Consider the function f(x) = 2^x
and function g
g(x) = f(x) + 6
How will the graph of function g differ from the graph of function ?

Answers:

Team A = 175 people

Team B = 150 people

This is before the 45 students transfer from A to B.

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

Explanation:

x = number of people in team A

y = number of people in team B

These counts are before the 45 pupils transfer from A to B.

The counts are in ratio 7:6, which means,

x/y = 7/6

6x = 7y

x = 7y/6

If we subtract 45 people from team A, we have x-45 people left. Those 45 people go to team B to have y+45 pupils there.

The quantities x-45 and y+45 are in ratio 2:3, so,

(x-45)/(y+45) = 2/3

3(x-45) = 2(y+45)

3x-135 = 2y+90

3(7y/6)-135 = 2y+90 .... plug in x = 7y/6

21y/6 - 135 = 2y+90

6*( 21y/6 - 135 ) = 6*(2y+90)

21y-810 = 12y+540

21y-12y = 540+810

9y = 1350

y = 1350/9

y = 150

x = 7y/6

x = 7(150)/6

x = 175

We have 175 people on team A, and 150 people on team B.

This is before the 45 students transfer from A to B.

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

Check:

x/y = 175/150 = (7*25)/(6*50) = 7/6

This shows x and y are in ratio 7:6 to match the instructions.

x-45 = 175-45 = 130

y+45 = 150+45 = 195

(x-45)/(y+45) = 130/195 = (2*65)/(3*65) = 2/3

And we have the updated counts in the ratio 2:3, which matches the stated info in the instructions. The answers are fully confirmed.

Answer:

LCD is the abbreviation for Least Common Denominator.

Step-by-step explanation:

To find the LCD of two numbers, you list out the multiples of each number. Then you look for the smallest multiple of both numbers and there you have it!

For example, if we had to find the LCD of 4 and 3, we'll first list out the multiples of both.

4: 4, 8, 12, 16, 20, ...

3: 3, 6, 9, 12, 15, ...

The first least multiple we found in those two numbers is 12.

Therefore, the LCD would be 12.

The lowest temperature with a z score of of -2.49 is 24.0 ˚F

Z scores, measures the amount of standard deviation sample X is from mean. the formula is below

z = (X - μ) / σ

Definition of variables

mean, μ = 4.4˚F

standard deviation, σ = 12.2 ˚F

X = lowest temperature

z = -2.49

substituting into the formula

-2.49 =  (X - μ) / σ

-2.49 = (X - 64.4) / 12.2

-2.49 * 12.2 = X - 64.4

-30.378 + 64.4 = X

X = 34.022

X = 34.0  (to one decimal place)

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The hypotenuse leg theorem states that two right triangles are congruent if the hypotenuse and one leg of one right triangle are congruent to the other right triangle's hypotenuse and leg side.

What is the hypotenuse leg theorem?

The hypotenuse leg theorem states that two right triangles are congruent if the hypotenuse and one leg of one right triangle are congruent to the other right triangle's hypotenuse and leg side.

The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

Hypotenuse-Leg (HL) for Right Triangles. There is one case where SSA is valid, and that is when the angles are right angles. In words, if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the triangles are congruent.

Hence, if the hypotenuse leg theorem states that two right triangles are congruent if the hypotenuse and one leg of one right triangle are congruent to the other right triangle's hypotenuse and leg side.

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Prices of two ratios in the ratio is 4 : 1.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio. The part-to-part ratio denotes how two distinct entities or groups are related.

For example, the ratio of boys to girls in a class is 12: 15, whereas, the part-to-whole ratio denotes the relationship between a specific group to a whole.

For example, out of every 10 people, 5 of them like to read books. Therefore, the part to the whole ratio is 5: 10, which means every 5 people from 10 people like to read books.

Let us assume price of radios are x and y

According to the question

[tex]\frac{x + 20}{y+20} =\frac{5}{2}\\2x+40=5y+100\\2x-5y=60[/tex]-------------------------- eq(1)

and

[tex]\frac{x-5}{y-5} =\frac{5}{1}\\5y-x = 20[/tex]

5y-x = 20

multiplying this equation by 2

we get

10y-2x = 40 ------------------ eq(2)

adding eq 1 and 2

we get

5y=100

y=20

solving further we get x=80

Thus the ratio is 4 : 1.

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The larger circle is, half of the line is used to form one large circle.

What is split in half?

To split or cause to split, especially violently, by cleaving into distinct pieces, typically into two nearly equal ones.

To split into a lesser number of things neatly or equally. The mirror collapsed and broke into three almost identical pieces.

Here, a 100-unit-long line is split in half.

That means a line is divided into two equal part with length 50 unit each.

Also, half of the line is used to form one large circle. The other half forms two identical smaller circles.

From this we can see that  half of the line is used to form one large circle is always a lager circle.

And other half forms two identical smaller circles are the smaller circles.

Hence, the larger circle is, half of the line is used to form one large circle.

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The selling price of the radio with a cost price of 550 and sold at a profit of 35 is 585.

The selling price is how much a buyer pays for a product or service.

To calculate the selling price of the radio, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the selling price of the radio is 585.

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The probability of advancing five spaces is 0.2307.

Given that, the odds in favor of advancing five spaces are 3/10.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

The probability of advancing five spaces can be obtained as:

P =Odds/1+Odds

= [tex]\frac{\frac{3}{10} }{1+\frac{3}{10} }[/tex]

= [tex]\frac{\frac{3}{10} }{\frac{13}{10} }[/tex]

= 3/13

= 0.2307

Therefore, the probability of advancing five spaces is 0.2307.

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With percent increase or decrease situations, you have to consider the starting point as being 100%.  So if the account increased by 27%, it's now 100% + 27% or 127% of it's original value.

As a decimal, 127% = 1.27.  So 1.27 is your multiplier in this example.

And 1.27 • 7600 = 9652, which is the ending balance.

This gets the same result as finding 27% of 7600 and adding it back on to 7600, but does it more efficiently.

Answer: Ad Hominum

Step-by-step explanation:

It just attacks the person.

The graph of the inequality with the solution is plotted and attached

Inequality is a mathematical statement expressing an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.

The graph of the two inequalities are plotted and some features of the graph include dashed lines: this is because no part of the inequalities has equal to

From the graph the two graphs intersect at point (2.182, 1.273)

The y-intercepts are marked on the graph

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SAS-side angle side.

Two triangles are considered to be congruent when all three corresponding sides and angles have the same size.

Let's investigate the queries.

The SAS criterion for triangle congruence states that two triangles are congruent if they have two pairs of congruent sides and if the included angle—the angle between the congruent sides—of one triangle coincides with the included angle of the other.

If two triangles' two sides are equal and their angle at their intersections is also equal, we can claim they are congruent using SAS.

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Answer:

6 ≤ x ≤ ∞

Step-by-step explanation:

The domain is the "allowable inputs" or x-values. We know that there cannot be a negative number under a radical, so that means "x-6" must be greater than or equal to zero. Thus, we can set up the equation:

x - 6 ≥ 0

x ≥ 6                  This is the domain

There aren't restrictions on positive x-values, so we can also write the domain as:

6 ≤ x ≤ ∞

The width and the length of the slab are 2 meters and 12 meters, respectively

From the question, we have the following parameters that can be used in our computation:

Width of a rectangular slab of concrete = 10m less than the length.

Area = 24 m²

These parameters can be represented as

Width = Length - 10

Area = Length * Width

So, we have

w = l - 10

A = lw

Also, we have

A = 24

Substitute w = l - 10 in A = lw

A = l(l - 10)

So, we have

l(l - 10) = 24

Expand

l² - 10l = 24

This gives

l² - 10l - 24 = 0

Expand

l² + 2l - 12l - 24 = 0

Factorize

(l + 2)(l - 12) = 0

So, we have

l = -2 and l = 12

The length cannot be negative

So, we have

l = 12

Recall that

w = l - 10

So, we have

w = 12 - 10

Evaluate

w = 2

Hence, the dimensions are 2 meters and 12 meters, respectively

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Possible question

The width of a rectangular slab of concrete is 10m less than the length. The area is 24 m ^2

Compute the dimensions of the slab

Side-Angle-Side (SAS) Rule prove the congruency of the triangle

What is a triangle ?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Triangles can be divided into three sorts based on the lengths of their sides, and they are: Scalene. Isosceles. Equilateral.

The Side-Angle-Side rule is used to demonstrate whether a set of triangles is congruent. According to the SAS rule, two sides and the included angle of one triangle must equal two sides and the included angle of another triangle in order for the two triangles to be considered congruent.

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Answer:

is

Step-by-step explanation:

The domain of g is identical to the domain of f.

They both have the same slope which means they have the same domain.

Answer:

is NOT

Step-by-step explanation:

the equation of g(x) is not the same as f(x)

so, g(x) and f(x) are NOT identical (aka not the same)

*domain is different by looking at b-value

Right angle is an angle of 90 degrees while complementary angles add up to 90 degrees.

When the sum of two angles is 90°, then the angles are known as complementary angles.

A right angle is an angle of 90°.

Perpendicular lines are lines that intersect at a 90° angle. Perpendicular lines forms a right angle.

The complementary angle theorem states, "If two angles are complementary to the same angle, then they are congruent to each other".

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The correct option regarding the expected profit of the company is given as follows:

Dugitalis can expected to make money from selling these processors.

In the long run, they should expect to make $116 on each processor sold.

The expected value of a discrete probability distribution is given by the sum of each outcome multiplied by it's respective probability.

The distribution of profits in this problem is given as follows:

For the second probability, we have the number 2348, which is the cost of manufacturing each processor, as 2800 - 452 = $2,348.

Then the expected profit over time is given as follows:

E(X) = 0.88 x 452 - 2348 x 0.12 = $116.

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We can use a double strategy to find the value of the given expression, which is 32.

Mathematical expressions are combinations of numerical variables and operations denoted by subtraction, addition, multiplication, and division signs.

Doubles' strategy is adding two same single-digit numbers or two-digit numbers so we can get the result equal to a number multiplied by 2.

Given 4 x 8, we can evaluate this expression by using the double strategy as follows:

4 x 8 = 2 x 8 + 2 x 8

        = 16 + 16

        = 32.

Therefore, the value of the expression 4 x 8 is 32.

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The measure of the angle ∠ABD is 64 degrees

From the question, we have the following parameters:

Ray BA bisects ∠CBD

∠CBD = 5x + 18

∠ABC = 3x - 2

Because of the bisection, we have

∠ABC = ∠ABD

∠ABC * 2 = ∠CBD

Substitute the known values in the above equation, so, we have the following representation

(3x - 2) * 2 = 5x + 18

Open the brackets

6x - 4 = 5x + 18

Evaluate the like terms

x = 2

Recall that

∠ABC = ∠ABD

So, we have

∠ABD = 3x - 2

This gives

∠ABD = 3 x 22 - 2

Evaluate

∠ABD = 64

Hence, the angle is 64 degrees

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The 3 medians of triangle are the line segments that connects a vertex to the midpoint of the opposite side.

A triangle is a three-sided polygon with three vertices and three sides that enclose three angles.It can be an acute-angled, obtuse-angled, or right-angled triangle depending on the angles measured. The sum of a triangle's interior angles is 180 degrees.

Median of a Triangle:-

Thus, the median of triangle line segment that connects a vertex to the midpoint of the opposite side.

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Answer: [tex]11\sqrt{3}-7\sqrt{6}[/tex]

Step-by-step explanation:

[tex]7\sqrt{3}-4\sqrt{6}+\sqrt{48}-\sqrt{54}\\\\=7\sqrt{3}-4\sqrt{6}+\sqrt{16 \cdot 3}-\sqrt{9 \cdot 6}\\\\=7\sqrt{3}-4\sqrt{6}+\sqrt{16}\sqrt{3}-\sqrt{9}\sqrt{6}\\\\=7\sqrt{3}-4\sqrt{6}+4\sqrt{3}-3\sqrt{6}\\\\=11\sqrt{3}-7\sqrt{6}[/tex]

Answer:

1.0

Step-by-step explanation:

Hope this helps! :)

The solution is, 1.0 when 25/24 as a decimal rounded to the nearest tenth .

Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.

here, we have,

given that, 25/24

now, we have to rounded to the nearest tenth

as decimal, so, we have to divide 25 by 24

i.e. 25/24 = 1.041

we get, 1.041 => 1.0

so, it is 1.0  a decimal rounded to the nearest tenth

Hence, The solution is, 1.0 when 25/24 as a decimal rounded to the nearest tenth .

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Answer:

1680

Step-by-step explanation:

Answer:

  zero

Step-by-step explanation:

You want to know the remainder of the polynomial function for the divisor to be a factor?

A divisor is a factor of the dividend in any division problem if and only if the remainder is zero (0).

The divisor will be a factor of a polynomial function if division of the function by that divisor has a remainder of zero.

The graph of exponential function y = 5.2^x

exponential function in the form y = ab^x + c

Exponential function:

An exponential function is a mathematical function of the following form: f ( x ) = a^x. where x is also a variable, and a is a constant called the base of the function.

where

a is the initial y - intercept.

b is the constant ratio.

c is the horizontal asymptote.

So, in this problem, we have:

constant ratio = 2

y-intercept at y = 5

horizontal asymptote at y = 0

The graph is in the image uploaded.

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Answer:

y=11x-5

Step-by-step explanation:

y=mx+b

28=11(3)+b

28=33+b

b=-5

y=11x-5

Answer:

12, 24,72,96,156

Step-by-step explanation:

1/2 package would be 1/2 of 24 which is 12

21 x 24 = 24

3 x 24 = 72

4 x 24 = 72

We know that 3 packages is 72 so 6 packages is double that at 144.  We also know that have a package is 12. so 144 + 12 = 156

Answer:

1/2 package = 1/2 of 24 = 12 pencils

1 package = 24 pencils

3 packages = 24*3 = 72 pencils

4 packages = 24*4 = 96 pencils

6 1/2 packages = 24*6.5 = 156

Step-by-step explanation:

1 package = 24 pencils

1/2 package = 1/2 of 24 = 12 pencils

1 package = 24 pencils

3 packages = 24*3 = 72 pencils

4 packages = 24*4 = 96 pencils

6 1/2 packages = 24*6.5 = 156