A 5'6" person walking down the street notices his shadow. If the angle of elevation from the tip of the shadow to the sun is 60°, what is the length of the shadow(round to 2 decimal places)?

Answer: Audrey is less than 17 years old (possible answers 16,15,14,13...)

Answer in inequality: x<17

Step-by-step explanation:

3x + 9 < 60

3x + 9 - 9 < 60 - 9

3x < 51

x<17

Answer: x<17

EXPLAIN

ekfnkw

Answer:

g(b)=4b+5

Step-by-step explanation:

because this is how you write it as a function

Answer:

First question

a = 1 , h = 0 , k = 6 ⇒ third answer

Second question

y = 2x² + 4 ⇒ second answer

Third question

No of the choices correct ⇒ fourth answer

Step-by-step explanation:

First question

∵ f(x) = x² + 6

- It is a quadratic function with general form ax² + bx + c

- Its vertex is (h , k), where h = -b/2a and k = f(h)

∵ a = 1 , b = 0 , c = 6

∴ h = 0/2(1) = 0

∴ f(0) = 0² + 6 = 6

∴ a = 1 , h = 0 , k = 6 ⇒ third answer

Second question

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

∵ y = 2x²

∵ y is shifted 4 units up

∴ k = 4

∴ y + 4 = 2x² + 4

∴ y = 2x² + 4 ⇒ second answer

Third question

∵ y = -2x² + 3

- It is a quadratic equation with general form ax² + bx + c

- It represented graphically by parabola

- If a is positive the parabola opens upward

- If a is negative the parabola opens downward

∵ a = -2

∴ The parabola opens downward

∴ No of the choices correct ⇒ fourth answer

it’s the last option

The  correct application of the quadratic formula is:

               [tex]x=\dfrac{9\pm \sqrt{(-9)^2-4(6)(22)}}{2(6)}[/tex]

The quadratic equation is given by:

[tex]y=6x^2-9x+22[/tex]

We know that the solution of the quadratic equation:

[tex]y=ax^2+bx+c[/tex]

is given by:

[tex]y=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Here we have:

[tex]a=6[/tex]

[tex]b=-9[/tex]

and

[tex]c=22[/tex]

Hence, the quadratic formula is given by:

[tex]x=\dfrac{-(-9)\pm \sqrt{(-9)^2-4\cdot (6)\cdot (22)}}{2\cdot (6)}[/tex]

i.e.

[tex]x=\dfrac{9\pm \sqrt{(-9)^2-4(6)(22)}}{2(6)}[/tex]

The E3 is the same as writing 10^3.

The answer would be 7.9 x 10^3

Answer:

3/8

Step-by-step explanation:

the formula to find average of a set of values is, you add all the numbers, then you divide by the total amount of numbers.

you can work backwards with your problem by multiplying 1/4*2

[tex] \frac{1}{4} \times 2 = \frac{1}{2} [/tex]

then you subtract 1/8 from that

[tex] \frac{1}{2} - \frac{1}{8} = \frac{3}{8} [/tex]

3/8 is the other number to get an average of 1/4

Answer:

2 square root 15, or the second one down

ANSWER

[tex]2 \sqrt{15} [/tex]

EXPLANATION

We want to simplify

[tex] \sqrt{60} [/tex]

There is a perfect square under the radical sign:

[tex] \sqrt{4 \times 15} [/tex] Split the radical sign for both factors:

[tex] \sqrt{4} \times \sqrt{15} [/tex]

Simplify the first factor

[tex]2 \sqrt{15} [/tex]

The second option is correct.

Answer:

(6x-5)(x+2)

Step-by-step explanation:

6x²+7x-10

= (6x-5)(x+2)

Answer:

The base b is 6m

Step-by-step explanation:

The area A of a triangle with base b and height h is given by the formula;

[tex]A=\frac{1}{2}*b*h[/tex]

The area of the triangle is given as 45 while the height h is 15. We substitute these known values into the formula above and solve for the unknown base;

[tex]45=\frac{1}{2}*b*15\\\\90=15*b[/tex]

We finally divide both sides by 15 to solve for b;

b = 90/15 = 6

Therefore, the base of the triangle is 6 m

Answer:

[tex]b = 6\ m[/tex]

Step-by-step explanation:

The area of a triangle is

[tex]A = 0.5b * h[/tex]

Where b is the base of the triangle and ha is the height.

In this case we have a triangle with area

[tex]A = 45\ m ^ 2[/tex]

and with height:

[tex]h = 15\ m[/tex]

So the base of the triangle is:

[tex]45 = 0.5b (15)\\\\b=\frac{45}{15*0.5}\\\\b=6\ m[/tex]

Finally the base of the triangle is b = 6 meters

Answer:

Part 1) The measure of angle d is 65°

Part 2) The measure of angle c is 89°

Part 3) The measure of arc a is 131°

Part 4) The measure of arc b is 47°

Step-by-step explanation:

we know that

In an inscribed quadrilateral, opposite angles are supplementary

step 1

Find the measure of angle d

∠d+115°=180°

∠d=180°-115°=65°

step 2

Find the measure of angle c

∠c+91°=180°

∠c=180°-91°=89°

step 3

Find the measure of arc a

we know that

The inscribed angle measures half that of the arc comprising

115°=(1/2)[99°+arc a]

230°=[99°+arc a]

arc a=230°-99°=131°

step 4

Find the measure of arc b

we know that

The inscribed angle measures half that of the arc comprising

∠c=(1/2)[arc a+arc b]

substitute the values

89°=(1/2)[131°+arc b]

178°=[131°+arc b]

arc b=178°-131°=47°

A figure which is formed by two rays or lines that shares a common endpoint is called an angle.

An arc is one of the portions of a circle. It is basically a part of the circumference of a circle.

The measure of the ∠d is 65 degrees.

The measure of the ∠c is 89 degrees.

The measure of the arc a is 131 degrees.

The measure of arc b is 47 degrees.

The value of each variable. For the circle, the dot represents the center.

A figure which is formed by two rays or lines that shares a common endpoint is called an angle.

An arc is one of the portions of a circle. It is basically a part of the circumference of a circle.

1. The measure of ∠d is;

∠d+ 115°= 180°

∠d= 180°-115°= 65°

The measure of the ∠d is 65 degrees.

2. The measure of ∠c is,

∠c+ 91°= 180°

∠c =180°-91° =89°

The measure of the ∠c is 89 degrees.

3. The measure of arc a is,

The inscribed angle measures half that of the arc comprising;

[tex]\rm 115=\dfrac{1}{2}[99+arc \ a]\\\\230=[99+arc a]\\\\arc \ a = 230-99\\\\arc \ a= 131[/tex]

The measure of the arc a is 131 degrees.

4. The measure of arc b is,

The inscribed angle measures half that of the arc comprising;

[tex]\rm 89=\dfrac{1}{2}[131+arc \ b]\\\\178=[131+arc \ b]\\\\arc \ b = 178-131\\\\arc \ b = 47[/tex]

The measure of arc b is 47 degrees.

To know more about Angle and Arc click the link given below.

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Answer:

The decimal form of 5/8 is 0.625

All you have to to is divide numerator by denominator

Ur percent would be 63% if rounded

If not then its 62%

ANSWER

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

EXPLANATION

The given function has equation

[tex]y = \tan( \frac{3}{4}x) [/tex]

This can be rewritten as

[tex]y = \frac{ \sin( \frac{3}{4}x ) } { \cos(\frac{3}{4}x )}[/tex]

The asymptote occurs at:

[tex]\cos(\frac{3}{4}x ) = 0[/tex]

This implies that,

[tex] \frac{3}{4} x = \frac{ \pi}{2} [/tex]

[tex]x = \frac{ \pi}{2} \times \frac{4}{3} [/tex]

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

Or

[tex]\frac{3}{4} x = - \frac{ \pi}{2} [/tex]

[tex]x = \frac{ - \pi}{2} \times \frac{4}{3} [/tex]

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

The second choice is correct.

Answer:

B) [tex]x = \frac{2\pi }{3}[/tex]

Step-by-step explanation:

this is the correct answer on ed-genuity, hope this helps! :)

Answer: -x^2+12x+3

Step-by-step explanation:

[tex]\text{Hey there!}[/tex]

[tex]\text{Both numbers are divisible to 4, so divide the numerator and denominator from 4}[/tex]

[tex]\frac{7,848\div4}{4\div4}[/tex]

[tex]\text{7,848}\div4=1,962[/tex]

[tex]\text{4}\div4=1[/tex]

[tex]\text{1,962}\div1=1,962[/tex]

[tex]\boxed{\boxed{\text{Answer: 1,962}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

The answer is 4 pounds

Step-by-step explanation:

10+14+40=64 oz 64/16 =4

Answer:

4 pounds

Step-by-step explanation:

40 ounces of chicken+ 10 ounces of vegetables+ 14 ounces of rice= 64 ounces of the whole chicken dish.

Now, convert the number of ounces into pounds.

There are 16 ounces in a pound

Or

16 ounces=1 pound

So, divide 16 into 64 to get the number of pounds, which is 4.

Hope this helps!

Answer:

The explicit formula is:

[tex]a_n = 200 +5(n-1)[/tex]

Step-by-step explanation:

Freya increases 5 yards daily to the number of yards she runs.

Note that the increase factor is constant, so this problem can be modeled using an arithmetic sequence.

The explicit formula for an arithmetic sequence is:

[tex]a_n = n_1 + d(n-1)[/tex]

Where:

[tex]a_n[/tex] is the number of yards that Freya runs on the day

[tex]a_1[/tex] is the number of yards that he runs on day 1

d is the increase factor. [tex]d = 5[/tex] yards

n is the number of days

Then as [tex]a_1 = 200[/tex] and [tex]d = 5[/tex], the explicit formula is:

[tex]a_n = 200 +5(n-1)[/tex]

Answer:

a_n = 200 (n-1)5

Step-by-step explanation:

just to simplify from those over achievers who confuse the living  h e l l out of everyone

Answer:

A=13+B

Step-by-step explanation:

Linda earns $13  each hour working part-time at a bookstore.

Linda earns $1 for each book she sells.

Let

A be the amount (in dollars) that Linda earns in an hour;

B be the number of books Linda sells in an hour.

So,

[tex]A=13+B\cdot 1\\ \\A=13+B[/tex]

The graph is shown in attached diagram

Answer:

Oxygen and Silicon

Step-by-step explanation:

Oxygen and Silicon make up 75% of the weight of the Earth's crust.

Answer = oxygen and silicone.

Answer:a

aStep-by-step explanation:    ive done it

The area of a triangle with a base of 6 cm and height of 8 cm, is 24 cm²

Area is the amount of space occupied by a two dimensional shape or object.

The area of a triangle is given by:

Area of triangle = (1/2) * base * height

Assume the triangle has a base of 6 cm and height of 8 cm, hence:

Area of triangle = (1/2) * 6 * 8 = 24 cm²

The area of a triangle with a base of 6 cm and height of 8 cm, is 24 cm²

Find out more on area at: https://brainly.com/question/25292087

Answer:

[tex]c = 4[/tex]

Step-by-step explanation:

For this triangle we have to

[tex]A=63\\C=49\°\\c=3\°[/tex]

Now we use the sine theorem to find the length of a:

[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]

Then:

[tex]\frac{sin(A)}{a}=\frac{sin(C)}{c}\\\\a=\frac{sin(A)}{\frac{sin(C)}{c}}\\\\a=c*\frac{sin(A)}{sin(C)}\\\\a=(3)\frac{sin(63)}{sin(49)}\\\\c=4[/tex]

____________________________________________________

Answer:

7 dollars

____________________________________________________

Step-by-step explanation:

To make solving this equation easier, lets turn the the information we got in the question into an actual equation.

Key information:

4 tickets

$12 popcorn

Spent a TOTAL of $40.

With the information above, we can use it to make an equation.

We would use the equation: y = mx + b

Since our "y" value would represent our total value, our total value is 40, so we would plug 40 into y.

Your equation should look like this:

40 = mx + b

Our "b" value represents our start value, and our start value would be 12 because we started with one $12 popcorn.

Your equation should look like this:

40 = mx + 12

Our "m" value would represent how many tickets we bought, so we would plug in 4 in m.

Our equation would be:

40 = 4x + 12

Now we can solve the equation:

We would move the 12 over to the left side of the equal sign by subtracting, then we would divide by 4.

[tex]40=4x+12\\\\28=4x\\\\7=x[/tex]

We should get ther answer of 7, that means that each ticket cost $7 dollars.

7 dollars should be your FINAL answer.

____________________________________________________

Answer:

One ticket = $7

Step-by-step explanation:

Forming the equation,

→ 4x + 12 = 40

Now the value of x will be,

→ 4x + 12 = 40

→ 4x = 40 - 12

→ x = 28/4

→ [ x = 7 ]

Hence, the value of x is 7.

Answer: x= 8

Step-by-step explanation:

x^2 = 64

sqrt{x^2} = sqrt64}

x = 8

The question is a binomial distribution problem in mathematics. You can use the binomial probability formula to calculate the probability that exactly 4 out of 8 treated dolphins are cured.

This mathematics problem involves understanding probability and the binomial distribution. The word 'exactly' is a clue that this is a binomial problem.

The general formula for a binomial probability is: P(X = k) = C(n, k) * (p^k) * ((1-p)^(n-k)), where:

So, if we substitute the values into the formula, we have:

P(X = 4) = C(8, 4) * (0.94^4) * ((1-0.94)^(8-4))

Therefore, Use this formula to find the probability that exactly 4 out of 8 dolphins are cured.

https://brainly.com/question/33993983

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Answer:

-36 • (22u + 1)

Step-by-step explanation:

Pulling out like terms :

2.1     Pull out like factors :

  -74u - 5  =   -1 • (74u + 5)

Equation at the end of step  2  :

 (6 • (58u + 1)) -  -6 • (74u + 5)

Step  3  :

Equation at the end of step  3  :

 6 • (58u + 1) -  -6 • (74u + 5)

Step  4  :

Pulling out like terms :

4.1      Pull out     6

Note that  -6 =(-1)• 6

After pulling out, we are left with :

     6 • ( (-1)  *  (58u+1) +( (-1)  *  (74u+5) ))

Step  5  :

Pulling out like terms :

5.1     Pull out like factors :

  -132u - 6  =   -6 • (22u + 1)

Final result :

 -36 • (22u + 1)

Answer:

[tex]\large\boxed{\sin2\theta=\dfrac{\sqrt3}{2},\ \cos2\theta=\dfrac{1}{2}}[/tex]

Step-by-step explanation:

We know:

[tex]\sin2\theta=2\sin\theta\cos\theta\\\\\cos2\theta=\cos^2\theta-\sin^2\thet[/tex]

We have

[tex]\sin\theta=\dfrac{1}{2}[/tex]

Use [tex]\sin^2\theta+\cos^2\theta=1[/tex]

[tex]\left(\dfrac{1}{2}\right)^2+\cos^2\theta=1\\\\\dfrac{1}{4}+\cos^2\theta=1\qquad\text{subtract}\ \dfrac{1}{4}\ \text{from both sides}\\\\\cos^2\theta=\dfrac{4}{4}-\dfrac{1}{4}\\\\\cos^2\theta=\dfrac{3}{4}\to\cos\theta=\pm\sqrt{\dfrac{3}{4}}\to\cos\theta=\pm\dfrac{\sqrt3}{\sqrt4}\to\cos\theta=\pm\dfrac{\sqrt3}{2}\\\\\theta\in[0^o,\ 90^o],\ \text{therefore all functions have positive values or equal 0.}\\\\\cos\theta=\dfrac{\sqrt3}{2}[/tex]

[tex]\sin2\theta=2\left(\dfrac{1}{2}\right)\left(\dfrac{\sqrt3}{2}\right)=\dfrac{\sqrt3}{2}\\\\\cos2\theta=\left(\dfrac{\sqrt3}{2}\right)^2-\left(\dfrac{1}{2}\right)^2=\dfrac{3}{4}-\dfrac{1}{4}=\dfrac{3-1}{4}=\dfrac{2}{4}=\dfrac{1}{2}[/tex]

Answer:

192 cups is equal to 12 gallons

Step-by-step explanation:

we know that

1 cup=0.0625 gal

or

1 gal=16 cups

Method 1

192 cups=192*0.0625=12 gal

Method 2

192 cups=192/16=12 gal

Answer:

Step-by-step explanation:

Convert 192 cups to gallons. Enter your answers in the boxes.

For the blanks answer it like this

There are   16 cups in 1 gallon. Therefore, 192 cups is equal to  

12  gallons.

Answer:

-51, -41, -38, 13, 41, 50

Step-by-step explanation:

The integers ordered from least to greatest are: -51, -41, -38, 13, 41, 50.

To order the integers from least to greatest, one must start by identifying the negative integers and then the positive integers. Among negative integers, the larger the absolute value, the smaller the number. Conversely, for positive integers, the larger the number, the greater it is.

Starting with the negative integers:

-51 is the smallest because it has the largest absolute value among the negative numbers.

-41 is the next smallest negative number.

-38 is the smallest negative number because it has the smallest absolute value among the negatives.

Now, moving on to the positive integers:

13 is the smallest positive number.

41 is the next smallest positive number.

50 is the largest positive number.

Putting it all together:

-51, -41, -38, 13, 41, 50.

Answer:

The domain of (f*g) (x) is the set of all real numbers; ( -∞, ∞)

Step-by-step explanation:

(f*g) (x) simply means we obtain the product of f(x) and g(x). We are given that;

f(x)=2x

g(x)= 1/x

(f*g) (x) = f(x) * g(x)

(f*g) (x) = 2x * 1/x = 2

This is a horizontal line defined everywhere on the real line. The domain of  (f*g) (x) is thus ( -∞, ∞)

Answer:

All real numbers

Step-by-step explanation:

Given : [tex]f(x)=2x[/tex]

           [tex]g(x)= \frac{1}{x}[/tex]

To Find : the domain of (f*g) (x)

[tex]f(x)=2x[/tex]

[tex]g(x)= \frac{1}{x}[/tex]

[tex](f\cdot g)(x)=2x \times \frac{1}{x}[/tex]

[tex](f\cdot g)(x)=2[/tex]

Since the value of [tex](f\cdot g)(x)=2[/tex]

So, the domain of the function is [tex](f\cdot g)(x)[/tex] is all real numbers .

Answer:

[tex](\frac{6}{n})-8[/tex] .

Step-by-step explanation:

Given  : "8 less than the quotient of 6 and a number".

To find : expression represents the following word phrase.

Solution : We have given 8 less than the quotient of 6 and a number.

According to question :

Quotient of 6 and n = [tex](\frac{6}{n})[/tex]  .

For less than we will use negative sign.

8 less than the quotient of 6 and a number.

[tex](\frac{6}{n})-8[/tex] .

Therefore,  [tex](\frac{6}{n})-8[/tex]  .

Answer:

Step-by-step explanation:

1. First, put together the information we have. Total = 121. Emily has 40% more than Carl, and Carl has 60% more than Antony.

2. Next, set each person as a variable. Antony = x. Carl = 1.6x. Emily = 1.4 times 1.6x.

3. Next, form an equation using these variables.

    x + 1.6x + (1.4 x 1.6x) = 121

    x + 1.6x + 2.24x = 121

    4.84x = 121

    x = 25

4. Finally, plug in x to our previous variables in step #2 to find the number of stamps Emily and Carl have.

Antony: x = 25 stamps

Carl: 1.6x = 40 stamps

Emily: 1.4 times 1.6x = 56 stamps

By the way, is this for RSM? If so, I am working on that problem right now and I searched up the solution but couldn't find it, so I stumbled upon this. I hope this helped!