You downloaded a video game to your computer. You have a 60-minute free block of time for the game. It
takes 5 minutes to set up the game and 7 minutes to play each level of the game. Write an inequality to
determine the number of levels you can play in 60 minutes. How many levels can you play for free? Write an Inequality

Answer: [tex]f(1)=1, f(2)=0, f(3)=2[/tex]

Step-by-step explanation:

[tex]0 \leq 0 \leq 1 \implies f(1)=1^2 =1\\\\1 < 1 \leq 2 \implies f(2)=-2+2=0\\\\2 < 3 \leq 3 \implies f(3)=3^2 -3(3)+2=2[/tex]

The figure above is a rectangle

The classifications of a rectangle are:

1. A rectangle has 4 sides and angles, therefore, it is a quadrilateral.

2. Each interior angle is a right-angle, that is 90⁰

3. The sum of the interior angles equals 360

4. The opposite sides are parallel

5. The opposite sides are equal

6. The diagonals bisect each other

7. The diagonals have the same length

Step-by-step explanation:

ax2+2x3−24x+1=y

Step 2: Add -2x^3 to both sides.

ax2+2x3−24x+1+−2x3=y+−2x3

ax2−24x+1=−2x3+y

Step 3: Add 24x to both sides.

ax2−24x+1+24x=−2x3+y+24x

ax2+1=−2x3+24x+y

Step 4: Add -1 to both sides.

ax2+1+−1=−2x3+24x+y+−1

ax2=−2x3+24x+y−1

Step 5: Divide both sides by x^2.

ax2

x2

=

−2x3+24x+y−1

x2

a=

−2x3+24x+y−1

x2

Answer:

a=

−2x3+24x+y−1

x2

Answer:

(x² -5x +13) + (x² +3x -6)

Step-by-step explanation:

(x² -5x +13) + (x² +3x -6)

x² -5x +13 + x² +3x -6

|x² + x²| |-5x + 3x| |+13 -6|

2x² -2x +7

The current exchange rate is 1 US dollar = 1 euro.

The exchange rate of a currency is the worth of one currency in respect to another, or the rate at which one currency will be exchanged for another.

The foreign exchange market, commonly known as Forex or FX, is a global decentralized market for currency trading that determines the exchange rates of such currencies.

A currency exchange rate is the rate at which one currency can be exchanged for another. In other words, the exchange rate is the price of one currency in terms of another.

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The lengths of PA and PB are 3.1622 units if the point is P (0, 5).

The distance between two points is defined as the length of the line segment between two places representing their distance. Most significantly, segments that have the same length are referred to as congruent segments and the distance between two places is always positive.

The formula of the distance between two points exists P(x₁, y₁) and Q(x₂, y₂) is given by:

d (P, Q) = √ (x₂ – x₁)² + (y₂ – y₁) ².

The given points exists A(1, 2) and B(–3, 4).

The perpendicular bisector of AB will pass through the midpoint of AB.

Now the perpendicular bisector of AB will meet the Y-axis at P(0, y).

∴ AP = BP

Applying the distance formula, we get4

⇒ PA² = PB²

⇒ (x₁ – 0)² + (y₁ – y)² =  (x₂ – 0)² + (y₂ – y)²

⇒ (1 – 0)² + (2 – y)² =  (–3 – 0)² + (4 – y)²

After solving, we get y = 5

Therefore, the point is P (0, 5).

Now calculating the lengths of PA and PB

PA = √(1 – 0)² + (2 – 5)² = 3.1622

PB = √(-3 – 0)² + (4 – 5)² = 3.1622

Therefore, the lengths of PA and PB are 3.1622 units.

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The area of the region within the square and without the circle is equal to 13.7 square inches.

In this problem we find the case of figure generated by a square and an inscribed circle. Then, the area of the region is found by subtracting the area of the circle from the area of the square. Then, the area is:

A = L² - 0.25π · D²

Where:

If we know that D = L = 8 in, then the area of the region is:

A = (8 in)² - 0.25π · (8 in)²

A = 64 in² - 50.265 in²

A = 13.735 in²

The area of the region is equal to 13.7 square inches.

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1) Given that an oatmeal cookie has these proportions, let's set a pair of ratios to get that:

Answer:

2(x + 9)

Explanation:

Let x represent the unknown value.

Double a quantity increased 9 means;

*We'll multiply the quantity by 2

*Increased by signifies addition

*Quantity means we'll put the expression after it in brackets

Let's go ahead and write the required algebraic expression;

The solution for the given algebraic expression is 1.

Yes, there is. When you solve any Math Operations, it is necessary to be attentive to the order of the solution.

First, you should solve the operation insides of Parentheses. After that priority is given to Exponents. Thereon,  you can solve multiplication or division operations from left to right. Finally, addition or subtraction  from left to right

See the order below

The question gives:

9/10 x 5/2 -5/4

Following the order of operations:

        9/10 * 5/2 = 45/20

             [tex]\frac{45:5}{20:5} =\frac{9}{4}[/tex]

     9/4 - 5/4 = 4/4 =1

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The decimal figure that would be added to 1/5 to give 3/6 = 0.3

A decimal form is defined as the expression of figures that are more than a whole number with the use of decimal point.

Examples of figures that are in decimal form include the following: 0.2, 0.3, 0.4, 0.5, 1.2, 2.2,3.3 and 4.4.

To represent the given fractions in decimal form;

1/5 = 0.2

3/6 = 0.5

Therefore, X + 0.2 = 0.5

make X the subject of formula,

X = 0.5 - 0.2

X= 0.3

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the data are normally distributed with a mean of 74.674.6 hours and a standard deviation of 9.19.1 hours. So  10.2% of gadgets were powered by batteries for fewer than 63 hours.

Given that,

Data have a mean of 74.6 hours and a standard deviation of 9.1 hours, and they are regularly distributed.

The standard deviation is defined as ?

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.

[tex]p(X\leq 63) = p(Z\leq 63-74.6/9.1)[/tex]

From standard deviation,

         [tex]p(X\leq 63) = p(Z\leq -1.279)= 0.1061[/tex]

a certain percentage of gadgets have battery life of less than 63 hours.

X= 63 hours

Percentage of devices ran on the batteries for fewer than 63 hours = 10.2%

Therefore, 10.2% of electronic devices had battery life of less than 63 hours

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Answer:

each cube is 5 feet long because 5*5*5 = 125

Step-by-step explanation:

Given the graph, you can identify that x-axis represents the number of the corresponding month, and the y-axis represents the Number of Newspapers distributed (in hundreds).

You know these points:

Notice that 200 school newspapers were distributed in the second month, and 300 school newspapers were distributed in the fourth month. Therefore, you can conclude that the number of school newspapers that were distributed in the second month must be between 200 and 300. You can set up that, for:

The y-value is:

Hence, the answer is: Second option.

The number of 1/4 pound bags that can be filled with this amount of nails is 2 1/3 bags.

The large bag contains 7/12 pound of nails.

We also want to fill them into 1/4 pounds of bags. The number of bags needed will be calculated through division. This will be:

= Amount in large bags / Smaller bags

= 7/12 ÷ 1/4

= 7/12 × 4/1

= 28/12

= 2 1/3

Therefore, 2 1/3 1/4 bags are required

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The function translation / transformation rules:

Function transformations specify how a function is moved on a graph and how its shape is altered. Translation, dilatation, and reflection are the three main categories of function transformations.

The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation. In particular, the change of algebraic equations is a typical kind of algebraic problem.

The function translation / transformation rules:

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Answer:

$134.50

Step-by-step explanation:

4200 x .035 = 134.50

3.5% Percent means per 100

3.5/100 when you divide by 100, you move the decimal two places to the left.

The commission amount is $147

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Mr. Webster sells vacation rentals and earns a 3.5% commission on every vacation rental he sells.

He sold $4200.

So, 3.5% of commission:

4200 x 3.5  / 100

= 147

Therefore, the commission is $147.

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At this rate, Tommy will earn $211.2 working for 12 hours.

The Unitary Method draws a relation between given data. Following the regular trend, information can be calculated. It is also called the 'Mango Method'.

At this rate, Tommy will earn $211.2 working for 12 hours.

The Unitary Method is only valid for regular increases or decreases. Information about unity is drawn from given data, which is multiplied as required. It is widely used in the calculation of prices, amounts, etc.

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Answer:

6.25 weeks

Step-by-step explanation:

Take 18.75 ÷ 3. The construction crew finishes 3 km per week. You should receive 6.25 by solving the equation. So, this is the answer.

We will have the following:

First, we can see that the probability of picking an even number at first is:

And then, the probability of picking another even card without replacing the previous one will be:

Now, the probability of this happening one after the other will be:

So, the probability will be of 20%.

In the two triangles FIH and GHI

IH is a common side

FI = GH

The angles are between the equal sides

Then the two triangles are congruent by SAS postulate

The answer is A

The value of a³b for the value of a=3 and b=-5-2i is -135-54i for the given complex number that defines "Complex numbers are the numbers that are expressed in the form of a+ib where, a, b are real numbers and 'i' is an imaginary number called “iota”."

Complex numbers are those that are expressed as a+ib, where a and b are real numbers and I is a fictitious number called a "iota." I has the value (√-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Re) and the imaginary number 3i (Im). In the 19th century, the term "complex numbers"—which denotes that they have both real and imaginary components—became widely used. Occasionally, the term "imaginary number" is used to describe a complex number that is not real or, more commonly, a number whose real part is zero (a.k.a "pure imaginary").

Here,

The value of a³b

=3³(-5-2i)

=27(-5-2i)

=-135-54i

For the given complex number that defines "Complex numbers are the numbers that are expressed in the form of a+ib where, a, b are real numbers and I is an imaginary number called "iota," the value of a³b is -135-54i.

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The domain of the given function given range is {1.25, -0.25, 1.25, 4.75}

The range of values that we are permitted to enter into our function is known as the domain of a function.

The x values for a function like f(x) make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of value.

Given the range of the function as {-5, -3, 0, 7}

Determine the domain from the function 4x - 2y = 5

4x - 2y = 5

4x - 2(-5) =5

4x + 10 = 5

4x = 5

x = 5/4 = 1.25

If y = -3

4x - 2y = 5

4x - 2(-3) =5

4x + 6 = 5

4x = -1

x = -1/4 = -0.25

If y = 0

4x - 2(0) =5

4x - 0 = 5

4x = 5

x = 5/4 = 1.25

If x = 7;

4x - 2y = 5

4x - 2(7) =5

4x - 14 = 5

4x = 19

x = 19/4 = 4.75

Therefore the equivalent domain of the function is {1.25, -0.25, 1.25, 4.75}

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Answer:

slope = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

3x + y = 8  ( subtract 3x from both sides )

y = - 3x + 8 ← in slope- intercept form

with slope m = - 3

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex]

The equation that passes through (-12, 15 with a slope of -1 in point slope form is y - 15 = - 1(x + 12)

Linear equation can be represented in different form such as point slope form, slope intercept form  and standard form.

Therefore, let's represent the line that passes through (-12, 15) with a slope of -1 in point slope form.

Hence,

y - y₁ = m(x - x₁)

where

Therefore,

m = slope = -1

using (-12, 15)

Hence,

y - 15 = - 1(x - (-12))

Therefore,

y - 15 = - 1(x + 12)

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Answer:

30 units

Step-by-step explanation:

point D is the midpoint of the bottom line, and we can infer 2 similar triangles from the markings on the triangle,

15  × 2  =ab

as CD is in the middle of the large triangle, the scale factor from the small triangle to the large triangle is 2.

Using the Pythagorean Theorem, it is found that:

A. The straight line distance between the school and the fire station is of 4.62 miles.

B. The distance between the school and the hospital is of 2.08 miles.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following rule:

[tex]h^2 = l_1^2 + l_2^2[/tex]

In the context of this problem, the distance between the school and the fire station is the hypotenuse of a right triangle with sides 4.3 and 1.7, hence:

d² = 4.3² + 1.7²

d = sqrt(4.3² + 1.7²)

d = 4.62 miles.

The hospital is 3.1 miles west of the fire station, hence the distance between the school and the hospital is the hypotenuse of a right triangle of sides 1.7 and 4.3 - 3.1 = 1.2, hence:

d² = 1.2² + 1.7²

d = sqrt(1.2² + 1.7²)

d = 2.08 miles.

The complete problem is given by the image at the end of the answer.

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Answer:

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

Step-by-step explanation:

[tex]\frac{6}{\sqrt{3} }[/tex]  They do not want a radical in the denominator.  So you need to multiple the numerators and the denominator by [tex]\sqrt{3}[/tex]

[tex]\frac{6}{\sqrt{3} }[/tex]  x  [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]  = [tex]\frac{6\sqrt{3} }{3}[/tex] = 2[tex]\sqrt{3}[/tex]

[tex] \frac{6}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } = \frac{6 \sqrt{3} }{3} = 2 \sqrt{3} [/tex]

hope it will work