Two more than the quotient of a number and 9 equals 5

Answer:

domain : - ∞ < x < 1

Step-by-step explanation:

the function is increasing on the upward part of the curve. that is

from negative infinity to the vertex at (1, 3 )

domain : - ∞ < x < 1

Answer:

Step-by-step explanation:

Ratio of length : width = 4 : 7

Length = 4x

Width = 7x

Longer side = 31.5 in

⇒ 7x = 31.5

Divide both sides by 7

x = 31.5/7

x = 4.5

length = 4x

           = 4*4.5

         l = 18 in

width =  31.5

       w = 31.5 in

\(\boxed{ \text {Perimeter of rectangle }= 2*l + 2*w}\)

                                      = 2*18 + 2*31.5

                                      = 36 +  63

                                      = 99 in

\(\boxed{ \text{Area of rectangle = l*w}}\)

                             = 18*31.5

                             =  567 in²

Answer:

5

Step-by-step explanation:

The constant of proportionality k is given by k=y/x

y=5, x=1,

k=5

Answer:

2z-4

Step-by-step explanation:

By using distributive property, 2/3 * 3z =  2z and 2/3 * -6 = -4

This means the answer is 2z-4

\(Answer: \large\boxed{2z-4}\)

Step-by-step explanation:

To solve:

\(\frac{2}{3} (3z-6)\)

We must use the distributive property and distribute 2/3 to the 3z and -6

...

\(\frac{2}{3} (3z-6)\)

\(=\frac{2}{3} (3z) + \frac{2}{3} (-6)\)

\(=\frac{6z}{3} + -\frac{12}{3}\)

\(=2z-4\)

Answer:

117/6=19.5

I hope this helped :)

Answer:

--------------------------

Let the number of pounds in each crate be x.

The total amount is 6x or 117 pounds. It is shown as an equation:

Solve it to find the best estimate:

Answer:

1632 inches squared

Step-by-step explanation:

Hi!

So the formula for area is length times width.

So you would multiply the length by the width which is 34 times 48 to get the area which is 1632 in squared.

Hope this helps!

Answer:

Carbon-14 loses around 10% ( 0.1 in decimal form) of its mass, after one millennium.

Then if we start with a mass A of Carbon-14, after one millennium we will have a mass equal to:

A - A*0.1 = A*(0.9)

After another millennium, we will have a mass equal to:

A*(0.9) - A*(0.9)*0.1 = A*(0.9)^2

And so on, this is an exponential decay.

We already can see the pattern here, after x millenniums, the mass of carbon-14 will be:

M(x) = A*(0.9)^x

Now, in this problem we have 600 grams of carbon-14, then the equation for the mass will be:

y = M(x) = 600g*(0.9)^x

And the graph of this equation is shown below.

Answer:

S(t)=600(0.9)

Step-by-step explanation:

Losing mass at a rate of 10\%10%10, percent per millennium means the sample keeps 100\%-10\%=90\%100%−10%=90%100, percent, minus, 10, percent, equals, 90, percent of its mass each millennium.

So each millennium, the size is multiplied by 90\%90%90, percent, which is the same as a factor of 0.90.90, point, 9.

If we start with the initial mass, 600600600 grams, and keep multiplying by 0.90.90, point, 9, this function gives us the mass of the sample ttt millennia from now:

S(t)=600(0.9)^tS(t)=600(0.9)

t

Answer:

18 more sessions

Step-by-step explanation:

Her goal is to practice 800 minutes.

She already did 175 minutes.

That means she has 800 - 175 = 625 minutes remaining, and she says that she will only practice in 35 minute sessions.

To determine the number of sessions she has left, just divide 625 by 35.

\(\frac{625}{35}\)

= 17.85714

However, you can't have a portion of a session, as she only does 35 mins every session. Therfore, she must do 18 more sessions.

~~~Harsha~~~

By trigonometric functions, the length of the hypotenuse is approximately equal to 131.571.

In this problem we find the measure of an angle and its opposite side from a right triangle, whose representation is shown in the image attached below.

Trigonometric functions are transcendent expression that relates an angle of the right triangle with two sides of the same. We can find the measure of the hypotenuse by the definition of the sine function:

sin θ = h / r

Where:

If we know that h = 45 and θ = 20°, then the length of the hypotenuse is:

r = h / sin θ

r = 45 / sin 20°

r ≈ 131.571

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Answer: -18 and 33

Step-by-step explanation:

r/3 < -6 means r<-18

3r+1 > 100 means r > 33

so the blanks are -18 and 33, respectively.

The statement "The range of F(x) = log base x is the set of all negative real numbers" is false.

A logarithmic function is a mathematical function that represents the logarithm of a number with respect to a given base. In other words, it is a function that relates a number to its logarithm. The general form of a logarithmic function is: f(x) = logₐ(x)

Here,
The natural logarithm function, ln(x), and the common logarithm function, log base 10 (x), both have domains of all positive real numbers, and their ranges are all real numbers. However, the logarithm function with base x, where x is a positive real number greater than 1, has a domain of all positive real numbers and a range of all real numbers. The logarithm function with base x, where x is a positive real number between 0 and 1, has a domain of all positive real numbers and a range of all negative real numbers.

Therefore, the statement is true only for the logarithm function with a base between 0 and 1, but false for the logarithm function with a base greater than 1.

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Answer:

  (-√8, -√6] ∪ [-√2, 0) ∪ (0, √2] ∪ [√6, √8)

Step-by-step explanation:

The inequality resolves into 4 inequalities. There are 4 intervals in the solution.

Starting at the left, for the absolute value argument less than 0:

  2 ≤ -(x^2 -4) . . . . . . . for x^2 -4 ≤ 0

  2 ≤ -x^2 +4

  -2 ≤ -x^2

  2 ≥ x^2 . . . . . . . . . . consistent with the above 4 ≥ x^2

  -√2 ≤ x ≤ √2 . . . . . square root; may be limited by other constraints

For the absolute value argument greater than 0:

  2 ≤ x^2 -4 . . . . . . . for x^2 -4 ≥ 0

  6 ≤ x^2 . . . . . . . . . .consistent with x^2 ≥ 4

  -√6 ≥ x ∪ x ≤ √6 . . . . take the square root

__

The inequality on the right can be written as the compound inequality ...

  -4 < x^2 -4 < 4

  0 < x^2 < 8 . . . . . add 4

  0 < |x| < √8 . . . . take the square root

This resolves to ...

  -√8 < x < 0 ∪ 0 < x < √8

__

So, the solution set is the set of values of x that satisfy these restrictions on x:

  -√2 ≤ x ≤ √2

  x ≤ -√6 ∪ x ≤ √6

  -√8 < x < 0 ∪ 0 < x < √8

That is a collection of 4 intervals:

  (-√8, -√6] ∪ [-√2, 0) ∪ (0, √2] ∪ [√6, √8)

_____

You may be expected to write √8 as 2√2.

__

These intervals are the portions of the red curve that lie between the two horizontal lines. The points on the upper (dashed) line are not part of the solution set. The points on the lower (solid) line are part of the solution set.

The range of the data is the difference between the highest and lowest values, which is 8 inches. Adding another plant with a height of 14 inches would not change the range, so the range would remain 8 inches.

Data is a collection of facts, figures, or information that can be processed and used to draw conclusions or make decisions. It can be stored in a variety of formats, including numerical, text, images, audio, and video. Data can be collected from a variety of sources, such as surveys, observations, experiments, or transactions. It can be used to inform decisions in areas such as business, health care, education, and research. Data can be analyzed to gain insight, develop strategies, identify trends, and make predictions. Data is a valuable resource and is increasingly important in today's digital age.

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FIFO - March cost of goods sold = $13,050. March 31 inventory = $7,350. LIFO - March cost of goods sold = $14,600. March 31 inventory = $5,800.

To calculate March cost of goods sold we need to add the given data for FIFO =

March cost of goods sold

= (2,800 + 3,700 + 6,550)

= 13,050

To calculate March cost of goods sold we need to add the given data for LIFO =

March cost of goods sold

= (3,400 + 4,400 + 6,800)

= 5,800

Sales data refers to the information collected and recorded about the transactions that occur when a business sells products or services to customers. This data typically includes details such as the date and time of the sale, the products or services sold, the quantity sold, the price paid, and the customer's information. Sales data is crucial for businesses as it helps them understand their sales performance, identify trends and patterns and make informed decisions about their pricing, marketing and inventory management strategies.

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Answer:

  a) x = 1 ± (3/7)√7

  b) (-∞, -5) ∪ [-2, 5) ∪ [6, ∞)

Step-by-step explanation:

You want solutions to the relations ...

We like to solve these in the form f(x) = 0. It helps avoid extraneous solutions.

  \(7+\dfrac{1}{x} -\dfrac{1}{x-2}=0\\\\\\\dfrac{7x+1}{x}-\dfrac{1}{x-2}=0\\\\\\\dfrac{(7x+1)(x-2)-x}{x(x-2)}=0\\\\\\ \dfrac{7x^2-14x-2}{x(x-2)}=0\)

The roots of the numerator quadratic are found by ...

  x² -2x -2/7 = 0 . . . . . divide by 7

  x² -2x +1 -9/7 = 0 . . . . add and subtract 1

  (x -1)² = 9/7 . . . . . . . . . . write as a square, add 9/7

  x -1 = ±√(9·7/49) = ±(3/7)√7 . . . . take the square root

  x = 1 ± (3/7)√7

Rational inequalities are best solved by identifying the roots of numerator and denominator. These tell you where the function changes sign. The end behavior of the rational function tells you what the signs are changing from.

  \(\dfrac{x^2-4x-12}{x^2-25}\ge 0\\\\\\\dfrac{(x+2)(x-6)}{(x+5)(x-5)}\ge0\)

This has a horizontal asymptote at y=1 for |x|→∞. It has vertical asymptotes at x=±5.

The sign changes occur at x ∈ {-5, -2, 5, 6}. The rational expression is positive (approaching +1) for x < -5 and for x > 6. It is negative in the adjacent intervals, so positive again for -2 < x < 5.

The inequality is satisfied for ...

Answer:

60 liters

Step-by-step explanation:

Answer:

C. 60 kilograms

Step-by-step explanation:

The person above me is incorrect because liters is used on liquids

Answer:

89, 178, 267, 356, 445, 534, 623, 712, 801, 890 and so on

1. The composite functions are two o more functions combining within another to create a new function.

So the correct notion is:

a. h(p(x))

b. ( s o t) (x)

c. f(g(x))

So the b. f(x) g(x) is not a notation of a composite function.

Answer: x=18

Step-by-step explanation: 16-18=-2

Good luck! :)

Answer: -18

Step-by-step explanation:  16-x = -2

x = -16-2      [16 changes to -16 when transferred to RHS]

x = -18

Hope it helped u,

mark as the brainliest

^_^

Step-by-step explanation:

3^6  = 3 * 3^5

 = 3 * 243 =  729

Answer:

177.84ft^2

Step-by-step explanation:

Area:

The rectangle is 15x7 or 105

The triangle is 1/2*12*9 = 54

The semi-circle is 1/2*3.14*12 = 18.84

18.84 + 105 + 54 = 177.84ft^2

Answer:

I've written it in the photo

The correct option for the expression (5 + 9) + 10 showing the associative property is  5+ (9 + 10) = 5 + 19 = 24

The associative property of addition states that the sum of three or more numbers remains the same regardless of how the numbers are grouped.

Given that, an expression, (5 + 9) + 10

According to associative property of addition, (a+b)+c = a+(b+c)

Therefore,

(5 + 9) + 10 = 5+(9+10)

= 5+19

= 24

Hence, the correct option for the expression (5 + 9) + 10 showing the associative property is  5+ (9 + 10) = 5 + 19 = 24

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If the graph of f(x) = x is shifted up 9 units, the equation of the new graph would be g(x) = x + 9.

In Mathematics, the translation of a geometric figure to the left simply means subtracting a digit from the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is shifted up simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image or parent function.

Translating the graph of the parent function f(x) = x by shifting it nine (9) units up, we have the following equation:

f(x) = x   →  g(x) = f(x) + 9

g(x) = x + 9

In this context, we can logically deduce that the parent function f(x) was shifted by nine (9) units up to create function g(x) as shown in the graph attached below.

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Answer: x = -1

Step-by-step explanation:

simplify 2(x + 7) 2 / 3 = 8 to 4x + 28 = 24 and then solve it from there

Answer:

31 + 32 + 33 = 96.

Step-by-step explanation:

I think you are meaning 96 not -96

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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3^-1 = 1/3

2^-3 = 1/8

(4.6) = 24

24 × 1/8 × 1/3 = 1

\( \huge{ \boxed{ \mathbf{ \blue{Problem:-

}}}}\)

\( \bold{ {3}^{ - 1 \ } (4 \times 6) \times {2}^{ - 3} }\)

\( \huge{ \boxed{ \bf{ \blue{Solution:-}}}}\)

\( \bold{ {3}^{ - 1}(4 \times 6) \times {2}^{ - 3} }\)

\( = \bold{ \frac{1}{3}^{1} (4 \times 6) \times { \frac{1}{2}^{3} } }\)

\( = \bold{ \frac{1}{3} \times 24 \times \frac{1}{8} }\)

\( \bold{= 1}\)

Answer:

\({ \tt{(f + g)x = ( {x}^{3} - 2 {x}^{2} + 1) + (4 {x}^{3} - 5x + 7)}} \\ \\ { \tt{(f + g)x = ( {x}^{3} + 4 {x}^{3}) + ( - 2 {x}^{2} ) + ( - 5x) + (1 + 7) }} \\ \\ { \boxed{ \rm{(f + g)x = {5x}^{3} - 2 {x}^{2} - 5x + 8 }}}\)

The perimeter of ΔMNP is calculated as; 130

From the given image, it is clear that some sides are congruent to others as indicated.

Thus, we see the following;

QM is parallel and congruent to RS.

Similarly, we see that QR is parallel and congruent to MS.

PR is parallel and congruent to QS.

NR = PR because of line segment division.

Thus, we can plug in the relevant values to get;

PR = QS = 22 = NR

Similarly, MS = SP = QR = 25

RS = x + 4 and so;

x + 4 + x + 4 = 5x - 34

42 = 3x

x = 14

MN = 5(14) - 34

MN = 36

Thus, the perimeter of ΔMNP = 36 + 25 + 25 + 22 + 22

= 130

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