brian is 6 feet tall and cast a 4 foot shadow. At the same time, a nearby flag pole cast a 20 foot shadow. How tall is the flag pole?

Answer:

variable, In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length).

Answer:

variable, In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length).

Step-by-step explanation:

In Maths, a variable is an alphabet or term that represents an unknown number or unknown value or unknown quantity. The variables are specially used in the case of algebraic expression or algebra. For example, x+9=4 is a linear equation where x is a variable, where 9 and 4 are constants.

Answer:

[tex]log_2(10)[/tex]

Simplify the equation using logarithms.

[tex]2^3x=10[/tex]

[tex]log_1_0(2^3x)=log_1_0(10)[/tex]

log rule ⇩

[tex]log_a(x^y)=y*log_a(x)[/tex]

move exponent out of log.

[tex]x*log_1_0(2)=log_1_0(10)[/tex]

isolate variable further

[tex]x*log_1_0(2)=log_1_0(10)[/tex]

[tex]x=\frac{log_{10}(10)}{log_{10}(2)}[/tex]

formula for combining logs. ⇩

[tex]\frac {log_b(x)}{log_b(a)}=log_a(x)[/tex]

the result ⇩

[tex]x=log_2(10)[/tex]

Answer:

6x² + 7x-20

A. (3x-4)(2x + 5)

The length of ribbon C is  37 feet.

The equation that can be used to determine the length of ribbon C is:

C = 34 + ( length of ribbon B - length of ribbon A)

C = 34 + (59 - 56)

C = 34 + 3

c = 37 feet

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The formula for calculating the mark up percentage is as follows:

sticker price - invoice price/invoice price • 100 = percent mark up

Percentage mark up can be described as follows:

percentage mark up = selling price per unit - cost price per unit / cost price per unit × 100

Therefore,

Mark up is the difference between a product's selling price and cost as a percentage of the cost.

Therefore, the formula for calculating the mark up percentage is as follows:

sticker price - invoice price/invoice price • 100 = percent mark up

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Answer:

140

Step-by-step explanation:

Angles in a triangle add up 180 :

180 = 107 + 33 + y

y = 180 - (107+33)

y = 180 - 140

y = 40

Angles on a straight line add up to 180 so :

180 = x + y

180 = x + 40

x= 180 - 40

x = 140

Hope this helped and have a good day

Answer:

x = 140°

Step-by-step explanation:

Concepts

The Exterior Angle Theorem states that the two remote angles in a triangle is equal to the exterior angle.

Application

In this case, the two remotes angles are 107 and 33°, and the exterior angle is x. Now, all we have to do is just add 107 and 33 to get our answer.

Solution

The time intervals when the riders could see Niagara falls are; 0.834 < t < 1.416 and (3.084, 3.666)

From the diagram attached, we can say that;

Period = 2π/k

where;

k = 2π/2.25

k = 8π/9

Thus;

h(t) = -(48/2) cos (8π/9)t + ((48/2) + 0.5)

h(t) = -24cos (8π/9)t + 24.5

Riders can see Niagara falls if they are higher than 41 meters above the ground. Thus;

41 = -24cos (8π/9)t + 24.5

41 - 24.5 = -24cos (8π/9)t

16.5 = -24cos (8π/9)t

-0.6875 = cos (8π/9)t

cos⁻¹0.6875 = (8π/9)t

t = 0.834 min

Thus, time interval is between;

0.834 < t < (2.25 - 0.834)

⇒ 0.834 < t < 1.416 and

(2.25 + 0.834) < t < (2.25 + 1.416)

⇒ (3.084, 3.666)

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Answer:

Step-by-step explanation:

The first shape has 6 sides. Hence, it is called a hexagon.

The second shape has 7 sides. Hence, it is called a heptagon.

The mathematical name for the given 2 polygons.

The first polygon has 6 sides with an angle sum of 720°, which means the mathematical name given for this polygon is,

[tex]\large\boxed {Hexagon}[/tex]

The second polygon has 7 sides with an angle sum of 900°, which means the mathematical name given for this polygon is,

[tex]\large\boxed {Heptagon}[/tex]

Hence, the first polygon is a hexagon and the second polygon is a heptagon.

Answer:

I guess, A is the wanted answer, but

A and D together are the really correct answer.

Step-by-step explanation:

if I understand this correctly, then

g(x) = sqrt(x - 3)

the domain of a function is the definition of all valid x (input) values.

the range of a function is the definition of all valid y (result) values.

well, the content (the arguments) of a square root cannot be negative (at least not while dealing with real numbers).

so, the answer options B and D are automatically out, because the domain contains values that would make the arguments of the square root negative.

I guess your teacher wants to focus only on the positive results of the square root, so A is the correct number.

BUT formally, without designated restrictions, a square root has always 2 solutions : a positive and a negative one.

because (-x)² = (x)² = x².

so, I would have to say that the really correct answer is

A + D, because the range contains both, the positive and the negative numbers.

Answer:

wouldn't be 4.5 or something close too that maybe 5 or 5.5

Step-by-step explanation:

I got you I think

Answer:

5.6

Step-by-step explanation:

If you add all the numbers together then divide it by 15 you would get 5.6

To hold 1,000,000 inflated balloons,

38 classrooms are needed.

In three-dimensional space,

the amount of space taken by an object is the volume of that object.

The volume of the cubic,

= length x width x height

Given:

The dimensions of the normal classroom are 15 ft × 50 ft × 35 ft.

The volume of the classroom,

= 15 ft by 50 ft by 35 ft.

= 26250 cubic feet.

The number of classrooms,

= 1,000,000 / 26250

Simplifying the fraction,

we get,

= 38.09

≈ 38 to the nearest whole number.

Therefore, 38 classrooms are required.

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Answer:

the correct answer is B

Step-by-step explanation:

A function g is the inverse for the function f if for y-f(x), x-g(y)

y=7x-6

Replace x with y

x=7y-6

Solve for y in x=7y-6

Switch sides

7y-6=x

Add 6 to both sides

7y-6+6=x+6

Simplify

7y=x+6

Divide both sides by the coefficient of y, which is 7. We have:

7y/7 = x/7+6/7

7y & 7 are cancelled out and we're left with: x/7 & 6/7

Now we find the LCM of the denominators which is 7.

7 divide the denominators equal 1, we use the to multiply the numerators, x & 6

our final answer= x+6/7

I hope this helps.

The equation that best models the data is (a) y = 186 - 6.2x

The data is not provided; so I would give a general guide on how to model a linear equation.

Assume the points on the line are:

(0,186) and (1,179.8)

Start by calculating the slope of the line using:

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

This gives

[tex]m = \frac{179.8 - 186}{1 - 0}[/tex]

Evaluate

m = -6.2

The equation is then calculated using:

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

This gives

y = -6.2(x - 0) + 186

Evaluate

y = -6.2x + 186

Rewrite as:

y = 186 - 6.2x

Hence, the equation that best models the data is (a) y = 186 - 6.2x

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The number of players the team can bring to the tournament is 21

From the question, we are to write an equation that can be used to solve the number of players the team can bring to the tournament

From the given information,

The members of the softball team raised $1405.25 and they rented a bus for $822.50

∴ They have $1405.25 - $822.50 left

Also, they budgeted $27.75 per player for meals

Then, x, the number of players the team can bring to the tournament is

x = ($1405.25 - $822.50) ÷ $27.75

x = $582.75 ÷ $27.75

x = 21

Hence, the number of players the team can bring to the tournament is 21.

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The equation written in standard form represents the number of servings of chicken strips and carrots that Will may have eaten is:

x*110 + y*29 = 333

We know that he consumed a total of 333 calories.

There are x chicken strips and y carrots, so we must have that:

x*110 + y*29 = 333

That is the equation in standard form that we must solve to find how many carrots and how many chicken strips he ate.

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Answer:

Divide 12 by -6

Step-by-step explanation:

Given =

AC = 6cm

BC = 9cm (hyp)

AB =

By pyth

A^2 = B^2 + C^2

9 = 6 + AB

AB = 9-6 = 3

AB =3

Hope this helps

Answer:

0.625

Step-by-step explanation:

The rationalization the denominator of the fraction  (6)/(4+\sqrt(5)) is [tex]\dfrac{6(4-\sqrt(5))}{11}[/tex].

Suppose the given fraction is [tex]\dfrac{a}{b+c}[/tex]

Then the conjugate of the denominator is given by b - c

Thus, rationalizing the fraction will give us

[tex]\dfrac{a}{b+c} \times \dfrac{b-c}{b-c} = \dfrac{a(b-c)}{b^2 - c^2}[/tex]

The given expression is

[tex]\dfrac{6}{4+\sqrt(5)}\\\\[/tex]

By rationalizing the denominator of the fraction

[tex]\dfrac{6}{4+\sqrt(5)}\times \dfrac{4-\sqrt(5)}{4-\sqrt(5)} \\\\\\\dfrac{6(4-\sqrt(5))}{4^2-(5)}\\\\\\\dfrac{6(4-\sqrt(5))}{11}[/tex]

Thus, the rationalization the denominator of the fraction  (6)/(4+\sqrt(5)) is [tex]\dfrac{6(4-\sqrt(5))}{11}[/tex].

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Answer:

35,000

Step-by-step explanation:

^4 means 4 zeros

10^4 = 10,000

3.5 times 10,000 =

35,000

The probability that an animal has stripes will be 0.86.

The probability that an animal has stripes will be:

= Orange stripes + Brown stripes + Grey stripes

= 0.16 + 0.3 + 0.4

= 0.86

The probability that an animal doesn't have stripes will be:

= 1 - 0.86

= 0.14

Therefore, the probability that an animal doesn't have stripes is 0.14.

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Answer:

  7.2 cm

Step-by-step explanation:

The height of the trapezium can be found by making use of the area formula with known values filled in.

__

The area of a trapezium is given by ...

  A = 1/2(b1 +b2)h . . . . b1, b2 are the parallel sides, h is the height

Using the given values, we have ...

  90 cm² = 1/2(6 cm +19 cm)h . . . . . . use the known values

  (90 cm²)/(12.5 cm) = h = 7.2 cm . . . . divide by the coefficient of h

The height of the trapezium is 7.2 cm.

The equation that defines the relationship between the height and the time and models the position of the ball in time is the quadratic function y = - 8 · t² + 24 · t.

Quadratic functions are polynomials of grade 2 of the form y = a · t² + b · t + c, where t and y are the time and the height of the ball, in seconds and feet, respectively. To determine the value of the three coefficients we need to know three different points of the form (t, y).

If we know that (t₁, y₁) = (0 s, 0 ft), (t₂, y₂) = (1 s, 16 ft) and (t₃, y₃) = (3 s, 0 ft), then the quadratic function is:

a · 0² + b · 0 + c = 0     (1)

a · 1² + b · 1 + c = 16      (2)

a · 3² + b · 3 + c = 0      (3)

The solution to this system is a = - 8, b = 24, c = 0.

The equation that defines the relationship between the height and the time and models the position of the ball in time is the quadratic function y = - 8 · t² + 24 · t.

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Answer:

it is -6. . . . . . . . . . . . . . . . .. ... . . . . . . .

Step-by-step explanation:

Because probability is always one(1).

Probability =

[tex]1 - \frac{2}{10} [/tex]

[tex] \frac{8}{10} [/tex]

[tex] \frac{4}{5} [/tex]

Is the probability of not choosing a red marble.

Answer:

52 x 7= 50 x 7 + 2 x 7

Step-by-step explanation: