Which interval describes where the graph of the function is negative?

The percentage change of the given exponential function f(x) = 400(0.85)^(x) is; 15%

How to Interpret Exponential decay function?

The general form of an exponential decay function is:  

y = a(1 – b)^(x)

where:

y is the final amount that remains after a period of time decayed

a is the initial amount

x is the time

Decay factor = (1 – b).

where;

b is the percent change written in decimal form.

We are given the exponential function as;

f(x) = 400(0.85)^(x)

Now, from the general form of an exponential decay function, we can say that;

1 - b = 0.85

b = 1 - 0.85

b = 0.15 or 15%

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Using the rules of complementary angles we calculate that the value of x is  12° .

Pairs of complementary angles have measures which are one right angle.

The two given angles are 29° and ( 5x + 1 )°.

There are a pair of complementary angles.

Therefore 29° + ( 5x + 1 )° = 90 °

or, 5x + 30° = 90 °

or, 5x = 60

or, x = 12°

Therefore using the rules of complementary angles we calculate the value of x is 12°.

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Answer:

Step-by-step explanation:

$4.69

Bouman contributed to taking the first photograph of a black hole as she and her team created an algorithm that makes it possible to collect data and combine it into one image.

The article highlighted the importance of Katie Bouman in leading her team who created a computer software capable of using an algorithm that analyzes data and creates an image based on it. Its elaboration took about two years to complete but the results were very promising and promoted a great advance for science.

In conclusion, Bouman and the team were able to develop series of algorithms that converted telescopic data into the historic photo shared by the world's media.

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The sequence of transformations that maps ∆ABC to ∆A′B′C′ is a reflection across the line y = x followed by a translation 10 units right and 4 units up.

A certain order of transformational occurrences is referred to as a transformational sequence. This indicates that more than one transformation is handled by a series of transformations, and the order in which they happen is important.

We are given that ΔA'B'C' exists formed after a sequence of transformations applied to ΔABC.

The first exists a reflection across a line and the second exists a translation.

The coordinates of point C exist (-4, -2). After reflection from the line y = x, the coordinates become (2, -4).

Also, the coordinates of point C' are (12, 0).

So, to get point C' from point C, we should add 10 units to the x-coordinate and 4 units to the y-coordinate.

The translation of 10 units right and 4 units up.

Therefore, the complete transformation is

The sequence of transformations that maps ∆ABC to ∆A′B′C′ is a reflection across the line y = x followed by a translation 10 units right and 4 units up.

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"Seven Year Rule," which is derived from Section 157(4) of the Planning and Development Act 2000, is not the same as this.

What does the seven-year time limit mean?

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Answer:

draw the diagram out

Step-by-step explanation:

BC=17-11

= 6

About Nevada state, it is true that "The rural air pollution level for this state is much higher or much lower than the rest of the states in the data set."

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Table of ordered pair for the equation y =-13x +4 is given by (0,4) and (1,-9).

As given in the question,

Given equation is equal to :

y = -13x + 4

Substitute x =0 in the given equation

y = -13 (0) + 4

⇒ y = 0 +4

⇒ y = 4

Ordered pair is (0,4)

Substitute x=1 in the given equation

y = -13(1) +4

⇒ y = -9

Ordered pair is (1,-9)

Table of the ordered pair is

x  :   0        1

y  :   4       -9

Graph of the two plot points A(0,4) and B(1,-9) attached.

Therefore, table of ordered pair for the equation y =-13x +4 is given by (0,4) and (1,-9).

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Answer:

40 + 6x = 3

Step-by-step explanation:

Multiple all the way through by 8

8( 5 + [tex]\frac{3}{4}[/tex] x) = ([tex]\frac{3}{8}[/tex])8

8(5) + [tex]\frac{8}{1}[/tex][tex](\frac{3}{4})[/tex]x = [tex]\frac{3}{8}[/tex][tex](\frac{8}{1})[/tex]

40 + 6x = 3

Answer:

4x^-x-1

Step-by-step explanation:

4x^-x/x^3-2

= 4x^-x/x

= 4x^-x-1

The correct options are-

1. The slope represents the rate of change of the data.

3. Sales increase $1,000 as ads increase by $1,000.

5. A positive slope infers a positive correlation.

Positive correlation:

From the scatter points on graph, its clear that the slope which is 15 is a positive correlation.

Now, to find the slope we see the change in y with respect to x.

Thus, the change in sales increase $1,000 as ads increase by $1,000.

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The complete question is-

The slope of the trend line is 15. What does that mean in regard to the data of the scatterplot? Check all that apply.

1. The slope represents the rate of change of the data.

2. Advertising costs increase $1,000 as sales increase by $1,000.

3. Sales increase $1,000 as ads increase by $1,000.

4. A positive slope infers a negative correlation.

5. A positive slope infers a positive correlation.'

Answer:

175 x 20

Step-by-step explanation:

You said that bacteria doubles every day, so it's x2. Since it's the course over 10 days, it's 10 x 2 = 20. So the expression is 175 x 20.

Translation of negative 6 units x, 1 units y composition reflection across the x-axis

The composition transformation that maps ABCD to A''B''C''D'' comprises

of two or more transformations that maps the image

The rule that describes the composition transformation that maps ABCD to

A''B''C''D'' is the option;

Translation of negative 6 units x, 1 units y composition reflection across the x-axis.

The given coordinates of parallelogram ABCD are (3, 5), (6, 5), (4, 1), (1, 1)

The coordinates of the parallelogram A'B'C'D' are; A'(3, -5), B'(6, -5), C'(4, -1), D(1, -1)

The coordinates of the parallelogram A''B''C''D'' are;

D(-5, 0), C''(-2, 0), A''(-3, -4), B''(0, -4)

The image of the point (x, y), following a reflection about the x-axis is the point (x, -y)

The difference in the coordinates of the parallelogram ABCD and A'B'C'D'

is the change in the sign of the y-coordinates

Therefore, the transformation that gives the parallelogram A'B'C'D' from

the parallelogram ABCD is a reflection about the x-axis

The difference between the coordinates of the vertices of the

parallelogram A'B'C'D' and the parallelogram A''B''C''D'', is a change in the

x-value by (-6), and a change in the y-value by (+1)

Therefore, the parallelogram A''B''C''D'' can be obtained from parallelogram

A'B'C'D', by a translation of -6 units (left) in the x-direction and a translation

of 1 unit, x in the y-direction

Which gives;

The composition transformation that maps the pre-image ABCD to the

final image A''B''C''D'', (given that in a composition transformation, the

transformation to the right is done first) are;

[tex]$\mathrm{T}_{-6,1} \cdot \mathrm{r}_{\mathrm{x}-\{axis}}(\mathrm{x}, \mathbf{y})$[/tex]which is the option;

Translation of negative 6 units x, 1 units y composition reflection across the x-axis

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Answer:

it is ten 10

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

-10+11+x = 0

1+x = 0

x = -1

Pythagoras theorem - The length of the third side is 6.71unit

What is Pythagoras theorem ?

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a key relationship in Euclidean geometry between a right triangle's three sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

The Pythagoras theorem's equation is as follows:

H² = P² + B²

The triangle's third side will be the following length:

Let x represent the triangle's third side's length.

9² = 6² + x²

81 = 36 + x²

x² = 45

x = 6.708

x = 6.71 units

Hence, the third side of the triangle is 6.71unit

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The graph intersects the x-axis at ( 1/2 , 0) .

A cartesian coordinate system, which uses signed distances between two fixed perpendicular oriented lines and the point measured in the same unit of length, uniquely identifies any point in a plane by a pair of numerical coordinates.

We know that at the x-axis the value of y is 0 .

Now substituting the value of y in the equation of the graph we get :

y = - 2x + 1

at y = 0 ,

0 = -2x + 1

or, -1 = -2 x

or, x =  1 / 2

Hence the co-ordinate of the point where the graph passes through x-axis is ( 1/2 , 0 ) .

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Using a linear function, it is found that:

a. The inequality for this situation is: 5 + 0.45x ≤ 12.

b. He can ride at most 15 miles without going over the limit.

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which the coefficients are described as follows:

For the context of this problem, the slope and the intercept are defined as follows:

Hence the cost function, considering x miles, is given as follows:

C(x) = 0.45x + 5.

He wanted to spend $12 or less on a beach bike rental, hence the inequality that models this situation is given by:

C(x) ≤ 12.

5 + 0.45x ≤ 12.

The inequality is solved similarly to an equality, isolating the variable and finding the range of values, hence the solution is found as follows:

0.45x ≤ 7

x ≤ 7/0.45

x ≤ 15.6 miles.

The greatest whole number of miles is of 15 miles, as for 16 miles, the cost would be above $12.

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Answer:

See attachment.

Step-by-step explanation:

Given absolute value function:

[tex]f(x)=|x-4|-2[/tex]

The parent absolute value function is f(x) = |x|.

Graph of the parent absolute value function:

Translations

[tex]\textsf{For $a > 0$}:[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}.[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}.[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.[/tex]

The graph of the given function is a transformation of the parent function by:

Therefore, the vertex of the given function is (4, -2).

Find two further points on the graph by inputting x-values either side of the x-value of the vertex into the given function:

[tex]\begin{aligned}\implies f(8)&=|8-4|-2\\&=|4|-2\\&=4-2\\&=2\end{aligned}[/tex]

[tex]\begin{aligned}\implies f(0)&=|0-4|-2\\&=|-4|-2\\&=4-2\\&=2\end{aligned}[/tex]

To draw the graph of the given function:

Answer:

Step-by-step explanation:

(a - b)² =

(a - b)(a - b) =

[(- 1)(b - a)] × [(- 1)(b - a)] =

(- 1)(- 1)(b - a)(b - a) =

(b - a)²

The solution to the linear-quadratic system of equations are: [tex]\begin{pmatrix}x=1,\:&y=3\\ x=-5,\:&y=-3\end{pmatrix}[/tex].

The Standard form for a quadratic equation is  ax²+ bx + c=0, where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

To solve a quadratic function, you should find the discriminant: D=b²-4ac and then use this variable in the formula: [tex]x=\frac{-b\±\sqrt{\Delta} }{2a}[/tex].

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=4x+3. Where:

m= the slope. It can be calculated for Δy/Δx .

b= the constant term that represents the y-intercept.

The question asks the solution of the system the following equations

y=x²+5x-3 (1)

y=2+x      (2)

Firstly, you should subtract equation 1 and 2, as result, you have

y-y= x²+5x-3 -(2+x)

y-y= x²+5x-3 -2 -x

0= x² +4x -5

After that for finding x, you should  solve the equation  x² +4x -5=0. Then,

D=b²-4ac

D= 4²-4*1*(-5)

D=16+20

d=36

Thus,

[tex]x=\frac{-b\±\sqrt{\Delta} }{2a}= \frac{-4\±\sqrt{36} }{2*1}= \frac{-4\±\ 6 }{2}[/tex]. Therefore

x1=(-4-6)/2= -10/2=-5

x2= (-4+6)/2 = 2/2=1

From equation 2 : y=2+x

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Answer:

a) ¹⁰√4

Step-by-step explanation:

(4 ⅖)¼ = 4 ^ 2/5 × 1/4 = 4^ 2/20 on simplifying further we get answer as a

7 1/5 divided by 8 in fraction form is 36 / 40 = 9/ 10 and in decimal form = 0.9

A fraction is a numerical expression expressing a portion of the whole. There are two parts: a numerator and a denominator. The denominator is the total number of pieces that make up the whole, while the numerator is the number of equally sized portions of the whole. For instance, in the percentage of 3/8 has a denominator of 8 and a numerator of 3.

We have been given that -

7 1/5 divided by 8

Rewrite as

(36/5) / 8

36 / 5×8

Multiplying 5 with 8 and we get

36 / 40

Follow these steps to convert an incorrect fraction to a mixed number: Subtract the denominator from the numerator. The quotient's whole number component should be written down. Write the leftover amount on top of the original denominator.

36/ 40 in decimal form = 0.9

0.9 = 0.9 × 10 /1 × 10

= 9 / 10

Hence, When 7 1/5 is divided by 8, the result is 36/40 (9/10) and 0.9 (in decimal notation).

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Step-by-step explanation:

that only means we need to put the given values into every place, where the variable is used in the expression.

this is straight forward.

x² for x = -9 means

(-9)² = 81

you remember, a² = a×a.

and when a is negative, this is then the multiplication of a negative number with a negative number, and that result is positive.

so, a square operation always delivers a positive result for real numbers as input, no matter if the input was already positive or negative.

Explanation:

the equation of a line in

slope-intercept form

is.

∙

x

y

=

m

x

+

b

where m is the slope and b the y-intercept

rearrange

2

x

−

3

y

=

12

into this form

subtract 2x from both sides

⇒

−

3

y

=

−

2

x

+

12

divide all terms by

−

3

⇒

y

=

2

3

x

−

4

←

in standard form

with

m

=

2

3

given a line with slope m then the slope of a line

perpendicular to it is

∙

x

m

perpendicular

=

−

1

m

⇒

m

perpendicular

=

−

1

2

3

=

−

3

2

⇒

y

=

−

3

2

x

+

b

←

is the partial equation

to find b substitute

(

2

,

6

)

into the partial equation

6

=

−

3

+

b

⇒

b

=

6

+

3

=

9

⇒

y

=

−

3

2

x

+

9

←

equation of perpendicular line

The number of packs of markers that Mr. Sowers can purchase is 6.

The maximum amount that Mr. Sowers can spend is $35. This means that the amount can either by $35 or less than $35. Thus, the inequality sign that would be used is the less than or equal to sign, ≤ .

total amount spent on the packet of markets ≤  budget

(cost of one packet x number of packets) ≤ $35

$5.49x ≤ $35

In order to determine the value of x, divide both sides of the equation by 5.49

x ≤ $35 / 5. 49

x ≤ 6.38

x ≤ 6

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The more likely event is (B) Enzo passes the test , the correct option is (B).

In the question ,

it is given that

the probability that Felipe will pass the test is 0.19

Converting 0.19 to percent , we get

0.19 = 0.19/100 = 19%

the probability that Enzo will pass the test is 1/4 ,

Converting 1/4 to percent , we get

1/4 = 1/4 * 100 = 100/4 =25%

hence , the probability of Felipe passing the test is 19% and the probability that Enzo passes the test is 25% ,

On comparing we see that 25% > 19% , which means Enzo has higher chance of passing the test than Felipe .

Therefore , the more likely event is (B) Enzo passes the test , the correct option is (B).

The given question is incomplete , the complete question is

Both Felipe and Enzo forgot to study for their science test. The probability of Felipe passing the test is .19 , the probability of Enzo passing the test is 1/4.

Which of these events is more likely?

(A) Felipe passes the test.

(B) Enzo passes the test.

(C) Neither. Both event are equally likely.

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