I need help on 4 word problems

Answer:

U2I282 88X29Z SMQ0J9WJ8D,E,F,BF

Step-by-step explanation:

Answer: 112 π

Step-by-step explanation:

Volume of a cylinder = π x r^2 x h

V = π x 16 x 7

V = 112π

Yes because if you do 19.99 times 6 you get 119.94

If x denotes the width (in feet) of the billboard, find a function in the variable x giving the area of the printed region of the billboard as a function of x is (150/x - 10)(x - 4).

A billboard designer has decided that a sign should have 5-ft margins at the top and bottom and 2-ft margins on the left and right sides.

x = width of the billboard designer

Total Area including margin = 150 ft^2

Height of the billboard = Area/width

Height of the billboard = 150/x

Before the height of the billboard = (150/x - 5 × 2)

Before the height of the billboard = (150/x - 10) ft

The width of the printed region billboard = (x - 2 × 2)

The width of the printed region billboard = (x - 4) ft

The area of the printed region of the billboard = The width of the printed region billboard × The height of the printed region billboard

The area of the printed region of the billboard = (150/x - 10)(x - 4)

To learn more about area of rectangle link is here

brainly.com/question/20693059

#SPJ4

The complete question is:

A billboard designer has decided that a sign should have 5-ft margins at the top and bottom and 2-ft margins on the left and right sides. Furthermore, the billboard should have a total area of 150 ft^2 (including the margins).

If x denotes the width (in feet) of the billboard, find a function in the variable x giving the area of the printed region of the billboard.

Area as a function of x =

(a) x -5 -3 0 2 4

   y 4 0 -6 -10 -14

(d) x -14 -10 -6 0 4

   y 4 2 0 -3 -5

These tables could be used to verify that the functions they represent are inverses of each other

To verify if two functions are inverses of each other, we need to check if the composition of the two functions gives the identity function.

In other words, if f and g are two functions, then we need to check if f(g(x)) = x and g(f(x)) = x for all x in their domains.

We can create two tables, one for f and one for g, and use them to compute the compositions.

If the compositions give the identity function, then the functions are inverses of each other.

Based on this, the two tables that could be used to verify that the functions are inverses of each other are:

(a) x -5 -3 0 2 4

    y  4 0 -6 -10 -14

(d) x -14 -10 -6 0 4

    y 4    2   0 -3 -5

We can use the values in these tables to compute the compositions f(g(x)) and g(f(x)) and check if they give the identity function.

To learn more on Functions click:

https://brainly.com/question/30721594

#SPJ1

Answer:

4

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

Answer:

R+12

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The half-life of the given exponential function is of 346.57 years.

It is the value of t when A(t) = 0.5A(0).

In this problem, the equation is:

\(A(t) = A(0)e^{-0.002t}\).

In which t is measured in years.

Hence the half-life is found as follows:

\(0.5A(0) = A(0)e^{-0.002t}\)

\(e^{-0.002t} = 0.5\)

\(\ln{e^{-0.002t}} = \ln{0.5}\)

\(0.002t = -\ln{0.5}\)

\(t = -\frac{\ln{0.5}}{0.002}\)

t = 346.57 years.

More can be learned about exponential functions at https://brainly.com/question/25537936

#SPJ1

The simplified form of the expression is \(-32\).

To simplify the expression, we can perform the calculations written below step by step:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\)

We follow the order of operations (PEMDAS/BODMAS):

Step 1: Simplify within parentheses:

\(\(4+6 = 10\)\).

Step 2: Perform multiplications and divisions from left to right:

\(\(-2(10) = -20\) and \(-2(4-1) = -2(3) = -6\)\).

Step 3: Evaluate the remaining additions and subtractions:

\(\(-20 + (-2) \cdot 6 = -20 - 12 = -32\)\).

Therefore, the simplified form of the expression \(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\) is \(-32\).\)

When simplifying an expression, several factors need consideration. First, apply the order of operations correctly, respecting parentheses and exponents. Next, combine like terms by adding or subtracting them. Distribute and simplify within parentheses or brackets as needed. Pay attention to negative signs and ensure their proper placement.

Finally, review the simplified expression to ensure accuracy and validity within the given context.

Note: The complete question is:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\), calculate the simplified form of this expression.

For more questions on simplified form of the expression:

https://brainly.com/question/28323654

#SPJ8

Answer:

3.999 millimeters.

Step-by-step explanation:

To find the height of the cylinder, we can use the formula for the volume of a cylinder:

V = πr²h

Given that the radius (r) of the cylinder is 4 millimeters and the volume (V) is 200.96 cubic millimeters, we can substitute these values into the formula and solve for the height (h).

200.96 = π(4²)h

200.96 = 16πh

To solve for h, we can divide both sides of the equation by 16π:

200.96 / (16π) = h

Using a calculator, we can calculate the approximate value of h:

h ≈ 200.96 / (16 × 3.14159)

h ≈ 3.999

Therefore, the height of the cylinder is approximately 3.999 millimeters.

Answer:

Negative 5

Step-by-step explanation:

\(10x+5-5=9x-5\)

\(10x+5-5\\= 10x+\left(5-5\right)\\= 5-5\\=0\\=10x+0\\=10x\)

--------------

\(9x-5\\= 9x-5\)

→ \(10x=9x-5\)

\(10x-9x=9x-5-9x\)

\(10x - 9x\\= 1x\\= 1 \times x\\= 1\)

\(9x-5-9x\\=9x\left(-5\right)-9x\\= 9x - 9x\\= 0 - \left(-5\right)\\= -5\\x = -5\)

Hope this helps!

Answer:

Maximum height = 346 feet

Step-by-step explanation:

Given that,

The height of the rocket, y in feet, is related to the  time after launch, x in seconds, by the given equation as follows :

\(y = -16x^2 + 136x + 57\) .....(1)

We need to find the maximum height reached by the rocket. For maximum height,

Put dy/dt = 0

So,

\(\dfrac{d}{dt}( -16x^2 + 136x + 57)=0\\\\-32x+136=0\\\\x=\dfrac{136}{32}\\\\x=4.25\)

No, put x = 4.25 in equation (1).

\(y = -16(4.25)^2 + 136(4.25)+ 57\\\\y=346\ feet\)

So, the maximum height reached by the rocket is equal to 346 feet.

Answer:

x = 10

Step-by-step explanation:

3x - 9 = 21

add 9 on both sides:

⇒ 3x - 9 + 9 = 21 + 9

⇒ 3x = 30

divide 3 on both sides:

⇒ \(\frac{3x}{x} = \frac{30}{3}\)

⇒ x = 10

to check answer, substitute x by 10 on the original equation:

⇒ 3x - 9 = 21

⇒ 3 x 10 - 9 = 21

⇒30 - 9 = 21

⇒ 21 = 21

The vertex of the given equation is (0,12) and (1, -10). The value of y-intercept will be -12.

Given equation :

y=(x−2)2−8

y = 2x - 4 - 8

= 2x - 12

The final equation is y = 2x - 12.

Compare this equation with slope and y-intercept formula :

y = mx+c

So that c = -12

The value of y-intercept according to the solution is -12.

To find the vertex. Let's assume x=0; Substitute in the equation

y = 2(0) -12

y = -12

The first vertex will be (0, -12)

If x = 1; y = 2(1) -12

y = -10

Then the second vertex will be (1, -10).

Hence, the vertex of the given equation is (0,12) and (1, -10). The value of y-intercept will be -12.

To know more about equation check the below link:

https://brainly.com/question/17145398

#SPJ1

Answer: 3.5

Step-by-step explanation:

Since 10% x 10 = 100%

So we have to do 35 ÷ 10

35 ÷ 10 = 3.5

In conclusion, 10% of 35 = 3.5

Hope this helps!

Answer:

65*

Step-by-step explanation:

12x-7+16x+19=180

28x=168

x=6

12(6)-7=65

Answer:

Rotation

Step-by-step explanation:

Answer:

That is just rotation.

Step-by-step explanation:

It is rotation because if you were to spin it to the right on a 57 degree it will be that angle.

It also not the others because if you were to put reflection that would it would the opposite.

The exact value of the given trigonometric function cot(π/3) is √3/3.

The cotangent (cot) of an angle is defined as the ratio of the adjacent side to the opposite side of a right triangle.

Here, given that an angle of π/3, which is not a right angle.

So, we need to use the trigonometric identities to find the value of cot(π/3).

cot(θ) = 1/tan(θ)

where θ is an angle in radians.

We know that the tangent of π/3 is √3, as this is the opposite side (which is the same as the sine) divided by the adjacent side (which is the same as the cosine) of a 30-60-90 right triangle.

So, cot(π/3) can be expressed as:

cot(π/3) = 1/tan(π/3)

= 1/√3

Multiplying the numerator and denominator by √3/√3, we get:

cot(π/3) = √3/3

Therefore, the exact value of cot(π/3) is √3/3.

Learn more about Trigonometric functions here:

brainly.com/question/6904750

#SPJ2

Answer:gcf is 12 .

     12(2+7)

Step-by-step explanation:write gcf first then this ( and then think what is 24 times 12 which is the GCF which is 2 and think what is 84 divide 12 which is 7.Now put 12 ( 2+7)

Hope it helps :)

The difference of the rational expressions 6/x - 5x/x+2 is (x + 12)/(x(x+2)).

Thus, the correct option would be:

C. (x + 12)/(x(x+2))

To find the difference of the rational expressions, we need to subtract the second expression from the first expression.

Let's simplify the expressions first:

The first expression is 6/x - 5x/(x+2).

To combine the terms, we need a common denominator, which is (x)(x+2).

Converting the first term, 6/x, to have a denominator of (x)(x+2), we get (6(x+2))/(x(x+2)).

Now, we can combine the terms:

[(6(x+2))/(x(x+2))] - [5x/(x+2)]

To subtract the fractions, we need to have a common denominator, which is (x)(x+2).

Expanding the numerators, we get:

[(6x + 12)/(x(x+2))] - [5x/(x+2)]

Now, we can subtract the fractions:

[(6x + 12 - 5x)/(x(x+2))]

Simplifying the numerator, we have:

(6x - 5x + 12)/(x(x+2))

Combining like terms, we get:

(x + 12)/(x(x+2))

Therefore, the difference of the rational expressions 6/x - 5x/x+2 is (x + 12)/(x(x+2)).

Thus, the correct option would be:

C. (x + 12)/(x(x+2))

For similar question on rational expressions.  

https://brainly.com/question/29061047

#SPJ8

Answer:

Gina has 5 large shipping boxes and 6 small shipping boxes.

Step-by-step explanation:

32 items to ship and 11 shipping boxes.

Large=4 items

4 X 5 = 20

Small=2 items

2 X 6 = 12

20 + 12 = 32

A boutique owner needs to sell $1,200 in clothing each week. This week, she is within $125 of her goal. The variable in the equation is

A variable is a quantity that could change depending on the circumstances of an experiment or mathematical problem.

Typically, a variable is denoted by a single letter. The general symbols for variables most frequently used are the letters x, y, and z.

In the context of the problem, the boutique owner wants to make $1,200 in clothing each week. This amount in made by the number of items sold as this is added to get to the amount the boutique owner is targeting

Learn more about variable:

https://brainly.com/question/25223322

#SPJ1

Since the lengths EH and FG have the identical slope ratios as the parallel lines problem that is being given, assertion 4 is true, and so statement 4 is: EHFG.

Two non-vertical lines with the same slope that are located in the same plane are said to be parallel. Two parallel lines cannot cross each other. Right angles connections are those that intersect two non-vertical line in the same plane at a right angle.

Here,

The slope values in EH and FG are the same.

the exhibited proof, which is zero.

This implies that they follow one another in a straight line.

Since the sections EH and FG share the same gradient values as the parallel lines problem that is being given, assertion 4 is true, and so statement 4 is: EH||FG.

To learn more about  parallel lines , visit

brainly.com/question/10790818

#SPJ1

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of periods is given as follows:

5 + 6 + 4 = 15.

The frequency of each class is given as follows:

Learn more about the concept of probability at https://brainly.com/question/24756209

#SPJ1

Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

Learn more on age word problems here;

https://brainly.com/question/17043336

#SPJ1

Answer:

23

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

The given function in a quadratic function in standard form where

a = -0.001, b = 3, and c = -1800

It is a parabola that is facing downwards, therefore, the vertex of this parabola, (x,y) is the maximum of the function where

x is the amount of books that the author must sell for the most profit, and

y is the max profit per day.

We can find the vertex using

Substitute the following values, and we get

Now that we have x, plug it in the original function to solve for y

We have determine that the vertex of the function is at (1500,450). We can now conclude that

The max profit per day is $450.

The amount of of books the author must sell for the most profit is 1500 books.