The front of a tent is an equilateral triangle with the ratio of its base, b, to its height, h, given by b over h equal fraction numerator 2 over denominator square root of 3 end fraction. What equation can be used to find the tent's height?

Answer:

The velocity would be - 91 ft/sec.

Step-by-step explanation:

Given,

The function that shows the position of the ball after t seconds,

[tex]s(t) = -16t^2 + 5t + 200[/tex]

Since, velocity is the changes in position with respect to time,

That is, if v(t) is the velocity of the ball after t second,

[tex]\implies v(t)=\frac{d}{dt}(s(t))[/tex]

[tex]=\frac{d}{dt}(-16t^2 + 5t + 200)[/tex]

[tex]=-32t+5[/tex]

Hence, the velocity after 3 seconds is,

[tex]v(3)=-32(3)+5=-96+5=-91\text{ ft per seconds}[/tex]

Answer:

5x + 3y ≤ 50

Step-by-step explanation:

Given,

The weight of each large book = 5 pounds,

And, the weight of each medium book = 3 pounds,

Thus,

The total weight in pounds of x large books and y medium books = x × weight of each large book + y × weight of each medium book

= 5x + 3y

According to the question,

Total weight ≤ 50 pounds  

( Note : at most = less than equal )

⇒ 5x + 3y ≤ 50

Which is the required inequality.

Answer:

c.

Step-by-step explanation:

Ratios are used to show the relationship of variables that are in proportions.

Given that:

[tex]Inches : Centimeter = 1: 2.54[/tex]

Multiply the ratio by 9, to calculate the equivalent of 9 inches

[tex]Inches : Centimeter = 1 \times 9: 2.54 \times 9[/tex]

[tex]Inches : Centimeter = 9: 22.86[/tex]

Hence, the equivalent of 9 inches is 22.86 centimeter

The relationship between both is as follows:

[tex]Inches : Centimeter = 1: 2.54[/tex]

Rewrite as:

[tex]\frac{Inches}{Centimeter} = \frac{1}{2.54}[/tex]

Cross multiply

[tex]Centimeter \times 1 = 2.54 \times Inches[/tex]

[tex]Centimeter= 2.54 \times Inches[/tex]

Hence, the relationship between them is: [tex]Centimeter= 2.54 \times Inches[/tex]

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The factored form of the given quadratic equation M² + 40M + 400 is (M + 20)², achieved by noticing that the equation is a perfect square trinomial.

The question asks you to find the factored form of the polynomial equation M² + 40M + 400. We can factor this equation by grouping. Factoring is the process of breaking down a complex equation into its simplest terms or variables.

Factoring the Equation

The first step to factoring is to look for a common factor among all the terms. In this case, we don't have one, so we move to the next step: factoring quadratics. A quadratic is an equation where the highest exponent is 2.

The equation given, M² + 40M + 400, it is a perfect square trinomial because 20² equals 400. Factored form of perfect square trinomial (a + b)² = a² + 2ab + b².

Setting a=M and b=20 (since (20)²=400), hence this polynomial factors to be (M + 20².

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Answer:

300 millions

Step-by-step explanation:

The U.S. Mint pays to produce every penny = $0.02

When the U.S. Mint pays more than $6 million in production cost.

The number of pennies are produced = [tex]\frac{6,000,000}{0.02}[/tex]

                                                               = 300,000,000

U.S. Mint produced 300 million pennies.

The U.S mint pays $0.02 to produce every single penny in the country

Therefore the amount of pennies that will be produced when Mint pays above $6,000,000 can be calculated as follows

= 6,000,000/0.02

= 300,000,000

Hence the number of pennies that will be produced when they pay more than $6 million is 300,000,000

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The value of the expression  4p − 2, when p = 8 is 30.

An expression is a mathematical statement which consists of variables, constants and mathematical operators.

The expression is :

4p -2

The number p is the variable, 4 is the coefficient of the variable and 4,2 are constants.

The variables are the unknown parameters, whose value is not known.

The coefficients of the variables are the numbers multiplied to the variable.

The constants are integers.

The number p is multiplied by 4 and then 2 is subtracted from it.

Subtraction is the basic mathematical operation.

The value of the expression has to be determined at p =8.

To determine, the value of the p will be substituted in the expression.

=> 4 * 8 -2

=> 32 -2

=> 30

The value of the expression when p=8 is obtained.

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To find the maximum number of consecutive positive integers that sum to less than 400, solve the inequality n(n+1)/2 < 400. The largest integer n that satisfies the inequality is 28, meaning up to 28 consecutive integers can be used.

To solve the question on the maximum number of consecutive positive integers that can be added together to create a sum less than 400, we can use the formula for the sum of an arithmetic series. The sum of the first n integers is n(n+1)/2. We want this sum to be less than 400, so we need to solve the inequality n(n+1)/2 < 400 for n.

The inequality simplifies to n^2 + n - 800 < 0. The roots of the equation n^2 + n - 800 = 0 can be found using the quadratic formula or by factoring when possible. The largest integer n that satisfies the inequality will give us the answer. Upon solving, we can find that n = 28 will be the largest integer before the sum exceeds 400. Therefore, we can add up to 28 consecutive positive integers to stay under the limit of 400.

The equation that represents the tuition cost C for x credit hours taken is C = 200x + 70 thus, option (A) is correct.

There are many different ways to define an equation.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

In another word, the equation must be constrained with some constraints.

As per the given,

Fixed cost = $70

Per credit hour fee = $200

For x credit hour = 200x

Tuition cost C = 200x + 70

Hence "The equation that represents the tuition cost C for x credit hours taken is C = 200x + 70".

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Answer:A) C = 200x + 70

Step-by-step explanation:

Answer:

19/20

Step-by-step explanation:

Answer:

The solution is    3 ± 2i .   The correct option is C.

Step-by-step explanation:

using the square root property of equality to solve  (x - 3)² = -4

we have;

(x - 3)² = -4

Take the square root of both-side

√(x - 3)² = ±√-4

x - 3  =  ±√4  × √-1

Not that square root of -1 is i

x - 3 = ±2i

Add 3 to both-side of the equation

x -3 + 3 = 3 ± 2i

x = 3 ± 2i

Therefore, the solution are 3 ± 2i

Answer:

8 cartons

Step-by-step explanation:

the average is 43, which would be the middle number, since 7 is odd, there would be 3 numbers below 43 and 3 numbers above 43

43 +3 = 46

The largest number is 46

The money saved by Natalie if, Natalie uses a 15% off coupon when she buys a camera, The original price of the camera is $45.00, is $6.75.

The percentage is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one-hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

Given:

Natalie uses a 15% off coupon when she buys a camera, The original price of the camera is $45.00,

Calculate the money saved by Natalie as shown below,

The money saved by the Natalie = 15% of the original price

The money saved by the Natalie = 15 / 100 × 45

The money saved by the Natalie = 0.15 × 45

The money saved by the Natalie = 6.75

Thus, the money saved by Natalie is $6.75.

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The population of the country will double its population in approximately 14 years at a rate of 5 % growth rate every year

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the population be = x

Let the number of years be time = t

Let the percentage of increase be = 5 %

Now , dx / dt = rate of increase of population per change in time

Here, ( dx/dt ) ∝ x

where , x is the population at any time t

Then ( dx/dt ) = Ax

where A is the proportionality constant.

Now , the equation is dx / x= A dt

On , Integrating with respect to x , we get

ln x = At + c

where c is the integration constant

So , on simplifying the equation , we get

Taking exponents on both sides of the equation ,

[tex]x=e^{rt + c}[/tex]

Let [tex]k=e^{c}[/tex]

So , the equation is

[tex]x= ke^{rt}[/tex]

Now ,  r is the rate of increase, and k is the initial population be x₀

And to find the time t taken to attain double population, so x = 2x₀

[tex]x= ke^{rt}[/tex]

Substituting the values in the equation , we get

[tex]2x_{0} =x_{0} e^{0.05t}[/tex]

[tex]2 = e^{0.05t}[/tex]

Taking logarithm on both sides,

[tex]ln 2=ln ( e^{0.05t} )[/tex]

0.69314=0.05t

t = 0.69317 / 0.05

t = 13.86294 years

Therefore , it takes 13.86294 years to double population

And , 13.86294 ≈ 14 years

Hence , The population of the country will double its population in approximately 14 years at a rate of 5 % growth rate every year

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Answer:

The correct answer is D.) x = 4

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