solve 3x+4y=17
5x+4y=27​

Answer:

Tony is not correct because 3(x^2-25) can be factored further. The final answer is 3(x+5)(x-5)

Step-by-step explanation:

Because the sine and cosine ratios involve dividing a leg (one of the shorter two sides) by the hypotenuse (the longest side), the ratio values will never be greater than one, because (some number) / (a larger number) is always less than one.

Sine & cosine are trigonometric functions of an angle in mathematics. In the context of a right triangle, the sine and cosine of an acute angle are defined as follows: for the specified angle, the sine is the ratio of the length of the side opposite that angle to the length of the triangle's longest side (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse.

The sine and cosine functions for an angle θ are simply denoted as sin θ and cos θ. In general, the definitions of sine and cosine can be extended to any real value expressed in terms of the lengths of specific line segments in a unit circle.

Learn more about sine and cosine

https://brainly.com/question/13813821

#SPJ4

Answer:

100%

Step-by-step explanation:

Answer:

100 percent

Step-by-step explanation:

This is very easy. Try learning it yourself as when you'll grow the stuff you are learning now will be essential to your learning. Your future learning depends on it.

The area will be 25cm²

HOPE IT HELPS YOU♡♡

The equation of the parabola is y = 2(x - 1)² + 3

From the question, we have the following parameters that can be used in our computation:

Vertex = (1. 3)

Point = (2, 5)

These parameters can be expressed as

(h, k) = (1, 3)

(x, y) = (2. 5)

A parabola can be represented as

y = a(x - h)² + k

Substitute the known values in the above equation, so, we have the following representation

y = a(x - 1)² + 3

Next, we have

5 = a(2 - 1)² + 3

Evaluate the difference and the exponent

5 = a + 3

So, we have

a = 2

Substitute a = 2 in y = a(x - 1)² + 3

y = 2(x - 1)² + 3

Hence, the equation is y = 2(x - 1)² + 3

Read more about parabola at

https://brainly.com/question/1480401

#SPJ1

To start a proof by contraposition, we need to assume the negation of the conclusion and then try to prove the negation of the premise.

In this case, the conclusion is "x is even" and the premise is "x is divisible by 4."

So, we should start with the assumption that x is an arbitrary natural number that is not even. This is the negation of the conclusion. From this assumption, we will try to prove that x is not divisible by 4, which is the negation of the premise.

Therefore, the correct assumption to start the proof by contraposition is: "x is an arbitrary natural number that is not even."

The other options are incorrect because they do not correctly negate the conclusion or the premise.

For example, "x is an arbitrary natural number that is divisible by 4 and not even" is not the negation of the conclusion, and "x is an arbitrary natural number that is odd" is not the negation of the premise.

To know more about contraposition click on below link:

https://brainly.com/question/5306301#

#SPJ11

mass (m) = 5.4g

Volume (V) = 2 cm^3

To find the density (p), we have to apply the next formula:

p= m/v

Replacing:

p´= 5.4/2 = 2.7 g/cm^3

There are 7 desserts that have both yogurt and fruit. Therefore, the answer to your question is 7.

To find out how many of the desserts with yogurt also include fruit, we need to use the concept of intersection in set theory. We can create two sets: one for desserts with yogurt and another for desserts with fruit.

The set of desserts with yogurt has 8 elements, and the set of desserts with fruit has 7 elements. We can represent these sets as follows:

Y = {yogurt desserts} = {1, 2, 3, 4, 5, 6, 7, 8}
F = {fruit desserts} = {1, 2, 3, 4, 5, 6, 7}

Now we need to find the intersection of these sets, i.e., the desserts that have both yogurt and fruit. To do this, we can count the number of elements in the set Y ∩ F:

Y ∩ F = {yogurt and fruit desserts} = {1, 2, 3, 4, 5, 6, 7}

So there are 7 desserts that have both yogurt and fruit. Therefore, the answer to your question is 7.

Visit here to learn more about  intersection :  https://brainly.com/question/14217061
#SPJ11

The cost of each entity: each pen is $\(1.75\), each folder is $\(2.50\), and each notebook is $\(1.75\).

Let's assign variables to the costs of each supply:

Let the cost of each pen be P dollars.

Let the cost of each folder be F dollars.

Let the cost of each notebook be N dollars.

According to the given information, we can form the following equations:

For Shane:

\(4P + 3F + 2N = 12.25 (Equation \ 1)\)

For Cheryl:

\(4F + 6N = 22 (Equation \ 2)\)

For Isaiah:

\(2P + F + 3N = 10.25 (Equation \ 3)\)

To solve this system of equations, we can use substitution or elimination method.

Using the elimination method, let's multiply Equation 2 by 2 and Equation 3 by 4 to eliminate F:

\(8F + 12N = 44 (Equation \ 4)\\8P + 2F + 12N = 41 (Equation \ 5)\)

Now, subtract Equation 4 from Equation 5 to eliminate F:

\(8P + 2F + 12N - (8F + 12N) = 41 - 44\\8P - 6F = -3\)

Simplifying further, we have:

\(8P - 6F = -3 (Equation \ 6)\)

Now, let's multiply Equation 1 by 4 and Equation 3 by 3 to eliminate N:

\(16P + 12F + 8N = 49 (Equation \ 7)\\6P + 3F + 9N = 30 (Equation \ 8)\)

Now, subtract Equation 8 from Equation 7 to eliminate N:

\(16P + 12F + 8N - (6P + 3F + 9N) = 49 - 30\\10P + 9F - N = 19\)

Simplifying further, we have:

\(10P + 9F - N = 19 (Equation \ 9)\)

Now we have a system of equations consisting of Equation 6, Equation 9, and Equation 2:

\(8P - 6F = -3 (Equation \ 6)\\10P + 9F - N = 19 (Equation \ 9)\\4F + 6N = 22 (Equation \ 2)\)

To find the values of P, F, and N, we can solve this system of equations using any suitable method, such as substitution or elimination.

For more such questions on cost of each entity:

https://brainly.com/question/22097711

#SPJ8

Answer:

(2A)/(r^2)=pi

Step-by-step explanation:

The goal is to get pi by itself, so you have to move all the other elements over

2A=pir^2

(2A)/(r^2)=pi

The solution to the system of equations is (15, 30).

A group of two or more equations that must be solved all at once is known as a system of equations. The system's equations each show how two or more variables relate to one another. The variables' values that satisfy every equation in the system can be discovered using algebraic techniques.

Algebraic systems of equations can be solved using a variety of techniques, such as substitution, elimination, and graphing. The substitution approach involves solving one equation for one variable in terms of the other variable, and then substituting the result for that variable's expression into the other equation.

The given system of equations are y=x + 15, y= 2x.

Substitute the value of y from equation 2 in equation 1:

x + 15 = 2x

15 = x

Substitute the value of x to get the value of y:

y = 2x = 2(15) = 30

Hence, the solution to the system of equations is (15, 30).

Learn more about system of equations here:

https://brainly.com/question/13760328

#SPJ1

Answer:

76

Step-by-step explanation:

to check if add all angles and see if they add to 180,

then find the sides that are congruent

Answer: 6/13

Step-by-step explanation:

6/13 is the simplest form

Answer:

Hi buddy

Step-by-step explanation:

step 1: just simply subtract the numerators because the denominators are the like numbers

:8-2=6

step 2 the answer is

6/13

NOTE: there Is no simple form because there is no simple form for 13

A 3-ary tree is a tree in which each internal node has exactly three children, there are 1086 leaf nodes in a 3-ary tree with 6 internal nodes.

For a 3-ary tree with 6 internal nodes, there will be a total of 7 levels (0 to 6). Consider the following formula for the number of nodes in a tree of height\(h: n = 1 + 3 + 3^2 + 3^ + ... + 3^h\) The given 3-ary tree has a height of 6, so its number of nodes is:\(n = 1 + 3 + 3^2 + 3^3 + 3^4 + 3^5 + 3^6\)

Using the geometric series formula, we can simplify this: \(n = (3^7 - 1) / 2n = (2186 - 1) / 2n = 1092\) The number of leaf nodes in a 3-ary tree with 6 internal nodes is:\(n - 6n - 6 = 1092 - 6n - 6 = 1086\) Therefore, there are 1086 leaf nodes in a 3-ary tree with 6 internal nodes.

See more about internal nodes at: https://brainly.com/question/29608280

#SPJ11

Answer:

(6, 8 )

Step-by-step explanation:

Assuming the dilatation is centred at the origin, then multiply the coordinates by the scale factor 2, that is

(3, 4 ) → (2(3) , 2(4) ) → (6, 8 )

The probability that at most 4 customers arrive within a 5-minute period is approximately 0.128 and the probability that the service time will be less than or equal to 30 seconds is 0.5276.

Given that during lunchtime, customers arrive at a postal office at a rate of 36 per hour. The interarrival time of the arrival process can be approximated with an exponential distribution. Customers can be served by the postal office at a rate of 45 per hour. The system has a single server. The service time for the customers can also be approximated with an exponential distribution.

We need to calculate the probability that at most 4 customers arrive within a 5-minute period.

We know that,

λ = 36 customers per hour

So, μ = 36 customers per 60 minutes

= 0.6 customers per minute

P(X ≤ 4) = P(0) + P(1) + P(2) + P(3) + P(4)

= e^-λ + λe^-λ + (λ^2 / 2)e^-λ + (λ^3 / 6)e^-λ + (λ^4 / 24)e^-λ

= e^-36 (1 + 36 + (36^2 / 2) + (36^3 / 6) + (36^4 / 24))≈ 0.128

We need to calculate the probability that the service time will be less than or equal to 30 seconds.

We know that,

μ = 45 customers per hour

= 0.75 customers per minute

P(T ≤ 30 seconds) = P(T ≤ 0.5 minutes)

= 1 - e^-μT

= service time

= 30 seconds

= 0.5 minutes

∴ P(T ≤ 0.5)

= 1 - e^-0.75

= 1 - 0.4724

= 0.5276

Hence, the probability that at most 4 customers arrive within a 5-minute period is approximately 0.128 and the probability that the service time will be less than or equal to 30 seconds is 0.5276.

To know more about probability visit:

https://brainly.com/question/31828911

#SPJ11

There are 360 possible pizza configurations possible.

To find the number of pizza configurations that a customer can choose, use the fundamental principle of counting where we multiply the number of choices for each category.

For the pizza size, there are 3 options to choose from.

For the toppings, there are 10 options for the first topping, 9 options for the second topping, and 8 options for the third topping.

However, since the order of the toppings doesn't matter (e.g. pepperoni, sausage, and mushroom is the same as mushroom, sausage, and pepperoni), we have to divide the result by the number of ways to arrange each group of toppings, which is 3! (factorial of 3).

So, the number of pizza configurations that a customer can choose can be calculated as follows:

Number of configurations = 3(10)(9)(8) / 3!

= 3(720) / 6

= 3(120)

= 360

Therefore, there are 360 possible pizza configurations that a customer can choose.

Learn more about fundamental principle of counting here: https://brainly.com/question/2063455

#SPJ4

Answer:

\(x^{4}\) - 6x³ + 35x² - 150x + 250

Step-by-step explanation:

note that i² = - 1

(x + 5i)(x - 5i)(x - 3 - i)(x - 3 + i) ← expand the first pair of factors using FOIL

= ( x² - 5ix + 5ix - 25i²)((x - 3) - i)((x - 3) + i) ← expand second pair using FOIL

= (x² - 25(- 1))((x - 3)²+ i(x - 3) - i(x - 3) - i²)

= (x² + 25)(x² - 6x + 9 - (- 1))

= (x² + 25)(x² - 6x + 9 + 1)

= (x² + 25)(x² - 6x + 10)

each term in the second factor is multiplied by each term in the first factor

= x²(x² - 6x + 10) + 25(x² - 6x + 10) ← distribute parenthesis

= \(x^{4}\) - 6x³ + 10x² + 25x² - 150x + 250 ← collect like terms

= \(x^{4}\) - 6x³ + 35x² - 150x + 250

Answer:

Well, count out how many nickels can go in $3.90. Then count out how many quarters. Make sure there are 6 more quarters than nickels, and make sure it all adds up to $3.90

Hope this helped! <3

Answer:

not a regular polygon

Step-by-step explanation:

A regular polygon is an n-sided polygon in which the sides are all the same length and are symmetrically placed about a common center

20c +9 is use the variable C to represent Carlos's savings.

What is simple solution to a variable?

A variable is a quantity that can be altered depending on the mathematical issue. The general letters that are utilized in many algebraic expressions and equations are x, y, and z.

                      To put it another way, a variable is a symbol for a numeric value for which there is no known value. In this case, x + 5 = 10. "X" in this case is a variable.

Product is multiplication.

The product of 20 and Chau's score would be written as 20c

Then you want 9 more, so you would add 9 at the end to get

20c +9

Learn more about variable

brainly.com/question/17344045

#SPJ1

Answer:

A. 5

Step-by-step explanation:

Answer:

It would take Michael 22 days

Explanation:

The end goal is to have 80 and we begin with 14

So, 80 - 14 = 66 pieces left to collect

If he collects 3 per day we'll divide 66 by 3, which equals 22

Therefore it takes him 22 days!

(hope this helps :D )

Answer: 22 days

Step-by-step explanation: 22 x 3 = 66, 66 + 14 equals 80

Answer:

1/2

Step-by-step explanation:

because 5 times 1/2 and you get 2 1/2

Given the two vectors are orthogonal vectors. Then, the value of k is found to be \(k=-\frac{25}{56}\).

When the two vectors are perpendicular or right angle to each other and their dot product value is equal to zero, they are considered orthogonal vectors. Consider two vectors u and v. These two vectors are considered orthogonal when their inner product is zero. That is, \(u\cdot v=u_1v_1+u_2v_2+\cdots+u_nv_n=0.\)

They also have a magnitude of 1. So the three conditions required for the vectors to be orthogonal are:

Given the two vectors,

 \(\mathbf{x}=\left[\begin{array}{ccc}-1\\-5\\14\end{array}\right]\)

\(\mathbf{y}=\left[\begin{array}{ccc}0\\5\\-4k\end{array}\right]\)

Then, their dot product is given as follows,

\(\begin{aligned}x\cdot y&=0\\(-1\times0)+(-5\times5)+(14\times-4k)&=0\\-25-56k&=0\\-56k&=25\\k&=\frac{-25}{56}\end{aligned}\)

The required answer is \(k=-\frac{25}{56}\).

To know more about orthogonal vectors:

https://brainly.com/question/28503609

#SPJ4

The complete question is -

Find the value of k for which the vectors \(\mathbf{x}=\left[\begin{array}{ccc}-1\\-5\\14\end{array}\right]\) and \(\mathbf{y}=\left[\begin{array}{ccc}0\\5\\-4k\end{array}\right]\) are orthogonal.

Answer:

Check pdf

Step-by-step explanation:

The radius of the larger circle is 12 inches. Then the area of the larger circle will be 144π square inches.

Let r be the radius of the circle. Then the area of the circle will be

A = πr² square units

The four small circles are identical. The total area of the small circles is 36π square inches. Then the radius of each small circle is given as,

36π = 4 × (πr²)

r² = 9

r = 3 inches

Then the radius of the larger circle is calculated as,

R = 4r

R = 4 × 3

R = 12

Then the area of the larger circle will be given as,

A = π × (12)²

A = 144π square inches

The radius of the larger circle is 12 inches. Then the area of the larger circle will be 144π square inches.

More about the area of a circle link is given below.

https://brainly.com/question/11952845

#SPJ2

The displacement and distance traveled depend on the given time interval.

To find the displacement, we need to integrate the velocity function from 0 to 5 or 0 to 5π, depending on the given time interval.

If the time interval is [0,5], we have:

Displacement = ∫[0,5] v(t) dt
Displacement = ∫[0,5] 6cos(t) dt
Displacement = [6sin(t)] from 0 to 5
Displacement = 6sin(5) - 6sin(0)
Displacement ≈ 2.785 meters

If the time interval is [0,5π], we have:

Displacement = ∫[0,5π] v(t) dt
Displacement = ∫[0,5π] 6cos(t) dt
Displacement = [6sin(t)] from 0 to 5π
Displacement = 0 - 6sin(0)
Displacement = 0 meters

To find the distance traveled, we need to integrate the absolute value of the velocity function over the given time interval.

If the time interval is [0,5], we have:

Distance = ∫[0,5] |v(t)| dt
Distance = ∫[0,5] |6cos(t)| dt
Distance = ∫[0,π/2] 6cos(t) dt + ∫[π/2,5] -6cos(t) dt
Distance = [6sin(t)] from 0 to π/2 + [-6sin(t)] from π/2 to 5
Distance = 6 - 6sin(5) ≈ 2.215 meters

If the time interval is [0,5π], we have:

Distance = ∫[0,5π] |v(t)| dt
Distance = ∫[0,5π] |6cos(t)| dt
Distance = ∫[0,π] 6cos(t) dt + ∫[π,2π] -6cos(t) dt + ∫[2π,3π] 6cos(t) dt + ∫[3π,4π] -6cos(t) dt + ∫[4π,5π] 6cos(t) dt
Distance = [6sin(t)] from 0 to π + [-6sin(t)] from π to 2π + [6sin(t)] from 2π to 3π + [-6sin(t)] from 3π to 4π + [6sin(t)] from 4π to 5π
Distance = 0 meters

Know more about displacement here;

https://brainly.com/question/30087445

#SPJ11

The probability of vowel or letter D is determined as 4/9.

The probability of vowel or letter D is calculated by applying the formula for probability of an event as follows;

Mathematically, the formula for probability is given as;

P (E) = number of outcomes in event E / total number of outcomes in sample space

If the lucky wheel is divided into 9 sectors of equal size lettered A through I, the number of outcomes include the following;

number of outcomes = A, B, C, D, E, F, G, H, I

vowels in the outcome = A, E, I

letter D in the outcome = D

number of outcomes = {A, E, I} or {D}

P(vowel or D) = 3/9 or 1/9

P(vowel or D) = 3/9 + 1/9

P(vowel or D) = 1/3 + 1/9

P(vowel or D) = 4/9

Learn more about probability here: https://brainly.com/question/25870256

#SPJ1