Graph the inequality.
y < −x + 3

Answer:

Domain of the function:

In interval notation: [6, ∞)

In set notation: {x: x∈R, x≥6}

Step-by-step explanation:

Remember that the the domain of the square root function are all the values such is is bigger than zero. We can express the later in set notation: {x: x∈R, x≥0}, or in interval notation: [0, ∞)

This is because the square root is not defined, in the real numbers, for negative values.

So, to find the domain of our function, we just need to set the thing inside the radical grater or equal than zero and solve for x:

The domain of the function is all the numbers bigger than 6, including 6.

Domain of the function: x will have values greater than or equal to 6 .

In interval notation: [6, ∞)

In set notation: {x: x∈R, x≥6}

Given, that function y = 2√x-6

Domain of the square root function are all the values which is greater than zero.

Express the later in set notation:

{x: x ∈ R, x≥0},

Interval notation: [0, ∞)

This is because the square root is not defined, in the real numbers, for negative values.

Domain of function y,

[tex]y= 2\sqrt{x-6}[/tex]

[tex]x-6\geq 0 \\x\geq 6[/tex]

The domain of the function is all the numbers greater than 6, including 6. Thus domain of function : [6, ∞) .

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If a right triangular prism's height is 1 inch. The produced solid has the following surface area: = 2,930.05 in².

A polyhedron with six vertices, nine edges, and five faces is a right triangular prism. Regular prisms have all of their triangles faces equilateral. The prism's rectangular faces will be congruent in this situation.

A triangular prism's total surface area is the sum of the areas of its three lateral faces (rectangles) as well as two bases (triangles). For something like the surface area of any prism, the most generic formula is:

Given:

Hight = 1 inches

Base of the prism = 10 inches.

The Hight if the base = 82 inches.

Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)

Surface area = 5(10× 10) + (0.5÷ 10 × 1) + 3(10× 82)

Surface area = 5(100) +0.05+ 3(810)

Surface area = 500 +0.05 + 2430

Surface area = 2,930.05 in²

The produced solid has a surface area of approximately = 2,930.05 in².

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System of liner equation [tex]x+3y-z=2[/tex],[tex]x+y-z=0[/tex] and [tex]3x+2y-3z=-1[/tex] has no solution.

What do you mean by system of linear equation?

A set of two linear equations with two variables is a system of linear equations.

Given:

[tex]x+3y-z=2[/tex]           ---1

[tex]x+y-z=0[/tex]             ---2

[tex]3x+2y-3z=-1[/tex]     ---3

Rearranging the equation 2

[tex]z=x+y[/tex]   ---4

Putting equation 4 in equation 1

⇒ [tex]x+3y-(x+y)=2[/tex]

⇒ [tex]x+3y-x-y=2[/tex]

⇒ [tex]2y=2[/tex]

⇒ [tex]y=1[/tex]

Putting equation 4 in equation 3

⇒ [tex]3x+2y-3(x+y)=-1[/tex]

⇒ [tex]3x+2y-3x-3y=-1[/tex]

⇒ [tex]-1y=-1[/tex]

⇒ [tex]y=1[/tex]

Putting value of y above

⇒ [tex]1=1[/tex]

Therefore, system of liner equation has no solution.

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Answer:

Deandre spent $36.50 on video games and DVD rentals in the past month.

Step-by-step explanation:

values

video game = $3.20

DVD = $4.90

let video games be represented with the variable v

dvd represented by the variable d

make an equation

7d + 1v = ?

plug in values

7(4.90) + 1(3.20) = ?

7 x 4.90 = 34.3

1 x 3.20 = 3.20

34.3 + 3.20 = 36.50

thus 7d + 1v = $36.50

The solution to the linear equations in three variable are x = 5, y = -11, and z = 3.

It is defined as the relation between three variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The three linear equations:

2x - y + 4z = 33  ..(i)

x + 2y - 3z = -26 ...(ii)

-5x - 3y + 5z = 23 ...(iii)

After solving the above linear equation by elimination method:

From the equation (i):

[tex]x=\dfrac{33+y-4z}{2}[/tex]  ....(iv)

Plug the above value in the equation (ii) and (iii)

[tex]\rm \dfrac{33+y-4z}{2}+2y-3z=-26\\\\\\\\ -5\cdot \dfrac{33+y-4z}{2}-3y+5z=23[/tex]

After solving the above linear equation in two variables:

y = -11

z = 3

Plug the above values in the equation (iv)

We get the value of x:

x = (33-11-3(4))/2

x = (33-11-12)/2

x = 10/2

x = 5

Thus, the solution to the linear equations in three variable are x = 5, y = -11, and z = 3.

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Answer:

65°

Step-by-step explanation:

  Exterior angle of a triangle equals the sum of opposite interior (remote) angles.

 3x - 10 = x + 15 + 25

 3x - 10 = x + 40

Add 10 to both sides,

       3x = x + 40 + 10

       3x = x +50

Subtract 'x' from both sides,

     3x- x = 50

         2x = 50

Divide both sides by 2

           x = 50÷ 2

           x = 25

Exterior angle = 3x -10

                        = 3*25 - 10

                        = 75 - 10

                        = 65°

Recall the definition of absolute value.

[tex]|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}[/tex]

Now,

[tex]x<1 \implies x-9 \le -8 < 0 \implies |x-9| = -(x-9) = 9 - x[/tex]

and

[tex]x<1 \implies x-6 \le -6 < 0 \implies |x-6| = -(x-6) = 6 - x[/tex]

so that

[tex]|x-9| + |x-6| = (9-x) + (6 - x) = \boxed{15 - 2x}[/tex]

The amount invested at 4% is $4,333.33

The amount invested at 7% is $8,666.67

What represents the amount invested at 4%?

Let assume that x is the amount invested in the bank certificate of deposit (CD account)  which earns 4%, in essence, the interest earned at 4% is the amount of money invested multiplied by 4%

interest at 4%=4%*x=0.04x

amount invested at 7%=13000-x

interest at 7%=7%*(13000-x)

interest at 7%=910-0.07x

total interest=0.04x+910-0.07x

total interest=910-0.03x

total interest earned=780

780=910-0.03x

0.03x=910-780

0.03x=130

x=130/0.03

x=amount invested  at 4%=$4,333.33

amount invested at 7%=$13,000-$4,333.33

amount invested at 7%=$8,666.67

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Answer:

83 [tex]\frac{8}{10}[/tex] π cm3

Step-by-step explanation:

[tex]\frac{1}{3}[/tex] π ([tex]4^{2}[/tex])(5) = 83.7758040957

Using linear functions, it is found that:

A linear function is modeled by:

y = mx + b

In which:

For Shop A, we have a linear function that:

Hence the functions are given by:

Due to the lower slope, shop A charges less per hour. The costs will be the same when:

A(x) = B(x)

3x + 9 = 4x + 6

x = 3.

The canoe must be rented for 3 hours for the costs to be the same.

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The property illustrated by each statement of if t-13=52, then 52=t-13 is commutative

t-13=52, then 52=t-13

The property illustrated to each statement is commutative because it shows that for some value of t both statements are equal.

In mathematics, a binary operation is commutative if changing the order of the operands does now not alternate the result. it's far a essential belongings of many binary operations, and lots of mathematical proofs rely on it. most acquainted as the call of the assets that says something like "3 + four = 4 + 3" or "2 × 5 = 5 × 2",

the property also can be utilized in greater superior settings. The name is wanted because there are operations, which includes department and subtraction, that do not have it (for example, "3 − five ≠ 5 − 3");

such operations are not commutative, and so are called noncommutative operations.

The idea that easy operations, along with the multiplication and addition of numbers, are commutative become for many years implicitly assumed.

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density

a derived unit is something that comes from using base units in mathematical operations.

When the number given of 15,587,252 is rounded off to the nearest 10 thousand, the result would be 15,590,000.

When rounding to the nearest ten thousand, you would look at the thousands number which is the 4th number before the decimal.

If this digit if more than 5, then you round the ten thousandth digit up to the nearest whole number. If the digit is less than 5, then you round down.

The number 15,587,252 has the thousands number as 7 which is more than 5 so the ten thousands number will be round up to:

= 15,590,000

Rest of the question:

Find out 15,587,252 to the nearest 10 thousand.

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Answer:-12+16x

Step-by-step explanation:

-5x-20+8+16x

-5x-12+16x

-12+16x

Answer: 11x-12

Step-by-step explanation:

It would be easier to rearrange this equation by degree (ie ax^2, ax^1, a)

You cannot subtract ax^1 by a, but you can subtract ax^1 by ax^1 (16x-5x)

We can also subtract a by a (-20+8)

Remember your positive and negative signs

The angle ∠3 = 153° by alternate angle theorem.

Parallel lines are those lines that are equidistant from each other and never meet.

Parallel lines cut by a transversal, forms different angle relationship like alternate angles, corresponding angles, etc.

Line a and m are parallel lines . Therefore, angles 1, 2, 3, 4, 5, 153 degrees are related base on alternate and corresponding relationship.

Hence,

∠3 = 153°(alternate angles)

Alternate angles are congruent.

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Answer: x=-2, 4/3

Step-by-step explanation:

-2|3x+1|=-10

-2|3x+1| / (-2) = -10/(-2)

-2|3x+1| / (-2) = 5

|3x+1|=5

3x+1=5

3x=4

x=4/3

3x+1=-5

3x=-6

x=-2

x=-2, 4/3

Answer:50.02

Step-by-step explanation:

This is about proper writing of decimals. We are given;(5 × 10) + (2 × 1/100) From BODMAS, let us first solve what is inside both brackets;5 × 10 = 502 × 1/100 = 2/100 = 0.02Since we have solved what is in the brackets, next is to add both of them;50 + 0.02 = 50.02Thus, the decimal equivalent is 50.02

Answer: it is 50.02

Step-by-step explanation: the decimals are equivalent

Answer:

Step-by-step explanation:

Answer:

there are many case and additional

items are needed to fulfill to order

of60items ordered

Step-by-step explanation:

Using integrals, it is found that the cumulative distribution function(cdf) at x = 2.27 is given by:

P(X ≤ 2.27) = 0.897.

The cumulative distribution function of a distribution given by f(x) at a value of x = x* is given by the following integral:

[tex]\int_{-\infty}^{x^{\ast}} f(x) dx[/tex]

For this problem, the distribution is given by:

[tex]f(x) = e^{-x}, x > 0[/tex]

Hence, at x = 2.27, the cdf is given by:

[tex]\int_{0}^{2.27} e^{-x} dx[/tex]

The infinity was replaced by 0 because the lower bound of the definition of the distribution is of 0. Hence:

[tex]\int_{0}^{2.27} e^{-x} dx = -e^{-x}|_{x = 0}^{x = 2.27}[/tex]

Applying the Fundamental Theorem of Calculus:

P(X ≤ 2.27) = -e^(-2.27) + e^0 = -e^(-2.27) + 1 = 0.897.

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Using proportions, the correct statement is given as follows:

Between 2010 and 2013, Mr. Jones' student loan balance decreased by 4750 dollars.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

His balance is only 100 - 71.4 = 28.6% of the initial balance of $6,400, hence it is currently of:

0.286 x 6400 = $1830.

The decrease was of:

6400 - 1830 = $4750.

Hence the correct statement is:

Between 2010 and 2013, Mr. Jones' student loan balance decreased by 4750 dollars.

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[tex]y \leqslant 2[/tex]

Answer: 6,249,715

Step-by-step explanation:

The number sequence is built like this:

Millions , hundred thousands + ten thousands + thousands , hundred + tens

+ ones

The millions place is the greatest value here, and the ones place is the least value in every situation involving whole numbers.

Answer:

0.35 feet per second

Step-by-step explanation:

To start, there's 3 feet in 1 yard.

So, we have to convert the 7 yards per minute to feet.

7 x 3 = 21

Then, we have to convert 21 feet per minute to X amount of feet per second.

To note, there are 60 seconds in a single minute

Therefore, you have to divide 21 by 60 to find the amount of feet in one second.

21 / 60 = 0.35

The answer is 0.35 feet per second

Circles are related to Pythagorean theorem in the sense that the equations are alike and the sides conforms to:

The distance between the two cities is 116.62 units (ignoring curvature)

If the curvature is not ignored then we sort for the angle subtended

The Pythagorean theorem relates the square of hypotenuse, square of the opposite, and the square of the adjacent as follows

hypotenuse^2 = opposite^2 + adjacent^2       equation 1

Representing a circle in a coordinate axis will give it values in coordinate form. Assuming the coordinate of the center is (x1, y1) and a point in the circumference is (x2, y2). The radius of the circle, r is given as

r^2 = (x2 - x1)^2 + (y2 - y1)^2                              equation 2

comparing equation 1 and 2 shows that

radius ≅ hypotenuse,  (x2 - x1)^2 ≅ opposite, and (y2 - y1)^2 ≅ adjacent

say A = (45, -123)

say B = (53.65, -6.7)

Let the distance between the two cities be d

d^2 = (53.65 - 45)^2 + (-6.7 - (-123) )^2

d^2 = 8.65^2 + 116.3^2

d = √13600.5125

d = 116.62 units (ignoring the earth curvature)

if the curvature is not ignored then we look for the angle subtends

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To calculate marginal cost ; we use "subtract the quantity change from the overall cost change."

The potential cost of increasing orange output from 50 to 80 units was (250 – 200) = 50 cherries.

The potential cost of increasing cherry production from 100 to 200 units was (86-80) = 6 oranges.

Opportunity cost for an orange right now is,

equals 1.67 cherries.

Opportunity cost is therefore 3.34 cherries for two oranges.

One cherry's opportunity cost is,

0.06 orange units

1.8 oranges are the opportunity cost of 30 cherries.

Conclusion

a. Cherry 50

b. Oranges, six

c. Cherry 3.34

d. Oranges, 1.8

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Check the picture below.

[tex]{\LARGE \begin{array}{llll} y = ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \textit{we know that} \begin{cases} x=0\\ y=40 \end{cases}\implies 40=ab^0\implies 40=a(1)\implies 40=a \\ ~\hfill \underline{y = 40b^x} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{we also know that} \begin{cases} x=3\\ y= 15 \end{cases}\implies 15 = 40b^3\implies \cfrac{15}{40}=b^3\implies \cfrac{3}{8}=b^3 \\\\\\ \sqrt[3]{\cfrac{3}{8}}=b\implies \cfrac{\sqrt[3]{3}}{\sqrt[3]{8}}=b\implies \cfrac{\sqrt[3]{3}}{2}=b~\hfill \underline{y = 40\left( \frac{\sqrt[3]{3}}{2} \right)^x}[/tex]

Answer:

-1/3

Step-by-step explanation:

The slope of the line passing through the points (-2, 5) and (1, 4) is m = -1/3.