Find the explicit form of the arithmetic function of n if the first term is 3 and the common difference is -4 . Then find the seventh term.

The domain of the ellipse is [-4. 6] and the range of the ellipse is [-4. 0]

The equation of the ellipse is given as:

4x^2 + 25y^2 – 8x + 100y + 4 = 0

Next, we plot the graph of the ellipse

See attachment for the graph of the ellipse

The domain

From the attached graph the minimum and the maximum values of x are:

Minimum = -4

Maximum = 6

So, the domain of the ellipse is [-4. 6]

The range

From the attached graph the minimum and the maximum values of y are:

Minimum = -4

Maximum = 0

So, the range of the ellipse is [-4. 0]

Hence the domain of the ellipse is [-4. 6] and the range of the ellipse is [-4. 0]

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the location of the g point is 3.

Two ratios are set to be equal in an equation called a proportion. You might express the ratio as 1: 3 for instance, if there is 1 boy and 3 girls.

Point G Partition the directed line segment form d to f into a

5:4 ratio

so,

g - d = (5/9) x (f - d)

We have that d = -2 and f = 7, Therefore

g - d = (5/9) x (f - d)

g + 2 = (5/9) x (7 + 2)

g + 2 = 5

g = 3

Therefore the location of the g point is 3.

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Answer: OPTION D

Step-by-step explanation:

Answer:

C.  Cube 2.

Step-by-step explanation:

Using PEMDAS  the first operation to be done is E (Exponent)  which is

2³.

We need at least 7 terms of the Maclaurin series for ln(1 + x)  to estimate ln 1.4 to within 0.0001

For given question,

We have been given a function f(x) = ln(1 + x)

We need to find  the estimate of In(1.4) within 0.001 by applying the function of the Maclaurin series for f(x) = In (1 + x)

The expansion of ln(1 + x) about zero is:

[tex]ln(1+x)=x-\frac{x^2}{2} + \frac{x^3}{3} -\frac{x^4}{4} +\frac{x^5}{5} -\frac{x^6}{6} +.~.~.[/tex]

where -1 ≤ x ≤ 1

To estimate the value of In(1.4), let's replace x with 0.4

[tex]\Rightarrow ln(1+0.4)=0.4-\frac{0.4^2}{2} + \frac{0.4^3}{3} -\frac{0.4^4}{4} +\frac{0.4^5}{5} -\frac{0.4^6}{6} +.~.~.[/tex]

From the above calculations, we will realize that the value of  [tex]\frac{0.4^5}{5}=0.002048[/tex] and [tex]\frac{0.4^6}{6}=0.000683[/tex]  which are approximately equal to 0.001

Hence, the estimate of In(1.4) to the term [tex]\frac{0.4^6}{6}[/tex]  is enough to justify our claim.

Therefore,  we need at least 7 terms of the Maclaurin series for function ln(1 + x)  to estimate ln 1.4 to within 0.0001

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Answer:

x^3+4x^2−23x+6

Step by Step:

(x−3)(x2+7x−2)

=(x+−3)(x2+7x+−2)

=(x)(x2)+(x)(7x)+(x)(−2)+(−3)(x2)+(−3)(7x)+(−3)(−2)

=x3+7x2−2x−3x2−21x+6

=x3+4x2−23x+6

Multiply = add powers

3 + - 1 = 2

- - means +

+ + means +

- + means -

Thus, answer is 2^2

Hope this helps!

Answer:

[tex]\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x=\dfrac{x}{9\sqrt{9-x^2}} +\text{C}[/tex]

Step-by-step explanation:

Fundamental Theorem of Calculus

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given indefinite integral:

[tex]\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x[/tex]

Rewrite 9 as 3²  and rewrite the 3/2 exponent as square root to the power of 3:

[tex]\implies \displaystyle \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x[/tex]

Integration by substitution

[tex]\boxed{\textsf{For }\sqrt{a^2-x^2} \textsf{ use the substitution }x=a \sin \theta}[/tex]

[tex]\textsf{Let }x=3 \sin \theta[/tex]

[tex]\begin{aligned}\implies \sqrt{3^2-x^2} & =\sqrt{3^2-(3 \sin \theta)^2}\\ & = \sqrt{9-9 \sin^2 \theta}\\ & = \sqrt{9(1-\sin^2 \theta)}\\ & = \sqrt{9 \cos^2 \theta}\\ & = 3 \cos \theta\end{aligned}[/tex]

Find the derivative of x and rewrite it so that dx is on its own:

[tex]\implies \dfrac{\text{d}x}{\text{d}\theta}=3 \cos \theta[/tex]

[tex]\implies \text{d}x=3 \cos \theta\:\:\text{d}\theta[/tex]

Substitute everything into the original integral:

[tex]\begin{aligned}\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x & = \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x\\\\& = \int \dfrac{1}{\left(3 \cos \theta\right)^3}\:\:3 \cos \theta\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{\left(3 \cos \theta\right)^2}\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{9 \cos^2 \theta} \:\: \text{d}\theta\end{aligned}[/tex]

Take out the constant:

[tex]\implies \displaystyle \dfrac{1}{9} \int \dfrac{1}{\cos^2 \theta}\:\:\text{d}\theta[/tex]

[tex]\textsf{Use the trigonometric identity}: \quad\sec^2 \theta=\dfrac{1}{\cos^2 \theta}[/tex]

[tex]\implies \displaystyle \dfrac{1}{9} \int \sec^2 \theta\:\:\text{d}\theta[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Integrating $\sec^2 kx$}\\\\$\displaystyle \int \sec^2 kx\:\text{d}x=\dfrac{1}{k} \tan kx\:\:(+\text{C})$\end{minipage}}[/tex]

[tex]\implies \displaystyle \dfrac{1}{9} \int \sec^2 \theta\:\:\text{d}\theta = \dfrac{1}{9} \tan \theta+\text{C}[/tex]

[tex]\textsf{Use the trigonometric identity}: \quad \tan \theta=\dfrac{\sin \theta}{\cos \theta}[/tex]

[tex]\implies \dfrac{\sin \theta}{9 \cos \theta} +\text{C}[/tex]

[tex]\textsf{Substitute back in } \sin \theta=\dfrac{x}{3}:[/tex]

[tex]\implies \dfrac{x}{9(3 \cos \theta)} +\text{C}[/tex]

[tex]\textsf{Substitute back in }3 \cos \theta=\sqrt{9-x^2}:[/tex]

[tex]\implies \dfrac{x}{9\sqrt{9-x^2}} +\text{C}[/tex]

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Answer:

(-6,4)

Step-by-step explanation:

You started at (-4,2)  The first number in the ordered pair moves the number left and right and the second number moved the point up and down.

We are first told to move the point 2 units to the left.  -4 is my left right number.  If I am at -4 and I go to unites to the left, I will be at -6.  My new point is now (-6,2).  Next we are told to go up 2.  The 2 number in my ordered pair tells me that I am 2 above the x axis.  Now I am going to go two more units up.  I am now at 4, so my new ordered pair after the translation is (-6,4)

coordinates of the point (−4, 2) after a translation 2 units left and 2 units up would be (-6, 4).

What is Translation ?

"Translation" moves points the same distance along lines that are parallel to each other.

Translation involves the initial object called the pre-image and the final object called the image. As you can see in the picture above, the rust-colored item represents the pre-image, and the blue item represents the image. Because of the arrow, we can tell the direction in which the image was moved. For other images, you may receive instructions on which image is the pre-image, or you may be asked to find the pre-image from the image.

Reflection, on the other hand, moves points along a specified line in such a way that the line bisects each line segment connecting corresponding pre-image points and image points

We are asked to find the coordinates of the points (-4,2) after a translation 2 units left and 2 units up.

We know that translating a point to the left by 'a' units means we need to subtract 'a' units from x-coordinate of the point.

Translation to 2 units left:

(-4,2) → (-4-2, 2)  → (-6, 2)

We know that translating a point to upwards by 'a' units means we need to add 'a' units to y-coordinate of the point.

Translation to 2 units up:

(-6, 2) → (-6, 2+2) → (-6, 4)

Therefore, coordinates of the point (−4, 2) after a translation 2 units left and 2 units up would be (-6, 4).

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Answer:

  138.37 g

Step-by-step explanation:

Mass is the product of density and volume.

  M = ρV = (0.685 g/mL)(202 mL) = 138.37 g

Answer:

5) 3(2+3x)+4(y+2x)-6

Step-by-step explanation: its gone be -6 either way

Answer:

9/14.

Step-by-step explanation:

The probability is given as a fraction or percentage.

9:5 odds in favour of a horse winning  means the horse will win 9 races for every 5 it does not win.

So the probability that this horse will win is 9/(9+5)

= 9/14.

The answer is J.

The probability of spinning B on Spinner 1 is equal to the ratio of number of B to the total number of letter spaces.

The probability of spinning 1 on Spinner 2 is equal to the ratio of number of 1 to the total number of number spaces.

The probability is equal to :

Answer:

J   [tex]\frac{1}{12}[/tex]

Step-by-step explanation:

• First, let's find the probability of landing a letter B in Spinner 1.

We have a total of eight possibilities, and two of them are the letter B.

∴ [tex]P(B) = \frac{2}{8}[/tex]

            = [tex]\bf \frac{1}{4}[/tex]

• Next, let's find the the probability of landing the number 1 on Spinner 2.

There are a total of six possibilities, and two of them are the number 1.

∴ [tex]P(1) = \frac{2}{6}[/tex]

           = [tex]\bf \frac{1}{3}[/tex]

• Now we have to calculate the probability of spinning a letter B and the number 1:

[tex]P(B \space\ and\space\ 1) = \frac{1}{4} \times \frac{1}{3}[/tex]

                   = [tex]\bf \frac{1}{12}[/tex]

Step-by-step explanation:

for TEXAS using permutation formula

we have:5!/1!1!1!1!1!=5!=120

for MEXICO using permutation formula

we have:6!/1!1!1!1!1!1!=6!=720

Split up the interval [0, 3] into 3 equally spaced subintervals of length [tex]\Delta x = \frac{3-0}3 = 1[/tex]. So we have the partition

[0, 1] U [1, 2] U [2, 3]

The left endpoint of the [tex]i[/tex]-th subinterval is

[tex]\ell_i = i - 1[/tex]

where [tex]i\in\{1,2,3\}[/tex].

Then the area is given by the definite integral and approximated by the left-hand Riemann sum

[tex]\displaystyle \int_0^3 f(x) \, dx \approx \sum_{i=1}^3 f(\ell_i) \Delta x \\\\ ~~~~~~~~~~ = \sum_{i=1}^3 (i-1)^3 \\\\ ~~~~~~~~~~ = \sum_{i=0}^2 i^3 \\\\ ~~~~~~~~~~ = 0^3 + 1^3 + 2^3 = \boxed{9}[/tex]

Answer: Divide the 4/4 then subtract that from 12.

Step-by-step explanation:

Use PEMDAS. The Division comes first, then the subtraction.

The lowest number of people at a table is 0.

A dot plot is a graph that is used to represent the frequency of a data set. The dots in a dot plot represent the frequency of a number. The greater the height of a number, the higher its frequency. A dot plot is also known as a strip plot or a dot chart.

Looking at the dot plot, it can be seen that there are two dots above 2. This means that at two tables there was no one there.

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If a palindrome is a string of characters the reads the same backward as it does forwards then there are 120 such palindromes after solving through permutations.

Given that a palindrome is a string of characters the reads the same backwards as it does forwards.

We are required to find the number of 6 letter palindromes.

Permutations is basically finding how many ways in which the some numbers or things can be arranged. It is expressed as [tex]nP_{r}[/tex]=n!/(n-r)!.

If there are 6 letters then in a palindrome 3 alphabets are used here to form a 6 letter word.

=6[tex]P_{3}[/tex]

=6!/(6-3)!

=6*5*4*3!/3!

=120 palindromes.

Hence if a palindrome is a string of characters the reads the same backward as it does forwards then there are 120 such palindromes.

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Based on the percentage discount that one gets from the promotion using a jar, the average discount amount the shoe store can expect to give each customer is $15.

The average discount in percentages will be:

= (3/6 x 10%) + (2/6 x 30%) + (1/6 x 60%)

= 5% + 10% + 10%

= 25%

The average discount in cash amounts is:

= 25% x 60

= $15

In conclusion, the average discount amount that the store can expect to give each customer in dollars is $15.

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The simplified form of the expression 7^x+1 + 7^x / 2×7^x as given in the task content follows from the laws of indices and is equal to; 4.

It follows from the task content that the expression whose simplified form is to be determined is given as; 7^x+1 + 7^x / 2×7^x.

On this note, it follows from the law of indices that; 7^x+1 = 7× 7^x.

Hence, we have; 7^x(7+1 ) / 2×7^x.

And upon simplification, we have; 8/2 = 4.

Consequently, we may conclude that the simplified form of the expression as given in the task content is; 4.

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your question is not clear

Answer:

At least 18 solid balls

Step-by-step explanation:

    [tex]\sf \boxed{\bf Volume \ of \ rectangular \ tank = length* width * height}[/tex]

Volume of empty space = Volume of the full tank - Volume of the tank till the water.

                                        = 20*10*13 - 20*10*11

                                        = 2600 - 2200

                                        = 400 cm³

Volume of 1 solid ball = 23 cm³

Number of solid ball to make the tank overflow = 400 ÷ 23

                                                                               ≈ 18 solid balls

The volume of the shelter is 1108.25 cu. ft.

A cuboid is a three-dimensional figure with 6 faces, all the faces are rectangular in shape.

The volume is the space occupied by it in a three-dimensional figure.

The volume of a cuboid whose length is l,

The width is w, and

Height is h.

V = length * Width * Height

V = lwh

The length of the shed is 16.25 ft.

The width of the shed is 11 ft.

The height of the shed is 6 1/5 ft

The height of the shed is 31/5 = 6.2ft.

The volume of the shed is given by

V = 16.25 * 11 * 6.2

V = 1108.25 cu.ft

Therefore, the shed has a volume of 1108.25 cu.ft.

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The value of the given function if x = 2 and y = 4 is 37 3/5

Functions are expressions used to determine the relationship between two or more variables.

For instance, f(x) is pronounced as the function of x. Given the expression below

(y+x)² + 4/5x

Given the following parameters

x = 2

y = 4

Substitute the given parameters

f(x,y) = (y+x)² + 4/5x

f(2, 4) = (4+2)² + 4/5(2)
f(2,4) = 6^2 +8/5

f(2, 4) = 36 + 8/5

f(2, 4) = 180+8/5

f(2, 4) =188/5

f(2, 4) = 37 3/5

Hence the value of the given function if x = 2 and y = 4 is 37 3/5

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Answer:

1. to add 9 to both sides

2. to multiply by 2 to both sides (horrible English)

3. x = -8

Step-by-step explanation:

why do you feel you are terrible at this ?

this is like a riddle or puzzle to solve. like a magic cube or changing a match in a pattern of matches to create another pattern.

let's try and explain this to you.

an equation is like a balance, where both cups are in perfect balance.

whatever value is on the left side, is exactly also on the right side. although it is not plainly visible and explainable, why they are equal.

so, to find out we need to transform the equation. and to keep the balance while transforming you have to do the same changes on both sides of the balance. until you find out what makes the cups equal.

if we destroy the balance at any point, we have no more chance to find out what made both sides equal in the first place, because there is no more original balance.

we can do all mathematical operations in the transformation.

we can add things, subtract things, multiply by a factor, divide by something, ... - anything.

x/2 - 9 = -13

to get clarity in our search for the reason of the equality we try to combine the same type of terms on one side of the equation, and the other type (or types) on the other side.

what types of terms do we have here ?

there is one with a variable (x/2), and there are constant terms (-9, -13).

so, what do I need to do to get rid of the constant term (-9) on the side of the variable term (so that this becomes the side with only variable terms) ?

I need to add 9, so the constant term on that side turns 0 and therefore disappears in the sum. but remember, the action has to be done on both sides.

so,

x/2 - 9 = -13 | + 9 on both sides

x/2 - 9 + 9 = -13 + 9

x/2 = -4

what else is now blocking our view on what x is ?

there is this 1/2 factor of x.

how do we get rid of this 1/2 ? by multiplying by 2. because 2× 1/2 = 1, and a factor of 1 disappears in a multiplication.

x/2 = -4 | ×2 on both sides

x/2 × 2 = -4 × 2

x = -8

and now we see what it is that kept both cups or sides in balance : x = -8

If Connie spent $26 on 8 books, The number of hard covers she buy is 5 hard cover.

Let h represent hard cover

Let p represent paperbacks

Formulate an equation

h + p= 8.......(1)

4h + 2p= 26......(2)

Multiply equation (1) by -2

-2h + -2p = -16

4h  +  2p   = 26

2h  +   0p =10

2h = 10

Divide both side by 2h

h=10/2

h =5 hard covers

Paper backs

P=5-2

P=3 paper backs

Therefore If Connie spent $26 on 8 books, The number of hard covers she buy is 5 hard cover.

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Answer:

See the attached picture.

Step-by-step explanation:

The box and whisker plot is plotted with minimum value 24, maximum value 58, first quartile 29, third quartile 52 and median 40.

Given that, the ages of 15 music teachers in a school district are 24, 26, 27, 29, 29, 32, 37, 40, 40, 41, 45, 52, 56, 56, 58.

A box and whisker plot also called a box plot displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. In a box plot, we draw a box from the first quartile to the third quartile. A vertical line goes through the box at the median.

Minimum value = 24

Maximum value = 58

First quartile = 29

Third quartile = 52

Median = 40

Therefore, the box and whisker plot is plotted with minimum value 24, maximum value 58, first quartile 29, third quartile 52 and median 40.

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Answer:

1. e

Step-by-step explanation:

18/3 +2(12-5)

=6+2(7)

=6+14

=20

[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{18}{3}+2(12-5) \end{gathered}$}[/tex]

Divide 18 by 3 to get 6.

Therefore, the correct option is "E".

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

[tex]\large\displaystyle\text{$\begin{gathered}\sf 30+\frac{4(4+1)}{2}-(3+1) \ \to \ \ [Add \ 4 \ plus \ 1] \end{gathered}$}[/tex]

It seems that none of the options is correct.