Is 10, 24, and 13 a Pythagorean triple?

A. yes
B. cannot tell
C. no​

Hello!

In the given figure we can see that it is a right angled triangle .

Where,

Base is 9

We have to find the value of x i.e Hypotenuse

Here we are given base and we need to find the Hypotenuse.

Also we have been given the value of theta = 45°

Using trigonometric ratio :

cos \(\theta = \dfrac{ B}{H} \)

As per the question we have hypotenuse = x

Plugging the required values,

\( \cos 45 \degree = \dfrac{9}{x} \)

\( \dfrac{1}{ \sqrt{2} } = \dfrac{9}{x} \: \: \: \: \bigg(\because \cos 45\degree = \dfrac{1}{\sqrt2} \bigg)\)

further solving by cross multiplication

\(x = 9 \sqrt{2} \)

Hence, The value of x is 9√2

Answer : Option 1

Hope it helps! :)

The scalar product of vectors a = 6i + 4j - 2k and b = 5i - 6j - 3k is 12.

To determine the scalar product (dot product) of two vectors a and b, which are given as

a = 6i + 4j - 2k and

b = 5i - 6j - 3k, follow these steps:

Write down the vectors a and b, with their corresponding components:

Vector a: 6i + 4j - 2k

Vector b: 5i - 6j - 3k

Multiply the corresponding components of the vectors:

Multiply the i-components: 6 * 5 = 30

Multiply the j-components: 4 * -6 = -24

Multiply the k-components: -2 * -3 = 6

Sum up the results from step 2:

30 + (-24) + 6 = 12

The obtained value is the scalar product of vectors a and b.

Therefore, the scalar product of vectors a = 6i + 4j - 2k and

b = 5i - 6j - 3k is 12. The scalar product represents the product of the magnitudes of the vectors and the cosine of the angle between them. In this case, the scalar product is a numerical value that indicates the degree of alignment or orthogonality between the vectors a and b.

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Answer:

Multiply the first equation by -1

Step-by-step explanation:

Here, we ware being asked the step to take to solve the simultaneous equation

What is right here is to multiply the first equation by -1

By multiplying the first equation by -1, we will have it that the value of y in that equation becomes negative

It is from here we can now add both equations together to have only real x terms

Answer:

17, 19

Step-by-step explanation:

Prime numbers' only factors are 1 and itself

Answer:

17 & 19

Step-by-step explanation:

you can multipy 3x5 to get 15 so thats not it

you can multiply 8x2 to get 16 so its not prime

you can multiply 9x2 and 6x3 so thats not it either

1 is the only thing that can go into 17 besides itself and 1 is the only thing that can go into 19 besides itself

Answer:

20%

Step-by-step explanation:

I hope this helps!

Answer:

$3,096

Step-by-step explanation:

To find the total interest Mr. Quesada will pay, we need to first calculate the total amount he will pay back, and then subtract the original amount borrowed.

The total amount Mr. Quesada will pay back over 24 months is:

$629 x 24 = $15,096

Subtracting the original loan amount, we get:

$15,096 - $12,000 = $3,096

So Mr. Quesada will pay a total of $3,096 in interest over the course of the loan.

Answer:

Step-by-step explanation:

slope= \(\frac{y2-y1}{x2-x1\\\\}\)= \(\frac{4-2}{0-(-1)\\}\)= \(\frac{2}{1} =2\)

y= mx + b

4= 2(0) + b

4= 0 + b

b=4

y=2x+4

Answer:

True

Step-by-step explanation:

The given statement "John Graunt is said to be the first to employ quantitative methods to describe population vital statistics" is true as he was interested in how various factors affected mortality rates and population growth.

Quantitative methods are used to quantify and assess data. These techniques are employed by statisticians and scientists in a variety of fields, including psychology, economics, and public health. Quantitative data can be transformed into statistical analyses to make sense of patterns, patterns, and relationships.

John Graunt was a London haberdasher who lived from 1620 to 1674. He is known as the father of vital statistics, and he was the first to employ quantitative methods to describe population vital statistics.

Graunt was interested in how various factors affected mortality rates and population growth, and he used statistical methods to investigate these issues.

In summary, John Graunt is said to be the first to employ quantitative methods to describe population vital statistics.

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Answer:

Step-by-step explanation:

Let the number = x

2x + 8 ≥ 4x                   Subtract 2x from both sides.

8 ≥ 4x - 2x                    Combine

8 ≥ 2x                           Divide by 2

8/2 ≥ 2x/2                    Combine

4 ≥ x

What this means is that the largest value the x can have is 4. Any number greater that 4 will make the use of ≥ incorrect.

The total area of the flower gardens is x(31 - 2x)/2 sq.ft.

(a) The area of the driving region is the area of a rectangle with length 50 ft and width 31 - 2x ft, where x is the length of one side of a parking space.

Since the parking spaces are congruent parallelograms, they can be divided into two congruent right triangles.

The base of each right triangle is x ft, the height is half of the width of the driving region, which is (31 - 2x)/2 ft.

The area of each parking space is the sum of the areas of the two congruent right triangles.

Therefore,

The total area of the surface to be paved is:

Area = Area of driving region + 4(Area of parking space)

= (50 ft) x (31 - 2x ft) + 4[2(x/2 ft) x ((31 - 2x)/2 ft)]

= 1550 - 100x + 2x(31 - 2x)

= 4\(x^2\) - 100x + 1550 sq.ft.

(b) The unpaved areas for flowers are congruent triangles each with base x ft and height (31 - 2x)/2 ft.

Therefore,

The total area of the flower gardens is:

Area = 2(Area of one triangle)

= 2[(x ft) x ((31 - 2x)/2 ft)/2]

= x(31 - 2x)/2 sq.ft.

The factor of 2 in the formula.

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Answer:

62.5 %

Step-by-step explanation:

Take the original amount and subtract the new amount

32-12 = 20

Divide by the original amount

20/32 =.625

Multiply by 100 to get to percent form

62.5 %

The maximum area of the rectangle inside the ellipse is 2ab.

Given that,

Ellipse = x2 / a2 + y2 / b2 = 1

we know the general coordinates of any point in an ellipse of the equation

x2 / a2 + y2 / b2 = 1 is (acosθ,bsinθ)

So, we take general vertices of rectangles as

(acosθ,bsinθ), (acosθ,-bsinθ), (-acosθ,bsinθ), and (-acosθ,-bsinθ)

So, we can see that length and breadth of the rectangle is 2acosθ and 2bsinθ

So, its area will be ab4sinθcosθ (Length x Breadth)

Applying trigonometric formula 2sinθcosθ=sin2θ, let area equals to A

Now A=2absin2θ

Now as the area is the maximum given in the question, we have to differentiate it with respect to θ

dA/dθ=2abcos2θ×2 (using dsin2θ / dθ=2cos2θ)

Equating dA / dθ=2abcos2θ×2=0, it means cos2θ=0 , which means 2θ =  π / 2 and θ=π / 4

So now we to put θ=π / 4 in the equation of area which is A=2absin2θ

We get as A=2absin2π / 4=2absinπ / 2=2ab

Hence the max area of the rectangle inside the ellipse is 2ab.

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No, a fraction is not a term. The distributive property can be applied to fractions because it is a general mathematical principle.

A fraction is not considered a term in the traditional sense. It is a mathematical expression that represents division. However, the distributive property can still be applied to fractions because the property itself is a fundamental rule of arithmetic that extends beyond specific types of expressions.

The distributive property states that for any real numbers a, b, and c:

a × (b + c) = (a × b) + (a × c).

When working with fractions, we can apply the distributive property as follows:

Let's consider the expression: a × (b/c).

We can rewrite this as: (a × b)/c.

Now, let's distribute the 'a' to 'b' and 'c':

(a × b)/c = (a/c) × b.

In this step, we applied the distributive property to the fraction (a/c) by treating it as a whole.

Although fractions represent division, we can still use the distributive property because it is a general mathematical principle that allows for manipulating expressions involving addition, subtraction, multiplication, and division.

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Answer: True

Step-by-step explanation:

the exponential function that goes through the points (0,2) and (3,686) is \(y = 2(7)^x\).

To write an exponential function in the form y = a(b)^x that goes through the points (0,2) and (3,686), we can use the point-slope form of a linear equation.

Step 1: Find the value of b:

Using the point (0,2), we have:

\(2 = a(b)^0\)

2 = a(1)

a = 2

Step 2: Substitute the value of a into the second point to find b:

\(686 = 2(b)^3\)

\(343 = b^3\)

b = ∛343

b = 7

Step 3: Write the exponential function:

Now that we have the values of a and b, the exponential function in the form y = a(b)^x is:

\(y = 2(7)^x\)

So, the exponential function that goes through the points (0,2) and \((3,686) is y = 2(7)^x.\)

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Either the first or the third choice is correct. We can't tell which one without seeing the rest of the words ... the ones that are cut out of the picture.

Answer:

see below

Step-by-step explanation:

dilated by 2/3 = shrink to 2/3, so it'll be smaller.

but their shape will be similar so correct answers:

Triangle X'Y'Z' is similar to triangle XYZ.

The perimeter of X'Y'Z' is 2/3 the perimeter of XYZ.

the area will be the square of the factor of 2/3

also it's been shrunk so it's not an enlargement

It will cost $211.05 to pour the concrete slab for the patio.

First, we have to convert the dimensions of the patio into yards.

11 feet = 3.67 yards (since there are 3 feet in a yard)

Next, we need to convert the depth of the concrete from inches to yards.

3 inches = 0.25 yards (since there are 36 inches in a yard)

Volume of patio is

Volume = Length x Width x Depth

= 3.67 yards x 3.67 yards x 0.25 yards

= 3.35 cubic yards

Cost = Volume x Price

= 3.35 cubic yards x $63.00

= $211.05

Therefore, it will cost $211.05 to pour the concrete slab for the patio.

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To calculate the amount put back into the business, we need to determine 20% of the profit. Here's the calculation:

Total profit = Ksh 225,000

Amount put back into the business = 20% of the profit

Amount put back into the business = 0.2 * Ksh 225,000

Amount put back into the business = Ksh 45,000

Therefore, Ksh 45,000 was put back into the business.\(\)

Thus, the interpretation in step 4 is incorrect or invalid, and option C is the most appropriate choice.

The best statement that applies to the given mathematical work is option C: The interpretation in step 4 is incorrect or invalid.

In the work provided, steps 1 to 3 correctly interpret the given statement. Step 1 sets x as the unknown quantity,

step 2 correctly represents "3 times a number" as x + 3, and step 3 represents "is added to itself" as + x.

However, in step 4, the student incorrectly adds the values from step 2 and

step 3 together, resulting in x + 3 + x. This is an error because the phrase "is added to itself" refers to adding the unknown quantity to itself, which should be represented as 2x.

The correct equation should be:

x + 3 + x = 30

By combining like terms, we get:

2x + 3 = 30

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Answer:

C = 207.55 + 223.07x

Step-by-step explanation:

Given the following :

Cost of community college:

Enrollment fee = 207.55

Fee per credit hour = 223.07

Attending the community College for 'x' credit hours can be represented by:

Total cost = C

[Enrollment fee + (fee per credit hour * number of credit hours)]

Number of credit hours = x

C = [207.55 + (223.07 * x)]

C = 207.55 + 223.07x

Therefore, the total cost 'C' of attending the community college for 'x' credit hour:

C = 207.55 + 223.07x

The values of u, v, u, v, and d(u, v) are given below:(a) u, v = 171(b) ||u|| = 13(c) ||v|| = 17(d) u/||u|| = (-12/13, 5/13), v/||v|| = (-8/17, 15/17)(e) d(u, v) = 2√29

Given inner product defined on Rn, u = (−12, 5), v = (−8, 15) and u, v = u · v. The values of u, v, u, v, and d(u, v) are to be calculated.

Solution: Given inner product defined on Rn, u = (−12, 5), v = (−8, 15) and u, v = u · v.

The dot product of u and v is given by u . v= (-12 * -8) + (5 * 15)u . v= 96 + 75u . v= 171

Now, we have to calculate the norm of u and v, which can be calculated as follows: ||u|| = √u1² + u2²||u|| = √(-12)² + 5²||u|| = √144 + 25||u|| = √169||u|| = 13

Similarly,||v|| = √v1² + v2²||v|| = √(-8)² + 15²||v|| = √64 + 225||v|| = √289||v|| = 17

Now, we have to calculate the unit vector of u and v. T

he unit vector of u and v is given by: u/||u|| = (-12/13, 5/13)v/||v|| = (-8/17, 15/17)Now, we have to calculate d(u, v). The formula to calculate d(u, v) is given by: d(u, v) = ||u - v||d(u, v) = √(u1 - v1)² + (u2 - v2)²d(u, v) = √(-12 - (-8))² + (5 - 15)²d(u, v) = √(-4)² + (-10)²d(u, v) = √16 + 100d(u, v) = √116d(u, v) = 2√29

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Answer:

True

Step-by-step explanation:

If dividing polynomial P(x) by polynomial Q(x) produces a remainder of 0, then it means that Q(x) is a factor of P(x). This is because when we divide P(x) by Q(x), we are looking for a polynomial that, when multiplied by Q(x), will give us P(x). If the remainder is 0, it means that Q(x) is a factor of P(x) because it can be multiplied by Q(x) to give us P(x) exactly, with no remainder.

The answer to 32z - 48 using factoring is 3/2.

Given,

32z - 48

We have to find the answer using factoring:

Factoring:

Finding things to multiply together to produce an expression is known as factoring. It is comparable to splitting an expression into numerous smaller expressions.

Here,

32z - 48 = 0

Add 48 to both sides

32z - 48 + 48 = 0 + 48

32z = 48

Divide 32 on both sides

32z/32 = 48/32

z = 48/32

Now, we can factorize 48/32

Take 2 as common factor

(48/2) / (32/2) = 24/16

Again, take 2 as common factor

(24/2) / (16/2) = 12/8

Now, take 4 as common factor

(12/4) / (8/4) = 3/2

Here, z = 3/2

That is, the answer for 32z - 48 using factoring is 3/2.

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Answer:

Option D: x = -2; x = 3/4

Step-by-step explanation:

Hello!

We can factor this expression and then find the zeroes to find our solutions.

We have to factor by grouping. Multiply the 1st and last term, 4x² and -6 is -24x², and find two factors that equal to -24x² and add up to the second term, 5x. 8x and -3x work for this.

Now, set the equation equal to zero.

Remember, if two numbers, a and b, multiply to 0, either a or b or both numbers must be zero. So now we set both factors to zero, hence the zero-product property.

And the next one:

The solutions are x = -2, and x = 3/4, or Option D

Teshawn, this is the solution:

As we had this same question before, the expected payoff is:

1/200 * 240 + 3/200 * 90 + 8/200 * 50 + 188/200 * 0

1.2 + 1.35 + 2 + 0

Therefore, the expected payoff for a raffle ticket is $ 4.55

Answer:

x = 112

Step-by-step explanation:

\(\frac{x}{48}\) = \(\frac{7}{3}\) ( cross- multiply )

3x = 7 × 48 = 336 ( divide both sides by 3 )

x = 112

Answer: im doing this for points

Step-by-step explanation ok

The value of a and b is 1.

The probability that Nate places the disk so that it is touching an equal number of shaded and unshaded squares is ab, where a and b are integers.

To find the value of a and b, we need to determine the total number of ways Nate can place the disk (the denominator of the probability fraction) and the number of ways he can place the disk so that it touches an equal number of shaded and unshaded squares (the numerator of the probability fraction).

Since the center of the circle must be at the meeting point of four squares, the only possible places for the center are the points where four squares meet. Since the grid is made of 2 cm x 2 cm squares, there are 4 shaded squares and 4 unshaded squares. So, there are 4 centers that could be placed on a shaded square and 4 centers that could be placed on an unshaded square.

So the denominator of the probability fraction is 8.

Now, to calculate the numerator, we need to determine the number of ways Nate can place the disk so that it touches an equal number of shaded and unshaded squares.

As the center of the circle is at the meeting point of four squares, the center of the circle is placed at the intersection of 2 shaded and 2 unshaded squares.

So, the numerator of the probability fraction is 8.

Therefore, the probability that Nate places the disk so that it is touching an equal number of shaded and unshaded squares is 8 ÷ 8 =1.

So the value of a and b is 1.

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