What is the intermediate step in the form (x+a)^2=b(x+a)
2 =b as a result of completing the square for the following equation?
x²-4x=45

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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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: can you show us the graph?

Step-by-step explanation:

Answer:

radius = 5

Step-by-step explanation:

Since the line is a tangent, that means the PT and OP are perpendicular (they make a right angle) Sooo, the triangle is a right triangle. Use Pythagorean Theorem to calculate or Pythagorean Triples for a shortcut (5, 12, 13)

r^2 + 12^2 = 13^2

r^2 + 144 = 169

Subtract 144

r^2 = 25

Squareroot both sides.

sqrt(r^2) = sqrt25

r = 5

The radius is 5.

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 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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The x- and y-coordinates of point C, which partitions the directed line segment from A to B into the ratio 3:10 is; (-2.6, 5.2)

The coordinate of the points are given as:

A(-4, 8)

B(2, -4)

Ratio of partition is given as; 3:10

Now, the point at the given ratio is calculated from the formula;

C = [(mx2 + nx1)/(m + n)], [(my2 + ny1)/(m + n)]

Thus;

C = [(3*2 + 10*-4)/(3 + 10)], [(3*-4 + 10*8)/(3 + 2)]

C = (-34/13, 68/13)

C = (-2.6, 5.2)

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Answer:

-2.6, 5.2

Step-by-step explanation:

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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Answer: B, D, E

Step-by-step explanation:

Statement 1 cannot be true because f(1)<0.

Statement 2 might be true.

Statement 3 cannot be true because if f is continuous, then for some value between -1 and 0, f(x) is positive by the Intermediate Value Theorem.

Statement 4 might be true.

Statement 5 might be true

The number of boys and girls assigned to each team is 6 and 15 respectively.

= 63/3

= 21 students

Number of girls = 5/7 × 63

= 315/7

Number of girls = 45 students

Number of boys = 63 - 45 = 18 students

If the three groups have equal composition of boys and girls, then,

Number of boys and girls in each group is 6 and 15 respectively.

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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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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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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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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

The value for each interior angle in the polygon will be 147.27°.

The total angles in the 11 sided polygon will be:

= (n - 2) × 180

= (11 - 2) × 180

= 9 × 180°

= 1620°

Each angle will be:

= 1620°/11

= 147.27°

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Answer:

  C.  Ian rode less than 1 hour

Step-by-step explanation:

It never hurts to think about what the problem statement is telling you. Ian rode at a speed that would take him 18 miles in 1 hour.

Clearly, Ian would pass the 15-mile mark in a 1-hour ride before an hour had elapsed. If he only rode 15 miles, he rode less than 1 hour.

The actual time Ian rode is given by the relation between speed, time, and distance.

  time = distance/speed

  time = (15 mi)/(18 mi/h) = (15/18) h = 5/6 h

Ian's riding time was 5/6 of an hour, which is less than 1 hour.

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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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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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 )

Answer:

wouldn't it be 0.1

Step-by-step explanation:

Answer:

E. Isosceles Triangle

Step-by-step explanation:

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

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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Hello,

Answer: We have f(x) = g(x) when x ≈ 1

(a) x = 1, is an approximate solution for f(x) = g(x).

Here, we have,

given that,

A graph of two functions is shown

f(x) and, g(x)

now, we have,

The graph has two functions, which are f(x) and g(x) and a graph.

In the graph, we can follow their intersections.

Those would be the parts of the line that would make the functions to have the same value.

The first intersection is really close to 1,

and second is very unclear, most likely beyond -2.5.

Since the highest number is 1 and the intersection is very close to 1,

we have to go with the approximate answer.

We have f(x) = g(x) when x ≈ 1.

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Answer:

adding

Step-by-step explanation:

Answer:

The slope formula is used to find the slope of a line that joins two points (x₁, y₁) and (x₂, y₂). Using this formula, the slope of the line is, m = (y₂ - y₁) / (x₂ - x₁). We can use the same formula to find the slope of a line from its graph also.

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:

(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

Minimizing the sum of the squared deviations around the line is called Least square estimation.

It is given that the sum of squares is around the line.

Least squares estimations minimize the sum of squared deviations around the estimated regression function. It is between observed data, on the one hand, and their expected values on the other. This is called least squares estimation because it gives the least value for the sum of squared errors. Finding the best estimates of the coefficients is often called “fitting” the model to the data, or sometimes “learning” or “training” the model.

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Answer:

y=3

Step-by-step explanation: