I need some extra detailed steps please

Angle 3 = 70 ( opposite angles equal each other)

Angle 1 = 90-70 = 20 ( angle 1 plus 70 = 90 )

angle 3 - angle 1 = 70 -20 = 50

 Answer is B

Answer:

C. [tex]x=50[/tex], [tex]y=10[/tex]

Step-by-step explanation:

We have been given an image of two intersecting lines. We are asked to find the value of x and y for our given diagram.

We know that when two line intersect each other, then vertical angles are congruent.

Using vertical angles theorem, we will get a system of equations as sown below:

[tex]3y=x-20...(1)[/tex]

[tex]5x-100=y+140...(2)[/tex]

From equation (1), we will get:

[tex]x=3y+20[/tex]

Upon substituting this value in equation (2), we will get:

[tex]5(3y+20)-100=y+140[/tex]

[tex]5*3y+5*20-100=y+140[/tex]

[tex]15y+100-100=y+140[/tex]

[tex]15y=y+140[/tex]

[tex]15y-y=y-y+140[/tex]

[tex]14y=140[/tex]

[tex]\frac{14y}{14}=\frac{140}{14}[/tex]

[tex]y=10[/tex]

Therefore, the value of y is 10.

To find the value of x, we will substitute [tex]y=10[/tex] in equation (1) as:

[tex]3*10=x-20[/tex]

[tex]30=x-20[/tex]

[tex]30+20=x-20+20[/tex]

[tex]50=x[/tex]

Therefore, the value of x is 50 and option C is the correct choice.

Answer:

Option C) x = 50, y = 10

Step-by-step explanation:

We are given a two pairs of vertically opposite angle in the image.

Vertically opposite angle is formed when two lines intersect anf they are always equal.

Thus, we can write:

[tex]3y = x -20\\\Rightarrow x - 3y = 20\\5x-100 = y +140\\\Rightarrow 5x - y =240[/tex]

Solving the two equations in two variable, we get:

[tex]x - 3y = 20\\5x - y =240\\\text{Multiplying first equation by 5}\\5x - 15y = 100\\\text{Subtracting the equations}\\5x - 15y-(5x-y) = 100-240\\-14y = -140\\y = 10\\ x - 3(10) = 20\\x = 20 + 30\\x =50[/tex]

The value of x is 50 and y is 10.

divide them:

52.50 / 7 = 7.50 dollars per hour

Answer: Slope = 8.5 and y-intercept = 6

Step-by-step explanation:

The intercept form of a linear equation is given by :_

[tex]y=mx+c[/tex], where m( coefficinet of x ) is the slope and c (constant term) is the y-intercept.

The given equation in intercept form : [tex]y = 8.5x + 6[/tex]

Here , the coefficient of c = 8.5

thus , the slope = 8.5

Also, the constant term = 6

Thus, the  y-intercept =6

Bioelectrical impedance machine can be used to determine a patient's body fat percentage

The body fat percentage of a human or other living being is the total mass of fat divided by total body mass, multiplied by 100

A doctor can use a bioelectrical impedance machine to determine a patient's body fat percentage.

This machine works by sending a small electrical current through the body and measuring how quickly it travels through different types of tissue.

Since fat and muscle have different electrical conductivity, the machine can estimate the amount of fat in the body based on the resistance to the current.

Hence, Bioelectrical impedance machine can be used to determine a patient's body fat percentage

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Answer:

Step-by-step explanation:

From the given triangle DEF, we have

[tex](EF)^{2}=(ED)^{2}+(DF)^{2}[/tex]

[tex](10)^{2}=(8)^{2}+(DF)^{2}[/tex]

[tex]100-64=(DF)^2[/tex]

[tex]DF=6[/tex]

Now, we know that SinE=[tex]\frac{Perpendicular}{Hypotenuse}[/tex], thus

[tex]SinE=\frac{DF}{EF}[/tex]

[tex]SinE=\frac{6}{10}=\frac{3}{5}[/tex]

Therefore, the value of SinE is [tex]\frac{3}{5}[/tex].

The joint PMF of X and Y is [tex]P(X = x, Y = y) = \frac{e^{-10} \cdot 10^x}{x!} \cdot \frac{x!}{y!(x-y)!} \cdot \left(\frac{3}{4}\right)^y \left(\frac{1}{4}\right)^{x-y}, \quad \text{for } y = 0, 1, \ldots, x \text{ and } x = 0, 1, 2, \ldots[/tex]

Distributions of X and Y

X is the total number of customers visiting the store in an hour, which follows a Poisson distribution with mean [tex]\lambda = 10[/tex]

[tex]P(X = x) = \frac{e^{-10} \cdot 10^x}{x!}, \quad x = 0, 1, 2, \ldots[/tex]

Given X = x the number of female customers Y follows a binomial distribution because each customer is independently female with probability [tex]p = \frac{3}{4}[/tex]

[tex]P(Y = y \mid X = x) = \binom{x}{y} \left(\frac{3}{4}\right)^y \left(\frac{1}{4}\right)^{x-y}, \quad y = 0, 1, \ldots, x[/tex]

Joint PMF of X and Y

To find the joint PMF P(X = x, Y = y, we use the law of total probability:

[tex]P(X = x, Y = y) = P(Y = y \mid X = x) \cdot P(X = x)[/tex]

Substitute the expressions for [tex]P(Y = y \mid X = x)[/tex] and P(X = x)

[tex]P(X = x, Y = y) = \left( \binom{x}{y} \left(\frac{3}{4}\right)^y \left(\frac{1}{4}\right)^{x-y} \right) \cdot \left( \frac{e^{-10} \cdot 10^x}{x!} \right)[/tex]

Simplify the expression:

[tex]P(X = x, Y = y) = \frac{e^{-10} \cdot 10^x}{x!} \binom{x}{y} \left(\frac{3}{4}\right)^y \left(\frac{1}{4}\right)^{x-y}.[/tex]

Answer:

n = 6.2f

Step-by-step explanation:

Answer:  [tex]r=(\frac{A}{P})^{\frac{1}{t}}-1[/tex]

Step-by-step explanation

Compound interest is the addition of interest to the principal sum of a deposit or a loan.

Let P = principal amount which was taken as a loan then the accumulated amount A is given by

[tex]A=P(1+r)^t[/tex].......(1)

where, r is the rate of simple annual interest in decimal.

t is the time applied for interest.

For solving r divide both sides of equation by P in (1),we get

[tex]\frac{A}{P}=(1+r)^t\\\Rightarrow(\frac{A}{P})^{\frac{1}{t}}=1+r\\\Rightarrow\ r=(\frac{A}{P})^{\frac{1}{t}}-1[/tex].

The required trinomial expression that is equivalent to  (2x+5)(3x-2) is 6x² + 11x - 10.

According to the question, we have to determine the trinomial expression that is equivalent to the  (2x+5)(3x-2).

A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the quadratic equation, cubic equation, etc. ax+b is a polynomial.

Here,
Given expression in the question,
=  (2x+5)(3x-2)
Following the distributive property
= 2x (3x - 2) + 5 (3x - 2)
= 6x² - 4x + 15x - 10
= 6x² - 11x - 10

Thus, the required trinomial expression that is equivalent to  (2x+5)(3x-2) is 6x² + 11x - 10.

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Final answer:

The trinomial expression equivalent to (2x+5)(3x-2) is calculated using the FOIL method, resulting in 6x² + 11x - 10.

Explanation:

To write a trinomial expression equivalent to the product of two binomials, (2x+5)(3x-2), we perform the multiplication by using the distributive property (also known as the FOIL method).

Multiply the first terms: 2x × 3x = 6x²

Multiply the outside terms: 2x × (-2) = -4x

Multiply the inside terms: 5 × 3x = 15x

Multiply the last terms: 5 × (-2) = -10

Combine like terms:

6x² + (15x - 4x) - 10 = 6x² + 11x - 10

The trinomial expression equivalent to (2x+5)(3x-2) is 6x² + 11x - 10.

The solution for ( y ) is ( y = 3.5 ).

To solve for y in the equation [tex]\( 10y + 3.8 = 38.8 \)[/tex], follow these steps:

Start with the given equation:

[tex]\[ 10y + 3.8 = 38.8 \][/tex]

Subtract 3.8 from both sides to isolate the term with  y:

[tex]\[ 10y + 3.8 - 3.8 = 38.8 - 3.8 \][/tex]

[tex]\[ 10y = 35 \][/tex]

Divide both sides by 10 to solve for  y :

[tex]\[ \frac{10y}{10} = \frac{35}{10} \][/tex]

y = 3.5

So, the solution for ( y ) is ( y = 3.5 ).

Solving this problem simply only requires us the knowledge of multiplication.

So we are initially given that there are 5 craft sticks. So if we need four times that amount, that is written as:

5 x 4

Which is equal to 20

So Jack needs 20

The instantaneous velocity of the ball when it hits the ground is found by deriving the height function and solving for the time of impact. The instantaneous rate of change of the surface area of a cylinder with respect to its radius when r = 4 is found by differentiating the surface area function and evaluating at r = 4.

The student's question involves two separate parts of physics and calculus related to kinematics and surface area calculations.

Part 1: Instantaneous Velocity of the Ball

The height, s, of a ball thrown straight down with initial speed 64 ft/sec from a cliff 80 feet high is given by s(t) = -16t2 - 64t + 80. The instantaneous velocity when the ball hits the ground is the derivative of position with respect to time, s'(t), evaluated at the time t when s(t) = 0 (when the ball hits the ground).

First, we find t by solving -16t2 - 64t + 80 = 0. Then, we find the derivative s'(t) = -32t - 64 and evaluate it at the found time, which gives us the instantaneous velocity.

Part 2: Rate of Change of Surface Area

The surface area of a right circular cylinder of height 4 feet and radius r feet is given by S(r) = 2πrh + 2πr2. The instantaneous rate of change of the surface area with respect to the radius, when r = 4, is the derivative dS/dr evaluated at r = 4. This is done by differentiating S(r) with respect to r and substituting r = 4 into the resulting expression.