A rectangular dog pen is constructed using a barn wall as one side and 120m of fencing for the other three sides. a) give a sketch of the situation. b) express the area in terms of x. c) sketch the graph. d) find the value of x that gives the greatest area. e) find the dimensions of the pen. f) state the domain.

The equation written in exponential form is (a) 2³ = 8

A symbol used to denote the action of raising to a power that is written above and to the right of a mathematical phrase.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Given equation is

㏒₂ 8 = 3

㏒ₐx = b

x = aᵇ

㏒₂8 = 3

8 = 2³

Hence, (a) 2³ = 8

Therefore, the equation written in exponential form is (a) 2³ = 8.

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Answer:

Step-by-step explanation:

x=3?

Answer:

3

Step-by-step explanation:

If you multiply 1 by 3 it gives you 3, the side of triangle B. Using that scale factor. you can then take the side of triangle B that is 9 and divide it by 3. That gives you the missing side of triangle A.

Hope this helps! :)

Equation for the function graphed is f(x) = -0.6 (x - 1)² ÷ (x + 1)(x + 3)

Given, the y-intercept is at (0, 0.2).

From the given graph, it can be deduced the vertical asymptotes are at x = -1, x = 1 and x = -3.

Which implies denominator is 0 and the function is undefined for x = -1, x = 1 or x = -3.

So, -1 and -3. are the roots of the denominator. As a result, the denominator equation has the form: (x + 1)(x + 3).

For finding the equation of the function f(x) = a(x - 1)² ÷ (x + 1)(x + 3)

Put f(0) = 0.2

f(0) = a(0 - 1)² ÷ (0 + 1)(0 + 3) = 0.2

a = - 0.6

∴ Equation is f(x) = -0.6(x - 1)² ÷ (x + 1)(x + 3) for y-intercept is at (0,0.2).

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Answer:

[tex]y=-\frac{4}{3}x+3[/tex]

Answer:

-2/3

Step-by-step explanation:

I graphed it

Answer:

a

Step-by-step explanation:

as all the other points had inflection

Answer:

75%

Step-by-step explanation:

If the ratio of red:blue is 3:1, then there are 4 (some multiple of 4) in all.

The ratio of red:total is 3:4

3/4 is .75, times by 100 to convert to a percent.

.75 × 100 is 75%

Answer: [tex]72z^{2} +55z-7[/tex]

Step-by-step explanation:

We multiply each component with each other:

8z * 9z = 72z^2

8z * -1 = -8z

9z * 7 = 63z

7 * -1 = -7

We then add it all together, 63z + -8z = 55z and get

[tex]72z^{2} +55z-7[/tex]

Answer:

221 760 inches

Step-by-step explanation:

So, 3.5miles * 63360= 221760 inches.

Formula: multiply the value in miles by the conversation factor '63360'.

Answer:b=6

Step-by-step explanation:

a) The 90% confidence interval to estimate the percentage of yellow peas is (23.09%, 29.03%.)

b) Based on the confidence interval, the results of the experiment do not appear to contradict the expectation that 25% of the offspring peas would be yellow.

Given:

Confidence level,c = 90% = 0.90

Number of successes, x = 153

Sample size,n = 434 + 153 = 587

a) The sample proportion is the number of successes divided by the sample size is,

p = x/n

p = 153/587

p ≅ 0.2606

For confidence level 1 - α = 0.90, determine [tex]z_{\alpha /2} = z_{0.05}[/tex] utilizing the normal probability table in the appendix

[tex]z_{\alpha /2} = 1.64[/tex]

The margin of error is calculated as:

[tex]E = z_{\alpha /2} \sqrt{\frac{p(1-p)}{n} }[/tex]

[tex]E = 1.64\sqrt{\frac{0.2606(1 -0.2606)}{587} }[/tex]

E ≅ 0.0297

Therefore, the boundaries of the confidence interval are:

p - E = 0.2606 - 0.0297 = 0.2309 = 23.09%

p + E = 0.2606 + 0.0297 = 0.2903 = 29.03%

We are 90% confident that the true percentage of yellow peas is between 23.09% and 29.03%.

b) As 25% is between 23.09% and 29.03%, and 25% of the offspring are expected to be yellow peas and thus the results do not contradict expectations.

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Answer:

74.44

Step-by-step explanation:

[tex]P(10)=0.018(10)^3-0.294(10)^2+3.065(10)+55.190 \\ \\ =74.44[/tex]

it is vital that we first find the gradient/slope between the points .

⇒[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} } \\m=\frac{2-(-2)}{0-2} \\m=\frac{4}{-2} \\m=-2[/tex]

The general equation of a straight line is given by y=mx+c I will use the points (0,2) to find the value of y since the other variables are found already.

[tex]2=-2(0)+c\\\\c=2[/tex]

⇒This tells us that the equation of the line is y=-2x+2

Answer:

There is a proportion of 0.94% cities with average city temperatures lower than that of Kabul

Step-by-step explanation:

In this question, we are to calculate the proportion of average city temperatures lower than that of Kabul.

Firstly, we shall calculate the z score

Mathematically;

z = (value - mean)/standard deviation = 15 - 19.7/2 = -4.7/2 = -2.35

so we are to calculate the probability of; P(z< -2.35) = 0.0094

This means there is a proportion of 0.94% cities with average city temperatures lower than that of Kabul

The logarithmic function log ( x³ y² ) when expressed in terms of log x and log y is 3 log ( x ) + 2 log( y).

The opposite of exponentiation is the logarithm. In other words, the exponent to which a fixed number, the base a, must be raised in order to create a specific number x, is represented by the logarithm of that number.

Consider the logarithmic function log x³ y⁴

Using the logarithmic formula,

log ( a b ) = log  (a) + log (b)

We have,

log( x³ y² )  = log ( x³ ) + log( y² )

By applying the logarithmic property:

log ( xⁿ ) = n log x

We have,

log x³ y² = log ( x³ ) + log( y² )

log x³ y² =  3 log ( x ) + 2 log( y)

Therefore, the function log ( x³ y² ) in terms of log x and log y is 3 log ( x ) + 2 log( y).

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The answer to your question is s. sqrt (316.9) = 17.8 when you take the square root of that number. As a result, the correct response is 17.8.

This is further explained below.

Generally, Because you need to calculate the sample standard deviation to answer the question, use the following formula:

[tex]s = \sqrt {{ \sum of x - \bar x}{(n - 1} }[/tex]

There are 9 numbers, there, so n - 1 = 8

find the mean

[tex]\bar x[/tex]: 15 + 42 + 53 + . . . + 47 = 227. 227 / 9

x= 25.2

After that, deduct one from each number and then square the output, as seen here:

(15 - 25.2) = 104.0 (42 - 25.2)²

= 282.2 (53 - 25.2)²

= 772.8

After that, total up all of those values. The response to this, using this illustration as an example, is

[tex]x=\frac{ 2,535.2}{ 8}[/tex]

x= 316.9.

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[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{4}\\ b=\stackrel{opposite}{2}\\ \end{cases} \\\\\\ c=\sqrt{4^2 + 2^2}\implies c=\sqrt{16 + 4}\implies c=\sqrt{20}[/tex]

We are looking for values of x that will not make the equation undefined .Obviously the function has restrictions we have to make sure that x-7 is always ≥0 because it is under a square root

[tex]x-7\geq 0\\x\geq 7[/tex]

The domain of the function is all the real numbers greater or equal to  7 .

x≥7 ε R

The most appropriate choice for corrosponding angle will be given by-

x = 2 is the correct answer

What is corrosponding angle?

At first we need to understood what is angle, parallel lines and transversal

Angle

When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.

Parallel lines

Two lines are said to be parallel if on extending them indefinitely, they will never intersect

Transversal

Transversal is a line that intersects two or more parallel lines

Corrosponding angle

The angles formed in the same position on the same side of transversal when a transversal cuts two or more parallel lines

Here,

(7x + 3)° and (8x + 1)° are corrosponding angles.

Lines m and n are parallel.

So corrosponding angles are equals

By the problem,

(7x + 3) = (8x + 1)

8x - 7x = 3 - 1

x = 2

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The lengths 8 cm, 14 cm, 15 cm can form a triangle

Given 8 cm, 14 cm, 15 cm

These can form a triangle if the sum of any two sides of the triangle is greater than the third side.

8 + 14 > 15

14 + 15 > 8

8 + 15 > 14

Since all the above are true, we conclude that they can form a triangle

The equation 8(x+2) can be expressed using the distributive property as 8x + 16.

The distributive property can be described as the as the multiplication system of solving a particular expressions easily through the process of distributing another number  within the given  brackets.

The expression that was given as  8(x+2) , if it so be solved using the distributive property the we will have 8x + 16 because this result means that it has been shared in to part,  because the multiplication operation has been performed on the given expression.

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Answer:

18 more tickets

Step-by-step explanation:

What we know:

We know that 65 Tickets is 1 Prize.

We know we have 1,282 tickets.

So if 65 tickets is one prize

then to figure out how many for twenty then we:

65 x 20 = 1300

Now to figure out how many more she needs at the least we:

1300 - 1282 = 18

So for 1 more prize she needs 18 more tickets.

The sum of mAB and mBC is equal

360 - mAC

which makes otion A the correct answer

The measure of angles 1, 2, and 3 in exercise 11. are 100°, 80°, and 100°.

The measure of angles 1, 2, and 3 in exercise 12. are 47°, 133°, and 47°.

The measure of angles 1, 2, and 3 in exercise 13. are 80°, 80°, and 100°.

The measure of angles 1, 2, and 3 in exercise 14. are 94°, 86°, and 94°.

For 11. part:

Considering a transversal p that cuts two parallel lines l and m,

Each pair of internal angles on the same side of a transversal that intersects two parallel lines are supplementary.

m∠1 + 80° = 180°

m∠1 = 180° - 80°

m∠1 = 100°

Similarly, m∠1 + m∠2 = 180°

⇒ 100° + m∠2 = 180°

⇒m∠2 = 180° - 100°

⇒m∠2 = 80°

and also, m∠2 + m∠3 = 180°

⇒ 80° + m∠3 = 180°

⇒m∠3 = 180° - 80°

⇒m∠3 = 100°

Therefore, m∠1 = 100°, m∠2 = 80° and m∠3 = 100°.

For 12. part:

m∠3 + 133° = 180°(interior angles are supplementary)

m∠3 =  180° - 133°

⇒m∠3 = 47°

m∠2 = 133°(alternate interior angles)

The angle vertically opposite to 133° would also be 133°.

So, 133° + m∠1 = 180°( interior angles are supplementary)

m∠1 = 47°

Therefore, m∠1 = 47°, m∠2 = 133° and m∠3 = 47°.

For 13. part:

m∠3 = 100° (vertically opposite angle)

Let's assume the angle adjacent to ∠3 is x.

m∠3 + m ∠x = 180° (Linear pair property)

100° + m ∠x = 180°

m ∠x = 180° - 100°

m ∠x = 80°

Therefore, m∠1 = m∠2 = m ∠x  = 80°(Corresponding angles are equal.)

For 14. part:

m∠1 + 86° = 180°(co-interior angles are supplementary)

m∠1 = 180°- 86° = 94°

The angle vertically opposite to m∠1 is also equal to 94°.

94° + m∠1 = 180°(co-interior angles are supplementary)

m∠2 = 86°

Similarly, the angle vertically opposite to m∠2 is also equal to 86°.

86° + m∠3 = 180°(co-interior angles are supplementary)

m∠3 = 94°

Therefore, m∠1 = 94°, m∠2 = 86° and m∠3 = 94°.

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Answer:

Step-by-step explanation:

it would be 42,32 i know

Answer:

no

Step-by-step explanation:

Generally you can't really compare two functions with a different denomination, and you want to multiply the fractions by some fraction: [tex]\frac{a}{a}[/tex] which simplifies to one so we're not changing the value of the fraction at all but it helps so we have the same denominator.

You'll notice we can multiply 4 by 2 to get 8, which would give us the same denominator as 8.

[tex]\frac{23}{4}*\frac{2}{2}=\frac{46}{8}[/tex]

Now it's much easier to compare: [tex]\frac{47}{8}\text{ and }\frac{46}{8}[/tex] and here all we have to compare is the numerators, and obviously 47 is greater than 46 so the 47/8 is greater than the 23/4. This means 47/8 is not less than 23/4

The retirement counselors at the Valley View Bank$454404.05 > $129818.11 > $108780.71, then the Venus have the largest accumulation.

[tex](1+10)^{15}[/tex]Venus invests $1,200 per year and stops after 15 years.

He can get money : [tex]1200*[/tex] [tex](1+10)^{15}[/tex] at the first year,

We can use ,

Compound interest formula, S = [tex]P*(1+i)^{n}[/tex]

Where,

P means the Principal

I means the interest

n means the year

S means the principal and interest

At the second year he can get,

= 1200 * [(1+[tex]\frac{10degrees}{1}[/tex]) + ([tex]1+[\frac{10degrees}{1} ]^{2}[/tex])

The money of first year has two years interest,

The money of second year has one year interest.

So, we can calculate the 15th year he can get :

= 1200 * [[tex](1+\frac{10degrees}{1}] ^{1}) +(1+(\frac{10degrees}{1} )^{2} )+......(1+(\frac{10degrees}{1})^{15} )[/tex]

= 1200 * [tex]\frac{(1*1)*(1-1*1^{15} )}{1-1*1}[/tex]

The sum of geometric progression,

[tex]S_{n} =\frac{a*(1-q)^{n} }{1-q}[/tex]  ,  q≠1

= $ 41939.67

The rest of years he can get money :

= 41939.67 * ([tex](1+10percent))^{40-15}[/tex]

= $ 454404.053

Kevin can get money 1200* [[tex](1+(\frac{10degrees}{1}) ^{1} )+.......(1+(\frac{10degrees}{1} )^{15} )[/tex]

= 41939.67 at 30th year

Finally he can get money = 41936.67 [tex](1+\frac{10degrees}{1}) ^{40-15*0}[/tex]

= $ 108780.71

Rafael can get money : 1200 * [[tex](1+(\frac{10degrees}{1}) ^{1} )+.......(1+(\frac{10degrees}{1} )^{25} )[/tex]

= $ 129818.11

$454404.05 > $129818.11 > $108780.71

Therefore,

The retirement counselors at the Valley View Bank$454404.05 > $129818.11 > $108780.71, then the Venus have the largest accumulation.

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[tex] \frac{10}{4} \times \frac{23}{6} \\ = \frac{230}{24} \\ = \frac{115}{12} \\ = 9 \frac{7}{12} [/tex]

ATTACHED IS THE SOLUTION

Answer:

48[tex]units^{2}[/tex]

Step-by-step explanation:

The most appropriate choice for slope of a line will be given by-

Slope of the line = [tex]\frac{-19}{12}[/tex]

What is slope of a line?

At first it is important to know about line.

Line is a geometrical object that has only length but no breadth and no height.

Slope of a line is the tangent of the angle which the line makes with the positive direction of x axis

If [tex]\theta\\[/tex]  is the angle which the line makes with the positive direction of x axis, then slope of the line is given by

m = [tex]tan\theta[/tex]

If the line passes through ([tex]x_1,y_1[/tex]) and ([tex]x_2, y_2[/tex]) , then

slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Here,

[tex]x_1 = -3, y_1 = 9. x_2 = 9, y_2 = -10[/tex]

Slope = [tex]\frac{-10 - 9}{9 - (-3))}[/tex]

         = [tex]\frac{-19}{12}[/tex]

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