What is the value of x?

Answers

Answer 1

Answer:

again, we're assuming that both triangles are similar, and thus using proportions.

$\stackrel{\textit{assuming the triangles are similar}}{\cfrac{x+1}{27}=\cfrac{5}{x-5}\implies x^2+x-5x-5=135}\implies x^2-4x-5=135 \n\n\n x^2-4x-140=0\implies (x-14)(x+10)=0\implies x = \begin{cases} 14~\textit{\large \checkmark}\n -10 \end{cases}$

we do not use the -10, because whatever value "x" may be, can't be negative or even 0.

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Explain why sketching y=sin(x) can help graph y=csc(x)

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The graph of csc x is a parabola with its vertex at the node of the graph of sin x.

y = csc (x) = 1/sin (x)

When you realize that sin (x) is an even function, you can conclude that csc(x) is also even.

Whenyou draw y = sin(x), you will see the zeroes of the function, which are values for which the funcion csc(x) is not defined, but goes to + or - infinity, i.e. you obtain the asymptotes.

You can also realize that the maximums of sin(x) will result in minimums of csc(x).

6.Write the equation in slope-intercept form for the line that passes through the given pointand is perpendicular to the given equation.5x + 3y = -21 and passes through (-5, 1)

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Let us first solve for the slope (m) of the perpendicular line.

$\text{ 5x + 3y = -21}$ $\text{ 3y = -5x - 21}$ $\text{ y =}\frac{-5x\text{ -21}}{3}$ $\text{ y = -}(5)/(3)x-7$

The slope of the perpendicular line is -5/3.

Thus, for the slope of the line, we get,

$\text{ m}_(\perp)\text{ = }(-5)/(3)$ $\text{ m = }(3)/(5)$

Let us solve for the value of b with the given value of slope (m) = 3/5 and (x,y) = (-5,1).

$\text{ y = mx + b}$ $1\text{ = (}(3)/(5))(-5)+b$ $1\text{ = -1 + b ; b = 1 + 1 = }2$

Let's now make the equation of the line using Slope-Intercept Form,

Given, m = 3/5 and b = 2

$\text{ y = mx+b}$ $\text{ y = (}(3)/(5))x\text{ + 2}$

$\text{ y = }(3)/(5)x\text{ +2}$

A study is under way in Yosemite National Forest to determine that adult height of American pine trees. Specifically, the study is attempting to determine what factors aid a tree in reaching heights greater than 60 feet tall. It is estimated that the forest contains 25,000 adult American pines. The study involves collecting heights from 250 randomly selected adult American pine trees and analyzing the results. Identify the population from which the study was sampled

Answers

Answer:

The 25,000 adult American pine trees in the forest.

Step-by-step explanation:

Consider the provided information.

It is given that the forest contains 25,000 adult American pines. The study involves collecting heights from 250 randomly selected adult American pine trees and analyzing the results.

A population is the set of data which includes all of the elements. If one or more observations are drawn form the population then it called a sample.

Here the population is 25,000 adult American pines.

Thus, the required answer is: The 25,000 adult American pine trees in the forest.

Quinton had a gross income of $2741.67 during each pay period in 2009. If he got paid monthly, how much of his pay was deducted for FICA in 2009?

Answers

Answer:

$2,516.85

Step-by-step explanation:

Quinton had a monthly gross income of $2741.67.

He was paid yearly = $2741.67 × 12 = $32,900.04

FICA tax is social security tax (6.2%) and medicare tax (1.45%)

FICA tax rate = 6.2% + 1.45% = 7.65%

FICA tax deduction = 7.65% × 32,900.04

= 0.0765 × 32,900.04

= $2,516.85

His pay was deducted for FICA $2,516.85

Answer:

$2516.85

Step-by-step explanation:

a p e x

An train station has determined that the relationship between the number of passengers on a train and the total weight of luggage stored in the baggage compartment can be estimated by the least squares regression equation y=103+30x. Predict the weight of luggage for a flight with 86 passengers.

Answers

Answer:

2683

Step-by-step explanation:

Using the linear regression equation that predict the relationship between the weight of the luggage and the total number of passenger y = 103 + 30x, we can plug in the number of passenger x = 86 to predict the weight of the luggage on a flight:

y = 103 + 30*86 = 2683

500% of 30% of 36 is what percent of 216?

Answers

500/100×30/100=5×30/100=1.5
1.5×36=54
216÷54=4
25%

What is the value of x?​

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What is the value of x?