What is the vertex of the function

Answer:

x = -14

Step-by-step explanation:

Divide each side by -3.

Subtract 9 from each side.

Answer:

x = -14

Step-by-step explanation:

-3(x + 9) = 15

The Length AB of the triangle ABC is 31.079m

Area is the total amount of space filled by a flat (2-D) surface or an object's shape.

A planar figure's area is the space that its perimeter encompasses.  Square units like cm²and m² are used to measure area. The area of a form is a two-dimensional quantity.

Area of oblique triangle: S(CAB)=AC*BC*sin(ACB)/2

Substituting the values;

AC=8.4m

S(ΔCAB)=100m²

(∠ACB)=40°

S(ΔCAB)=(8.4×BC×Sin40°)/2

100=(8.4×BC×Sin40°)/2

BC=37.041m

Law of cosines:

AB²=AC²+BC²-2AC×BC×cos(∠ACB)

Substitute  the values,

AC=8.4m, ∠ACB=40 ° , BC=37.041 we get:

AB²=8.4²+37.041²-2×8.4×37.041×cos40°

AB=31.079m

Hence, The Length AB of the triangle ABC is 31.079m.

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Step-by-step explanation:

since sqrt(25)×sqrt(25) = 25, then x can be any number, because x = x in all cases. and then both sides of the equation are always equal, no matter what value we give x, as long as x is a factor in both sides.

sqrt(25)×x×sqrt(25) = 25x

is always true for every x.

if the question would be

sqrt(25)×x×sqrt(25) = 25

then the answer can only be x = 1. because for every other value of x the equality is destroyed.

Answer:

they share some features like;exponents,

mathematical signs, variables and more

The shared feature is that the 3 are functions relating y and x, and the uniqueness is on the exponent (or degree for the first two cases).

A linear function is:

y = a*x + b

A quadratic function is:

y = a*x^2 + b*x + c

An exponential function is:

y = A*(b)^x

So, the thing that we can see that the functions have in common is that in all of them, the variable y depends on the variable x.

Well, the exponents are clearly different.

The linear function is of degree 1, the quadratic function is of degree 2, and in the exponential function the variable is in the exponent (it is not a polynomial like in the first two cases).

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Answer:

35 : 28

Step-by-step explanation:

Add the values:  5 + 4 = 9

Divide 63 by the sum of the values:  63 ÷ 9 = 7

Mulitply the values of the original ratio by 7:  5x7 : 4x7 = 35 : 28

The probability that x is greater than or equal to 1 is 0.875 or 87.5%

To find the probability that x, the number of heads in three tosses of a fair coin, is greater than or equal to 1, we can use the following steps:

1. Determine the total possible outcomes: There are 2 outcomes for each coin toss (heads or tails), so for 3 tosses, there are 2^3 = 8 possible outcomes.
2. Count the outcomes where x is greater than or equal to 1: We have 7 favorable outcomes (HHH, HHT, HTH, THH, HTT, THT, and TTH). The only outcome not included is TTT (no heads).
3. Calculate the probability: Divide the number of favorable outcomes by the total possible outcomes.

Probability(x ≥ 1) = (favorable outcomes) / (total possible outcomes) = 7 / 8 = 0.875

So, the probability that x is greater than or equal to 1 is 0.875 or 87.5%.

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Answer:

3 integers

Step-by-step explanation:

-1, 0, 1 lie between the integers - 2 and 2

Answer:

\(P=24\: m\)

\(A=41.52 \m^{2}\)

Step-by-step explanation:

El perímetro de un hexágono se calcula de la siguiente manera:

\(P=6*l\)

l es el lado del hexágono l = 4 m

Entonces P es:

\(P=6*4=24\: m\)

El área del hexágono puede calcularse de la siguiente manera:

\(A=\frac{P*Ap}{2}\)

P es el perímetro = 24 m

Ap es la apotema = 3.46 m

El Area sera:

\(A=\frac{24*3.46}{2}\)

\(A=41.52 \m^{2}\)

Espero te haya sido de ayuda!

Statistics report that the average successful quitter is able to stop smoking after multiple attempts, usually between 8 to 10 times.  everyone's journey to quitting smoking is unique and may take more or fewer attempts to achieve success.

According to statistics, the average successful quitter is able to stop smoking after attempting to quit 6 to 30 times. This number varies due to individual factors and the methods used for quitting. Remember, persistence is key, and it is never too late to quit smoking for a healthier lifestyle.

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The system of equations are:

A = 80x + 70    

A = 980 - 50x  

Weeks: x = 7 weeks

Amount of money: $630

Let x represent the number of weeks it will take for both girls to have the same amount of money.

Let A represent the amount both will have equally after x number of weeks.

Thus:

For Kendra, the equation is:

A = 80x + 70    -----(1)

For Mallory, the equation is:

A = 980 - 50x   ------(2)

Thus, for both to have the same amount of money:

80x + 70 = 980 - 50x

80x + 50x = 980 - 70

130x = 910

x = 910/130

x = 7 weeks

A = 80(7) + 70

A = $630

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Answer:

Step-by-step explanation:

Solving systems of equations gives the points of intersection when the equations are graphed.

The answer is 3.

Answer:

\(13x-25y+21\)

Step-by-step explanation:

\(\longmapsto\) \(5(2y-3x)+7(4x-5y+3)\)

Use the distributive property to multiply 5 by 2y-3x:

\(\longmapsto\) \(10y-15x+7\left(4x-5y+3\right)\)

Use the distributive property to multiply 7 by 4x-5y+3:

\(\longmapsto\) \(10y-15x+28x-35y+21\)

Combine like terms: -15x and 28x= 13x, and Combine 10y and -35y =

-25y:

\(\longmapsto\) \(-25y+13x+21\)

_______________________

Answer:

The correct answer is:

c. Time is an exponent while the other units are factors.

Explanation:

In the compound interest formula, time is the exponent.

Since it is the exponent, this tells us how many times the base is multiplied by itself.  As such, it has a larger effect on the answer than any other piece of the equation.

Answer:

4

Step-by-step explanation:

Four people will play basketball, so 10 - 4 = 6.

Half as many people will play baseball, and half of 4 is 2, so 6 -2 = 4.

The rest will play soccer, which is 4.

Victor's online business involves selling software applications along with technical support. With a competitive price of $130 per product, he also incurs monthly fixed expenses of $850. By hiring college students for technical support, he pays them $15 per hour for 3 hours per customer.

Victor's plan to set up an online business selling software applications is a good initiative. The price of $130 including technical support is competitive and can attract potential customers. His monthly fixed expenses amounting to $850 should be carefully monitored to avoid overspending.
Hiring college students to provide technical support is a great way to save on costs. Paying them $15 per hour for 3 hours per customer is also reasonable and can motivate them to do their best. Victor can leverage on their skills and eagerness to learn, while at the same time providing them with a valuable experience.
In summary, Victor's plan to set up an online business is promising. He just needs to make sure to closely monitor his expenses and find creative ways to save on costs without compromising the quality of his product and technical support. Hiring college students is one of those ways that can benefit both his business and the students involved.

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Answer:

5.99 dollars per pound

Step-by-step explanation:

Convert to a decimal by dividing the numerator by the denominator.

Answer: 71

Step-by-step explanation:

Answer

Explanation:

Volume of a cylinder is expressed as;

If the radius is doubled and the height is unchanged, then;

r2 = 2r

h2 = h

Get the volume of the new cylinder

(a) The probability that the parking lot will be full on any given day is approximately 0.8413.(b) The company needs at least 355 cars to use the parking lot to make a profit, and the probability of making a profit depends on the distribution of the number of cars arriving and the associated costs and revenue.

To calculate the probability that the parking lot will be full on any given day, we need to find the probability that the number of cars arriving exceeds or equals the maximum capacity of 400.

Let X be the number of cars arriving at the parking lot each day. X follows a normal distribution with a mean (μ) of 378 and a variance (σ^2) of 484. The standard deviation (σ) is the square root of the variance, which is sqrt(484) = 22.

We can standardize the distribution using the z-score formula:

z = (X - μ) / σ

For the parking lot to be full, we want to find the probability that X is greater than or equal to 400. So, we calculate the z-score for X = 400:

z = (400 - 378) / 22

z = 22 / 22

z = 1

Using the standard normal distribution table or a statistical software, we can find the probability corresponding to a z-score of 1. In this case, it is approximately 0.8413.

Therefore, the probability that the parking lot will be full on any given day is approximately 0.8413.

To determine the number of cars needed for the company to make a profit, we need to consider the costs and revenue. The company incurs a cost of 2,832 Dirhams per day to operate the parking lot. It charges 8 Dirhams per day for each car that uses the parking lot.

Let's denote the number of cars as N. To make a profit, the revenue generated from the number of cars (8 * N) must exceed the operating cost (2,832 Dirhams).

8 * N > 2,832

Solving for N:

N > 2,832 / 8

N > 354

Therefore, the company needs at least 355 cars to use the parking lot in order to make a profit.

To calculate the probability that the company will make a profit, we need to find the probability that the number of cars arriving (X) is greater than or equal to 355. We can use the normal distribution with the given mean and variance to calculate this probability.

To find the probability that the company will make a profit and the parking lot is not full, we need to calculate the probability that the number of cars is greater than or equal to 355 (for making a profit) and less than 400 (not full). This probability can also be calculated using the normal distribution with the given mean and variance.

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Answer:

The point of intersection between 2x+3y=12 and 2x-y=4 is (3,2)

Step-by-step explanation:

The option that is a statistical question is how many miles do the students in your class run each week? (option b)

A statistical question is a question that can be answered by collecting data that have varying values.

For example, the number of miles that the students in your class run each week is statistical question because each student would run. This is because data would be collected from more than one student and the students would have varying miles that they run.

The number of pets your grandparents have is not a statistical questions because they can only have a set number of pets.

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Answer:

B. How many miles do the students in your class run each 

Step-by-step explanation:

The simplified form of the expression 1/5 divied by 2 as a fraction is 1/10.

Given the expression in the question;

1/5 divied by 2

1/5 ÷ 2

To simplify, multiply 1/2 by the reciprocal of 2

1/5 ÷ 2

1/5 × 1/2

Simplify

( 1 × 1 ) / ( 5 × 2 )

( 1 ) / ( 5 × 2 )

Multiply 5 and 2

( 1 ) / ( 10 )

1/10

Therefore, the simplified form is 1/10.

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To find the new yearly cost of gasoline, we need to calculate the number of gallons used and multiply it by the cost per gallon.

1. First, calculate the number of gallons used per year: 15,000 miles ÷ 24 miles per gallon = 625 gallons per year.
2. Then, calculate the new number of gallons used per year with the car that gets x more miles per gallon: 15,000 miles ÷ (24 + x) miles per gallon = 625 ÷ (24 + x) gallons per year.
3. Finally, multiply the new number of gallons by the cost per gallon ($3.60): 625 ÷ (24 + x) gallons per year × $3.60 per gallon = $2250 ÷ (24 + x) yearly cost of gasoline.

The expression for the new yearly cost of gasoline is $2250 ÷ (24 + x).
Answer with more than 100 words: The expression for the new yearly cost of gasoline is calculated by dividing the total distance driven per year (15,000 miles) by the new car's fuel efficiency (24 + x miles per gallon). This will give us the number of gallons needed per year. Then, we multiply this by the cost per gallon ($3.60) to find the new yearly cost. So, the expression is $2250 ÷ (24 + x). This expression allows us to evaluate the new cost based on different values of x, which represents the additional miles per gallon the new car gets compared to the old one.

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The number that Joseph is thinking of that is between 15 and 30 is 16.

The first step is to determine the squares between 15 and 30. The square of a number is the product of a number with itself. For example, 16 is a square number.

Squares between 15 and 30 = 16, 25

The next step is to determine the even number. An even number is a number that is perfectly divisible by 2. An example of an even number is 4.

The even number that is a square between 15 and 30 is 16.

The last step is to determine the composite number. A composite number is a number that has more than 2 factors.

Factors of 16 = 1, 2, 4, 8, 16

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Answer:

3.3h-3.1d-17

Step-by-step explanation:

Answer:

65 years old.

Step-by-step explanation:

If her age is 10 t + u (where t is the tens digit and u is the units digit) then reversing the digits gives 10 u + t. and the sum is 11 t + 11 u, which is a multiple of 11. We know this has to be a square number. Ong Xing Cong from Singapore sent in the following solution.

11 t + 11 u = 11 x 11 = 121

t + u = 11

65 - 56 = 3 x 3

She is 65 years old.

The best solutions do not need trial and improvement methods and they show that the answer or answers found are the only possible answers. Knowing the digits add up to 11 ( t + u = 11), you can also use (10 t + u ) - (10 u + t ) = 9 t - 9 u = 9( t - u ) As this is also a square number you know ( t - u ) is either 1, 4, or 9. The solutions for 4 and 9 don't give whole number values for t in 0  t  9.

The math teacher age is 65 years old.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given:

My age in years is not a prime, but is odd.

That means, the number is 10m+ n.

Where m is the digits having the place value 10 and n is the unit digit.

Also, when the digits in my age are reversed and the new number added to my age, the result is a perfect square.

That means,

10n + m + 10m + n,

= 11m + 11n

= 11(m+n)

= multiple of 11.

= 11 x 11

= 121

= 65 + 56

Of course, if you prefer, you can take my age and reverse the digits and subtract that from my age and still get a perfect square.

That means,

10n +m - 10m - n,

= 9n - 9m

= 9(n-m)

= 9

= 65 - 56

Therefore, the age is 65.

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If the xylem vessel radii are related by Murray's law for plants, then the total cost of transport and maintenance is minimized.

a. To minimize the total cost T(r) + M(r), we need to find the value of r that minimizes the sum of these two functions. We can do this by taking the derivative of the sum with respect to r and setting it equal to zero:

d/dR(T(R) + M(R)) = 0

Using the given equations for T(r) and M(r), we can simplify this expression:

d/dR(0.071(f^2L/R^2)(R^2 + (rT)^2) + bπR^2L) = 0

Expanding the first term and simplifying, we get:

d/dR(0.071f^2L + 0.071rT^2L/R^2 + bπR^2L) = 0

Simplifying further, we get:

-0.142f^2L/R^3 + 2bπRL = 0

Solving for R, we get:

R = (2bπL/0.142f^2)^(1/4)

Substituting the given value for rT, we get:

R = 1.76(f^2L/b)^(1/4)

b. To show that the radii of the vessels are related by Murray's law for plants, we need to minimize the total cost for the two vessels subject to the constraint that the total flow rate is conserved. That is, we have:

f = f1 + f2

where f1 and f2 are the flow rates in the two vessels.

The total cost is given by:

T(R) + M(R) = 0.071(f1^2L/R^2)(R^2 + (rT)^2) + bπR^2L + 0.071(f2^2L/R^2)(R^2 + (rT)^2) + bπR^2L

Simplifying and setting the derivative with respect to R equal to zero, we get:

-0.142L/R^3(f1^2 + f2^2) + 2bπL = 0

Using the relationship between R and flow rate derived in part (a), we can substitute for R:

-0.142L(2bπL/f^2)^(3/4)(f1^2 + f2^2)/f^3 + 2bπL = 0

Simplifying and using the conservation of flow rate, we get:

f1^2 + f2^2 = f^2/2

Substituting for f1 and f2 in terms of the radii r1 and r2, we get:

πr1^4 + πr2^4 = (f^2/2bπL)^(2/3)

This equation is equivalent to Murray's law for plants:

R^3 = r1^3 + r2^3

So we have shown that if the xylem vessel radii are related by Murray's law for plants, then the total cost of transport and maintenance is minimized.

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The given geometric series is divergent.


To determine whether the geometric series is convergent or divergent, we need to first identify the common ratio (r). Let's analyze the given series:

7, 6, 36/7, 216/49, ...

To find the common ratio, divide the second term by the first term, and the third term by the second term:
r1 = 6 / 7
r2 = (36/7) / 6 = 6 / 7

Since r1 = r2, the common ratio (r) is 6/7.

Now we can determine if the series is convergent or divergent. A geometric series converges if the absolute value of the common ratio (|r|) is less than 1, and diverges otherwise.

In this case, |r| = |6/7| = 6/7, which is less than 1. However, the first term of the given series is 7, which doesn't belong to the geometric sequence with a common ratio of 6/7. The correct geometric sequence should be:

6, 36/7, 216/49, ...

So, the given series is not a geometric series, and thus we cannot determine if it's convergent or divergent using the geometric series test. Since it doesn't form a proper geometric sequence, we can conclude that it is divergent.

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The Riemann sum for the given function over the interval [1, 5] using eight subintervals and taking the sample points to be left endpoints is approximately equal to -0.9866767.

Given that, we are to evaluate the Riemann sum for f(x) = ln(x) - 0.7 over the interval [1, 5] using eight subintervals, taking the sample points to be left endpoints.

Let's first determine the width of each subinterval.

Using the interval [1, 5], we have that Δx = (b-a)/n, where b is the upper limit (5), a is the lower limit (1) and n is the number of subintervals (8).∴ Δx = (5 - 1)/8 = 4/8 = 1/2 Hence, the width of each subinterval is 1/2.

The left endpoints of the eight subintervals are {1, 3/2, 2, 5/2, 3, 7/2, 4, 9/2}.

Therefore, the Riemann sum is given by:[ln(1) - 0.7](1/2) + [ln(3/2) - 0.7](1/2) + [ln(2) - 0.7](1/2) + [ln(5/2) - 0.7](1/2) + [ln(3) - 0.7](1/2) + [ln(7/2) - 0.7](1/2) + [ln(4) - 0.7](1/2) + [ln(9/2) - 0.7](1/2)  = -0.9866767

Hence, the Riemann sum for the given function over the interval [1, 5] using eight subintervals and taking the sample points to be left endpoints is approximately equal to -0.9866767.

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