3 ( � − 2 ) + � − 1 = 3(x−2)+x−1= 5 5

The approach used to solve equations with integer coefficients & constants can also be used to solve equations with fractional / decimal coefficients and constants.

An equation is a mathematical statement that expresses the equality of two expressions. It is a relationship between two or more variables, such as x + y = z. Equations are used to solve a wide variety of problems in mathematics, physics, chemistry, engineering and other scientific fields.

The main difference is that when solving equations with fractional or decimal coefficients and constants. For example, if you have an equation with a decimal coefficient, divide both sides by the coefficient to make the coefficient 1 before you can use the same steps to solve the equation.

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The equation of the line, given the ordered pair and the y - intercept, is y = -2 x + 2

The slope ( m ) is - 2

The equation for a linear model takes the form :

y = mx + b

m =  slope

b = y - intercept

As we have the ordered pair, and the y - intercept, we can find the slope:

y = mx + b

- 4 = 3 x slope + 2

3 x slope = - 4 - 2

Slope = - 6 / 3

Slope = - 2

The equation is therefore:

y = -2 x + 2

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Answer:

Step-by-step explanation:

The expression is equivalent is 6x/4 + 24y/12

Algebraic expressions are described as expressions composed of variables, terms, factors, constants, and coefficients.

These expressions also consisting of mathematical operations, such as;

Given the expression;

1/4(3x+4y) + 3(1/4x+ 2/3y)

expand the bracket

3x/4 + 4y/4 + 3/4x + 3/3y

collect like terms

3x/4 + 3/4x + 4y/4 + 3/3y

add like terms

3x + 3x/4 +  12y + 12y /12

add the numerators

6x/4 + 24y/12

Hence, the expression is 6x/4 + 24y/12

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Answer: The dependent variable is the time it takes to come to a complete stop. The independent variable is the speed at which you drive your car.

The dependent variable is the amount of food there will be. The independent variable is the number of students who attend the fiesta lunch.

Step-by-step explanation:

This polynomial represents the area of the platform.A = w(w + 2)^2. the area of the rectangular platform is 56 square feet and the length of the platform is 2 feet longer than 3 times its width

A = w(w + 2)^2

A = Area of the platform

w = width of the platform

Since the area of the rectangular platform is 56 square feet and the length of the platform is 2 feet longer than 3 times its width, we can represent this statement mathematically as:

A = w(w + 2)^2

This polynomial represents the area of the platform.

A = w(w + 2)^2

A = w^2 + 2w^2

A = 3w^2

A = 56

3w^2 = 56

w^2 = 56/3

w = √56/3

A = w(w + 2)^2, area of the rectangular platform is 56 square feet and the length of the platform is 2 feet longer than 3 times its width.

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Answer:

64c = 32pt

Step-by-step explanation:

There are 2 cups in 1 pt. 64 divided by 2 is 32pt.

Also, just imagine the cups as double the number of the pints

Ex. 32 + 32 = 64

Frannie listened to 1/30 of her music collection while on vacation.

We have been given that Frannie put 1/5 of her music collection on an mp3 player. while on vacation, she listened to 1/6 of the music on the player.

To find the amount of music collection listened to by Frannie, while on vacation, we need to find  1/5 of 1/6.

The amount of music collection listened to by Frannie on the vacation: =1/5*1/6

=1/30

Therefore, Frannie listened to 1/30 of her music collection while on vacation.

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The multiplication of the numbers given to the reduced form is 10/7.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

The given expression is 5 × 2/7

One of the number is a whole number and the other is a fraction.

We can write 5 as 5/1 in terms of fraction and then multiply the numerators and the denominator.

(5/1) × (2/7) = (5×2) / (1 × 7) = 10/7, which is in the lowest form.

Hence the solution of the multiplication is 10/7.

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Answer:4x-15

Step-by-step explanation:

Answer:

4x-15 <---

Step-by-step explanation)

1) Distribute the X to both the x and the -3

2) You'll end up with, 5x-15-x=...

3) And, now look at the like terms. The like terms in this case are 5x and the -x.

4) 5x-x =4x

5) And, now put them together, and you'll get 4x-15!

HOPE IT HELPS! <3

Answer:

The graph of the line x = 12 is a vertical line.

A vertical line is a line with a constant x-value, in this case x = 12, so all the points on the line will have an x-coordinate of 12, regardless of their y-coordinate. All the point on the line will have the same x-coordinate and it will be parallel to the y-axis.

It does not have a slope, does not cross the y-axis, it is not horizontal.

The length of the rectangular field is 200 meters.

Given, we have length of the field equal to twice its breadth. Let the breadth of the field be "b". Therefore, length will be "2 x b". Now, Meghna jogged around the field 5 times which means she covered the perimeter of the field 5 times. We know that the perimeter of a rectangular field is [tex]2(l+b)[/tex] where l is the length of the rectangle and b is the breadth.

After jogging around the field 5 times, she covered a distance of 3 km. Converting kilo meters into meters: 3km ⇒ 3 x 1000 =  3000 meters. Now, We can equate the perimeter of the rectangle with  the given information like this :

⇒[tex]2(l+b) * 5 = 3000m[/tex]

We already know that length = 2b, therefore putting in the equation gives us :

⇒ 2(2b+b) x 5 = 3000m

⇒2(3b) x 5 = 3000m

⇒10(3b) = 3000m

⇒30b = 3000m

Dividing both sides of the equation with 30,

⇒b = 100 m

Since, length = 2b, Therefore Length ⇒ 2 x 100m = 200m

∴ The length of the field is 200m

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The SAS congruency is applied here.

Hence,

[tex] \frac{TR}{JK} = \frac{RS}{JL} = \frac{TS}{KL} \\ \frac{24}{x} = \frac{12}{6} = \frac{y}{15} \\ \frac{24}{x} = 2 \\ x = 48 = JK[/tex]

[tex] \frac{y}{15} = 2 \\ y = 30[/tex]

Perimeter =

[tex]6 + 30 + 48 \\ 36 + 48 \\ = 84[/tex]

When the line of slope of 3 passes through two points, the value of y is -8.

The slope or gradient of a line in mathematics is a number that describes both the direction and the steepness of the line. The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope is a numerical value that describes the steepness of a line and is typically calculated by dividing the vertical distance by the horizontal distance (rise over run) between two points.

Here,

m=3

m=(y2-y1)/(x2-x1)

3=(y+5)/(-3+(2))

-3=y+5

y=-8

The value of y is -8 when the line of slope of 3 is passing through 2 points as given.

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The ratios 6:16 and 21:56, 9/11 = 27/15, and y=5x do not form a true proportion. Hence, options A, C, and, D are the correct options.

A true proportion is when both the ratios presented are equal. This can be verified by putting them in their respective fractional form. For example, let's take the ratios in the second option -

= 2/10 and 15/75

Here, we can see that 2*5 = 10 and 15*5 = 75

Hence these can be written as

= 2/2*5 and 15/15*5

Hence, these fractions are the same and as a result, the ratios form a true proportion.

As for the other ratios in question -

A) 6/16 is not equal to 21/56

C) 9/11 is not equal to 27/15

D) y= 5x are not proper ratios and are not equal

Thus, options A, C, and, D are the correct options.

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The description of the route of the limousine is

First, the limousine drives 18 blocks right and 8 blocks down and then it drives 17 blocks left and 2 blocks up

From the question, we have the following parameters that can be used in our computation:

T<18, -8> o T<-17, 2>

The above parameters represent the transformation and the positions of the limousine

The above statement represents the direction in words

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Yes, Chris has enough money to buy 30 folders and 30 pens.

The cost of the stationaries Chris bought are as follows:

Chris wants to buy 30 pens and 30 folders and he has only £60.

Let's check If he has has enough money to buy the products.

Therefore,

3 pens cost £2.25

1 pen  = ?

cost of 1 pen = 2.25 / 3 = 0.75 dollars

5 folders cost £5.80

1 folder = ?

cost of 1 folder = 5.80 / 5 = 1.16 dollars

Hence,

30(0.75) + 30(1.16) = 22.5 + 34.8 = 57.3 dollars

Therefore, he has enough money to buy 30 folders and 30 pens

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By comparative methods, the values of variables p and q such that p · x + 6 = 3 · (x + q) are 3 and 2, respectively.

In this question we find the case of a linear equation with three variables (p, q, x). Theoretically, it cannot be solved because the number of variables is greater than number of equations. Nonetheless, we can infer the values of p and q by means of comparative methods and equality properties.

First, write the linear equation:

p · x + 6 = 3 · (x + q)

Second, expand the expression by algebra properties:

p · x + 6 = 3 · x + 3 · q

Third, compare terms on each side of equality:

p = 3

6 = 3 · q

q = 2

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The probability that Jennifer selects two vowels is 24%.

Probability is a way to gauge how likely something is to happen. Many things are difficult to predict with absolute certainty. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

Here, the probability that Jennifer selects two vowels is:

= 3/5 × 2/5.

= 6 / 25

= 24%.

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Answer:15 nickels per minute (I believe)

Step-by-step explanation:

First, we want to know how much she got paid in total dollar amount, we'll break it up into nickels later. We know Jackie was paid $45 per hour, but we want to figure out how much per minute she makes. There are 60 minutes in an hour, so divide 45 by 60 ( 45/60 in a calculator).

The answer for 45/60 would then be 0.75. This means Jackie gets paid 75 cents a minute. Since a nickel is worth 5 cents, we just need to divide 75 by 5. Then, we get 15.

Now we know Jackie gets paid 15 nickels per minute. I assume this would be put in aspect ratio form by saying "Jackie gets paid 15 nickels per every one minute of work." but that may depend on how your teacher wants you to word your answer. I hope this helps :)

There is good evidence that smoking rates for young teens in Massachusetts have decreased.

To answer this question, we need to calculate the proportion of teens in the sample who said they smoked (63/273). This gives us a sample proportion of 0.23, which is lower than the long-run average smoking prevalence in the state (26%). This suggests that there is good evidence that smoking rates for young teens have decreased.

We can also calculate a confidence interval to further assess the evidence. A 95% confidence interval for the true proportion of teens in Massachusetts who smoke would be (0.17, 0.29). This confidence interval does not contain the long-run average smoking prevalence of 26%, which suggests that there is a statistically significant decrease in smoking rates for young teens in Massachusetts.

Overall, there is good evidence that smoking rates for young teens in Massachusetts have decreased.

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Answer:x<1

Step-by-step explanation:

move constant -5x>-2-3

Add alike numbers (-2 and -3)

-5x>-5

Divide both sides by -5

Then flip the inequality sign

x<1

Answer:

Step-by-step explanation:

Add 3 to the -2

-5x > 1

Divide by -5 the sign switches because of the negative

x < - 1/5 or X < -0.2

An equation in point slope form for the line that passes through (-4, 3) and whose slope is 3 is equal to y - 3 = 3(x + 4).

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

Next, we would determine the linear equation representing the line which passes through the points (-4, 3) and has a slope of 3 by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 3 = 3(x - (-4))

y - 3 = 3(x + 4)

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Taking into account the definition of wavelength, frecuency and propagation speed, the wavelength of a wave with a frequency of 4.11×10⁴ Hz is 7299.27 m.

Wavelength is the minimum distance between two successive points on the wave that are in the same state of vibration. It is expressed in units of length (m).

Frequency is the number of vibrations that occur in a unit of time. Its unit is s⁻¹ or hertz (Hz).

The propagation speed is the magnitude that measures the speed at which the wave disturbance propagates along its displacement.

The propagation speed relate the wavelength (λ) and the frequency (f) using the following equation:

v = f×λ

In this case, you know:

v= 3×10⁸ m/s

f= 4.11×10⁴ Hz

λ= ?

Replacing:

3×10⁸ m/s= 4.11×10⁴ Hz× λ

Solving:

λ= 3×10⁸ m/s ÷ 4.11×10⁴ Hz

λ=7299.27 m

In summary, the wavelength of the wave is 7299.27 m.

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The eigenvectors of AAH are called the left-singular vectors of A and the eigenvectors of AHA are the right-singular vectors of A . They are called this way because of their use in singular value decomposition. Say A=UΣVH , then the columns of U are the left-singular vectors and the columns of V are right-singular vectors.

We know that the non-zero eigenvalues of AAH  and AHA are the same, they are the squares of the singular values of A . A singular of value of A is a value σ such that Av=σu   AHu=σv where u is a left-singular vector and vs a right-singular vector. This can be taken as the definition of singular value, left-singular vector (which is an eigenvector of AAH) and right-singular vector (which is an eigenvector of AHA).the left-singular and right-singular vector pair works with AAH and AHA

AAHu=σAv=σ2u

AHAv=σAHu=σ2v

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Q: What is the relationship between the eigenvectors of AAT and ATA?

We will add 2 ml of klotrix to the orange juice for a 20.5kg patient.

We know that , 1 kg=2.20462 pounds

Therefore, 20.5kg=20.5x2.20462 pounds= 45.195 pounds or 45.195 lb

Additionally we have, 1 lb = 0.35 mEq

Therefore, 45.195 lb=  0.35 mEq × 45.195 = 15.818 mEq.

Also, 8mEq=1 mL

By using unitary method,

1 mEq=1/8 mL

Converting 15.818 mEq to mL, we get

15.818mEq = 15.818 ÷ 8 = 1.9 mL

Thus, 15.818mEq  = 1.9 mL

Rounding off the answer we get,

The amount of klotrix required to add to the orange juice for a 20.5 kg patient is 2mL

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Solving a system of equations we will see that the efficiency of the first car is 25 miles per gallon, and the one of the second car is 35 miles per gallon.

Let's define the variables:

x = fuel efficiency of the first car.

y = fuel efficiency of the second car.

We know that the sum is equal to 60 miles per galon, thus:

x + y = 60

We also know that the he first car consumed 35 gallons of gas and the second consumed 20 gallons of gas. The two cars drove a combined total of 1575 miles, this can be written as:

35x + 20y = 1575

Then we have a system of equations:

x + y = 60

35x + 20y = 1575

We can isolate x on the first equation to get:

x = 60 - y

And substitute that in the other equation:

35*(60 - y) + 20y = 1575

2100  - 15y = 1575

2100 - 1575 = 15y

525/15 = y

35 = y

And x = 60 - y = 60 - 35 = 25

These are the efficiencies.

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Answer:

Uncle Bill is 40 years old.

Step-by-step explanation:

Jim is 8 years old, and Uncle Bill is 5 TIMES older, meaning he is 5x8. Which would be 40 years old.