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Find domain and range of this linear graph

Answer:

answer,(2)x≥-1

Step-by-step explanation:

it was right

The equation of the line is x+y-4=0.

What is an equation?

A formula known as an equation uses the equals sign (=) to express how two expressions are equal.

Main Body:

we know that one point form of a line is

y-y₁= m(x-x₁)   ,  where m= slope

now given is a point (-3,7) and m=-1

y-7 =(-1)(x+3)

x+y-4=0

Hence the answer is x+y-4 =0

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Answer:

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The graph has two local maximums and two local minimums.

The intervals between those points are the increasing intervals.

Refer to the attached, where the intervals are marked.

The intervals are

Using differentiation, 36 feet is the maximum height, in feet, that the object will reach.

In the given question,

An object is launched directly in the air at a speed of 32 feet per second from a platform located 20 feet above the ground.

The position of the object can be modeled using the function [tex]f(t)=-16t^2+32t+20[/tex], where t is the time in seconds and f(t) is the height, in feet, of the object.

We have to find the maximum height, in feet, that the object will reach.

The given function is [tex]f(t)=-16t^2+32t+20[/tex].

To find the maximum height we differentiate the function with respect to t

[tex]\frac{df}{dt}=-32t+32[/tex]

As we know that at the maximum point the slope of the tangent is zero.

So df/dt = 0

So -32t+32=0

Subtract 32 on both side

-32t+32-32=0-32

-32t=-32

Divide by -32 on both side

-32/-32 t = -32/-32

t=1

Therefore at t=1 the function have maximum value. So we put t=1 in the given equation.

[tex]f(1)=-16(1)^2+32\times1+20[/tex]

f(1)=(-16)×1+32×1+20

Simplifying

f(1)=-16+32+20

f(1)=36 feet.

Hence, 36 feet is the maximum height, in feet, that the object will reach.

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The length of shortest piece is 4 inches, middle sized piece is 9 inches and that of longest piece is 27 inches.

According to the question,

We have the following information:

A piece of pipe is 40in. long. It is cut in to 3 pieces. The longest piece is 3 times as long as the middle sized piece and the shortest piece is 23 in. shorter than the longest piece.

Let's take the length of middle sized piece to be x inches.

Length of longest piece = 3x inches

Length of shortest piece = (3x-23) inches

Now, we have the following expression:

x+3x+3x-23 = 40

7x-23 = 40

Adding 23 on both the sides:

7x = 40+23

7x = 63

Dividing by 7 on both the sides:

x = 63/7

x = 9 inches

Length of longest piece = 3*9 inches

Length of longest piece = 27 inches

Length of shortest piece = (27-23) inches

Length of shortest piece = 4 inches

Hence, the length of shortest piece is 4 inches, middle sized piece is 9 inches and that of longest piece is 27 inches.

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The coordinates  of the point that is one half the distance between A and B is (5/2, 11/2)

The point with the distance that is one half the distance between A and B is the midpoint of A and B.

The coordinate of the midpoint of a line is the half x values and y values. Thus: Xm = (X1 + X2)/2 and Ym = (Y1 + Y2)/2

where m is the midpoint

Given: A(-1, -2) and B(6, 12)

X1 = -1, Y1 = -2 and X2 = 6, Y2 = 12

Xm = -1+6 /2 = 5/2

Ym = -2+12 = 11/2

Therefore, the coordinates  of the point that is one half the distance between A(-1, -2) and B(6, 12) is (5/2, 11/2)

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Step-by-step explanation:

there is no interest and such involved. it is a straight forward calculation to allow the lender to accumulate enough funds (= the ESCROW account as part of the mortgage account structure) to be able to pay the taxes once a year on behalf of the owners.

so, the tax is $1.50 for every $100 of the assessed value of the house.

how many $100 units are in that value ?

180,000 / 100 = 1,800 units.

that means the tax for that house is

1800 × 1.5 = $2,700

in order for the lender to accumulate $2,700 in the ESCROW account in a year (= 12 months), the monthly contribution has to be

2700 / 12 = $225.00

130 units should be manufactured to minimize the cost.

Calculation

by using the quadratic formula

[tex]x = \frac{-b\sqrt{b^{2}-4ac} }{2a}[/tex]

where, a = 0.15, b = -39 and c = 4500

x= [tex]\frac{-b}{2a} = \frac{39}{0.3} =130[/tex]

Hence, 130 units should be manufactured to minimize the cost of fax machines

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130 units should be manufactured to minimize the cost.

Calculation

by using the quadratic formula

[tex]x = \frac{-b\sqrt{b^{2}-4ac} }{2a}[/tex]

where, a = 0.15, b = -39 and c = 4500

x= [tex]\frac{-b}{2a} = \frac{39}{0.3} =130[/tex]

Hence, 130 units should be manufactured to minimize the cost of fax machines

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The measure of the angle for the given trigonometric function is 30°.

Given that, [tex]sin^{-1}(0.5)[/tex].

Trigonometric angles are the angles in a right-angled triangle using which different trigonometric functions can be represented. Some standard angles used in trigonometry are 0º, 30º, 45º, 60º, 90º.

Trigonometry angle can be expressed in terms of trigonometric ratios as,

θ = [tex]sin^{-1[/tex] (Perpendicular/Hypotenuse)

θ =[tex]sin^{-1[/tex] (0.5)

= [tex]sin^{-1[/tex] (1/2)

= 30°

Therefore, the measure of the angle for the given trigonometric function is 30°.

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Let the number be n.

Then the expression is:

Answer:

Step-by-step explanation:

Forming the expression,

→ 4x + x

Let's solve the expression,

→ 4x + x

→ 5x

Hence, the answer is 5x.

Answer:

[tex]y+17=-2(x-14)[/tex]

Step-by-step explanation:

The equation of the line passing through the point [tex](x_1, y_1)[/tex] and slope [tex]m[/tex] is [tex]y-y_1=m(x-x_1)[/tex].

a) An algebraic expression for the gasoline left in the fuel tank is L = 0.4w.

b) If w = 15.5, the amount of gasoline left in the tank at the end of the journey was 6.2 gallons.

An algebraic expression is a mathematical statement that combines constants and variables together with mathematical operands.

The mathematical operands include addition, subtraction, division, multiplication, etc.

Let L = the amount of gasoline left

Let the full capacity of the fuel tank = w gallons

Gasoline consumed on the journey = 60% = 0.6

L = w - 0.6w

L = 0.4w

If w = 15.5

L = 0.4(15.5)

= 6.2 gallons

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Answer:

yes

Step-by-step explanation:

because 4

Answer:

Step-by-step explanation:

average rate of change

[tex]=\frac{25-(-10)}{9-2} \\=\frac{35}{7}\\=5[/tex]

Step-by-step explanation:

6x-4+60=14x-8

6x+56=14x-8

8x=64

x=8

The equivalent rational expression with the same denominator as given will be 8(c - 8)/[(c - 3)(5c - 9)(c - 8)] and  2c(c - 3)/[(c - 3)(5c - 9)(c - 8)].

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

As per the given expression,

8/(5c² - 6c - 27) , 2c/(5c² - 31c - 72)

Now, take the first denominator,

5c² - 6c - 27 = 5c² - 15c + 9c - 27

⇒ 5c(c - 3) - 9(c - 3)

⇒ (c - 3)(5c - 9)

Take the second denominator

5c² - 31c - 72 = 5c² - 40c + 9c - 72

⇒ 5c(c - 8) + 9(c - 8)

⇒ (c - 8)(5c + 9)

Therefore, the expression converts as,

8/[(c - 3)(5c - 9)] , 2c/[(c - 8)(5c + 9)]

8/[(c - 3)(5c - 9)] = 8(c - 8)/[(c - 3)(5c - 9)(c - 8)]

2c/[(c - 8)(5c + 9)] = 2c(c - 3)/[(c - 3)(5c - 9)(c - 8)]

The denomiantor of both expression are same.

Hence "The equivalent rational expression with the same denominator as given will be 8(c - 8)/[(c - 3)(5c - 9)(c - 8)] and  2c(c - 3)/[(c - 3)(5c - 9)(c - 8)]".

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The structured question below,

Answer:

  y = 2x +2

Step-by-step explanation:

You want the equation of the line through points (-4, -6) and (2, 6).

The slope of the line is given by the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (6 -(-6))/(2 -(-4)) = 12/6 = 2

The point-slope equation of a line is ...

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

Using the point (2, 6) and the found value of slope, an equation for the line can be written:

  y -6 = 2(x -2) . . . . point-slope equation for the line

Solving this equation for y and simplifying, we get the slope-intercept equation of the line.

  y = 2x -4 +6 . . . . . eliminate parentheses, add 6

  y = 2x +2 . . . . . . . . simplify; slope-intercept equation

The correct answer is Option A.

Randomization important because it is used to ensure all treatment groups receive experimental units .

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Answer:

the answer is c. to ensure that all treatment groups are roughly equivalent regarding the variability within the experimental units

Step-by-step explanation:

Answer:

Mediterranean Paradise has 30 fewer deluxe staterooms than three times the number of deluxe staterooms on the

Pacific Paradise.

Step-by-step explanation:

Answer:

[tex]d=-6[/tex]

[tex]a_9=-49[/tex]

Step-by-step explanation:

If the first term of a sequence is [tex]-1[/tex] and the second term is [tex]-7[/tex], then each successive term in the sequence is [tex]6[/tex] less than the previous term. The common difference is [tex]-6[/tex] ( [tex]d=-6[/tex] ).

The formula representing the arithmetic sequence is:

[tex]a_n=-6n+5[/tex]

Therefore, the ninth term in the sequence is:

[tex]a_9=-6(9)+5[/tex]

[tex]a_9=-54+5[/tex]

[tex]a_9=-49[/tex]

Answer:

76%

Step-by-step explanation:

100%-24%=76%

Answer:

60 ways;

GOOD LUCK!

Step-by-step explanation:

The word CHEWY has 5 letters, Therefore, it can be arranged in 5!/2! = 120/2 = 60 ways.

Probability = number of desired event occurrences/number of events in sample space = 9/36 = 1/4

Probability is the branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely it is that a claim is true. The probability of an event is a number between 0 and 1, with 0 signifying impossibility and 1 expressing certainty.

A compound event is made up of two separate events.

Here is a table of probable sums of two die rolls. Die 1 and Die 2 values are listed along the side and top. The figures are roughly near the middle. The sum of Die 1 = 2 and Die 2 = 2 is 4, for example.

          Die 2

Die1    1   2   3   4   5   6

1         2   3   4   5   6   7

2         3   4   5   6   7   8

3         4   5   6   7   8   9

4         5   6   7   8   9   10

5         6   7   8   9   10 11

6         7   8   9   10 11  12

Rolling two dice yields 6 * 6 = 36 possible outcomes, or 36 possible sums. There are 36 occurrences in the sample space.

Looking at the table, a 3 or a 9 happens as the sum 9 times, resulting in 9 of the 36 potential occurrences having a sum of 3 or 9.

Probability = number of desired event occurrences/number of events in sample space = 9/36 = 1/4

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Answer:

y=60°, x=60°

Step-by-step explanation:

X=60° Angles in a Equaliteral triangles are all 60°

Alternate angle to get the base angle close to y

Y=60° because of Isoceless angles

Answer: (D) [tex]y=3x-5[/tex]

Step-by-step explanation:

Using the points (0, -5) and (2, 1), the slope of the line is [tex]\frac{-5-1}{0-2}=3[/tex].

Since the y-intercept is -5, the equation is [tex]y=3x-5[/tex].

Answer:

Step-by-step explanation:

You want the result of a division operation performed on numbers written in scientific notation.

In each case, the result number will have a repeating decimal fraction. We show 4 significant figures in the answer. The number of significant figures you need to use will depend on what you're using the answer for. If you are required to match the precision of the numbers here, you will want to use 1 significant figure.

The rules of exponents apply, so the exponent of the result will be the difference of the exponents of numerator and denominator. As always, if the numerator mantissa is smaller than the denominator mantissa, the result will be a fraction, so adjustment of the exponent will be necessary.

  = (5/3)×10^(-10-(-9)) = 1.667×10^-1

  = (1/3.5)×10^(-9-(-9)) = 0.2857×10^0 = 2.857×10^-1

__

Additional comment

Any scientific or graphing calculator and any spreadsheet can accept input in scientific notation and format the output in the same way.

You need to be careful with the way you enter the multiplier. Most calculating platforms accept the E notation shown in the attachment. If you use multiplication (×10^-9, for example), then the denominator number will need to be enclosed in parentheses. The third line of the second attachment shows the result of not using parentheses: the multiplier intended for the denominator instead multiplies the result of the division. (This behavior is required by the Order of Operations.)

If  a multipack of crisps contains 10 packets. the least and the greatest weights of the multipack is 315, 325.

Range = 31.5≤  x < 32.5

Range = 31.5≤  10 < 32.5

Hence,

Lowest and greatest possible for 32 grams

Lowest possible = 31.5 grams

Greatest possible =32.4 grams

Since multipack of crisps contain is 10 packets hence.

Least weight = 31.5 grams × 10

Least weight =315

Greatest weight = 32.5 grams × 10

Greatest weight = 325

Therefore 315 and 325 are the weight.

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1. Dianely's salary can be represented with the following table of values for 5 years as follows:

Year         Salary

1            $40,000

2           $42,500

3           $45,000

4           $47,500

5          $50,000

2. The equation to model Dianely's salary after n years is S = 40,000 + 2,500n.

An equation is a mathematical statement equating two or more mathematical expressions.

Equations use variables, numbers, mathematical operands, and the equation symbol (=).

Dianely's initial salary = $40,000

Salary raise per year = $2,500

Dianely's salary after n years in equation form, S = 40,000 + 2,500n.

Year         Salary

1            $40,000

2           $42,500 (40,000 + 2,500)

3           $45,000 (42,500 + 2,500)

4           $47,500 (45,000 + 2,500)

5          $50,000 ($47,500 + 2,500)

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standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ 3}(x-\stackrel{x_1}{(-4)}) \implies y -1= 3 (x +4) \\\\\\ y-1=3x+12\implies y=3x+13\implies -3x+y=13\implies \boxed{3x-y=-13}[/tex]

Answer:

Lee would have $1.30 left.

Step-by-step explanation:

7 x 5 = $35

6 x .25 = $1.50

Altogether, Lee has $36.50 before buying the jacket

$36.50 - 35.20 = $1.30

The shaded area under the standard normal curve is 2.58%.

According to z-score table,

Area for < 2.23 = 0.9871

Area for >2.23 = 1 - 0.9871

                        = 0.0129

Area for < 2.23 = 0.0129

Total area = 0.0129 + 0.0129

                 = 0.0258

Area percent = 0.0258*100

                      = 2.58%

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