Lisa is four years younger than her sister. Which expression below stands for the sum of Lisa’s age and her sister’s age? (if you see this question pls answer) ty!

None of these
(x − 4) − x
x − (x − 4)
(x + 4) − x

Answer:

[tex]x > \frac{2(5 + 2y)}{5} \\ \\ x < \frac{2y - 7}{3} [/tex]

Step-by-step explanation:

[tex]1. \: 5x > 10 + 4y \\ 2. \: x > \frac{10 + 4y}{5} \\ 3. \: x > \frac{2(5 + 2y)}{5} \\ \\ \\ 1. \: 3x < - 7 + 2y \\ 2. \: 3x < 2y - 7 \\ 3. \: x < \frac{2y - 7}{3} [/tex]

In mathematics, an inverse function is one that "reverses" another function. The inverse of the function f(x) = (x+1)² is √x−1.

The inverse function of a function f in mathematics exists a function that reverses the operation of f. If the inverse of f exists, it is shown by the f⁻¹. The inverse of f exists if and only if f is bijective.

An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f ⁻¹.

If we restrict the domain to [−1,∞), then this new function has an inverse:

g(x) = (x+1)² with x ≥ −1

y = (x+1)²

if and only if

x+1 = √y (We do not need ±√y because of the restriction on x.)

x = √y−1

g−1(x) = −√x−1

If we restrict the domain to (−∞, −1], we get

h(x) = (x+1)² with x≤−1

y = (x+1)²

if and only if

x+1 = −√y (We need only −√y because of the restriction on x.)

x = −√y−1

h − 1(x) = √x−1

The inverse of the function f(x) = (x+1)² is √x−1.

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The subtraction of the expression 10√27 - 4√12 is 22√3.

Combining things and counting them as one big group is done through addition. In math, addition is the process of adding two or more integers together.

In mathematics, subtraction involves removing anything from a group or a number of objects. What is left in the group gets smaller when you subtract.

Consider the expression,

y = 3√20x + 8√45x - 4√5x

Now, the number in the root can also be written as:

20 = 2 × 2 × 5

45 = 5 × 3 × 3

Therefore,

y = 3√20x + 8√45x - 4√5x

y = 3( √[2 × 2 × 5] )x + 8( √[5 × 3 × 3] )x - 4√5x

y = 3 × 2√5x + 8 × 3√5x - 4√5x

y = √5x ( 3 × 2 + 8 × 3 - 4 )

y = √5x ( 6 + 24 - 4 )

y = 26√5x

The value of the expression 3√20x + 8√45x -4√5x is 26√5x.

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The width of the box whose height is given as 7 inches and length is three inches more than the width given a volume of 910 is; 10 inches.

It follows from the task content that the height of the box is; 7 inches.

Let, x = width of the box and;

x+ 3 = length of the box.

Therefore, since the volume of a box is given by the formula;

V = l × b × h

Therefore, we have;

910 = 7 (x) (x+3)

Divide both sides by; 7

130 = x² + 3x

x² + 3x -130 = 0.

(x+13) (x-10) = 0

Therefore, x = -13 or x = 10.

Ultimately, the possible values of the width are; -13 or 10.

Since the width cannot be a negative number, it follows that the width of the box in discuss is; 10 inches.

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The length of skid marks of a car that is going 65 miles per hour is approximately equal to 211 feet.

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

In this scenario, the formula (expression) which is being used by this investigator is given by:

S = 2√(5L)

Where:

Making L the subject of formula, we have:

S²/4 = 5L

L = S²/20

Substituting the given parameters into the formula, we have;

L = 65²/20

L = 4,225/20

Length of skid marks, L = 211.25 ≈ 211 feet.

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The total amount of coal delivered in these two months is equal to 6.35 tons.

A conversion factor can be defined as a number that is typically used to convert (change) a number in one (1) set of units to another, either by dividing or multiplying.

Generally speaking, an appropriate conversion factor to an equal value must be used when it is necessary to perform any mathematical conversion.

Conversion:

1 lbs = 0.0005 tons

1500 lbs = 0.75 tons

1200 lbs = 0.6 tons.

Now, we can determine the total amount of coal delivered in these two months:

Total amount of coal = 3 tons + 0.75 tons + 2 tons + 0.6 tons

Total amount of coal = 6.35 tons.

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Answer: the correct answer is B.0. Step-by-step explanation: there is no value for x.

The $53 money they spend on equipment if the group of friends was working on a student film that had a budget of $900. They used 53% of their budget on equipment.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

A group of friends was working on a student film that had a budget of $900. They used 53% of their budget on equipment.

The money spend on equipment = 53% of $900

The money spend on equipment = (53/100)900

= 0.53x100

= $53

Thus, the $53 money they spend on equipment if the group of friends was working on a student film that had a budget of $900. They used 53% of their budget on equipment.

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The slope of the line is equal to 1 and a point lying on the line with the given equation is (7, 3).

The equation of the line is given as y + 3 = x + 7. First, we write the equation of the line in proper form. It can be written in slope-intercept form as y = mx + c where m is known as the slope of the line and c is the intercept made by the line.

Now, according to the equation given in question.

y = x + 7 - 3

y = x + 4

If we compare this equation with the slope-intercept form of line, we get the slope equal to one.

y = mx + c

y = x + 4

=> m = 1 and c = 4.

A point which satisfies the equation y = x + 4 can be (7, 3) as

7 = 3 + 4

=> 7 = 7 (L.H.S. = R.H.S.)

Thus, slope of the line is equal to 1 and a point lying on the line with the given equation is (7, 3).

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Answer:

BRO I TRIED THIS BEFORE

YOU JUST NEED TO SEARCH IT IN gogle

Answer:

d=12.5

hope this helps :)

Using sine formula, the seat on a Ferris wheel is 50√3 feet closer to the ground after rotating 60°.

One of the 6 trigonometric functions is the sine function. Sine function can be described as the ratio of the length of the opposite side of the triangle to its hypotenuse.

sin x = (opposite side) / (hypotenuse)

where "opposite side" is the length of the side opposite to angle x

If the wheel rotates 60°, causing the height of the seat to decrease, using sin formula, solve for the vertical distance between the positions before and after the rotation.

sin x° = (opposite side) / (hypotenuse)

where x = 60

opposite side = vertical distance between the positions before and after the rotation

hypotenuse = radius = 200 feet/2 = 100 feet

sin 60° = opposite side / 100 feet

opposite side = 50√3 feet

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Answer:

[tex]8.50h = 6.50h + 15[/tex]

The unit price is $2.5

34 mile taxi ride will cost $85

18 mile taxi ride costs $7.20

The cost of 1 mile is

= 18/7.20

= 2.5

The unit price is $2.5 for 1 mile

The cost of 34 mile taxi ride can be calculated as follows

= 2.5 × 34

= 85

Hence the 34 mile taxi ride will cost $85

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Answer:

the slope would be -3 because it takes the place of the m in y=mx+b

Step-by-step explanation:

The machine will display the digit 71 if she pressed a 77 number.

According to the statement

We have to find that the digit shown by the machine.

So, For this purpose, we know that the

Digits are the single numbers used to represent values in math

From the given information:

At the fair, Kate found a strange machine with a sign on it labeled, "Enter a number. When she pushed the number 15, the machine displayed 9. When she entered 23, the machine displayed 17. Perplexed, she tried 100, and the machine displayed 94.

From this

we find that the machine displayed a number after subtracting 6 from the pressing digit in the machine.

For example, When she pushed the number 15, the machine displayed 9.

Displaying digit = 15-9

6 = 6.

If she pressed a 77 number then machine will display

77 -6 = 71.

So, The machine will display the digit 71 if she pressed a 77 number.

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The value of g (7) is 16.

What is Piecewise function?

A piecewise function is a function which built from pieces of different functions over different intervals.

The given function is;

g (x) = x² - 5             , x ∈ (-∞, -7)

      = 9x - 17            , x ∈ [-7, 2]

      = (x + 1) (x - 5)    , x ∈ (2, ∞)

Now, Find the value of g (7) as;

Since, Number 7 is belong in interval (2, ∞).

Hence, To find the value of g (7) we use the function,

g (x) = (x + 1) (x - 5)    , x ∈ (2, ∞)

Substitute x = 7 we get;

g (x) = (7 + 1) (7 - 5)

g (7) = 8 * 2

g (7) = 16

Hence, The value of g (7) is 16.

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Answer:

A) 3.5

Step-by-step explanation:

                4.3t + 6.8 = 8.4t - 7.55

         Subtract 8.4t from both sides,

              4.3t - 8.4t +6.8 = -7.55

        Combine like terms,

                      -4.1t  + 6.8 = -7.55

                  To isolate 't' first subtract 6.8 from both sides.

                   -4.1t  = -7.55 - 6.8

                   -4.1t  = -14.35

                Divide both sides by (-4.1)

                      t = -14.35 ÷ (-4.1)

                      t =  3.5

Answer:

3√2

Step-by-step explanation:

Square root of 18 is equal to 3√2 in radical form and 4.24264068712 in decimal form.

Answer:

Hope this helps!

The length of TO is 6.66  and of BO is 3.32

In the problem we are given that BT=10 TO=2x amd BO=4x-10

We have to find the value of x in order to find the values of length of  BO and TO.

BT=BO+TO

4x-10+2x=10

6x=20

x=3.33

The length of TO is 6.66

and of BO is 3.32

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Answer:

10

Step-by-step explanation:

substitute the given values into the expression

ab + c

= 2(3) + 4

= 6 + 4 = 10

Hey there!

ab + c

= 2(3) + 4

= 6 + 4

= 10

Therefore, your answer should be:

10

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

A recipe uses 2 cups of milk to make 6 servings. If the same amount of milk is used for each serving, Two gallons of milk will make 192 servings

Given data

2 cups of milk to make 6 servings.

Assuming

1 gallon 4 quarts

1 quart 2 pints

1 pint 2 cups

1 cup = 8 fluid ounces

if 1 quart 2 pints, then 4 quarts will be

= 4 * 2 = 8 pints

if 1 pint 2 cups, then 8 pints will be

= 8 * 2 = 16 cups

if 1 gallon is 16 cups, the 2 gallons will be

= 16 * 2 = 32 cups

If 1 cup is 6 servings, then 32 cups will be

= 32 * 6 = 192 servings

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When the result of subtracting 13 from the sum of two consecutive numbers is 18. The numbers are 15 and 16. The correct option is d.

From the information, the result of subtracting 13 from the sum of two consecutive numbers is 18.

Let the numbers be x and x+1.

Therefore, (x + x + 1) - 13 = 18

2x + 1 - 13 = 18

2x - 12 = 18

2x = 18 + 12

2x = 30

Divide

x = 30/2

x = 15

Therefore, when the result of subtracting 13 from the sum of two consecutive numbers is 18. The numbers are 15 and 16. The correct option is d.

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The acceleration of the bicyclist is 6.83 m/s².

The given parameters;

Initial velocity of the bicycle (u) = 21 m/s

Distance travel by the bicycle (s) = 32.3 m

We have to find the acceleration of the bicyclist.

How to calculate the acceleration?

If the initial velocity is u, final velocity is v and distance travel by object is s then we can calculate acceleration as;

v² = u² + 2as

Initial velocity of the bicycle (u) = 21 m/s

Distance travel by the bicycle (s) = 32.3 m

Final velocity of the bicycle (v) = 0

Hence, The acceleration of the bicycle is calculated as follows;

v² = u² + 2as

Where, v is the final velocity of the bicycle.

0 = u² + 2as

2as = - u²

a =  - u²/2s

a = - (21)²/2*32.3

a = - (21)²/64.6

a = -441/64.6

a = -6.83

| a | = 6.83 m/s²

The acceleration of the bicyclist is 6.83 m/s².

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The required answer for the given expression is 0.

Simplification generally means finding an answer for the complex calculation that may involve numbers on division, multiplication, square roots, cube  roots, plus and minus.

Now the given expression is,

|8-40/4^3| 4^2 - 8

Solving the mod first,

Since 4^3 = 64 ; 4^2 = 16,

and 8 - 40 = -32

Therefore,

|8-40/4^3| 4^2 - 8 = |-32/64|16 - 8

Now solving

⇒ 32/64 = 1/2

Therefore we get,

|8-40/4^3| 4^2 - 8 = |-31/2| 16 - 8

Now since, |-a| = a

therefore, |-1/2| = 1/2

Therefore we get,

|8-40/4^3| 4^2 - 8 = (1/2) 16 - 8

Now, since (1/2) 16 = 8

Therefore we get

|8-40/4^3| 4^2 - 8 = 8 - 8

solving we get,

|8-40/4^3| 4^2 - 8 = 0

this is the required answer for the given expression.

Thus, the required answer for the given expression is 0.

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Answer: 2

Step-by-step explanation:

4x-2y=6

Divide both parts of the equation by 2:

2x-y=3

2x-y+y=3+y

2x=3+y

2x-3=3+y-3

2x-3=y

y=2x-3

Answer:

[tex]\frac{\sqrt{3}}{2}[/tex]

Step-by-step explanation:

Sine is positive in the second quadrant, so:

[tex]\sin \frac{240^{\circ}}{2}=\sqrt{\frac{1-\cos 240^{\circ}}{2}} \\ \\ =\sqrt{\frac{1.5}{2}} \\ \\ =\sqrt{3/4} \\ \\ =\frac{\sqrt{3}}{2}[/tex]

The function according to the rigid transformation g(k + 3) = - 4 · f(k + 3), where f(x) = x² - x - 1, is equal to the quadratic equation g(k + 3) = - 4 · k² - 20 · k - 44.

In this problem we find the definition of a quadratic equation and besides we are asked to find the result of horizontal translation, a reflection about the x-axis and a dilation, all of them rigid transformations. In other words, we must look for the resulting expression according to this definition:

g(k + 3) = - 4 · f(k + 3)

g(k + 3) = - 4 · [(k + 3)² - (k + 3) - 1]

g(k + 3) = - 4 · [(k² + 6 · k + 9) - (k + 3) - 1]

g(k + 3) = - 4 · (k² + 5 · k + 11)

g(k + 3) = - 4 · k² - 20 · k - 44

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