find the value of x for the triangle or rectangle... plz help asap 4 both

S1 = speed of boat 1

 t1 =  time to do 1400 meters (boat 1)

S1*t1 = 1400

S2  = speed of boat 2

1400 + S2*t1 = X

t2 = time to do X + 600 (boat 2)

S1*t2 = X + 600

S2*t2 = 2X - 600

S1 = 1400/t1

S2 = (X-1400)/t1

T = t2/t1  

1400*T = X + 600

X*T - 1400*T = 2X - 600

X = 3600 meters

 River is 3600 meters wide

Answer:

The length of the other leg is 48 feet

Step-by-step explanation:

To find the length of the other leg, we will simply follow the steps below;

We will use the Pythagoras theorem formula to solve;

Write down the  Pythagoras theorem formula

opposite²  + adjacent² = hypotenuse²

Let the value of the other leg be x

From the question given;

hypotenuse = 50, a leg, say the opposite = 14

Lets substitute into our formula;

opposite²  + adjacent² = hypotenuse²

14²  +  x²  = 50²

196  + x² = 2500

subtract 196 from both-side of the equation

196 - 196 + x² = 2500 - 196

x² = 2304

Take the square root of both-side of the equation

√x² = √2304

x = 48 feet

The length of the other leg is 48 feet

The value of x is 559.5.

An algebraic equation can be defined as mathematical statement in which two expressions are set equal to each other.

To solve the equation [tex]\(45(15x+20)7x=56(12x*24)+6\)[/tex], follow these steps:

First, distribute the multiplication on both sides of the equation:

[tex]\(45 \cdot 15x + 45 \cdot 20 - 7x = 56 \cdot 12x - 56 \cdot 24 + 6\)[/tex]

[tex]\(675x + 900 - 7x = 672x - 1344 + 6\)[/tex]

Next, combine like terms on both sides:

[tex]\(668x + 900 = 672x - 1338\)[/tex]

Now, move all terms involving [tex]\(x\)[/tex] to one side and constants to the other side:

[tex]\(668x - 672x = -1338 - 900\)[/tex]

[tex]\(-4x = -2238\)[/tex]

To find [tex]\(x\)[/tex], divide both sides by [tex]\(-4\)[/tex]:

[tex]\(x = \frac{-2238}{-4}\)[/tex]

[tex]\(x = 559.5\)[/tex]

So, the value of x is 559.5.

The probability that a person picked at random from the group is a male or is fit to climb Mount Shasta is 47.2%.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of sample

Take 12 of 200 to determine the number of fit men,

Fit men = 12% × 200

Fit men = 0.12 × 200

Fit men = 24

Since they are asking males and the number of people fits enough, you must subtract the fit men from the fit people so you are not doubling the men

60 - 24 = 36

Add the fit people to the male group,

36+200 = 236

The probability will be calculated as,

P = 236/500

P = 118/250

P = 59/125

P = 47.2%

The probability is 47.5%.

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The required angle can be found by solving the equation as 24°.

A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.

Suppose the measure of  required angle be x.

Then, its complement can be written as 90 - x.

As per the question, the following equation can be formed as,

x + 42 = 90 - x

⇒ 2x = 48

⇒ x = 24

Hence, the measure of the required angle is 24°.

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Answer:

6 sections.

Step-by-step explanation:

Malcom uses a marker to draw a straight line on a piece of paper.

The line is [tex]\frac{2}{3}[/tex] feet long.

He wants to divide the line into sections of [tex]\frac{1}{9}[/tex] feet long.

The number of sections would be = [tex]\frac{\frac{2}{3}}{\frac{1}{9} }[/tex]

             = [tex]\frac{2}{3}[/tex] × [tex]\frac{9}{1}[/tex]

            = [tex]\frac{18}{3}[/tex]

            = 6 sections

There would be 6 sections.

Step-by-step explanation: To understand how to combine like terms, let's look at an example.

9c + 2c

The two parts of this expression, +9c and +2c, are called terms. The numbers in front of the variables, +9 and +2, are called coefficients.

Since the variables, c and c, are identical, the two terms in this problem are called like terms.

Like terms can be added together by simply adding their coefficients.

So in this problem, since 9 + 2 = 11, 9c + 2c is simply 11c.

Answer: r=L-3

Step-by-step explanation:

A = E

B = F

C = G

Look for the equation which has the same placement. Your answer should be B) BC=FG

Answer: Second option [tex]BC\cong FG[/tex] is the correct option.

Explanation:

If two triangles are congruent then their corresponding sides are congruent.

In [tex]\triangle ABC[/tex] and [tex]\triangle EFG[/tex], AB, BC, and CA are corresponding to EF, FG and GE respectively.

Therefore, if [tex]\triangle ABC\cong \triangle EFG[/tex] then,

[tex]AB\cong EF[/tex],

[tex]BC\cong FG[/tex],

And, [tex]CA\cong GE[/tex]

Therefore, only second option is correct.

The chain rule allows you to find the derivative of a function that is a composition of other functions. With an example, we calculated dz/dt with z = y^3 and y = 2t+1. While calculators can help, understanding the process is key.

The chain rule in calculus is a theorem that allows you to find the derivative of a composite function. If a variable z depends on the variable y, which itself depends on another variable t, then z, is a function of t. The chain rule could be mathematically expressed as dz/dt = (dz/dy) × (dy/dt).

For instance, if z = y^3 and y = 2t+1, we can calculate dz/dt by first finding the derivatives dz/dy and dy/dt, which are 3y² and 2, respectively. We then substitute y = 2t+1 into dz/dy to get dz/dy = 3(2t+1)². Therefore, using the chain rule, dz/dt = 3(2t+1)² × 2.

While your request mentions a calculator, knowing these steps should enable you to perform the operation using most scientific calculators. However, understanding the process is very important before relying on technology.

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The final expression for [tex]\frac{dz}{dt}[/tex] incorporates the partial derivatives and the derivatives of x and y with respect to t.

Given the function z = xy⁷ - x²y, where x = t² + 1 and y = t² - 1, we are to find [tex]\frac{dz}{dt}[/tex].

[tex]\frac{dz}{dt}[/tex] = ([tex]\frac{dz}{dx}[/tex]) × ([tex]\frac{dx}{dt}[/tex]) + ([tex]\frac{dz}{dy}[/tex]) × ([tex]\frac{dy}{dt}[/tex]).

Let's find [tex]\frac{dx}{dt}[/tex] and [tex]\frac{dy}{dt}[/tex]:

⇒ [tex]\frac{dx}{dt}[/tex] = d(t² + 1) ÷ dt = 2t

⇒ [tex]\frac{dy}{dt}[/tex] = d(t² - 1) ÷ dt = 2t

⇒ [tex]\frac{dz}{dx}[/tex] = y⁷ - 2xy

⇒ [tex]\frac{dz}{dy}[/tex] = 7xy⁶ - x²

x = t² + 1, y = t² - 1

⇒ [tex]\frac{dz}{dx}[/tex] = (t² - 1)⁷ - 2(t² + 1)(t² - 1)

⇒ [tex]\frac{dz}{dy}[/tex] = 7(t² + 1)(t² - 1)⁶ - (t² + 1)²

Finally, we combine these to find [tex]\frac{dz}{dt}[/tex]:

⇒ [tex]\frac{dz}{dt}[/tex] = ([tex]\frac{dz}{dx}[/tex]) × ([tex]\frac{dx}{dt}[/tex]) + ([tex]\frac{dz}{dy}[/tex]) × ([tex]\frac{dy}{dt}[/tex]).

Substituting everything into this formula:

⇒ [tex]\frac{dz}{dt}[/tex] = [(t² - 1)⁷ - 2(t² + 1)(t² - 1)] × 2t + [7(t² + 1)(t² - 1)⁶ - (t² + 1)²] × 2t

Complete question:

Use the Chain Rule to find [tex]\frac{dz}{dt}[/tex].

z = xy⁷ - x²y, x= t² + 1, y = t² - 1

The amount paid per movie is $4.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Charge per movie = $5

The fifth movie charge = $0

Now,

The charge for 5 movies.

= 5 x 4 + 0

= 20

This means,

5 movies cost $20

The cost of one movie.

= 20/5

= $4

Thus,

The cost per movie is $4.

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Answer:

1) 8

2) 5

3) False

4) Option B

Step-by-step explanation:

1) We have to find the remainder when we divide (x² + 4) by (x - 2)

To get the remainder we will put x = 2 in (x² + 4)

= (2)² + 4

= 8

2). We have to evaluate f(-1) using substitution in f(x) = 2x³ - 3x² - 18x - 8

f(-1) = 2(-1)³ - 3(-1)²- 18(-1) - 8

      = 2(-1) - 3 + 18 -8

      = -2 - 3 + 18 - 8

      = 5

3) The point (1, 0) lies on the graph of p(x) = [tex]x^{4}-2x^{3}-x+2[/tex]

If this point lies on the graph then p(1) should be equal to zero.

p(1) = 1³ - 7(1)² + 7(1) - 9

     = 1 - 7 + 7 - 9

     = -8 ≠ 0

Therefore, It's false.

4). (x - 1) is a factor of p(x) = x³ - 7x² + 15x - 9

Now we will factorize it further when (x - 1) is a zero factor.

By Synthetic division

1 |  1    - 7     15    -9

           1      -6     9

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

    1     -6      9     0

Now we have got the expression as (x - 1)(x²- 6x + 9)

Or (x -1)(x² - 6x + 9) = (x - 1)(x - 3)(x - 3)

Therefore, Option B. is the answer.

since line MO bisects, that means both angles are the same

6x-22 = 2x +34

6x = 2x +56

4x=56

x = 56/4 = 14

x=14

6(14)-22 = 62

2(14)+34 = 62

62+62 = 124

angle LMN = 124 degrees