A rectangular yard measures 8m x 6m. What happens to the area if each dimension is doubled?​

Given f(x)=2−∣x−5∣

Domain of f(x) is defined for all real values of x.

Since, ∣x−5∣≥0⟹−∣x−5∣≤0

⟹2−∣x−5∣≤2⟹f(x)≤2

Hence, range of f(x) is (−∞,2].

The domain of the function  y= 2√x-6 is [6, ∞).

A relation is a function if it has only One y-value for each x-value.

In the given function, we have a square root of x-6 which means that the value inside the square root must be non-negative, otherwise the function will not be real.

Therefore, we have x - 6 ≥ 0

Adding 6 to both sides, we get:

x ≥ 6

So, the domain of the function y = 2√(x-6) is all real numbers greater than or equal to 6.

In interval notation, we can write the domain as:

Domain: [6, ∞)

Hence, the domain of the function  y= 2√x-6 is [6, ∞).

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Answer:

(a) 7 + 3( n - 1 )

(b) 1006

Step-by-step explanation:

ARITHMETIC SEQUENCE.

The number of term of an Arithmetic progression has the formular :

nth term = a + ( n - 1 ) d

a = 7

d = 10 - 7 = 3

nth term = 7 + ( n - 1 ) 3

= 7 + 3n - 3

= 7 + 3( n - 1 )

Therefore,

the nth term of the sequence

= 7 + 3( n - 1 )

(b) For the 1000th term

= 7 + 3 ( 1000-1 )

= 7 + ( 999 )

7 + 999 = 1006

Therefore,

the 1000th term = 1006

Each daylily cost $3 and one bunch of ornamental grass cost $8.

Build two equation's: (Let 'd' be daylilies, 'o' be ornamental grass)

$118 on 2 daylilies and 14 bunches of ornamental grass.

$98 on 14 daylilies and 7 bunches of ornamental grass.

Make d subject for first equation.

2d + 14o = 118

2d = 118 - 14o

d = (118 - 14o)/2

d = 59 - 7o

Insert this into second equation.

14(59 - 7o) + 7o = 98

826 - 98o + 7o = 98

-91o = -728

o = 8

Find value of d:

d = 59 - 7o

d = 59 - 7(8)

d = 3

Answer:

Cost of one daylily = $3

Cost of one bunch of ornamental grass = $8

Step-by-step explanation:

Define the variables:

Given information:

Create a system of equations with the given information and defined variables:

[tex]\begin{cases}2d+14g=118\\14d+7g=98 \end{cases}[/tex]

Multiply the second equation by 2:

[tex]\implies 2(14d+7g)=2(98)[/tex]

[tex]\implies 28d+14g=196[/tex]

Subtract the first equation from this equation to eliminate the variable g:

[tex]\begin{array}{r r r}28d & +14g = & 196\\- \quad \quad2d & +14g = & 118\\\cline{1-3}26d & = & 78\end{array}[/tex]

Solve for d:

[tex]\implies 26d=78[/tex]

[tex]\implies d=3[/tex]

Substitute the found value of d into one of the equations and solve for g:

[tex]\implies 2d+14g=118[/tex]

[tex]\implies 2(3)+14g=118[/tex]

[tex]\implies 6+14g=118[/tex]

[tex]\implies 14g=112[/tex]

[tex]\implies g=8[/tex]

Therefore, the cost of one of each plant is:

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The value of n is calculated as n = 2 times 10 superscript 16.

The product of 1.3 times 10 Superscript negative 4 and a number n results in 2.6 times 10 Superscript 12.

Simplification, in mathematics, is to solve the equation through mathematical operations

1.3 x 10^-4 x n = 2.3 x  10^12
n = 2 x 10^ 16

Thus the value of n is calculated as n = 2 times 10 superscript 16.

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Answer:

y=3

Step-by-step explanation:

The statement which best describes the translation from the graph y= 6x² to the graph of y = 6(x+1)² is; The translation represents a unit shift rightward.

The translation involved in the transformation of the graph as given in the task content represents a rightward shift of the graph y = 6x² by 1 unit.

On this note, it follows that the translation involved between the two graphs is; a unit shift to the right.

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Answer:

Step-by-step explanation:

one unit to the right

Answer:

adding

Step-by-step explanation:

The value of p is 60°

The figure given is a triangle and it is important to note that sum of angles in a triangle = 180 degrees

The other sides are gotten by;

Angle on a straight line = 180

110 + x = 180

x = 180 - 110

x = 70

The other interior angle

130 + y = 180

y = 180 - 130

y = 50

We have,

x + y + p = 180

70 + 50 + p = 180

120 + p = 180

p = 180 -120

p = 60°

Thus, the value of p is 60°

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Answer:

the answer is C, I got it too from the website, I got the answer from it

Answer:

E. Isosceles Triangle

Step-by-step explanation:

It is because it has 2 equal sides and 2 equal angles.

The range of this function is all real numbers such that 0 ≤ y ≤ 40.

A range is the set of all real numbers that connects with the elements of a domain. This simply means that, a range is the solution set on the y-axis.

Based on the table (see attachment), we can logically deduce that when the time (x) is zero (0), the amount of water remaining in the bathtub (y) is 40.

Therefore, the range of this function is all real numbers such that 0 ≤ y ≤ 40.

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Hence, the function increases at a constant multiplicative rate..

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). A function has three parts, a set of inputs, a set of outputs, and a rule that relates the elements of the set of inputs to the elements of the set of outputs in such a way that each input is assigned exactly one output.

We know,

the answer is (B) the function increases at a constant multiplicative rate.

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The ordered pair that is the possible solution for the equation is (-6,0) (0,-4).

The slope-intercept form of a linear equation takes the form y= mx + b.

Here:

The function f(x) = y = [tex]\mathbf{-\dfrac{2}{3}x-4}[/tex]

[tex]\mathbf{y = -\dfrac{2}{3}x-4}[/tex]

The slope (m) = -2/3

The x-intercept is the value of x for which y = 0

The y-intercept is the value of y for which x = 0

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Using the z-distribution, the 99% confidence interval of the population mean number of days it takes to find a job is (35.38, 44.62).

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

In this problem, we have a 99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.

The other parameters are:

[tex]\overline{x} = 40, \sigma = 10, n = 31[/tex]

Hence the bounds of the interval are:

[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 40 - 2.575\frac{10}{\sqrt{31}} = 35.38[/tex]

[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 40 + 2.575\frac{10}{\sqrt{31}} = 44.62[/tex]

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Answer:

[tex]y = \dfrac{1}{2}x-4[/tex]

Step-by-step explanation:

       [tex]\sf slope = m =\dfrac{1}{2}\\\\Point (2, -3) ; x_1 = 2 \ \& y_1 = -3\\\\\boxed{\bf y - y_1 =m(x -x_1)}[/tex]

         [tex]\sf y - [-3] = \dfrac{1}{2}(x - 2)\\\\y + 3 = \dfrac{1}{2}x - 2*\dfrac{1}{2}\\\\y + 3 = \dfrac{1}{2}x-1\\\\[/tex]

                [tex]\sf y = \dfrac{1}{2}x - 1 - 3\\\\ y =\dfrac{1}{2}x-4[/tex]

Answer:

the answer to this problem is D:(-2,4)(1,1)

Answer:

B

Step-by-step explanation:

y = x² → (1)

y = 3x - 2 → (2)

substitute y = x² into (2)

x² = 3x - 2 ← subtract 3x - 2 from both sides

x² - 3x + 2 = 0 ← in standard form

(x - 1)(x - 2) = 0 ← in factored form

equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 2 = 0 ⇒ x = 2

substitute these values into (2) for corresponding values of y

x = 1 : y = 3(1) - 2 = 3 - 2 = 1 ⇒ (1, 1 )

x = 2 : y = 3(2) - 2 = 6 - 2 = 4 ⇒ (2, 4 )

For the given system of equation, the value of x = 4 and the value of y = -1

From the question, we are to solve the given system of equations

-7x + 4y = -32 -------- (1)

9x - 2y = 38   -------- (2)

From equation (2)

9x - 2y = 38

2y = 9x - 38

y = 4.5x - 19 -------- (3)

Substitute this into equation (1)

-7x + 4y = -32

-7x + 4(4.5x -19) = -32

-7x + 18x - 76 = -32

-7x + 18x = -32 + 76

11x = 44

x = 44/11

x = 4

Substitute the value of x into equation (3)

y = 4.5x - 19

y = 4.5(4) - 19

y = 18 - 19

y = -1

Hence, the value of x = 4 and the value of y = -1

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The inequality shows that the number of texts will be 205.

The carriers charged $59 and 20 cents after. Therefore, the inequality to illustrate the information will be:

Let t be the number of texts.

59 + 0.2t = 100

0.2t = 100 - 59

0.2t = 41

t = 205

The number of texts will be 205.

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The required possible values of x is 1. Hence the option A. is correct.

The triangle is geometric shape which includes 3 sides and sum of interior angle should not grater than 180°.

Since. in the question we have two known sides of the right angle triangle. The number of possible values of x will be 1. because with the help of other two side third side can be calculate.

Thus, the required possible value of x will be 1.

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[tex]\angle FHD=74^{\circ}[/tex] (alternate segment theorem)

[tex]x=77^{\circ}[/tex] (angles in a triangle add to 180 degrees)

Answer: can you show us the graph?

Step-by-step explanation:

Answer:

12ft

Step-by-step explanation:

length of one side of the square now

32ft / 4 = 8ft

length of one side of the square before decreasing the length

(original lenght)

8ft +4ft = 12ft

Absolutely, over result will match in part b and c

Geogebra tools are software which is used to study an absolute geometry with zero errors.

Since, Geogebra contains various tools, In part b we have drawn a square through polygon command. Its allows  to select the number of sides, so we select 4 cause square requires 4 equal sides.
Now, we very it in c part just by drawing a 4 connected lines which have 90° adjacent angles.
                    Here, by comparing their geometry it seems identical

Thus, the result, in part b and c matches for each other.

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Using the inverse function concept, the table that represents the inverse of the table given is table a.

The inverse of the function is given by the set that contains point (y,x), that is, the coordinates are exchanged.

In the table given, we have points (0,0), (2,1) and (4,2), hence the inverse table has points (0,0), (1,2) and (2,4), which is table a.

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[tex]A_{ij}[/tex] refers to the entry of [tex]A[/tex] in row [tex]i[/tex] and column [tex]j[/tex].

When [tex]i=j[/tex], the entry in question lies on the diagonal. In this case, [tex]A_{ij}=0[/tex] so

[tex]A = \begin{bmatrix} 0 & \square & \square \\ \square & 0 & \square \\ \square & \square & 0 \end{bmatrix}[/tex]

When [tex]i<j[/tex], the row number is smaller than the column number, which happens for each [tex]A_{ij}[/tex] in the upper half of [tex]A[/tex].

[tex]A = \begin{bmatrix} 0 & -1 & -1 \\ \square & 0 & -1 \\ \square & \square & 0 \end{bmatrix}[/tex]

When [tex]i>j[/tex], the row number is larger, which happens everywhere else in the matrix.

[tex]A = \begin{bmatrix} 0 & -1 & -1 \\ 1 & 0 & -1 \\ 1 & 1 & 0 \end{bmatrix}[/tex]

The volume of the ring-shaped remaining solid is 1797 cm³.

The volume is the total space occupied by an object.

The volume of a sphere of radius r units is given as (4/3)πr³.

The volume of a cylinder with radius r units and height h units is given as πr²h.

In the question, we are asked to find the volume of the remaining solid when a sphere of radius 9cm is drilled by a cylindrical driller of radius 5cm.

The volume will be equal to the difference in the volumes of the sphere and cylinder, where the height of the cylinder will be taken as the diameter of the sphere (two times radius = 2*9 = 18) as it is drilled through the center.

Therefore, the volume of the ring-shaped remaining solid is given as,

= (4/3)π(9)³ - π(5)²(18) cm³,

= π{972 - 400} cm³,

= 572π cm³,

= 1796.99 cm³ ≈ 1797 cm³.

Therefore, the volume of the ring-shaped remaining solid is 1797 cm³.

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Answer:

1. to c.

2. to d.

3. to a.

4. to b.

Step-by-step explanation:

These answers should be right.

Hope this helps!

The matching of the polynomials to their correct names are:

a. h(x) = 15x+2 is a linear binomial

b. j(x)=x²-3x³ + 9x²  is a  Quartic trinomial

c. f(x)= 3x² - 5x+7 is a Quadratic trinomial

d. 8(x)=-5x³ is a Cubic monomial

A polynomial is an expression having more than one algebraic terms.

1) A quadratic trinomial is a polynomial that is defined as a quadratic expression with all three terms in the form of ax² + bx + c, where a, b, and c are numbers and not a 0.

2) A cubic monomial is defined as a a monomial that has a degree of 3.

3) Linear binomial is defined as a polynomial with two terms whose variable has degree 1. For example, 4x − 5 or 3x + 12 are both linear binomials.

4) A quartic trinomial is defined as a polynomial with three terms having the highest degree 4

Thus:

a. h(x) = 15x+2 is a linear binomial

b. j(x)=x²-3x³ + 9x²  is a  Quartic trinomial

c. f(x)= 3x² - 5x+7 is a Quadratic trinomial

d. 8(x)=-5x³ is a Cubic monomial

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Answer:

The answer is 20

Step-by-step explanation:

Their are two bases and three sides in a triangular prism so the total surface area is 20