Please help meeeeeee!!​

Equation of line parallel to y = − 2 x − 3 and passing through the point (3,-3) is y = -2x + 3.

When two lines are called parallel?

Two lines are parallel lines if they do not intersect.

The slopes of the lines are the same.

f(x)= mx + b and g(x)= nx + c are parallel if m = n.

According to the given question:

Given equation of line is y = −2x − 3

If the new line is parallel, then it will have the same slope.

y = -2x + b

Now this line passes through the point (x,y) = (3,-3) so put in the x and y values into the equation above, solve for b

-3 = -2(3) + b

b = 3

Therefore the required equation of line is

y = -2x + 3

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The required domain and the range of the given function are (-2, 3) and (2, -3) respectively.

Given that,
To determine the domain and the range of the function given in the graph.

The domain is defined as the values of the independent variable for which there is a certain value of the dependent variable exists in the range of the function.

Here,
From the graph, the domain of the function is defined for x = -2 to x = 3,
While the range of the graph for a given function is defined for y = 2 to y = -3 corresponding to the domain.

Thus, the required domain and the range of the given function are (-2, 3) and (2, -3) respectively.

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Answer:

380 seconds

Step-by-step explanation:

Convert 6 minutes to seconds by multiplying 6 times 60, because there are 60 seconds per minute.
6 x 60 = 360

Now add the 20 seconds.
360 + 20 = 380

6 minutes and 20 seconds are equal to 380 seconds.

Answer:

x ≈ 11.3

Step-by-step explanation:

using the cosine ratio in the right triangle

cos61° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{DE}{DF}\) = \(\frac{5.5}{x}\) ( multiply both sides by x )

x × cos61° = 5.5 ( divide both sides by cos61° )

x = \(\frac{5.5}{cos61}\) ≈ 11.3 ( to the nearest tenth )

Answer:

There is no difference.

Step-by-step explanation:

When it comes to significant figures, they matter.

However, if you just add zeros, they essentially just become placeholders. 3 already has 0 for decimals, so it is equal to 3.0 and 3.00.

Step-by-step explanation:

x=-5 f(x)=4x

f(x)=4(-5)

f(x)=-20

x=3 f(x)=4(3)

f(x)=12

The monthly amortization on the automobile loan, given the loan amount, the period, and the compounding frequency, is ₱ 18, 901.68

The monthly amortization is constant so it will be an annuity. Seeing as we have the loan amount, this means that the present value of an annuity formula can be used to find the monthly amortization.

First, find the period in months:

= 5 x 12 months a year

= 60 months

The interest in months :

= 9 . 5 % / 12 months per year

= 9.5 / 12 %

The monthly amortization is:

= Loan amount / ( Present value interest factor of annuity, 60 periods, 9.5 / 12 %)

= 900, 000 / 47.614827336156

= ₱ 18, 901.68

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Answer:

b = 13.5

Step-by-step explanation:

2 -b/3 = -5/2

im assuming we want to find b. therefore we want b = something. so because b is on top of a fraction right now, I will multiply both sides by 3 so -b is not on top of a fraction anymore.

6 -b = -15/2

we should get rid of the divided by 2 on the other side too, to make it easier. we can do this by multiplying 2 on both sides.

12 - 2b = -15

remember, we want to isolate b. so first we should get rid of the 12 next to the 2b. we can do this by subtracting 12 on both sides!

-2b = -27  

finally, we can divide both sides by -2 and b will be isolated!

b = 13.5

The length of the guy wire to the nearest foot would be = 10 ft.

The relationship between the tower, guy wire and pole forms the shape of a right angle triangle.

The distance from the stake to the pole (opposite) =a = 5 ft

The distance from the pole to the tower (adjacent) =b= 9ft

The length of the guy wire= c = X

Using the Pythagorean formula:

c² = a² + b²

c² = 5² + 9²

c² = 25+81

c² = 106

C = √106

C= 10 ft ( to the nearest foot)

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Complete question:

A guy wire runs from the top of a cell tower to a metal stake in the ground. Sophie places a 7 ft tall pole to support the guy wire. After placing the pole, Sophie measures the distance from the stake to the pole to be 5 ft. She then measures the distance from the pole to the tower to be 9 ft. Find the length of the guy wire, to the nearest foot.

The formula for this linear function is f(x) = mx + b, where m is the slope (in this example, -350), and b is indeed the y-intercept (750,000 in this case).

An equation expressing the connection between the expressions on either side of a sign. Normally, it has an equal sign and just one variable. such as: 2x - 4 is equal to 2. The variable x is present in the example above.

Workers who complete the computer security course will each receive a reimbursement of $350.

We deduct $350x from of the initial $750,000 to determine how much money will remain inside the education fund once x employee gets the reimbursement.

Thus, f(x) = 750,000 - 350x is the equation again for function that describes that amount of money still in the fund when x employees receive the refund.  

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Since the ratio of women to men is 7 to 4, we can say that for every 7 women there are 4 men, we can also say that for a total of 11 employees (4 + 7 = 11) 7 of them are women, then we can formulate this ratio as a fraction like this:

women to employee = 7/11

Then by multiplying the total number of employees by 7/11 we can calculate how many of them are women, then we get:

women = 319×7/11 = 203

Then, a total of 203 women work for the company

Answer:

  a.  $150

  b.  $158.25

Step-by-step explanation:

The amount of tax is the product of the tax rate and the price being taxed. This relation can let us solve for the price.

  tax = tax rate × price

  price = tax/(tax rate) = $8.25/0.055 = $150.00

The purchase price of the table saw is $150.00.

__

The total price is the sum of the purchase price and the tax.

  total price = price + tax

  total price = $150.00 +8.25 = $158.25

The total price of the table saw is $158.25.

The standard error is 0.0912.

The standard error (SE) is a measure of the precision of the sample mean estimate compared to the true population mean. To calculate the SE, we use the formula SE = standard deviation / square root of sample size.

In this scenario, the population parameter is 0.7, and the sample size is 30. If we assume that the sample mean is an unbiased estimator of the population mean, then the SE can be calculated using the above formula. However, we do not know the standard deviation of the population, so we use the sample standard deviation as an estimate.

Assuming the sample is large enough to assume normality, the formula becomes SE = \(\sqrt{(0.7*0.3)/30}\)   = 0.0912. Therefore, the standard error for a sample size of 30 is 0.0912. This means that if we were to take multiple samples of size 30 from the same population, the standard deviation of the means of those samples would be around 0.0912 away from the population parameter of 0.7 on average.

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In general, if the range of a function is y≥−1, its inverse has a domain of y≥−1. So, the range of the inverse of the cubic root function is y≥−1.

The range of a cubic root function becomes the domain of a cube function and vice versa since a cubic root function is an inverse function of a cube function. Therefore, the cube function's range is x3 if the cubic root function's domain is x3.

A function's inverse typically has a domain of y1 if its range is y1. Therefore, y1 is the domain of the inverse of the cubic root function.

Describe a function.

A function is a mathematical relationship between a domain—a set of inputs—and a range—a set of outputs. Each input in the domain is given a distinct output, known as the function value, by a function. An equation or graph can be used to depict the function value.

A function is typically represented symbolically by an equation that describes the relationship between the inputs and outputs and a letter, like f or g, as well as the letter. For instance, the equation of a function that accepts a value of x as input and produces its square is f(x) = x2.

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Answer:

x = 65.26 degrees or x = 245.26 degrees.

Step-by-step explanation:

To solve the equation 4tan(x)-7=0 for 0<=x<360, we can first isolate the tangent term by adding 7 to both sides:

4tan(x) = 7

Then, we can divide both sides by 4 to get:

tan(x) = 7/4

Now, we need to find the values of x that satisfy this equation. We can use the inverse tangent function (also known as arctan or tan^-1) to do this. Taking the inverse tangent of both sides, we get:

x = tan^-1(7/4)

Using a calculator or a table of trigonometric values, we can find the value of arctan(7/4) to be approximately 65.26 degrees (remember to use the appropriate units, either degrees or radians).

However, we need to be careful here, because the tangent function has a period of 180 degrees (or pi radians), which means that it repeats every 180 degrees. Therefore, there are actually two solutions to this equation in the given domain of 0<=x<360: one in the first quadrant (0 to 90 degrees) and one in the third quadrant (180 to 270 degrees).

To find the solution in the first quadrant, we can simply use the value we just calculated:

x = 65.26 degrees (rounded to two decimal places)

To find the solution in the third quadrant, we can add 180 degrees to the first quadrant solution:

x = 65.26 + 180 = 245.26 degrees (rounded to two decimal places)

So the solutions to the equation 4tan(x)-7=0 for 0<=x<360 are:

x = 65.26 degrees or x = 245.26 degrees.

Answer: $400

Step-by-step explanation:

Discount = 15%

The original price/value of an item is always 100%

So selling price (%) = original price - discount = 100%-15% = 85%

We got selling price as 85%

This implies that 85% = 340

Let's find 1% first, then 100%

1% = 340÷85 = 4

100% = 4 × 100 = $400

The usual (normal/original) price is $400

Juan sold a bicycle at a discount of 15% if the selling price was $340 then the usual price of the bicycle was $400.

percentage, a relative value indicating hundredth parts of any quantity.

Let's represent the usual price of the bicycle by P.

Since Juan sold the bicycle at a discount of 15%, the selling price (S) would be 85% of the usual price (P).

We can express this relationship as an equation:

S = 0.85P

We also know that the selling price of the bicycle was $340.

Substituting S = $340 into the equation above, we get:

$340 = 0.85P

To find P, we can solve for it:

P = $340 / 0.85

P = $400

Therefore, the usual price of the bicycle was $400.

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Answer:

a.) 3x+2y=34 is the equation. 2 pairs could be 10,2 and 8,5.

b.) .5x+2y=14

c.) 8,5

Step-by-step explanation:

because both 8 and 5 work in both equations 3(8)+2(5)=34

.5(8)+2(5)=14

From the given number line, the variable "m" could take the values of -2, -3.5, 0, and -5

To determine which values the variable "m" could take from the given number line, we need to identify the points or intervals on the number line that correspond to the possible values of "m".

Looking at the number line, we can see the following values:

-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5

From this list, the values that "m" could take are:

-2, -3.5, 0, -5

These values are present on the number line, indicating that they are possible values for "m".

Therefore, the variable "m" could take the values -2, -3.5, 0, and -5 from the given number line.

It's important to note that the values -7 and 4 are not present on the number line, so they are not possible values for "m" based on the information provided.

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Answer: the number of devices expected to fail during the second month is 24

Step-by-step explanation:

Given that

The device has a constant failure rate with MTTF of 2 months.

As the device has constant failure rate so it has exponential failure distribution

f(t) = λe^-λt

Here MTTF = 1/ λ

so  λ = 1/2 Months⁻¹ = 0.5 Months⁻¹ and from the question,  Number of devices = 100

E( 1 < x < 2) = E ( x < 2) - E (x < 1)

so E(x < X) can be calculated with λ  = 0.5 Months⁻¹ will be calculated as the failure function

f(x) = λ exp ( - λ×t) for t > 0

F (x>0) = 1 - exp( - λx)

so E ( 1 < x < 2) = E ( x < 2) - E (x < 1)

E ( x < 2) = 1 - exp(-0.5 × 2) = 0.6321 ; E (x<1) = 1 - exp(-0.5 × 2) = 1 - exp( -0.5) = 0.3934

so E ( 1 < x < 2) = 0.6321 - 0.3934 = 0.2387

so the number of devices expected to fail during the second month is;

100 × 0.2387 = 23.87 ≈ 24

Answer:

g(x) = -f(x)

Step-by-step explanation:

Function G is the inverse of function F.

Step-by-step explanation:

x = the number

4x - 96 = x

3x = 96

x = 32

Answer:

The total number of ways the researcher can select  5 women and 5 men for a study is 7,56,756.

Step-by-step explanation:

The complete question is:

From a group of 10 women and 15 men, a researcher wants to randomly select  5 women and 5 men for a study in how many ways can the study group be selected?

Solution:

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

 \({n\choose k}=\frac{n!}{k!\cdot (n-k)!}\)

The number of women in the group: \(n_{w}=10\).

The number of women the researcher selects for the study, \(k_{w}=5\)

Compute the total number of ways to select 5 women from 10 as follows:

\({n_{w}\choose k_{w}}=\frac{n_{w}!}{k_{w}!\cdot (n_{w}-k_{w})!}=\frac{10!}{5!\cdot (10-5)!}=\frac{10!}{5!\times 5!}=252\)

The number of men in the group: \(n_{m}=15\).

The number of men the researcher selects for the study, \(k_{m}=5\)

Compute the total number of ways to select 5 men from 15 as follows:

\({n_{m}\choose k_{m}}=\frac{n_{m}!}{k_{m}!\cdot (n_{m}-k_{m})!}=\frac{15!}{5!\cdot (15-5)!}=\frac{15!}{5!\times 10!}=3003\)

Compute the total number of ways the researcher can select  5 women and 5 men for a study as follows:

\({n_{w}\choose k_{w}}\times {n_{m}\choose k_{m}}=252\times 3003=756756\)

Thus, the total number of ways the researcher can select  5 women and 5 men for a study is 7,56,756.

Point H is the ortho-center of our given triangle and option c is the correct choice.

We have been given an image of a triangle. We are asked to find the term that describes point H.

We can see that point H is the point, where, all the altitudes of our given triangle EFF are intersecting.

We know that ortho-center of a triangle is the point, where all altitudes of triangle intersect. Therefore, point H is the ortho-center of our given triangle and option c is the correct choice.

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Answer:

About 8.2 years.

Step-by-step explanation:

The minivan was purchased for $35,000 and it depreciates according to the function:

\(\displaystyle V(t)=35000\Big(\frac{1}{2}\Big)^{t/3}\)

Where t is the time in years.

And we want to determine how long it will take for the minivan to depreciate to 15% of its initial value.

First, find 15% of the initial value. This will be:

\(0.15(35000)=5250\)

Therefore:

\(\displaystyle 5250=35000\Big(\frac{1}{2}\Big)^{t/3}\)

Solve for t. Divide both sides by 35000:

\(\displaystyle 0.15=\Big(\frac{1}{2}\Big)^{t/3}\)

We can take the natural log of both sides:

\(\displaystyle \ln(0.15)=\ln(0.5^{t/3})\)

Using logarithmic properties:

\(\displaystyle \ln(0.15)=\frac{t}{3}\ln(0.5)\)

Therefore:

\(\displaystyle t=\frac{3\ln(0.15)}{\ln(0.5)}=8.2108...\)

So, it will take about 8.2 years for Tenzin's minivan to depreciate to 15% of its initival value.

Answer: 16

Step-by-step explanation:

1. Distribute the 12 to the x variable and the constant.

You will get 12x - 240 = -48

2. -48 + 240 = 192. You now have 12x = 192

3. solve for x. x = 192/12 -> x = 16

Answer:

That would just be magical- like let's imagine how it would turn out. :>

Step-by-step explanation:

Answer:

Move all numbers without a variable

Step-by-step explanation:

you want to get the variable by itself so you'll add 6 to both sides of the = sign making it 4u = 30 then you'll divide both sides by 4 making u = 7.5