A tree outside Ellie's house casts a 125-foot shadow. At the same time of the day, Ellie casts a 5.5-foot shadow. If Ellie is 4 feet 10 inches tall, how tall is the tree in feet?

Answer:

[tex]t=7.4years[/tex]

Step-by-step explanation:

Let's clear t from the equation [tex]N=16.10^{0.15t}[/tex]. In order to clear t, we have to apply [tex]log_{10} (x)[/tex] in both side of the equations.

[tex]log_{10}N=log_{10}(16.10)^{0.15t}[/tex]

By using properties of the logarithm

[tex]log_{10} (a.b)}= log_{10}a+log_{10}b[/tex]

We obtain:

[tex]log_{10}N=log_{10}(16)+log_{10} (10^{0.15t})[/tex]

Ordering using the logarithm property  [tex]log_{10}a^{n} =nlog_{10}a[/tex] and [tex]log_{10} 10=1[/tex]

[tex]log_{10}N=log_{10}(16)+0.15tlog_{10}10[/tex]  

[tex]log_{10}N=log_{10}(16)+0.15t[/tex]

Clearing t

[tex]t=\frac{log_{10}N-log_{10}(16)}{0.15}[/tex] using the logarith property [tex]log_{10}a-log_{10}b=log_{10}\frac{a}{b}[/tex]

we obtain:

[tex]t=\frac{log_{10}\frac{N}{16} }{0.15}[/tex]

The number of Elm trees is N = 204

Solving

[tex]t=\frac{log_{10}\frac{204}{16} }{0.15}\\t=\frac{log_{10}12.75}{0.15}=7.370[/tex]

Round to the nearest tenths place [tex]t=7.4years[/tex]

Answer:

$179.17

Step-by-step explanation:

You already know the formula but you have it typed incorrectly.  The rt is raised as a power to the e.  Just in case you didn't know that.  Filling in our formula with what we have gives us:

[tex]A(t)=125e^{(.18)(2)[/tex]

Simplify that power to .36 and we have

[tex]A(t)=125e^{.36}[/tex]

Now raise e to the power of .36 on your calculator and get

A(t)= 125(1.433329415)  and

A(t) = $179.17

Answer:

C 179 is the answer.

Step-by-step explanation:

m<6 = 180° - m<3

m<6 = 180° - 130°

m<6 = 50°

Answer: m6 equals 50 degrees

Step-by-step explanation: Since AB and CD are parallel u just solve for m2 which is the same as m6 which would be 180-130=50

Starting from the Pythagorean identity, we deduce

[tex]\sin^2(x)+\cos^2(x) = 1 \iff \cos^2(x) = 1-\sin^2(x) \iff \cos(x) = \pm\sqrt{1-\sin^2(x)}[/tex]

If we plug in the value 7/10 for sin(x), we have

[tex]\cos(x) = \pm\sqrt{1-\dfrac{49}{100}} = \pm\sqrt{\dfrac{51}{100}}=\pm\dfrac{\sqrt{51}}{10}[/tex]

Answer:

The Answer is likely 60.

Step-by-step explanation:

Two standard deviations from 70 is 60, because the actual deviation is 5, so 2 of those equals 10. 10 - 70 = 60.

Answer:

60

Step-by-step explanation:

Two standard deviations below the mean is:

70 - 2(5) = 60

Answer:

x = -9

Step-by-step explanation:

Multiply both sides by √(x - 6) to eliminate the fraction:

√(3x) = 3√(x - 6)

Now square both sides:  

3x = 9(x - 6), or 3x = 9x - 54.  

Combining the x terms results in -6x = -54, and thus x = 9.

Answer:

The correct answer is option D.  x = 9

Step-by-step explanation:

From the attached question we get an expression,

√3x/√(x - 6) = 3

To find the solution of given expression

√3x/√(x - 6) = 3

Squaring both side we get,

3x/(x - 6) = 9

3x = 9 * (x - 6)

3x = 9x - 54

9x - 3x = 54

6x = 54

x = 54/6 = 9

Therefore the correct option is D.  x = 9

Step-by-step answer:

Given:

Geometric sequence with

second term, T2 = 6

third term, T3 = 12

Wants to have the explicit and recursive rules.

Solution:

common ratio, r = 12/6 = 2

Therefore the first term, T1

= second term /r

= 6/2

=3

Thus the absolute rule is

Tn = T1 *r^(n-1)      where T1 = 3, r=2.  Check: T3 = T1*2^(3-1) = 3*2^2=12 ...good

The recursive rule (depending on the previous term)

Tn = Tn-1*r = 2*Tn-1

The explicit rule for the sequence is a_n = 3 * 2^(n-1), and the recursive rule is a_n = a_(n-1) * 2. These were determined by identifying the common ratio of the sequence as 2.

In a geometric sequence, each term is generated by multiplying the previous term by a common ratio. Given the second term (6) and third term (12) in the sequence, we can identify the common ratio by dividing the third term by the second term. So, 12 divided by 6 equals 2. Therefore, the common ratio is 2.

So, the explicit rule (the nth term) of this sequence would be: a_n = a_1 * r^(n-1) = 6 / 2 * 2^(n-1) = 3 * 2^(n-1).

The recursive rule for the sequence would be: a_n = a_(n-1) * r = a_(n-1) * 2.

To summarize, we determined the common ratio to be 2 by dividing the third term by the second term. We then used this ratio to create the explicit and recursive rules for the geometric sequence.

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Answer:

Step-by-step explanation:

x² + 5x – 104 = 0

Factor using the AC method.  Here, a = 1 and c = -104.  Multiplied together, ac = -104.  Factors of -104 that add up to +5 are +13 and -8.

(x + 13) (x - 8) = 0

x = -13, 8

A negative width doesn't make sense, so x = 8.  Therefore, the width is 8 inches and the length is 5 more than that, or 13 inches.

Answer:

width = 8

length = 13

Step-by-step explanation:

All that is left to do is factor the results that you have

x^2 + 5x - 104 = 0

You need two numbers that are fairly close together (ignore the sign differ by 5) and multiply to 104.

The two numbers are 8 and 13

More formally stated, the quadratic can be factored to

(x + 13)(x - 8) = 0

x - 8 =0

x - 8 + 8 = 8 + 0

x = 8

x + 13 = 0 has no meaning.

That means that the width ( a positive number ) = 8

The length is 5 more = 13

Answer:

If you could insert a picture of the graphs that would help! thank you!

Step-by-step explanation:

Answer:

6√2.

Step-by-step explanation:

The two radii are equal length and form a right angle, so the resulting triangle is 45-45-90.  Therefore, the length of the chord (the hypotenuse of the triangle) is 6√2.

Answer: 45°

Step-by-step explanation:

There are 180 degrees in a triangle so

180-80=100-55=45°

Answer:

d. 3x³ and 2x³

Step-by-step explanation:

In standard form, the terms of a polynomial expression are written in order of descending powers of the variable. There will be only one term for any given power of the variable.

Here, there are two terms that have x to the third power. These terms must be combined to write the expression in standard form. They are the only terms that can be combined: 3x³ + 2x³ = 5x³.

Answer:

b = 17

Step-by-step explanation:

Since PQ = RQ then ΔPQR is isosceles and QS is a perpendicular bisector

Hence PS = RS = 17 ⇒ b = 17

Answer:

33.75

Step-by-step explanation:

Step 1- Find the decimal form of 35%

Step 2- When you find that multiply that by 25

Step 3- When you find the answer to step 2 add that to 25

That is your answer

Final answer:

The price that Fred will pay the groomer the next time when his dog has a haircut is  $33.75.

Explanation:

The question asks us to calculate the new price Fred will pay for his dog's haircut after the groomer increases the price by 35%. To find the new price, we'll use the formula for calculating percentage increase, which is: New Price = Original Price + (Original Price * Percentage Increase).

First, convert the percentage increase to a decimal by dividing it by 100, so 35% becomes 0.35. Then, multiply the original price of $25 by 0.35 to find the amount of the increase, which is $8.75.Finally, add the increase to the original price to find the new price, which is $25 + $8.75 = $33.75. So, Fred will pay $33.75 the next time his dog has a haircut.

Fluid ounces, 47 more

Answer:

F. Hyperbola

Step-by-step explanation:

In each napped, you'll have a parabola, combined they form an hyperbola.

It's one of the various shapes that can be produced by a plane intercepting a right circular cone, as you can see in the attached picture.

Each plane intersection is different, based on the angle and the position it passes through.

I hope that helps.

Answer:

hyperbola

Step-by-step explanation:

apeex

Let's call dimes x and the quarters x+3 since we have 3 more of them.

x+x+3=45

2x=42

x=21

we have 21 dimes and 23 quarters

21*0.10=2.1

23*0,25=5.98

if we add those together it equals 8.08

Answer:

$8.10

Step-by-step explanation:

Let d and q represent the # of dimes and quarters, respectively.  Then write equations reflecting this story:

q = d + 3, and d + q = 45.  Substitute d + 3 for q in the second equation, obtaining:

d + d + 3 = 45, or 2d = 42, or d = 21.  Then there are 21 dimes and 24 quarters.  That comes to $2.10 + $6.00, or $8.10.

Answer:

a) Function

b) Not a function

c) Function

d) Not a function

Step-by-step explanation:

a) Domain = { 7,-6,2}

   Range = {5,0,3}

It is a function as every value in domain has some and unique value mapped to it in Range

b)

Domain = { 7,-6,2}

   Range = {5,0,-2,3}

It is not a function as -6 value in domain has two values mapped to it in Range

c)

Domain = { 7,2}

   Range = {-6,-7}

It is a function as every value in domain has some and unique value mapped to it in Range

d)

Domain = { 7,-6}

   Range = {5,0,3}

It is not a function as 7 value in domain has two values 3 and 5 mapped to it in Range

Answer:

26

Step-by-step explanation:

80 divided by three = 26.666666

26 times 3 = 78

2 leftover

The number sticker each student get is 26 and the number stickers teacher got is 2.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Given that, three friends buy one pack of 80 stickers.

Now, number of stickers each friend = 80/3

3|80|26

  78
_____
   2

Therefore, the number sticker each student get is 26 and the number stickers teacher got is 2.

To learn more about the division visit:

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see picture attached.

i hope this helped !!

ANSWER

Point-slope form:

[tex]y + 5 = -3(x - 1)[/tex]

Slope-intercept form;

[tex]y = - 3x - 2[/tex]

EXPLANATION

The point-slope form of a line is given by:

[tex]y-y_1=m(x-x_1)[/tex]

We need to find the slope using the formula:

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

Let us substitute the point (1, –5) and (–3, 7).

This implies that,

[tex]m = \frac{7 - - 5}{ - 3 - 1} [/tex]

[tex]m = \frac{12}{ - 4} = - 3[/tex]

The point slope form now becomes,

[tex]y - - 5 = - 3(x - 1)[/tex]

[tex]y + 5 = -3(x - 1)[/tex]

To find the slope intercept form, we expand to obtain;

[tex]y = - 3x + 3 - 5[/tex]

[tex]y = - 3x - 2[/tex]

Answer:

the third one.

Answer: C) V = 562.5π [tex]in^{3}[/tex] ; S = 225π [tex]in^{2}[/tex]

Step-by-step explanation: Please see the image below!

Answer:

To eliminate x multiply the first equation by 3 and the second equation by 4

To eliminate y multiply the first equation by 3 and the second equation by 2

Step-by-step explanation:

We are given a system of linear equations;

4x-2y=7

3x-3y=15

solving by elimination means that we shall be getting rid of one of the variables in order to determine the other. In this case we can either eliminate x or y. In order to eliminate any of these variables, we first must make their coefficients equal in both equations. To eliminate x;

Multiply the first equation by 3 and the second equation by 4.

To eliminate y;

Multiply the first equation by 3 and the second equation by 2.

Let [tex]a_1,\ldots,a_4[/tex] denote the ages of the 4 candidates. Then

[tex]\dfrac{a_1+a_2+a_3+a_4}4=40[/tex]

[tex]a_1+a_2+a_3+a_4=160[/tex]

[tex]\dfrac{a_1+a_2+a_3}3+\dfrac{a_4}3=\dfrac{160}3[/tex]

The average age of the first 3 candidates is 42, so

[tex]\dfrac{a_4}3=\dfrac{160}3-42[/tex]

[tex]\implies\boxed{a_4=160-3\cdot42=34}[/tex]

Answer:

E = (3b+28)/2

T=3b+28

E= t/2

Step-by-step explanation:

The coat of the 4 pizzas would be $28, and an unknown amount of breadsticks that cost 3 dollars each.

Im going to use B as the amount of breadsticks bc i dont know what its supposed to be but that should be the correct answer.

T=3b+28

E= t/2

Answer:

D. 2(√{x} + √{x - 2})

Step-by-step explanation:

As hinted in the question, we have to simplify the denominator.

To understand it easier, let's imagine we have x - y in the denominator.  If we multiply it with x + y we'll get x² - y², right?  Check the next line:

(x - y) (x + y) = x² + xy -xy - y² = x² - y²

If we have the square of those nasty square roots, it will be much simpler to deal with.  So, let's multiply the initial fraction using x+y, but with the real values:

[tex]\frac{4}{\sqrt{x} - \sqrt{x - 2} } * \frac{\sqrt{x} + \sqrt{x - 2}}{\sqrt{x} - \sqrt{x - 2}} = \frac{4(\sqrt{x} + \sqrt{x - 2})}{(\sqrt{x} )^{2} - (\sqrt{x - 2} )^{2} }[/tex]

Then we simplify:

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

Answer is D. 2(√{x} + √{x - 2})

Answer:

7ab+5

Step-by-step explanation:

add like terms (3ab+4ab=7ab)

5 doesn't have a like term so it stays by itself

Hey there! :)

3ab + 4ab + 5

In order to simplify this, we must add like terms. In addition, when simplifying, you can ONLY add like terms.

Since both "3ab" & "4ab" contain "ab," you are able to combine them together!

When combining like terms, you only add the numerical value, not the letters.

This leaves us with : 7ab + 5

Therefore, your answer is 7ab + 5

~Hope I helped!~

Answer:

Option a) x = −1, 5.4

Step-by-step explanation:

we have

[tex]f(x)=x^{2} -x-12[/tex]

[tex]g(x)=3.4x-6.6[/tex]

equate f(x) and g(x)

[tex]x^{2} -x-12=3.4x-6.6[/tex]

Solve the quadratic equation by graphing

The solutions are x=-1 and x=5.4

see the attached figure

Answer:

x= -1, 5.4

Step-by-step explanation:

[tex]f(x)= x^2-x-12[/tex]

[tex]g(x)= 3.4x -6.6[/tex]

f(x) is a quadratic equation and g(x) is a linear equation

To find f(x)= g(x) we need to find the point where the graph  of f(x) and g(x) intersects.

The quadratic equation f(x) and linear equation g(X) intersects at two points

from the graph f(x)= g(x) at x= -1 and x=5.4

Answer:

https://socratic.org/questions/how-do-you-write-the-equation-of-the-quadratic-function-with-roots-6-and-10-and-

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Given the roots are x = 6 and x = 10, then

the factors are (x - 6) and (x - 10)

The quadratic is then the product of the roots

y = a(x - 6)(x - 10) ← a is a multiplier

To find a substitute (8, 2) into the equation

2 = a(2)(- 2) = - 4a ( divide both sides by - 4 )

a = - [tex]\frac{1}{2}[/tex]

Hence

y = - [tex]\frac{1}{2}[/tex](x - 6)(x - 10) ← expand factors

y = - [tex]\frac{1}{2}[/tex](x² - 16x + 60) ← distribute

y = - [tex]\frac{1}{2}[/tex] x² + 8x - 30

Answer:

20√2 meters (approximately 28.28 m)

Step-by-step explanation:

It may help to make a diagram. Because this is a 45 45 90 triangle, you can use those rules to help solve.

Final answer:

The distance from the top of a totem pole to the end of its shadow, when the angle of elevation of the sun is 45 degrees, is approximately 28.28 meters.

Explanation:

The student has presented a problem that involves using trigonometry to calculate the distance from the top of a totem pole to the end of its shadow when the angle of elevation of the sun is 45 degrees. To solve this, we can use the concept of right-angled triangles and the properties of special triangles, specifically a 45-45-90 triangle where the two legs are congruent. Since the angle of elevation is 45 degrees and the length of the shadow is given as 20 meters, we know that in this special right triangle, the lengths of the two legs are equal. Therefore, the distance from the top of the totem pole to the end of the shadow (the hypotenuse of the triangle) is the length of the shadow times the square root of 2, based on the Pythagorean theorem.

Using the formula hypotenuse = leg × √2, we substitute the leg length of 20 meters to get hypotenuse = 20 m × √2, which equals approximately 28.28 meters.