You are a loan officer at the West Elm Savings and Loan. Mr. and Mrs. Brady are in your office to apply for a mortgage loan on a house they want to buy. The house has a market value of $180,000. Your bank requires 1/5

Using double angle identity, we are able to prove tan(x)(1 + cos(2x)) = sin(2x).

To prove the identity tan(x)(1 + cos(2x)) = sin(2x), we can start by using trigonometric identities to simplify both sides of the equation.

Starting with the left-hand side (LHS):

tan(x)(1 + cos(2x))

We know that tan(x) = sin(x) / cos(x) and that cos(2x) = cos²(x) - sin²(x). Substituting these values, we get:

LHS = (sin(x) / cos(x))(1 + cos²(x) - sin²(x))

Next, we can simplify the expression by expanding and combining like terms:

LHS = sin(x) / cos(x) + sin(x)cos²(x) / cos(x) - sin³(x) / cos(x)

Simplifying further:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

Now, let's work on the right-hand side (RHS):

sin(2x)

Using the double angle identity for sine, sin(2x) = 2sin(x)cos(x).

Now, let's compare the LHS and RHS expressions:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

RHS = 2sin(x)cos(x)

To prove the identity, we need to show that the LHS expression is equal to the RHS expression. We can combine the terms on the LHS to get a common denominator:

LHS = [sin(x) - sin³(x) + sin(x)cos²(x)] / cos(x)

Now, using the identity sin²(x) = 1 - cos²(x), we can rewrite the numerator:

LHS = [sin(x) - sin³(x) + sin(x)(1 - sin²(x))] / cos(x)

    = [sin(x) - sin³(x) + sin(x) - sin³(x)] / cos(x)

    = 2sin(x) - 2sin³(x) / cos(x)

Now, using the identity 2sin(x) = sin(2x), we can simplify further:

LHS = sin(2x) - 2sin³(x) / cos(x)

Comparing this with the RHS expression, we see that LHS = RHS, proving the identity.

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Answer:

Step-by-step explanation:

Set up an equation:

7x + 10x + 13x = 100000 and solve for x:

30x = 100000 so

x = 3333.33

Anna gets 7(3333.33) = 23333.31

Louise gets 10(3333.33) = 33333.33

Lacey gets 13(3333.33) = 43333.29

Given:

Triangle ABC is similar to triangle XYZ.

In triangle ABC AB=2, BC=4, CA=3.

In triangle XYZ, XY=7, YZ=14, ZX=N.

To find:

The length of ZX.

Solution:

If two triangles are similar, then their corresponding sides are proportional.

Since \(\Delta ABC\sim \Delta XYZ\), therefore

\(\dfrac{AB}{XY}=\dfrac{BC}{YZ}=\dfrac{CA}{ZX}\)

\(\dfrac{2}{7}=\dfrac{4}{14}=\dfrac{3}{N}\)

\(\dfrac{2}{7}=\dfrac{2}{7}=\dfrac{3}{N}\)

\(\dfrac{2}{7}=\dfrac{3}{N}\)

On cross multiplication, we get

\(2\times N=3\times 7\)

\(2N=21\)

Divide both sides by 2.

\(N=\dfrac{21}{2}\)

\(N=10.5\)

Therefore, the length of side ZX is 10.5 units.

The technology and their functions are :

IPS (Intrusion Prevention System) and IDS (Intrusion Detection System) are security technologies designed to protect computer networks from security threats such as cyber attacks, malware, and other malicious activities.

IDS monitors network traffic for any suspicious activity or security breaches and alerts the network administrator of any detected security issues. IPS builds upon the IDS technology by not only detecting security breaches but also automatically blocking or preventing them.

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Answer:

The equation Jared can use to find the rate at which he drove is:

rate (r) = distance (d) / time (t)

So in this case, Jared can plug in the values he knows into the equation:

r = 15 miles / 0.5 hours

Solving for r, he can find the rate at which he drove:

r = 30 miles per hour.

So Jared drove at a rate of 30 miles per hour.

Step-by-step explanation:

PLEASE GIVE BRAINLIEST

Answer:

The shape of an object looks the same when an object is rotated on it's own axis

The complete statement should be If 3m = 7n, then m/n = 7/3. The proportion was obtained by solving for m, and then using the converse of the cross products property. Option B

The converse of the cross products property states that if two ratios are equal, then the product of the means is equal to the product of the extremes.

To justify the answer, you solve for m/n in the original equation by dividing each side by 3n, which gives you m/n = 7/3.

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Answer:

75.6

Step-by-step explanation:

(30 ×30)/100=32.4

108-32.4=75.6

Answer:

£90 more

Step-by-step explanation:

4+1=5

150/5=30

I:T

4:1 ×30

120:30

120-30=90

Answer:

107.8

Step-by-step explanation:

There are X automobiles, with a mean of 12.5 cars. The standard deviation for X is also SD = 12.0.

First, a data set's mean and standard deviation convey distinct information. The average (center) of a data collection is provided by mean (it is a measure of central tendency). You may learn about the range (dispersion) of data around the mean by looking at the standard deviation. We may investigate a data set's characteristics and characterize it using both the mean and standard deviation. To provide confidence intervals for data that has a normal distribution, they are frequently combined. If two or more data sets need to be compared:

The mean reveals whether data set is, on average, greater or lower (or better or worse). We can determine whether data set has a wider dispersion using the standard deviation (higher standard deviation means data is more spread out from the mean). Second, there are variations in how each metric is calculated. In particular, we utilize squaring to get the standard deviation but not the mean. We completely avoid using squaring when determining the mean of a data collection. Simply multiplying the total number of data points in the set by the sum of all the values in the data set yields the answer.

The mean is calculated as follows:

Mean = (all data values added together) / (number of data values)

However, when calculating standard deviation, we do employ squaring. We take the square of the deviation between each data point and the mean in particular.

The standard deviation equation is as follows:

Finally, when we add the identical value to each data point in the data set, the mean and standard deviation "respond" differently. If we multiply every value in a data collection by the constant "K":

No of the size of the data collection, the mean rises by precisely K.

No matter how many observations are in the data collection, the standard deviation does not vary. The identical value is then added.

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Answer: 60

Step-by-step explanation:

list all of the multiples and choose the least common number

10:   10  20  30  40  50  60  70  80  90  100

12:   12  24  36  48  60  72  84  96

find a number that shares all the prime factors of the two numbers

prime factors of 10: 2, 5

prime factors or 12: 2, 2, 3

LCM = 60

\(\left|\dfrac{2}{13}t-11\right|-10=-16\\\\\left|\dfrac{2}{13}t-11\right|=-6\\\\x\in\emptyset\)

yes,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

Answer:

well for the 10 it is a 4/52 chance and for face cards, 16/52

Step-by-step explanation:

Answer: It would be area, because it involves multiplying length by width, therefore covering the inside

Step-by-step explanation:

The value of the car is $30675.

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Here, we have

Given: A new car is purchased for $33, 000 and over time its value depreciates by one-half every 4 years.

We have to find the value of the car to be $9, 300.

Then the value of the car is given by the linear equation. Then the line is passing through (0, $33,000) and (4, $9,300). Then we have

Let y be the value of the car and x be the number of years. Then we have

y - 33000 = (-9300/4)(x-0)

y + 2325x = 33000

Then the value of the car of a year after it was purchased, to the nearest hundred dollars will be

y + 2325(1) = 33000

y = 33000 - 2325

y = 30675

Hence, the value of the car is $30675.

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The solution must be inside the area in green

we have the next points

A. (-4, 2) point in yellow

B. (-1, -11) point in green

C. (4, 2) point in purple

D. (0, 0) point in red

E. (-4, -2)​ point in blue

as we can see the only points that are a solution

B. (-1, -11)

C. (4, 2)

D. (0, 0)

Answer:

Is 03.841

Step-by-step explanation:

To find the critical value needed to test the claim that the sentence is independent of the plea, we need to perform a chi-square test of independence. The critical value is based on the significance level (α) and the degrees of freedom.

In this case, the given significance level is 0.05. Since the table represents a 2x2 contingency table (two categories for plea and two categories for sentence), the degrees of freedom (df) can be calculated as (number of rows - 1) * (number of columns - 1) = (2 - 1) * (2 - 1) = 1.

To find the critical value at a significance level of 0.05 with 1 degree of freedom, we consult a chi-square distribution table or use statistical software.

The critical value for a chi-square test with 1 degree of freedom and a significance level of 0.05 is approximately 3.841.

Therefore, the correct answer is 03.841.

Answer:

its 6 pounds :)

Step-by-step explanation:

hope this helps <3

Answer:

7 Pounds 2 Ounces

Step-by-step explanation:

Each pound is 16oz.

Answer:

$6

Step-by-step explanation:

Answer:

it would be a 14$ t-shirt there for you save 6 dollars.

Step-by-step explanation:

do the math in a calculator. :D

Answer:

A 2-column table with 5 rows. Column 1 is labeled x with entries negative 5, negative 4, negative 3, negative 2, negative 1. Column 2 is labeled y with entries 5, 5, 5, 5, 5.

Step-by-step explanation:

The table with all y-values the same will graph as a horizontal line, a line with a slope of zero.

Apparently, the first table is like that.

Answer:

A is the answer

Step-by-step explanation:

just took the test

The volume of the closet space = 207,936 in³

The volume of the one roll of toilet paper = 141.3in³

To calculate the volume of the closet, the formula that should be used is the formula for the volume of a rectangle = length×width×height.

Where;

length = 57 in

width = 57

height = 64

volume = 57×57×64 = 207,936 in³

The volume of the toilet paper with the shape of a cylinder would be = πr²h

where;

radius = diameter/2= 6/2=3in

height = 5 in

volume of cylinder = 3.14×3×3×5 =141.3in³

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Given the following expression:

Remember that we have the following general rule:

this rule is called the distributive property, which is used on our given expression.

Answer:

THE ANSWER IS 81/16 OR C

Step 1

Write an expression that can help find the original salary

Step 2

Simplify the equation

Hence, Tricia's Original weekly salary in dollars per week=$700

The surface area of a cylinder is 284m² and it's volume is 366.9m³

To find the surface area and volume of a cylinder, we need to know the radius (r) and height (h) of the cylinder. The formulas for the surface area (A) and volume (V) of a cylinder are as follows:

From the given question, the data are;

a. The surface area of the cylinder is;

SA = 2π(4)² + 2π(4)(7.3)

SA = 283.999≈284m²

b. The volume of the cylinder is

v = πr²h

v = π(4)²(7.3)

v = 366.9m³

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Answer:

17

Step-by-step explanation: