Write an equation that is perpendicular to the line y = 5x - 1 and passes through the point (10, 8)

Answer:

if you make 4 free throws for every 10 shots taken you would make 20 out of 50 free throws

Step-by-step explanation:

So we have shown that the largest possible area of the triangle is \(a^2,\)which occurs when the third side has length 3a and the height is a.

We can use the formula for the area of a triangle, which is A = (1/2)bh, where b is the length of the base and h is the height. In this case, we know that the base has length 2a, so we need to find the height.

Let's call the third side of the triangle, which is not given, b. We know that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, so we have:

a + 2a > b

3a > b

We can rearrange this to solve for b:

b < 3a

Now, let's use the formula for the area of a triangle:

A = (1/2)bh

We want to maximize A, so we want to maximize h. We know that h is the height of the triangle, which is perpendicular to the base, so it forms a right angle. We can use the Pythagorean theorem to find h in terms of a and b:

\(h^2 = b^2 - a^2\)

We can substitute our inequality for b:

\(h^2 < (3a)^2 - a^2\)

\(h^2 < 8a^2\)

h < √(8\(a^2\))

h < 2 √(2)a

Now we can use the formula for the area of the triangle again:

A = (1/2)bh

A < (1/2)(2 √(2)a)(a)

A < \(a^2\) √(2)

So we have shown that the largest possible area of the triangle is \(a^2,\)which occurs when the third side has length 3a and the height is a.

Learn more about  Pythagorean theorem

https://brainly.com/question/14930619

#SPJ4

The area left for children for playing 114464 sq. m

As per the given data inside a park:

The length of the park is 400 m

The breadth of the park is 300 m

The formula for the area of the park = Length × Breadth

= (400 × 300) sq. m

= 120000 sq. m

The width of the walking track inside the park is 4 m

The length of the park without the walking track

= 400 − (4 + 4) m

= 400 − 8 m

= 392 m

The breadth of the park without the walking track

= 300 − (4 + 2) m

= 300 − 8 m

=292 m

Area of the park without the walking track:

= 392 × 292

= 114464 sq. m

Therefore the area left for children for playing other than the walking track is 114464 sq. m.

For more questions on the area

https://brainly.com/question/17677554

#SPJ4

The triangle that is similar to the triangle ΔABC is the triangle ΔJKL, the correct option is therefore;

B. ΔJKL, in which m∠J = 15° and m∠L = 45°

Triangles are similar if they have the same measure of two of their interior angles, and therefore, have the same shape, but they may have different size.

The specified known angles of the triangle indicates that the known angles are;

m∠A = 15°, m∠B = 120°

Therefore, the third angle of the triangle is; 180 - (15 + 120) = 45

The third angle of the is 45 degrees

Therefore, the triangle that is similar to the specified triangle has an angle interior angle of either; 15°, or 120°, or 45°

Learn more on similar triangles here: https://brainly.com/question/29782809

#SPJ1

the average number of pairs of consecutive integers in a randomly selected subset of 5 distinct integers chosen from the set{1,2,3,...,30} is 2/3

There are 29 possible pairs of consecutive integers namely p1 = { 1,2} ....... ,p29= {29,30}

define a random variable Xi with Xi =1 if pi is a part of the 5 elements subset and 0 otherwise then the number of pairs of consecutive integers in a 5 selection is given by the sum X1+ .........+X29

E[ Xi]= 28C3/ 30C5

        = 2/3

Hence ,  the average number of pairs of consecutive integers in a randomly selected subset of 5 distinct integers chosen from the set{1,2,3,...,30} is 2/3

learn more about of subset here

https://brainly.com/question/23454979

#SPJ4

Therefore , the solution of the given problem of area comes out to be  15 square units.

How much space it occupies on the surface is a reliable indication of its overall dimensions. The nearby surroundings are considered when calculating a triangular shape's surface. Something's total dimensions are determined by its surface area. The total of the capacities for each of a cuboid's six rectangular sides makes up its internal water capacity. To calculate the size of the box, use the following method.

Here,

We must measure the lengths of the sides of the polygon and sum them up to determine its perimeter.

The length of each edge can be determined using the distance formula:

=> CD = √((2 - 2)² + (1 - 4)²) = √(9) = 3

=>  DE = √(7 - 2)² + (4 - 4)²) = 5

=>  EF = √((7 - 7)² + (1 - 4)²) = 3

=>  FC = √(7 - 2)² + (1 - 1)²) = 5

As a result, the boundary is:

CD = DE + EF + EF + FC = 3 + 5 + 3 + 5 = 16

Area of CDE = 1/2*base*height*1/2*DE*CD =1/2*5*3*area of CDE, which equals 7.5.

Area of CEF = 1/2*3*5=7.5

Consequently, the polygon's size is:

Size = CDE + CEF combined, which equals 7.5 + 7.5 = 15 square units.

To know more about area visit:

brainly.com/question/2835293

#SPJ1

V can be expressed as a linear combination of vectors in S₁. This implies that S₁ U S₂ is linearly dependent.

To prove the statement, let's break it down into two parts and prove each part separately:

Part 1: If S₁ U S₂ is linearly dependent, then span(S₁) ∪ span(S₂) ‡ {0}.

Part 2: If span(S₁) ∪ span(S₂) ‡ {0}, then S₁ U S₂ is linearly dependent.

Part 1: If S₁ U S₂ is linearly dependent, then span(S₁) ∪ span(S₂) ‡ {0}.

Assume S₁ U S₂ is linearly dependent. This means there exist scalars c₁ and c₂, not both zero, such that c₁S₁ + c₂S₂ = 0

Since S₁ and S₂ are linearly independent, neither of them can be written as a linear combination of the other. Therefore, at least one of the scalars c₁ and c₂ must be non-zero. Without loss of generality, assume c₁ ≠ 0.

Now, rearranging the equation, we have c₁S₁ = -c₂S₂. Dividing both sides by c₁ (which is non-zero), we get S₁ = (-c₂/c₁)S₂.

This shows that S₁ is a scalar multiple of S₂. Therefore, span(S₁) ⊆ span(S₂).

Since c₁ ≠ 0, we also have -c₂/c₁ ≠ 0. Thus, the zero vector {0} can be expressed as a non-trivial linear combination of vectors in span(S₁) and span(S₂), i.e., span(S₁) ∪ span(S₂) ‡ {0}.

Part 2: If span(S₁) ∪ span(S₂) ‡ {0}, then S₁ U S₂ is linearly dependent.

Assume span(S₁) ∪ span(S₂) ‡ {0}. This means there exists a non-zero vector v such that v ∈ span(S₁) ∪ span(S₂).

Since v is non-zero, it can be expressed as a non-trivial linear combination of vectors in either span(S₁) or span(S₂). Without loss of generality, assume v is a linear combination of vectors in span(S₁).

Therefore, v can be expressed as a linear combination of vectors in S₁. This implies that S₁ U S₂ is linearly dependent.

By proving both parts, we have shown that S₁ U S₂ is linearly dependent if and only if span(S₁) ∪ span(S₂) ‡ {0}.

In summary, we have proven that if S₁ U S₂ is linearly dependent, then span(S₁) ∪ span(S₂) ‡ {0}, and conversely, if span(S_1) \cup span(S_2)) ‡ {0}, then S₁ U S₂ is linearly dependent.

for more such question on linear   visit

https://brainly.com/question/2030026

#SPJ8

Answer:

Step-by-step explanation:

1

3

3(x² + 1)

2

6

6(3y² - 1)

3

m²

m²(n² + 3)

4

6

6(x³ + 6)

5

6

6(x³ + 3x² + 4)

6

5

5(a³ + 5a² - 7a + 4)

7

8

8(2m³ + 3m² + 2)

8

5

5(5x²y + 3xy² + 6)

9

16x

16x(2x^4 + 4x³ + 1)

10

7xy

7xy(3x²y - x + 6)

11

-a^4

-a^4(3a² + 4a + 1)

12

4xy

4xy(x - 4xy + 5y)

13

6y

6y(-4x² + x²y + 5y)

14

2

2(9a² - 18a²b² + 22b²)

15

-3xy

-3xy(5x²y + 15xy + 11y)

16

4ab

4ab(ab^6 - 8ab^5 + 4b)

17

17xy

17xy(x - 2)

18

n

n(3m² - 39m²n - 13n)

19

5t

5t(-8t + ts + 20s²)

20

p

p(6p³q + qr - 3r)

Difference between the fees of Ahab and his sister is \(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)

Review the following subtraction rules and properties:

Given: Ahab pays dollars for one year's tuition fees and his sister pays dollars fees in tuition for the first year

To find: Difference in tuition fees paid by Ahab and his sister?

Solution:

To find the difference in their fees we have to perform simply normal subtraction

Subtract the fees of his sister from Ahab's fees which is as follows:

\(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)

Hence the difference between the fees of Ahab and his sister is \(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)

Learn more about Subtraction here:

https://brainly.com/question/1927340

#SPJ4

Answer:

(1, 6) is the solution

Step-by-step explanation:

-2x + 6y = 34

2x + 2y = 14;     divide by 2

x + y = 7;        subtract x

y = 7 - x

let's substitute y with 7 - x in first equation

-2x + 6*(7 - x) = 34;    expand multiplication

-2x + 6*7 - 6*x = 34;    group

-8x + 42 = 34;         subtract 42

-8x = 34 - 42 = -8;      divide by -8

x = 1

y = 7 - 1 = 6

It is the only solution, as we've arrived at exact numbers.

(a) The domain closed and bounded.

(b) The domain bounded.

(c) The domain closed.

(d) The domain bounded.

(e) The domain closed and bounded.

(f) The domain closed and bounded.

In this question, we have been given some domains.

We need to check which domains are closed and which are bounded.

A domain of function is said to be closed if the region R contains all boundary points.

A bounded domain is nothing but a domain which is a bounded set.

(a) {(x,y)∈R2:x^2+y^2≤1}

The domain of x^2+y^2≤1 contains set of all points (x, y) ∈R2

so, the domain closed and bounded.

(b) {(x,y)∈R2:x2+y2<1}

The domain of x^2+y^2 < 1 contains set of all points (x, y) ∈R2

so, the domain is bounded.

(c) {(x,y)∈R2: x ≥ 0}

The domain of x ≥ 0 is R2 - {x < 0}

So, the domain is closed.

(d) {(x, y) ∈ R2 : x > 0,y > 0}

The domain is R2 - {(x, y) ≥ 0}

So, the domain is bounded.

(e) {(x, y) ∈ R2 : 1 ≤ x ≤ 4, 5 ≤ y ≤ 10}

The domain is closed and bounded.

(f) {(x,y)∈R2:x>0,x^2+y^2≤10}

The domain is closed and bounded.

Learn more about the domain here:

https://brainly.com/question/28135761

#SPJ4

Answer:

12x²y(2xy - 1)

Step-by-step explanation:

Given

24x³y² - 12x²y ← factor out 12x²y from each term

= 12x²y(2xy - 1)

Answer:

The first one

The second one

The third one

The fifth one

Step-by-step explanation:

answer:

8.037m

step-by-step explanation:

the total of two or more addends is the sum of the numbers added.

your two addends are 5.89 and 2.147, so add them together.

5.89+2.147

=5.89+2.147

=8.037

the answer is 8.037m

Nadia has constructed a pentagonal prism

We know that, a pentagonal prism has two pentagonal bases like top and bottom and five rectangular sides.

If we consider the bottom view of  pentagonal prism then it would be pentagon in shape.

If we consider the side view of  pentagonal prism then it would be rectangular in shape.

If we consider the front view of  pentagonal prism then it would be rectangle.

Therefore, Nadia has constructed a pentagonal prism

Learn more about the  pentagonal prism here:

https://brainly.com/question/26709266

#SPJ1

Answer:

16 feet

Step-by-step explanation:

Answer:

.25 inches per hour

Step-by-step explanation:

.5 ft

-----------

day

We need to get to inches

1 ft = 12 inches

.5 ft          12 inches      

----------- * ------------

day             1 ft  

We also need to convert days to minutes

1 day = 24 hours

.5 ft           12 inches             1 day          

----------- * ------------   * -------------    

day             1 ft       24 hours      

6 inches

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

24 hours

.25 inches per hour

We have to convert 0.5ft/day to in/hr

So

So

Convert

Answer:

plug in the missing numbers and you have the answers

Step-by-step explanation:

Answer:

.8Km

Step-by-step explanation:

There is exactly 100,000 CM in every KM, if someone such as Ben was to measure out 80,000, to convert to KM you'd take the given value and divide by the appropriate values.

80,000cm / 100,000cm = .8 KM

Answer:

11 = Y+5

Step-by-step explanation:

Answer:

i could be B or A not sure tho

Answer: it 5 cuh

Step-by-step explanation:

Answer:

4.58 * 10 ^ -5

Step-by-step explanation:

0.0000458

Move the decimal 5 places to the right to get a number between 1 and less than 10

00004.58

That will give us an exponent of -5 ( the negative is because we moved it to the right)

4.58 * 10 ^ -5

━━━━━━━☆☆━━━━━━━

▹ Answer

4.58 * 10⁻⁵

▹ Step-by-Step Explanation

The decimal point is moved 5 times to the left, meaning the scientific notation will be negative. Therefore, the answer is 4.58 * 10⁻⁵.

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

\( x\approx 18.0\)

Step-by-step explanation:

Here, a = 30, b = 16, C = x

By law of cosines

\( {c}^{2} = {a}^{2} + {b}^{2} - 2ab \cos C \\ \\ {x}^{2} = {30}^{2} + {16}^{2} - 2 \times 30 \times 16 \: cos 30 \degree \\ \\ {x}^{2} = 900 + 256 - 960 \times \frac{ \sqrt{3} }{2} \\ \\ {x}^{2} = 1156 - 480 \times \sqrt{3} \\ \\ {x}^{2} = 324.615612 \\ \\ x = \sqrt{324.615612} \\ \\ x = 18.0170922 \\ \\ x \approx \: 18.0\)

The probability of a core of the two odd number be 1/4.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

The outcome of one die has no bearing on the outcome of the other since the two dice are independent.

In this instance, a complex event's probability is calculated by adding its component simple event probabilities.

Three odd and three even results occur from each roll of the dice. So, the probability of getting an odd number exists \($\frac{3}{6}=\frac{1}{2}$\)

The probability that this happens with both dice exists \($\frac{1}{2} \cdot \frac{1}{2}=\frac{1}{4}$\)

It is relatively simple to list the "excellent" possibilities in this situation because there are a total of 36 outcomes (all numbers from 1 to 6 for one die and the same for the other die). The positive results are

(1, 1), (1, 3), (1, 5)

(3, 1), (3, 3), (3, 5)

(5, 1), (5, 3), (5, 5)

And in fact, 9 good outcomes over 36 total outcomes means

\($\frac{9}{36}=\frac{1}{4}$$\)

To learn more about probability refer to:

https://brainly.com/question/13604758

#SPJ1

To find the absolute maximum and minimum values of f on the given interval, we need to first take the derivative of f and set it equal to zero to find the critical points.

Then, we will check the endpoints of the interval to see if they give us any maximum or minimum values. Taking the derivative of f, we get f'(t) = 5 - (5/2) csc^2(t/2). Setting this equal to zero and solving for t, we get t = π/2, 3π/2. These are the critical points.

Next, we need to check the values of f at the critical points and the endpoints of the interval. At t = π/4, f(π/4) = 5π/4 + 5√2, and at t = 7π/4, f(7π/4) = -3π/4 - 5√2. At the critical points, f(π/2) = 5√2 and f(3π/2) = -5√2.

Therefore, the absolute maximum value of f on the interval [π/4, 7π/4] is 5π/4 + 5√2, and the absolute minimum value of f on the interval is -3π/4 - 5√2.

As there are no critical points in the given interval, the absolute maximum and minimum values must occur at the endpoints. By comparing the function values at these endpoints, we can determine the absolute maximum and minimum values:

Absolute minimum value: min{f(π/4), f(7π/4)}
Absolute maximum value: max{f(π/4), f(7π/4)}

Keep in mind that you'll need to calculate the actual function values at the endpoints to determine the numerical values of the absolute minimum and maximum.

To know more about derivative click here

brainly.com/question/29096174

#SPJ11

Answer:

Multiply the bottom equation by -3/2 then add the equations.

Multiply the top equation by-3. then add the equations

Step-by-step explanation:

Given the simultaneous equation

2x- 6y=6  ... 1

6x - 4y = 2 ... 2

To eliminate a variable, we have to make the coefficient of one of the variable to be the same.

Multiply equastion 1 by -3

-6x+18y= -18  

6x - 4y = 2

Add the result:

-6x + 6x + 18y-4y = -18+2

18y-4y = -18+2

14y = -18

y = -9/7

Another way is to Multiply the bottom equation by -3/2 then add the equations.

Multiplying equation 2 by -3/2 will give;

6x(-3/2) - 4y(-3/2) = 2(-3/2)

-9x + 6y = -3

Add to equation 1;

2x- 6y=6

-9x + 2x + 0 = -3+6

-7x = 3

x = -3/7

Hence the correct two options are;

Multiply the bottom equation by -3/2 then add the equations.

Multiply the top equation by-3. then add the equations

A) Given that all people work at the same steady rate and 6 people stuff flyers in 5 minutes, then 12 (=2*6) people will need 2.5 (=5/2) minutes, 30 (=5*6) people will need 1 (=5/5) minutes, etc. Then, the relationship is inverse.

The formula that relates the variables is:

people = k/time

Replacing with people = 6 and time = 5, we get.

6 = k/5

6*5 = k

k = 30

For 5 people:

5 = 30/time

time = 30/5

time = 6 minutes

people | time

5 | 6

6 | 5

12 | 2.5

30 | 1

Answer: a. Here is a sketch of the wooden board with dimensions 54 cm by 90 cm:

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

|               |

|               |

|               |

|               |

|               |

|               |

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

Possible side lengths for the squares could be:

9 cm (since both 54 and 90 are divisible by 9)

6 cm (since both 54 and 90 are divisible by 6)

3 cm (since both 54 and 90 are divisible by 3)

b. To find the largest side length of the squares, we need to find the greatest common divisor (GCD) of 54 and 90. The GCD of 54 and 90 is 18. Therefore, the largest side length you can choose is 18 cm. This is because 18 cm is a divisor of both 54 and 90, ensuring that the board can be evenly divided into square pieces of that size.

c. To find the number of square pieces, we divide the dimensions of the board by the side length of the squares. In this case, if we use 18 cm as the side length, we can divide both 54 cm and 90 cm by 18 cm.

Number of square pieces = (54 cm ÷ 18 cm) * (90 cm ÷ 18 cm) = 3 * 5 = 15

Therefore, you will have 15 square pieces if you choose a side length of 18 cm.

Step-by-step explanation: Hope this helps :D

Answer:10

Step-by-step explanation: