What is the solution of the system of equations? 6x-2y = 4 -9x+3y = 12

Let's begin by listing out the information given to us:

distance between Vincent & Frank = 32km

distance equivalent is given by 1km=0.62 miles​

We will convert the distance from km to miles using the conversion factor:

Options B and D makes the equation true

The equation: 2x + 4y = 24

Using substitution, we will pick each of the points and replace them in the equation to determine which two options are true.

They would be true if the right hand side is equal to the left hand side

a) (x, y) = (2, -5)

2(2) + 4(-5) = 24

4 - 20 = 24

-16 = 24

left hand side is not equal to the right hand side

b) (x, y) = (0, 6)

2(0) + 4(6) = 24

0 + 24 = 24

24 = 24

left hand side is equal to the right hand side (true)

c) (x, y) = (0, 12)

2(0) + 4(12) = 24

0 +48 = 24

48 = 24

left hand side is not equal to the right hand side

d) (x, y) = (6, 3)

2(6) + 4(3) = 24

12 + 12 = 24

24 = 24

left hand side is equal to the right hand side (true)

Options B and D makes the equation true

The total amount that was raised by the volleyball team is  $1,225.

Percentage is the fraction of an amount that is usually expressed as a number out of hundred. The sign that is used to represent percentages is %.

The first step is to determine the total number of snacks sold.

Total number of snacks sold = number of pretzels and cheese puffs sold / percentage representing pretzels and cheese puffs

210 / (10% + 20%)

210 / 30%

210 / 0.30 = 700

The second step is to multiply the total number of snacks by the cost per snack

Total cost of the snacks = cost per snack x total number of snacks

700 x $1.75 = $1,225

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Answer:

what she does (annoy, annoys) me a lot

The Variance of the given data set given the sample mean as 7 is; C: 10

We want to find the variance of the given data and the formula is;

Var = ∑(x_i - x)²/(n - 1)

From the table, we see that;

∑(x_i - x)² = 4 + 4 + 16 + 0 + 16

∑(x_i - x)² = 40

Now, the number of terms is 5 and as such;

Variance = 40/(5 - 1)

Variance = 40/4

Variance = 10

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Let j be the number of times Neishai jogs in h hours.

It is given that Neishai jogs around the block 4 times every hour. This means that after 1 hour, she jogs 4 times. After 2 hours, she jogs:

After 3 hours, she jogs:

After h hours, she jogs:

Therefore, the number of times Neishai jogs around the block is given using the equation:

OPTION B is the correct option.

The equation that represents the proportional relationship is;

A: y = 16.99x

The general equation for a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept which is the point where x is 0

Now, we are told that Sandra signed up for a workout which had a cost of getting 12 months for just $16.99 per month.

What this means is that if she signs up right now, it is a window of opportunity to get 12 months at probably a discount.

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Complete question is;

Sandra signed up for Workout Jazz during the spring special. Which equation represents the proportional relationship? Sign up now and get 12 months for just $16.99 per month

A y = 16.99x

B y = 12x

C y= 16.99x + 12

D y= 12x + 16.99

We need to know conversion of units to solve the given problem. The density of the material in grams per quart is 136.35 grams per quart.

We have been given the density of a certain material in pounds per cubic foot of volume. The density is 9 pounds per cubic foot of volume. We need to convert pounds per cubic foot to grams per quart, we need to separately convert pounds to grams and convert cubic foot to quart. Since it is density so we need to divide the value of pound in gram by the value of one cubic foot in quart and multiply the density to this value to get the desired result.

1 pound=453.592 grams

1 cubic foot= 29.94 quart

9 pounds per cubic foot= 9x 453.592/29.94=136.35 grams per quart

Therefore the density of the material in grams per quart is 136.35 grams per quart.

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The restaurant bill = $59.23

Megan wants to leave 30% as a tip

so, the tip = 30% of 59.23 = 0.3 x 59.23 = 17.769

So, He will leave = 59.23 + 17.769 = 76.999

so, he will leave $77 to the nearest dollar

By applying the Empirical Rule, the value of x is equal to: A. 8.

The Empirical Rule is also known as the 68-95-99.7 rule and it simply refers to a statistical rule which states that the middle 95% of a normal distribution would be within two (2) standard deviations of its mean.

This ultimately implies that, 95% of a normal distribution would fall within two (2) standard deviations of its mean in accordance with the Empirical Rule.

By applying the Empirical Rule, the value of x is given by:

x = μ + 2σ

Substituting the given points into the formula, we have;

x = 4 + 2(2)

x = 4 + 4

x = 8.

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Complete Question:

Suppose X ~ N(4, 2). What value of x is two standard deviations to the right of the mean?

8

10

7

6

Answer:

0.09, Because we have the tenths, hundredths, and thousandths with possible others.

Yes . The given relation is a function

{ (3, 14) (20, 2) (2,4) (8, -15) (1, -11) (-9, 6) } is a function.

Here { (3, 14) (20, 2) (2,4) (8, -15) (1, -11) (-9, 6) }

In the given relation each value x is related to only one element in y.

So the  given relation is a function.

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you. aren't.

alone..........

Step 1

All integers are rational numbers. All integers are subset of rational number.

Rational numbers are numbers that can be express as fraction

Inteers are both positive and negative natural numbers.

Therefore,

6/2 = 3 is an integer

-4.0 is a negative integer

-15/3 = -5 is a negative integer

7.5 is a rational number but not an integer.

Hence, 7.5 DOES NOT BELONG TO THE SUBSET OF INTEGERS

Given that the table have equivalent ratios, let's find the missing values.

To find the missing values, find the ratio:

Thus, we have:

The possible side lengths of HJK are 6,9,12

Mathematically, when two triangles are similar, then the ratio of their sides are equal

For the first triangle, we have the side dimensions of 4, 6 and 8

This can be written in its lowest ratio as 2:3:4

Any triangle that would be of similar measure should have dimensions of same ratio

Thus, we have this as;

6:9:12

If we reduce this ratio using 3, we will have 2:3:4

Answer:

38

Step-by-step explanation:

multiply 14.25 with 4 tgeb divide by 1.5

When adding or subtracting decimal numbers, you will have to line up the decimal points

Hence, the sta

A rotating light is located 14 feet from a wall, then the rate is 45.3492 feet per second.

A rotating light is located from a wall = 14 feet

The light completes one rotation every 4 seconds.

Light's angle is = 10 degrees

Let x be the distance from the bottom of the perpendicular from light to wall to projection of line on the wall at a time t

Then,

tan θ = x/14

x = 14 tan θ

θ = w t = 10°

Where,

Angular velocity is the rate of change of the position angle of an object with respect to time, so w = theta / t, where w = angular velocity, theta = position angle, and t = time.

w = angle velocity

So,

w = [tex]\frac{2\pi }{2}[/tex]

w = [tex]\pi[/tex]

Here,

Rate : [tex]\frac{dx}{dt}[/tex] = [tex]\frac{d}{dt} (14tanwt)[/tex]

[tex]\frac{d}{dt}[/tex]tan w t = [tex]sec^{2}[/tex]w t

= 14 *w* [tex]sec^{2}[/tex]w t

= 14*[tex]\pi[/tex]*[tex]sec^{2}[/tex]10°

= 45.3492 feet per second

( round to 4 decimal places )

Therefore,

A rotating light is located 14 feet from a wall, then the rate is 45.3492 feet per second.

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The complete factorization of x3-2x²+x-2 is (x+2)(x+1)(x-1)

Here is the step-by-step solution.

[tex]x^{3} -2x^{2} +x-2\\\\x^{2} (x-2) -1 (x-2)\\\\(x^{2} -1) (x-2)\\(x+2)(x-1)(x+1)[/tex]

The complete factorization of the polynomial equation is

OD. (x+2)(x + 1)(x-1).

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Notice that the graph of

is the graph of

reflected over the x-axis.

Now, the graph of the parent function is:

therefore, the graph of f(x) is:

Points:

3

2.25

opposite of 4 = - 4

the opposite of a number is the result of that number multiply by -1

The, the opposite of 4 is (4(-1))= - 4

To put the points in a number line, you have to organize the numbers from less to greatest

The mixed numer can be writen also as: negative One and 1/2 is equal to - -1.5, negative per negative is +

Then you have the next order from less to greatest:

-4

-(-1 1/2)

2.25

3

To put that point in a number line you need to choose a scale to tick marks: As you have decimal number, the scale could be 0.5.

You have the next number line:

Then the point will be:

Between each interger you have a tick mark in the middle: Betwwen 0 and 1 you have 0.5, between 1 and 2 you have 1.5, etc.

Answer:

-10b - 7

Step-by-step explanation:

-11b - 4 - (-b + 3)

-11b - 4 + b - 3

-10b - 7

I hope this helps!

Answer:

10b-1

Step-by-step explanation:

Step 1 :write out what the question means

-b+3-( - 11b - 4)

Step 2:multiply and collect like terms

-b+3+11b+4

11b-b+3+4=10b+7

Answer of this composite function is 3x-2.

(ƒ · g)(x) is a composite function and it has meaning  x = g(x) should be substituted in f(x).

Given ƒ(x) = x + 1, g(x) = 3x - 3

so, f(x)=f(g(x))=f(3x-3)= 3x-3+1= 3x-2

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The proportion that represents the down payment is 20% or 0.2 of the condominium's value.

2. The down payment is $25,000.

The down payment is the proportion required to secure a purchase transaction.

The down payment is an upfront cost that the purchaser settles in cash before being granted a long-term credit (loan or mortgage).

The purpose of a down payment is to reassure the lender of the borrower's ability to repay the loan.

To compute the down payment, apply the down payment percentage or proportion to the value of the asset.

The cost of the condominium = $125,000

Down payment = 20%

20% = $25,000 ($125,000 x 20%)

Mortgage loan = $100,000 ($125,000 - $25,000)

Thus, in this situation, the down payment is 20% of the cost of the property.

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To find:

The unit price for the 16-ounce package.

Solution:

The price of a 16-ounce pack is $1.69. So, the rate of the package per ounce is given by:

Thus, the rate of the 16-ounce pack is 0.106 dollars per ounce.

The acceleration of the particle is found as 3 m/s.

For the given question,

The distance covered by the particle 's' is given by the equation;

s = (3/2)t² - 3t

Where t is the time taken in seconds.

Differentiate twice the equation will given the value of acceleration.

Differentiate once will given velocity.

v = 3t - 3

Differentiate again to get the acceleration.

a = 3

Thus, the acceleration of the particle is found as 3 m/s.

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Given the functions:

We must answer the question for the function:

c) Domain and range

First of all, we must analyze the domain of the function. Because the funcion h(x) is given by the equotient of two functions, f(x) and g(x), the domain of h(x) are all the values of x = 1 for which we have

g(x) ≠ 0. We see that the function g(x) is zero when x = 1 or x = -1. So the domain of the function is:

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually) after we have substituted the domain. Plotting the function, we get the following graph:

From the graph, we see that the function h(x) takes all the values from -∞ to +∞. So we conclude that the range of the function is:

a) Zeros

The zeros of a function are the values for which we have h(x) = 0. Looking at the function, we see that it seems to be zero at x = -1 but that number is not in the domain of the function. So we conclude that the function has not any zero.

b) Asymptotes

By definition, an asymptote is a straight line that constantly approaches a given curve but does not meet at any infinite distance. Looking again at the graph of the function, we see that the function has one asymptote at:

d) Continuity

Looking at the domain of the function, we see that the domain is a union of intervals because the function is not defined at the values x = -1 and x = 1. So we conclude that the function is not continuous.

e) Not defined values

As we mentioned in the point of the domain, the function is not defined at the values x = -1 and x = 1. The explanation is the one given in that point.

End behaviour of the function

To find the end behaviour of the function, we can look at the graph, or we can also rewrite the function in the following way:

For x ≠ -1 we can cancel the repeated terms in numerator and denominator, and we get:

If we compute the limits of the function as x → -∞ and x → ∞, we get:

So the end behaviour of the function is y → 0.

Answers

a) The function has not any zeros

b) x = 1

c) Domain = (-∞,-1) U (-1,1) U (1,∞)

Range = (-∞,∞)

d) The function is not continuous.

e) The function is not defined at x = -1 and x = 1