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Considering the contour diagram, fₓ (1, 3) is traced to be 10

A contour line for a function of two variables, more generally speaking, a curve that connects places where the function has the same specific value.

A topographic map, for example, which displays valleys, hills, and the steepness or gentleness of slopes, is an example of a map with contour lines.

The elevation difference between successive contour lines is known as the contour interval in a contour map.

Using the map provided point (1, 3) is traced to the contour line that has the mark of 10

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Answer:

One shirt costs $7.50.

One pair of shorts cost $15.45

Step-by-step explanation:

Step-by-step explanation:

the unit rate for 60 miles per hour is 60 miles/hour.

a) The inequality that represents the scenario is 10 + x ≥ 24.

b) The solution of the inequality is x ≥ 14.

c) The fewest number of boxes of fudge at the fudge shop Monday morning is 14.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

a) Let x denote the amount of fudge at the shop.

Helena prepares 10 pounds of fudge containing nuts.

The Inequality can be

10 + x ≥ 24

b) The inequality can be solved as

10 + x ≥ 24

x ≥ 24 -10

x ≥ 14

c) The fewest number of boxes would be almost 14 boxes.

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The evaluation of the rhombus ABCD and are as follows;

a. The sides of the Δs ABC and ADC are all congruent, therefore, ΔABC ≅ ΔADC by SSS

b. The opposite sides and opposite angles of ABCD are congruent, the adjacent angles are supplementary, therefore, ABCD is a parallelogram by its properties which defines a parallelogram

A rhombus is a quadrilateral that has four sides which are congruent and the opposite sides are parallel, therefore a rhombus is a special form of a parallelogram.

a. The specified details in the question are;

AB ≅ BC

AB ≅ AD

AB ≅ CD

Therefore; BC ≅ AD ≅ CD, by transitive property of congruency

AB = BC, AB = AD, AB = CD, BC = AD = CD, by definition of congruency

AC is congruent to AC by reflexive property of congruency, therefore;

ΔABC ≅ ΔADC by Side-Side-Side, SSS, congruency rule

b. ∠D ≅ ∠B by Corresponding Parts of Congruent Triangles are Congruent, CPCTC

∠DAC ≅ ∠DCA by base angles of an isosceles triangle, ΔADC

∠BAC ≅ ∠BCA by base angles of an isosceles triangle, ΔABC

∠DAC ≅ ∠BAC by CPCTC

∠DAC = ∠BAC by definition of congruency

∠DCA ≅ ∠BCA by CPCTC

∠DCA = ∠BCA, definition of congruency

∠DAB = ∠DAC + ∠BAC (Angle addition postulate)

∠DCB = ∠DCA + ∠BCA (Angle addition postulate)

∠DAC + ∠BAC = ∠DCA + ∠BCA substitution property

∠DAB = ∠DCB by substitution property

∠DAB ≅ ∠DCB definition of congruency

The opposite angles of the quadrilateral ABCD are congruent,

The opposite sides are congruent

∠D + ∠DCA + ∠DAC = 180° (angle sum property of a triangle)

∠D + ∠ADC + ∠BCA = 180° (substitution property)

Similarly;

∠B + ∠BAC + ∠DAC = 180°

Adjacent angles of the quadrilateral ABCD are supplementary, therefore;

Quadrilateral ABCD is a parallelogram, by the properties of a parallelogram

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The number of cans in each box is 80.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of rows in each layer = 8

Number of cans in each row = 5

Number of layers = 2

The total number of cans.

= Cans x Rows x Layer

= 5 x 8 x 2

= 40 x 2

= 80

Thus,

There are 80 cans in each box

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According to the end behavior of the function h(z) = 5x³-9x²+4x+96, the graph is positive on the intervals (-∞, -8) and (-4, 3).

What is a polynomial function?

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.

The given polynomial function is -

h(z) = 5x³-9x²+4x+96

The end behavior of a function f(x) describes the behavior of the function as x approaches +∞, and as x approaches -∞.

Domain of function h(z) = -∞<x<∞

The end behavior of the function h(z) is -

lim x→∞, (5x³-9x²+4x+96) = ∞

as x→∞, h(z)→∞

lim x→-∞, (5x³-9x²+4x+96) = -∞

as x→-∞, h(z)→-∞

Therefore, the graph is positive on the intervals (-∞, -8) and (-4, 3).

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Observing the given question, This is the problem of cryptarithmetic , Using the rules based on cryptarithmetics, The answer is 10890.

Mathematical conundrums called cryptarithmetic problems use letters from the alphabet in place of the digits. Use the trial-and-error procedure while keeping in mind the aforementioned considerations to solve cryptarithmetic problems by replacing values for the letters. Depending on whether we have a carry from A+A or not, A can now either be 2 or 3. However, since E=2, A must be 3, and there is a carry as a result.

Cryptarithm, a type of mathematical game where the object is to solve an arithmetic puzzle in which the numerical digits have been replaced with letters. Cryptarithm, a type of mathematical game where the object is to solve an arithmetic puzzle in which the numerical digits have been replaced with letters.

Applying cryptarithmetic rules,

First alphabets can't be zero and same digit can't be used for different alphabets.

we get, CBDE + ABAE = AEDCE as 9480+1410 = 10890

AEDCE = 10890.

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The graph of the function y = ∛(x +1 ) - 2 is represented by the graph represented by option 1.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.

The graph of the function y = ∛(x +1 ) - 2 is attached with the answer below,

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Answer:

A. 18

Step-by-step explanation:

............... .....k

The equation have the same solution as 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p

Given: 2.3p – 10.1 = 6.5p – 4 – 0.01p.

Using this given property, let's write the equation

We can subtract like terms (6.5p– 0.01p = 6.49p) to get:

2.3p – 10.1 = 6.5p – 0.01p – 4

2.3p – 10.1 = 6.49p – 4

Also, we can multiply both sides of the algebraic equation by 100:

(2.3p – 10.1) x 100 = (6.5p – 4 – 0.01p) x 100

230p – 1010 = 650p – 400 – p

Therefore, the equations have the same solution as 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p. The 2nd and 3rd options are the answers

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The number of string pieces which Ken has after he cuts the string into 0.19 meter lengths is; 9.

It follows from the task content that initially, Ken has 1.71 meters of string. However, he cuts the string into 0.19 meters strings.

It is however required that the number of string pieces he has after cutting the 1.71 meter string into 0.19 meters lengths be determined.

On this note; the number of 0.19 string lengths he has can be evaluated by estimating the quotient as follows;

= 1.71 / 0.19

= 9.

On this note, Ken would have 9 pieces of the 0.19 meters strings.

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Answer:

Provided at image

Step-by-step explanation:

Green dot = -3.5

Red dot = -5/6

Orange dot = 2.3

Since there are 5 lines between every 1 number, you can divide 100/6 to see the distance between the lines (16.6666) and plug in the points.

The graph of the line y = 0.4x is attached below.

There is independent quantity, and a quantity which depends on it (dependent quantity). When independent quantity moves by a unit measurement (single unit increment), the increment in dependent quantity is called rate of increment of dependent quantity per unit increment in independent quantity.

We are given that the line that represents a proportional relationship between y and x where the unit rate of change of y with respect to x is 0.4.

The graph of the line with the slope m and the y-intercept , has the form as;

y = mx + c

In this case the rate of change  is 0.4 ; therefore we have the equation

y = 0.4x

The graph of the line is attached.

Here we have set b = 0 by default.

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Answer: Simile since as is used.

Answer:

Jayden will earn $3.21 x 18 = $<<3.21*18=57.78>>57.78 from running 18 miles.

So he will have $7.69 + $57.78 = $<<7.69+57.78=65.47>>65.47 in total.

Step-by-step explanation:

The number of toy pachyderms that Mr. Paxon can pack per hour will be 120 per hour. And the number of hours to pack 660 pachyderms will be 5.5 hours.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

Mr. Paxon can pack 960 toy pachyderms in an eight-hour shift.

The number of toy pachyderms that Mr. Paxon can pack per hour will be given as,

Rate = 960 / 8

Rate = 120 per hour

At that rate, the number of hours to pack 660 pachyderms will be given as,

⇒ 660 / 120

⇒ 5.5 hours

The number of toy pachyderms that Mr. Paxon can pack per hour will be 120 per hour. And the number of hours to pack 660 pachyderms will be 5.5 hours.

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The bearing of R from  P is 172°.

The horizontal angle between an object's direction and either north or another object is known as a bearing or azimuth in navigation. You can specify the angle value in a number of different angular units, including degrees, mils, and grad.

The angle between the magnetic north and the absolute bearing

The angle between the craft's forward motion and the relative bearing.

Given The bearing of P from Q is 040°.

The bearing of R from Q is 124°.

QR = QP.

Bearing angles are 180 degrees different than forward-bearing angles. This difficulty can be resolved by combining these relations with the standard angle sum relation for triangles.

Angle PQR will be the difference in the bearings from Q to P and Q to R:

 ∠PQR = 124° -40° = 84°

Triangle PQR is isosceles, so the base angle at P will be ...

 ∠QPR = (180° -  84°)/2 = 48°

The bearing from P to R will be 48° less than the bearing from P to Q. The bearing from P to Q is 180° more than the bearing from Q to P.

PR bearing = PQ bearing - ∠QPR

= PQ bearing - 48°

= (40° +180°) - 48° = 172°

  Hence, The bearing of R from P is 172°.

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Answer:

-6 , 19 , 29

Step-by-step explanation:

range = output which is required

domain = input which are given -2,3,5

simply plot the value domain one by one in given equation

Answer:

6

Step-by-step explanation:

[tex]\frac{24-x}{x}=3 \\ \\ 24-x=3x \\ \\ 24=4x \\ x=6[/tex]

Answer:

5.25

Step-by-step explanation:

Let the number be x. The equation is:

24 - x / x = 3

We can rearrange this equation to solve for x:

24 - x = 3x

21 = 4x

x = 21/4

x = 5.25

So the value of the number is 5.25.

Answer:

Step-by-step explanation:

m∠O = 118 because opposite angles of a parallelogram are equal

LNO forms a triangle and the sum of the interior angles of a triangle is 180.

To find m∠NLO:

22 + 118 +  m∠NLO = 180

m∠NLO = 180 - 22 - 118 = 40

The ratio of dogs to cats is 7 to 9

From the question, we have the following parameters that can be used in our computation:

You have 99 cats and 77 dogs and 10998 horses

The ratio is represented as

Ratio = Dogs : Cats

Substitute the known values in the above equation, so, we have the following representation

Dogs : Cats = 77 : 99

Divide by 11

Dogs : Cats = 7 : 9

Hence, the ratio is 7 to 9

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Answer:

8 quarts of white soda

The interval that is the most appropriate for creating the histogram is: 0 – 9, 10 – 19, 20 – 29, 30 – 39, 40 – 50. Option A

In order to get the best interval, we would have to check the distance that lies in the data from what the question has told us.

The tickets are sold each day for ten days. Hence we would have to look for the interval that lies between 10 days.

From the options we have here, option A is seen to lie between the distance of 10 days. 0 - 9 is 10 days e.t.c

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Answer:

0 – 14, 15 – 29, 30 – 44, 45 – 59, 60 – 74

Step-by-step explanation:

The value of 3.2 times 3.2 to the second power to the fourth power to all is [tex](3.2)^{12}[/tex].

The amount of times a number has been multiplied by itself is shown by its exponent.

3.2 to the second power is represented as [tex](3.2)^2[/tex].

3.2 times 3.2 to the second power, thus, is represented as:

[tex](3.2) (3.2)^2[/tex]

Since, the base is similar, the powers can be added:

[tex](3.2)^{1+2}\\\\(3.2)^3[/tex]

Now, the fourth power to all is represented as:

[tex]((3.2)^3))^4\\[/tex]

Using the rule of exponents [tex]((a^m))^n = a^{mn}[/tex] we have:

[tex](3.2)^{3*4}\\\\(3.2)^{12}[/tex]

Hence, the value of 3.2 times 3.2 to the second power to the fourth power to all is [tex](3.2)^{12}[/tex].

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Answer:

(5,6)

Step-by-step explanation:

x -y = -1

x - 3y = -13 ⇒ multiply through by -1 ⇒ -x + 3y = 13  Add this to the first equation

-x + 3y = 13

x   -  y = -1

       2y = 12  Divide both sides by 2

         y = 6

To find y substitute 6 for y in the equation x - y = -1

x - 6 = -1  Add 6 to both sides

x = 5

(5,6)

The period of function sinx + cosx = 2π besides that period of Sinx= 2π also cosx = 2π​.

The Least common multiple of two or more numbers are the smallest number that is multiple of two or more numbers.

Here, The period of function sin x + cos x = 2π

And, The period of Sin x= 2π and cos x = 2π​

Now, We know that;

If period of Sin x= 2π and cos x = 2π​

Then, The period of function sin x + cos x = LCM {2π , 2π }

                                                                 = 2π

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Answer:

The period of a function is the smallest positive number 'p' such that f(x+p) = f(x) for all x in the domain of f.

To find the period of the function sinx + cosx, we can use the fact that sin(x+π/4) = sinx*cos(π/4) + cosx*sin(π/4) = (sqrt(2)/2)*sinx + (sqrt(2)/2)*cosx. Therefore, sinx + cosx = sqrt(2)*sin(x+π/4).

Now, we know that the period of sin(x+π/4) is 2π since sin(x+π/4) = sin((x+π/4)+2kπ) for all integers k. Therefore, the period of sinx + cosx is also 2π/sqrt(2), which simplifies to π*sqrt(2).

To answer your question, the period of sinx and cosx are both 2π because they are fundamental trigonometric functions with a repeating pattern every 2π radians. However, when we add them together as in sinx + cosx, their pattern changes and becomes more complex.

(x - 3 + i)(x² - 3x - 10)  This means that 3 - i is a zero of f(x). This is because when f(3 - i) is evaluated, the result is 0. The factorization of f(x) shows that 3 - i is a zero of the function.

Factorization is the process of breaking a number or expression into its prime factors. This is done by expressing the number as a product of its prime factors. Factorization is a key concept in mathematics, particularly in algebra and number theory. Factorization can be used to simplify expressions and equations, and it is often used to solve problems involving divisibility and prime numbers. Factorization can also be used to find the greatest common divisor, least common multiple, and other properties of numbers.

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