how is the e - lambda figured out as 0.00248?

By solving a quadratic equation we will see that the number can be:

8 or -5.

The product of a number N, and 3 less than the number, is equal to 40.

This is written as:

[tex]N*(N - 3) = 40[/tex]

Now we need to solve this for N.

[tex]N^2 - 3N = 40[/tex]

[tex]N^2 - 3N - 40 = 0[/tex]

Then we need to solve this quadratic equation:

[tex]N = \frac{-(-3) \pm \sqrt{(-3)^2 - 4*1*(-40)} }{2} \\\\N = \frac{3 \pm 13 }{2}[/tex]

Then we have two solutions:

These are the two possible solutions.

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By analyzing the end behavior of the graphed function, we conclude that the graphed function is an exponential one.

On the graph, we can see that as the independent variable (the one in the horizontal axis) tends to large negative values, the dependent variable (the one in the vertical axis) tends to zero.

And, as the independent variable increases in the positive domain, also does the dependent variable. So we have an increasing function

Finally, we can see that the range (set of the outputs) of the function is the set of values larger than zero.

These 3 are characteristics of exponential functions, so we conclude that the graphed function is an exponential one, thus the correct option is the first one.

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Answer:

Logarithmic

Step-by-step explanation:

HS Teacher

By the 30 - 60 - 90 theorem the right options of the multiple choice question is:

A. The hypotenuse is twice as long as the shorter leg.

D. The longer leg is √3 times as long as the shorter leg.

In this problem we must look for the right choices in a multiple choice question. According to the Euclidean geometry, 30 - 60 - 90 have the following properties:

Thus, the right options of the multiple choice question is:

A. The hypotenuse is twice as long as the shorter leg.

D. The longer leg is √3 times as long as the shorter leg.

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Answer:

[tex]x=2^{\frac{2}{3}}[/tex]

Step-by-step explanation:

1) Add 8 to both sides.

[tex]2x^3=8[/tex]

2) Divide both sides by 2.

[tex]x^3=\frac{8}{2}[/tex]

3) Simplify [tex]\frac{8}{2}[/tex] to 4.

[tex]x^3=4[/tex]

4) Take the cube root of both sides.

[tex]x=\sqrt[3]{4}[/tex]

5) Rewrite 4 as 2².

[tex]x=\sqrt[3]{2^2}[/tex]

6) Use this rule: [tex]{({x}^{a})}^{b}={x}^{ab}[/tex].

[tex]x=2^{\frac{2}{3}}[/tex]

Decimal Form: 1.587401

__________________________________________

Check the answer:

[tex]2x^3-8=0[/tex]

1) Let [tex]x=2^\frac{2}{3}[/tex].

[tex]2(2^{\frac{2}{3} })-8=0[/tex]

2) Use this rule: [tex](x^a)^b=x^{ab}[/tex].

[tex]2\times2^{\frac{2\times3}{3} } -8=0[/tex]

3) Simplify 2 * 3 to 6.

[tex]2\times2^{\frac{6}{3} } - 8 =0[/tex]

4) Simplify 6/3 to 2.

[tex]2\times2^2-8=0[/tex]

5) Use Product Rule: [tex]x^ax^b=x^{a+b}[/tex].

[tex]2^3-8=0[/tex]

6) Simplify 2^3 to 8.

8 - 8 = 0

7) Simplify 8 - 8 to 0.

0 = 0

Thank you,

Eddie

The x- and y- coordinates of point E, which partitions the directed line segment from J to K into a ratio of 1:4 is (17, 11)

The midpoint of a line is the point that bisects or divides the line into two equal parts

If the line JK is partitioned into the ratio 1:4 with the following coordinates

J(-15, -5) and K(25, 15)

Using the expression below;

M(x, y) =[mx1+nx2/m+n, my1+ny2/m+n]

Substitute the ratio and the coordinates

M(x, y) =[1(-15)+4(25)/4+1, 1(-5)+4(15)/1+4]

M(x, y) = [(85)/5, 55/5]

M(x, y) = (17, 11)

Hence the x- and y- coordinates of point E, which partitions the directed line segment from J to K into a ratio of 1:4 is ((17, 11)

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In  triangle ABC, if m∠B = 90°, BH = AH, and the ratio of m∠A to m∠C is 1:2, then m∠BHA = 120° (C).

In the next given equilateral triangle ABC, y = 70°.

Finding m∠BHA:

In triangle ABC, it is given that,

∠B = 90°

And m∠A : m∠C = 1:2

Let us assume m∠A is x. Then, m∠C = 2x

According to the angle sum property of a triangle,

∠A + ∠B + ∠C = 180°

90° + x + 2x = 180°

90° + 3x = 180°

3x = 90°

x = 30°

⇒ In triangle ABC, ∠A = 30° and ∠C = 60°

Now, in triangle AHB, it is also given that,

BH = AH

⇒ ∠ABH = ∠A = 30°

Thus, according to the angle sum property of a triangle,

∠ABH + ∠A + ∠BHA = 180°

30° + 30° + ∠BHA = 180°

∠BHA = 180° - 60°

∠BHA = 120°

Finding y in the Second Triangle:

Since triangle ABC is equilateral,

∠A = ∠B = ∠C = 60°

∴ x + 2x + 3x = 60°

6x = 60°

x = 10°

In triangle ABD, using angle sum property of triangle,

x + ∠B +  ∠BDA = 180°

10° + 60° + ∠BDA = 180°

∠BDA = 180° - 70°

∠BDA = 110°

Now, since, ∠BDA and y are linearly adjacent  angles,

∠BDA + y = 180°

110° + y = 180°

y = 180° - 110°

y = 70°  

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The features that exist present in this polar graph is that D. Symmetry about the polar axis θ = 0.

A polar curve exists as a form constructed utilizing the polar coordinate system. Polar curves exists determined by points that exist at a variable distance from the origin (the pole) depending on the angle calculated off the positive x-axis.

The polar graph can be said to contain a symmetry about the polar axis which indicates that theta or θ exists equivalent to 0.

This exists because the graph is symmetric about the x-axis. This indicates that all the lines of symmetry can be seen intersecting the graph at x = 0. This demonstrates that there exists indeed symmetry in the polar graph.

Therefore, the correct answer is option D. symmetry about the plane θ = 0

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The total number of ways are formed is 4.43 x 10^10 by rounding to the hundredths place.

According to the statement

we have given that the some numbers of the songs which are added by the larrisa in her playlist.

And we have to tell the ways which are formed with the help of the combination and permutations.

So, For this purpose we know that the

The first condition we have given that the

"play no more than 4 blues songs" - indicates playlist can contain 0, 1, 2, 3, or 4 blues songs. You need to analyze five different cases and add them up together in the end. From 7 blues songs, you can either "pick" 0, 1, 2, 3, or 4. Since order matters, it's a permutation, not a combination.

Afterwards, it gets tricky. Consider the first case, where we have 0 blues songs. This means that there are 10 spaces for the remaining (3+5+7 = 15) songs, which means that they can be arranged in (7P0 ∙ 15P10) ways.

For the next case, where we have 1 blues songs, it means that there are 9 spaces for the remaining 15 songs, which means that they can be arranged in (7P1 ∙ 15P9) ways. Continue doing this for the cases of 2, 3, and 4 blues songs and add up all the cases together.

And from this way we get the all combinations which are formed.

So, For this purpose

n = (7P0 ∙ 15P10) + (7P1 ∙ 15P9) + (7P2 ∙ 15P8) + (7P3 ∙ 15P7) + (7P4 ∙ 15P6) = 4.43459016×1010,

which rounded to the hundredths place, is 4.43 x 10^10 possible playlists.

So, The total number of ways are formed is 4.43 x 10^10 by rounding to the hundredths place.

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Answer:

Step-by-step explanation:

Answer:

R-1={(2,1),(3,2),(9,3),(5,4)

Step-by-step explanation:

R-1={(2,1),(3,2),(9,3),(5,4) because (- 1) means reverse in relation

If the cost of goods manufactured of $918,700 and cost of goods sold is $955,448. The average manufacturing cost per unit assuming 18,374 units were produced is $102 per unit.

Using this formula to determine the average manufacturing cost per unit

Average manufacturing cost per unit= Total cost/Number of units produced

Where:

Total cost=$918,700+$955,448=$1,874,148

Number of units produced=18,374 units

Let plug in the formula

Average manufacturing cost per unit=$918,700+$955,448/18,374

Average manufacturing cost per unit=$1,874,148/18,374

Average manufacturing cost per unit=$102 per unit

Therefore the average manufacturing cost per unit assuming 18,374 units were produced is $102 per unit.

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The relation that is also a function is described as follows:

A nonlinear function on a coordinate plane vertex at (minus 3, minus 2) passes through (minus 7, 0), and (minus 6, minus 4).

A relation is a function if each value of the input is mapped to only one value of the output.

In this problem, we have that:

Hence a function is given by:

A nonlinear function on a coordinate plane vertex at (minus 3, minus 2) passes through (minus 7, 0), and (minus 6, minus 4).

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The vertex form of the quadratic equation, written in standard form, f(x) = 2 · x² - 20 · x + 8 is f(x) + 75 = 2 · (x - 5)².

In this problem we have a quadratic equation in standard form, whose form is defined by f(x) = a · x² + b · x + c, where a, b, c are real coefficients, and we need to transform it into vertex form, defined as:

f(x) - k = C · (x - h)²       (1)

Where:

This latter form can be found by algebraic handling. If we know that f(x) = 2 · x² - 20 · x + 8, then its vertex form is:

f(x) = 2 · x² - 20 · x + 8

f(x) = 2 · (x² - 10 · x + 4)

f(x) + 2 · 25 = 2 · (x² - 10 · x + 25)

f(x) + 75 = 2 · (x - 5)²

The vertex form of the quadratic equation, written in standard form, f(x) = 2 · x² - 20 · x + 8 is f(x) + 75 = 2 · (x - 5)².

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Answer:

B = - 23

Step-by-step explanation:

5(B + 4) = 3(B - 1) + B ← distribute parenthesis on both sides

5B + 20 = 3B - 3 + B

5B + 20 = 4B - 3 ( subtract 4B from both sides )

B + 20 = - 3 ( subtract 20 from both sides )

B = - 23

Answer:

57

Step-by-step explanation:

-7a + 4b

Let a = -3  b = 9

Substitute the values in

-7(-3) + 4(9)

Multiply

21 + 36

Add

57

Answer:

D is the correct answer -3+8=5 ,1+4=5

Answer:

t = 4b

Step-by-step explanation:

Each bag costs 4 dollars.

hope this helps! <3

Answer:

  e)  y = √(x) +5

Step-by-step explanation:

The graph shown is the graph of the square root function shifted upward 5 units. There is no translation left or right.

A function can be translated h units right and k units up by the following:

  g(x) = f(x -h) +k

When the function is f(x) = √x, and it is translated 5 units up, but none left or right, we have ...

  g(x) = f(x-0) +5

  y = √(x) +5 . . . . . . matches choice e

Answer:

Perimeter = 72 meters

Step-by-step explanation:

Let L be the length and W the width of the rectangle

We have the following relationship

L = 2W + 6

Area of the rectangle = LW = (2W+6)W   by substituting for L

Area =

2W² + 6W =260 ==> 2W² + 6W -260 = 0

Dividing both sides by 2 yields

W² + 3W -130 = 0

This is a quadratic equation which can be solved using the formula for the roots of the equation ie the values of W which satisfy the above equation

However in this case it is easier to solve by factorization

W² + 3W -130  

= W² + 13W - 10W - 130
= W(W + 13) -10(W + 13)

= (W+13)(W-10) = 0

This means W is either -13 or W = 10

Since W cannot be negative, we get W = 10 and

L = 2(10) + 6 = 26

Perimeter of a rectangle is given by

2(L + W) = 2(26 + 10) = 2(36) = 72  Answer

Answer:

23

Step-by-step explanation:

if you have 8 apples in a box, and then you put 15 additional apples into the box - how many apples are in the box ?

you see that is the same problem as the symbolized scenario with 2 lines being connected.

you have a string (e.g. for a kite) of 8 meters. and then you tie another string of 15 meters to it - how long is the new combined string ?

you really need help with that ?

8 + 15 = 23

The number of the students in the school that have had algebra is 203

The given parameters in the question are

The number of students that had algebra in the school is calculated as:

Algebra = Proportion of students taking algebra * Number of students in the school

The above equation can be represented as:

Algebra = np

Substitute values for n and p in the above equation

So, we have

Algebra = 290 * 70%

Express 70% as decimal i.e. 0.70

So, we have

Algebra = 290 * 0.70

Evaluate the product i.e. multiply 290 and 0.70

So, we have

Algebra = 203

Hence, the number of the students in the school that have had algebra is 203

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angle at y and w are equal

hence, 54°=w

54°+w+x =180°

x=180-(54°+54°)

x=72°

The height of the container be so as to minimize cost will be 1.20. inches.

The volume of the box will be:

= 2x × 3x × h

= 6x²h

Volume = 6x²h

12 = 6x²h

h = 2x²

The cost function will be:

C = 2.60(2)(6x²) + 4.30(12x)h

C = 31.2x² + 51.6xh

Taking the derivative

62.4x + 51.6h

h = 1.20

Therefore, the height of the container be so as to minimize cost will be 1.20 inches.

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Answer:

x = 3

Step-by-step explanation:

see image. Instead of distributive property, let's multiply by 2 to get rid of the fraction and also the parenthesis on the left. See image.

Then subtract 5 and finally, divide by 3 to solve. See image.

Answer:

(0, -2)

Step-by-step explanation:

The equation of y axis is x = 0. So, the y intercept is located at point (0, b). Therefore we can substitute 0 into x in the given equation to find b and hence the coordinates of the y intercept.

3x - 7y = 14

3*0 - 7y = 14

-7y = 14

y = -2

Answer:

  1/4

Step-by-step explanation:

The sum of an infinite geometric series is given by the formula ...

  S = a/(1 -r)

where 'a' is the first term, and r is the common ratio.

Here, the first term is 1/12, and the common ratio is ...

  (1/18)/(1/12) = 12/18 = 2/3

Then the sum is ...

  S = (1/12)/(1 -2/3) = (1/12)/(1/3) = 3/12 = 1/4

The sum of the infinite series is 1/4.

Step-by-step explanation:

We can determine whether the change represents exponential growth or decay by seeing whether the number being raised to x is between 0 and 1, or greater than 1.

In the equation [tex]y = 540(1.04)^x[/tex], y will increase every time that x increases, as we are multiplying by a number greater than 1 every time.

Hence, this exponential function represents exponential growth.

The percentage rate of increase for this function would be how much the y-value increases each time. Since we are multiplying by 1.04, each time the new value is 104% the original y-value. Hence, the percentage increase is 4%.

The order of temperature values become -16.7°C > -11.15°C > -7°C > 3°C And -16.7°C is the coolest temperature and 3°C is the warmest as compare to others.

According to the statement

we have given that the some values of the temperatures and we have to write it in the order from the coolest to the warmest means in increasing order.

So, For this purpose,

The given values of temperatures are:

3°C , -7°C , 2°F, 262 K

Firstly convert into one form

So, convert all values in Celsius form,

3°C = 3°C

-7°C = -7°C

2°F = -16.7°C

262 K = -11.15°C

Now arrange into the order from coolest to warmest

So, it will become

-16.7°C > -11.15°C > -7°C > 3°C

So, -16.7°C is the coolest temperature and 3°C is the warmest as compare to others.

The order of temperature values become -16.7°C > -11.15°C > -7°C > 3°C And -16.7°C is the coolest temperature and 3°C is the warmest as compare to others.

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If Caisse can download a maximum of 1000 mb of songs or movies then the inequality that represents the number of movies and songs that Caisse downloads each month is 85x+4y<1000.

Given that Caisse can download a maximum of 1000 mb of songs or movies to her smartphone each month. the file of each movie is 85mb, and the file of each song is 4mb.

We are required to find the inequality that represents the number movies and songs that Caisse downloads each month.

Inequality is like an equation that shows the relationship between variables that are expressed in greater than, less than , greater than or equal to , less than or equal to sign.

let the number of movies be x and the number of songs be y.

According to question Caisse cannot download more than 1000 mb, so we will use less than towards equation.

It will be as under:

85x+4y<1000.

Hence if Caisse can download a maximum of 1000 mb of songs or movies then the inequality that represents the number of movies and songs that Caisse downloads each month is 85x+4y<1000.

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Check the picture below.

Answer:

7.....gggggggggggggggh