Consider the function f(x)=3^x and the translation if f(x) named g(x). Janeen created a table for select values of x. What can be concluded about the relationship between two functions?

By applying the quadratic formula we conclude that the roots of the quadratic equation y = 2 · x² - 4 · x - 3 are 1 + 0.5√10 and 1 - 0.5√10, respectively.

All quadratic equations of the form a · x² + b · x + c = 0 have two roots that can be found by using the quadratic formula:

[tex]x = \frac{-b \pm \sqrt{b^{2}-4\cdot a \cdot c}}{2\cdot a}[/tex]     (1)

If we know that a = 2, b = - 4 and c = - 3, then the roots of the quadratic equations are:

[tex]x = \frac{4 \pm \sqrt{(-4)^{2}-4\cdot (2) \cdot (- 3)}}{2\cdot (2)}[/tex]

[tex]x = 1 \pm \frac{\sqrt{40}}{4}[/tex]

[tex]x = 1 \pm \frac{\sqrt{10}}{2}[/tex]

By applying the quadratic formula we conclude that the roots of the quadratic equation y = 2 · x² - 4 · x - 3 are 1 + 0.5√10 and 1 - 0.5√10, respectively.

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Answer:

1.a.  skew

1.b.  parallel

1.c.  none of the above

1.d.  perpendicular

1.e.  parallel

1.f.  skew

2.a.  never

2.b.  always

2.c.  always

2.d.  sometimes, sometimes, sometimes

Step-by-step explanation:

For these questions, it is critical to know the definitions of each of the terms.

Problem Breakdown

1.a.  skew  [tex]\overset{\longleftrightarrow}{AB} \text{ and } \overset{\longleftrightarrow}{EF}[/tex]

Point E is not on line AB.  Any three non-linear points form a unique plane (left face), so A, B, and E are coplanar.  Point F is not in plane ABE.  Since line EF and line AB do not intersect and are not coplanar, they are skew.

1.b.  parallel [tex]\overset{\longleftrightarrow}{CD} \text{ and } \overset{\longleftrightarrow}{EH}[/tex]

Line CD is parallel to line AB, and line AB is parallel to line EH.  Parallel lines have a sort of "transitive property of parallelism," so any pair of those three lines is coplanar and parallel to each other.

1.c.  none of the above  [tex]\overset{\longleftrightarrow}{AC} \text{ and } \overset{\longleftrightarrow}{GA}[/tex]

Line AC and line GA share point A, necessarily intersecting at A.  Therefore, line AC and line GA cannot be parallel or skew.

Any three points form a unique plane, so these two lines are coplanar, however, do they form a right angle?  If the figure is cube-shaped, as depicted, then no.

Note that each line segment AC, AG, and CG are all the diagonal of a cube face.  A cube has equal edge lengths, so each of those diagonals would be equal.  Thus, triangle ACG is an equilateral triangle.

All equilateral triangles are equiangluar, and by the triangle sum theorem, the measures of the angles of a planar triangle must sum to 180°, forcing each angle to have a measure of 60° (not a right angle).  So, lines AC and GA are not perpendicular.  (If the shape were a rectangular prism, these lines still aren't perpendicular, but the proof isn't as neat, there is a lot to discuss, and a character limit)

"none of the above"

1.d.  perpendicular  [tex]\overset{\longleftrightarrow}{DG} \text{ and } \overset{\longleftrightarrow}{HG}[/tex]

Line DG and line HG share point G, so they intersect.  Both lines are the edges of a face, so they intersect at a right angle.  Perpendicular

1.e.  parallel  [tex]\overset{\longleftrightarrow}{AC} \text{ and } \overset{\longleftrightarrow}{FH}[/tex]

Line AC is a diagonal across the top face, and line FH is a diagonal across the bottom face.  They are coplanar in a plane that cuts straight through the cube from top to bottom, but diagonally through those faces.

1.f.  skew  [tex]\overset{\longleftrightarrow}{CD} \text{ and } \overset{\longleftrightarrow}{AG}[/tex]

Point A is not on line CD, and any three non-linear points form a unique plane (the top face), so C, D, and A are coplanar.  Point G is not in plane ACD. Since line CD does not intersect and is not coplanar with line AG, by definition, the lines are skew.

2.a.  Two lines on the top of a cube face are never skew

Two lines are on a top face are necessarily coplanar since they are both in the plane of the top face.  By definition, skew lines are not coplanar.  Therefore, these can never be skew.

2.b.  Two parallel lines are always coplanar.

If two lines are parallel, by definition of parallel lines, they are coplanar.

2.c.  Two perpendicular lines are always coplanar

If two lines AB and CD are perpendicular, they form a right angle.  To form a right angle, they must intersect at the right angle's vertex (point P).

Note that A and B are unique points, so either A or B (or both) isn't P; similarly, at least one of C or D isn't P.  Using P, and one point from each line that isn't P, those three points form a unique plane, necessarily containing both lines.  Therefore, they must always be coplanar.

2.d.  A line on the top face of a cube and a line on the right side face of the same cube are sometimes parallel, sometimes skew, and sometimes perpendicular

Consider each of the following cases:

These 4 cases prove it is possible for a pair of top face/right face lines to be parallel, perpendicular, skew, or none of the above.  So, those two lines are neither "always", nor "never", one of those choices.  Therefore, they are each "sometimes" one of them.

Answer:

There are 7 sides.

Step-by-step explanation:

Let's Use the formula that states that the sum of the angles of an n-sided polygon is given by.

S=(n−2)180

Since we are given that the two angles are right, the angles and each of the remaining angles is 144.

And Therefore, the sum is:

S=90

(n−2)144

(n−2)180

=90

+90

+(n−2)144

⇒(n−2)180

−(n−2)144

=180

⇒(n−2)(180

−144

)=180

⇒(n−2)(36

=180

⇒n−2=

36

180

​⇒n−2=5

⇒n=5+2=7

Hence, the polygon has 7 sides.

The number of sides of the polygon such that one angle is the right angle will be 6.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.

In any closed polygon, the number of sides is equal to the number of interior angles.

Suppose the number of sides is n in the given polygon.

Sum of angles = 90° + 126° × (n - 1)

The sum of angles is given as, 180(n - 2)

90° + 126° × (n - 1) = 180(n - 2)

90 + 126n - 126 = 180n - 360

180n - 126n = 90 - 126 + 360

54n = 324

n = 6

Hence "The number of sides of the polygon such that one angle is the right angle will be 6".

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Ivanna's score was at the 36th percentile, will be 99.64 and Aldo's score was at the 19th percentile, will be 99.81.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Last year, over 10,000 students took an entrance exam at a certain state university.

Let the maximum score be 100.

Ivanna's score was at the 36th percentile, will be

⇒ [(10,000 – 36) / 10,000] x 100

⇒ 99.64

Aldo's score was at the 19th percentile, will be

⇒ [(10,000 – 19) / 10,000] x 100

⇒ 99.81

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Answer:

sorry

Step-by-step explanation:

Answer:

Range =  4365-4635

Step-by-step explanation:

4500 * 3/100 = 135

4500 + 135  = 4635

4500 - 135  = 4365

Range =  4365-4635

The actual range of resistance is from 4365 ohms to 4635 ohms.

To express the tolerance in ohms, we need to calculate 3% of the rated resistance, which is 4500 ohms.

Tolerance in ohms = 3% of 4500 ohms

Tolerance in ohms = 0.03 * 4500

Tolerance in ohms = 135 ohms

The actual range of resistance can be found by adding and subtracting the tolerance from the rated resistance:

Lower limit = Rated resistance - Tolerance

Lower limit = 4500 ohms - 135 ohms

Lower limit = 4365 ohms

Upper limit = Rated resistance + Tolerance

Upper limit = 4500 ohms + 135 ohms

Upper limit = 4635 ohms

So, the actual range of resistance is from 4365 ohms to 4635 ohms.

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Answer:

y = 3x - 2

Step-by-step explanation:

The number beside the x is the slope. The number at the end of the equation is the y-intercept.

All the answers are in this form:

y = mx + b

m is the slope.

b is the y-intercept.

With a 3 filled in for slope and -2 filled in for the y-intercept, you get:

y = 3x + -2

is the same as,

y = 3x - 2

Answer:

D

Step-by-step explanation:

We can test each pair making each ratio into its simplest form.

For A 2/3 is already in its simplest form and 9/15=3/5. they are not equivalent.

For B, 5/8 is already in its simplest form and 15/21=5/7. they are not equivalent.

For C, 3/12=1/4, and 6/18=1/3. They are not equivalent.

For D, 4/10=2/5, and 12/30=2/5. They are equivalent.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Let's see which ones are equivalent}\\\huge\textbf{to each other, shall we?}\\\\\\\huge\textbf{We will convert the given fractions to}\\\huge\textbf{decimals or make the fractions on the}\\\huge\textbf{right to easier to solve or comparing it}\\\huge\textbf{to the one on the left.}[/tex]

[tex]\huge\textsf{Option A.}[/tex]

[tex]\mathsf{\dfrac{2}{3}, \dfrac{9}{15}}[/tex]

[tex]\mathsf{\dfrac{2}{3}}\\\\\mathsf{= 2\div3}\\\\\mathsf{= 0.66\overline{6}7}\\\\\\\mathsf{\dfrac{9}{15}}\\\\\mathsf{= \dfrac{9\div3}{15\div3}}\\\\\mathsf{= \dfrac{3}{5}}\\\\\\\\\mathsf{\dfrac{2}{3} \neq \dfrac{9}{15}}[/tex]

[tex]\huge\textsf{Option B.}[/tex]

[tex]\mathsf{\dfrac{5}{8}, \dfrac{15}{21}}[/tex]

[tex]\mathsf{\dfrac{5}{8}}\\\\\mathsf{= 5\div8}\\\\\mathsf{= 0.625}\\\\\\\mathsf{\dfrac{15}{21}}\\\\\mathsf{= \dfrac{15\div3}{21\div3}}\\\\\mathsf{= \dfrac{5}{7}}\\\\\mathsf{\dfrac{5}{8}\neq \dfrac{15}{21}}[/tex]

[tex]\huge\textsf{Option C.}[/tex]

[tex]\mathsf{\dfrac{3}{12}.\dfrac{6}{18}}[/tex]

[tex]\mathsf{\dfrac{3}{12}}\\\\\mathsf{= 3 \div 12}\\\\\mathsf{= 0.25}\\\\\\\\\mathsf{\dfrac{6}{18}}\\\\\\\mathsf{= \dfrac{6\div3}{18\div3}}\\\\\\\mathsf{= \dfrac{2}{6}}\\\\\\\mathsf{= \dfrac{2\div2}{6\div2}}\\\\\\\mathsf{= \dfrac{1}{3}}\\\\\\\mathsf{\dfrac{3}{12}\neq \dfrac{6}{18}}[/tex]

[tex]\huge\textsf{Option D.}[/tex]

[tex]\mathsf{\dfrac{4}{10}, \dfrac{12}{30}}[/tex]

[tex]\mathsf{\dfrac{4}{10}}\\\\\mathsf{= 4\div10}\\\\\mathsf{= 0.40}\\\\\\\mathsf{\dfrac{6}{18}}\\\\\mathsf{= \dfrac{12\div3}{30\div3}}\\\\\mathsf{= \dfrac{4}{10}}\\\\\mathsf{= \dfrac{4}{10}}\\\\\mathsf{= \dfrac{4\div2}{10\div2}}\\\\\mathsf{= \dfrac{2}{5}}\\\\\mathsf{\dfrac{4}{10} = \dfrac{12}{20}}[/tex]

[tex]\huge\text{Thus, your answer should be: \boxed{\mathsf{Option\ D. \dfrac{4}{10}, \dfrac{12}{30}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

According to the information in the table, it can be inferred that the trend of the results is positive but does not have an exact linear fit (option B).

To calculate the average of the results we must add all the results and divide the result by the number of years as shown below.

Additionally, to identify if the trend is positive or negative, we must see if the results increase or decrease year after year. From the above, it is possible to infer that it is a positive trend.

On the other hand, it can be stated that it does not have an exact linear fit because the increase is not constant each year.

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The value of the integration is

[tex]\int {\frac{-7x^{3} }{x^{3}+1} } \, dx =7x - \frac{7}{3} \ln(x+1) + \frac{7}{6} ln (x^{2} -x+1)-\frac{7\sqrt{3} }{3} tan^{-1} (\frac{2x-1}{\sqrt{3} })+C[/tex], where C is an integrating constant.

We know that finding the area of the curve's undersurface is the process of integration. To do this, cover the area with as many tiny rectangles as possible, then add up their areas. The sum gets closer to a limit that corresponds to the area under a function's curve. Finding an antiderivative of a function is the process of integration. If a function can be integrated and its integral over the domain is finite with the given bounds, then the integration is definite.

Here, we have to determine the value of the given integral

[tex]\int {\frac{-7x^{3} }{x^{3}+1} } \, dx[/tex].

So,

[tex]\int {\frac{-7x^{3} }{x^{3}+1} } \, dx = 7 \int {\frac{1-x^{3}-1 }{x^{3}+1} } \, dx[/tex][tex]= 7 \int [{1-\frac{1 }{x^{3}+1} } ]\, dx =7\int \, dx - 7 \int {\frac{1 }{x^{3}+1} } \, dx[/tex] ...(1)

Now,

[tex]\frac{1}{x^{3} +1} = \frac{1}{(x+1)(x^{2} -x+1)}[/tex]

We can write

[tex]\frac{1}{(x+1)(x^{2} -x+1)}=\frac{A}{(x+1)} + \frac{Bx+C}{(x^{2} -x+1)}[/tex]

i.e. [tex]1 = A(x^{2} -x+1)+(Bx+C)(x+1)[/tex]

i.e. [tex]1 = Ax^{2} -Ax + A+Bx^{2} +Bx+Cx+C[/tex]

i.e. [tex]1=(A+B)x^{2} +(-A+B+C)x +(A+C)[/tex]

Comparing both sides, we get

[tex]A+B=0 \implies B = -A[/tex] ...(2)

[tex]-A+B+C = 0 \implies -A+(-A)+C=0 \implies -2A+C=0[/tex] ...(3)

[tex]A+C=1[/tex] ...(4)

Subtracting (3) from (4),

[tex]A+C+2A-C=1-0 \implies 3A=1 \implies A=\frac{1}{3}[/tex]

From (4), [tex]C= 1-\frac{1}{3} =\frac{3-1}{3} =\frac{2}{3}[/tex]

From (2), [tex]B =-\frac{1}{3}[/tex]

We get

[tex]\frac{1}{x^{3}+1 } =\frac{1}{3} \frac{1}{(x+1)} - \frac{1}{3} \frac{x-2}{x^{2} -x+1}[/tex]

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

[tex]=\frac{1}{3} \frac{1}{(x+1)} - \frac{1}{6} \frac{2x-1-3}{x^{2} -x+1}[/tex]

[tex]=\frac{1}{3} \frac{1}{(x+1)} - \frac{1}{6} \frac{2x-1}{x^{2} -x+1}+\frac{3}{6} \frac{1}{x^{2} -x+1}[/tex]

[tex]=\frac{1}{3} \frac{1}{(x+1)} - \frac{1}{6} \frac{2x-1}{x^{2} -x+1}+\frac{1}{2} \frac{1}{x^{2} -x+1}[/tex]

Integrate both sides,

[tex]\int \frac{1}{x^{3}+1 }\, dx =\frac{1}{3} \int \frac{1}{(x+1)} \, dx - \frac{1}{6} \int \frac{2x-1}{x^{2} -x+1}\, dx+\frac{1}{2} \int \frac{1}{x^{2} -x+1}\, dx[/tex]

i.e. [tex]\int \frac{1}{x^{3}+1 }\, dx =\frac{1}{3} \ln(x+1) - \frac{1}{6} ln (x^{2} -x+1)+\frac{\sqrt{3} }{3} tan^{-1} (\frac{2x-1}{\sqrt{3} })[/tex]

From (1),

[tex]\int {\frac{-7x^{3} }{x^{3}+1} } \, dx =7x - \frac{7}{3} \ln(x+1) + \frac{7}{6} ln (x^{2} -x+1)-\frac{7\sqrt{3} }{3} tan^{-1} (\frac{2x-1}{\sqrt{3} })+C[/tex]

Therefore, the value of the integration is

[tex]\int {\frac{-7x^{3} }{x^{3}+1} } \, dx =7x - \frac{7}{3} \ln(x+1) + \frac{7}{6} ln (x^{2} -x+1)-\frac{7\sqrt{3} }{3} tan^{-1} (\frac{2x-1}{\sqrt{3} })+C[/tex], where C is an integrating constant.

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Ella can buy a house worth $5 million

Loan is the amount of money borrowed from a bank or any other person , The amount has to be returned back with a Interest.

It is given that

The maximum loan Ella can get from the bank is $445,000

Ella has $55,000 available to make the down payment.

The highest value home that she can purchase is the sum of money she has and the maximum amount of money she can get from the bank.

It is given by

$445,000 +  $55,000

$500,000

Therefore Ella can buy a house worth $5 million

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Answer:

7x-1 + 2x-1 =7 ..... given

9x-2 = 7

9x = 9

x = 1

Step-by-step explanation:

This is the answer of the above condition.

Please mark as BRAINLIEST and THANK ME.

Answer:

y + 6 = -1/2(x-3)

Step-by-step explanation:

let me know if you want an explanation

Answer:

2a² + 2b²

Step-by-step explanation:

(a - b)² + (a + b)² ← expand both factors using FOIL

= a² - 2ab + b² + a² + 2ab + b² ← collect like terms

= 2a² + 2b²

Step-by-step explanation:

Expand both classic quadratics and combine like terms to find the sum:

(a−b)2+(a+b)2

Answer:

Its A

Step-by-step explanation:

I said so

Answer:

Step-by-step explanation:

2x-10=8

2x = 10 + 8

2x = 18

x = 18 : 2 =

x = 9

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

check

2 * 9 - 10 = 8                         (remember PEMDAS)

18 - 10 = 8

8 = 8

the answer is good

The value of k is 4 and the value of a is 5

The table of values is given as:

x=2,3,a

y=20,40,104

The variation is given as:

[tex]y\ \alpha\ x^2+1[/tex]

Express as an equation

y = k(x^2 + 1)

When x = 2, y = 20.

So, we have:

[tex]20 = k(2^2 + 1)[/tex]

Evaluate the sum

20 = 5k

Divide by 5

k = 4

Hence, the value of k is 4

In (a), we have:

y = k(x^2 + 1)

Substitute 4 for k

y = 4(x^2 + 1)

When x = a, y = 104.

So, we have:

104 = 4(a^2 + 1)

Divide by 4

26 = a^2 + 1

Subtract 1 from both sides

a^2 = 25

Take the square root

a = 5

Hence, the value of a is 5

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Answer:

jxdhjsssdddddsssssdd

Answer:

increasing

Step-by-step explanation:

look left to right, line goes up

Answer: [tex]x=\frac{c-k}{8}[/tex]

Step-by-step explanation:

[tex]1) \text { } 8x+c=k \text{ (given)}\\\\2) \text { }8x=c-k \text{ (subtract } k \text{ from both sides)}\\\\3) \text { } \boxed{x=\frac{c-k}{8}} \text{ (divide both sides by 8)}[/tex]

Answer:

B will be the answer...

Step-by-step explanation:

The second equation in system B is only in terms of y, so we need to use elimination to eliminate the x term from the second equation in system A.

To do that, we need to multiply the first equation by 5.

5 (-x − 2y = 7)

-5x − 10y = 35

Add to the second equation.  Notice the x terms cancel out.

(-5x − 10y) + (5x − 6y) = 35 + (-3)

-16y = 32

Combining this new equation with the first equation from system A will get us system B.

-x − 2y = 7

-16y = 32

Answer:

To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by 6. The solution to system B will be the same as the solution to system A.

Step-by-step explanation:

exact answer

Answer:

can you give upload the pictures

The equation of the line is y = 0.8x - 1.4 if the  slope of the line is 0.8 and line passes through coordinates (-2,-3)

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

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

The slope m = 0.8

The line passing through coordinates (-2,-3)

y = mx + c

y = 0.8x + c

Plug the point in the equation.

-3 = 0.8(-2) + c

c = -1.4

y = 0.8x - 1.4

Thus, the equation of the line is y = 0.8x - 1.4 if the  slope of the line is 0.8 and line passes through coordinates (-2,-3)

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Answer:

Step-by-step explanation:

The value of the asset in 2012, 2014, and 2017 are 8119.72, 13933.55 and, 31321.23, respectively. A function assigns the values.

A function assigns the value of each element of one set to the other specific element of another set.

Given the assets (in billions of dollars) for a financial firm can be approximated by the function [tex]A(x)=318e^{0.27x}[/tex], where x=7 corresponds to the year 2007. Therefore, the assets value in the following years will be,

A.) 2012 - [tex]A(12)=318e^{0.27\times 12} = 8,119.72[/tex]

B.) 2014 - [tex]A(14)=318e^{0.27\times 14} = 13,933.5[/tex]

C.) 2012 - [tex]A(17)=318e^{0.27\times 17} = 31,321.23[/tex]

Hence, the value of the asset in 2012, 2014, and 2017 are 8119.72, 13933.55 and, 31321.23, respectively.

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Answer:

8 in the box.

Step-by-step explanation:

As, it is given that 35 students study Biology.

So, in Biology circle,

15+7+5+x=35

27+x=35

x=35-27

x=8

Answer:

6.3 *30= 189; so 4 cotton swabs

15-(5)/5-10=10/-5=-2 hope it helps!

Answer:

well the answer is 4 have a good day

Answer:

The answer will be J

Step-by-step explanation:

Since you see, that the 67,896 will need to be rounded. It rounds up to 70,000 so you can elinmate M & N. 22% can be converted as a decimal to 0.2, also equals to 0.20. So elinmate L. Now you have J and K. You always times with these kinds of percentage.

Therefore the Answer Will Be J: 70,000 timed by 0.20.

Expert-Certifieder of Cousin.