Find each sum or difference. Write the result in standard form.

(2.7m^2 - 3.1n) - (4n^2 + 5.1m)

The graph of the system of linear equations is shown in the image below, where the solution is: (3, 1)

The coordinates where x - 2y = 1 intersects the x-axis (horizontal axis) is: (-14, 0)

Given the linear equations:

5x – y = 14 ---> equation 1

x – 2y = 1 ---> equation 2

Rewrite both equations in slope-intercept form as y = mx + b, where b represents the y-intercept of the line and m represents the slope.

5x - y = 14

-y = -5x + 14

y = 5x - 14 (slope is 5 and y-intercept is -14)

x - 2y = 1

-2y = -x + 1

y = 1/2x - 1/2 (slope is 1/2, and the y-intercept is -1/2).

Therefore, the graph of the system of linear equations is shown in the image below, where the solution is: (3, 1)

The coordinates where x - 2y = 1 intersects the x-axis (horizontal axis) is: (-14, 0)

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Answer:5/2 and 2 1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

2.5 as a mixed number is 2 1/2 since 1/2 = 0.5

2.5 as an improper fraction is 5/2

Answer:

2

Step-by-step explanation:

Triangle side theorem states the sum of the lengths of any two sides of a triangle must be greater than the remaining side

3 + 2 = 5     third side would have to be LESS than 5

            so the only answer is 2 cm

The resulting product of the expression is 13 1/8

Fractions are written as a ratio of two integers

Given the following expression

-4 1/6 * -3 15/100

Convert to improper fraction to have:

-25/6 * -315/100

-1/6 * -315/4

315/24

13 1/8

Hence the resulting product of the expression is 13 1/8

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Answer:

I´m pretty sure it is 1.8 miles

Step-by-step explanation:

The inverse of a function when x = -1 is g^-1(-1) = -5/2

Linear functions are function that has a leading degree of 1. Given the expression below;

g(x) = 2x + 4

Determine the inverse

y = 2x + 4

Replace y with x

x = 2y + 4

Make y the subject of the formula

2y = x - 4

y = (x-4)/2

g^-1(x) = (x-4)/2

Substitute x = -1 into the equation

g^-1(x) = (-1-4)/2

g^-1(-1) = -5/2

Hence the inverse of a function when x = -1 is g^-1(-1) = -5/2

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The number of tacos that is needed for 3 students is 8 tacos.

The first step is to determine the number of tacos that is needed for one student. To determine this value, divide the total number of tacos by the total number of students.

Division is the mathematical operation that is used to determine the quotient of two or more numbers. Division entails splitting a number into equal groups using another number. The sign used to denote division is ÷

Tacos that should be prepared for one student = total tacos / number of students

= 40 / 15

In order to determine the number of tacos needed for 3 students, multiply the result gotten in the previous step by 3. Multiplication is the process used in determining the product of two or more numbers. The sign used to denote multiplication is x .

Tacos needed for 3 students = (40 / 15) x 3 = 8

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The height of the water tower is found to be 54.66 meters.

A free-falling object is one that is falling solely due to gravity.

Some key features regarding the acceleration due to gravity are-

Now, according to the question;

It takes a watermelon 3.34 sec to reach the ground.

Use the equation of motion in straight line.

D  =  (1/2) x (gravity) x (time)²

D is the height of the water tower.

    =  (1/2) x (9.8 m/s²) x (3.34 sec)²

   =   (4.9 m/s²)  x  (11.16 sec²)

D = 54.66 meters.

Thus, the height of the water tower is estimated as 54.66 meters.

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Answer:

y = 2/3x - 8/3

or 2x = 3y + 8

Step-by-step explanation:

2x = 3y + 4

3y = 2x - 4

y = 2/3x - 4/3

If two lines are parallel, their slopes are equal

if m = 2/3, y = -2, x = 1

y = mx + b

-2 = 2/3(1) + b

-2 = 2/3 + b

b = -2 - 2/3 = -8/3

y = 2/3x - 8/3

or 3y = 2x - 8

or 2x = 3y + 8

The table that represents the linear function is table (B)

As a general rule, a linear function is any function that has a constant rate of change

This means that as the function independent value changes by a constant, the function dependent value changes by a constant

In other words, as the function x value changes by a constant, the function y value changes by a constant

Using the above as a guide, we can see the table B represents a linear function

This is so because, as x increases by 3, the y value decrease by -2

Hence, the table that represents the linear function is table (B)

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The proof of the inequality → (a + b)²/2 ≥ 2ab, is given below -

We have the following inequality -

(a + b)²/2 ≥ 2ab

We have to prove it.

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

According to the question, we have -

Inequality -

(a + b)²/2 ≥ 2ab

Proof -

Starting from the inequality - (a - b)² ≥ 0

(a - b)² ≥ 0

a² + b² - 2ab ≥ 0

a² + b² - 2ab + 2ab ≥ 2ab

a² + b² ≥ 2ab

Add - 2ab on both sides, we get -

a² + b² + 2ab ≥ 4ab

(a + b)² ≥ 4ab

Divide both sides by 2, we get -

(a + b)²/2 ≥ 2ab

Hence Proved.

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The inequality form of the given expression is:

x < -8 or x > 0

The interval notation is : (−∞,−8)∪(0,∞)

Given, the expression is |x + 4| - 4 > 0

An inequality is a relationship that shows a non-equal comparison between two numbers or mathematical expressions.

Isolate the variable by dividing each side by factors that don't contain the variable.

⇒  |x + 4| - 4 > 0

⇒  |x + 4|  > -4

Remove mod.

⇒ x + 4 > -4 or  x - 4 > -4

⇒ x > -4 -4 or x > -4 +4

⇒ x <-8 or x > 0

Hence the internal notation is :

(−∞,−8)∪(0,∞)

The required graph is plotted.

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Answer:

17/-11

Step-by-step explanation:

why,because reciprocal in mathematics means changing the numerator to the denominator and denominator to numerator.

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Answer:

b = 0.5

Step-by-step explanation:

a = b x h

7 = 14b  Divide both sides by 14

0.5 = b

The inverse of the function → y= f(x) = 1/7x - 1/7​ is -

f⁻¹(x) = 7x + 1.

We have -

y = f(x) = x/7 - 1/7

We have to find its inverse function.

Inverse of a function can be calculated by following the steps mentioned below -

Step 1 -  Replace 'y' with 'x' and vice - versa.

Step 2 - Rewrite the equation by solving for 'y'.

Step 3 - Replace 'y' with f⁻¹(x).

According to the question, the equation given is as follows

y = f(x) = x/7 - 1/7

Replace 'y' with 'x', we get -

x = y/7 - 1/7

Now, solve for y -

y/7 = x + 1/7

y = 7(x + 1/7)

y = 7x + 1

Replace 'y' with f⁻¹(x) -

f⁻¹(x) = 7x + 1

Hence, the inverse of the function → f(x) = 1/7x - 1/7 is -

f⁻¹(x) = 7x + 1.

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A clockwise 360 degrees angle rotation will make the figure rotate onto themselves.

Any angle rotations other than a 0 degree or a 360 degree will change the figure and so does not rotate onto themselves.

To rotate onto themselves, which means the figure should not be changed after the rotation transformation, we have to rotate it 360 degrees.

We are asked for a clockwise angle rotation, so the require angle rotation is of 360 degrees.

0 degree angle rotation will not make a rotation. So we will go with a 360 degree rotation. Any figure after a 'full circle' clockwise rotation will goes onto themselves.

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d. 15p + 100 = 30p + 75

Tim owns 74 socks, the colours of which are unknown.

He does, however, have an additional pair that is white rather than black.

Therefore, it suggests that we are working with the two hues white and black.

The result of dividing the total number of socks by two is:

= 74/2

= 37 socks, two pairs each for black and white.

But let's not forget that Tim has a pair of white socks in addition to his black pair.

The total number of white socks is equal to= 37+1= 38 socks.

Total black sock pairs= 37-1=36 socks.

Last but not least, the question asks us to count the number of single socks rather than pairs.

For white then:

There will be = (38x 2) socks per pair.

= 76 socks

For Black

The individual socks will be = (36 × 2)socks

= 72 socks

We can then deduce that there are 76 individual socks for white and 72 individual socks for black.

The solution would have to be four. Despite the large number of socks in the drawer, there are only three different colours, so if you take four socks, you will undoubtedly find at least one pair that matches.

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The length of a right triangle's hypotenuse with a theorem created long ago is c² = a² + b², where 'c' = the hypotenuse of the right triangle and 'a' and 'b' are the other two legs.

We need to find the length of a right triangle's hypotenuse with a theorem created long ago.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

The Pythagoras theorem equation is expressed as, c² = a² + b², where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs. Hence, any triangle with one angle equal to 90 degrees produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.

Therefore, the length of a right triangle's hypotenuse with a theorem created long ago is c² = a² + b², where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs.

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Answer: 1

I did this problem a couple times and got 1 every time

Answer:

-3/5, -1/10, -0.8, 0.3, 1/2, 5/8

Step-by-step explanation:

negatives are always less than positive numbers. As you can see the first numbers that are negative count down and then once it turns positive the numbers count up. For example, it goes -3,-1,-0 then 0,1,5

Answer:

The difference would be Unionville would have had 24.6 in. of rain and Arges only had 8.1 in

Step-by-step explanation:

Answer:

120% = 162

10% = 13.5

100% = 135

so it's £135

hope this works :)

Answer:

33.7

Step-by-step explanation:

Complementary angles are angles that when added, sum up to 90*

First, make the equation, x being the missing angle
90*= x + 56.3

Rewrite the equation to find the missing angle
90 - 56.3 = x

x= 33.7

Answer:33.7°

Step-by-step explanation:

To find the complement of an angle, subtract that angle's measurement from 90 degrees. The result will be the complement

90° - 56.3°

=33.7°

Answer:

8 significant digits

Step-by-step explanation:

Let's count

6040.0050

⬇ ⬇⬇⬇.⬇ ⬇⬇ ⬇

1 234 567 8

therefore it's 8 significant figures

Using translation concepts, the graph that shows that function f(x) = x with an input of f(x - 3) is given by:

A coordinate plane with a line passing through (negative 2, negative 5), (0, negative 3), and (3, 0).

The input of the function, of f(x - 3), is missing.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For this problem, the function is:

f(x) = x.

The translation is in the input, f(x - 3), meaning that the function is shifted 3 units right and defined by:

f(x - 3) = x - 3.

Hence three points on the graph are:

Hence the correct description is:

A coordinate plane with a line passing through (negative 2, negative 5), (0, negative 3), and (3, 0).

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Answer:

D

Step-by-step explanation:

Answer:

698,000

Step-by-step explanation:

7×10^5=700000

2×10^3=2000

700,000-2000=698,000

The given 7 * [tex]10^5[/tex] is 3.5*10² times larger than 2 * 10³.

Given that,

To determine, how many times larger is 7 x 10^5 than 2 x 10^3.

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
We have two values, here we have to determine the relationship between the two values.

[tex]ratio = 7*10^5 / 2 * 10^3\\Ratio = 3.5 * 10 ^2[/tex]
Implies,
[tex]7*10^5 = 3.5*10^2 (2 * 10^3)[/tex]

Thus, the given 7 * [tex]10^5[/tex] is 3.5*10² times larger than 2 * 10³.

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Based on the information given, the value of x is 40 degrees

Corresponding angles are defined as any pair of angles which on the same side of one or two lines, there is a  cut through by a transversal.

It is also important to note that when a transversal intersects two parallel lines, the corresponding angles of the lines would be equal.

Given the angles;

We have that;

Angle 2 = Angle 3

Substitute the values

2x + 5 = 85

collect like terms

2x = 85 - 5

2x = 80

Make 'x' the subject by dividing both sides by 2

2x/ 2 = 80/ 2

x = 40 degrees

Thus, the value of x is 40 degrees

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Answer:

36 = 2 x 2 x 3 x 3

Answer:

2 2/3 * 2 2/3 = 64/9 = 7 1/9 ≅ 7.1111111

Step-by-step explanation:

The result:

2 2/3 * 2 2/3 = 64/

9

= 7 1/

9

≅ 7.1111111

Spelled result in words is sixty-four ninths (or seven and one ninth).

How do we solve fractions step by step?

Conversion a mixed number 2 2/

3

to a improper fraction: 2 2/3 = 2 2/

3

= 2 · 3 + 2/

3

= 6 + 2/

3

= 8/

3

To find a new numerator:

a) Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/

3

= 6/

3

b) Add the answer from previous step 6 to the numerator 2. New numerator is 6 + 2 = 8

c) Write a previous answer (new numerator 8) over the denominator 3.

Two and two thirds is eight thirds

Multiple: 8/

3

* 8/

3

= 8 · 8/

3 · 3

= 64/

9

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(64, 9) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - eight thirds multiplied by eight thirds is sixty-four ninths.

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