.

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Answer:

See below.

Step-by-step explanation:

We are asked to simplify the equation.

First, we should Combine Like Terms.

Combining Like Terms is adding terms that are alike.

For example, 4x and 11x are like terms since there's no differences than the coefficient, which can be different.

Let's combine like terms for this problem now.

Combine Like Terms:

[tex]\frac{2}{5} x+ 7 - \frac{2}{3} x -15\\\\\frac{2}{5} x - \frac{2}{3} x = \frac{6}{15} x - \frac{10}{15} x=-\frac{4}{15} x\\\\7 - 15 = -8[/tex]

We should have;

[tex]- \frac{4}{15} x - 8[/tex]

This will be our final answer.