how can i solve literal equations?

Answer:

x=3

Step-by-step explanation:

3x-7=2

  +7  +7

3x=9

Divide by 3.

3x divided by 3 is x.

9 divided by 3 is 3.

x=3

Hope this helps.

Answer:a

Step-by-step explanation: 25x8=200

(10x25)-50=200

The equation of the line in the slope-intercept form is given y= 3x + 3 .

The graph of the equation y = mx + c is a line with m as the slope and m and c as the y-intercept. In the slope-intercept representation of the linear equation, the values of m and c are real numbers. A line's slope, expressed in m, indicates how steep it is. A line's gradient is also referred to as its slope occasionally. The y-coordinate of the point where the line's graph meets the y-axis is known as the y-intercept, or c, of a line.

The  equation of the line is given by 12x - 4y = -12 .

This is the standard form of the line.

Now to represent the line in the slope-intercept form we need to write the equation for y in terms of x.

or, 12x-4y=-12

or, -4y = -12x - 12

or, y = (-12x - 12 ) ÷ (-4)

or, y = 3x + 3

Here the slope is 3 and the y-intercept is also 3.

Therefore the slope-intercept form of the line is given by y = 3x + 3

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Answer:

[tex]\sqrt{3}[/tex]

Step-by-step explanation:

[tex]\frac{\sqrt{15} }{\sqrt{5} }[/tex]

to rationalise the denominator multiply numerator/ denominator by [tex]\sqrt{5}[/tex]

= [tex]\frac{\sqrt{15} }{\sqrt{5} }[/tex] × [tex]\frac{\sqrt{5} }{\sqrt{5} }[/tex]

= [tex]\frac{\sqrt{75} }{5}[/tex]

= [tex]\frac{\sqrt{25(3)} }{5}[/tex]

= [tex]\frac{5\sqrt{3} }{5}[/tex]

= [tex]\sqrt{3}[/tex]

Answer:

n² p²r³

Step-by-step explanation:

n ⋅ n ⋅ p ⋅ p ⋅ r ⋅ r ⋅ r

Write using exponents

There are 2 n terms

n²⋅ p ⋅ p ⋅ r ⋅ r ⋅ r

There are 2 p terms

n² p²⋅ r ⋅ r ⋅ r

There are 3 r terms

n² p²r³

======================================================

Explanation:

Start at -4 on the x axis.

Draw a vertical line until reaching the curve.

Then draw a horizontal line until reaching the y axis.

You should arrive at y = -5. This tells us f(-4) = -5

The input x = -4 leads to the output y = -5

The point (-4, -5) is on the graph. This is the highest point, so it's the vertex of the V shape.

See the diagram below.

Answer:

1/4

Step-by-step explanation:

You jumped rope of 1/3 of 3/4 hour.

In math, "of" usually means times.

1/3 of 3/4 hour = 1/3 × 3/4 hour = (1 × 3)/(3 × 4) hour = 3/12 hour = 1/4 hour

Answer: 1/4

-33 is the value of √x² - y² at x = 3 and y = -6.

The expression given in the question is √x² - y² and we have to find the value of this expression when the value of x is 3 and the value of y is -6.

In order to evaluate √x² - y²  simply put x = 3 and y = -6 and then solve accordingly.

Let's proceed to solve the expression,

√x² - y²

at x = 3 and y = -6. we have

= √3² - (-6)²

= √9-36

= 3-36

= -33

⇒√x² - y² = -33

∴ On solving, √x² - y² for x = 3 and y = -6 we get -33 as its evaluation.

Hence, -33 is the required answer.

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Answer:

i think the answer is 0.00263157895

The interval where the function is nonlinear and decreasing is 0 < x < 4

The straight lines on the graph are the intervals where the graph is linear

This means that the straight lines on the graph will not be considered

Considering the curve, the graph decrease from x = 0 to x = 4

This can be rewritten as:

0 < x < 4

Hence, the interval where the function is nonlinear and decreasing is 0 < x < 4

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Answer:

see picture

Step-by-step explanation:

Please look at explaination

Average Speed is 23/32 laps per minute.

In the given statement is:

Carlos jogged 5 3/4 laps around the school track in 8 minutes.

What is Average speed?

Average Speed is calculated by dividing the total distance travelled by the time interval. For example, Someone who takes 40 minutes to drive 20 miles north and then 20 miles south (to end up at the same place), has an average speed of 40 miles divided by 40 minutes, or 1 mile per minute (60 mph)

Now, According to the Question:

5 3/4laps = 23/4 laps

23/4 ÷8

=23/4 × 1/8

=23/32

So, 23/32 laps per minute

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For the given systems of equations, we have that:

1) The infinite solutions have the following format: (3y - 12, y, 10y - 31).

2) There is one solution: (1.58, -3.45, 3.89).

3) There is one solution: (3, 2, 4).

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For item 1, the system is:

From the first equation, we have that:

z = 3x + y + 5.

Replacing on the second equation, we have that:

-4x + 2y + 3x + y + 5 = 17

-x + 3y = 12

x = 3y - 12.

Replacing on the third equation, we have that:

-2x - 4y + 3x + y + 5 = -7

x - 3y = -12

Since x = 3y - 12:

3y - 12 - 3y = -12

0 = 0.

Free variable, hence:

The infinite solutions have the following format: (3y - 12, y, 10y - 31).

For item 2, the system is:

From the first equation:

x = -4 - 5y - 3z.

Replacing on the second equation:

-4 - 5y - 3z + 2y - 3z = 9.

-3y -6z = 13.

3y + 6z = 13.

Replacing on the third equation:

-3(-4 - 5y - 3z) + 2y + 3z = -12

12 + 15y + 9z + 2y + 3z = -12

17y + 12z = -14.

From the second equation, we have that:

z = (13 - 3y)/6.

Hence, replacing on the third again:

17y + 2(12 - 3y) = -14

11y + 24 = -14.

y = -3.45.

z = (13 - 3 x (-3.45))/6 = 3.89.

x = -4 - 5(-3.45) - 3(3.89) = 1.58.

Hence:

There is one solution: (1.58, -3.45, 3.89).

For item 3, the system is:

From the second equation:

z = 5x + 2y - 15.

Replacing on the first:

-4x - 2y + 5(5x + 2y - 15) = 4

-4x - 2y + 25x + 10y - 75 = 4

21x + 8y = 79.

Replacing on the third:

5x - 2y - 3(5x + 2y - 15) = -1

5x - 2y - 15x - 6y + 45 = -1.

-10x - 8y = -46.

Adding both resulting equations, we have that:

11x = 33.

x = 3.

Then

21x + 8y = 79.

63 + 8y = 79

8y = 16

y = 2.

z = 5x + 2y - 15 = 5(3) + 2(2) - 15 = 4.

There is one solution: (3, 2, 4).

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The 94 ft. by 50 ft dimensions of the court obtained from a similar question posted online, gives;

a. The ordered pair representing the location of the player in the bottom right corner is (47, -25)

b. The distance traveled by the ball obtained using Pythagorean theorem, is approximately 53.2 feet.

The possible dimensions of a rectangular court obtained from a similar question posted online are;

Length of the basketball court = 94ft.

Width of the basketball court = 50 ft.

From the question, we have;

Location of the court center = The origin of a coordinate plane

a. The ordered pair that represent the location of a player in the bottom right corner is found as follows;

Let (x, y) represent the coordinates of the bottom right corner of the court, we have;

Horizontal distance from the center of the court (the origin) to the right boundary of the court, x = (94 ft.)/2 = 47 ft.

Vertical distance from the center to bottom of the court, y = (50 ft.)/2 = 25 ft.

Following the convention of points to the right and above the origin being positive, while points below the origin are negative, we have;

The ordered pair (the coordinates of the player) that represents the location of the player in the bottom right corner is therefore;

b. The distance, d, that the ball travels is given by Pythagorean theorem as follows;

d = √((47 - 0)² + ((-25) - 0)²) = √(2834) ≈ 53.2

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The equation of the line that passes through the points is y = -x - 8

The points are given as:

(−1,−7) and (−8,0)

Calculate the slope (m) using

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

So, we have

m = (0 + 7)/(-8 + 1)

This gives

m = -1

The equation of the line that passes through the points is then calculated as

y = m(x - x1) + y1

So, we have

y = -1(x + 8) + 0

This gives

y = -x - 8

Hence, the equation of the line that passes through the points is y = -x - 8

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The equivalent equation for the given equation is 2.3p - 10.1 =6.49p - 4. Therefore, option B is the correct answer.

Given that, 2.3p – 10.1 = 6.5p – 4 – 0.01p.

We need to find which equations have the same solution as the given equation.

Equivalent equations are algebraic equations that have identical solutions or roots. Adding or subtracting the same number or expression to both sides of an equation produces an equivalent equation. Multiplying or dividing both sides of an equation by the same non-zero number produces an equivalent equation.

Now, 2.3p - 10.1 = 6.5p - 4 - 0.01p can be simplified as follows:

To add or subtract terms of algebraic equations group like terms add numerals and keep the variables the same.

That is, 2.3p - 10.1 = (6.5p - 0.01p) - 4  

⇒2.3p - 10.1 =6.49p - 4

The equivalent equation for the given equation is 2.3p - 10.1 =6.49p - 4. Therefore, option B is the correct answer.

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It would take the assistant 20 hours to do the job alone.

From the information given, we have that;

Let the gardener be x

His assistant be y

So,

y = 1/ 5

x + y = 1/ 4

Substitute the value

x = 1/ 4 - 1/ 5

Find the LCM

x =  1 / 20

Take the reciprocal

x = 20 hours

Thus, it takes the assistant 20 hours to do the job alone.

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Calculating the numeric value of the given function, it is found that Rob will have $2,603.16 in his account in one year.

To find the numeric value of a function, we replace each instance of the variable by the desired value.

For this problem, the expression for the amount that he has into his account after w weeks is given by:

A(w) = 0.04w² + 45w + 155.

One year has 52 weeks, hence w = 52, and the amount is given finding the numeric value as follows:

A(52) = 0.04(52)² + 45(52) + 155 = $2,603.16.

Rob will have $2,603.16 in his account in one year.

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The expression -6/25: 5 2/5 is simplified to -30/675

Ratio can be defined as the comparison of two numbers or elements indicating their sizes in relation.

It is represented using the symbol ':'

Example;

The ratio of 3: 5 is written as 3/ 5

Given the expression;

-6/25: 5 2/5

Convert 5 2/5 into an improper fraction = 27/5

We have

-6/ 25 : 27/ 5

Take the ratio

- 6/ 25 ÷ 27/ 5

Take the inverse of the divisor and multiply

- 6/ 25 × 5/ 27

-30/675

Thus, the expression -6/25: 5 2/5 is simplified to -30/675

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Answer:

y=3 or just put 3

Step-by-step explanation:

After using distributive property we find the solution of 5 × 198 is 990.

What is Distributive property?

By the rule of distributive property, multiplying the sum of two or more addends by a number gives the same result as when each addend is multiplied individually by the number and the products are added together.

The expression is given as;

5 × 198

Now, By using distributive property we calculate as;

5 × 198 = 5 × ( 200 - 2 )

           = (5 × 200) - (5 × 2)

           = 1000 - 10

           = 990

Hence, After using distributive property we find the solution of 5 × 198 is 990.

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The largest integer is 0 (first option).

Integers are whole numbers. An integer is number that is not a fraction and not a decimal. Integers can either be positive, negative or zero. An example of an integer is 100, - 100 and 0.

An even number is a number that is divisible by 2 into two equal halves. An example is 2, 4, 6, 8. Consecutive even integers are whole even numbers that follow each other on the number line. An example is 2, 4, 6, 8.

If 0 is the largest number, the other three consecutive even integers would be : 0, -2, - 4, - 6. The sum of these numbers is -12.

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The correct answer would be "A. $2,075 = $1,500 + (.0575*s)" total sales.

A sale is a deal in which two or more parties trade products or services for cash or other assets, usually between a buyer and a seller. It is an agreement between a buyer and seller on the price of a security and the delivery of the security to the buyer in exchange for the agreed-upon compensation constitutes a sale in the financial markets. The transaction is not regarded as a sale if the product or service in issue is given by one party to the other without receiving payment, but rather as a gift or donation.

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Answer:

Wait, can you explain the answer choices, I don't understand them.

Step-by-step explanation:

The statement is false, a counterexample is given by using the numbers 1 and -1.

Here we have the statement:

"The sum of two numbers is always greater than their difference"

So we just need to find two numbers such that the statement is false.

This is really trivial, for example, we can propose the numbers 0 and 0.

The sum gives 0 + 0 = 0

The difference is 0 - 0 = 0

The sum is not greater than the difference.

Now, I will propose a less trivial counterexample, let's use the numbers 1 and -1.

The sum gives 1 + (-1) = 1 - 1 = 0

The difference gives: 1 - (-1) = 1 + 1 = 2

The difference is larger than the sum, so we found a counterexample for the given statement.

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the system of inequalities that represents the possible length in meters, l, and the possible width in meters, w, of the pool is given as w ≤ l - 10 and 2 l + 2 w > 62.

Let the length of the pool be x.

So, ATQ, the width will be represented by the inequality:

x - 10 ≥ width

w ≤ x - 10

w ≤ l - 10

Also, it is given that, the perimeter of the pool is more than 62 m
So, we get that:

P > 62

Also, we know that:

P = 2 l + 2 w

So, we get that:

2 l + 2 w > 62.

Therefore, the system of inequalities that represents the possible length in meters, l, and the possible width in meters, w, of the pool is given as w ≤ l - 10 and 2 l + 2 w > 62.

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Answer:

D

Step-by-step explanation:

i’m pretty sure

Answer: a. (0, -300), (1, -180), (2, -60), (7, 540)

b. T=120D-300

c. $28080

Step-by-step explanation:

a. T=120D-300 ==> per week

D=0: T=120(0)-300

D=0: T=-300 ==> (0, -300)

D=1: T=120(1)-300

D=1: T=120-300

D=1: T=-180 ==> (1, -180)

D=2: T=120(2)-300

D=2: T=240-300

D=2: T=-60 ==> (2, -60)

D=7: T=120(7)-300

D=7: T=840-300

D=7: T=540 ==> (7, 540)

b. T=120D-300

c. T=120(7)-300

T=840-300

T=$540 per week

1 year = 52 weeks

540*52=$28080

Rhode Island has a smaller population.

Here,

According to the 2010 census, the population of Nebraska was 1.8 × 106 people.

We have to find the smaller population.

What is Product?

The multiply of two or more number is called Product.

Now,

The population of Nebraska was 1.8 × 106 people.

1.8 x 106 = 190.8

And,

The population of California = 3.7 x 107 = 395.9

The population of Rhode Island = 1.1 x 106 = 116.6

The population of Texas = 2.5 x 107 = 267.5

The population of Missouri = 6 x 106 = 636

Hence, Rhode Island has a smaller population.

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