A man tied a rope to the top of a tree, which is 'x' m tall. The other end of the rope was tied to
the ground, 20 m away from the base of the tree. Given that the length of the rope is 16 m
longer than the height of the tree, find the height of the tree.
(by using pythagoras' theorem)​

Answer:

c.

Step-by-step explanation:

That is the only answer choice that makes the most sense.

±10 = √100; in this case, they want the non-negative value, so it is 10.

Answer: c. 100

Step-by-step explanation: √-81 and √-3 are not possibly unless complex numbers applied

√100 = 10 > 9 valid answer

√27 = 5.196 < 9 invalid answer

√3 = 1.732 < 9 invalid answer

√81 = 9 ≡ 9 invalid answer

Only c is the answer.

Hope it helped!

Answer with step-by-step explanation:

1) Inverse of [tex]f(x) = 6x -24[/tex]:

Make the function equal to y to get [tex]y=6x-24[/tex].

Now making [tex]x[/tex] the subject of the function:

[tex]6x=y+24\\\\x=\frac{y+24}{6} \\\\x=\frac{y}{6} +4[/tex]

Change back the variable [tex]y[/tex] to [tex]x[/tex] and this is the inverse.

[tex]f'(x)=\frac{x}{6} +4[/tex]

2. Inverse of [tex]g(x) = 3x^2 - 5[/tex]:

Making the function equal to y to get: [tex]y=3x^2 - 5[/tex]

Now making [tex]x[/tex] the subject of the function:

[tex]3x^2=y+5\\\\x^2=\frac{y+5}{3}[/tex]

Taking square root on both sides to get:

[tex]x=\sqrt{\frac{y+5}{3} }[/tex]

Change back the variable [tex]y[/tex] to [tex]x[/tex] and this is the inverse.

[tex]g'(x)=\sqrt{\frac{x+5}{3} }[/tex]

Answer:

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

2)  [tex]g^{-1}(x)=\sqrt{\frac{x+5}{3}}[/tex]

Step-by-step explanation:

1) To find the inverse of the function [tex]f(x) = 6x -24[/tex] you need to follow these steps:

- Since [tex]f(x)=y[/tex], you can rewrite the function:

 [tex]y = 6x -24[/tex]

- Solve for "x":

[tex]y+24=6x\\\\x=\frac{y+24}{6}\\\\x=\frac{y}{6}+4[/tex]

- Exchange the variables:

[tex]y=\frac{x}{6}+4[/tex]

Then, the inverse is:

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

2) To find the inverse of the function [tex]g(x) = 3x^2 - 5[/tex] you need to follow these steps:

- Since [tex]g(x)=y[/tex], you can rewrite the function:

 [tex]y= 3x^2 - 5[/tex]

- Solve for "x":

[tex]y= 3x^2 - 5\\\\\frac{y+5}{3}=x^2\\\\x=\sqrt{\frac{y+5}{3}}[/tex]

- Exchange the variables:

[tex]y=\sqrt{\frac{x+5}{3}}[/tex]

 Then, the inverse is:

[tex]g^{-1}(x)=\sqrt{\frac{x+5}{3}}[/tex]

Answer:

10

Step-by-step explanation:

I am pretty sure this is the answer because, the two sides added have to be greater than the longest side.

Answer:

it will be c because have area in box of 12,672

Answer:

D. 3,568

Step-by-step explanation:

We are looking for SURFACE area not area

A=2(wl+hl+hw)=2·(18·16+44·16+44·18)=3568

Answer:

5 = y

Step-by-step explanation:

As discussed in my video on my channel [Username: MATHEMATICS WIZARD], whenever you are dividing mixed numbers, fractions, etcetera, you multiply the first term by the divisor's multiplicative inverse [reciprocal].

Ex: 2 ÷ 1⁄11 → 2 × 11

I hope this helps, and as always, I am joyous to assist anytime.

Answer:

7 lbs

Step-by-step explanation:

Given:

apples per pound= 88 cents

total money= $6.00

                   =600 cents

Now

1 lb= 88 cents

let x be the pounds of apple in 600 cents then

x lb=600 cents

By cross-multiplication we get:

600=88x

x=600/88

x= 6.81

x=7 pounds

7 pounds of apple can be bought by $6.00 !

Answer: 7 lb

Step-by-step explanation:

You know that in that fruit stand each pound of apple costs 88 cents.

Therefore, if you have $6.00, you need to divide this amount by 88 cents ($0.88 ) in order to calculate the pounds of apples you can buy.

Therefore, the pounds of apples you can buy to the nearest whole number is the following:

[tex]amount\ of\ apples=\frac{6.00}{0.88}=7\ lb[/tex]

Answer:

1. Rectangle

2. 376.8 cm

3. 379.94 square feet

4. –4 and 4

Step-by-step explanation:

A square is always a rectangle.

If a wheel has a radius of 15 cm, it would travel approximately 376.8 cm per 4 revolutions.

If the diameter of a circular garden is 22 feet, the approximate area of the garden is 379.94 square feet.

The solutions to the equation y2 – 1 = 15 is –4 and 4.

rectangle

376.8 cm

379.94 square feet

–4 and 4

Answer:

Problem: [tex]\frac{x-8}{x+11} \cdot \frac{x+8}{x-11}[/tex]

Answer: [tex]\frac{x^2-64}{x^2-121}[/tex]

Step-by-step explanation:

[tex]\frac{x-8}{x+11} \cdot \frac{x+8}{x-11}[/tex]

Writing as one fraction:

[tex]\frac{(x-8)(x+8)}{(x+11)(x-11)}[/tex]

Now before we continue, notice both of your bottom and top are in the form of (a-b)(a+b) or (a+b)(a-b) which is the same format.

That is, we are multiplying conjugates on top and bottom.

When multiplying conjugates, all you have to do it first and last.

For example:

[tex](a-b)(a+b)=a^2-b^2[/tex].

So your problem becomes this after the multiplication of conjugates:

[tex]\frac{x^2-64}{x^2-121}[/tex]

Answer:

[tex] \frac { ( x - 8 ) ( x + 8 ) } { ( x + 1 1 ) ( x - 1 1 ) } [/tex]

Step-by-step explanation:

We are to find the product of the rational expression below:

[tex] \frac { x - 8 } { x + 1 1 } \times \frac { x + 8 } { x - 1 1 } [/tex]

We are to multiply these terms by taking the LCM to get:

[tex] \frac { ( x - 8 ) ( x + 8 ) } { ( x + 1 1 ) ( x - 1 1 ) } [/tex]

Since the signs of all the terms are different so we cannot add them up.

Answer:

17.8 cm²

Step-by-step explanation:

Given 2 similar figures with linear ratio = a : b, then

ratio of areas = a² : b²

For the 2 similar cones

ratio of radii = 2 : 5, hence

ratio of areas = 2² : 5² = 4 : 25

Let x be the area of the smaller cone then by proportion

[tex]\frac{x}{4}[/tex] = [tex]\frac{111}{25}[/tex] ( cross- multiply )

25x = 444 ( divide both sides by 25 )

x = 17.76

Hence area of smaller cone = 17.8 cm² ( to the nearest tenth )

17.8 cm²

The total area of the surface of a 3-dimensional figure. The surface area of the solid object is the measure of the total area that the surface of the object occupies.

we must to course choose 3 dissimilar faces to capture length l, width w, or height h:

Given 2 similar figures with linear ratio = a: b, then

ratio of areas = a² : b²

For the 2 similar cones

ratio of radii = 2 : 5, hence

ratio of areas = 2² : 5² = 4 : 25

Let x be the area of the smaller cone then by proportion

[tex]\frac{x}{4} =\frac{111}{25}[/tex]

=  ( cross- multiply )

25x = 444 ( divide both sides by 25 )

x = 17.76

therefore an area of smaller cone = 17.8 cm² ( to nearest tenth )

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Answer:

60%

Step-by-step explanation:

To find percent change you take the new value, subtract it from the old value and then put that number over the original value. In this case it would be 960-600=360, 360/600=36/60=6/10 or 60 percent.

Answer:

D

Step-by-step explanation:

Answer:

90 yards

Step-by-step explanation:

If the length of a rectangle is four times it’s width and the area of the rectangle is 324 ft.², its perimeter is 90 yards.

Formula: Length = Area / Width

P = 2(4x) + 2(x)

P = 72 + 18

Its perimeter if 90 ft.

If length of the rectangle be l & width of the rectangle be w.

Then Area of the rectangle (A) = Length × Width

                                                   = (l × w) sq. unit

If length of the rectangle be l & width of the rectangle be w.

Then, Perimeter of the rectangle = 2×(l+w) unit

Given, Area of the rectangle = 324 sq. ft

Let, Width (w) = x unit

So, Length (l) = 4 times it's width = 4x unit

∴ Area = l × w = (4x)(x)

⇒ 324 = 4x²

⇒ x² = 324/4

⇒ x² = 81

⇒ x = [tex]\sqrt{}[/tex]81

⇒ x = 9  (neglecting negative value)

So, it's width = 9 ft.

Then, its length = (4×9) ft. = 36 ft.

∴ Perimeter =  2×(l+w) =  2×(36+9) ft. =  (2×45) ft. = 90ft.

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Answer:

[tex]10^4[/tex] or 10000

Step-by-step explanation:

So this is just a moving over of decimal.  It is a factor of 10. How many factors of 10 depends on many times we need to bring that decimal to the right.

Let's count.

3.4758.17

    | | | |

    That is 4 times to the right.

So you need 4 factors of 10, or [tex]10^4[/tex].

You need to multiply by [tex]10^4[/tex] (or 10000)

10,000

In your question, it asks what number you have to multiply by to get from 3.475817 to 34,758.17.

In order to find your answer, we can perform the quickest way to find the answer by moving the decimal place to the right.

To get from 3.475817 to 34,758.17, we're going to need to move the decimal place 4 times to the right, due to the fact that we're trying to get to a number where the decimal place is farther to the right.

We know that decimals goes by 10s, meaning that we would need to multiply by 10 in each move.

In other words, every time we move the decimal point to the right, we're multiplying by 10.

Since we moved 4 times, we need to multiply 10, 4 times.

[tex]10*10*10*10=10,000[/tex]

When you mutliply the 10s, you should get 10,000.

This means that you need to multiply by 10,000 to get from 3.475817 to 34,758.17

You can multiply 3.475817 by 10,000 to see if it gets you 34,758.17

[tex]3.475817 * 10000=34,758.17[/tex]

When you multiply the numbers, you would get 34,758.17, meaning that the answer is CORRECT.

P(1, 4), Q(6, 4), R(6, 1), and S(1, 1)

New coordinates of the rectangle after a reflection over the x-axis is:

P'(1, -4), Q'(6, -4), R'(6, -1), and S'(1, -1)

New coordinates of the rectangle after a reflection over the y-axis is:

P"(-1, 4), Q"(-6, 4), R"(-6, 1), and S"(-1, 1)

.

Answer:

Over the Y axis.

P(-1, 4), Q(-6, 4), R(-6, 1), and S(-1, 1)

Over the X axis:

P(1, -4), Q(6, -4), R(6, -1), and S(1, -1)

Step-by-step explanation:

In order to finde the new coordinates after a reflection on the Y or X axis, you just have to change the sign of the opposite variable, for example if you want to reflect the points on the Y axis you change the signs of all the X´s on the points, and the same with the reflections of the X axis, you have to change the signs of all the Y´s on the points.

[tex]\log_ab-\log_ac=\log_a\dfrac{b}{c}\\\\\log_315-\log_310=\log_3\dfrac{15}{10}=\boxed{\log_3\dfrac{3}{2}}[/tex]

Answer:

B.

Step-by-step explanation:

They have the same base so use the quotient rule (since they have a minus sign in between).

We are using this rule: [tex] log_a(b)-log_a(c)=log_a(\frac{b}{c})[/tex]

So we have  [tex] log_3(15)-log_3(10)=log_3(\frac{15}{10})[/tex]

We can reduce the inside fraction... 15/10=3/2

So the answer is B.

Answer:

a) P(z<-0.66) = 0.2546

b) P(-1<z<1) = 0.6826

c) P(z>1.33) = 0.9082

Step-by-step explanation:

Mean = 300

Standard Deviation = 75

a) Less than 250 hours

P(X<250)=?

z = x - mean/ standard deviation

z = 250 - 300 / 75

z = -50/75

z = -0.66

P(X<250) = P(z<-0.66)

Looking for value of z = -0.66 from z score table

P(z<-0.66) = 0.2546

b. Between 225 and 375 hours

P(225<X<375)=?

z = x - mean/ standard deviation

z = 225-300/75

z = -75/75

z = -1

z = x - mean/ standard deviation

z = 375-300/75

z = 75/75

z = 1

P(225<X<375) = P(-1<z<1)

Looking for values from z score table

P(-1<z<1) = P(z<1) - P(z<-1)

P(-1<z<1) = 0.8413 - 0.1587

P(-1<z<1) = 0.6826

c. More than 400 hours

P(X>400) =?

z = x - mean/ standard deviation

z = 400-300/75

z = 100/75

z = 1.33

P(X>400) = P(z>1.33)

Looking for value of z = 1.33 from z-score table

P(z>1.33) = 0.9082

Answer:

c) 325

Step-by-step explanation:

The fraction of students that went to the movies is 14/112. To find the number of students who went to the movies from a larger group, you have to find a fraction equal to 14/112, whose denominator is 2600 (the number of students from the larger group).

14/112 = x/2600

You can do cross multiplication here. Cross multiplication is multiplying the denominator of one fraction by the numerator of the fraction equivalent to it. That product will be equal to the numerator of the first fraction * denominator of the second fraction.

112*x = 14*2600

x = 325

Approximately 325 students out of 2600 students would've gone to the movie last weekend.

Answer:

[tex]\frac{5\pi }{18}[/tex]

Step-by-step explanation:

To convert from degree to radian measure

radian measure = degree measure × [tex]\frac{\pi }{180}[/tex]

For 50°, then

radian = 50 × [tex]\frac{\pi }{180}[/tex]

Cancel the 50 and 180 by 10, leaving

radian measure = [tex]\frac{5\pi }{18}[/tex]

5

Step-by-step explanation:

You can use Tan(45)=S/5 to solve for S. Tan basically means Opposite/Adjacent. So the opposite side is S and the adjacent side is S. You plug tan(45) into your calc and then multiply it by 5.

Proportion Below

Tan(45)/1 = S/5

You cross multiply to get Tan(45)*5=S

S would be 5

To check you can use the Pythagorean theorem a^2+b^2=c^2

5^2+5^2=

[tex] {5}^{2} + {5}^{2} = \sqrt{50} [/tex]

25+25=50

Answer:

9x^8

Step-by-step explanation:

A perfect square is a number that has a whole number square rooth. Therefore we need to find two numbers 'a' and 'b' that satisfy the following equation:

3x^4 = sqrt(ax^b)

(3x^4)^2 = ax^b

9x^8 = ax^b

a=9 and b=8.

Therefore, the term 9x^8 is a perfect square of the root 3x^4.

Final answer:

The 100th term of the arithmetic sequence is found using the formula an = a1 + (n-1)d. In this sequence, the 100th term is -290.

Explanation:

The question asks for the 100th term of an arithmetic sequence with a common difference. The given sequence is 7, 4, 1, -2, ... which shows a constant decrease of 3 between consecutive terms, hence it's an arithmetic sequence with a common difference (-3). To find the 100th term (a100) of the sequence, we can use the formula for the nth term of an arithmetic sequence: an = a1 + (n-1)d, where a1 is the first term, and d is the common difference.

Plugging in the values, we get:

We calculate the 100th term as follows:

a100 = 7 + (100 - 1)(-3)

a100 = 7 - 297

a100 = -290

Therefore, the 100th term of the sequence is -290.

Answer:

Yea, it is A

Step-by-step explanation:

Answer:

It's B. 40,653

Step-by-step explanation:

Answer:b

Step-by-step explanation:

Answer:

2, 10.

Smallest number = 20.

Step-by-step explanation:

It must have 2 as a factor because 4 is a factor,  and 2 is a factor of 4.

Also 4 *5 = 20 so 10 must be a factor.

The smallest number possible is 20.

The smallest number that has both 4 and 5 as factors is 20. In addition to 4 and 5, this number also has 1, 2, 10, and 20 as factors.

When a number has 4 and 5 as factors, this means that it must be a multiple of both 4 and 5. As a result, the smallest number this could be would be 20 (since 4*5 equals 20). Moreover, that given number will also have 1, 2, and 10 as factors. This is because 1 is a factor of every number, 2 is a factor of every even number, and 10 is a result of 2*5.

The number will also be divisible by 20 itself, because any number must be divisible by itself. This basic fact is often forgotten but very important.

To summarize, the factors of the smallest possible number would be 1, 2, 4, 5, 10, and 20.

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Answer: Last Option

[tex]V=240\ cm^3[/tex]

Step-by-step explanation:

The formula for calculating the volume of a prism is:

[tex]V = lwh[/tex]

Where l is the length, w is the width and h is the length.

In this case we know that:

[tex]l=10\ cm\\w=3\ cm\\h=8\ cm[/tex]

Therefore:

[tex]V =10*3*8[/tex]

[tex]V=240\ cm^3[/tex]

Answer: [tex]240\ cm^3[/tex]

Step-by-step explanation:

The volume of a right rectangular prism is given by :-

[tex]\text{Volume}=lwh[/tex] , where l is length , w is width and h is the height of the right rectangular prism.

In the given picture , we have the length of the prism = 10 cm

Width of the prism = 3 cm

Height of the prism = 8 cm

Then , the volume of a right rectangular prism will be :-

[tex]\text{Volume}=10\times3\times8\\\\\Rightarrow\ \text{Volume}=240\ cm^3[/tex]

Answer:

other answer is wrong this is the correct answer 100%

Step-by-step explanation:

x= 1

and

x= "n.a."

Answer:

Exponent.

[tex]\Huge \boxed{25}[/tex]

Step-by-step explanation:

2 is should be exponent.

5 is the base.

In the expression 5², the 2 represents the exponent.

[tex]\displaystyle 5^2=5\times5=25[/tex]

Exponent, and 25 is the correct answer.

The 2 in [tex]5^{2}[/tex] would represent the exponent.

An exponent is the number of times a base is multiplied by itself. The base on the other hand is the number that is being raised to a certain power.

Image is provided

Answer:

[tex]f(a)=5-8a+15a^2[/tex]

[tex]f(a+h)=5-8a-8h+15a^2+30ah+15h^2[/tex]

[tex]\frac{f(a+h)-f(a)}{h}=-8+30a+15h[/tex]

Step-by-step explanation:

We are given [tex]f(x)=5-8x+15x^2[/tex].

We want to find [tex]f(a)[/tex] so we just replace the x there with a giving us:

[tex]f(a)=5-8a+15a^2[/tex].

We want to find [tex]f(a+h)[/tex] so we just replace x with (a+h) now giving us:

[tex]f(a+h)=5-8(a+h)+15(a+h)^2[/tex].

We will need to distribute and multiply things out here for later use so let's go ahead and do that:

[tex]f(a+h)=5-8(a+h)+15(a+h)^2[/tex]

[tex]f(a+h)=5-8a-8h+15(a+h)(a+h)[/tex]

[tex]f(a+h)=5-8a-8h+15(a^2+2ah+h^2)[/tex]

[tex]f(a+h)=5-8a-8h+15a^2+30ah+15h^2[/tex]

We want to find [tex]\frac{f(a+h)-f(a)}{h}[/tex] where h is not 0.

This requires the parts we found above:

[tex]\frac{f(a+h)-f(a)}{h}[/tex]

[tex]\frac{(5-8a-8h+15a^2+30ah+15h^2)-(5-8a+15a^2)}{h}[/tex]

There are some thing that will zero out (cancel out) in the numerator.

You have 5-8a+15a^2 in both parenthesis and you are subtracting so that part zero's out so you have this now:

[tex]\frac{-8h+30ah+15h^2}{h}[/tex]

Now you can divide h from top and bottom giving you:

[tex]\frac{-8+30a+15h}{1}[/tex]

[tex]-8+30a+15h[/tex]

Answer:

y = 1/2 x + 8

Step-by-step explanation:

We are given the y intercept and the slope, so we can write the equation using the slope intercept form

y = mx+b  where m is the slope and b is the y intercept

y = 1/2 x + 8

Answer:

c. 6 units

Step-by-step explanation:

The diameter of a circle with a circumference of 18.84956 is 6 units.

Use the formula: C=2πr

d=C

π=18.85

π≈6

Answer:

$1440

Step-by-step explanation:

First find the the area with feet.

18*16=288

Now convert into sq. yards

288/3=96

Finally, multiply 96 by 15

96*15=1440

$1440

Answer:

$1440

Step-by-step explanation:

It will cost $1440 to carpet a rectangular floor 18 by 16 feet if the carpet costs $15 a square yard.

18 feet ⋅ 16 feet = 288

288 feet ÷ 3 = 96

96 ⋅ 15 = 1440