I need help with this problem

If the shortest leg of the small triangle is 4 in and the hypotenuse is 12 in and the shortest leg of the large triangle 8 in, then the length of the hypotenuse of the large triangle is 24 inches.

We know that two triangles are proportional if their corresponding sides are in proportion to each other. That is, the ratio of the lengths of the corresponding sides is the same for both triangles.

Let's denote the length of the hypotenuse of the large triangle by "h". We can set up a proportion using the given information:

shortest leg of small triangle / hypotenuse of small triangle = shortest leg of large triangle / hypotenuse of large triangle

Plugging in the values we get:

4/12 = 8/h

Simplifying the equation we get:

h = (12*8)/4 = 24

To explain the solution, we used the fact that similar triangles have proportional sides. We then used the given information about the lengths of the sides of the small and large triangles to set up a proportion and solve for the unknown length of the hypotenuse of the large triangle.

The key to this problem was recognizing the relationship between similar triangles and using that relationship to set up and solve a proportion.

To learn more about triangle click on,

https://brainly.com/question/8425335

#SPJ4

Answer:

Step-by-step explanation:

Given the information that the polynomial function P(x) has leading coefficient 1, has roots of multiplicity 2 at x = 1 and x = 0, and a root of multiplicity 1 at x = -5, we can use this information to find a possible formula for P(x).

A polynomial function's roots are the values of x that make the function equal to zero. If a root has multiplicity n, it means that (x - root) is a factor of the polynomial function n times.

So, based on the given information, we know that P(x) must be divisible by the factors (x - 1)^2, (x - 0)^2, and (x + 5), and that the leading coefficient must be 1.

Putting it all together, a possible formula for P(x) is:

P(x) = (x - 1)^2 (x - 0)^2 (x + 5) = (x^2 - 2x + 1)(x^2)(x + 5) = x^6 - 7x^5 + 17x^4 - 22x^3 + 17x^2 - 7x + 5

So, the possible formula for P(x) is P(x) = x^6 - 7x^5 + 17x^4 - 22x^3 + 17x^2 - 7x + 5.

Answer:   [tex]P(\text{x}) = \text{x}^2(\text{x}-1)^2(\text{x}+5)[/tex]

Explanation:

If k is a root of P(x), then x-k is a factor. The multiplicity is the exponent for that factor.

For instance, the root x = 1 with multiplicity 2 leads to the factor [tex](\text{x}-1)^2[/tex]

The leading coefficient is the number out front. For example, if the leading coefficient was 8, then we'd have [tex]P(\text{x}) =8\text{x}^2(\text{x}-1)^2(\text{x}+5)[/tex]

However, we change that "8" to a "1" since the leading coefficient is 1 here.

That's how we get to

[tex]P(\text{x}) = 1\text{x}^2(\text{x}-1)^2(\text{x}+5)[/tex] aka [tex]P(\text{x}) = \text{x}^2(\text{x}-1)^2(\text{x}+5)[/tex]

Optionally if you were to expand everything out, combine like terms, and simplify then you'd get

[tex]P(\text{x}) = \text{x}^2(\text{x}-1)^2(\text{x}+5) = \text{x}^5 + 3\text{x}^4- 9\text{x}^3+5\text{x}^2[/tex]

I don't recommend doing this because you lose the information about the roots along with their corresponding multiplicities. It's better to keep things factored.

You can use a graphing tool like Desmos or GeoGebra to verify the answer.

The percentage of students who are doing their homework regularly is 75%.

A universal set in set theory is a set that includes itself as well as all other items. A universal set's nonexistence in set theory as it is typically expressed can be demonstrated in a number of different ways. However, a universal set is a part of several unconventional set theory variations.

To find the percentage of students who are doing their homework regularly,

We find the total students and this is 75 + 5 = 80 students

The percentage is 60/80 * 100

= 75%

Read more about universal sets here:

https://brainly.com/question/17885920

#SPJ1

Answer:

12 [tex]in^{3}[/tex]

Step-by-step explanation:

Volume is the length x  the width x the height

The rectangle of the bottom would be

(4)(2)(1) = 8

The rectangle on the top would be

(1)(2)(2) = 4

8 + 4 = 12 [tex]in^{3}[/tex]

The relationship between precalculus and calculus has been explained and both precalculus and calculus deals with the tangent of the line, slope of the line, y intercept, velocity etc.

Precalculus is the study of mathematics or the course that includes algebra, trigonometry etc. to make a student for study the calculus . The precalculus covers the topics likes complex numbers, composite numbers, trigonometric functions, vectors, matrices, probability etc.

Calculus is the study of mathematics that deals with the rate of changes. Applications of the calculus are finding the slope of the curve, finding the area of region, calculation of x intercept and y intercept etc.

Both precalculus and calculus deals with the tangent of the line, slope of the line, y intercept, velocity, acceleration, area, volume etc.

Therefore, the relationship between precalculus and calculus has been explained

Learn more about Calculus here

brainly.com/question/6581270

#SPJ4

Answer: 0.32 or 32%

Step-by-step explanation: 8/25

Horizontal lines have a slope of zero, since the "rise" is; zero.

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Since we know that Vertical lines have an undefined slope, since the "offset" is zero, and division by zero is not allowed.

If the slope has a value of zero, the line is horizontal, neither increases nor decreases.

Therefore,

Horizontal lines always have an equation of the form; y = a

Vertical lines always have an equation of the form; x = b

Learn more about slope here:

https://brainly.com/question/2503591

#SPJ9

It will take 5.189 hours to get doubled the size of Sample.

A relation of the form y = [tex]a^x[/tex], with the independent variable x ranging over the entire real number line as the exponent of a positive number a.

Given:

Growth rate = 5.8%

The continuous exponential growth model for populations is given by:

P(t)= [tex]P_0 e^{rt[/tex]

So, r= 5.8%

r = 0.058

Now, the time taken to double the sample then P(t) = 2P(0).

So, P(t)= [tex]P_0 e^{0.058t[/tex]

2P(0) = [tex]P_0 e^{0.058t[/tex]

[tex]e^{0.058t[/tex] = 2

Taking log on both side

log [tex]e^{0.058t[/tex] = log 2

0.058 t = 0.301

t= 0.301/ 0.058

t = 5.189

Learn more about exponential Function here:

https://brainly.com/question/23064497

#SPJ1

The equation of the cubic function is 2( x-4) (x-3) x+3)

A cubic function is a polynomial function of degree 3 and is of the form f(x) = ax3 + bx2 + cx + d, where a, b, c, and d are real numbers and a ≠ 0.

The equation of a cubic function is given as;

x³-(a+b+c) x² + ( ab+bc+ca) x + abc

where a,b,c are the root of the cubic function

a = 4, b = 3 and c= -3

a+b+c = 4+3-3 = 4

ab = 4×3 = 12

bc = -3×3 = -9

ca = -3×4 = -12

ab+bc+ca = 12-9-12 = -9

abc = 4×3×-3 = -36

therefore;

x³-( 4)x² + ( -9)x -36

x³-4x²-9x -36

therefore y = a( x-4) (x-3) x+3)

at point (2,20)

substitute x by2 and y by 20

20 = a( -2) (-1) (5)

20 = a10

a = 20/10

a= 2

therefore the equation of the cubic function is

2( x-4) (x-3) x+3)

learn more about cubic function from

https://brainly.com/question/20896994

#SPJ1

The values of x and y are given as follows:

Similar polygons are polygons that share these two features presented as follows:

The proportional relationship for the side lengths in this problem is given as follows:

x/10.5 = 5/y = 5/7.5.

Hence the value of x is given as follows:

7.5x = 5 x 10.5

x = 5 x 10.5/7.5

x = 7.

The value of y is given as follows:

5/y = 5/7.5

y = 7.5.

More can be learned about similar triangles at brainly.com/question/14285697

#SPJ1

Answer:

17.6 feet.

Step-by-step explanation:

The length of the I-beam can be calculated as follows:

Weight = Length * Weight per Foot

Rearranging this equation:

Length = Weight / Weight per Foot

Substituting the given values:

Length = 444.5 lb / 25.4 lb/ft = 17.6 ft

So, the length of the I-beam is 17.6 feet.

The requried solution of the system of equations is (-1, -2). Option C is correct.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
Two intersecting lines will have exactly one solution (i.e., a unique point of intersection) if and only if they are not parallel.

In other words, if the slopes of the two lines are different, they will intersect at a single point. This is because the slopes of the lines determine how steep they are, and if they are not the same, they will eventually cross at a single point. So from the graph, both lines intersect at (-1, -2) implying that The solution is (-1, -2).

Learn more about simultaneous equations here:

https://brainly.com/question/16763389

#SPJ9

Answer:

15

Step-by-step explanation:

9/21 aproximatly = 0.42 then x35 = 15

The area of the attached figure is 32 square mm

The similar question is added as an attachment

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

A square a triangle and a parallelogram

The shapes can be combined to

a triangle and a parallelogram

So, we have

Area = Sum of individual areas

Using the dimensions of the shapes as a guide, we have the following:

Area = 0.5 * 2 * 8 + 4 * 6

This gives

Area = 32

Hence, the area is 32 square mm

Read more about area at

https://brainly.com/question/22972014

#SPJ1

(a) When q = 0 or q = 1, we get p = 0.5, but for other values of q, the optimal value of p is different.

(b) When q = 1, the expected score is 1, which is the maximum possible score.

(c) The optimal value of p also depends on the value of q in this case.

a) The expected score of the meteorologist can be expressed as the weighted average of the two possible scores, where the weights are the probabilities of it raining or not raining:

Expected score = p(1 - (1 - q)^2) + (1 - p)(1 - q^2)

To maximize the expected score, we need to differentiate it with respect to p, set the derivative equal to zero, and solve for p. This gives:

2q(1 - q) = 1 - 2p

Solving for p, we get:

p = (1 - 2q + 2q^2) / 2

So the optimal value of p depends on the value of q. When q = 0 or q = 1, we get p = 0.5, but for other values of q, the optimal value of p is different.

b) If the meteorologist chooses p = q, then the expected score simplifies to:

Expected score = q(1 - (1 - q)^2) + (1 - q)(1 - q^2)

= q^3 + (1 - 2q)q^2 + (1 - q)

To find the maximum expected score, we can take the derivative of this expression with respect to q, set it equal to zero, and solve for q. This gives:

3q^2 - 4q + 1 = 0

This quadratic equation has two roots: q = 1/3 and q = 1. When q = 1, the expected score is 1, which is the maximum possible score. When q = 1/3, the expected score is (8/27), which is the maximum score for any value of q between 0 and 1.

c) If the payoffs are {1 - (1 - p)^2, 1 - 1.1p^2}, then the expected score of the meteorologist is:

Expected score = p(1 - (1 - q)^2) + (1 - p)(1 - 1.1q^2)

To maximize this expected score, we can differentiate it with respect to p, set the derivative equal to zero, and solve for p. This gives:

2.2q^2 - 2q + 1 = 2p

Solving for p, we get:

p = (2.2q^2 - 2q + 1) / 2

So, in this scenario, the value of q also affects the ideal value of p.

To learn more about expected score here:

https://brainly.com/question/28000192

#SPJ4

Answer:

The mistake they made was that they subtracted [tex]2y[/tex] from [tex]2y[/tex] and got [tex]0y[/tex]. Instead of subtracting, they should have added it.

Step-by-step explanation:

Given:

[tex]8x+2y=44\\5x+2y=35[/tex]

We can combine the system of equations into a single equation:

[tex]13x+4y=79[/tex]

From this step, we can conclude that the answer for part b is incorrect. The mistake they made was that they subtracted [tex]2y[/tex] from [tex]2y[/tex] and got 0y. Instead of subtracting, they should have added it.

We can continue solving the system of equations by writing y in terms of x.

[tex]8x+2y=44\\2y=44-8x\\y=22-4x[/tex]

now substitute this into the single equation:

[tex]13x+4y=79\\13x+4(22-4x)=79\\13x+88-16x=79\\-3x+88=79\\-3x=-9\\x=3[/tex]

Since we now know that [tex]x=3\\[/tex], we can substitute this into the equation we made for y.

[tex]y=22-4x\\y=22-4(3)\\y=22-12\\y=10[/tex]

The solution for the system of equations is [tex]x=3[/tex] and [tex]y=10\\[/tex].

1/(x+1)(x-2) is the simplified form of the expression

Given the expression below

x+2/4x²+5x+1 · 4x+1/x²-4

Factorise the quadratic expressions

4x²+5x+1 = 4x²+4x + x+1

4x²+5x+1 = 4x(x+1)+1(x+1)

4x²+5x+1 = (4x+1)(x+1)

For the expression x²-4

x²-4 = (x+2)(x-2)

Substitute

x+2/4x²+5x+1 · 4x+1/x²-4 = x+2/(4x+1)(x+1) · 4x+1/(x+2)(x-2)

x+2/4x²+5x+1 · 4x+1/x²-4 = 1/x+1 · 1/x-2

x+2/4x²+5x+1 · 4x+1/x²-4  = 1/(x+1)(x-2)

Hence the simplified form of the expression is 1/(x+1)(x-2)

Learn more on simplifying the expression here: https://brainly.com/question/28036586

#SPJ1

Answer:

Step-by-step explanation:

213232131123123123123123

1. To find the class width, we first need to find the range of the data, which is the difference between the maximum and minimum values: 68 - 10 = 58. Then, we divide the range by the number of classes to get the class width: 58 / 7 = 8.29. However, we will round up to the nearest whole number, so the class width is 9.

2. The lower class limits are 10, 19, 28, 37, 46, 55, and 64, since we add the class width to the lower limit of each previous class to find the lower limit of the next class.

3. The upper class limits are 18, 27, 36, 45, 54, 63, and 68, since we add the class width to the lower limit of each class to find the upper limit of that class.

The missing value in the expression A = -2(x-9)² + ? is 162, which represents the maximum area of the storage bin.

A perfect Square is defined as an integer multiplied by itself to generate a perfect square, which is a positive integer. Perfect squares are just numbers that are the products of integers multiplied by themselves.

To complete the perfect square, we need to factor out the coefficient of the squared term (-2) from the expression:

A = -2x² + 36x

A = -2(x² - 18x)

Next, we need to add and subtract the square of half the coefficient of the x-term (-18/2 = -9) inside the parentheses:

A = -2(x² - 18x + (-9)² - (-9)²)

Simplifying the expression inside the parentheses, we get:

A = -2[(x - 9)² - 81]

Distributing the -2, we get:

A = -2(x - 9)² + 162

Therefore, the missing value in the expression is 162.

Learn more about the perfect square here:

https://brainly.com/question/10170393

#SPJ9

Answer:

x=6

Step-by-step explanation:

the two dashes show that the two lines are parallel, so 23=3x+5; subract 5 from both sides to get 18=3x, so x=6

ΔXVZ and ΔXWY are similar by SAS property of similarity.

We have,

ΔXVZ and ΔXWY

XW/WV = XY/YZ

15/20 = 27/36

3/4 = 3/4

The ratio of two pairs of corresponding sides is equal. ______(1)

And,

m∠XWY = m∠XVZ = 90

The included angle of the two triangles is equal. ________(2)

Now,

From (1) and (2),

ΔXVZ and ΔXWY are similar.

By SAS property of similarity.

Thus,

ΔXVZ and ΔXWY are similar by SAS property of similarity.

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ4

Answer:

add wtwo numbers x by 3? I am sorry don't understand question

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is d. f(x) = 3 (x-4) (x+2).

Answer:

To solve this problem, we need to use the formula for compound interest:

A = P * (1 + r/n)^(nt)

where:

A = future value of the account

P = present value (the contributions)

r = interest rate (as a decimal)

n = number of times the interest is compounded per year

t = number of years

First, we need to find the future value of the account (A) after 10 years of withdrawals at $10,000 per quarter. This means there will be 40 quarters in total ($10,000 * 40 = $400,000).

Next, we need to find the present value of the account (P) after 15 years of contributions.

Let's call the quarterly contributions "x".

We can set up the equation as follows:

$400,000 = x * (1 + 0.08/4)^(4 * 15) - $10,000 * (1 + 0.08/4)^(4 * 10)

We can now solve for x using a financial calculator or by using a programming language to perform the calculation. The result of this calculation is that Mike's quarterly contributions should be $2,597.29 in order to accomplish his goal.

For given linear inequalities in step 3 and 7 properties shown are Commutative property and addition property of inequality.

What exactly is a linear inequality?

In mathematics, inequality denotes a mathematical statement with no equal sides. An inequality happens in mathematics when a connection results in a non-equal comparison of two expressions or two numbers. Any of the inequality symbols, such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), or not equal to symbol (≠), replace the equal sign "=" in the sentence. In mathematics, inequalities are classified into three types: polynomial inequalities, rational inequalities, and absolute value inequalities.

The characters "< and >" denote severe inequalities, whereas ‘≤’ and ‘≥’  denote slack inequalities. A linear inequality looks to be a linear equation, however the formula is different.

Now,

As stated in Commutative property the order in addition does not matter and in addition property the value added on both sides does not affect the result.

In step 3 we can write this as 5x-x-5<11x+x-21

which will not change result and

in step 7, 21 is added both sides which will not change result.

Hence,

           For given linear inequalities in step 3 and 7 properties shown are Commutative property and addition property of inequality.

To know more about linear inequalities visit the link

https://brainly.com/question/11897796?referrer=searchResults

#SPJ1

Answer:because angles in a triangle add up to 180 degrees.

Step-by-step explanation:

A=40

C=30

So 180-40-30=110